[Journal] IEEE Transactions on Microwave Theory and Techniques. Vol. 63. No 12 [2]

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DECEMBER 2015

VOLUME 63

NUMBER 12

IETMAB

PART II OF TWO PARTS SPECIAL ISSUE ON 2015 INTERNATIONAL MICROWAVE SYMPOSIUM

2015 Symposium Issue

Phoenix, AZ, USA, site of the 2015 IEEE MTT-S International Microwave Symposium

(ISSN 0018–9480)

IEEE MICROWAVE THEORY AND TECHNIQUES SOCIETY The Microwave Theory and Techniques Society is an organization, within the framework of the IEEE, of members with principal professional interests in the field of microwave theory and techniques. All members of the IEEE are eligible for membership in the Society upon payment of the annual Society membership fee of $17.00, plus an annual subscription fee of $25.00 per year for electronic media only or $46.00 per year for electronic and print media. For information on joining, write to the IEEE at the address below. Member copies of Transactions/Journals are for personal use only. ADMINISTRATIVE COMMITTEE T. LEE, President A. ABUNJAILEH S. BARBIN

R. HENDERSON, Secretary

K. WU, President Elect

T. BRAZIL M. GOUKER

R. GUPTA W. HONG

J. LASKAR G. LYONS

A. JACOB S. KOUL

M. MADIHIAN S. PACHECO

Honorary Life Members T. ITOH R. SPARKS

G. PONCHAK S. RAMAN

M. GOUKER, Treasurer J. RAUTIO S. REISING

M. SALAZAR-PALMA A. SANADA

D. SCHREURS J. WEILER

Distinguished Lecturers

P. STAECKER K. TOMIYASU

R. CAMERON R. H. CAVERLY G. CHATTOPADHYAY

T.-W. HUANG M. JARRAHI J. J. KOMIAK

E. MCCUNE A. MORTAZAWI T. OHIRA

D. WILLIAMS

Past Presidents J. PAWLAN J. C. PEDRO A. STELZER

J. YAO H. ZIRATH T. ZWICK

R. WEIGEL (2014) M. GUPTA (2013) N. KOLIAS (2012)

MTT-S Chapter Chairs Albuquerque: E. FARR Argentina: A. M. HENZE Atlanta: K. NAISHADHAM Austria: A. SPRINGER Baltimore: I. AHMAD Bangalore/India: K. VINOY Beijing: Z. FENG Belarus: S. MALYSHEV Benelux: G. VANDENBOSCH Boston: C. GALBRAITH Bombay/India: M. V. PITKE Brasilia: J. BEZERRA/ M. VINICIUS ALVES NUNES Buenaventura: C. SEABURY Buffalo: M. R. GILLETTE Bulgaria: K. ASPARUHOVA Canada, Atlantic: Z. CHEN Cedar Rapids/Central Iowa: C. G. XIE Central & South Italy: L. TARRICONE Central No. Carolina: Z. XIE Central Texas: J. PRUITT Centro-Norte Brasil: M. V. ALVES NUNES Chengdu: Z. NEI Chicago: D. ERRICOLO Cleveland: M. SCARDELLETTI Columbus: A. O’BRIEN Connecticut: C. BLAIR Croatia: D. BONEFACIC Czech/Slovakia: J. VOVES Dallas: R. SANTHAKUMAR Dayton: A. TERZUOLI Delhi/India: A. BASU

Denver: M. JANEZIC Eastern No. Carolina: T. NICHOLS Egypt: E. HASHEESH Finland: V. VIIKARI Florida West Coast: J. WANG Foothills: M. CHERUBIN France: D. BAJON Germany: G. BOECK Greece: R. MAKRI Gujarat/India: S. CHAKRABARTY Harbin: Q. WU Hawaii: K. MIYASHIRO Hong Kong: H. WONG Houston: S. A. LONG Houston, College Station: G. H. HUFF Hungary: L. NAGY Huntsville: H. SCHANTZ Hyderabad/India: S. R. NOOKALA India: D. BHATNAGER India/Kolkata: S. SANKARALINGAM Indonesia: E. T. RAHARDJO Israel: S. AUSTER Japan: N. SUEMATSU Kansai: T. ISHIZAKI Kingston: S. PODILCHAK Kitchener-Waterloo: R. R. MANSOUR Lebanon: E. NASSAR Lithuania: B. LEVITAS Long Island/New York: S. PADMANABHAN Los Angeles, Coastal: V. RADISIC Los Angeles, Metro/San Fernando: T. CISCO

Macau: C. C. PONG Madras/India: S. SALIVAHANAN Malaysia: M. K. M. SALLEH Malaysia, Penang: B. L. LIM Melbourne: R. BOTSFORD Mexican Council: R. M. RODRIGUEZ-DAGNINO Milwaukee: S. G. JOSHI Monterrey/Mexico: R. M. RODRIGUEZ-DAGNINO Morocco: M. ESSAAIDI Montreal: K. WU Morocco: M. ESSAAIDI Nagoya: J. BAE Nanjing: W. HONG Nanjing, Hangzhou: L. SUN New Hampshire: E. H. SCHENK New Jersey Coast: J. SINSKY New South Wales: Y. RANGA New Zealand: A. WILLIAMSON North Italy: G. OLIVERI North Jersey: A. K. PODDAR Northern Australia: J. MAZIERSKA Northern Canada: M. DANESHMAN Northern Nevada: B. S. RAWAT Norway: M. UBOSTAD Orange County: H. J. DE LOS SANTOS Oregon: K. MAYS Orlando: K. KARNATI Ottawa: Q. ZENG Philadelphia: A. S. DARYOUSH Phoenix: S. ROCKWELL

DOMINIQUE SCHREURS KU Leuven B-3001 Leuven, Belgium

Editorial Assistants MARCIA HENSLEY USA ENAS KANDIL Belgium

Sweden: A. RYDBERG Switzerland: M. MATTES Syracuse: D. MCPHERSON Taegu: Y.-H. JEONG Tainan: H.-H. CHEN Taipei: C. MENG Thailand: C. PHONGCHAROENPANICH Toronto: G. V. ELEFTHERIADES Tucson: H. XIN Tunisia: A. GHARSALLAH Turkey: B. SAKA Twin Cities: C. FULLER UK/RI: A. REZAZADEH Ukraine, East: N. K. SAKHNENKO Ukraine, Kiev: Y. PROKOPENKO Ukraine, Rep. of Georgia: K. TAVZARASHVILI Ukraine, Vinnitsya: V. M. DUBOVOY Ukraine, West: I. IVASENKO United Arab Emirates: N. K. MALLAT Uttar Pradesh/India: M. J. AKHTAR Vancouver: S. MCCLAIN Venezuela: J. B. PENA Victoria: K. GHORBANI Virginia Mountain: T. A. WINSLOW Washington DC/Northern Virginia: T. IVANOV Western Saudi Arabia: A. SHAMIM Winnipeg: P. MOJABI Xian: X. SHI

Associate Editors

Editors-In-Chief JENSHAN LIN Univ. of Florida Gainesville, FL32611-6130 USA

Pikes Peak: K. HU Poland: W. J. KRZYSZTOFIK Portugal: J. CALDINHAS VAZ Princeton/Central Jersey: W. CURTICE Queensland: K. BIALKOWSKI Rio de Janeiro: J. R. BERGMANN Rochester: M. SIDLEY Romania: T. PETRESCU Russia, Moscow: V. A. KALOSHIN Russia, Nizhny-Novgorad: G. L. PAKHOMOV Russia, Novosibirsk: A. YAROSLAVTSEV Russia, Saratov/Penza: M. D. PROKHOROV Russia, Saint Petersburg: S. P. ZUBKO Russia, Siberia: V. V. SUHOTIN Russia, Tomsk: D. ZYKOV San Diego: J. TWOMEY Santa Clara Valley/San Francisco: N. SHAMS Seattle: S. EBADI Seoul: C. SEO Serbia and Montenegro: B. MILOVANOVIĆ Shanghai: J. MAO Singapore: Z. YANG South Africa: A. LYSKO South Australia: T. KAUFMANN South Brazil: J. R. BERGMANN Southeastern Michigan: T. OZDEMIR Southern Alberta: E. FEAR Spain: J. I. ALONSO Springfield: P. R. SIQUEIRA Sri Lanka: A. U. A. W. GUNAWARDENA St. Louis: D. BARBOUR

NUNO BORGES CARVALHO Universidade de Aveiro Aveiro, Portugal

J.-C. CHIAO Univ. of Texas at Arlington Arlington, TX USA

JIASHENG HONG Heriot-Watt Univ. Edinburgh, UK

LUCA PERREGRINI Univ. of Pavia Pavia, Italy

OLGA BORIC-LUBECKE Univ. of Hawaii at Manoa Manoa, HIUSA

GILLES DAMBRINE Univ. of Lille Lille, France

T.-W. HUANG Nat. Taiwan Univ. Taipei, Taiwan

CARLOS SAAVEDRA Queen’s Univ. Kingston, ON, Canada

SHENG-FUH R. CHANG Nat. Chung Cheng Univ. Chiayi County, Taiwan

ROBERTO GOMEZ-GARCIA Univ. Alcala Madrid, Spain

JON MARTENS Anritsu Morgan Hill, CA USA

MARTIN VOSSIEK Friedrich-Alexander Univ. Erlangen-Nuremburg Erlangen, Germany

FRANCISCO MESA Universidad de Sevilla Seville, Spain

X. CHEN Nat. Univ. Singapore Singapore

A. RIDDLE, Editor-in-Chief, IEEE Microwave Magazine J. PAPAPOLYMEROU, Editor-in-Chief, IEEE Microwave and Wireless Component Letters HOWARD E. MICHEL, President BARRY L. SHOOP, President-Elect PARVIZ FAMOURI, Secretary JERRY L. HUDGINS, Treasurer ROBERTO DE MARCA, Past President

P. H. SIEGEL, Editor-in-Chief, IEEE Trans. Terahertz Science and Technology R. MIYAMOTO, Web Master

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Digital Object Identifier 10.1109/TMTT.2015.2503944

DECEMBER 2015

VOLUME 63

NUMBER 12

IETMAB

(ISSN 0018-9480)

PART II OF TWO PARTS SPECIAL ISSUE ON 2015 INTERNATIONAL MICROWAVE SYMPOSIUM

2015 Symposium Issue

Guest Editorial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. T. Rodenbeck

4199

MICROWAVE SYMPOSIUM PAPERS

EM Theory and Analysis Techniques Accurate and Stable Matrix-Free Time-Domain Method in 3-D Unstructured Meshes for General Electromagnetic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J. Yan and D. Jiao Alternative Method for Making Explicit FDTD Unconditionally Stable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Md. Gaffar and D. Jiao Accurate Parametric Electrical Model for Slow-Wave CPW and Application to Circuits Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Bautista, A.-F. Franc, and P. Ferrari Devices and Modeling High-Speed Antenna-Coupled Terahertz Thermocouple Detectors and Mixers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J. A. Russer, C. Jirauschek, G. P. Szakmany, M. Schmidt, A. O. Orlov, G. H. Bernstein, W. Porod, P. Lugli, and P. Russer Reliable Microwave Modeling by Means of Variable-Fidelity Response Features . . . . . . . . . . . . . . . . . . . S. Koziel and J. W. Bandler Consistent DC and RF MOSFET Modeling Using an -Parameter Measurement-Based Parameter Extraction Method in the Linear Region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F. Zárate-Rincón, R. Torres-Torres, and R. S. Murphy-Arteaga Bayesian Optimization for Broadband High-Efficiency Power Amplifier Designs . . . . . P. Chen, B. M. Merrick, and T. J. Brazil Theory and Implementation of RF-Input Outphasing Power Amplification . . . . . . . . . . . . . . . . . . . . T. W. Barton and D. J. Perreault Hysteresis and Oscillation in High-Efficiency Power Amplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . J. de Cos, A. Suárez, and J. A. Garc´ıa Digitally Assisted Analog/RF Predistorter With a Small-Signal-Assisted Parameter Identification Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H. Huang, J. Xia, A. Islam, E. Ng, P. M. Levine, and S. Boumaiza Digital Compensation for Transmitter Leakage in Non-Contiguous Carrier Aggregation Applications With FPGA Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. Yu, W. Cao, Y. Guo, and A. Zhu

4201 4215 4225

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(Contents Continued on Page 4198)

(Contents Continued from Page 4197) Passive Circuits Coupling-Matrix-Based Design of High- Bandpass Filters Using Acoustic-Wave Lumped-Element Resonator (AWLR) Modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. Psychogiou, R. Gómez-García, and D. Peroulis Ultra-Miniature SIW Cavity Resonators and Filters . . . . . . . A. Pourghorban Saghati, A. Pourghorban Saghati, and K. Entesari Design and Multiphysics Analysis of Direct and Cross-Coupled SIW Combline Filters Using Electric and Magnetic Couplings . . . . . . . . . . . . . . . S. Sirci, M. A. Sánchez-Soriano, J. D. Mart´ınez, V. E. Boria, F. Gentili, W. Bösch, and R. Sorrentino Exact Design of a New Class of Generalized Chebyshev Low-Pass Filters Using Coupled Line/Stub Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E. Musonda and I. C. Hunter Propagating Waveguide Filters Using Dielectric Resonators . . . . . . . . . . . . . . . . . . . . . . . . . C. Tomassoni, S. Bastioli, and R. V. Snyder Self-Biased Y-Junction Circulators Using Lanthanum- and Cobalt-Substituted Strontium Hexaferrites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. Laur, G. Vérissimo, P. Quéffélec, L. A. Farhat, H. Alaaeddine, E. Laroche, G. Martin, R. Lebourgeois, and J. P. Ganne A 2.45 GHz Phased Array Antenna Unit Cell Fabricated Using 3-D Multi-Layer Direct Digital Manufacturing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T. P. Ketterl, Y. Vega, N. C. Arnal, J. W. I. Stratton, E. A. Rojas-Nastrucci, M. F. Córdoba-Erazo, M. M. Abdin, C. W. Perkowski, P. I. Deffenbaugh, K. H. Church, and T. M. Weller Hybrid and Monolithic RF Integrated Circuits A Reconfigurable K-/Ka-Band Power Amplifier With High PAE in 0.18- m SiGe BiCMOS for Multi-Band Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . K. Ma, T. B. Kumar, and K. S. Yeo A Broadband GaN pHEMT Power Amplifier Using Non-Foster Matching . . . . . . . . . . . . . . . S. Lee, H. Park, K. Choi, and Y. Kwon Generalized Stability Criteria for Power Amplifiers Under Mismatch Effects . . . . . . . . . . . . . A. Suárez, F. Ramírez, and S. Sancho Highly Efficient and Multipaction-Free P-Band GaN High-Power Amplifiers for Space Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . N. Ayllon and P. G. Arpesi A Highly Efficient LTE Pulse-Modulated Polar Transmitter Using Wideband Power Recycling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H.-S. Yang, C.-W. Chang, and J.-H. Chen A Transformer-Based Poly-Phase Network for Ultra-Broadband Quadrature Signal Generation . . . . . . . J. S. Park and H. Wang Optimized Design of Frequency Dividers Based on Varactor-Inductor Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . M. Pontón and A. Suárez GaN Microwave DC–DC Converters . . . . . . . . . . . . . . . . I. Ramos, M. N. Ruiz Lavín, J. A. García, D. Maksimovi´c, and Z. Popovi´c Common-Base/Common-Gate Millimeter-Wave Power Detectors . . . . . . . . . . . A. Serhan, E. Lauga-Larroze, and J.-M. Fournier Instrumentation and Measurement Techniques Modelling and Measurements of the Microwave Dielectric Properties of Microspheres . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. A. Abduljabar, X. Yang, D. A. Barrow, and A. Porch Hybrid Nonlinear Modeling Using Adaptive Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P. Barmuta, G. Avolio, F. Ferranti, A. Lewandowski, L. Knockaert, and D. M. M.-P. Schreurs RF Systems and Applications A 2.45-GHz Energy-Autonomous Wireless Power Relay Node . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M. Del Prete, A. Costanzo, A. Georgiadis, A. Collado, D. Masotti, and Z. Popovi´c 3D-Printed Origami Packaging With Inkjet-Printed Antennas for RF Harvesting Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J. Kimionis, M. Isakov, B. S. Koh, A. Georgiadis, and M. M. Tentzeris Ambient RF Energy Harvesting From a Two-Way Talk Radio for Flexible Wearable Wireless Sensor Devices Utilizing Inkjet Printing Technologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J. Bito, J. G. Hester, and M. M. Tentzeris Breaking the Efficiency Barrier for Ambient Microwave Power Harvesting With Heterojunction Backward Tunnel Diodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. H. P. Lorenz, S. Hemour, W. Li, Y. Xie, J. Gauthier, P. Fay, and K. Wu Cooperative Integration of Harvesting RF Sections for Passive RFID Communication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G. Andia Vera, D. Allane, A. Georgiadis, A. Collado, Y. Duroc, and S. Tedjini A Distributed Positioning System Based on a Predictive Fingerprinting Method Enabling Sub-Metric Precision in IEEE 802.11 Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S. Maddio, M. Passafiume, A. Cidronali, and G. Manes Real-World Implementation Challenges of a Novel Dual-Polarized Compact Printable Chipless RFID Tag . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M. A. Islam and N. C. Karmakar Gesture Sensing Using Retransmitted Wireless Communication Signals Based on Doppler Radar Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F.-K. Wang, M.-C. Tang, Y.-C. Chiu, and T.-S. Horng 2015 INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Available online at http://ieeexplore.ieee.org

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 63, NO. 12, DECEMBER 2015

Guest Editorial

T

HIS Special Issue of this TRANSACTIONS is comprised of expanded papers from the 2015 IEEE Microwave Theory and Techniques Society (IEEE MTT-S) International Microwave Symposium (IMS 2015), held May 17–22, 2015, in Phoenix, AZ, USA, under the leadership of Steering Committee General Chair Vijay Nair. 8626 conference participants enjoyed outstanding weather and good fellowship in this uniquely scenic destination. Numerous activities included 75 technical sessions, panels, and workshops; an exhibition featuring 620 companies, including 67 first-time exhibitors; the vibrant Student Paper Contest and Student Design competitions; and a new RF Bootcamp course. As always, the highlight of the conference was the Technical Program, representing the latest advances in the state-ofthe-art in microwave theory and techniques. As illustrated in Table I, IMS 2015 was truly international in scope. A total of 818 manuscripts from 43 countries were submitted in December 2014 to the IMS 2015 Technical Program Committee, chaired by Chuck Weitzel. Of those manuscripts, 453 papers (a 55% acceptance rate) from 36 countries were accepted for presentation in podium and interactive forum settings. These conference papers are available for download on IEEE Xplore. All authors were invited to significantly expand their IMS 2015 papers for consideration in this TRANSACTIONS’ Special Issue. Of 102 papers submitted for consideration, 37 have been accepted for publication. This year, as in previous years, the editorial process for this TRANSACTIONS’ Special Issue has been entirely handled by the same Editors-in-Chief and Associate Editors who are responsible for the regular issues of this TRANSACTIONS. This policy ensures that all the papers presented in this Special Issue have been evaluated, not only using the same process as regular-issue papers, but also by the same Editors and Editorial Review Board as for regular-issue papers. Please join us in thanking the Editors, the reviewers, and most importantly, the authors for preparing this issue for publication according to a highly constrained publication timeline. Their efforts ensure that the IEEE MTT-S IMS and this TRANSACTIONS continue to represent the latest advances of significance to our profession.

TABLE I IMS 2015 ACCEPTED PAPERS BY COUNTRY

CHRISTOPHER T. RODENBECK IMS 2015 Special Issue U.S. Naval Research Laboratory Washington, DC 20375 USA

Digital Object Identifier 10.1109/TMTT.2015.2496698

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Christopher T. Rodenbeck (S’97–M’04–SM’09) received the B.S. (summa cum laude), M.S., and Ph.D. degrees in electrical engineering from Texas A&M University, College Station, TX, USA, in 1999, 2001, and 2004, respectively. In December 2014, he joined the U.S. Naval Research Laboratory, Washington, DC, USA, where he is currently jump starting a new department focused on millimeter-wave airborne radar. From 2004 to 2014, he was with Sandia National Laboratories, Albuquerque, NM, USA, where he led a multidisciplinary advanced/exploratory technology development effort for microwave and sensor applications. During the summers of 1998–2000, he was with TriQuint Semiconductor, Dallas, TX, USA, as an Intern with the Monolithic Microwave Integrated Circuit (MMIC) Design Group. He has authored or coauthored more than 83 papers and government reports in the microwave and millimeter-wave fields. He holds several patents. His publication topics concern the design of GaAs and silicon-on-insulator RF integrated circuits (RFICs), low-temperature co-fired ceramic (LTCC) multichip modules, radar receiver optimization, microwave power combining, ultra-wideband radar, the design of antennas at frequencies from UHF through millimeter wave, radiation effects, and semiconductor device modeling. Since 2011, he has been an associate editor for the Encyclopedia of Electrical and Electronics Engineering (Wiley), responsible for the microwave theory and techniques subject area. Dr. Rodenbeck was the recipient of fellowships from NASA, the State of Texas “to advance the state of the art in telecommunications,” Texas A&M, and TxTEC in support of his graduate studies. He has also been supported by Raytheon, TriQuint Semiconductor, the Office of the Secretary of Defense, NASA Jet Propulsion Laboratory, NASA Glenn Research Center, and the U.S. Army Space Command under research grants. He was the Principal Investigator for a research and devlopment program that received the 2012 NNSA Award of Excellence. He was the recipient of the 2015 IEEE Microwave Thoery and Techniques Society (IEEE MTT-S) Outstanding Young Engineer Award, a 2013 Sandia Innovator Award, and a 2011 internal citation for “Excellence in Radar Technology Leadership.”

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Accurate and Stable Matrix-Free Time-Domain Method in 3-D Unstructured Meshes for General Electromagnetic Analysis Jin Yan, Student Member, IEEE, and Dan Jiao, Senior Member, IEEE

Abstract—We develop a new time-domain method that is naturally matrix free, i.e., requiring no matrix solution, regardless of whether the discretization is a structured grid or an unstructured mesh. Its matrix-free property, manifested by a naturally diagonal mass matrix, is independent of the element shape used for discretization and its implementation is straightforward. No dual mesh, interpolation, projection, and mass lumping are required. Furthermore, we show that such a capability can be achieved with conventional vector basis functions without any need for modifying them. Moreover, a time-marching scheme is developed to ensure the stability for simulating an unsymmetrical numerical system whose eigenvalues can be complex-valued and even negative, while preserving the matrix-free merit of the proposed method. Extensive numerical experiments have been carried out on a variety of unstructured triangular, tetrahedral, triangular prism element, and mixed-element meshes. Correlations with analytical solutions and the results obtained from the time-domain finite-element method, at all points in the computational domain and across all time instants, have validated the accuracy, matrix-free property, stability, and generality of the proposed method. Index Terms—Electromagnetic analysis, finite-difference time domain (FDTD) methods, matrix-free methods, time-domain finite-element methods, time-domain methods, unstructured mesh.

I. INTRODUCTION

M

ANY engineering challenges demand an efficient computational solution of large-scale problems. If a computational method can be made matrix free, i.e., free of matrix solutions, then it has a potential of solving very large scale problems. Among existing computational electromagnetic methods, the explicit finite-difference time-domain (FDTD) method [1], [2] is free of matrix solutions. However, it requires a structured orthogonal grid for space discretization. To overcome this limitation, many nonorthogonal FDTD methods have been developed such as the curvilinear FDTD [3]–[5], contour and conformal FDTD [6]–[8], discrete surface integral (DSI) methods

Manuscript received June 15, 2015; revised September 05, 2015; accepted October 19, 2015. This work was supported in part by the NSF under Grant 1065318, and by DARPA under Grant HR0011-14-1-0057. This paper is an expanded version from the IEEE MTT-S International Microwave Symposium, Phoenix, AZ, USA, May 17–22, 2015. The authors are with the School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2015.2495257

[9], generalized Yee-algorithms [10]–[15], and the Finite Integration Technique with affine theories [16]. Needless to say, they have significantly advanced the capability of the original FDTD method in handling unstructured meshes. In existing nonorthogonal FDTD methods, a dual mesh is generally required. The dual mesh needs to satisfy a certain relationship with the primary mesh. Such a dual mesh may not exist in an unstructured mesh. For cases where the dual mesh exists, the accuracy of many nonorthogonal FDTD methods can still be limited. This is because in these methods, the field unknowns are placed along the edges of either the primary mesh or the dual mesh, and are assumed to be constant along the edges. Restricted by such a representation of the fields, one can only obtain the dual field accurately (second-order accurate) at the center point of the loop of the primary field, and along the direction normal to the loop area. Elsewhere and/or along other directions, the accuracy of the dual field cannot be ensured. However, the points and directions, where the dual fields can be accurately obtained, are not coincident with the points and directions of the dual fields located on the dual mesh, in an unstructured mesh. Actually, the only mesh that can align the two is an orthogonal grid, which is used by the traditional FDTD method. As a result, the desired dual fields have to be obtained by interpolations and projections, the accuracy of which is difficult to control in an arbitrary unstructured mesh. It is observed that many interpolation and projection schemes lack a theoretical error bound. The same is true to the primary fields obtained from the dual fields. In addition to accuracy, stability is another concern since the curl operation on is, in general, not reciprocal to that on in existing methods developed for irregular meshes. It can be proved that such a nonreciprocal operation can result in complex-valued or negative eigenvalues in the underlying numerical system. They make a traditional explicit time-marching absolutely unstable. This fact was also made clear in [15]. As a consequence, it remains a research problem how to ensure both accuracy and stability of an FDTD-like method in an unstructured mesh. The finite-element method in time domain (TDFEM) [17] has no difficulty in handling arbitrarily shaped irregular meshes, but it requires the solution of a mass matrix, thus not being matrix-free in nature. The mass-lumping has been used to diagonalize the mass matrix in TDFEM, and also finite integration technique [16]. But it requires well-shaped elements to be accurate [18]. In addition to mass lumping, orthogonal vector basis functions have been developed to render the mass matrix diagonal [19], [20]. These bases are element-shape dependent. They

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also rely on an approximate integration to make the mass matrix diagonal. In recent years, Discontinuous Galerkin time-domain methods [21], [22] have been developed, which only involve the solution of local matrices of small size. However, this is achieved by not enforcing the tangential continuity of the fields across the element interface at the same time instant. Certainly, an accurate result would still have to satisfy the continuity conditions of the fields. Not satisfying them has implications in either accuracy or efficiency. For example, it is observed that a Discontinuous Galerkin time-domain method typically requires a time step much smaller than that of a traditional explicit time-domain method for accurate transient analysis. Recently, a new time-domain method is developed in [23], which requires no matrix solution regardless of whether the discretization is a structured grid or an unstructured mesh. Since the curl operation on and that of are enforced to be reciprocal of each other in [23], although the stability is guaranteed for an arbitrary unstructured mesh, the accuracy remains to be a strong function of mesh quality. In this paper, we develop an accurate and stable matrix-free time-domain method that is independent of the element shape used for discretization. The tangential continuity of the fields is satisfied across the element interface at each time instant. No dual mesh, interpolation, projection, and mass-lumping are needed. The accuracy and stability are both guaranteed for an arbitrary unstructured mesh. This method is also made very easy to implement. In addition, in a structured grid and with zerothorder vector bases, the proposed method reduces exactly to the FDTD. The basic idea of this paper was outlined in [24], where 2-D formulations are provided, and modified higher-order bases are developed to achieve a matrix-free method. In this paper, we present 3-D formulations of [24] for general electromagnetic analysis. We also show the proposed matrix-free method can be formulated without modifying the traditional vector basis functions. In addition, a comprehensive analysis is conducted on the accuracy and stability of the proposed method. Numerical results on various highly unstructured triangular, tetrahedral, triangular prism meshes as well as meshes with mixed-elements are presented to demonstrate the accuracy, matrix-free property, and generality of the proposed method.

II. PROPOSED FRAMEWORK FOR CREATING A MATRIX-FREE TIME-DOMAIN METHOD In this section, we present a general framework for creating a matrix-free time-domain method independent of the shape of the elements used for discretization. We separate the presentation of the framework from that of the detailed formulations (to be given in next section) because the formulation corresponding to the proposed framework is not unique. Under the proposed framework, we can develop different formulations to achieve a matrix-free time-domain method. Consider a general electromagnetic problem involving arbitrarily shaped geometries and materials. For such a problem, an unstructured mesh with arbitrarily shaped elements is more accurate and efficient for use, as compared to an orthogonal grid. The elements do not have to be of the same type. They can be a mix of different types of elements such as tetrahedral, triangular

prism, and brick elements. Starting from the differential form of Faraday's law and Ampere's law (1) (2) we pursue a discretization of the two equations in time domain, which can yield a numerical system free of matrix solutions independent of the element shape used for discretization. A. Discretization of Faraday's Law To discretize Faraday's law, we propose to expand the electric field in each element by a set of vector bases as the following: (3) where is the unknown coefficient of the th vector basis , and is the number of vector bases in each element. The degrees of freedom of the vector bases are defined not only on the faces of the element but also inside the element. Such a choice of vector bases permits accurate generation of the other field unknown at any point along an arbitrary direction, without a need for interpolation and projection. Substituting the expansion of into (1), computing at points , and then taking the dot product at each point respectively, of the resultant with unit vector we obtain

(4) which can be compactly written into the following linear system of equations: (5) where is a diagonal matrix of the permeability, is a global vector of length whose th entry is (6) and

is a sparse matrix, the nonzero entries of which are (7)

where denotes the global index of the -point, and is the global index of the 's vector basis function. Let be the is of total number of vector bases used to expand . The size . During the procedure of constructing , the tangential continuity of is enforced since the tangential electric fields at the element interface are uniquely defined in global vector , and shared in common by all elements. B. Discretization of Ampere's Law To discretize Ampere's law, we apply it at points, and then take the dot product of the resultant with unit vector at each point, where and are

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associated with the degrees of freedom of the vector bases used in (3). We obtain (8) where

3

where is the time step, and the time instants for and , denoted by superscripts, are staggered by half. Neither (11) nor (12) involves a matrix solution. Equations (5) and (10) can also be solved in a second-order based way. Taking another time derivative of (10) and substituting (5), we obtain

(9) which is at point along the direction. The at point in (8) is generated by using the fields [obtained from is located at an element (5)] encircling . For example, if interface, the fields used to generate it are sampled across the elements sharing . A detailed formulation with guaranteed accuracy will be given in next section. As a result, we obtain the following discretization of Ampere's law (10) where is a sparse matrix of size , and notes the discretized eration, the th entry of is , and the are the diagonal matrices of permittivity, and ductivity respectively.

deopand con-

C. Connecting Ampere's Law to Faraday's Law In order to connect (10) to (5), we need to find the relationship between and . In [24], by making a minor modification . In this of the traditional vector bases, we make work, we show the traditional vector bases can also be kept as they are without any need for modification. In this case, we can find an analytical relationship between and as , with an extremely simple block diagonal matrix whose diagonal blocks are either of size 1 1 or 2 2. The detailed formulation of will be given in next section. In addition, when generating (5), apparently, we have an infinite number of choices of the points and the directions for computing the discrete . However, to connect (5) to (10), we need to keep in mind that the -points and directions we choose should facilitate accurate generation of the desired in (5) so that we can march on in time step by step—from to via (5), and then from back to through (10). D. Time Marching A leap-frog-based time discretization of (5) and (10) clearly yields a time-marching scheme free of matrix solutions as follows:

(11)

(12)

(13) where (14) It is evident that the above numerical system is also free of matrix solutions with a central-difference based discretization in time. This is because the matrix in front of the second-order time derivative, which is known as mass matrix, and the matrix before the first-order time derivative are both naturally diagonal. Since the matrices are made naturally diagonal in the proposed method, no approximation-based mass-lumping is needed. It is also worth mentioning that the leap-frog-based time discretization shown in (11) and (12) is the same as the central-difference-based explicit discretization of the second-order system (13). This can be readily seen by writing the counterpart of (12) for evaluating , i.e., replacing by in (12), subtracting the resultant from (12), and then substituting (11) to replace the term. Since (11) and (12) are the same as the explicit discretization of (13), we can directly solve (13), which also has only half a number of unknowns. If unknowns are needed, they can readily be recovered from through (11). E. Remark In the framework described above, we expand into certain vector basis functions in each element, while sampling the unknowns at discrete points to generate desired unknowns. One can also switch the roles of the electric and magnetic fields: expand the into vector basis functions in each element, while sampling the unknowns. Which way to use depends on the convenience for solving a given problem. III. PROPOSED FORMULATIONS In this section, we present detailed formulations to realize the aforementioned matrix-free framework with guaranteed accuracy and stability. Since 2-D formulations have been presented in [24], 3-D formulations will be the focus of this section. A. Accurate Construction of

and

's Degrees of Freedom

A common choice of the vector basis functions for expanding the fields is the zeroth-order curl-conforming bases (edge elements) [25]. These bases have constant tangential components along the edges where they are defined. The field representation in the traditional FDTD is, in fact, a zeroth-order vector basis representation in an orthogonal cell. However, the zeroth-order vector bases have a constant curl in every element. Using such bases to represent , the resultant is a constant in each element, and the is only second-order accurate at the center point of each element. From such discrete -fields, we cannot

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Fig. 1. (a) Locations of point . (b) Locations of

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points required for the accurate evaluation of points with zeroth-order vector bases.

at

reversely obtain the unknowns associated with the zerothorder vector bases accurately in an arbitrarily shaped element. To help understand the aforementioned point more clearly, take a 2-D problem discretized into arbitrarily shaped triangular elements as an example. Consider an arbitrary th edge. With the zeroth-order vector bases to expand , the shown in (9) has the unit vector tangential to the th edge, and the center point of the th edge, as illustrated in Fig. 1. To obtain such an accurately from the discrete (now only since the problem is 2-D), the two -points should be located on the line that is , as perpendicular to the th edge and centered at the point shown in Fig. 1(a). In this way, the edge is perpendicular to the -loop (in the plane defined by -direction and the line normal to the edge), and resides at the center of the loop. As a result, an accurate can be obtained from a space derivative of the two unknowns. However, using the zeroth-order edge elements, the curl of is constant in every element, thus we cannot generate at the desired points accurately. From another perspective, we can view the obtained at the center point of every element to be accurate. However, in an arbitrary unstructured mesh, the line segment connecting the center points of the two elements sharing an edge may not be perpendicular to the edge, and the two center points may not have the same distance to the edge either, as illustrated in Fig. 1(b). To overcome the aforementioned problem, we propose to use higher-order curl-conforming vector bases to expand in each element. With an order higher than zero, the curl of and hence is at least a linear function of , , and in each element. With this, the can be obtained at an arbitrary point along an arbitrary direction accurately from (5). We hence can use this freedom to choose points and directions in such a way that they can reversely generate unknowns accurately from (10). First-order bases are sufficient for use. Certainly, one can employ bases whose order is even higher. This is one of the reasons why the detailed formulations corresponding to the proposed framework are not unique. In this work, first-order bases are used, since they satisfy the need of the proposed matrix-free method and they minimize computational overhead as compared to other bases. For completeness of this paper, in Appendix, we list all the twenty first-order bases in a tetrahedral element [26] together with their degrees of freedom defined in terms of locations and projection directions . B. Relationship Between

discrete electric fields at points along directions as defined in (9). If , then . Hence, (10) and (5) are directly connected to each other. Among higher-order vector basis functions [26], the vector bases associated with edges satisfy naturally. However, the bases defined on the faces and those inside the element, in general, do not. This problem can be solved by modifying the original higher-order vector bases to make , as done in [24]. We can also keep the original higher-order vector bases as they are, but find the relationship between and as follows. Substituting (3) into (9), we have (15) from which we obtain (16) where

matrix obviously has the following entries: (17)

is of size but an extremely simple matrix—It is a The block diagonal matrix with each diagonal block of size either 1 or 2. To be specific, for the vector basis function whose degree of freedom is associated with edges, the and elsewhere in the th row ; for the vector basis function whose degree of freedom is not associated with edges, it is either defined on faces or inside the element. Such a basis function comes in as a pair, for which there are two nonzero elements on the th row of , and two nonzero elements on the th row of , forming a 2 2 diagonal block in as the following (18) The off-diagonal terms in the above do not vanish because for face or internal degrees of freedom, the basis function pair associated with each point are not perpendicular to each other in terms of the vector basis's direction. Overall, the can be written as

(19)

where each diagonal block is equal to either 1 or a 2 2 matrix shown in (18), which can be readily inverted to obtain , denoted by . Obviously, is also a block diagonal matrix whose diagonal blocks are of size either 1 or 2. As a result, we find a closed-form relationship between from as (20) Equation (5) hence can be rewritten as

and

The vector contains the unknown coefficients of vector contains the basis functions as shown in (3), while vector

(21) Thus, (10) and (5) are connected to each other.

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Fig. 2.

points and directions for generating

C. Accurate Construction of and Directions

.

and Choice of

's Points

To construct (10) accurately, we propose to use an -loop uniquely defined for each 's degree of freedom to obtain the desired in (5). This loop centers each 's degree of freedom, and is also positioned perpendicular to the 's degree of freedom. This -loop can be chosen in its simplest manner: a 1-D line segment in 2-D settings, and a 2-D rectangular loop centering and normal to the 's degree of freedom in 3-D problems, as shown in Fig. 2. Regardless of the shape of the element, such a rectangular loop can always be defined for each unknown. Along this loop, we select the middle points of the four sides as -points and the four unit vectors tangential to each side as -directions to generate . As a result, each unknown is associated with four -points and directions. These -points are all located inside the elements that share the unknown, instead of being selected on the faces of the elements. In this way, each point is located only in one element, and hence the -field at the point can be readily found from (5). The set of -points and -directions defined for each makes the whole set of -points denoted by , and the whole set of -directions denoted by . With the aforementioned choice of -points and directions, in (8) can be accurately discretized with secondthe order accuracy as the following (22) where is the distance between and , while is the distance between and as illustrated in Fig. 2. With (22), we obtain (23) where denotes the global index of the -point associated with is simply two times the distance between the the , and -point ( ) and the -point . Each row of has only four nonzero elements. Obviously, there is no need to construct a dual mesh for as the -points and -directions we select are individually defined for each unknown, which do not make a mesh. In addition, regardless of the choice of -points and directions, there is no difficulty in generating corresponding from (5) accurately, due to the use of higher-order basis functions. D. Imposing Boundary Conditions The proposed method, in its first-order form (11)–(12), conforms to that of the FDTD numerical system; in its secondorder form (13), conforms to the second-order wave equation

5

based TDFEM. Hence, the boundary conditions in the proposed method can be implemented in the same way as those in the TDFEM and FDTD. Below we provide more details. For closed-region problems, the perfect electric conductor (PEC), the perfect magnetic conductor (PMC), or other nonzero prescribed tangential or tangential are commonly used at the boundary. To impose prescribed tangential at boundary points, in (5), we simply set the entries at the points to be the prescribed value, and keep the size of the same as before to produce all discrete from the discrete . In (10), since the entries at the points are known, the updating of (10) only needs to be performed for the rest entries. As a result, we can remove the rows from corresponding to the boundary fields, the same as before. while keeping the column dimension of The above treatment, from the perspective of the second-order system shown in (13), is the same as keeping just rows of , providing the full-length (with the boundary entries specified) for the multiplied by , but taking only the rows of all the other terms involved in (13). To impose a PMC boundary condition, the total unknown number is without any reduction. Equation (5) is formulated as it is since the -points having the PMC boundary condition can be placed outside the computational domain. As for (10), there is no need to make any change either since the tangential is set to be zero outside the computational domain. The end result is the same as a TDFEM numerical system subject to the second-kind boundary condition. For open-region problems, the framework of (5) and (10) in the proposed method is conformal to that of the FDTD. As a result, the various absorbing boundary conditions that have been implemented in FDTD such as the commonly used PML (perfectly matched layer) can be implemented in the same way in the proposed matrix-free method. IV. TIME MARCHING FREE OF MATRIX-SOLUTION WITH GUARANTEED STABILITY A leap-frog-based time marching shown in (11)–(12) as well as a central-difference based time discretization of (13) is absolutely matrix-free, i.e., free of a matrix solution. However, both are absolutely unstable since the curl-curl operator here is an unsymmetrical matrix. This is not only true for the proposed method but also true for any method whose curl operation on one field unknown is not the reciprocal of the curl operation on the other field unknown. To prove, we can perform a stability analysis of (11)–(12) and (13) [27], [28]. The -transform of the central-difference based time marching of (13), or (11)–(12) after eliminating , results in the following equation: (24) where is the eigenvalue of . The two roots of (24) can be readily found as (25) If is Hermitian positive semidefinite like that resulting from TDFEM or FDTD in an orthogonal grid, all its eigenvalues are nonnegative real. Thus, we can always find a time step to make

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in (25) bounded by 1, and hence the explicit simulation of (13) as well as (11)–(12) is stable. Such a time step satisfies , where is the maximum eigenvalue of , which is also 's spectral radius. However, if is not symmetrical, which is the case in the proposed method and many existing nonorthogonal FDTD methods, its eigenvalues either are real (can be negative) or come in complex-conjugate pairs. For complex-valued eigenvalues as well as negative ones, the , and neither two roots and shown in (25) satisfy of them has modulus equal to 1. As a result, the modulus of one of them must be greater than 1, and hence the explicit time-domain simulation of (13) and (12) must be unstable. However, if we choose to make symmetric, the accuracy cannot be guaranteed in a general unstructured mesh. This dilemma is solved as follows without sacrificing the matrix-free merit of the proposed method. Basically, we can start with the following backward-difference based discretization of (13) [17]:

Since is not diagonal, (29) requires a matrix solution. To avoid that, we can solve this problem as follows. Let the diagonal part of be , which means (31) Front multiplying both sides of (29) by

, we obtain (32)

where

is the right hand side of (29), and (33)

Although (29) permits the use of any large time step, when we choose the time step based on that of a conventional explicit method, the time step satisfies (34) and therefore (35)

(26) associated with is chosen at the th time where the step instead of the th step. Performing a stability analysis of (26) for lossless cases, we find the two roots of as (27) As a result, the can still be bounded by 1 even for an infinitely large time step. However, this does not mean the backward difference is unconditionally stable since now the can be complex-valued or even negative. To make the magnitude of (27) bounded by 1, we find that the time step needs to satisfy the following condition (28)

where denotes the imaginary part of . It is obvious to see that the scheme is stable for large time step, but not stable for small time step. Such a requirement happens to align with preferred choices of time step, since a large time step is desired for an efficient simulation. Rearranging the terms in (26), we obtain

(29) where (30)

This time step is also the time step required by accuracy when space step is determined by accuracy. Since in (31) is diagonal, the norm of its inverse can be analytically evaluated as (36) We therefore obtain from (35) and (36) (37) As a result, the inverse of as a series expansion

can be explicitly represented (38)

which can be truncated after the first few terms without sacrificing accuracy due to (37). Thus, the system matrix has an explicit inverse, and hence no matrix solution is required in the proposed method. The final update equation becomes (39) is a diagonal matrix which is 's inverse. The number where of terms is guaranteed to be small (less than 10) since (37) holds true, and the central-difference-based time step (34) is usually not chosen right at the boundary, , but smaller for better sampling accuracy. Notice that the spectral radius of , as revealed in (37), is essentially the square of the ratio of the actual time step used to the largest time step permitted by the stability of a conventional explicit scheme . It is a constant irrespective of the mesh quality. Therefore, the convergence of (38) is guaranteed and the convergence rate does not depend on the mesh quality. Notice that using (38) does not change the stability analysis since it is used to obtain the inverse of system matrix, which does not change the backward difference based time marching scheme.

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The computational cost of (39) is sparse matrix-vector multiplications since each term can be computed from the previous term. For example, if we first compute , then the second term in (39) can be obtained from . Let the resultant be . The third term relating to is nothing but . Therefore, the cost for computing each term in (39) is the cost of multiplying by the vector obtained at the previous step, thus efficient. V. RELATIONSHIP WITH FDTD In a regular orthogonal grid and with the zeroth-order vector bases, the proposed method reduces exactly to the FDTD. This is very different from the mixed formulation like [29] where mass lumping has to be used to prove equivalency. To explain, for a 2-D rectangular grid and a 3-D brick-element based discretization, with a zeroth-order edge vector basis used in each rectangular or brick element, the operation of in the proposed method is the same as how the curl of is discretized in the FDTD; and the operation of with is the same as how the curl of is discretized in the FDTD. naturally satisfies in an orthogFurthermore, since onal grid, the resulting numerical system is symmetric and positive semidefinite. Hence the original leap-frog explicit time marching is stable without any need for special treatment. That is also why in a traditional FDTD with an orthogonal grid, an explicit time marching is never observed to be absolutely unstable because the system matrix is symmetric. To see the above point more clearly, take the 2-D rectangular grid as an example. The is simply a union of at the center point of each edge, with being either or along each edge; and the is nothing but the vector containing at the center point of each rectangular patch. Each row of has four nonzero elements as each element has four bases. Multiplying the th row of by is nothing but (40) where , , , are the global indexes of the four edge basis functions in the rectangular element where the point is located, and and are the two side lengths of the rectangular element. It is evident that (40) is the same as that performed in the FDTD to produce the at the center of each -loop. With , the operation of is to do (41) where is simply the length of the side that is perpendicular to edge in a rectangular element. Obviously, the above is the same as that used in the FDTD to calculate fields, which is an accurate discretization of of second-order accuracy at the center point of an edge for along the edge. In addition, even in an orthogonal grid, the implementation of the proposed method is more convenient, since no dual grid is needed. After is formed for the grid, is known as without any construction cost. For unstructured meshes, the FDTD method would fail, whereas the proposed method is accurate and stable regardless of how irregular and unstructured the mesh is.

Fig. 3. Simulation of wave propagation and reflection in a 2-D triangular mesh. (a) Mesh. (b) Illustration of incident wave and truncation boundary conditions.

VI. NUMERICAL RESULTS In this section, we simulate a variety of 2- and 3-D unstructured meshes to demonstrate the validity and generality of the proposed matrix-free method in analyzing arbitrarily shaped structures and materials discretized into unstructured meshes. The accuracy of the proposed method is validated by comparing with both analytical solutions and the TDFEM method that is capable of handling unstructured meshes but not matrix-free. A. 2-D Triangular Mesh The first example is a wave propagation and reflection problem in an 2-D triangular mesh shown in Fig. 3(a). Some mesh elements are very skewed due to fine features in a narrow gap whose size is less than a few . The dielectric in the red shaded region and 1 elseconstant is where. The incident is specified as , where , , s, and denotes the speed of light. The top, bottom and right boundaries are terminated by PEC, while the left boundary is truncated by the sum of the incident and reflected fields as illustrated in Fig. 3(b). Since the left boundary is not close to the dielectric discontinuity, the reflected field at the left boundary can be analytically approximated as , is the -coordinate at the left boundary, and is the where width of the computational domain. In the proposed method, the number of expansion terms used is 9 in (38). For comparison, we simulate the same example by TDFEM since it is capable of handling unstructured meshes. The time step used in both methods is . In Fig. 4(a), the electric fields at two

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Fig. 5. Illustration of the tetrahedron mesh of a 3-D structure.

Fig. 4. Simulation of a 2-D triangular mesh. (a) Electric fields at two points. (b) Entire solution error versus time.

points

and randomly selected are plotted in comparison with TDFEM results. The directions of the two fields are respectively , and . Excellent agreement can be observed with TDFEM results. Such an agreement is also observed at all points for all time. As shown in Fig. 4(b), the entire solution error as compared with the TDFEM solution is less than 2% at all time instants. A few peak errors are due to the comparison with close-to-zero fields. The entire solution error is defined by (42)

where denotes the entire unknown vector of length solved from the proposed method, and denotes the reference solution, which is TDFEM result in this example. B. Wave Propagation in a 3-D Box Discretized into Tetrahedral Mesh A 3-D box discretized into tetrahedral elements is simulated in free space. The mesh details are shown in Fig. 5. The discretization results in 544 edges and 350 elements. To investigate the accuracy of the proposed method in such a mesh, we consider that the most convincing comparison is a comparison with analytical solution. We hence study a free-space wave propagation problem whose analytical solution is known. To simulate such an open-region problem, we impose an analytical boundary condition, i.e., the known value of tangential , on the outermost boundary of the problem; we then numerically simulate

Fig. 6. Simulation of a 3-D box discretized into tetrahedral elements. (a) Simulated two electric fields in comparison with analytical results. (b) Entire solution error for all unknowns versus time.

the fields inside the computational domain and correlate results with the analytical solution. The structure is illuminated by a plane wave having , where , , and . The time step used in the proposed method is , which is the same as what a traditional central-difference based TDFEM has to use for stability. The number of expansion terms is 9 in (38). In Fig. 6(a), we plot the first and 1832th entry randomly selected from the unknown vector, which represent , with , and 1832 respectively. From Fig. 6(a), it can be seen clearly that the electric fields solved from the proposed method have an excellent agreement with analytical results. To further verify the accuracy of the proposed method in the entire computational domain, we assess the entire solution error (42) as a function of time, where the reference solution is analytical result . In Fig. 6(b), we plot across the

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Fig. 8. Illustration of the tetrahedron mesh of a sphere structure.

Fig. 7. (a) Entire solution error versus time of all unknowns obtained from -rows of equations. (b) Entire solution error versus time of all obtained -rows of equations. from

whole time window in which the fields are not zero. It is evident that less than 4% error is observed at each time instant, demonstrating the accuracy of the proposed method. The center peak in Fig. 6(b) is due to a comparison with close to zero fields. In addition to the accuracy of the entire method, we have also examined the accuracy of the individual , and separately, since each is important to ensure the accuracy of the whole scheme. First, to solely assess the accuracy of , we perform the time marching of (5) only without (10) by providing an analytical to (5) at each time step. The resultant is at each time step. As can then compared to analytical be seen from Fig. 7(a) where the following -error

Fig. 9. Simulation of a 3-D sphere discretized into tetrahedral elements. (a) Two electric fields in comparison with analytical results. (b) Entire solution error for all unknowns versus time.

(43) unknowns is is plotted with respect to time, the error of all less than 3% across the whole time window, verifying the accuracy of . Similarly, in order to examine the accuracy of , we perform the time marching of (10) only without (5) by providing an analytical to (10) at each time step. The relative error of all unknowns shown in (42) as compared to analytical solutions is plotted with time in Fig. 7(b). Again, very good accuracy is observed across the whole time window, verifying the accuracy of . C. Wave Propagation in a Sphere Discretized into Tetrahedral Mesh The third example is a sphere discretized into tetrahedral elements in free space, whose 3-D mesh is shown in Fig. 8.

The discretization results in 3183 edges and 1987 tetrahedrons. Again, we set up a free-space wave propagation problem in the given mesh to validate the accuracy of the proposed method against analytical results. The incident has the same form in as that of the first example, but with accordance with the new structure's dimension. The outermost boundary of the mesh is truncated by analytical fields. The , which is the same as that time step used is used in a traditional TDFEM method. The number of expansion terms is 9 in (38). The two degrees of freedom of the electric field, whose indices in vector are 1 and 9762, respectively, are plotted in Fig. 9(a) in comparison with analytical data. Excellent agreement can be observed. In Fig. 9(b), we plot the entire solution error shown in (42) versus time. Less than 3% error is observed in the entire time window. It is evident that the proposed method is not just accurate at certain points, but

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Fig. 10. Top view of the triangular prism mesh of an coaxial cylinder structure.

Fig. 11. Simulation of a 3-D coaxial cylinder discretized into triangular prism elements. (a) Two electric fields in comparison with analytical results. (b) Entire solution error for all unknowns versus time.

accurate at all points in the computational domain for all time instants simulated. D. Coaxial Cylinder Discretized Into Triangular Prism Mesh The fourth example has an irregular triangular prism mesh, the top view of which is shown in Fig. 10. The structure has two layers of triangular prism elements (into the paper) with each layer being 0.05 m thick. The discretization results in 3092 edges and 1038 triangular prisms. Both the innermost and outermost boundaries are terminated by exact absorbing boundary condition, which is the analytical tangential on the boundary. The incident has the same form as that in the first example, but with . The used is and the number of expansion terms is 9. Two observation points, whose indices in vector are 1 and 11 272 respectively, are chosen

Fig. 12. Simulation of a mesh having different types of elements. (a) Illustration of the mesh. (b) Two electric fields in comparison with analytical results. (c) Entire solution error for all unknowns versus time.

to plot the electric fields in Fig. 11(a). Excellent agreement with analytical solutions can be observed. In Fig. 11(b), we plot the entire solution error shown in (42) versus time in comparison with the reference results which are analytical solutions. Again, excellent accuracy (less than 0.7% error) is observed at all points in the computational domain for all time instants simulated. E. Mesh With Mixed Elements We have examined the capability of the proposed method in handling meshes made of different types of elements. This mesh is illustrated in Fig. 12(a), which consists of 1312 triangular elements in the center and 84 rectangular elements surrounding it. In each triangular element, there are eight first-order vector bases; and in each rectangular element, there are 12 first-order vector bases. The interface between a rectangular and a triangular element is an edge, where the degrees of freedom from both elements are shared in common to ensure the tangential

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Fig. 13. Illustration of materials and geometry of a package inductor.

continuity of the fields. A wave propagation problem is simulated in this mixed-element mesh. The incident field is a plane wave having , where , and . The time step used is . In Fig. 12(b), the electric fields at two randomly selected points are plotted in comparison with analytical data. Excellent agreement can be observed. In Fig. 12(c), the entire solution error is plotted as a function of time. Again, excellent accuracy is observed, which verifies the capability of the proposed method in handling meshes having mixed types of elements. Such a capability also facilities a convenient implementation of various absorbing boundary conditions such as the perfectly matched layer. F. S-Parameter Extraction of a Lossy Package Inductor In this example, we simulate a package inductor made of lossy conductors of conductivity 5.8e+7 S/m, and embedded in a dielectric material of relative permittivity 3.4. Its geometry and material parameters are illustrated in Fig. 13. The inductor is discretized into five layers of triangular prism elements, the thickness of each of which is 6.5, 30, 6.5, 8.5, and 30 from bottom to top, respectively. The top view of the mesh is shown in Fig. 14(a). The boundary conditions are PEC on the top and at the bottom, and PMC on the other four sides. A current source is launched respectively at the two ports of the inductor. It has a Gaussian derivative pulse of , with , and . The number of expansion terms is 10 used in this simulation. The voltages obtained at both ports with port 1 (upper port) excited and port 2 open are plotted in Fig. 14(b) in comparison with the TDFEM results. Excellent agreement can be observed. The -parameters are also extracted and compared with those generated from the TDFEM. Very good agreement can be seen from Fig. 14(c) and (d) across the entire frequency band. G. CPU Time and Memory Comparison Among existing time-domain methods for handling unstructured meshes, the TDFEM only requires a single mesh like the proposed method. The TDFEM also has guaranteed stability and accuracy, and it ensures the tangential continuity of the fields across material interfaces. We hence choose the TDFEM to benchmark the performance of the proposed method. The example considered is a large-scale example having millions of unknowns, since small examples are not challenging to solve, which is true to almost every time-domain method. The computational domain is a circular cylinder of radius 1 m

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and height 5 m, which is discretized into 25 layers of triangular prism elements. The thickness of each layer is 0.02 m. The incident field is a plane wave having , where , and . The time step used is , which is the same in the TDFEM and the proposed method. The number of expansion terms used in the proposed method is nine in (38). The zeroth-order vector bases are employed in the TDFEM, whereas the first-order bases are used in the proposed method. This comparison is, in fact, disadvantageous to the proposed method since the sparse pattern resulting from a higher-order-bases based discretization is much more complicated and the system matrix has many more nonzeros, as compared to the zeroth-order-based discretization. However, if the proposed method is able to show advantages even for such a disadvantageous comparison, then its efficiency gain over the same-order TDFEM would become even more obvious. The triangular prism discretization results in 3 718 990 unknowns in the zeroth-order TDFEM. We find that the TDFEM simulation cannot be performed on our desktop PC that has 16-GB memory due to the TDFEM's large memory requirement. This is because although the explicit TDFEM only requires solving a mass matrix, which is sparse and simple, its and factors are generally dense. Although the mass matrix is time independent, and hence we only need to factorize it once. The TDFEM still has to be equipped with sufficient memory to store and factors to carry out the following backward and forward substitutions for the matrix solution at each time step. Certainly, iterative solvers can be used to reduce memory usage, however, they are not cost-effective in time-domain analysis since many right hand sides need to be simulated, and the number of right hand sides is equal to the number of time steps. We hence find a computer that has 128-GB memory so that the TDFEM simulation can be successfully performed on this example. On this computer, it takes the TDFEM 2109.44 s and more than 72-GB memory to finish the LU factorization of the mass matrix. The CPU time cost at each time marching step is 9.31 s, which is one backward and forward substitution time. For a fair comparison, a similar number of unknowns is generated in the proposed method. The resulting system matrix size is 3 741 700. In contrast to the 2109.44 s cost by TDFEM for factorization, the proposed method has no factorization cost since it is free of matrix solution. In contrast to the 72-GB memory required by the TDFEM, the proposed method only takes 6.2-GB memory to store the sparse matrices, as it does not need to store and since the mass matrix is diagonal. The CPU run time of the proposed method at each time step is 3.76 s, which is spent on a few matrix-vector multiplications. From the aforementioned comparison, the computational efficiency of the proposed method can be clearly seen. Recently, advanced research has also been developed to reduce the computational complexity of a direct matrix solution [30]. However, not solving a matrix always has its computational advantages as compared to solving a matrix. We have also compared the accuracy between the two methods using the analytical data as the reference, since the example is set up to have an analytical solution. The entire solution error of the proposed method measured by (42) is shown to across the entire time window. The entire be less than

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Fig. 14. Simulation of a 3-D package inductor with dielectrics and lossy conductors. (a) Top view of the triangular prism element mesh. (b) Time-domain voltages at the two ports. (c) Magnitude of -parameters. (d) Phase of -parameters.

. The solution error of the TDFEM is shown to be less than accuracy of the proposed method is satisfactory. Meanwhile, the slightly better accuracy of the Galerkin-based TDFEM could be attributed to the fact that it satisfies the Maxwell's equations in an integration sense across each element, whereas the proposed method let the Maxwell's equations be satisfied only at discrete and points. Furthermore, in the TDFEM, both Faraday's law and Ampere's law are satisfied in the same element, whereas in the proposed method, the second law is satisfied across the elements over the loops orthogonal to the first field unknowns. In addition, the time discretization scheme may also contribute to the difference in accuracy. VII. CONCLUSION In this paper, a new matrix-free time-domain method with a naturally diagonal mass matrix is developed for solving Maxwell's equations in 3-D unstructured meshes, whose accuracy and stability are theoretically guaranteed. Its property of being free of matrix solution is independent of element shape, thus suitable for analyzing arbitrarily shaped structures and materials discretized into unstructured meshes. The method is neither FDTD nor TDFEM, but it possesses the advantage of the FDTD in being naturally matrix free, and the merit of the TDFEM in handling arbitrarily unstructured meshes. No dual mesh, mass-lumping, interpolation, and projection are required. In addition, the framework of the proposed method permits the use of any higher-order vector basis function, thus allowing for any desired higher order of accuracy in both electric and magnetic fields. Moreover, the formulations presented in this paper do not require any modification on the traditional vector bases. Extensive numerical experiments on unstructured triangular, tetrahedral, triangular prism meshes, and mixed elements have validated the accuracy, matrix-free property, stability, and

generality of the proposed method. Comparisons have also been made with the TDFEM in unstructured meshes in CPU time, memory consumption, and accuracy, which demonstrate the merits of the proposed method. APPENDIX FIRST-ORDER CURL-CONFORMING VECTOR BASIS FUNCTIONS In a tetrahedral element, among the 20 first-order vector bases [26], there are 12 edge vector basis functions, which are defined as

(44) where

are volume coordinates, and denote the normalized zeroth-order edge bases as

follows:

(45) in which is the length of the th edge. The degrees of freedom of the 12 edge vector bases shown in (44) are located respec-

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tively at the following points in each element, with their corresponding projection directions defined as: (48)

REFERENCES

(46) where denotes the vector pointing from node to node . There are also two vector basis functions whose degrees of freedom are located at the center point of each face. In total, there are eight such bases, which are

(47) and corresponding unit The locations vectors associated with the above eight face vector bases are

[1] K. S. Yee, “Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media,” IEEE Trans. Antennas Propag., vol. AP-14, no. 3, pp. 302–307, May 1966. [2] A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method. Boston, MA, USA: Artech House, 2000. [3] R. Holland, “Finite-difference solution of maxwell's equations in generalized nonorthogonal coordinates,” IEEE Trans. Nucl. Sci., vol. NS-30, no. 6, pp. 4589–4591, Dec. 1983. [4] M. Fusco, “FDTD algorithm in curvilinear coordinates [EM scattering],” IEEE Trans. Antennas Propag., vol. 38, no. 1, pp. 76–89, Jan. 1990. [5] J.-F. Lee, R. Palandech, and R. Mittra, “Modeling three-dimensional discontinuities in waveguides using nonorthogonal FDTD algorithm,” IEEE Trans. Microw. Theory Techn., vol. 40, no. 2, pp. 346–352, Feb. 1992. [6] T. G. Jurgens and A. Taflove, “Three-dimensional contour FDTD modeling of scattering from single and multiple bodies,” IEEE Trans. Antennas Propag., vol. 41, no. 12, pp. 1703–1708, Dec. 1993. [7] S. Dey and R. Mittra, “A locally conformal finite difference time domain (FDTD) algorithm for modeling three-dimensional perfectly conducting objects,” IEEE Microw. Guided Wave Lett., vol. 7, no. 9, pp. 273–275, 1997. [8] Y. Hao and C. J. Railton, “Analyzing electromagnetic structures with curved boundaries on Cartesian FDTD meshes,” IEEE Trans. Microw. Theory Techn., vol. 46, no. 1, pp. 82–88, Jan. 1998. [9] M. Madsen, “Divergence preserving discrete surface integral methods for maxwells equations using nonorthogonal grids,” J. Comput. Phys., vol. 119, pp. 34–45, 1995. [10] C. Chan, J. Elson, and H. Sangani, “An explicit finite-difference timedomain method using whitney elements,” in Proc. IEEE Int. Symp. Antennas Propag. (AP-S), 1994, vol. 3, pp. 1768–1771. [11] S. Gedney, F. Lansing, and D. Rascoe, “A full-wave analysis of passive monolithic integrated circuit devices using a generalized yee-algorithm,” IEEE Trans. Microw. Theory Techn., vol. 44, no. 8, pp. 1393–1400, Aug. 1996. [12] A. Bossavit and L. Kettunen, “Yee-like schemes on a tetrahedral mesh, with diagonal lumping,” Int. J. Numer. Modelling-Electron. Networks Devices Fields, vol. 12, no. 1, pp. 129–142, 1999. [13] C. F. Lee, B. J. McCartin, R. T. Shin, and J. A. Kong, “A triangle grid finite-difference time-domain method for electromagnetic scattering problems,” J. Electromagn. Waves Appl., vol. 8, no. 4, pp. 1429–1438, Aug. 1994. [14] M. Hano and T. Itoh, “Three-dimensional time-domain method for solving maxwells equations based on circumcenters of elements,” IEEE Trans. Magn., vol. 32, no. 3, pp. 946–949, May 1996. [15] S. Gedney and J. Roden, “Numerical stability of nonorthogonal fdtd methods,” IEEE Trans. Antennas Propag., vol. 48, no. 2, pp. 231–239, Feb. 2000. [16] M. Cinalli and A. Schiavoni, “A stable and consistent generalization of the fdtd technique to nonorthogonal unstructured grids,” IEEE Trans. Antennas Propag., vol. 54, no. 5, pp. 1503–1512, May 2006. [17] D. Jiao and J. Jin, “Finite element analysis in time domain,” in The Finite Element Method in Electromagnetics. Hoboken, NJ, USA: Wiley, 2002, pp. 529–584. [18] M. Feliziani and F. Maradei, “Hybrid finite-element solutions as time dependent maxwells curl equations,” IEEE Trans. Magn., vol. 31, no. 3, pp. 1330–1335, May 1995. [19] D. A. White, “Orthogonal vector basis functions for time domain finite element solution of the vector wave equation,” IEEE Trans. Magn., vol. 35, no. 3, pp. 1458–1461, May 1999. [20] D. Jiao and J. Jin, “Three-dimensional orthogonal vector basis functions for time-domain finite element solution of vector wave equations,” IEEE Trans. Antennas Propag., vol. 51, no. 1, pp. 59–66, Jan. 2003. [21] S. D. Gedney et al., “The discontinuous galerkin finite element time domain method (DGFETD),” in Proc. IEEE Int. Symp. Antennas Propag., 2008, p. 4. [22] S. D. Gedney, J. C. Young, T. C. Kramer, and J. A. Roden, “A discontinuous galerkin finite element time-domain method modeling of dispersive media,” IEEE Trans. Antennas Propag., vol. 60, no. 4, pp. 1969–1977, Apr. 2012.

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[23] J. Yan and D. Jiao, “A matrix-free time-domain method independent of element shape for electromagnetic analysis,” in Proc. IEEE Int. Symp. Antennas Propag. (AP-S), 2014, pp. 2258–2259. [24] J. Yan and D. Jiao, “Accurate matrix-free time-domain method in unstructured meshes,” in Proc. IEEE Int. Microw. Symp. (IMS), 2015, pp. 1–4. [25] J. Jin, The Finite Element Method in Electromagnetics. Hoboken, NJ, USA: Wiley, 2014. [26] R. D. Graglia, D. R. Wilton, and A. F. Peterson, “Higher order interpolatory vector bases for computational electromagnetics,” IEEE Trans. Antennas Propag., vol. 45, no. 3, pp. 329–342, Mar. 1997. [27] D. Jiao and J. M. Jin, “A general approach for the stability analysis of time-domain finite element method,” IEEE Trans. Antennas Propag., vol. 50, no. 11, pp. 1624–1632, Nov. 2002. [28] Q. He, H. Gan, and D. Jiao, “Explicit time-domain finite-element method stabilized for an arbitrarily large time step,” IEEE Trans. Antennas Propag., vol. 60, no. 11, pp. 5240–5250, Nov. 2012. [29] M.-F. Wong, O. Picon, and V. F. Hanna, “A finite element method based on Whitney forms to solve maxwells equations in the time domain,” IEEE Trans. Magn., vol. 31, no. 3, pp. 1618–1621, May 1995. [30] B. Zhou and D. Jiao, “Direct finite-element solver of linear complexity for large-scale 3-d electromagnetic analysis and circuit extraction,” IEEE Trans. Microw. Theory Techn., vol. 63, no. 10, pp. 3066–3080, Oct. 2015.

Jin Yan received the B.S. degree in electronic engineering and information science from the University of Science and Technology of China, Hefei, China, in 2012. She is currently working toward the Ph.D. degree in electrical engineering at Purdue University, West Lafayette, IN, USA. She currently works in the On-Chip Electromagnetics Group at Purdue University. Her research is focused on computational electromagnetics, high-performance VLSI CAD, and fast and high-capacity numerical methods. Ms. Yan was the recipient of an Honorable Mention Award of the IEEE International Symposium on Antennas and Propagation in 2015.

Dan Jiao (S'00–M'02–SM'06) received the Ph.D. degree in electrical engineering from the University of Illinois at Urbana-Champaign, Urbana, IL, USA, in 2001. She then joined the Technology Computer-Aided Design (CAD) Division, Intel Corporation, until September 2005, where she was a Senior CAD Engineer, Staff Engineer, and Senior Staff Engineer. In September 2005, she joined Purdue University, West Lafayette, IN, USA, as an Assistant Professor with the School of Electrical and Computer Engineering. She is currently a Professor with Purdue University. She has authored 3 book chapters and over 230 papers in refereed journals and international conferences. Her current research interests include computational electromagnetics; high-frequency digital, analog, mixed-signal, and RF integrated circuit (IC) design and analysis; high-performance VLSI CAD; modeling of microscale and nanoscale circuits; applied electromagnetics; fast and high-capacity numerical methods; fast time-domain analysis; scattering and antenna analysis; RF, microwave, and millimeter-wave circuits; wireless communication; and bio-electromagnetics. Dr. Jiao has served as the reviewer for many IEEE journals and conferences. She is an Associate Editor of the IEEE TRANS. ON COMPONENTS, Packaging, and Manufacturing Technology. She received the 2013 S. A. Schelkunoff Prize Paper Award of the IEEE Antennas and Propagation Society, which recognizes the Best Paper published in the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION during the previous year. She was among the 21 women faculty selected across the country as the 2014–2015 Fellow of ELATE (Executive Leadership in Academic Technology and Engineering) at Drexel, a national leadership program for women in the academic STEM fields. She has been named a University Faculty Scholar by Purdue University since 2013. She was among the 85 engineers selected throughout the nation for the National Academy of Engineerings 2011 US Frontiers of Engineering Symposium. She was the recipient of the 2010 Ruth and Joel Spira Outstanding Teaching Award, the 2008 National Science Foundation (NSF) CAREER Award, the 2006 Jack and Cathie Kozik Faculty Start up Award (which recognizes an outstanding new faculty member of the School of Electrical and Computer Engineering, Purdue University), a 2006 Office of Naval Research (ONR) Award under the Young Investigator Program, the 2004 Best Paper Award presented at the Intel Corporations annual corporate-wide technology conference (Design and Test Technology Conference) for her work on generic broadband model of high-speed circuits, the 2003 Intel Corporations Logic Technology Development (LTD) Divisional Achievement Award, the Intel Corporations Technology CAD Divisional Achievement Award, the 2002 Intel Corporations Components Research the Intel Hero Award (Intel-wide she was the tenth recipient), the Intel Corporations LTD Team Quality Award, and the 2000 Raj Mittra Outstanding Research Award presented by the University of Illinois at Urbana-Champaign.

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Alternative Method for Making Explicit FDTD Unconditionally Stable Md. Gaffar and Dan Jiao, Senior Member, IEEE

Abstract—An alternative method is developed to make an explicit FDTD unconditionally stable. In this method, given any time step, we find the modes that cannot be stably simulated by the given time step, and deduct these modes directly from the system matrix (discretized curl-curl operator) before the explicit time marching. By doing so, the original FDTD numerical system is adapted based on the desired time step to rule out the root cause of instability. The resultant explicit FDTD marching is absolutely stable for the given time step no matter how large it is, and irrespective of space step. The accuracy is also guaranteed for time step chosen based on accuracy. Numerical experiments have validated the accuracy, efficiency, and unconditional stability of the proposed new method for making an explicit FDTD unconditionally stable. Index Terms—Explicit methods, finite-difference time-domain method (FDTD), stability, unconditionally stable methods.

I. INTRODUCTION

F

INITE-DIFFERENCE TIME-DOMAIN (FDTD) method [1], [2] is one of the most popular time domain methods for electromagnetic analysis. This is largely attributed to its simplicity and optimal computational complexity at each time step gained by not solving a matrix. However, the time step of a traditional FDTD is restricted by space step for stability, as dictated by the well-known Courant-Friedrichs-Lewy (CFL) condition. When the space step can be chosen based on accuracy for sampling the working wavelength, the time step dictated by the CFL stability condition agrees well with the time step required by accuracy. Hence, the dependence of time step on space step does not become a concern. However, when the problem being simulated involves fine features relative to working wavelengths such as an on-chip nanometer integrated circuit working at microwave frequencies, or a multiscaled system spanning a wide range of geometrical scales, the time step determined by space step for a stable FDTD simulation can become many orders of magnitude smaller than the time step required by accuracy. Due to such a small time step, a tremendous number of time steps must be simulated to reach the time corresponding to the working frequency, which is computationally prohibitive. From

Manuscript received June 19, 2015; revised September 10, 2015, October 21, 2015; accepted October 23, 2015. Date of publication November 11, 2015; date of current version December 02, 2015. This work was supported in part by a grant from NSF under award No. 1065318, and a grant from DARPA under award HR0011-14-1-0057. This paper is an expanded version from the IEEE MTT-S International Microwave Symposium, Phoenix, AZ, USA, 17–22 May 2015. The authors are with the School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907 USA (e-mail: [email protected]). Digital Object Identifier 10.1109/TMTT.2015.2496255

the accuracy point of view, such a choice of time step is not necessary, and hence the time step’s dependence on space step is a numerical problem that must be overcome. Implicit unconditionally stable FDTD methods [3]–[13] have been developed to overcome the dependence of time step on space step. In these methods, the time integration technique is changed to a different way such that the resulting time marching scheme has an error amplification factor bounded by 1, thus ensuring stability. However, the implicit methods require a matrix solution, the efficiency of which is not desired when a large problem size is encountered. In addition, it is observed that the accuracy of the implicit methods can degrade greatly with the increase of time step. Late-time instability has also been observed among existing implicit unconditionally stable FDTD methods. Recently, advanced research [14]–[18] has been pursued to address the time step problem in the framework of the original explicit time-domain methods. In [15], [17], [18], the root cause of instability is identified for explicit time-domain methods, based on which an explicit and unconditionally stable time-domain finite-element method (TDFEM) is successfully developed in [15], [17] and the same capability is demonstrated for FDTD in [18]. The root-cause analysis shown in [15], [17], [18] is different from a conventional stability analysis [2], [19]. In a conventional stability analysis, the time step required for a stable time-domain simulation is derived and used to guide the choice of time step. From such a stability analysis, apparently, except for choosing the time step based on the stability criterion, there is no other way forward to make an explicit method stable. On the contrary, the root-cause analysis given in [17], [18] reveals that when an explicit time-domain method becomes unstable, not every eigenmode present in the field solution becomes unstable. Only a subset of eigenmodes is unstable, while the rest of the eigenmodes are still stable. This subset of eigenmodes is the root cause of instability, which are termed unstable modes. These modes have eigenvalues (characterizing the rate of field variation in space) greater than that can be accurately captured by the given time step, thus causing instability. When the time step is chosen based on accuracy, the unstable modes are not required by accuracy. Hence, they can be removed without affecting the accuracy. Based on the root-cause analysis, in [18], an explicit FDTD that is unconditionally stable is developed. It has also been extended to analyze general lossy problems in [21], [22]. In this method, the field solution is expanded into stable eigenmodes, and the numerical system is also projected onto the space of stable eigenmodes. The resulting explicit time-marching is absolutely stable for the given time step no matter how large it

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is. Comparisons with state-of-the-art implicit unconditionally stable FDTD methods have also shown clear advantages of the new explicit method in accuracy, dispersion error, and stability in addition to computational efficiency [22]. This is mainly because in an implicit unconditionally stable method, the root cause of instability that makes an explicit method unstable is not removed from the numerical system. When a large time step beyond CFL condition is used, the root cause, which is unstable modes, cannot be accurately simulated by the given time step. Although they are suppressed to be stable, they can still negatively affect the overall accuracy and stability of the implicit method. To preserve the advantage of the explicit FDTD in avoiding solving a matrix equation, a preprocessing algorithm is developed in [18] to extract the stable eigenmodes from the field solutions obtained from the traditional explicit FDTD. The time window simulated in the preprocessing step is much smaller than that of the entire time window to be simulated. However, since the time step required by a traditional FDTD method is used in the preprocessing step, the speedup of the overall scheme can become limited by the preprocessing step. In this work, we develop a new explicit and unconditionally stable FDTD method. This new method eliminates the traditional FDTD-based preprocessing in [18]. Meanwhile, it permits the use of a large time step upfront in the explicit time marching by deducting the unstable modes directly from the FDTD system matrix. The unstable modes have the largest eigenvalues of the system matrix, and hence they can be efficiently found in complexity, with the number of unstable modes. Using the proposed method, one only needs to perform a very minor modification on the traditional FDTD to make it unconditionally stable. Hence, the proposed method is convenient for use. The basic idea of this work has been presented in our IMS conference paper [20]. In this paper, we expand [20] to address aspects that have not been addressed before, including algorithm details, complexity and accuracy analysis, open-region problems, how to efficiently find unstable modes, and comparisons with the previous explicit and unconditionally stable FDTD method [18]. Extensive numerical experiments and comparisons with existing methods have demonstrated the unconditional stability, accuracy, and efficiency of the proposed alternative explicit and unconditionally stable method. II. PRELIMINARIES Before presenting the proposed work, it is necessary to review the root cause of instability [17], [18]. Using a matrix notation, we can rewrite the FDTD updating equations into the following compact form: (1) (2) where denotes the vector of electric field unknowns placed along the edges of the primary grid, denotes the vector of magnetic field unknowns along the edges of the dual grid, is the vector of current sources whose entry is with being current density, is time step, superscripts such as , and denote the time instant, and are

sparse matrices representing the discretized , and operators, respectively. As can be seen from (1) and (2), the computations involved in the FDTD are sparse matrix-vector multiplications. Equations (1) and (2) solve both and . We can also eliminate one field unknown to see the root cause of instability more easily. Rewriting (2) for , we find (3) Subtracting (3) from (2), and using (1) to replace the term of in the resultant, we arrive at (4) where

, which is actually at the -th time instant. Equation (4) is nothing but a central-difference based discretization of the following second-order wave equation (5) where (6) The solution to (5) at any time is a time-dependent superposition of the eigenmodes of . Performing a -transform of (4), it can be found the eigenmodes, whose eigenvalues satisfy the following condition, can always be stably simulated by the given time step (7) The root cause of instability is thus the eigenmodes whose eigenvalues are greater than , which are termed unstable modes. In a traditional explicit time-domain method, the underlying numerical system and thereby the eigenmodes governing the field solution are not changed, but the time step is adjusted based on the CFL condition so that a time-domain simulation can be made stable. The CFL condition essentially requires the time step to be chosen based on the largest eigenvalue of , so that (7) is satisfied for all eigenmodes present in the numerical system. In an explicit and unconditionally stable method like [17], [18], the desired time step is not changed, but the numerical system is changed so that only those eigenmodes that can be stably simulated by the given time step are kept, while the unstable modes are discarded. In this way, the dependence of the time step on space step is removed, and an explicit method can also be made unconditionally stable. III. PROPOSED METHOD From the root-cause analysis reviewed in the previous section, it is evident that once a space discretization is done, whether there exist unstable modes or not is known for a given time step, regardless of time marching. Therefore, the source of instability is inherent in the system matrix resulting from the space discretization, rather than in the field solution. To completely remove such a source, the system matrix has to be

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changed. In this section, we present proposed method, explain how it works, and analyze its complexity and accuracy. In addition, we also describe how to handle open-region problems in the proposed method.

Since , where is the diagonal matrix of eigenvalues, using (13), we obtain

A. Method

which can further be written as

(14)

Let denote the matrix formed by all the unstable modes, with each column being an eigenvector of whose eigenvalue is greater than . How to efficiently find will soon be given in next section. Right now, assume has been generated. In the proposed method, we use to directly change the original system matrix to a new system matrix

is the eigenvector matrix of stable eigenmodes, where and are diagonal matrices containing stable and unstable eigenvalues, respectively. Multiplying both sides of (15) by , since ’s eigenvectors are orthogonal, we obtain

(8)

(16)

For an that is Hermitian and positive semi-definite, the above is equal to

Thus, substituting (16) into (8) and using (15), (8) is nothing but

(9) i.e., multiplying by from the right. We then perform an explicit FDTD simulation on the new system matrix . If a second-order based system shown in (4) is employed, we simply modify it to (10) and march on in time step by step. If the original FDTD-based first-order system given in (1) and (2) is used, we update them to

(11) which is the same as (10). This can be readily verified by eliminating unknowns from (11). One can also eliminate unknowns to obtain an equation for , which is the -based counterpart of (10). In this case, becomes , and in (11), the term does not exist in the first row, but appears in front of in the second row. After obtaining the solution of from (10) or (11), we need to add one more important step to make the solution correct, which is (12) Obviously, the aforementioned method only requires a very minor modification in the traditional FDTD, and hence the method is convenient for use. Now, we shall explain how the proposed method works. B. How It Works? The new system matrix consists of the stable eigenmodes only, and hence the source of instability is completely removed. To prove, we first utilize the property of the eigenvectors of . Since is Hermitian positive semi-definite, its eigenvectors are orthogonal. Hence, the following property holds true: (13)

(15)

(17) and hence the space of stable modes only. Since is symmetric as can be seen from (17), (8) is the same as (9). However, for non-symmetric such as the one resulting from a lossy analysis [22], (8) is different from (9), and (8) is the correct one to use since it is still made of modes only, while (9) is not. In addition, in this case, the should be orthogonalized to satisfy before being removed from , and the in (8) is replaced by . After updating the system matrix from to that is free of the source of instability, we can perform the explicit FDTD time-marching on with absolute stability. However, after implementing (10) and (11), we found the result is indeed stable but not accurate. Interestingly, if is found by first obtaining all eigenvectors of , and then selecting from them, the accuracy is good. However, if is found by computing the unstable eigenvectors of only, the results do not match the reference data. Certainly, the first approach that finds all eigenvectors is not practical for use when problem size is large, and the second approach is the one that can truly make the proposed method useful in practice. To figure out the problem, we compare the modes found by the second approach with those found by computing all eigenvectors of . They show good agreement with each other. Therefore, the accuracy of is not a problem. This has led to the finding that the updated matrix has additional zero eigenvalues, the eigenvectors corresponding to these additional zero eigenvalues are not the eigenvectors of the original matrix , and they make the result wrong. To explain, the as shown in (17) has rank , where is the number of stable eigenmodes of . On the other hand, is a matrix of size . Hence, the additional eigenvalues are zero, whose eigenvectors make an additional nullspace. As a result, when computing (10) or (11), the field solution is not only the superposition of the modes, but also the additional nullspace modes as the following: (18) are corresponding coefficient vectors. The true where and solution should satisfy . Hence, the result of (18) is wrong. When is found by computing all the eigenvectors of

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and from them choosing , (17) matches that in (15) very well. Hence, the contribution of the additional nullspace in (17) is almost zero. However, this is not the case when is found from computing only the eigenvectors of that violate (7). To solve this problem, after obtaining the solution of from (10) or (11), we need to add (12) to make the solution correct. This treatment removes the second term in (18). This is because must be in the space of since it is not in . By deducting from , all of the -components and thereby -components are removed, making ’s solution correct. It is also worth mentioning that if nullspace, whose eigenvectors are also termed DC modes, does not make an important contribution in the field solution such as in the case of an electrically large antenna, the step of (12) is not needed. To use an infinitely large time step without making the FDTD unstable, we simply remove all the eigenmodes of whose eigenvalues are nonzero. To use other time step sizes, we remove eigenmodes adaptively based on the given time step. As a result, the proposed method flexibly permits the use of any time step independent of space step, thus being explicit and unconditionally stable.

hence , thus beyond the maximum frequency required to be captured by accuracy. The above accuracy analysis is for source-free problems. The same holds true for problems with sources, as shown by the analysis given in Section IV.B, and specifically (40) of [18]. D. Treatment of Open-Region Boundary Conditions In open-region problems, the computational domain can be truncated by various Absorbing Boundary Conditions (ABC) such as Perfectly Matched Layers (PML). Since the field solution inside PML is fictitious, and there is no fine feature inside the PML region either, we do not perform any special treatment in the PML region, but to conduct the FDTD simulation as it is. In the solution domain, we update the system matrix by deducting the unstable modes from it. Basically, we divide the unknown into two groups, one inside the solution domain denoted by , and the other elsewhere such as boundary, PML or other ABCs, denoted by . The same is done for unknown . Subsequently, the sparse matrices and are cast into the following form:

C. Complexity and Accuracy Analysis 1) Complexity Analysis: As compared to the original FDTD, the only additional computation involved in the proposed method is the computation of at each time step, as shown in (10) and (11). The can be efficiently evaluated by two matrix-vector multiplications: first, computing , the cost of which is ; second, multiplying the resultant by , the cost of which is also . If one computes first, the resultant matrix is a dense matrix of size . Multiplying such a dense matrix by would cost operations, which is expensive when is large. Therefore, the approach of doing two matrix-vector multiplications should be used to obtain . 2) Accuracy Analysis: When the time step is chosen based on accuracy, the unstable modes are not required by accuracy, and hence they can be deducted from the system matrix without affecting accuracy. To explain, in the proposed method, we expand the space dependence of the field solution using the eigenmodes of as follows: (19) is the time-dependent coefficient of the -th eigenwhere mode . In a source-free problem, the is analytically known as [18] (20) arbitrary coefficients. Hence, the square root of with the eigenvalue is also the frequency of the field’s time variation, i.e., . This is, in fact, dispersion relation. In free space, the is analytically known as , where is free-space wave number. In inhomogeneous problems, the is not analytically known but can be numerically found. When the time step is chosen based on accuracy such as . The unstable modes have , and

(21) With the above, rewriting (11) separately for , we obtain

and

(22) IV. FINDING UNSTABLE MODES For any given time step , the unstable modes are the eigenmodes of whose eigenvalues are greater than . Hence, the unstable modes have the largest eigenvalues of . Since is sparse, the computing task becomes how to find the largest eigenpairs of a sparse matrix. The Arnoldi method is particularly suited for this computing task [23]. In steps, it can find a complete set of largest eigenvalues and eigenvectors. When the matrix is Hermitian, the Arnoldi process reduces to Lanczos method. A -step Arnoldi method on matrix is to carry out the following computation: (23) where is a unitary matrix of size is a small upper Hessenberg matrix of dimension is the -th column of identity matrix , and is a column vector of length yielding an matrix. When the norm of and hence the norm of goes to zero, the eigenvalues of are the eigenvalues of the original matrix , and multiplied by the eigenvectors of are the eigenvectors of . The detailed algorithm for realizing (23) can be found from Algorithm 3.7 of [23]. The overall computational cost is simply sparse matrix-vector multiplications, each of which is multiplied by an intermediate vector

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one has to use a shift-invert technique to transform the eigenvalues of interest (now smallest eigenvalues) to the largest eigenvalues of a new matrix. This new matrix can be written as , where is a shift value chosen to be small so that the smallest eigenvalues can become the largest ones of the new matrix. It is evident that finding the eigenvalues of is computationally much more expensive as compared to finding the eigenvalues of , since a matrix solution is involved. Furthermore, in steps, we cannot guarantee finding a complete set of smallest eigenvalues since is empirical. Moreover, has a nullspace whose eigenvalues are zero. The size of nullspace grows with . In other words, when matrix size increases, the number of eigenvectors whose eigenvalues are zero also increases. This further increases the computational cost. In contrast, the preprocessing algorithm developed in [18] is an efficient and reliable algorithm for finding a complete set of stable eigenmodes. The problem of the increasing size of the nullspace is also well handled in this preprocessing algorithm. This is because all the nullspace eigenvectors share the same eigenvalue (zero) in common. Given a right hand side (source) vector, the contributions from the nullspace eigenvectors are grouped together and become a single vector. Hence, the algorithm in [18] does not suffer from the issue of increasing nullspace size. V. COMPARISON WITH PREVIOUS METHOD First, we prove the proposed new method is mathematically equivalent to the previous method [18]. In previous method [18], the fields are expanded in the space of stable modes, and the numerical system is projected onto the space of stable modes. Consider the solution of (4), the is expanded as , and the time-dependent unknown coefficient vector is solved from the following equation: generated during the -step process, and the orthogonalization of the resulting vectors. The complexity of the sparse matrix-vector multiplications is , while the complexity of orthogonalization is , and hence the overall complexity is . This is much more efficient than a brute-force eigenvalue solution. A straightforward -step Arnoldi process cannot ensure the largest eigenpairs to be found in steps. Spurious eigenvalues may also be produced. We hence employ the implicitly restarted Arnoldi method [23] to systematically drive the residual of (23) to be zero. For completeness of this paper, we give the algorithm of implicitly restarted Arnoldi method as shown in Algorithm 1, which is modified to suit the need of this work. In this algorithm, from Step 4 to 12 is to shift unwanted eigenvalues so that the next initial vector is rich in the wanted eigenvectors. The computational cost from Step 4 to 12 is negligible as compared to Step 3, since these steps are performed on small matrices of size . The computational complexity of Step 3 is , where is proportional to . The cost of Step 13 is again negligible since it is performed on a small matrix of size . Overall, the complexity of Algorithm 1 is for finding largest eigenpairs of . One may wonder why we do not use the same procedure to find the stable eigenmodes. The stable eigenmodes turn out to have the smallest eigenvalues of . To find them efficiently,

(24) In the proposed method, we solve (10). Substituting (17) into it, we obtain (25) , since in the new method we do not Here, let explicitly expand the field solution in the space. Vector hence consists of the coefficients corresponding to both the , and the modes. Multiplying (25) by , with (12), we obtain , and satisfying the same equation as (24). Hence, the proposed new method is mathematically equivalent to the previous method. Therefore, its accuracy and stability are both ensured. However, the two methods are computationally different. In the previous method [18], a traditional FDTD-based preprocessing is developed to find the space of stable modes. In the proposed method, no such preprocessing is required, and hence the method is not subject to the constraint of the traditional FDTD's time step. In the previous method, the numerical system is projected onto the space of stable modes; in the proposed method, the unstable modes are directly deducted from the numerical system to eradicate the root cause of instability. In the

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previous method, the explicit marching is performed on a reduced order system since the number of stable modes is smaller than the original system size; in the proposed method, there is no reduction in system order. In the previous method, if the number of stable modes is large, the modes can be broken into bands and found band by band independent of each other; in the proposed method, if the number of unstable modes is many, the computational cost for finding them remains to be and, in general, cannot be made smaller. Overall, when the number of unstable modes is not large, the proposed method is efficient for use. This is typically true in many problems solved by the FDTD: the fine features only occupy a small portion of the entire space discretization. The proposed method is also much more convenient for implementation. In addition, by removing just one unstable mode whose eigenvalue is the largest, one already can use a time step larger than the CFL time step using the proposed method; by removing the highest two unstable eigenmodes, one can use an even larger time step; and so on. Hence, with negligible computational cost, the proposed method allows for the use of a time step beyond the stability criterion. In contrast, in the method of [18], the time step in the preprocessing procedure is restricted by the time step required by stability. The computational overhead is more for one to use a time step beyond the CFL condition. Certainly, the two methods can be combined to accentuate the advantages of both methods. For example, when the number of unstable modes is many, from the proposed method, we can still remove a certain number of unstable modes within feasible run time, based on which the time step can be immediately enlarged although it has not been enlarged to the time step allowed by accuracy yet. Using the resulting updated system matrix, and hence a much increased time step, the preprocessing step in [18] can be accelerated greatly to identify the stable modes. The proposed method hence does not need to finish the simulation of the entire time window, but a small window simulated in the preprocessing step. The previous method can then be used to carry out explicit marching efficiently: the system has a much reduced order and is diagonal, in addition, the computation of the term in the proposed method is also avoided. VI. NUMERICAL RESULTS A. Demonstration of Unconditional Stability First, we demonstrate the unconditional stability of the proposed method using an example that has an analytical solution. It is a 3-D parallel plate structure whose dimension is 900 m, 6 m, and 1 m along -, -, and -direction, respectively. The space step is 0.2 m, 0.85714 m, and 90 m, respectively along -, -, and -direction. This structure is excited at the near end by a current source that has a very low frequency pulse of with s, and s. The time step required by sampling accuracy thereby is at the level of s, while that dictated by the CFL condition for stability is s. Hence, there is a more than 160 orders of magnitude difference in the two time steps. With a time step of s, the proposed method stably simulated the structure with excellent accuracy. As can be seen from Fig. 1(a), the voltages generated from the proposed method and

Fig. 1. Demonstration of unconditional stability. (a) Voltage waveforms. (b) Entire solution error as a function of time.

the analytical solution are on top of each other. Notice that the structure behaves as a capacitor at very low frequencies, and hence the near- and far-end voltages are identical to each other. The s appears to be already an extremely large time step. In fact, the proposed method allows for a time step of infinity. The includes all the eigenmodes whose eigenvalues are nonzero, leaving zero eigenvalues only, and hence permitting an infinitely large time step. The number of modes is 561. In addition to examining the solution accuracy at selected points, we have also assessed the entire solution error by measuring , where consists of all electric field unknowns in the computational domain solved from the proposed method, whereas is obtained from the analytical solution. The entire solution error is shown in Fig. 1(b) as a function of time, verifying the accuracy of the proposed method at all points in the computational domain at each time instant. Notice that the error is plotted as it is instead of a percentage error. It takes the proposed method 2.99 s to finish the entire simulation including the time for finding unstable modes. To finish the same simulation, the FDTD would have to take more than s (the expanding universe time). This example appears to be dramatic, however, it is necessary to examine whether a

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Fig. 3. Simulation of a mm-level cavity. (a) Electric fields obtained from the proposed method at two points using different tme steps. (b) Comparison with the ADI and HIE methods for the electric field simulated.

B. Parallel Plate Excited by a Current Source at Higher Frequencies

Fig. 2. Simulation of a 3-D parallel plate structure. (a) Voltage waveforms. (b) Entire solution error as a function of time. (c) The ratio of the unstable modes component to the entire field solution.

method is truly unconditionally stable. This example also shows clearly that the dependence of time step on space step is a numerical problem, instead of a fundamental physical law one has to obey.

Next example is the same structure but with a fast Gaussian derivative pulse having a maximum input frequency 34 GHz. Since the space discretization remains the same, the time step required by a stable FDTD simulation remains to be s, while the time step required by sampling accuracy is s. The proposed method is able to generate accurate and stable results using the time step of s. As shown in Fig. 2(a), the voltage waveforms simulated by the proposed method are in excellent agreement with those from the conventional explicit FDTD. The accuracy is further demonstrated by the entire solution error plotted in Fig. 2(b) as a function of time. The CPU time cost by the proposed method is approximately 6.013 s with 3.251 s for time marching, and the rest for finding the unstable modes. Compared with 6875.4 s required by the conventional explicit FDTD, the speedup of the proposed method is 1145.9. In this example, we have also examined the weights of the unstable modes in the field solution. Let the weights be denoted by . It can be computed at each time step from , where is the reference FDTD solution. As can be seen

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Fig. 5. Entire solution error for simulating a 3-D on-chip bus structure.

s solely determined by accuracy, whereas the time step used by the conventional FDTD is s. The number of modes removed is 288. In Fig. 3(a), we plot the electric fields at two points, mm, and mm, respectively, in comparison with the FDTD solutions. Excellent agreement can be observed. The total simulation time of the proposed method is 5.74 s including the time for finding , and that for performing (11)–(12), in contrast to the 27.37 s cost by FDTD. The average entire solution error is found to be less than 3%. We have also simulated this example using the ADI and the HIE method [24] using the time step of s. In Fig. 3(b), we compare the voltages at point simulated by the three methods, which further verifies the accuracy of the proposed method. The proposed method flexibly adapts the eigensystem based on the required time step. For example, if the required time step is s instead of s, the eigenvalues are accordingly removed from the largest down to . The results are equally accurate as can be seen from Fig. 3(a). The CPU time for this case is 19.03 s. D. Open-Region Radiation

Fig. 4. Simulation of an open-region problem. (a) Structure. (b) Electric field at the observation point. (c) Entire solution error.

clearly from Fig. 2(c), the weights of the discarded unstable modes are small as compared to the entire field solution. C. Millimeter-Level Cavity Previous structures have very fine features relative to working wavelengths. Next, we consider a millimeter cavity whose space discretization is comparable to that required by the input spectrum. The overall dimension is 19.4 mm 12.4 mm 0.14118 mm. The space step along -, -, and -direction is respectively 1.8 mm, 1.8 mm, and 0.03529 mm. A current element of length 0.0334 mm is located in middle of the cavity along -direction. The proposed method uses a time step of

Next, we simulate an open-region problem with a dipole antenna radiating in presence of multiple dielectric cylinders, as illustrated in Fig. 4(a). The solution domain is 15.7 mm by 10.3 mm, surrounded by a 10-layer PML region. The maximum space step size is m. The smallest space step is m. There are three cylinders situated on the left side of the solution domain and a current source along -direction located on the upper right corner. The pulse of the current source is a Gaussian derivative with a maximum input frequency of Hz. The cylinders have relative permittivity . The time step required by stability is s, whereas the time step used by the proposed method is s. The proposed method takes s to finish the entire simulation, while the FDTD costs s. The electric field at the observation point shown in Fig. 4(a) is plotted and compared with that of traditional explicit FDTD in Fig. 4(b). The entire solution error is shown in Fig. 4(c). Excellent accuracy is observed.

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able to use the time step required by accuracy, s, to obtain accurate results. In contrast, the conventional FDTD must use a time step of s to ensure stability. The total CPU time of the proposed method is 7.12 s, whereas that of the conventional FDTD is 7 426 s. The speedup of the new method over the FDTD is approximately 1 043. The number of removed eigenmodes is 536 in this example. The entire solution error is plotted in Fig. 5 as a function of time, revealing good accuracy of the proposed method. The speedup of the method in [18] over the traditional FDTD is 47. Hence, the proposed method is more efficient in simulating this example. F. Electromagnetic Interference (EMI) Example In the last example, we simulate an EMI example as illustrated in Fig. 6(a), and compare the performance of the proposed method with the method of [24]. The structure is a cube of side length 11 cm truncated by perfect electric (PEC) boundary conditions all around. In the center, there is a PEC sheet with five slots. The thid slot has a width of 0.25 mm, and others are of width 1 cm. Then we set the total at the center point of the lower-half domain to be with s, and s. The third slot is discretized along into 5 uniform cells. The cell size is 1 cm along -, and -direction, respectively, and 0.02 cm along in the areas other than the third slot. We compare the results obtained from the conventional FDTD, the proposed method, and the HIE in [24], for a time step of 0.166 ps which is the time step of the conventional FDTD, and the time step of 1.66 ps, respectively. The obtained for the two choices of the time step at the center point of the upper domain are plotted in Fig. 6(b), and (c), respectively. The HIE is shown to be unstable for the time step of 1.66 ps, whereas the proposed method still generates stable and accurate results.

VII. CONCLUSION

Fig. 6. Simulation of an EMI problem. (a) Illustration of the structure. (b) Electric field at the observation point using a time step of 0.166 ps. (c) Electric field at the observation point using a time step of 1.66 ps.

E. On-Chip 3-D Bus Next, an on-chip 3D bus structure embedded in an inhomogeneous stack of dielectrics is simulated. The proposed method is

In this paper, an alternative method is developed to achieve unconditional stability in an explicit FDTD simulation. It retains the strength of FDTD in avoiding matrix solutions, while eliminating its shortcoming in time step. The unstable modes are directly deducted from the original FDTD numerical system to eradicate the root cause of instability. Since the unstable modes have the largest eigenvalues and the FDTD system matrix is sparse, the unstable modes can be efficiently and reliably found in complexity, where is the number of unstable modes. The proposed method only requires a very minor modification on the traditional FDTD to make it unconditonally stable. Its implementation is hence convenient. Numerical experiments and comparisons with existing explicit FDTD methods have demonstrated the superior performance of the proposed method in stability, accuracy, and efficiency. The essential idea of the proposed method can also be applied to other time domain methods. The proposed method complements the capability offered by the original explicit and unconditionally stable FDTD [18]. Recently, this work has also been extended for analyzing general lossy problems in [25].

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REFERENCES [1] K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwells equations in isotropic media,” IEEE Trans. Antennas Propagat., vol. 14, no. 5, pp. 302–307, May 1966. [2] A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method. Boston, MA, USA: Artech House, 2000. [3] T. Namiki, “A new FDTD algorithm based on alternating-direction implicit method,” IEEE Trans. Microw. Theory Tech., vol. 47, no. 10, pp. 2003–2007, Oct. 1999. [4] F. Zheng, Z. Chen, and J. Zhang, “A finite-difference time-domain method without the courant stability conditions,” IEEE Microwave Guided Wave Lett., vol. 9, no. 11, pp. 441–443, Nov. 1999. [5] G. Sun and C. W. Trueman, “Unconditionally stable Crank-Nicolson scheme for solving two-dimensional Maxwell's equations,” Electron. Lett., vol. 39, no. 7, pp. 595–597, Apr. 2003. [6] J. Lee and B. Fornberg, “A splitting step approach for the 3-D Maxwell's equations,” J. Comput. Appl. Math, vol. 158, no. 2, pp. 485–505, 2003. [7] G. Zhao and Q. H. Liu, “The unconditionally stable pseudospectral time-domain (PSTD) method,” IEEE Microw. Wireless Compon. Lett., vol. 13, no. 11, pp. 475–477, Nov. 2003. [8] J. Shibayama, M. Muraki, J. Yamauchi, and H. Nakano, “Efficient implicit FDTD algorithm based on locally one dimentional scheme,” Electron. Lett., vol. 41, no. 19, pp. 1046–1047, Sep. 2005. [9] Y. S. Chung, T. K. Sarkar, B. H. Jung, and M. Salazar-Palma, “An unconditionally stable scheme for the finite-difference time-domain method,” IEEE Trans. Microw. Theory Tech., vol. 59, no. 1, pp. 56–64, Jan. 2011. [10] Z. Chen, Y. T. Duan, Y. R. Zhang, and Y. Yi, “A new efficient algorithm for the unconditionally stable 2-D WLP-FDTD method,” IEEE Trans. Antennas Propag., vol. 61, no. 7, pp. 3712–3720, Jul. 2013. [11] Z.-Y. Huang, L.-H. Shi, B. Chen, and Y. H. Zhou, “A new unconditionally stable scheme for FDTD method using associated hermite orthogonal functions,” IEEE Trans. Antennas and Propag., vol. 62, no. 9, pp. 4804–4808, Sep. 2014. [12] E. L. Tan, “Fundamental schemes for efficient unconditionally stable implicit finite-difference time-domain methods,” IEEE Trans. Antennas Propagat., vol. 56, no. 1, pp. 170–177, Jan. 2008. [13] M. Gaffar and D. Jiao, “A simple implicit and unconditionally stable FDTD method by changing only one time instant,” in Proc. IEEE Int. Symp. Antennas Propagat., Jul. 2014, pp. 1–2. [14] A. Ecer, N. Gopalaswamy, H. U. Akay, and Y. P. Chien, “Digital filtering techniques for parallel computation of explicit schemes,” Int. J. Computat. Fluid Dynamics, vol. 13, no. 3, pp. 211–222, 2000. [15] Q. He and D. Jiao, “An explicit time-domain finite-element method that is unconditionally stable,” in Proc, 2011 IEEE Int. Symp. Antennas Propag., Jul. 2011, pp. 4–. [16] C. Chang and D. S. Costas, “A spatially filtered finite-difference time-domain scheme with controllable stability beyond the CFL limit,” IEEE Trans. Microw. Theory and Tech., vol. 61, no. 3, pp. 351–359, Mar. 2013. [17] Q. He, H. Gan, and D. Jiao, “Explicit time-domain finite-element method stabilized for an arbitrarily large time step,” IEEE Trans. Antennas Propag., vol. 60, no. 11, pp. 5240–5250, Nov. 2012. [18] Md. Gaffar and D. Jiao, “An explicit and unconditionally stable FDTD method for electromagnetic analysis,” IEEE Trans. Microw. Theory Tech., vol. 62, no. 11, pp. 2538–2550, Nov. 2014. [19] D. Jiao and J. M. Jin, “A general approach for the stability analysis of time-domain finite element method,” IEEE Trans. Antennas Propagat., vol. 50, no. 11, pp. 1624–1632, Nov. 2002. [20] Md. Gaffar and D. Jiao, “An alternative method for making an explicit FDTD unconditionally stable,” in Proc. IEEE Int. Microwave Symp. (IMS), May 2015, pp. 1–4. [21] Md. Gaffar and D. Jiao, “An explicit and unconditionally stable FDTD method for the analysis of general 3-D lossy problems,” in Proc. IEEE Int. Microwave Symp. (IMS), Jun. 2014, pp. 1–4. [22] M. Gaffar and D. Jiao, “An explicit and unconditionally stable FDTD method for the analysis of general 3-D lossy problems,” IEEE Trans. Antennas Propag., vol. 63, no. 9, pp. 4003–4015, Sep. 2015. [23] D. C. Sorensen, “Implicit application of polynomial filters in a k-step arnoldi method,” SIAM J. Matrix Analysis Appl., vol. 13, no. 1, pp. 357–385, 1992.

[24] J. Chen and J. Wang, “A three-dimensional semi-implicit FDTD scheme for calculation of shielding effectiveness of enclosure with thin slots,” IEEE Trans. Electromagn. Compat., vol. 49, no. 2, pp. 354–360, 2007. [25] M. Gaffar and D. Jiao, “A new explicit and unconditionally stable FDTD method for analyzing general lossy problems,” in Proc. IEEE Int. Symp. Antennas Propag., Jul. 2015, pp. 1–2. Md. Gaffar received the B.Sc. degree in electrical engineering from the Bangladesh University of Engineering and Technology (BUET), Dhaka, Bangladesh in October, 2009. Since 2011, he has been pursuing the Ph.D. degree in school of electrical and computer engineering at Purdue University, West Lafayette, IN, USA. His research interests include computational electromagnetics and semiconductor physics. Mr. Gaffar has received academic awards in recognition of his research achievements, including the Best Poster Award (among all groups) and Best Project Award in communication and Electromagnetic in EEE Undergraduate Project Workshop (EUProW) 2009. At Purdue, his research has been recognized by the IEEE International Microwave Symposium Best Student Paper Finalist Award in 2013 and 2015, and the 2014 IEEE International Symposium on Antennas and Propagation Honorable Mention Paper Award.

Dan Jiao (S’00–M’02–SM’06) received the Ph.D. degree in electrical engineering from the University of Illinois at Urbana-Champaign, IL, USA, in 2001. She then worked at the Technology Computer-Aided Design (CAD) Division, Intel Corporation, until September 2005, as a Senior CAD Engineer, Staff Engineer, and Senior Staff Engineer. In September 2005, she joined Purdue University, West Lafayette, IN, USA, as an Assistant Professor with the School of Electrical and Computer Engineering, where she is now a Professor. She has authored three book chapters and over 230 papers in refereed journals and international conferences. Her current research interests include computational electromagnetics, high-frequency digital, analog, mixed-signal, and RF integrated circuit (IC) design and analysis, high-performance VLSI CAD, modeling of microscale and nanoscale circuits, applied electromagnetics, fast and high-capacity numerical methods, fast time-domain analysis, scattering and antenna analysis, RF, microwave, and millimeter-wave circuits, wireless communication, and bio-electromagnetics. Dr. Jiao has served as the reviewer for many IEEE journals and conferences. She is an Associate Editor of the IEEE TRANSACTIONS ON COMPONENTS, PACKAGING, AND MANUFACTURING TECHNOLOGY. She received the 2013 S. A. Schelkunoff Prize Paper Award of the IEEE Antennas and Propagation Society, which recognizes the Best Paper published in the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION during the previous year. She was among the 21 women faculty selected across the country as the 2014–2015 Fellow of ELATE (Executive Leadership in Academic Technology and Engineering) at Drexel, a national leadership program for women in the academic STEM fields. She has been named a University Faculty Scholar by Purdue University since 2013. She was among the 85 engineers selected throughout the nation for the National Academy of Engineerings 2011 US Frontiers of Engineering Symposium. She was the recipient of the 2010 Ruth and Joel Spira Outstanding Teaching Award, the 2008 National Science Foundation (NSF) CAREER Award, the 2006 Jack and Cathie Kozik Faculty Start up Award (which recognizes an outstanding new faculty member of the School of Electrical and Computer Engineering, Purdue University), a 2006 Office of Naval Research (ONR) Award under the Young Investigator Program, the 2004 Best Paper Award presented at the Intel Corporations annual corporate-wide technology conference (Design and Test Technology Conference) for her work on generic broadband model of high-speed circuits, the 2003 Intel Corporations Logic Technology Development (LTD) Divisional Achievement Award, the Intel Corporations Technology CAD Divisional Achievement Award, the 2002 Intel Corporations Components Research the Intel Hero Award (Intel-wide she was the tenth recipient), the Intel Corporations LTD Team Quality Award, and the 2000 Raj Mittra Outstanding Research Award presented by the University of Illinois at Urbana-Champaign.

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Accurate Parametric Electrical Model for Slow-Wave CPW and Application to Circuits Design Alfredo Bautista, Anne-Laure Franc, and Philippe Ferrari, Senior Member, IEEE

Abstract—In this paper, a predictive electrical model of the slow-wave coplanar waveguide structure (S-CPW) is presented. The model was developed under the assumption of Quasi-TEM propagation mode. This assumption allows treating separately the electric field from the magnetic field. Therefore, inductive and capacitive effects are processed apart. Within this context, analytical formulas, parameterized by S-CPW geometric dimensions, are given for each electric parameter in the model, including resistances that account for losses. The model was validated with electromagnetic simulations and measurement results on several integrated technologies. An excellent agreement was achieved over a wide frequency band from DC up to 110 GHz, with a maximum error of 10%. Consequently, the model provides a fast and powerful tool for designing circuits based on S-CPW. The developed model enables a better insight of how geometries influence the overall S-CPW performance. The model was applied to the design of a quarter-wave length transmission lines and tunable phase shifter. The transmission lines were optimized in terms of performance, minimum length or surface. The tunable phase shifter was designed by embedding varactors in the S-CPW floating shield. These designs highlight the efficiency of the model for complex optimization or complex circuits design, respectively. Index Terms—Electromagnetic modeling, millimeter-wave integrated circuits, slow-wave coplanar waveguide (S-CPW).

I. INTRODUCTION

I

N RECOGNITION of ongoing demands for higher data rate communication systems, special attention has been focused on millimeter-wave (mm-wave) frequencies. Communication systems working at this frequency range include a wide variety of passive circuits such as matching networks, baluns, phase-shifter, couplers, power dividers among others. Unfortunately, it is well known that losses in passive devices rise as frequency increases, degrading the circuits' quality factor, and thus affecting the entire system performance. In consequence, designing high performance passive circuits is a fundamental task. Previous works reported in [1]–[4] suggest that slow-wave coplanar waveguide (S-CPW) structure is the best basic cell for Manuscript received July 02, 2015; revised September 22, 2015, October 16, 2015; accepted October 18, 2015.Date of publication November 17, 2015; date of current version December 02, 2015. This paper is an extended version from the IEEE MTT-S International Microwave Symposium, 17-22 May 2015, Phoenix, USA. A. Bautista and P. Ferrari are with the Université de Grenoble Alpes, IMEP-LAHC, F-38010, Grenoble, France and also with CNRS, IMEP-LAHC, F-38000, Grenoble, France (e-mail: [email protected]; [email protected]). A.-L. Franc is with the Université de Toulouse, INPT, UPS; LAPLACE, ENSEEIHT, BP7122, F-31071, Toulouse, France, and also with CNRS, LAPLACE, F-31071 Toulouse, France (e-mail: anne-laure.franc@laplace. univ-tlse.fr). Digital Object Identifier 10.1109/TMTT.2015.2495242

elite passive devices at mm-wave. S-CPW gathers both high quality factor and compactness, providing a solution in the development of high performance building blocks. Most of current efforts for improving circuits' performance are based on S-CPW. For example, recent works at mm-wave use S-CPW for designing power splitters [2], mixers [5], band-pass filters [6], Lange couplers [7] or high directivity coupled-line couplers [8] and switched transmission lines [9]. They are also implemented in active circuitry like power amplifiers [10]–[12]. In order to find the most suitable S-CPW, all of these designs were carried out by deep optimization steps using full-wave 3D-EM tools. Designers are forced to recursively face the same procedure for each different CMOS/BiCMOS technology owing to the dissimilarities of their Back-End-Of-Line (BEOL). That leads to long development times, without any degree of certainty of getting the best design. From that it is highly important to provide designers with an accurate electrical model based on S-CPW geometries parameters, allowing proper optimizations based on very fast circuit simulations. The S-CPW concept was first introduced in [13], and since then many papers have been focused on developing an appropriate model [14]–[18]. Despite all these efforts, most of the proposed models are not based upon physics but on fitting equations with several correction parameters. For instance [14] presents a simplistic model were the inductance depends on many fitting coefficients. A more complex model can be found in [15]. However, the RLCG topology was employed inappropriately since it is not S-CPW compliant, as shown in [18]. Indeed, most of the electric field is stored between the CPW strips and the floating strips. So, no electric field flows through the bulk silicon, leading to negligible substrate losses. In the counterpart, losses in the floating shield are not taken into account in the conventional RLCG model, whereas they are important in advanced CMOS technologies since the thickness of the metal layers used for the S-CPW shielding ribbons is only hundreds of nanometers. A physical compatible model was presented in [16]. This complex topology is the result of a non-optimal structure. The model proposed is not predictive since it depends on many fitting parameters. A better tentative of modeling shielded transmission line was presented in [17]. The model is based on a time domain approach. Even if this model considers losses, they are not based on the physical interpretation. Furthermore, losses in the shielding strips are not considered. On the other hand, a physics based electrical model with a RLRC topology was presented in [18], with a deep understanding of the physics. Although it gives a detailed model, closed forms formulas for electrical parameter estimation were not carried out. In [19], the au-

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Fig. 2. RLRC electrical equivalent model for S-CPW.

Fig. 1. A 3D schematic view of the S-CPW topology in CMOS or Bi-CMOS technologies.

thors presented a brief explanation of the parametric model. The modeling of the inductance and capacitance were briefly described, but the resistances' modeling was not addressed. In this work, an accurate and detailed formulation for each element of the RLRC model proposed in [18] is developed. It is based on the assumption of Quasi-TEM propagation mode. The developed equations are wide band and accurate in all current CMOS/BiCMOS technologies without the need of fitting factors. They are mostly based on physical models already presented in the literature, refined for particular S-CPW needs. In Section II the RLRC topology is briefly described. The model formulation is then developed in Section III. Results are presented in Section IV and compared with measurements and 3D-EM simulations for several CMOS/BiCMOS technologies. Section V presents two practical applications of the model for design optimization purposes. Finally, discussion and conclusions are given in Section VI. II. RLRC MODEL A S-CPW is composed of a conventional CPW transmission line loaded by a patterned shield, which is electrically floating (Fig. 1). In CMOS/BiCMOS technologies, the periodic shield is implemented below the CPW strips. Therefore, the electric field is trapped in between the CPW strips and the shield preventing conductive losses in the bulk silicon. In contrast, the magnetic field is not perturbed due to its conservative properties. The RLRC model shown in Fig. 2 was proposed in [18], except the strip-to-strip capacitance that was added here in order to consider cases with small gaps too. It consists of an inductance due to the current propagation in the CPW, a capacitance related to the capacitive effect between the due to CPW strips and the shield, a coupling capacitance the electric coupling between the signal and the ground strips, created by the current flowing in the floating shield, and resistances. The latter reflect the conductive losses in the CPW , and the strips , the conductive losses in the shield . In contrast eddy current losses in the patterned shield with the RLCG model, this model does not include conductance since the electric field does not penetrate the bulk substrate, and losses in the insulating layers between the metals of the BEOL are negligible compared to conductive losses. So far, to extract the component values, two simulations were still needed [18]: an electric and a magnetic simulation. The

Fig. 3. Photography of a S-CPW fabricated in 28-nm CMOS STMicroelectronics technology.

electric simulation allows and calculation, whereas the magnetic simulation gives , and . Hereinafter, will not be considered because we do not have accurate model in the literature. Eddy currents are negligible on a well-designed S-CPW up to more than 100 GHz. However, they should be taken into account at higher frequencies. From these components, the parameters of the transmission line can be calculated, e.g., propagation constant and characteristic impedance. All the required equations are detailed in [18]. In the following, the study focuses on developing accurate parametric formulations for all the model components (except in order to avoid electromagnetic simulations and, thus, allowing fast design optimization, as for microstrip lines or conventional CPW. III. QUASI-TEM ANALYSIS The work reported in [19] presented a brief explanation of the parametric model and gave the method for the calculus of the inductance and the capacitance , respectively. In this section, a much more detailed derivation of each model component is exposed. In particular the calculus of the resistances modeling losses is addressed. The development of the scalable predictive model is based on the assumption of Quasi-TEM propagation mode. This assumption allows inductive and capacitive elements to be calculated independently. In similar fashion, conductive losses are splitted in the CPW strips and in the patterned shield. This approach allows a better understanding of how the S-CPW's geometries influence each electrical component in the model. A. Inductance Inductance is created by the magnetic field generated by current flowing in the central strip and ground. Currents flowing in the floating shield do not play any role in the inductance as they are flowing perpendicularly to the propagation direction. Therefore, adding a floating shield to the CPW does not affect the inductance. Based on this fact, classical CPW's inductance formulation can be used without lack of accuracy.

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Fig. 5. Cross-section showing the electric field lines considered for the capacitance calculus. Fig. 4. Inductance of two S-CPWs fabricated in 28-nm CMOS STMicroelectronics technology. Model presented in dashed line. Measurements presented in continuous line.

Hence, inductance segmentation approach proposed in [20] is used. This method divides the spectrum in four domains. When the frequency increases, the first domain is limited by the frequency at which currents approximate to DC distribution. The second limit is associated to the frequency at which the internal current distribution in the center becomes uniform. The last limit is fixed by the skin-effect. In Fig. 4, this method is compared to the measurements of two S-CPW transmission lines implemented in the 28-nm CMOS STMicroelectronics technology. The inductance was extracted from the measured parameters by using the well-known relation . It can be noticed that the prediction is excellent in the whole band of interest (DC to 110 GHz). Resonances appearing in the measurement results are due to the long electrical length of the S-CPW, because of the slow-wave effect. They correspond to electrical lengths which are multiples of a half wavelength. However, except resonances, this result validates the calculus of the S-CPW inductance by using the formulation used for CPW. B. Capacitance The estimation of the S-CPW capacitance is an issue. So far, few attempts of capacitance evaluation have been reported. For example, the work reported in [14] exhibits a weak understanding of the S-CPW that leads to a misinterpretation of the electric field behavior. Effectively, the fitted equations describe a null shielding effect. In the work presented in [17], authors have clearly neglected the capacitance estimation. Consequently, the characteristic impedance is misreckoning when implementing the patterned shield in different BEOL levels. To the best author's knowledge, the S-CPW capacitance estimation was presented for the first time in [19]. However, just a brief of the methodology was exposed. The current work presents an extended and deeper explanation. In addition, the designed rule for preventing electric field leakage is explained in detail. The capacitance estimation is based on the work presented in [21]. As shown in Fig. 5, specific field lines topology is assumed, depending on the considered region. In [21], the capacitance is calculated by solving integral equations, whereas in our

Fig. 6. Capacitance convergence for m.

m,

m and

case it is calculated with a sum for more flexibility. The upper point charge capacitance of [21] is not considered here since it is not based on correct physical interpretation. Moreover, the estimation of the lower point charge capacitance is different. Then, the capacitance is separated in four regions (Fig. 5), named bottom plate, point charge, fringe, and upper plate capacitances. Notice that signal-to-ground and leakage electric fields through the floating shield are neglected in this first step. For each region, the electric field is discretized in electric field lines created by point charges. Accordingly, the capacitance at each region is given, in the general case, by the sum of these electric field lines (1) (1) is the dielectric constant in vacuum, is the relawhere tive dielectric constant, is the width of the conductor, is its length, and is the height or distance between conductors. This generalization simplifies the calculation for each region and the problem becomes just a matter of: (i) defining the path described by each electric field line, and (ii) choose the number of field lines that must be considered for proper convergence. Fig. 6 shows the capacitance error in function of the number of electric field lines . Here, the capacitance is calculated for different values of . Then, when is large enough, the computed capacitance remains constant. At this point the convergence is achieved. From this convergence study, as a rule of thumb is set to 100.

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Fig. 7. Fringe region. Path description of the electric field distribution for the fringe capacitance calculus.

Fig. 9. Upper plate region. Path description of the electric field distribution for the upper plate capacitance calculus.

The electric field going from the top of the strip towards the floating shield creates the region called upper plate (Fig. 9). This region contributes less in the total capacitance, however it is not negligible. The electric field lines describe a circular path, with a radius going from to (6) (6)

Fig. 8. Angle point charge region. Path description of the electric field distribution for the fringe capacitance calculus.

The bottom plate region has a constant height, thus (1) becomes the well-known plate capacitance (2), when considering the whole bottom plate width

The radius can be expressed as (7) Therefore, the upper plate capacitance is given by (see Appendix C)

(2) (8) For fringe and upper plate regions, the formulation is based on the assumption that the electric field lines describe a circular path as illustrated in Fig. 7. In the fringe region, the height ( depends on the radius, so is computed as follows: (3) substituting (3) instead of in (1) and as the width, the fringe capacitance becomes (see Appendix A) (4) A particular case is the angle point charge capacitance (Fig. 8), named . This capacitance is created by the electric field lines at the bottom edges of the strips. The electric field lines describe a parabolic path and they are delimited by the height ( . By considering this trajectory and substituting in (1), this capacitance can be approximated by (5). Note that is independent of (see Appendix B) (5)

Finally, the total signal strip capacitance is computed by the sum of the contribution of all regions (9) Fig. 10 shows the comparison between the herein proposed model and the model proposed in [21], when only the capacitance linked to the signal strip is considered. In this case the capacitance is the same as the microstrip one. Then, the electromagnetic simulation was performed by considering a conventional microstrip line. When the main contribution of the signal strip relies in the plate capacitance, i.e., small heights or big widths, the influence of the upper plate is lower, therefore the error in both methods are less than 5%. However, when the influence of the upper plate capacitance starts to be important, the method proposed in [21] overestimates the capacitance and the error increases up to 20%, whereas the error is still lower than 5% with the proposed formulation. Since the floating shield ends at the external edge of the ground, the external electric field behaves slightly different from the one previously discussed (Fig. 5). Therefore, for computing the capacitance created between the ground and the floating shield, the four regions are separated into internal and

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TABLE I CAPACITANCE ZONES

STRIP-TO-STRIP

Fig. 10. Signal strip capacitance

estimation versus dioxide height.

Fig. 12. Electric field lines in zone B.

Fig. 11. Ground capacitance estimation.

external. The internal capacitances are the same than the signal capacitances, the same equations can be safely used. External electric field lines describe circular paths and they are segmented in the same different regions. Then, the aforementioned methodology applies for defining the path that each electric field line describes. It has been assumed that all electric field lines are centered in O (Fig. 5). Therefore, finding the of each external region is a trivial task. Fig. 11 shows the importance of computing the external capacitance contribution. When the lower plate and the floating shield are close, the electric field is mainly stored between them: the main contribution is given by the plate capacitance and the external electric field contributes less in the total capacitance. As a consequence, the external electric field can be neglected for smaller . In the other hand, as the distance increases, the electric field is distributed proportionally among all regions: plate capacitance decreases and the total capacitance starts to depend upon all regions. Therefore, the external relative contribution increases, leading to a misestimating of the total capacitance if the external electric field is not considered. The accuracy of the model is also depicted in Fig. 11. While considering the contribution of the external electric field, the error remains lower than 5% for all heights. This confirms the hypotheses of the electric field behavior. So far, strip-to-strip capacitance and leakage through the shield have not been taken into account. In practical cases, the strip-to-strip capacitance is negligible for bigger

than , but this is no longer the case when . In order to calculate , four zones are considered, in function of , as indicated in Table I. In each zone it is assumed that the electric field lines tend to take the shortest path to the ground. Zone A is delimited for bigger than two times , leading to a neglegible . In other words, when this conditions holds true, all the electric field lines of the upper plate go directly towards the floating shield, and there is no direct coupling between signal strip and ground strip. As soon as the gap is smaller than two times (Zone B), the electric field lines are splitted into two different directions: a part of the electric field lines of the top plate goes directly to the ground strip and the other part goes towards the floatting shield (Fig. 12). Therefore, the width of the upper plate ( in (8) has to be substituted by the effective width : (10) The electric field lines that go from the signal strip to the . This capacitance ground strip, lead to the capacitance can be approximated by using the fringe capacitance (4), when replacing by , and by . Then the strip-to-strip capacitance is equal to (11) with (12)

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Fig. 14. Electric field lines in zone D.

Fig. 13. Electric field lines in zone C.

(13) conFig. 13 depicts the behaviour in zone C. Here, the sidered in Fig. 12 is zero since all the electric field lines of the upper plate region are going from the top plate of the signal strip directly to the top plate of the ground strip. Therefore, in is equal to . In addition, the thickness considered to calculate is modified, since a portion of the electric field lines goes straight from the signal strip to the ground strip. This portion creates a capacitance named . is the sum of and , where

Fig. 15.

coupling capacitance estimation.

(14) (15) where and

is the width and are equal to

is the height.

(22) Then (23)

(16) where (17) For estimating stitued by (18) and

and is calculated as (19)

(24)

is sub-

(18) (19) The zone D (Fig. 14) considers that (4) and (8), as defined in Figs. 12 and 13, are zero, since all the electric field lines in these regions go directly to the ground. Accordingly, the width in is equal to . In this zone, part of the electric field lines that leads to the capacitance goes direclty to the ground. Therefore, and become (20) (21)

Fig. 15 shows the comparison of a simulation carried out with HFSS, with the proposed model. The height was kept constant while the gap varies from 5 m to 28 m, which correspond to usual values, and for two different cases. It can be seen that the coupling capacitance increases with the reduction of the gap. The model accurately predicts the capacitance along all variations of the gap with an error lower than 5%. So far, the capacitance created between the bottom plate and the floating shield has been approximated as a single element . This approximation is almost true if the floating shield is well designed so that no electric field lines leak to the substrate. However, this is not always the case, and the model can be improved. To consider this leakage, the electric field is separated in different regions, as shown in Fig. 16. For SS smaller than , the electric field will be completely confined between the strip and the floating shield. If SS in-

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Fig. 18. Photography of the S-CPW fabricated in the BiCMOS 130-nm STMicroelectronics technology. Fig. 16.

capacitance advanced estimation.

C. Losses There are three main contributions of losses as previously explained: conductive losses in the CPW strips, conductive losses in the floating shield and losses created by eddy currents flowing in the floating shield. The latter are not considered since no physical model is really consistent. However, they can become non negligible when the working frequency is greater than about 100 GHz, depending on the S-CPW geometry. Conductive losses in the CPW are modeled by the method proposed in [20]. As already stated, this method holds as the magnetic field in the S-CPW and conventional CPW behaves almost identically. Conductive losses in the floating shield are simply modeled as (26) where is the shield period distance between the ground strips

, and D is the .

D. Floating Shield: Inductance The current flowing in the shield ribbons introduces an inductive effect . This inductance has to be taken into account when wide gaps and/or high frequencies are considered [23]. This inductance is approximated by Fig. 17. (a) Capacitance estimation in function of . tenuation constant in function of

, (b) Normalized at-

(27)

creases beyond this limit, the electric field leaks to the substrate. This can be seen by the drop in the total capacitance as SS increases (Fig. 17(a)). The leaked field penetrates the lossy substrate causing an increase in the losses. This behaviour is illustrated in Fig. 17(b), where the normalized attenuation constant was extracted from HFSS simulations carried out for different ratios. The normalized attenuation constant was calculated as follows: the attenuation constant in function of the ratio is divided by the attenuation constant when there is no electric field leakage to the substrate (25). An important rule can be derived: a ratio greater than 0.5 is needed in order to ensure that leakage represents less than 5% of the total attenuation constant value

(25)

where must be extracted for each technology. As explained in [23], the value of has been fixed by fitting several measurement results and taking the average value. IV. RESULTS Fig. 18 shows the fabricated S-CPWs in the BiCMOS 130-nm technology from STMicroelectronics. In Fig. 19 the comparison between the model and the measurements results are presented. The model was also validated on the 28-nm (Table II), and 55-nm from STMicroelectronics. The mm-wave measurement setup is presented in Fig. 20. In the results presented in Fig. 19, three different topologies were implemented in the BiCMOS 130-nm technology, with high, low and medium (50 ) characteristic impedance, respectively. The S-CPWs were implemented using different metal layers. The names of the S-CPWs are given as follows:

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Fig. 20. Photography of the measurement set-up.

TABLE II MEASUREMENTS VERSUS MODEL RESULTS AT 60 GHZ FROM VARIOUS TECHNOLOGIES

V. REAL USER CASES Fig. 19. Comparison between the model and the measurement results. (a) Characteristic impedance, (b) effective dielectric constant, and (c) attenuation constant (measurement results in black, model in gray).

“CPW M6M5 Shield M3” means that the CPW strips were fabricated by the stack of metal 5 and metal 6 layers, whereas the floating strips were fabricated in Metal 3 layer. Table II presents the comparison between the model and the measurements at 60 GHz, for S-CPWs having different characteristic impedances implemented in the 28 nm from STMicroelectronics, 0.35 m AMS, and 0.13 m and 0.25 m technology from IHP, respectively. The purpose of these two comparisons is to show that the model accurately predicts the S-CPW's performance when using different geometries implemented in different BEOL and different metal layers from various technologies. In all cases, the prediction error remains lower than 10% (for all the parameters, i.e., the characteristic impedance, effective dielectric constant, and attenuation constant).

This section provides the reader with practical cases to exemplify how the model can be exploited. Two cases are shown: the first addresses the optimization of a 50 S-CPW with electrical length of 90 while the second allows the user to be directly involved with the RLRC model. A. 50

S-CPW Optimization

There are plenty of circuits that require transmission lines. For example power dividers, branch line couplers, etc. Consequently, this section presents the case where a quarter wavelength 50- S-CPW is needed. Due to the topology (geometries and metal layers), any S-CPW will have a lot of different ways to be implemented. Therefore, designers have to firstly set out the requirements, in terms of performance and/or surface. These requirements will define the geometries that fit the best the S-CPW. For example Table III presents three different solutions for a 50- S-CPW in the BiCMOS 55-nm technology. In the first case, the transmission line is selected to reach the highest

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50

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TABLE III S-CPW PHYSICAL AND ELECTRICAL (60 GHZ) PARAMETERS FOR THREE DIFFERENT DESIGN REQUIREMENTS

quality factor achievable in the given technology. In the second case, the transmission line length has been minimized , and the last one is the less bulky (Surface min). The quality factor at 60 GHz, physical length and surface area are given in Table III, highlighting the different targeted goal. A maximum Q factor of 50 can be reached for an overall surface of 0.058 mm , whereas a minimum surface equal to 0.023 leads to a Q-factor limited to 20. The importance of showing these three different cases is not to present a set of rules but to show the flexibility of the model. The model allowed obtaining these results in a matter of seconds. When comparing to the developing time of any 3D EM, that presents a clear advantage. In addition, the user can set up any desired goal for any desired S-CPW.

Fig. 21. Phase shifter electrical model.

B. Tunable Phase-Shifter The synthesis tool allows the user to manipulate directly the RLRC model in a CAD tool (like Cadence for example). To illustrate this point, a S-CPW based tunable phase shifter is considered (see Fig. 21(a)). Here, the floating shield is broken between the signal and the ground, to allow connecting varactors in between. As a consequence, the total S-CPW's capacitance is variable and is equal to (28) is the varactor's capacitance value and is the parwhere asitic capacitance coming from the coupling between the two extremities of the broken floating shield. The equivalent model is shown in Fig. 21(b). Notice that the other elements in the electrical model remain unaltered. The variation in the total capacitance modifies the phase constant of the transmission line. Thus, the absolute S-CPW's phase can be changed. Normally, for designing this type of tunable phase shifter, a 3D EM simulation tool is needed, together with a deep understanding of the S-CPW's physical behavior, and round-trips between 3D-EM tools and CAD tool (Cadence for example) are necessary. This procedure drives to long developing times. The model proposed in this paper allows the designer to make a quick optimization by scripting it directly in any CAD tool. In this example, a 30 tunable phase shifter at 60 GHz working frequency was designed, while targeting the maximum allowed Figure of Merit (FoM) defined by the ratio of , and the maximum insertion the phase shift in degrees (29). First, the varactors where chosen to loss in dB

Fig. 22. Photograph of the phase shifter, with DC control pads on each side of the phase shifter.

have the maximum tuning range (TR) given by the technology ( in the 55-nm technology from STMicroelectronics) with a quality factor of 8. Once the varactor has been chosen, the next step is to find the geometries and stack that gives the desired phase shift with the maximum FoM. By using the model and replacing the equivalent capacitance of the S-CPW by (20), it is possible to make a quick parametric analysis for finding the desired results. (29) The phase shifter was then fabricated in the 55-nm technology from STMicroelectronics (Fig. 22). The performance of the phase shifter is shown in Fig. 23, where measurement and simulation results (obtained from the model proposed in this paper) are compared. Fig. 23(a) shows the maximum phase shift versus frequency. It is possible to see that the model accurately predicts the behavior across the whole frequency band. Fig. 23(b) shows the . The FoM is shown in phase shift versus the tuning voltage Fig. 23(c). Measurement and simulation results show very good agreement. VI. CONCLUSION In this work, a full parametric electrical model, which is derived from physical analysis, is proposed for S-CPW transmis-

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APPENDIX A For computing the fringing capacitance, it has been considered that the electric field lines describe a quarter of circle. Then (3) can be rewritten as (A-1) where

is (A-2)

Substituting (A-1), (A-2) in (1), and the width being equal to the thickness of the strip ( the fringe capacitance is (A-3)

APPENDIX B For deriving the angle point charge capacitance, it is considered that the electric field lines describe a parabolic path and they are delimited by the height . Then, by taking the perimeter of a parabola we obtain the path that each electrical field line describes

(A-4) Substituting (A-4) in (1) and considering the width as angle point charge capacitance becomes

, the

(A-5) and (A-5) can be approximated as (A-6) Fig. 23. Phase shifter measurements versus model results: (a) Maximum phase shift,(b) phase shift as a function of the control voltage at 60 GHz, and (c) FoM.

sion lines. This tool was validated in several CMOS technologies: 0.35 m AMS, 0.25 m IHP, 0.13 m STMicroelectronics, 0.13 m IHP, 55-nm STMicroelectronics, and 28-nm STMicroelectronics. It successfully estimates the behavior of the S-CPW, without the need of any fitting or correction parameter. Even more, it allows fast optimization without the need of 3D-EM simulators. The tool was implemented in MATLAB and can be provided to any user by request. This will help designers to deal with the several criteria of S-CPW, i.e., characteristic impedance, electrical performance (Q factor), physical length (effective dielectric constant), and total width.

APPENDIX C The same approach as is used to derive the upper capacitance. Here, it is considered that the electric field describes a circular path (A-7) By substituting (A-7) in (1) and the width with plate capacitance is

the upper

(A-8)

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ACKNOWLEDGMENT The work presented here has been performed in the RF2THZ SiSoC project of the EUREKA program CATRENE, in which the French partners are funded by the DGCIS. REFERENCES [1] J. J. Lee and C. S. Park, “A slow-wave microstrip line with a high-Q and a high dielectric constant for millimeter-wave CMOS application,” IEEE Microw. Wireless Componen. Lett., vol. 20, no. 7, pp. 381–383, Jul. 2010. [2] A.-L. Franc, E. Pistono, N. Corrao, D. Gloria, and P. Ferrari, “Compact high-Q, low-loss transmission lines and power splitters in RF CMOS technology,” in Proc. Int. Microwave Symp., Baltimore, MD, Jun. 7–9, 2011, pp. 1–4. [3] K. Kim and C. Nguyen, “An ultra-wideband low-loss millimeter-wave slow-wave wilkinson power divider on 0.18 SiGe bicmos process,” IEEE Microw. Wireless Componen. Lett., vol. 25, no. 5, pp. 331–333, May 2015. [4] T. Cheung and J. R. Long, “Shielded passive devices for silicon-based monolithic microwave and millimeter-wave integrated circuits,” IEEE J. Solid-State Circuits, vol. 41, no. 5, pp. 1183–1200, May 2006. [5] I. C. H. Lai, Y. Kambayashi, and M. Fujishima, “60-GHz CMOS down-conversion mixer with slow-wave matching transmission lines,” in Proc. IEEE Asian Solid-State Circuits Conf., Nov. 2006, pp. 195–198. [6] A.-L. Franc et al., “High-performance shielded coplanar waveguides for the design of CMOS 60-GHz bandpass filters,” IEEE Trans. Electron Devices, vol. 59, no. 5, pp. 1219–1226, May 2012. [7] M. Kärkkäinen, D. Sandström, M. Varonen, and K. A. I. Halonen, “Transmission line and lange coupler implementations in CMOS,” in Proc. 5th European Microwave Integrated Circuits Conf., Paris, France, Sep.–Oct. 26–1, 2010, pp. 357–360. [8] J. Lugo, A. Bautista, F. Podevin, and P. Ferrari, “High-directivity compact slow-wave CoPlanar waveguide couplers for millimeter-wave applications,” in Proc. EuMC, Oct. 2014, pp. 1072–1075. [9] T. LaRocca, S.-W. Tam, D. Huang, Q. Gu, E. Socher, W. Hant, and F. Chang, “Millimeter-wave CMOS digital controlled artificial dielectric differential mode transmission lines for reconfigurable ICs,” in Proc. IEEE Int. Microw. Symp., Atlanta, USA, Jun. 15–20, 2008, pp. 181–184. [10] X. Tang, E. Pistono, P. Ferrari, and J.-M. Fournier, “Enhanced performance of 60-GHz power amplifier by using slow-wave transmission lines in 40 nm CMOS technology,” Int. J. Microw. Wireless Technol., vol. 4, pp. 93–100, Feb. 2012. [11] M. Varonen, M. Kärkkäinen, M. Kantanen, and K. A. I. Halonen, “Millimeter-wave integrated circuits in 65-nm CMOS,” IEEE J. Solid-State Circuits, vol. 43, no. 9, pp. 1991–2001, Sep.. 2009. [12] T. La Rocca, J. Y.-C. Liu, and M.-C. F. Chang, “60 GHz CMOS amplifiers using transformer-coupling and artificial dielectric differential transmission lines for compact design,” IEEE J. Solid-State Circuits, vol. 44, no. 5, pp. 1425–1435, May 2009. [13] S. Seki and H. Hasegawa, “Cross-tie slow-wave coplanar waveguide on semi-insulating Ga-As substrates,” Electron. Lett., vol. 17, no. 25, pp. 940–941, Dec. 1981. [14] T. Masuda, N. Shiramizu, T. Nakamura, and K. Washio, “Characterization and modeling of microstrip transmission lines with slow-wave effect,” in Proc. Topical Meeting on Silicon Monolithic Integrated Circuits in RF Syst., Orlando, FL, Jan. 23–25, 2008, pp. 155–158. [15] A. Sayag, D. Ritter, and D. Goren, “Compact modeling and comparative analysis of silicon-chip slow-wave transmission lines with slotted bottom metal ground planes,” IEEE Trans. Microw. Theory Techn., vol. 57, no. 4, pp. 840–847, Apr. 2009. [16] I. C. H. Lai, Y. Kambayashi, and M. Fujishima, “Characterization of high Q transmission line structure for advanced CMOS processes,” IEICE Trans. Electron., vol. E89-C, no. 12, pp. 1872–1879, Dec. 2006. [17] L. F. Tiemeijer, R. M. T. Pijper, R. J. Havens, and O. Hubert, “Low-loss patterned ground shield interconnect transmission lines in advanced IC process,” IEEE Trans. Microw. Theory Techn., vol. 55, no. 3, pp. 561–570, Mar. 2009.

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[18] A.-L. Franc, E. Pistono, G. Meunier, D. Gloria, and P. Ferrari, “A lossy circuit model based on physical interpretation for integrated shielded slow-wave CMOS coplanar waveguide structures,” IEEE Trans. Microw. Theory Techn., vol. 61, no. 2, pp. 754–763, Feb. 2013. [19] A. Bautista, A. Franc, and P. Ferrari, “An accurate parametric electrical model for slow-wave CPW,” in International Microwave Symposium 2015, Phoenix, USA, May 17–22, 2015, pp. 1–4. [20] W. Heinrich, “Quasi-TEM description of MMIC coplanar lines including conductor-loss effects,” IEEE Microw. Theory Techn., vol. 41, no. 1, pp. 45–42, Jan. 1993. [21] W. Zhao, X. Li, S. Gu, S. H. Kang, M. Nowak, and Y. Cao, “Field-based capacitance modeling for sub-65 nm on-chip interconnect,” IEEE Trans. Electron Devices, vol. 56, no. 9, pp. 1862–1872, Sep. 2009. [22] A.-L. Franc, E. Pistono, and P. Ferrari, “Design guidelines for high performance slow-wave transmission lines with optimized floating shield dimensions,” in Proc. Eur. Microw. Conf., Paris, France, Sep. 28–30, 2010, pp. 1190–1193. [23] A.-L. Franc, E. Pistono, and P. Ferrari, “Dispersive model for the phase velocity of slow-wave CMOS coplanar waveguides,” in Proc. 45th EuMC, Paris, France, Sep. 6–11, 2015.

Alfredo Bautista was born in Victoria, Mexico, in 1980. He received the M.Sc. degree from the Instituto Tecnológico y de Estudios Superiores de Monterrey, Monterrey, Nuevo León, México, in 2005 and the Ph.D. degree from the Joseph Fourier University, Grenoble, France in 2009. From 2010 to 2012, he held a postdoctoral position in the CEA-LETI, Grenoble, France, and from 2012 to 2015, in the INP, Grenoble, France. His current technical interests focus in modelling passive devices for mm-wave, design of phase-shifter, VCOs, and analog integrated circuits.

Anne-Laure Franc was born in France in 1985. She received the engineer and M.Sc. degrees from the Cergy-Pontoise University, Paris, France, in 2008 and the Ph.D. degree from Grenoble University, Grenoble, France, in 2011. In 2012, she had a postdoctoral position with Darmstadt University, Darmstadt, Germany and she held a temporary lecturer and research assistant position in the Grenoble-Alpes University, Grenoble, France in 2013. Since September 2013, she has been an Associate Professor with the University of Toulouse, Toulouse, France. Her research interests focus on tunable microwave components.

Philippe Ferrari (SM’03) received the Ph. D. degree from INP Grenoble, Grenoble, France, in 1992. He joined the University of Savoy, France, as an Assistant Professor, and was involved in the development of RF characterization techniques and nonlinear transmission lines. Since 2004, he is a Professor at the Grenoble-Alpes Universitym Grenoble, France. His main research interests concern tunable devices, and new circuits based on slow-wave transmission lines. He is author or co-author of more than 180 international papers, and co-holder of five patents. He is a member of the editorial board of the International Journal on RF and Microwave Computer-Aided Engineering, and an Associate Editor of the International Journal of Microwave and Wireless Technologies.

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High-Speed Antenna-Coupled Terahertz Thermocouple Detectors and Mixers Johannes A. Russer, Member, IEEE, Christian Jirauschek, Member, IEEE, Gergo P. Szakmany, Mark Schmidt, Alexei O. Orlov, Gary H. Bernstein, Fellow, IEEE, Wolfgang Porod, Fellow, IEEE, Paolo Lugli, Fellow, IEEE, and Peter Russer, Life Fellow, IEEE

Abstract—An antenna-coupled nanothermocouple (ACNTC) is an integrated structure consisting of a dipole nanoantenna and a nanothermocouple (NTC). ACNTCs are excellently suited as polarization-sensitive detectors and mixers for the long-wavelength far-infrared range around 30 THz. Radiation collected by the integrated nanoantenna and fed into the hot junction creates a temperature difference between the hot and cold junctions of the thermocouple, which results in open-circuit voltage due to the Seebeck effect. Due to the geometry-dependence of the Seebeck coefficient in nanowires, we realize single-metal ACNTCs. The fundamentals of single-metal NTCs are discussed. The thermal dynamics of NTCs is investigated showing that NTCs could exhibit mixer and detector intermediate frequency and low frequency cutoffs beyond 100 GHz. We provide experimental evidence of ACNTCs. Index Terms—Heat conduction, Seebeck effect, terahertz (THz) detector, thermocouple (TC).

I. INTRODUCTION

T

HERMOCOUPLEs (TCs) are excellently suited as detectors for the long-wavelength far-infrared range around 30 THz. The detector operation of TCs is based on Joule heating of the TCs by the incident radiation and the Seebeck effect, i.e., the thermoelectric effect that directly converts a temperature difference to an electric voltage [1], [2]. The TC, like any thermodynamic device, is subject to the restrictions of Carnot's theorem stating that the efficiency of any heat engine operating beis tween two heat reservoirs at absolute temperatures [3]. In limited to a maximum value of order to enhance the efficiency of the TC, the radiation to be detected should be collimated within a small area of a nanothermocouple (NTC) so that the electron temperature at the NTC junction gains a strong increase. In this work, we show that NTCs are extremely fast detectors with response times in the picosecond area. This property will Manuscript received July 01, 2015; revised September 22, 2015 and October 22, 2015; accepted October 23, 2015. Date of publication November 12, 2015; date of current version December 02, 2015. C. Jirauschek thanks the Deutsche Forschungsgemeinschaft for funding under Project DFG JI 115/4-1. G. P. Szakmany gratefully acknowledges financial support from the Notre Dame Joseph F. Trustey Fund for Postdoctoral Scholars. This paper is an expanded version from the IEEE MTT-S International Microwave Symposium Phoenix, AZ, USA May 17–22, 2015. J. A. Russer, C. Jirauschek, M. Schmidt, P. Lugli, and P. Russer are with the Institute for Nanoelectronics, Technische Universität München, 80333, Munich, Germany. G. P. Szakmany, A. O. Orlov, G. H. Bernstein, and W. Porod are with the Center for Nano Science and Technology, University of Notre Dame, Notre Dame, IN 46556 USA.. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2015.2496379

open new areas of applications in the terahertz (THz) frequency bands, so far accessible only in the microwave and millimeterwave bands so that the THz bands will gain additional interest from system engineers so far mainly concerned with applications up into the millimeterwave region only. Fast NTC detectors may be employed in imaging, communications and sensing applications. Currently, TCs are commonly used in applications for which fast response times are not critical, and cut-off frequencies of some kHz and below are sufficient, and they receive little consideration as elements in RF or THz engineering. However, fast NTCs have also a rather interesting potential for applications in microwave engineering. High efficiency is desirable in communications and sensing applications since it governs the sensitivity of the device. Antenna-coupled nanothermocouples (ACNTCs) are integrated structures consisting of a dipole nanoantenna and a NTC connected to the antenna feed [4]. The nanoantenna collimates the IR energy incident within the effective aperture of the antenna and feeds it into the thermocouple. The dipole nanoantenna yields polarization-sensitive detection. This induces a temperature difference between the hot junction at the nanoantenna feed and the remote cold junction. Due to the Seebeck effect, an open-circuit voltage arises across the antenna feed port. The hot junction of the NTC is located at the center of the dipole-antenna where the antenna current exhibits its maximum, resulting in optimum device response. In [5], we have shown that NTCs can also be formed by two nanowires of the same metal but different cross-sectional areas. Compared with conventional bi-metallic TCs, fabrication of such shape-engineered mono-metallic nanowire TCs is much easier, and mass-production of mono-metallic TCs could be accomplished by simple manufacturing technologies. Since the NTC junction exhibits transverse dimensions of a few tens of nanometers and the TC junction is metallic without depletion layer, there would be a frequency limitation due to a junction capacitance at the RF side in case of an ideal broadband nanoantenna shape. Due to the non-perfect conductivity of the antenna and the finite antenna cross-sectional area at the feed point there will be some cutoff frequency, however somewhere in the far-infrared region. Since the Seebeck effect is conveyed by Joule heating, the TC is essentially a square-law detector. Due to the small thermal volume of the TC hot junction, the detector and mixer time-constant is on the order of picoseconds. Therefore, we can expect extremely high bandwidths in detector and mixer applications. In [6], we discussed the possible application of ACNTCs as detectors in far-infrared sensor and communication systems. The dynamics of ACNTCs has been investigated in [7]–[9] and it was shown there that due to its low thermal capacity, an ACNTC is an extremely fast square-law detector with cutoff frequencies up to several hundred GHz.

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RUSSER et al.: HIGH-SPEED ANTENNA-COUPLED TERAHERTZ THERMOCOUPLE DETECTORS AND MIXERS

In this extended paper, we also provide experimental results confirming response times of ACNTC in the RF regime. In our investigations, we expand the theoretical model for the Seebeck coefficient of single-metal thermocouples and on the modeling framework for ACNTC in THz detector and mixer applications. In Section II we describe the properties of single-metal nanothermocouples (SMNTCs) and discuss the theoretical fundamentals of SMNTCs on the basis of the Seebeck theory and the Fuchs-Sondheimer model. The fabrication of ACNTC is described in Section III. In Section IV, the thermal diffusion in the thermocouple is modeled and compact lumped-element equivalent-circuit models are established describing the electric and thermal behavior of ACNTCs. The pulse-response for the NTC is computed. In Section V, the detector and mixer properties of ACNTCs are investigated on the basis of the lumped element equivalent circuit models of ACNTCs. Detection measurements laser operating at 10.6 are presented with a modulated in Section VI. II. THEORETICAL MODEL FOR THE SEEBECK COEFFICIENT OF A SINGLE-METAL THERMOCOUPLE TCs composed by two conductors and with Seebeck and , containing two junctions show an opencoefficients circuit Seebeck voltage (1) if there is a temperature difference between the two junctions. Usually thermocouples are made from two different metals exhibiting different Seebeck coefficients. Demodara et al. [10] have shown that in thin films the reduction of the electron mean free path by additional scattering yields a thickness dependence of the Seebeck coefficients. The calculation of this geometry-dependent Seebeck coefficient is essential in order to determine the efficiency of single metal thermocouples, as used for detecting radiation in the terahertz regime from a nanoantenna [4]. As compared to thin films, thin wires that are used for the NTCs only have two additional surface scattering planes; thus, the size effect can be expected to be a scaled problem. Calculations for the conductivity of a thin wire were done by Dingle [11] and MacDonald and Sarginson [12] based on the Fuchs-Sondheimer model. In the following, we first use this model to investigate the Seebeck coefficient of thin films rather than wires due to more available experimental data for films. Afterwards we provide a formula for the Seebeck coefficient of wires based on the conductivity model of Dingle, and use it to confirm our measured results. Elaborate microscopic models for the theoretical calculation of the Seebeck coefficient have been developed [13]–[18]. However, here our focus is on more-compact, semi-empirical models that provide insight into the geometric dependence and serve as a guidance to experimentalists. For a monocrystalline thin metal film with thickness the Seebeck coefficient can be calculated in the framework of the Fuchs-Sondheimer model based on the first order solution of the linearized Boltzmann equation to [19]

(2)

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Here, is the (absolute) ambient temperature, the charge of the Fermi energy, the Boltzmann constant, an electron, with the electron mean free path of the bulk material

and

(3)

(4) The surface scattering is modeled by the specularity parameter [20], which is independent of the direction of motion of the electrons and the energy (a direction-dependent model was developed by Stoffer [21]). It is assumed that a fraction of electrons is reflected specularly at the boundary and still contributes of the electrons is to the current, whereas the fraction reflected diffusely and does not contribute to the current anyand , given by more [20]. The parameters (5a) (5b) describe the derivative of the electron mean free path of the bulk material and the area of constant energy at the Fermi energy. These parameters cannot be extracted from a compact model and have to be measured in addition to the transport parameters and ; thus, the measured values are highly dependent on the structure of the fabricated material and the production process [22]. Several investigations to determine those paand as shown rameters yielded contradicting values of below. It can be concluded that correct annealing is a significant factor in generating monocrystalline structures with a negligible amount of impurities [23]–[29]. All of these authors found significant effects in the change of the transport parameters when the film structure differed from a monocrystalline structure. The available data for the transport properties have therefore to be seen in a critical manner. An asymptotic approximation for relatively large films is obtained from (2) as [19] (6) It should be noted that the previous expressions refer to unsupported metal films, hence substrate effects are not considered. A discussion of such effects can be found in [30]. For practical purposes it is more convenient to express the Seebeck coefficient in terms of the temperature coefficient of resistance (t.c.r.) [31], yielding (7) where the subscripts and 0 refer to the film and the bulk material, respectively. Because the t.c.r. can be easily extracted from experiment, the determination of and is not necessary to obtain a value for . In addition, to eliminate the unknown it is advantageous to calculate the difference between the thin-film and the bulk-material Seebeck coefficients given by (8)

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FOR

AND ABSOLUTE

TABLE I FOUND BY DIFFERENT SOURCES OBTAINED BY THERMOPOWER MEASUREMENTS

with the Seebeck coefficient of the bulk material (9) This makes it possible to determine by interpreting as . can be found by two meaa linear function in and or from the slope of , given by surements of . The parameter can then be determined using (9). If the structure of the metal is not monocrystalline, the grain boundary scattering has to be taken into account. This is the case when the electron mean free path is equal to or smaller [19]. Models for grain than the average grain diameter boundary scattering were developed by Mayadas-Shatzkes [32] and Pichard, Tellier, and Tosser [33]. The Fuchs-Sondheimer model is derived from the Boltzmann equation, which is a semiclassical diffusive transport equation based on the free electron model. In this free electron model and [23]. Here, the Fermi surface is assumed to be spherical, and the isotropic relaxation time is constant over the Fermi surface. This is not the case for real metals such as silver, copper, or gold for which the Fermi surfaces are distorted at eight of the fourteen Brillouin zone planes. As expected, experimental results differ from the values predicted by the free electron model because of this deviation. Table I summarizes and for different metals. selected measured values for Copper, silver, and gold are chosen because these metals have a similar shape of the Fermi surface. and As mentioned above, the contradicting values of can be ascribed to differences in the production process of the of all the presented metals can film. The negative sign of be explained by the decrease in area of the distorted Fermi surfaces with increasing energy because of the contact zones of the Brillouin boundary [29]. By comparing the experimental data for silver in Fig. 1 and copper in Fig. 2 from Narasimha Rao, Mohan and Reddy with the exact Fuchs-Sondheimer model (2) and the thick film approximation (6), a qualitatively good match between theory and data can be observed. However, the weak slope of the curve of the exact calculation based on (2) produces a large error for a thickness below the electron mean free path. This implies that the Fuchs-Sondheimer model is an inadequate description of the very thin film behaviour. It is surprising that the thick film approximation curve shows a better agreement than the exact curve since it is . The opposite sign of for copper and only valid for silver is due to the different energy dependence of the electron mean free path.

Fig. 1. Difference of the Seebeck coefficient between the bulk material and a nm [29], , thin film with thickness for silver, [36], ; other parameters and measurement data from [27].

Fig. 2. Difference of the Seebeck coefficient for copper, nm, , [36], ; other parameters and measurement data from [25].

It should be pointed out that the Fuchs-Sondheimer model only provides a good match with experiment for extremely is a perfectly rough surface) according rough surfaces ( to [22]. But a more critical problem is the availability of a complete set of measurement data including all transport parameters for different metals providing consistent results. In summary the presented data fits relatively well the measurements of Narasimha Rao, Mohan, and Reddy for a monocrystalline film with a rough surface. For very thin films, a more accurate model is needed that also takes quantum effects into account to describe the size effect more precisely. In the case of wires, an approximate formula for thick wires (width and height greater than the electron mean free path) of arbitrary cross-section was developed by Dingle [11] for the , given by wire conductivity (10) is the perimeter and is the wire cross-section Here, area. By inserting above formula for the wire conductivity into the general expression for the Seebeck coefficient

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Fig. 3. Calculated Seebeck coefficient of the single-metal NTC as a function of width of the first wire segment for various widths of the second wire segment. is set to 17.22. The height is 45 nm,

and taking into account the energy dependence of the electron mean free path, we obtain (11) with the geometry factor (12) As expected, (11) can be simplified to (6) for films with thick. For single-metal NTCs with different wire cross nesses sections, one has to subtract the Seebeck coefficients of the two and , yielding single wires with different geometry factors (13) This formula is evaluated based on two available measurement results for Pd/Pd single-metal NTCs with a height of 45 nm and widths of 80 nm/470 nm [8] and 50 nm/200 nm (Section VI of this paper), respectively. The measured Seebeck coefficients for [8] and 0.86 , these two NTCs are respectively. , In the following, we assume the parameter values [37], , and . The material parameters and are taken from [38], but vary with the production process conditions as discussed above. From (13), and 11.66 by using the data of the first we obtain and second thermocouple, respectively. This uncertainty in the may again be partially due to the production exact value of process conditions, as also discussed above in the context of Table I. In addition, substrate effects and the fact that the wire segments are connected at a 90 angle at the hot junction, as discussed in Section III, affect the measurement results, but are not explicitly considered in the theoretical model. Thus, fitting (13) to the measurement results yields an effective value for , which also accounts for these effects. Fig. 3 shows the geometry dependence of the Seebeck coefficient, where we here take the . averaged value From Figs. 1, 2, and 3 it can be concluded that the efficiency of the NTC is maximized when a thin segment, with a thickness on the order of the electron mean free path, is connected to bulk material or to dimensions which are much greater than the electron mean free path. A large geometrical difference of the two segments leads to a large relative Seebeck coefficient and thus,

Fig. 4. Scanning electron micrograph of (a) an ACTC and (b) a thermopile constructed from several ACTCs connected in series.

according to (1), to a higher Seebeck voltage. Quantum size effects beyond the electron mean free path length could improve the Seebeck coefficient even more and should be further investigated. III. FABRICATION OF THE ANTENNA-COUPLED SINGLE-METAL NANOTHERMOCOUPLE Now we present the fabrication method of single-metal ACNTCs using the same metal for both the antenna and the NTC. Fig. 4(a) shows that the hot junction of the NTC is located at the center of the antenna, where the radiation-induced antenna current is at maximum and hence the heating is largest. The hot junction of the NTC is formed from a junction of narrow and wide wire segments from the same metal. The single-metal NTC operation is based on the structure size dependence of the absolute Seebeck coefficient in nanowires [5]. When the mean free path of electrons is comparable to the physical dimensions of a conductor, the absolute Seebeck coefficient is decreased from its bulk value due to the increased electron scattering. We exploit this property for single-metal NTCs by constructing them from the same metal nanowires, but with two different cross sections. As a result, the relative Seebeck coefficient between the two wire segments is nonzero, because the reduction of the absolute Seebeck coefficient is more pronounced in the narrow wire segment. Similar to our previous work [5], [4], [39], the antenna-coupled single-metal nanothermocouples were patterned by electron beam lithography, and metalized by 45-nm-thick electron beam evaporated Pd. The 50 nm and 200 nm wide wire segments are joined at 90 deg at one end, and connected to the bonding pads at their other ends, as shown in Fig. 4. The dipole antenna, long, is connected to the NTC at its center. The which is 2.4

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Fig. 5. Perspective view on the disk with heated patch.

measured electrical resistance of these devices is 2.1 . Fabrication complexity of such devices is greatly reduced compared to bi-metallic ACNTCs [4], since only one lithography and one deposition step is required. We constructed antenna-coupled thermopiles by connecting several ACNTCs in series to increase the output voltage of the detector. Fig. 4(b) shows such a linear thermopile array, where each individual ACNTC possesses its own read-out circuit, allowing thermopile-length-dependent measurements. IV. THERMAL CONDUCTION

Fig. 6. Time dependence of (normalized) for variable circular patch radius , for an initial penetration depth nm at nm for nm nm nm, nm computed from (14) and from the . Foster topology equivalent circuit (Fig. 8(b)) for

Fig. 7. Equivalent circuit of the thermocouple.

For the purpose of investigating the thermal heat conduction, we approximate the TC structure by a circular thermocouple patch. This patch models the hot junction of the ACTC. The , and its thickpatch is sitting on a substrate, its diameter is as shown in Fig. 5. Excited by an impulsive heating ness is , the temperature time dependence at by the patch at time is obtained for this structure by solving the diffusion equation [8] as

(14) The thermal diffusivity obtained for silicon as substrate material , considering a thermal conductivity is , density , and specific . We have varied the circular patch heat radii and have assumed an initial penetration depth nm at nm, nm. The time dependence of obtained is plotted in Fig. 6 and shows that is independent of for small times below 1 ps. In this case, the time evolution is predominantly determined by diffusion in -direction. As time advances, and spatial extension of the diffusion spread of gets on the order of , we find a strong dependence of the time on the junction radius . evolution of In order to model the dynamics of the TC, we have implemented in a previous work [6] an equivalent circuit that acelement, for the temperature decay counted, using a single with a single time constant. A single time constant, however, is not sufficient for modeling the thermal subsystem accurately, since there are several regions with variable heat capacity and

variable heat conductivity that govern the process. Hence, introducing several time constants will improve accuracy [40]. Using Foster or Cauer equivalent circuit topologies, we can synthesize lumped element equivalent circuit models with the desired accuracy [41], [42]. The TC is modeled by an equivalent circuit consisting of three parts, as shown in Fig. 7: the left-hand side models the (radio frequency) part, the center part represents electric the thermal equivalent circuit, and on the right-hand side, the (low frequency) part is equivalent circuit for the electric given. The antenna's open-circuit voltage, caused by the incielectrical field, is denoted as , and its radiation dent , resistance, its inductance, and capacitance are denoted as , and , respectively. Joule heating occurs in the TC juncpower , where tion due to the dissipation of the is the junction resistance and is the current in the junction resistance. The junction capacitance is denoted as . The dissipated power controls the current in the thermal equivalent circuit, which governs together with the thermal impedance the temperature enhancement . This temperature enhancement induces a Seebeck voltage in the circuit modeling of the electric low-frequency part. The inner resistance for the LF . Having obtained the solution of the diffucircuit model is sion equation, equivalent circuits can be used to model the . For this purpose we have to consider thermal impedance the frequency poles of this solution. In the complex frequency plane, the poles are located on the negative real axis. Two topologies for lumped element equivalent circuits are depicted in Fig. 8: The Cauer type topology (a) yields a ladder network with capacitors and resistors as the parallel and the series elements, respectively. The Foster type topology (b) yields -circuits connected in series. parallel

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For the case of negligible junction capacitance obtain

we (21)

In the tuned case we obtain

with harmonic excitation (22)

The square-law rectification is accomplished in the thermal part of the equivalent circuit. The heat generated in the theris related to mocouple junction with the electric resistance the flowing electric current via Fig. 8. Circuit modeling the thermal transfer function of the thermocouple: a) Cauer type RC equivalent circuit, b) Foster type RC equivalent circuit.

(23) In the complex frequency domain this equation becomes

For the Cauer topology equivalent circuit, given in Fig. 8(a), is of the form the thermal impedance (15)

where is the complex frequency. of the Foster topology equivalent circuit The impedance (Fig. 8(b)) is given by (16) with the time constant inverse Fourier transform of

. The pulse response is the , given by (17)

We used the analytic solution (14) to obtain the thermal time response of the TC with parameters stated above, and we compared these results to the matched equivalent Foster topology model. The equivalent circuit model exhibits three elements , , , , with , . This comparison is given in Fig. 6. V. THZ DETECTORS AND MIXERS Consider the equivalent circuit of the thermocouple depicted in Fig. 7. This circuit represents a quadratic detector. The right-hand and left-hand electric equivalent circuits are linear, whereas the thermal circuit in the center exhibits quadratic transfer characteristics. The left-hand electric equivalent circuit can be described in frequency domain by (18) (19) This yields

(20)

(24) and are the electric junction current and the where heat, respectively in the frequency domain and the operator denotes the convolution operation. The time derivation is considas ered as a thermal current and the temperature increase a thermal voltage. Its Fourier transform we denote with . is given by The temperature increase due to the heat (25) is given by (15) or (16), where the thermal impedance respectively. The right-hand electric equivalent circuit in Fig. 7 is the linear circuit describing the intermediate frequency or low-freaccounts quency output. The controlled voltage source for the thermal voltage excited via the Seebeck effect. The is given by output voltage (26) Inserting (25), (24), and (22) yields

The open-circuit output voltage given by

for

(27) is (28)

Fig. 9 shows the frequency response for nm computed from the a circular patch radius Foster topology equivalent circuit (Fig. 8(b)) using (16). The elements with equivalent circuit model exhibits three , , , , , . For the chosen parameters the computed 3 dB cutoff frequency is 136.6 GHz in the mixer mode and 206.8 GHz in the detector mode. the thermoDue to the broad-band characteristics at the couple is perfectly suited for mixer applications for frequencies input signal voltage with up to 30 THz. Consider an amplitude modulated with the signal the carrier frequency , (29)

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The autoconvolution of

is given by

Fig. 9. Frequency response for a circular patch radius nm computed from the Foster topology equivalent circuit (Fig. 8(b)) using (16); 3 dB cutoff frequency marker for mixer and detector mode .

The Fourier transform of

is symbolically denoted by (30)

and defined via (31) From (29), (30), and (31) we obtain (32) We superimpose a harmonic local oscillator signal . Its Fourier transform is

(39) Assuming the magnitude of the frequency difference to be small compared to the frequencies and we have in the first line of (39) the low-frequency and dc components of and the local oscillator the direct rectification of the signal signal . The second and third lines exhibit the intermediate and the lines frequency part with frequencies around 4 to 7 contain spectral parts around twice the local oscillator . These frequencies around are frequency, i.e., around . We need only to consider the low-frefiltered out by quency part playing a role in direct detector applications (40)

(33)

and the intermediate frequency part playing a role in mixer applications

(34)

(41)

The total input signal of the thermocouple is

This yields in the frequency domain

Inserting (40) into (28) yields the open-circuit output voltage for (35)

and The Fourier transform of the product of two signals is given by the convolution of the respective spectra, i.e., (36) where the convolution

We note

is defined by

(42) The output frequency characteristics of the detector is deterand represented in Fig. 9 for a NTC diameter mined by cutoff frequency equal to the of 25 nm, showing a detector thermal cutoff frequency of 260.8 GHz. In general the expresdenotes the spectrum of the square-law recsion tified AM signal envelope. For the case of mixer operation we insert (41) into (28) and obtain the open-circuit output voltage

(37) (43)

(38)

signal with the frequency is shifted by the local osThe to the intermediate frequency . cillator frequency The intermediate frequency band again is limited by the thermal cutoff frequency of 136.6 GHz. In the mixer case, the envelope

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Fig. 10. Open-circuit voltage as a function of thermopile length.

spectrum distortion.

is frequency shifted but exhibits no nonlinear

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Fig. 11. Scanning electron micrograph of the NTCs for frequency-dependent . measurements. The hot and cold (not shown) junctions are separated by 400 A thermopile was constructed from the NTCs by connecting them in series at their terminals.

VI. MEASUREMENTS Infrared measurements of the devices were performed by a laser operating at 28.3 THz. The laser linearly polarized beam was square-wave modulated by a mechanical chopper at 1 kHz. In order to maximize the device response, the polarization angle of the laser beam was set parallel to the antenna axis by a half-wave plate. The open-circuit voltage response was measured by a custom made pre-amplifier and with standard lock-in techniques. We measured the open-circuit voltage response of the thermopile with various lengths, as shown in Fig. 10. The response followed the thermopile addition rule, i.e., is a linear function of the number of ACNTCs in the thermopile. This confirms our assumption that the radiation-induced antenna currents heat the hot junction of the NTC, and shows that antennacoupled single-metal thermocouples and thermopiles function , as IR detectors. The relative Seebeck coefficient is 0.86 as measured by the characterization platform introduced in [39] for a single-metal NTC constructed from 50 and 200 nm wide Pd wire segments. Our IR experimental setup does not allow direct measurement of the frequency-dependent response of ACNTCs. Therefore, the frequency-dependent response of the NTCs was determined by pulse heating of the hot junctions using an acousto-optic modulator and a laser diode. To characterize the frequency-dependent response of NTCs to pulsed heating, we built the structure shown in Fig. 11. The geometry of the hot junctions is nominally identical in both structures (ACNTC and NTC) to avoid the impact of the thermal conductivity and geometry of the antenna on the response time of the NTC. The cold junctions for the frequency-dependent away from the hot junctions measurements are located 400 to ensure that the laser beam does not illuminate the cold junctions and so they remain at ambient temperature. We also constructed a thermopile by connecting four NTCs in series at their terminals. Now we discuss the various components of our experimental setup as shown in Fig. 12. Our heat source is an AlGalnP laser diode (HL6545MG), operating at 660 nm in a constant emission mode. The laser beam is collimated and focused to form a

Fig. 12. Measurement set-up.

200- -diameter spot at the devices, which was determined by the widely-used knife edge measurement technique. In order to perform frequency-dependent measurements, the beam is square-wave modulated with an acousto-optic modulator (AOM) between 30 kHz and 6.5 MHz. The signal generated by the NTCs in response to the laser-induced temperature oscillations is detected by an SR844 high frequency lock-in amplifier, which was synchronized to the AOM driver. In order to avoid the intrinsic bandwidth limitation of the measurement due to the low-pass filter by the source resistance and the input capacitance, the input impedance of the lock-in was set to 50 . Fig. 13 shows the open-circuit voltage response of a NTC and a four-NTC-long thermopile as a function of modulation frequency from 30 kHz to 6.5 MHz. From the figure we can determine that the 3 dB level of the measured signal is about 3.9 MHz. However, there is no physical reason to believe that the attenuation of the measured NTC signal is due to the thermal time constant of the NTC; rather it is caused by: 1) parasitic low-pass filtering, and 2) frequency-dependent intensity of the modulated laser beam. First, the resistance of the lead lines of the NTC (8 ) along with the cable capacitances form a low-pass filter, which limits the bandwidth of the measurements. This effect is evident form the different 3 dB levels of the single NTC (3.9 MHz) and the thermopile (3.5 MHz), which has about four times larger resistance and cable capacitance. Second, the intensity of the modulated laser beam is frequency dependent, as shown in Fig. 13 by the output beam

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and low-frequency bandwidths in detector applications, both on the order of 100 GHz will be feasible. This will open the door for novel future applications in the THz bands. Future detector and mixer experiments with ACNTCs excited by two-frequency far-infrared signals will push forward the experimental validation of the broadband detector and mixer properties of ACNTCs. REFERENCES

Fig. 13. Frequency-dependent response of the NTCs and a four-NTC-long thermopile. The reference measurement shows frequency-dependent intensity of the laser beam caused by the AOM.

intensity of the AOM measured by a photo diode (PD). Therefore, the incident power on the NTC as a function of frequency is not uniform, which results in an attenuation of the measured signal. Fig. 13 also shows that, by comparing the NTC response to the PD response, the fluctuation in the measured thermal response is not the property of the NTC, but is rather a frequency-dependent intensity fluctuation of the laser beam introduced to the system by the AOM. VII. CONCLUSION AND OUTLOOK In this work we describe the design, fabrication, and theoretical and experimental investigation of single-metal ACNTCs. ACNTCs are excellently suited as polarization-sensitive detectors and mixers for the long-wavelength far-infrared range around 30 THz. The theoretical fundamentals of the geometry-dependent Seebeck effect facilitating single-metal ACNTCs have been discussed. In thin films, the influence of surface electron scattering on the mean free path of the electrons yields a geometry dependence of the Seebeck effect, and makes SMTCs possible. We have given the experimental evidence for single-metal ACNTCs. The theoretical analysis of the thermal dynamics of NTCs has shown that detector low-frequency bandwidths and mixer intermediate-frequency beyond 100 GHz could be expected. This makes TCs presently the fastest THz detectors, suitable for broadband detector and heterodyne receiver applications. The combination with state of the art coherent terahertz sources, such as quantum cascade laser structures for room temperature terahertz frequency conversion [43]–[45], will pave the way for many innovative applications. We experimentally demonstrated that ACNTCs are able to detect and rectify long-wave infrared radiation at 10.6 wavelength. We also demonstrated that such NTCs are able to follow thermal oscillations in the MHz range; however, the bandwidth limitations of our experimental setup does not allow the determination of the cut-off frequency of these devices. Although our experimental investigations proved that NTCs exhibit detection bandwidths at least in the MHz range and consequently will be applicable for many sensing and communications applications, our theoretical investigations have shown that intermediate frequency bandwidths in mixer applications

[1] N. F. Mott and H. Jones, The Theory of the Properties of Metals and Alloys. London: Oxford Univ. Press, 1936. [2] F. L. Bakker, J. Flipse, and B. van Wees, “Nanoscale temperature sensing using the Seebeck effect,” J. Appl. Phys., vol. 111, no. 8, pp. 084306–084306-4, 2012. [3] D. C. Agrawal and V. J. Menon, “The thermoelectric generator as an endoreversible Carnot engine,” J. Phys. D: Appl. Phys., vol. 30, no. 3, p. 357, 1997. [4] G. P. Szakmany, P. M. Krenz, A. O. Orlov, G. H. Bernstein, and W. Porod, “Antenna-coupled nanowire thermocouples for infrared detection,” IEEE Trans. Nanotechn., vol. 12, no. 2, pp. 163–167, Dec. 2013. [5] G. P. Szakmany, A. O. Orlov, G. H. Bernstein, and W. Porod, “Singlemetal nanoscale thermocouples,” IEEE Trans. Nanotechn., vol. 13, no. 6, pp. 1234–1239, 2014. [6] G. P. Szakmany, A. O. Orlov, G. H. Bernstein, W. Porod, M. Bareiss, P. Lugli, J. A. Russer, C. Jirauschek, P. Russer, M. T. Ivrlač, and J. A. Nossek, “Nano-antenna arrays for the infrared regime,” in 18th Int. ITG Workshop on Smart Antennas (WSA), Erlangen, March 2014. [7] J. A. Russer and P. Russer, “Dynamics of long-wave infrared range thermocouple detectors,” in Proc. XXXIst URSI General Assembly and Scientific Symp., Beijing, China, Aug. 17–23, 2014, pp. 1–4. [8] J. A. Russer, C. Jirauschek, G. P. Szakmany, A. O. Orlov, G. H. Bernstein, W. Porod, P. Lugli, and P. Russer, “A nanostructured long-wave infrared range thermocouple detector,” IEEE Trans. Terahertz Sci. Technol., vol. 5, no. 3, pp. 335–343, May 2015. [9] J. A. Russer, C. Jirauschek, G. P. Szakmany, A. O. Orlov, G. H. Bernstein, W. Porod, P. Lugli, and P. Russer, “Antenna-coupled terahertz thermocouples,” in Proc. IEEE MTT-S IMS, May 2015, pp. 1–4. [10] V. Damodara and N. Soundararajan, “Size and temperature effects on the Seebeck coefficient of thin bismuth films,” Phys. Rev. B, vol. 35, no. 12, pp. 5990–5996, Apr. 1987. [11] R. Dingle, “The electrical conductivity of thin wires,” Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, vol. 201, no. 1067, pp. 545–560, 1950. [12] D. MacDonald and K. Sarginson, “Size effect variation of the electrical conductivity of metals,” Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, vol. 203, no. 1073, pp. 223–240, 1950. [13] A. T. Ramu, L. E. Cassels, N. H. Hackman, H. Lu, J. M. Zide, and J. E. Bowers, “Rigorous calculation of the Seebeck coefficient and mobility of thermoelectric materials,” J. Appl. Phys., vol. 107, no. 8, p. 083707, 2010. [14] R. Kim, S. Datta, and M. S. Lundstrom, “Influence of dimensionality on thermoelectric device performance,” J. Appl. Phys., vol. 105, no. 3, p. 034506, 2009. [15] B. Wang, J. Zhou, R. Yang, and B. Li, “Ballistic thermoelectric transport in structured nanowires,” New J. Phys., vol. 16, no. 6, p. 065018, 2014. [16] L. Hicks and M. Dresselhaus, “Thermoelectric figure of merit of a onedimensional conductor,” Phys. Rev. B, vol. 47, no. 24, p. 16631, 1993. [17] D. Broido and T. Reinecke, “Theory of thermoelectric power factor in quantum well and quantum wire superlattices,” Phys. Rev. B, vol. 64, no. 4, p. 045324, 2001. [18] M. Cattani, M. Salvadori, A. Vaz, F. Teixeira, and I. Brown, “Thermoelectric power in very thin film thermocouples: Quantum size effects,” J. Appl. Phys., vol. 100, no. 11, p. 4905, 2006. [19] C. R. Tellier and A. J. Tosser, Size Effects in Thin Films. Amsterdam: Elsevier, 1982. [20] E. Sondheimer, “The mean free path of electrons in metals,” Adv. Phys., vol. 1, no. 1, pp. 1–42, Jan. 1952. [21] S. B. Soffer, “Statistical model for the size effect in electrical conduction,” J. Appl. Phys., vol. 38, no. 4, pp. 1710–1715, 1967. [22] J. Sambles, “The resistivity of thin metal films some critical remarks,” Thin Solid Films, vol. 106, no. 4, pp. 321–331, 1983. [23] W. F. Leonard and H.-Y. Yu, “Thermoelectric power of thin copper films,” J. Appl. Phys., vol. 44, no. 12, pp. 5320–5323, 1973.

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[24] R. Suri, A. Thakoor, and K. Chopra, “Electron transport properties of thin copper films. I.,” J. Appl. Phys., vol. 46, no. 6, pp. 2574–2582, 1975. [25] V. V. R. Narasimha Rao, S. Mohan, and P. J. Reddy, “Electrical resistivity, TCR and thermoelectric power of annealed thin copper films,” J. Phys. D: Appl. Phys., vol. 9, no. 1, p. 89, 1976. [26] H.-Y. Yu and W. F. Leonard, “Thermoelectric power of thin silver films,” J. Appl. Phys., vol. 44, no. 12, pp. 5324–5327, 1973. [27] V. V. R. Narasimha Rao, S. Mohan, and P. J. Reddy, “The size effect in the thermoelectric power of silver films,” Thin Solid Films, vol. 42, no. 3, pp. 283–289, 1977. [28] S. F. Lin and W. F. Leonard, “Thermoelectric power of thin gold films,” J. Appl. Phys., vol. 42, no. 9, pp. 3634–3639, 1971. [29] M. Hubin and J. Gouault, “Resistivity and thermoelectric power beand of gold and silver thin films formed tween and studied in ultrahigh vacuum,” Thin Solid Films, vol. 24, no. 2, pp. 311–331, 1974. [30] C. Pichard, A. Tosser, and C. Tellier, “Thermoelectric power of supported thin polycrystalline films,” J. Mater. Sci., vol. 17, no. 1, pp. 10–16, 1982. [31] W. Leonard and S. Lin, “Thermoelectric power of thin metal films,” J. Appl. Phys., vol. 41, no. 4, pp. 1868–1868, 1970. [32] A. Mayadas and M. Shatzkes, “Electrical-resistivity model for polycrystalline films: The case of arbitrary reflection at external surfaces,” Phys. Rev. B, vol. 1, no. 4, p. 1382, 1970. [33] C. Pichard, C. Tellier, and A. Tosser, “A three-dimensional model for grain boundary resistivity in metal films,” Thin Solid Films, vol. 62, no. 2, pp. 189–194, 1979. [34] R. Angus and I. Dalgliesh, “Thermopower and resistivity of thin metal films,” Phys. Lett. A, vol. 31, no. 5, pp. 280–281, 1970. [35] M. Angadi and S. Shivaprasad, “Thermoelectric power measurements in thin palladium films,” J. Mater. Sci. Lett., vol. 1, no. 2, pp. 65–66, 1982. [36] H. Ibach and H. Lüth, Solid-State Physics: An Introduction to Principles of Material Science. Berlin: Springer, 2003. [37] F. Mueller, A. Freeman, J. Dimmock, and A. Furdyna, “Electronic structure of palladium,” Phys. Rev. B, vol. 1, no. 12, p. 4617, 1970. [38] S. Shivaprasad, L. Udachan, and M. Angadi, “Electrical resistivity of thin palladium films,” Phys. Lett. A, vol. 78, no. 2, pp. 187–188, 1980. [39] G. P. Szakmany, P. M. Krenz, L. C. Schneider, A. O. Orlov, G. H. Bernstein, and W. Porod, “Nanowire thermocouple characterization platform,” IEEE Trans. Nanotechn., vol. 12, no. 3, pp. 309–313, May 2013. [40] V. Székely, “A new evaluation method of thermal transient measurement results,” Microelectron. J. , vol. 28, pp. 277–292, 1997. [41] V. Székely and T. Van Bien, “Fine structure of heat flow path in semiconductor devices: A measurement and identification method,” SolidState Electron., vol. 31, no. 9, pp. 1363–1368, Sep. 1988. [42] Y. C. Gerstenmaier, W. Kiffe, and G. Wachutka, “Combination of thermal subsystems modeled by rapid circuit transformation,” in Proc. THERMINIC, 2007, pp. 115–120. [43] K. Vijayraghavan, Y. Jiang, M. Jang, A. Jiang, K. Choutagunta, A. Vizbaras, F. Demmerle, G. Boehm, M. C. Amann, and M. A. Belkin, “Broadly tunable terahertz generation in mid-infrared quantum cascade lasers,” Nat. Commun., vol. 4, p. 2021, 2013. [44] C. Jirauschek, A. Matyas, P. Lugli, and M.-C. Amann, “Monte carlo study of terahertz difference frequency generation in quantum cascade lasers,” Opt. Express, vol. 21, no. 5, pp. 6180–6185, 2013. [45] Q. Lu, N. Bandyopadhyay, S. Slivken, Y. Bai, and M. Razeghi, “Continuous operation of a monolithic semiconductor terahertz source at room temperature,” Appl. Phys. Lett., vol. 104, no. 22, pp. 221105–221105-5, 2014.

Johannes A. Russer (M’09) received the Dipl.-Ing. (M.S.E.E.) degree in electrical engineering and information technology from the Universität Karlsruhe, Karlsruhe, Germany, in 2003. In 2004, he joined the University of Illinois at Urbana-Champaign, Urbana-Champaign, IL, USA, as a Research Assistant, where he received the Ph.D. E.E. degree in 2010. From 2007 to 2010, he was with Qualcomm Inc. as an intern. Since 2010, he has been a Postdoctoral Research Fellow at the Institute of Nanoelectronics of the Technische Universität München (TUM), Munich, Germany.

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Dr. Russer received the Best Student Paper Award at the IEEE International Microwave Symposium in 2008. In 2015, he received the best paper award from the ITG (German Society for Information Technology). He is a member of VDE, and of the Eta Kappa Nu honor society.

Christian Jirauschek (S’03–M’04) received the Dipl.-Ing. and Ph.D. degrees in electrical engineering from the Universität Karlsruhe (TH), Karlsruhe, Germany, in 2000 and 2004, respectively. From 2002 to 2005, he worked at the Massachusetts Institute of Technology (MIT), Cambridge, MA, USA. He then joined the Institute of Nanoelectronics at Technische Universität München (TUM), Munich, Germany, where, since 2007 he headed an independent junior research group within the Emmy Noether program of the Deutsche Forschungsgemeinschaft (DFG). In 2014, he received a Heisenberg professorship grant from the DFG. His research interests include modeling in the areas of photonics and nanoelectronics.

Gergo P. Szakmany received the Diploma in electrical and computer engineering from the Pazmany Peter Catholic University, Budapest, Hungary in 2007, and the M.S. and Ph.D. degrees in electrical engineering from the University of Notre Dame, Notre Dame, IN in 2011 and 2013, respectively. He is continuing his research at the University of Notre Dame on antenna-coupled infrared detectors as a Postdoctoral Research Associate. His research interests focuses on submicron device fabrication and characterization.

Mark Schmidt received the B.Sc. degree from the Technische Universität München (TUM), Munich, Germany, in 2014, where he specialized on high frequency engineering. He is currently pursuing a M. Sc. degree at TUM. He is working at the Institute of Nanoelectronics of the Technische Universität München (TUM), Munich, Germany, on the modeling of infrared-range thermocouple detectors. His research interests include theory, design, and applications in the areas of photonics, radio-frequency engineering, and energy harvesting.

Alexei O. Orlov received the M.S. and the Ph. D. degrees in physics from the Moscow State University, Moscow, Russia, in 1983 and 1990, respectively. He is currently is a Research Professor at the University of Notre Dame, Notre Dame, IN, USA. From 1983 to 1993, he worked at the Institute of Radio Engineering and Electronics of the Russian Academy of Sciences, Moscow, Russia. During this time, he conducted research on mesoscopic and quantum ballistic effects in electron transport of GaAs field-effect transistors. He was a visiting fellow at the University of Exeter, Exeter, UK in 1993, and joined the Department of Electrical Engineering at the University of Notre Dame in 1994. His research interests include experimental studies of mesoscopic, single-electron, and molecular electronic devices and sensors, nanomagnetics, and quantum-dot cellular automata. He has authored or co-authored more than 150 journal publications.

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Gary H. Bernstein (S’78–M’79–SM’95–F’06) received the B.S.E.E. degree from the University of Connecticut, Storrs, CT, USA, (with honors), in 1979, and the M.S.E.E. degree from Purdue University, West Lafayette, IN, USA, in 1981. He received the Ph.D. in electrical engineering from Arizona State University, Tempe, AZ, USA, in 1987, after which he spent a year there as a postdoctoral fellow. During the summers of 1979 and 1980, he was a Graduate Assistant at Los Alamos National Laboratory Los Alamos, NM, USA, and in the summer of 1983, interned at the Motorola Semiconductor Research and Development Laboratory, Phoenix, AZ, USA. He joined the Department of Electrical Engineering at the University of Notre Dame, Notre Dame, IN, USA, in 1988 as an Assistant Professor, and was the Founding Director of the Notre Dame Nanoelectronics Facility (NDNF) from 1989 to 1998. He has authored or co-authored more than 200 publications in the areas of electron beam lithography, nanomagnetics, quantum electronics, high-speed integrated circuits, electromigration, MEMS, and electronics packaging. He was promoted to the rank of Professor in 1998, and served as the Associate Chairman of his department from 1999 to 2006. Dr. Bernstein received an NSF White House Presidential Faculty Fellowship in 1992, and was named a Frank M. Freimann Professor of Electrical Engineering in 2010.

Wolfgang Porod (M’86–SM’90–F’01) received the M.S. and Ph.D. degrees from the University of Graz, Graz, Austria, in 1979 and 1981, respectively. After appointments as a Postdoctoral Fellow at Colorado State University, Fort Collins, CO, USA, and as a Senior Research Analyst at Arizona State University, Tempe, AZ, USA, he joined the University of Notre Dame (UND) in 1986 as an Associate Professor. He now also serves as the Director of Notre Dame's Center for Nano Science and Technology. He is currently a Frank M. Freimann Professor of Electrical Engineering at the UND. His research interests are in the area of nanoelectronics, with an emphasis on new circuit concepts for novel devices. He has authored some 300 publications and presentations. He has served as the Vice President for Publications for the IEEE Nanotechnology Council (2002–2003), and he was appointed an Associate Editor for the IEEE TRANSACTIONS ON NANOTECHNOLOGY (2001–2005). He has been active on several committees, in organizing special sessions and tutorials, and as a speaker in IEEE Distinguished Lecturer Programs.

Paolo Lugli (M’01–SM’07–F’11) received the Degree in physics from the University of Modena, Modena, Italy, in 1979. He received the Master of Science degree in 1982, and the Ph.D. degree in 1985, both in electrical engineering, from the Colorado State University, Fort Collins, CO, USA. In 1985, he joined the Physics Department of the University of Modena as a Research Associate. From 1988 to 1993, he was Associate Professor of Solid State Physics with the engineering faculty of the 2nd University of Rome “Tor Vergata”. In 1993, he was appointed as Full Professor of Optoelectronics at the same university. In 2002, he joined the Technical University of Munich, Munich, Germany, where he was appointed Head of the newly created Institute for Nanoelectronics. His current research interests include nanoimprint lithography, the modeling, fabrication, and characterization of organic devices for electronics and optoelectronics applications, the design of circuits and architectures for nanostructures and nanodevices, the numerical simulation of microwave semiconductor devices, and the theoretical study of transport processes in nanostructures. He is author of more than 350 scientific papers and co-author of the books “The Monte Carlo Modelling for Semiconductor Device Simulations” (Springer: 1989) and “High Speed Optical Communications” (Kluver Academic: 1999). Dr. Lugli served as General Chairman of the IEEE International Conference on Nanotechnology held in Munich in 2004. He is a mmber of the German National Academy of Science and Engineering (ACATECH).

Peter Russer (F’94–LF’13) received the Dipl.-Ing. (M.S.E.E.) degree in 1967 and the Dr. Techn. (Ph. D.E.E.) degrees in 1967 and 1971, respectively, both from the Vienna University of Technology, Vienna, Austria. In 1971, he joined the Research Institute of AEG-Telefunken in Ulm, Germany. From 1981 to 2008, he was Professor and Head of the Institute for High Frequency Engineering at the Technische Universität München (TUM), Munich, Germany. From October 1992 to March 1995, he was Director of the Ferdinand-Braun-Institut für Höchstfrequenztechnik, Berlin. From 1997 to 1999, he was Dean of the Department of Electrical Engineering and Information Technology of the TUM. His current research interests include electromagnetic fields, numerical electromagnetics, metamaterials, integrated microwave and millimeter-wave circuits, statistical noise analysis, electromagnetic compatibility, and quantum nanoelectronics. He has published more than 800 scientific papers and five books including “Electromagnetics, Microwave Circuit and Antenna Design for Communications Engineering” (Boston: 2006). Dr. Russer was elected Member of ACATECH in 2006. In 2006, he received the Distinguished Educator Award and in 2012, the Microwave Pioneer Award, both of the IEEE MTT Society, and in 2009, the Distinguished Service Award from the European Microwave Association. In 2007, he received an honorary Doctor degree from the Moscow University of Aerospace Technologies. In 2010 he was awarded the Golden Ring of Distinction of the German Association for Electrical, Electronic and Information Technologies (VDE).

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Reliable Microwave Modeling by Means of Variable-Fidelity Response Features Slawomir Koziel, Senior Member, IEEE, and John W. Bandler, Life Fellow, IEEE

Abstract—In this work, methodologies for low-cost and reliable microwave modeling are presented using variable-fidelity response features. The two key components of our approach are: 1) a realization of the modeling process at the level of suitably selected feature points of the responses (e.g., -parameters versus frequency) of the structure at hand and 2) the exploitation of variable-fidelity EM simulation data, also for the response feature representation. Due to the less nonlinear dependence between the coordinates of the feature points on the geometrical parameters of the structure of interest, the amount of training data can be greatly reduced. Additional cost reduction is obtained by means of generating the majority of the training data at a coarse-discretization EM simulation level and exploiting the correlations between the EM models of various fidelities. We propose two ways of combining the low- and high-fidelity data sets: 1) an external approach, through space mapping (simpler to implement) and 2) an internal approach, using co-kriging (more flexible and potentially offering better accuracy). The operation and performance of our modeling techniques are demonstrated by three microstrip filter examples and a compact rat-race coupler. A comprehensive verification and comparisons with several benchmark techniques, as well as application examples (filter optimization) are also provided. Index Terms—Co-kriging, computer-aided design, feature-based modeling, kriging, microwave component modeling, space mapping (SM), surrogates modeling.

I. INTRODUCTION

A

CCURATE evaluation of the electrical performance of microwave structures can be obtained through high-fidelity full-wave electromagnetic (EM) analysis. Unfortunately, this comes at considerable computational cost, particularly for complex devices/circuits and when interactions (EM couplings) Manuscript received June 19, 2015; revised September 03, 2015; accepted October 20, 2015. Date of publication November 11, 2015; date of current version December 02, 2015. This work was supported in part by the Icelandic Centre for Research (RANNIS) under Grant 130450051 and Grant 141272051, and in part by the Natural Sciences and Engineering Research Council of Canada under Grant RGPIN7239-11 and Grant STPGP447367-13, and in part by Bandler Corporation. This paper is an expanded version from the IEEE MTT-S International Microwave Symposium, Phoenix, AZ, USA, May 17–22, 2015. S. Koziel is with the School of Science and Engineering, Reykjavík University, 101 Reykjavík, Iceland, and also with the Faculty of Electronics, Telecommunications, and Informatics, Gdańsk University of Technology, 80-233 Gdańsk, Poland (e-mail: [email protected]). J. W. Bandler is with the Simulation Optimization Systems Research Laboratory and Department of Electrical and Computer Engineering, McMaster University, Hamilton, ON L8S 4K1, Canada, and also with the Bandler Corporation, Dundas, ON L9H 5E7, Canada (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2015.2495266

with the environment are included. Consequently, the utilization of EM simulations in a design process, e.g., for parametric optimization, uncertainty quantification, or tolerance-aware design (design centering), may be prohibitive, as multiple evaluations of the structure at hand are involved. Executing such tasks in a reasonable timeframe requires fast and accurate replacement models (surrogates). Fast surrogate models can be constructed using two classes of techniques: 1) response surface approximation (RSA) [1] and 2) physics-based surrogate modeling [2], [3]. The first relies on approximating sampled high-fidelity EM simulation data. The most popular methods include neural networks [4], [5], kriging interpolation [6], support vector regression [7], [8], radial-basis function interpolation [9], the Cauchy method [10], as well as Gaussian process regression (GPR) [11], [12]. The advantages of the RSA surrogates include their versatility (as data-driven models they are easily transferable between various problem domains) and speed (once established, the RSA model is computationally cheap to evaluate). On the other hand, approximation models are not suitable for handling multi-dimensional parameter spaces. If the number of parameters exceeds just a few, the amount of training data necessary to ensure sufficient accuracy of the model (typically, below 5% of the relative RMS error [13]) grows very quickly so that the effort for model construction may not be practically justified (unless the model is to be reused under various design scenarios) or even feasible. The second class of techniques for constructing fast surrogates—physics-based modeling—relies on appropriate correction of an underlying low-fidelity model such as an equivalent circuit (popular method: space mapping (SM) [14], [15]). Physics-based surrogates require less training data and-due to the problem-specific knowledge embedded in the low-fidelity model-offer better generalization. However, they are less generic, more complex to implement, and their applicability is typically limited to cases when fast low-fidelity models are available; their accuracy depends on the reliability of the low-fidelity model; and it might not be straightforward to accommodate additional training data (if available) [16]. To some extent, these issues can be alleviated by combining SM with an approximation-based correction layer (e.g., [17], [18]). Reduction of the number of training points for approximation-based surrogates can be achieved by realizing the modeling process in an alternative representation of the system responses, where the dependence of the alternative responses on the designable parameters is less nonlinear. This approach has been explored, e.g., in the shape-preserving response prediction (SPRP) technique [19] or in [20] for inverse modeling of filters. A recent modeling technique [21] utilizes the concept of feature points

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similar to those in SPRP but with considerably simpler implementation (achieved by abandoning the use of so-called reference designs [21]). Feature-based modeling has been demonstrated to ensure good accuracy using a fraction of the training points required by conventional methods [21]. As indicated in [21], further reduction of the setup cost of the surrogate model can be achieved by using variable-fidelity EM simulation within the feature-based modeling framework. In [22], densely sampled low-fidelity EM model data was supplemented by sparsely sampled high-fidelity EM data with the two data sets blended (at the level of response features) into a single surrogate using co-kriging [23]. In this work, we provide extensive numerical validation of this approach. In addition, in Section II, we propose an alternative (external) way of combining low- and high-fidelity feature-based surrogates using SM. The latter is simpler and easier to implement than [22] while ensuring similar accuracy. Our test cases provided in Section III include three microstrip filter examples and a compact rat-race coupler. Application of the variable-fidelity feature-based models for design optimization is also demonstrated. II. VARIABLE-FIDELITY FEATURE-BASED MODELING In this section, we formulate the surrogate modeling problem, recall the concept of feature-based surrogates, and redefine the concept within a variable-fidelity setting. A. Surrogate Modeling , the response We denote by vector of the microwave device of interest. In particular, may represent at chosen frequencies, to , i.e., . is assumed to be evaluated using high-fidelity EM analysis. Consequently, it is computationally expensive. The task is to build a fast surrogate (replacement) model that represents in . Given sufficient accuracy of , it can be used in place of for solving design tasks that require multiple, high-cost evaluations of the latter. Let be the training set so that the responses of the high-fidelity model at , are known. Conventional response surface modeling attempts to directly model , . In many cases, the surrogate is created as an ensemble of RSA models constructed for individual frequencies, i.e., obtained by approximating the data sets , for . Sometimes [23], frequency is treated as an additional designable parameter, so that the RSA surrogate is constructed by approximating the data pairs . B. Variable-Fidelity Response Features Given the high nonlinearity of typical responses of microwave devices with respect to their designable parameters, particularly for filters, the direct modeling of the high-fidelity model responses is a challenging task that requires large data sets using (cf.

Fig. 1. Family of responses for a microstrip bandpass filter evaluated , : high-fidelity model along a selected line segment (—) and low-fidelity model . Selected feature points and groups and for . of corresponding points marked (o) for

Fig. 2. Selected feature point plots between designs and : (a) frequency and (b) levels. They correspond to two feature points: center frequency of the filter (– – –) and 10 dB level on the left-hand side of the passband (—); thick and thin lines are used for high- and low-fidelity model feature points, respectively.

Section II-A) and which is virtually impossible in high-dimensional design spaces. The key concept behind the modeling techniques considered here that allow reduction of the number of training points in the modeling process are certain response features [21]. The feature points (cf. Fig. 1) may include points corresponding to specific response levels (e.g., 10 dB, 3 dB), as well as those allocated in between fixed-level points (e.g., uniformly spaced in frequency). As indicated in Fig. 2 the dependence of the feature points on the design parameters is much less nonlinear than those of the original responses (here, -parameters), and thus easier to model. Feature-based modeling was originally introduced in [21]. It relies on extracting the feature points from the sampled EM-simulated responses at the training locations, constructing the RSA models of the individual feature points, and synthesizing the surrogate response at a design of interest from these RSA models. In this work, we utilize training data acquired from variable-fidelity simulations: from sparsely-sampled points and from densely-sampled data obtained from coarse-discretization EM simulations (low-fidelity model ), . Although and are misaligned (cf. Fig. 1), they are also well correlated so that the initial surrogate model obtained from the data can be enhanced by using a few points to construct the accurate, final surrogate model. We use the notation , , and to denote the th feature point of , and to denote the th feature ; and denote the frequency and point of magnitude (level) components of (similarly for ).

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with (4) and are predicted feature point locations corresponding to , the design being considered; , , is a discrete set of frequencies at which the response of the structure is being evaluated (cf. Section II-A). According to the internal approach, both and are implemented through co-kriging as in (2). denotes a function that interpolates the level vector and frequency vector into the response at a given frequency . Because and (i.e., frequencies and levels of the feature points) are less nonlinear than the original responses , a substantially smaller number of training points is necessary to ensure faithful modeling. Also, excellent correlation between and (cf. Fig. 2) allows for further reduction of the surrogate model setup cost because a very limited number of samples is sufficient to elevate the -based kriging model to high-fidelity accuracy through co-kriging. where

Fig. 3. Co-kriging concept: model (—), model (– – –), model sam, model samples . Kriging interpolation of model samples ples is not an adequate representation of the model (limited data set). of blended and data provides better acCo-kriging interpolation curacy at a lower computational cost.

C. Variable-Fidelity Feature-Based Modeling: The Internal Approach Multi-fidelity feature-based modeling is a two-step process. First, we construct approximation surrogates and , , corresponding to the feature points. In the internal approach presented in this section, the construction of and is based on both high-fidelity and low-fidelity training points and their corresponding feature points , and , . Blending these two types of data sets is realized through co-kriging [20] as described in the next paragraph. Let be the set of responses associated with the training set (i.e., low-fidelity feature points through ). The kriging interpolant is given as [13]

D. Variable-Fidelity Feature-Based Modeling: The External Approach The internal approach presented in Section II-C combines the low- and high-fidelity training data at the level of the feature points. In the external approach outlined below, the high-fidelity data is included through a SM correction of the initial featurebased surrogate model obtained as in (1), (2), however, using the low-fidelity training data only. The SM correction is realized at the level of the original responses as follows [15]: (5)

(1) where and are Vandermonde matrices of the test point and the base set , respectively; is determined by generalized least squares (GLS), is an vector of correlations between the point and the base set , where the entries are , and is a correlation matrix, whose entries are given by ). We use the exponential correlation function . The regression function is constant, and . Co-kriging is a type of kriging where the and model data are combined to enhance the prediction accuracy (cf. Fig. 3). Co-kriging is a two-step process: first a kriging model of the coarse data is constructed and, on the residuals of the fine data , a second kriging model is applied, where ; can be approximated as . The co-kriging interpolant is defined as [25] (2) , and can be found in [25]. Definitions of , , The multi-fidelity feature-based surrogate (the internal approach) is defined as (3)

such that , with , , being components of . Here, the model parameters (diagonal matrix), (square matrix), (column vector), and are obtained from the standard parameter extraction procedure needed by SM, namely, where

is a frequency scaled model

(6) If the correlation between the low- and high-fidelity models is sufficient (which is normally the case when both models are based on EM analysis), the correction given by (5) and (6) should significantly improve the accuracy of the surrogate. It should also be noted that the computational cost of surrogate model identification [i.e., solving the parameter extraction process (6)] can be neglected compared to the high-fidelity data acquisition because it is realized at the level of a fast feature-based model . E. Internal Versus External Approach Apart from considerable conceptual differences between the internal and external approaches, i.e., blending in the high-fidelity model data at the level of the response features rather than

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at the level of the original responses, the external approach is simpler to implement. On the other hand, the internal approach can be more flexible because the inclusion of a larger amount of high-fidelity training data should lead to an improvement of model accuracy. This may not be the case for the external approach (beyond a certain number of points) due to the fixed number of degrees of freedom of the surrogate (5) (the number of model parameters depends on the problem's dimensionality but not on the cardinality of the data set). III. VERIFICATION EXAMPLES In this section, we provide a comprehensive benchmarking of the multi-fidelity feature-based modeling techniques of Section II and demonstrate applications of the feature-based surrogate models in design optimization. A. Test Cases and Experimental Setup In order to illustrate the operation and performance of the proposed modeling techniques we consider three microstrip filter examples and a compact coupler. The first example (Filter 1) is the stacked slotted resonators bandpass filter [26] shown in Fig. 4(a). The high-fidelity filter model is simulated in Sonnet em using a grid of 0.05 mm 0.05 mm. The low-fidelity model is also simulated in Sonnet on a 2 mm 2 mm grid. The substrate parameters are thickness 0.635 mm, and permittivity . The designable parameters are . The region of interest is defined as the interval with and . The second structure (Filter 2) is the fourth-order ring resonator bandpass filter [27] shown in Fig. 4(b). The high-fidelity filter model is simulated in FEKO using 952 triangular meshes. The low-fidelity FEKO model utilizes 174 meshes. The substrate parameters are thickness 1.52 mm, and permittivity . The designable parameters are . The region of interest is defined as the interval with and . The last filter structure considered here (Filter 3) is the microstrip bandpass filter with open stub inverter [28]shown in Fig. 4(c). The high-fidelity filter model is simulated in FEKO using 432 triangular meshes. The low-fidelity FEKO model utilizes 112 meshes. The substrate parameters are thickness 0.508 mm, and permittivity . The designable parameters are . The region of interest is defined as the interval with and . The final test structure is a folded rat-race coupler (RRC) [29] shown in Fig. 4(d). The structure is implemented on RF-35 substrate , 0.762 mm, ). The designable parameters are given by: , with , fixed (all dimensions in millimeters). The high- and low-fidelity models of the structure are both implemented in CST Microwave Studio ( mesh cells, simulation time 15 min for and 8000 mesh cells, simulation

Fig. 4. Filter structures used for feature-based modeling verification: (a) stacked slotted resonators filter [26]; (b) fourth-order ring resonator bandpass filter [27]; (c) bandpass filter with open stub inverter [28]; (d) rat-race coupler [29].

time 20 s for terval

). The region of interest is defined as the inwith and . Model accuracy is verified using the relative error measure expressed in percent and averaged over 100 random test designs. The multi-fidelity feature-based models (both the internal and external versions) are compared with the following modeling methods: • regular (single-fidelity) feature-based modeling [21]; • generalized shape-preserving response prediction (GSPRP) [19]; • direct kriging interpolation of the high-fidelity data [6]; • response surface modeling using radial-basis functions [9]. The kriging model utilizes a Gaussian correlation function [6], whereas the radial-basis function model uses Gaussian basis functions [6]. The length-scale parameter of the latter is optimized using cross-validation [6]. For all the above modeling

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TABLE I MODELING RESULTS FOR FILTER 1

TABLE II MODELING RESULTS FOR FILTER 2

Fig. 5. Model responses at the selected (random) test designs: high-fidelity and model (—) and multi-fidelity feature-based model (set up with points) (o): (a) Filter 1; (b) Filter 2; and (c) Filter 3; and (d) RRC.

methods, five different cases are considered with the number of training points varying between and . B. Numerical Results and Comparisons With Benchmark Methods The results are gathered in Tables I–IV. Fig. 5 shows the highfidelity and feature-based model responses at selected test points for Filters 1 to 3 and for the RRC. The following observations can be made.

• Both the internal and external multi-fidelity feature-based models ensure excellent accuracy even with a very small number of high-fidelity training samples (specifically, 20 and 50). • The internal feature-based modeling approach is generally better than the external approach, however, the latter is still considerably better than a single-level feature-based surrogate for a small number of training samples and comparable or better overall. • Asymptotically (i.e., for the number of high-fidelity training points increasing to 400), both multi-fidelity feature-based modeling methods are comparable or better than the single-fidelity feature-based models and ones based on GSPRP. • All modeling approaches exploiting the concept of response features are considerably more accurate than

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TABLE III MODELING RESULTS FOR FILTER 3

TABLE IV MODELING RESULTS FOR THE RRC

Fig. 6. Optimization results: (a) Filter 1; (b) Filter 2; (c) Filter 3; (d) RRC. For (a)–(c), responses shown as (– – –) and (—) for the multi-fidelity feature-based surrogate model responses (the internal approach) at the initial design and at the optimized design; corresponding verification by high-fidelity model responses shown as (o). For (d), thin lines show surrogate responses at the initial design, thick lines show the surrogate responses as the optimized design; corresponding verification by high-fidelity model responses shown as (o); 280-MHz bandwidth of the optimized coupler marked with horizontal line.

conventional modeling techniques working directly with the original system responses, here, -parameters versus frequency. The above conjectures are consistent throughout all the test cases considered in this paper. It should also be emphasized that the benchmarking is quite comprehensive, both with respect to the competitive methods (four techniques) and with respect to the training set size (from 20 to 400 samples). Perhaps the most important point is that—according to the authors' knowledge—multi-fidelity feature-based modeling (both the internal and external approaches) are the only methods that

result in excellent (and practically usable) accuracy for an extremely small number of training points (20 and 50 samples). At the same time, one should bear in mind the limitations of the method, namely, the necessity of maintaining consistency of the feature points across the entire training set. For certain structures, such as the ones utilized in this work, as well as other structures with well-defined response “shapes” (e.g., coupling structures, narrow-band antennas, certain integrated photonic components such as microring resonators) it is easy to achieve. For other structures, such as high-order filters, feature-based modeling may be the method of choice for local modeling for, e.g., statistical design purposes [30].

KOZIEL AND BANDLER: RELIABLE MICROWAVE MODELING BY MEANS OF VARIABLE-FIDELITY RESPONSE FEATURES

C. Application Examples: Design Optimization As an additional verification, the multi-fidelity feature-based surrogate models have been utilized for parametric optimization of the Filters 1 through 3 as well as the RRC. The following design specifications are considered. • Filter 1: 1 dB for 2.35 GHz 2.45 GHz, 20 dB for 2.2 GHz and 2.6 GHz. • Filter 2: 1 dB for 1.75 GHz 2.25 GHz, 20 dB for 1.5 GHz and 2.5 GHz. • Filter 3: 1 dB for 1.95 GHz 2.05 GHz, 20 dB for 1.8 GHz and 2.2 GHz. • RRC: Obtain an equal power split, i.e., at the operating frequency of 1 GHz; simultaneously maximize the 20 dB bandwidth (symmetrically) around for and . In all cases, the multi-fidelity feature-based surrogate constructed using the internal approach and 50 high-fidelity training samples (200 low-fidelity samples) has been used in the process. The initial and final responses obtained by optimizing the feature-based surrogate model (the final design is verified by the high-fidelity model) are shown in Fig. 6. The design specifications for the filter structures are marked using thick horizontal lines. Because of the very good accuracy of the surrogates, no further design tuning was found necessary. In the case of RRC, the bandwidth of the optimized coupler is 280 MHz with the power split error 0.2 dB at 1 GHz. IV. CONCLUSION Variable-fidelity feature-based techniques for low-cost surrogate modeling of microwave structures have been proposed. Reduction of the computational cost associated with setting up surrogate models has been achieved by combining two basic components: 1) the exploitation of certain feature points, which allows us to move the modeling process to an alternative representation of the system response, where the functional landscape is much less nonlinear than for the original responses (in particular, the frequency-dependent -parameters) and 2) the utilization of variable-fidelity EM simulations, where an initial surrogate created with densely sampled coarse-discretization EM simulation data is enhanced by sparsely sampled high-fidelity EM data. Two approaches to blending the variable-fidelity EM data into the final surrogate have been proposed, i.e., an internal one (based on co-kriging at the level of the feature points), and an external one (based on SM). As demonstrated by three microstrip filters and a rat race coupler example and comparisons with several benchmark techniques, both of our multi-fidelity feature-based approaches outperform not only conventional approximation modeling methods but also feature-based approaches that exploit single-fidelity EM simulations. Significant improvement of the predictive power of the surrogate is especially observed for small high-fidelity training sets. This opens new opportunities for construction of quasi-global surrogates for applications such as parametric design optimization (also demonstrated in this work). According to our knowledge, no surrogate modeling technique reported in the literature so far exhibits comparable

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performance. At the same time, one needs to bear in mind the limitations of the method, namely, the necessity of maintaining consistency of the feature point sets across the surrogate model domain. Consequently, our method is less versatile than general-purpose approximation techniques. On the other hand, with careful definition of the response features, as well as for numerous cases where the system response is well-defined in terms of its shape (microwave couplers, low-order filters, narrow-band antennas, phased array antennas, various classes of integrated photonic devices, wireless power transfer systems, etc.) but also higher-order filters in terms of local modeling for statistical/robust design application and uncertainty quantification, multi-fidelity feature-based modeling may be the method of choice for rapid construction of fast, accurate and reusable surrogates. REFERENCES [1] T. W. Simpson, J. Peplinski, P. N. Koch, and J. K. Allen, “Metamodels for computer-based engineering design: Survey and recommendations,” Eng. With Comput., vol. 17, no. 2, pp. 129–150, Jul. 2001. [2] J. W. Bandler, Q. S. Cheng, S. A. Dakroury, A. S. Mohamed, M. H. Bakr, K. Madsen, and J. Søndergaard, “Space mapping: The state of the art,” IEEE Trans. Microw. Theory Techn., vol. 52, no. 1, pp. 337–361, Jan. 2004. [3] S. Koziel and J. W. Bandler, “Recent advances in space-mapping-based modeling of microwave devices,” Int. J. Numer. Modelling, vol. 23, no. 6, pp. 425–446, Nov. 2010. [4] H. Kabir, Y. Wang, M. Yu, and Q. J. Zhang, “Neural network inverse modeling and applications to microwave filter design,” IEEE Trans. Microw. Theory Techn., vol. 56, no. 4, pp. 867–879, Apr. 2008. [5] Y. Cao, X. Chen, and G. Wang, “Dynamic behavioral modeling of nonlinear microwave devices using real-time recurrent neural network,” IEEE Trans. Electron Devices, vol. 56, no. 5, pp. 1020–1026, May 2009. [6] N. V. Queipo, R. T. Haftka, W. Shyy, T. Goel, R. Vaidynathan, and P. K. Tucker, “Surrogate-based analysis and optimization,” Progr. Aerosp. Sci., vol. 41, no. 1, pp. 1–28, Jan. 2005. [7] L. Xia, J. Meng, R. Xu, B. Yan, and Y. Guo, “Modeling of 3-D vertical interconnect using support vector machine regression,” IEEE Microw. Wirel. Comp. Lett., vol. 16, no. 12, pp. 639–641, Dec. 2006. [8] A. J. Smola and B. Schölkopf, “A tutorial on support vector regression,” Statist. Comput., vol. 14, no. 3, pp. 199–222, Aug. 2004. [9] M. D. Buhmann and M. J. Ablowitz, Radial Basis Functions: Theory and Implementations. Cambridge, U.K.: Cambridge University, 2003. [10] A. G. Lamperéz, P. K. Sarkar, and M. S. Palma, “Generation of accurate rational models of lossy systems using the Cauchy method,” IEEE Microw. Wirel. Comp. Lett., vol. 14, no. 10, pp. 490–493, Oct. 2014. [11] C. E. Rasmussen and C. K. I. Williams, Gaussian Processes for Machine Learning. Cambridge, MA, USA: MIT Press, 2006. [12] J. P. Jacobs and J. P. De Villiers, “Gaussian-process-regression-based design of ultrawide-band and dual-band CPW-fed slot antennas,” J. Electromagn. Waves Appl., vol. 24, pp. 1763–1772, 2010. [13] I. Couckuyt, F. Declercq, T. Dhaene, H. Rogier, and L. Knockaert, “Surrogate-based infill optimization applied to electromagnetic problems,” Int. J. RF Microw. Comput.-Aided Eng., vol. 20, no. 5, pp. 492–501, Sep. 2010. [14] J. W. Bandler, N. Georgieva, M. A. Ismail, J. E. Rayas-Sánchez, and Q. J. Zhang, “A generalized space mapping tableau approach to device modeling,” IEEE Trans. Microw. Theory Techn., vol. 49, no. 1, pp. 67–79, Jan. 2001. [15] J. W. Bandler, Q. S. Cheng, and S. Koziel, “Simplified space mapping approach to enhancement of microwave device models,” Int. J. RF Microw. Comput.-Aided Eng., vol. 16, no. 5, pp. 518–535, Sep. 2006. [16] S. Koziel, J. W. Bandler, and K. Madsen, “Theoretical justification of space-mapping-based modeling utilizing a data base and on-demand parameter extraction,” IEEE Trans. Microw. Theory Techn., vol. 54, no. 12, pp. 4316–4322, Dec. 2006. [17] S. Koziel and J. W. Bandler, “A space-mapping approach to microwave device modeling exploiting fuzzy systems,” IEEE Trans. Microw. Theory Techn., vol. 55, no. 12, pp. 2539–2547, Dec. 2007.

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[18] S. Koziel and J. W. Bandler, “Modeling of microwave devices with space mapping and radial basis functions,” Int. J. Numer. Modell., vol. 21, no. 3, pp. 187–203, May 2008. [19] S. Koziel and L. Leifsson, “Generalized shape-preserving response prediction for accurate modeling of microwave structures,” IET Microw., Ant. Prop., vol. 6, no. 12, pp. 1332–1339, Sep. 2012. [20] E. Menargues, S. Cogollos, V. E. Boria, B. Gimeno, and M. Guglielmi, “An efficient computer-aided design procedure for interpolating filter dimensions using least squares methods,” in Eur. Microw. Integr. Circuits Conf., 2012, pp. 250–253. [21] S. Koziel, J. W. Bandler, and Q. S. Cheng, “Low-cost feature-based modeling of microwave structures,” presented at the IEEE MTT-S Int. Microw. Symp., Tampa, FL, USA, 2014. [22] S. Koziel and J. W. Bandler, “Accurate modeling of microwave structures using variable-fidelity response features,” presented at the IEEE MTT-S Int. Microw. Symp., Phoenix, AZ, USA, 2015. [23] M. C. Kennedy and A. O'Hagan, “Predicting the output from complex computer code when fast approximations are available,” Biometrika, vol. 87, pp. 1–13, 2000. [24] J. P. Jacobs and S. Koziel, “Two-stage framework for efficient Gaussian process modeling of antenna input characteristics,” IEEE Trans. Antennas Propag., vol. 62, no. 2, pp. 706–713, Feb. 2014. [25] S. Koziel, S. Ogurtsov, I. Couckuyt, and T. Dhaene, “Variable-fidelity electromagnetic simulations and co-kriging for accurate modeling of antennas,” IEEE Trans. Antennas Propag., vol. 61, no. 3, pp. 1301–1308, Mar. 2013. [26] C. L. Huang, Y. B. Chen, and C. F. Tasi, “New compact microstrip stacked slotted resonators bandpass filter with transmission zeros using high-permittivity ceramics substrate,” Microw. Opt. Tech. Lett., vol. 50, no. 5, pp. 1377–1379, May 2008. [27] M. K. M. Salleh, G. Pringent, O. Pigaglio, and R. Crampagne, “Quarter-wavelength side-coupled ring resonator for bandpass filters,” IEEE Trans. Microw. Theory Techn., vol. 56, no. 1, pp. 156–162, Jan. 2008. [28] J. R. Lee, J. H. Cho, and S. W. Yun, “New compact bandpass filter resonators with open stub inverter,” IEEE Miusing microstrip crow. Guided Wave Lett., vol. 10, no. 12, pp. 526–527, Dec. 2000. [29] S. Koziel, A. Bekasiewicz, P. Kurgan, and J. W. Bandler, “Expedited multi-objective design optimization of miniaturized microwave structures using physics-based surrogates,” presented at the IEEE MTT-S Int. Microw. Symp., Phoenix, AZ, USA, 2015.

[30] S. Koziel and J. W. Bandler, “Rapid yield estimation and optimization of microwave structures exploiting feature-based statistical analysis,” IEEE Trans. Microw. Theory Techn., vol. 63, no. 1, pp. 107–114, Jan. 2015. Slawomir Koziel (M'03–SM'07) received the M.Sc. and Ph.D. degrees in electronic engineering, the M.Sc. degree in theoretical physics, and the M.S. degree in mathematics from Gdańsk University of Technology, Gdańsk, Poland, in 1995, 2000, 2000, and 2002, respectively, and the Ph.D. degree in mathematics from the University of Gdańsk, Gdańsk, Poland, in 2003. He is currently a Professor with the School of Science and Engineering, Reykjavík University, Reykjavík, Iceland. He is also a Visiting Professor with Gdańsk University of Technology. His research interests include CAD and modeling of microwave circuits, simulation-driven design, surrogate-based optimization, space mapping, circuit theory, analog signal processing, evolutionary computation, and numerical analysis.

John W. Bandler (S'66–M'66–SM'74–F'78–LF'06) studied at Imperial College, London, U.K., and received the B.Sc. (Eng.), Ph.D., and D.Sc.(Eng.) degrees from the University of London, London, U.K., in 1963, 1967, and 1976, respectively. He joined McMaster University, Hamilton, ON, Canada, in 1969, where he is now a Professor Emeritus. He founded Optimization Systems Associates Inc. in 1983 and sold it to Hewlett-Packard in 1997. He is President of Bandler Corporation, Dundas, ON, Canada. Dr. Bandler is a Fellow of several societies, including the Royal Society of Canada and the Canadian Academy of Engineering. In 2004, he was a recipient of the IEEE MTT-S Microwave Application Award. He was a recipient of the IEEE Canada McNaughton Gold Medal in 2012, the Queen Elizabeth II Diamond Jubilee Medal in 2012, the IEEE MTT-S Microwave Career Award in 2013, and the McMaster University's Faculty of Engineering Research Achievement Award in 2014.

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Consistent DC and RF MOSFET Modeling Using an -Parameter Measurement-Based Parameter Extraction Method in the Linear Region Fabián Zárate-Rincón, Student Member, IEEE, Reydezel Torres-Torres, Senior Member, IEEE, and Roberto S. Murphy-Arteaga, Senior Member, IEEE

Abstract—This paper demonstrates the feasibility of using data extracted from experimental -parameters to implement models to accurately represent MOSFET behavior under DC and RF regimes with consistency. For this purpose, a method to extract the MOSFET's drain-to-source conductance, the subthreshold swing, the source/drain resistance, the effective gate length, and the threshold voltage is proposed. The method is based on the determination of the inverse of the channel resistance that is directly related to the previously mentioned parameters. Hence, two-port -parameter measurements of common-source configured RF-MOSFETs with different gate lengths are performed, varying the gate-to-source voltage from the subthreshold region to strong inversion. In order to verify the validity and consistency of the method, excellent correlation of DC and RF models with experimental data is achieved. Index Terms—MOSFET parameters, RF-MOSFET, ters, small-signal model.

-parame-

I. INTRODUCTION

I

N ORDER TO determine MOSFET parameters such as the drain-to-source conductance , the subthreshold swing , the source and drain resistances, the effective gate length , and the threshold voltage , DC measurements are conventionally performed with the device biased in the linear region to guarantee a uniformly inverted channel [1], [2]. Nevertheless, since and present a strong bias dependence due to the LDD (lightly-doped drain) regions [3], experimentally obtaining MOSFET's fundamental parameters from solely DC measurements by using regressions involving experimental data at multiple gate-to-source voltages is very difficult. Moreover, since the channel resistance is inversely proportional to , and become comparable to Manuscript received June 25, 2015; revised September 15, 2015; accepted October 17, 2015. Date of publication November 13, 2015; date of current version December 02, 2015. This work was supported in part by CONACyT, Mexico, under Grant 83774-Y and IMEC, Leuven-Belgium, supplied the test structures. This paper is an expanded version from the IEEE MTT-S International Microwave Symposium, Phoenix, AZ, USA, May 17–22, 2015. The authors are with the Instituto Nacional de Astrofísica, Óptica y Electrónica (INAOE), Department of Electronics, Tonantzintla, Puebla, 72840, Mexico (e-mail: [email protected]; [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2015.2495363

in strong inversion, particularly for nanometer devices. Alternatively, regressions of the experimentally determined total drain-to-source resistance as a function of the gate mask-length can be performed for parameter extraction. However, the variation of the MOSFET parasitic resistances with impedes the accurate determination of , and using data measured from several devices [3]. Furthermore, DC methods commonly underestimate due to the difficulty of completely removing the effect of the parasitic series resistances, implying that methods relying on curve extrapolations involving obtained in this regime will be inaccurate. Due to this fact, it is common to find discrepancies in the values obtained for a particular parameter when using different DC-measurement based approaches. Therefore, the intrinsic properties of a MOSFET have to be obtained by considering its bias-dependent and geometry-dependent characteristics, which will allow obtaining physically based parameters for the implementation of scalable models. This can be achieved by means of RF-measurements [4]. In a previous work on multi-fingered transistors with different gate lengths [5], we presented the correlation of DC extracted parameters to -parameter based methods using the inverse of . In that paper, we describe the noticeable variation of the bias-dependent source and drain resistances for devices with different layouts, which points out the importance of using measurements performed on a single device to correctly determine the corresponding parameters. In fact, using this concept, in [6] the series parasitic resistances obtained from DC and RF data are consistent. However, the dependence of these resistances with voltage is not considered. Using a straightforward small-signal equivalent circuit element extraction method for n-channel RF-MOSFETs with different gate lengths, this work shows how to reproduce DC measurements from RF data in the linear region. This can be correctly achieved from high frequency measurements by performing data regressions involving the experimentally dependent , and at different bias conditions. Even when the methodology is developed and verified here with experiments performed on planar bulk MOSFETs, it can be applied to other types of transistors presenting a similar small-signal representation, such as finFETs [7]. In fact, with the appropriate assumptions, the proposal can be adapted to analyze the impact of less studied effects impacting the performance of diverse advanced devices.

0018-9480 © 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

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Fig. 1. Conceptual depiction of the small-signal equivalent circuit for a . MOSFET at strong inversion and Fig. 2. Micrograph of the device under test for

nm.

II. TEST STRUCTURES AND RF MEASUREMENTS To develop and validate the modeling and parameter extraction methodology proposed in this paper, a group of multi-finger microwave MOSFETs in a common source configuration, with nm, 90 nm, and 120 nm, were fabricated gate lengths in a conventional CMOS process. For these devices, the finger and the number of fingers were fixed at width and 64, respectively. The devices under test (DUTs) present a shallow trench isolation scheme and a ground shield with the purpose of increasing the bulk resistance to avoid undesirable coupling through the substrate. The pads built for probing purposes are made of aluminum and are placed at the top metal layer. The performance of the transistors is improved by using a polysilicon/SiON gate and a guard ring. With the purpose of performing two-port -parameter and DC measurements on the DUTs, vector network analyzer (VNA) and semiconductor device analyzer (SDA) setups were used, respectively. This also requires the use of two pitch ground-signal-ground (GSG) probes for the RF expericurves. ments, and DC probe needles for obtaining Before measuring the -parameters, the VNA setup was calibrated using an off-wafer line-reflect-match (LRM) algorithm to remove the undesirable effects of the cables and probes as well . In addition, as for establishing the reference impedance to a two-step de-embedding procedure using the measurements of on-wafer “open” and “short” dummy structures was carried out to subtract the effect of the pad parasitics from the measurements. Bear in mind, however, that the effect of the extrinsic MOSFET's parasitics (e.g., the multifingered gate electrode resistance) is not removed when applying this de-embedding procedure, which is described, as well as the dummy structures in [8]. These measurements were performed up to 60 GHz under from the subthreshold redifferent bias conditions, varying , gion to strong inversion. This allowed the extraction of and . The considered small-signal equivalent circuit is presented in Fig. 1, where is the gate resistance, is the is the gate-to-source capacitance, is bulk resistance, and are the junction cathe gate-to-drain capacitance, pacitances, and is the drain-to-source capacitance. A microphotograph of one of the DUTs and the experimental setup are presented in Figs. 2 and 3, respectively.

Fig. 3. Experimental setup used to perform RF measurements under different bias conditions, illustrating the vector network analyzer (VNA), the power supply and the probe station.

III. DETERMINATION OF THE CHANNEL RESISTANCE AND THE SERIES PARASITIC RESISTANCES The procedure relies on the extraction of the small-signal from the -parameters under different bias-conditions. This parameter is related to the drain-to-source current and to . There are several works focused on the extraction of it [9]–[13]. In this work, the device is biased from sub-threshold to strong inversion while maintaining . This ensures that the transistor is operating in the linear region, in which the channel can be considered as uniformly inverted. Under this regime, and can be appropriately obtained at different . Bear in mind, however, that the substrate losses in CMOS technologies become significant at high-frequencies, which requires the extraction of the substrate parasitics previous to finding and . Thus, after obtaining these parasitics represented by means of , and , the corresponding effects can be removed from the experimental data. The most suitable bias condition to perform the extraction of the substrate elements is set to and (i.e., the zero-bias cold-FET condition). In this regime, there is no inversion channel under the gate oxide, and thus is not defined and can be neglected in the small-signal equivalent circuit, which allows easily determining and by means of [14]. Consecutively, is approximately equal to . Once obtaining these values, their undesirable effect can be subtracted from the experimental -parameters, collected in the

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continue with the procedure, is transformed into -parameters . Hence, from for transistors operating within the strong inversion regime at , the following relations can be established [15] (3) (4)

Fig. 4. Real part of and , and with the corresponding linear regresnm at and sion (continuous line) of MOSFETs with .

In addition, the imaginary part of written as

-parameters

can be (5) (6)

where

(7)

(8)

Fig. 5. Simulated (continuous line) and measured (symbols) -parameters up and to 60 GHz of MOSFETs with two different gate lengths at .

matrix, by using the following equation that expresses the corrected -parameter matrix (1) is associated with the parallel between where the impedance and that occurs since the source terminal is tied to the bulk terminal, and the superscript is used to define - or -parameters at after removing the substrate parasitic network. Since the inversion channel acts as a conductive shield, becomes much less than the other capacitances and then, it can be neglected. On the other hand, can be expressed as (2) The additional consideration of including and in comparison with our previous work in [5] allows one to achieve better results when frequency becomes higher. Furthermore, it is important to remark that the only bias dependence to be taken into account in the substrate elements due to its noticeable impact on the device's output characteristics is related to the bulkto-source voltage . In fact, as a result of the weak dependence of the rest of the substrate network components on the gate and drain biasing voltages, the removal of , and extracted at the zero-bias FET condition is performed on measurements under different at . In addition, to

In this equation, and are the -parameters at zero-bias. Furthermore, can be obtained using (5) through (8). Then, and can be extracted by means of (3) and (4). Fig. 4 shows the real part of the -parameters and the obtained values for at and . Notice that the plotted -parameters are in the order of ohms, and include the contribution of the channel resistance as well as that of the series resistances. Moreover, can be determined from the linear regression of as a function of at lower frequencies. Hence, when the value for the series resistances is determined, it is possible to assess the corresponding impact on the device's input and output impedances by carrying out a comparison involving these curves. In order to verify the extracted equivalent circuit elements, a comparison between curves obtained from simulations using the model in Fig. 1 and measured -parameters is performed up to 60 GHz for different and , which is presented in Fig. 5 through Fig. 8. This shows the validity of reproducing small-signal data at microwave frequencies using the extracted parameters. It is important to remark the fact that although model-experiment correlation at the higher measured frequencies is acceptable, some data dispersion is observed in the experimental data beyond 50 GHz since the open-short de-embedding procedure exhibits limited accuracy at these frequencies [8]. The procedure previously mentioned can be also used in the case of similar technologies such as finFets since the equivalent circuit does not significantly vary. However, the parasitic capacitances associated with the fin should be taken into account in and as follows [16] (9) (10)

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Fig. 6. Magnitude and phase of simulated (continuous line) and measured up to 60 GHz of MOSFETs with two different gate lengths at (symbols) and .

Fig. 7. Simulated (continuous line) and measured (symbols) -parameters up nm at different and . to 60 GHz of MOSFETs with

where and are intrinsic capacitances, is the external capacitance and is the internal capacitance. IV. EXTRACTION OF MOSFET PARAMETERS As mentioned before, the bias dependence of and complicates the MOSFET's parameter extraction from DC data in short-channel transistors because these parasitic resistances are of the same order of magnitude as when the inversion channel is formed. This happens due to the use of LDD regions, which is also an issue in bulk finFETs [7]. So, due to the corresponding voltage drop across and , which also depends on , when there is a current flowing through the channel, it is not straightforward to accurately model . For this reason, based on the obtained value by using RF measurements, the MOSFET's parameters can be found in an alternative and efficient fashion. An important advantage of the RF procedure in the linear region is that the resistances can be determined at , which avoids the voltage drop across . First, let us define a current that is flowing through the channel when a given intrinsic voltage is applied to it. For this assumption, and were previously removed from the transistor. In the case of the subthreshold swing , the following expression can be used:

Fig. 8. Magnitude and phase of simulated (continuous line) and measured up to 60 GHz of MOSFETs with nm at different (symbols) and .

(11) Fig. 9. Determination of the subthreshold swing.

which can be rewritten as (12) This can be done because is fixed at a given value and thus it does not alter the result. Furthermore, notice that , which allows defining as

of the previously mentioned curves in the subthreshold region. After applying this methodology, the obtained values are 114 mV/dec for nm and 77 mV/dec for nm. On the other hand, can be normalized by in order to find a mathematical relation between this one and as follows:

(13) (14) as a function Fig. 9 shows the curves of the inverse of of in a semi-logarithmic plot for MOSFETs with two different gate lengths. Based on (14), corresponds to the slope

This expression avoids using the total resistance extracted from DC data (i.e., that includes not only the

ZÁRATE-RINCÓN et al.: CONSISTENT DC AND RF MOSFET MODELING USING AN EXTRACTION METHOD

Fig. 10. Linear extrapolation of nm. imum slope point with

Fig. 11. Extraction of

and

against

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at its maxFig. 12. Linear regressions to obtain obtained from RF measurements at

at different .

voltages using

through the SDL method.

characteristics of the channel but also those of the pads, source and drain terminals. Therefore, using (14), which is corrected from the drain and source series parasitics, can be obtained by applying the well-known linear extrapolation method. As shown in Fig. 10, is obtained in this case. For comparison purposes, was also determined using the second derivative of the logarithm (SDL) method [2], obtaining practically the same value for as shown in Fig. 11. This is due to the fact that the SDL method also removes the effect of the MOSFET's series parasitics from the experimental data. Bear in mind, however, that the later approach is highly sensitive to the measurement noise since a second order derivative of experimental data greatly magnifies this noise. Furthermore, one expects that the versus data would present a linear trend to find related to the point in which but this does not happen in practice due to the dependence of and on . This problem can only be solved by subtracting these parasitic resistances from for each value of . In the linear region, can be expressed as (15) as a function of are preThe linear regressions of sented in Fig. 12, showing an excellent agreement with the extracted values. In this way, can be found from the extrapolation to , where . This procedure can be followed for all values of voltage. Once is known, is easily determined from (15). Fig. 13 shows the resulting data for devices with different gate mask length. The considerable variation between the curves in this figure points out the importance of a methodology not relying on regressions varying assuming negligible changes in the parameters for devices with

Fig. 13. versus . presenting different

curves showing the noticeable difference for devices

different geometries. On the other hand, notice that for the considered devices approaches Lg only at when part of the LDD regions under the gate become inverted. Thus, even though different gate lengths are considered in Fig. 13, the trend of the corresponding curves is approximately the same since the doping profile is the same for all the devices. In order to compare the previous results, is also obtained by using the RF capacitance method presented in [4]. For this purpose, the gate-to-channel capacitance related to must be determined as follows: (16) where (17) In Fig. 14, the linear regression of as a function of for different is shown. In a similar way to , can be found from the extrapolation to . Moreover, the comparison between the proposed and RF capacitance methods is presented in Fig. 15 which shows that a good agreement is achieved for values greater than 0.4 V when the inversion channel is completely formed. It is important to mention that the capacitance method is not accurate at lower voltages in which depends not only on intrinsic characteristics but also on extrinsic components. V. VALIDATION OF THE PROPOSED METHODOLOGY In order to prove the validity of the extracted parameters, it is necessary to use an expression that allows reproducing the DC

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Fig. 16. Correlation of (19) with experimental data for different Fig. 14. Linear regressions to obtain obtained from RF measurements at

at different .

.

voltages using

Fig. 17. Inverse of extracted (symbols) and simulated (continuous lines) as a function of for different . Fig. 15. Comparison of RF capacitance method.

versus

obtained from proposed method and

measurements from the obtained from RF data. To accomplish this, a semi-empirical equation can be used [2]:

(18) is the main branch of the Lambert W function, and where are fitting parameters, is the mobility degradation coefficient and is equal to the ideality factor times the thermal voltage . Notice that the previous equation can be used from the subthreshold region to strong inversion. Since is related to , can be found from (18), which is given by

(19) . However, it is more convenient to express with as a function of with the aim of simplifying the representation of since the Lambert W function cannot be expressed in terms of elementary functions. Accordingly, can be determined from

Fig. 18. Derivative of the inverse of extracted (symbols) and simulated (conagainst for different . tinuous lines)

to experimentally obtained can be achieved, as is illustrated in Fig. 16 for different . Due to the non-linear form of (20), the Levenberg-Marquardt algorithm was used for obtaining the corresponding parameters through least squares optimization. The resulting values for these parameters are listed in Table I. Moreover, in order to gain insight from this model implementation, it is more illustrative to plot the inverse of and its derivative obtained from the explicit expression (19). The corresponding curves are respectively plotted in Figs. 17 and 18. On the other hand, it is known that the parasitic resistances can be modeled as follows [17], [18]: (21)

(20)

(22) Based on this expression, it is possible to accurately represent for a wide range of values. In this the extracted fashion, a good agreement between (20) and data corresponding

where nents,

and and

are the bias-independent compoare the bias-dependent components,

ZÁRATE-RINCÓN et al.: CONSISTENT DC AND RF MOSFET MODELING USING AN EXTRACTION METHOD

TABLE I PARAMETERS USED FOR IMPLEMENTING THE (20).

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MODEL GIVEN BY

Fig. 21. Measured (symbols) and simulated (continuous lines) for different at . of

Fig. 19. Linear regressions (continuous lines) of and as a . These regressions are used to analytically obtain function of the parameters in (20) and (21).

as a function

However, it is well known that is higher than for since there is no inversion channel, and thus, . The comparison between measured and simulated can be seen in Fig. 20. After determining from (24), related to can be accurately obtained by using RF data, fixing at a given value that guarantees the operation of the device in the linear region. The corresponding curves of measured and simulated are presented in Fig. 21, achieving a good agreement with experimental data. In this way, it is demonstrated that DC and RF measurements can be correlated through semi-empirical equations, taking into account the bias-dependent component of parasitic resistances. This allows characterizing the transistor with LDD regions, maintaining the coherence between RF and DC data. VI. CONCLUSION

Fig. 20. Measured (symbols) and simulated (continuous lines) for different . tion of

and for

as a func-

and

are fitting parameters. The linear regressions are presented in Fig. 19, from which and are determined for nm. The difference between and is due to the variation of the fabrication process when LDD regions are made and the design of the multi-fingered transistors in which drain and source have different areas. Finally, can be expressed as and

(23)

REFERENCES

or

(24) where is valid for

Model implementations for representing MOSFETs DC and high-frequency small-signal behavior were carried out in the linear operation region directly using -parameter measurements. Excellent model-experiment correlations were achieved at several bias conditions and for devices presenting different geometry. It was shown that MOSFET's parameters such as the drain-to-source conductance, the subthreshold swing, the effective gate length and the threshold voltage can be obtained using RF measured data allowing one to implement DC models in a consistent way. In order to verify this fact, the paper presented in the IMS 2015 was enriched here by showing the feasibility of representing current–voltage curves measured with a semiconductor-device analyzer using parameters obtained by processing experimental -parameters. In addition, thorough comparisons were also performed to point out the advantages of directly implementing DC models using experimental RF data.

. The previous equation , since it is not defined at .

[1] K. Terada, “Reconsideration of effective MOSFET channel length extracted from channel resistance,” in Proc. Int. Microelectron. Test Structures Conf., Udine, Italy, Mar. 2014, pp. 3–7. [2] A. Ortiz, F. J. García, J. Muci, A. Terán, J. J. Liou, and C. S. Ho, “Revisiting MOSFET threshold voltage extraction methods,” Microelectron. Rel., vol. 53, no. 1, pp. 90–104, Jan. 2013. [3] J. Kim, J. Lee, I. Song, Y. Yun, J. D. Lee, B. G. Park, and H. Shin, “Accurate extraction of effective channel length and source/drain series resistance in ultrashort-channel MOSFETs by iteration method,” IEEE Trans. Electron Devices, vol. 55, no. 10, pp. 2779–2784, Oct. 2008.

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[4] S. Lee, “A new RF capacitance method to extract the effective channel length of MOSFET's using -parameters,” in IEDM Tech. Dig., Hong Kong, 2000, pp. 56–59. [5] F. Zárate-Rincón, R. S. Murphy-Arteaga, and R. Torres-Torres, “Correction of DC extracted parameters for microwave MOSFETs based on -parameter measurements,” in Proc. IEEE MTT-S Int. Microw. Symp. Dig., Phoenix, AZ, May 2015, pp. 1–4. [6] J. A. Reynoso-Hernandez, F. E. Rangel-Patiño, and J. Perdomo, “Full RF characterization for extracting the small-signal equivalent circuit in microwave FET's,” IEEE Trans. Microw. Theory Techn., vol. 44, no. 12, pp. 2625–2633, Dec. 1996. [7] P. Magnone, V. Subramanian, B. Parvais, A. Mercha, C. Pace, M. Dehan, S. Decoutere, G. Groeseneken, F. Crupi, and S. Pierro, “Gate voltage and geometry dependence of the series resistance and of the carrier mobility in FinFET devices,” Microelectron. Eng., vol. 85, no. 8, pp. 1728–1731, Aug. 2008. [8] R. Torres, R. S. Murphy, and J. A. Reynoso, “Analytical model and parameter extraction to account for the pad parasitics in RF-CMOS,” IEEE Trans. Electron Devices, vol. 52, no. 7, pp. 1335–1342, Jul. 2005. [9] J. P. Raskin, G. Dambrine, and R. Gillon, “Direct extraction of the equivalent circuit parameters for the small signal SOI MOSFET's,” IEEE Microw. Guided Wave Lett., vol. 7, no. 12, pp. 408–410, Dec. 1997. [10] A. Pascht, M. Grözing, D. Wiegner, and M. Berroth, “Small-signal and temperature noise model for MOSFETs,” IEEE Trans. Microw. Theory Techn., vol. 50, no. 8, pp. 1927–1934, Aug. 2002. [11] G. Crupi, D. M. M.-P. Schreurs, B. Parvais, A. Caddemi, A. Mercha, and S. Decoutere, “Scalable and multibias high frequency modeling of multi fin FETs,” Solid-State Electron., vol. 50, no. 10/11, pp. 1780–1786, Nov./Dec. 2006. [12] J. Wood, D. Lamey, D. C. M. Guyonnet, D. Bridges, N. Monsauret, and P. H. Aaen, “An extrinsic component parameter extraction method for high power RF LDMOS transistors,” in Proc. IEEE MTT-S Int. Microw. Symp. Dig., Atlanta, GA, Jun. 2008, pp. 607–610. [13] F. Zarate, G. A. Alvarez, R. Torres, R. S. Murphy, and S. Decoutere, “Characterization of RF-MOSFETs in common-source configuration at different source-to-bulk voltages from -parameters,” IEEE Trans. Electron Devices, vol. 60, no. 8, pp. 2450–2456, Aug. 2013. [14] R. Torres and R. S. Murphy, “Straightforward determination of smallsignal model parameters for bulk RF-MOSFETs,” in Proc. IEEE Int. Caracas Conf. on Devices, Circuits and Syst., Dominican Republic, Nov. 2004, pp. 14–18. [15] D. Schreurs, Y. Baeyens, B. Nawelaers, W. De Raedt, M. Van Hove, and M. Van Rossum, “ -parameter measurement based quasistatic large-signal cold HEMT model for resistive mixer design,” Int. J. Microw. Millimetre-Wave Comp.-Aided Eng., vol. 6, no. 4, pp. 250–258, Jul. 1996. [16] J. Alvarado, J. C. Tinoco, V. Kilchytska, D. Flandre, J. Raskin, A. Cerdeira, and E. Contreras, “Compact small-signal model for RF FinFETs,” in Proc. Int. Caribbean Conf. on Devices, Circuts and Syst., Playa del Carmen, Mar. 2012, pp. 1–4. [17] E. Torres, R. Torres, G. Valdovinos, and E. Gutiérrez, “A method to determine the gate bias-dependent and gate bias-independent components of MOSFET series resistance from -parameters,” IEEE Trans. Electron Devices, vol. 53, no. 3, pp. 571–573, Mar. 2006.

[18] K. Y. Lim and X. Zhou, “A physically based semi-empirical series resistance model for deep-submicron MOSFET I-V modeling,” IEEE Trans. Electron Devices, vol. 47, no. 6, pp. 1300–1302, Jun. 2000.

Fabián Zárate Rincón (S’14) received the B.S. degree in electronic engineering from the University of Quindio, Armenia, Colombia, in 2006, and the M.S. degree in electronics from the National Institute for Astrophysics, Optics and Electronics (INAOE), Puebla, Mexico, in 2012. He is currently pursuing the Ph.D. degree in electronics at INAOE. From 2006 to 2010, he was a Research Assistant with the University of Quindio. His research interest includes the study of semiconductor devices operating at microwave frequencies.

Reydezel Torres-Torres (S'01–M'06–SM'15) received the Ph.D. degree from from the National Institute for Astrophysics, Optics and Electronics (INAOE), Puebla, Mexico. He is a senior researcher in the Electronics Department of INAOE in Mexico. He has authored more than 70 journal and conference papers and directed six Ph.D. and 15 M.S. theses, all in experimental high-frequency characterization and modeling of materials, interconnects, and devices for microwave applications and has worked for Intel Laboratories in Mexico and IMEC in Belgium.

Roberto S. Murphy-Arteaga (M'92–SM'02) received the B.Sc. degree in physics from St. John's University, Collegeville, MN, USA, and the M.Sc. and Ph.D. degrees from the National Institute for Research on Astrophysics, Optics and Electronics (INAOE), Tonantzintla, Puebla, México. He has taught graduate courses at the INAOE since 1988, totaling over 100 taught undergrad and graduate courses. He has given over 80 talks at scientific conferences and directed seven Ph.D. theses, 13 M.Sc. and 2 B.Sc. theses. He has published more than 120 articles in scientific journals, conference proceedings and newspapers, and is the author of a text book on electromagnetic theory. He is currently a Senior Researcher with the Microelectronics Laboratory, INAOE, and the Director of Research of the INAOE. His research interests are the physics, modeling and characterization of the MOS Transistor and passive components for high frequency applications, especially for CMOS wireless circuits, and antenna design. He is the President of ISTEC, a member of the Mexican Academy of Sciences, and a member of the Mexican National System of Researchers (SNI).

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Bayesian Optimization for Broadband High-Efficiency Power Amplifier Designs Peng Chen, Student Member, IEEE, Brian M. Merrick, Member, IEEE, and Thomas J. Brazil, Fellow, IEEE

Abstract—This paper proposes a novel, optimization-oriented strategy for the design of broadband, high-efficiency power amplifiers (PAs) using Bayesian optimization (BO). The optimization algorithm optimizes the drain waveforms by maximizing the fundamental output power while minimizing the harmonic and dissipated components. The optimization process is automated using simulation software. Circuit-based BO and electromagnetic-based (EM-based) BO are applied to design 10 and 30 W PAs. The 10 W PA designed using circuit-based BO achieves a drain efficiency higher than 60% with output power greater than 39.8 dBm from 1.5 to 2.5 GHz, while the 30 W PA designed using EM-based BO offers a drain efficiency higher than 57% with output power greater than 43.8 dBm across the band. Upon comparison of results, it is revealed that the proposed strategy outperforms a commercial electronic design automation (EDA) software's built-in optimizer, thus demonstrating that the EM-based BO is well-suited to the challenge of high power designs. Index Terms—Bayesian optimization, broadband, drain waveforms, Gaussian process, high efficiency, power amplifier (PA).

I. INTRODUCTION

M

ODERN wireless communication systems, which have high transmission rates and spectral efficiency, are creating a growing demand for broadband high-efficiency power amplifiers (PAs). A series of high-efficiency PA modes, such as Class-F and Class-J, have been developed over the past few decades [1]–[5]. These new PA modes have received widespread interest since they allow designers to analyze PA performance from the point of view of waveform engineering [6], [7]. The non-overlapping of the drain voltage and drain current waveforms has been recognized as a key criterion in achieving high efficiency in PA designs. Based on this concept, continuous modes have been studied in order to give greater flexibility to the drain waveforms for wideband designs [8]–[12]. In practical PA designs, the desired waveforms are often achieved through tuning the harmonic impedances presented by the matching networks. In order to realize a broadband design, the matching networks require multiple

Manuscript received July 01, 2015; revised September 10, 2015; accepted October 17, 2015. Date of publication November 11, 2015; date of current version December 02, 2015. This work was supported by a research grant from Science Foundation Ireland (SFI) under its Investigators Programme 2012, Grant 12/IA/1267. This paper is an expanded version from the IEEE MTT-S International Microwave Symposium, Phoenix, AZ, USA, May 17–22, 2015. The authors are with the School of Electrical and Electronic Engineering, University College Dublin, Dublin 4, Ireland (e-mail: [email protected]; [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2015.2495360

sections of transmission lines, generally greater than 10 in total. This tuning work places a great demand on design experience, especially when the efficiency needs to remain at a high level across the band. The broadband matching problem can be regarded as a high-dimensional optimization problem. In view of this, it is helpful to apply an optimization-oriented technique to tackle this problem. Although commercial EDA software packages, such as ADS, AWR, etc., are quite useful in microwave circuit optimization, their built-in optimizers may fail to find a satisfactory solution when the dimension of variables is very high or the optimization goals are stringent. To overcome this limitation, it is necessary to develop modifiable, intelligent algorithms tailored to specific optimization tasks. To date, a number of optimization algorithms, such as space mapping [13], [14], artificial neural networks [15]–[17], and shape-preserving response [18], have been successfully exploited to the applications of filters, couplers, antennas, and transistor models. In the field of intelligent algorithms, Bayesian optimization (BO) is an example of a supervised learning algorithm, used for the global optimization of an expensive objective function in a high-dimensional space [19], [20]. It is particularly useful when the objective function is non-convex and multi-modal, especially when closed-form expressions for the objective function or its derivatives do not exist. Since the objective function is an unknown “black-box,” BO typically assumes that the function is sampled from Gaussian processes (GP) [21]. Due to its good properties of flexibility and tractability, BO is able to capture the characteristics of the unknown function by building a GP model based on the training data. After that, BO exploits an acquisition function to determine the next point to evaluate [22]. By repeating these steps, BO has the ability to achieve the global optimum value for the unknown objective function. In [23], we applied Gaussian processes regression (GPR) to optimize the harmonic impedances for a continuous Class-F power amplifier design. Compared to [23], this paper expands GPR into the framework of BO, and applies BO to optimize the drain waveforms of an active circuit rather than of a passive circuit. In addition, the dimension of variables is increased up to 28, which is double that of [23]. Moreover, circuit simulation and electromagnetic (EM) simulation-based optimization are both implemented to design 10 and 30 W broadband high-efficiency PAs. In this paper, Section II first discusses the high-efficiency PA theory which serves as the objective function for the PA design optimization. Section III is devoted to describing the framework of Bayesian optimization, which is composed of Bayesian inference, modeling, prediction, and acquisition

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100% efficiency requires (3), (4) to satisfy the following condition [2]:

(5)

III. BAYESIAN OPTIMIZATION

Fig. 1. Power conversion in a PA system.

A. Bayesian Inference functions. Section IV describes the proposed automatic optimization-oriented strategy for PA design. Section V validates the proposed method through the presentation of 10 and 30 W broadband high-efficiency PA designs. In this section, the algorithm convergence and measured results are shown to demonstrate that the proposed method is well-suited to broadband high-efficiency PA designs. Comparison designs using the ADS simulated annealing optimizer are also provided. Finally, in Section VI, conclusions are given. II. HIGH-EFFICIENCY PA THEORY

In this paper, the problem of interest is to find the best design parameters for the matching networks such that the PA achieves high efficiency. The optimization problem can be viewed as a probability event , where denotes the design parameters and denotes the observed PA efficiency. Suppose that the “black-box” function is defined as (6) where is a weighting vector and is a feature space mapping. Given a set of training design parameters, the accumulated observations are . Let's define as the prior probability which represents the belief about prior to the observation of , and as the likelihood function which expresses how probable high efficiency is given the function . According to Bayes' theorem, the posterior probability for the function after observing takes the form

The high efficiency PA modes, for instance the Class, achieve high efficiency due to the non-overlapping voltage and current waveforms present at the internal drain. It is of no doubt that waveform engineering has become a critical guiding principle in high-efficiency PA designs. In order to fully understand how the drain voltage and drain current significantly affect the efficiency, it is necessary to analyze the power conversion in a PA system. In Fig. 1, the PA receives power both from the input signal and the DC supply. Since the input power is assumed to be totally dissipated in the input network and the transistor, it does not contribute directly to the output power. In (1), the DC power supplied to the device exits the device in three parts: in the form of heat dissipated in the active devices, , as a radio frequency (RF) signal at the fundamental and RF signals at the harmonics . As a consequence, the drain efficiency is calculated by (2) and and are defined in (3), (4)

indicates the probability to evaluate the where weighting vector after the observations. Although the integrated term (8) cannot be expressed in a closed-form, it is a normalization constant. Thus, the posterior probability is proportional to the likelihood of given multiplied by the prior probability of

(1)

(9)

(2)

In practice, the maximum a posteriori (MAP) metric is a common approximation used to estimate (9), and is written in the following form [19]:

(7) (8)

(3) (10) (4) B. Modeling and Prediction and represent the drain voltage and drain current where at the th harmonic with intersection angle . It was pointed out by Colantonio that a PA with zero dissipated power, i.e., non-overlapping drain waveforms, may only have an efficiency of approximately 80%, depending on the waveforms. The ideal

1) “Black-Box” Modeling: As discussed before, a “black-box” function which represents the PA system needs to be found for the optimization design. The weighting vector is determined by fitting (6) to the training data. When training the model, an error term is introduced to measure the misfit

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Fig. 2. Exponential family distribution.

Fig. 3. GP model with training data.

between the function and the training data. One simple error function, which is widely applied [19], is given by

Substituting (12) into (13) and (14), the negative log likelihood function for (13) and (14) are derived as

(11) is a penalty term used to control the over-fitting where phenomenon, called regularization, and governs the balance between the sum-of-squares error term and the regularization term. As can be seen from (10), the probability distribution plays a critical role in Bayesian optimization. There are many distributions which can be used to form building blocks for complex models, such as the beta distribution, the Dirichlet distribution, and the exponential family distribution [19]. Fig. 2 describes the variation in correlation with the distance between two points for the exponential family distribution. The correlation decreases when two points move far away, while it increases when they are close. In the case of , it is called a Gaussian distribution, which has a smoothness correlation over different points. The Gaussian distribution is written in the following form:

(15)

(16) Similarly, taking the negative logarithm of (10) and combining with (15) and (16), the maximum of the posterior probability is equal to the minimum of (17)

Due to these good properties, a Gaussian distribution is wellsuited for the distribution of continuous variables in a high-dimensional space [20]. Assuming that the observed high efficiency, , has a Gaussian distribution with a mean equal to , given the design parameters, , then the likelihood function of (10) is expressed as

Comparing (11) with (17), we can see that maximizing the posterior probability is equivalent to minimizing the error function with the regularization parameter . As a consequence, an accurate model for the PA system can be constructed based on the training data. This regression method is known as Gaussian processes regression (GPR), fitting the training data with a mean and a standard deviation , as depicted in Fig. 3. 2) Prediction from GP Model: A Gaussian process is a probability distribution over the function such that the values of evaluated at different points jointly have a Gaussian distribution. Suppose that can be separated into two joint Gaussian distributed subsets, and

(13)

(18)

(12)

where is the inverse variance of the Gaussian distribution. The prior probability is commonly selected as a Gaussian distribution with a mean equal to 0 and an inverse variance of , and can be written as (14)

(19) (20) where (19) and (20) represent the corresponding partitions of the mean vector and the covariance matrix , respectively.

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In Bayesian optimization, there are four commonly-used acquisition functions: probability of improvement (PI), expected improvement (EI), upper confidence bound, and entropy search [24]–[27]. In this paper, the first two acquisition functions are applied in order to search for the optimal values for the design parameters. 1) Probability of Improvement: PI evaluates at the point where the improvement will most likely occur [24]. However, PI focuses on local optimization such that the points have high uncertainty. Given the current maximum point , PI is calculated by

TABLE I SUMMARY OF BAYESIAN OPTIMIZATION

The conditional distribution lowing mean and covariance:

is expressed with the fol(30) (21) (22)

When applying the GP model for new predictions, it is necessary to add a noise term which serves as the unmatched error. Here, the function (6) is modified to the following form: (23) where is specified by a mean function and a kernel function , such that , and the noise also has a Gaussian distribution . According to the GP properties, the values from the observation will have a multivariate Gaussian distribution , with the kernel matrix given by .. .

..

.

.. .

(24)

where the kernel function denotes the covariance matrix between and . The new value , which is predicted from the GP model at the new point has a joint Gaussian distribution with (25)

where represents the current best value, and are calculated from (27), (28), and is the normal cumulative distribution function. 2) Expected Improvement (EI): EI has been shown to be an efficient criterion for finding the global optimum in many “black-box” functions [25]. It allows us to make a tradeoff between the local optimization and the global search. This acquisition can be computed analytically as if if (31) (32) where denotes the probability density function. In (31), the first term chooses the points where the mean is high while the second term targets the points where the variance is large. Considering constraint conditions for the objective function, PI can be used to calculate the probability of being greater than the constraint limit [24]. In this situation, one model is built for the objective function; the other is for the constraint function. Since the two models are independent, the new point in (29) is obtained by maximizing (33)

(26) Referring to (21) and (22), the predicted data the GP model is specified as a Gaussian distribution

from (27) (28)

C. Acquisition Functions for Searching

Table I summarizes the algorithm steps of Bayesian optimization. It is worth noting that two major choices significantly affect the global search of Bayesian optimization. The first is selecting an appropriate GP distribution and a kernel function for the modeling; the second is choosing an acquisition function to guide the search. IV. OPTIMIZATION-ORIENTED STRATEGY

After building the GP model, a non-trivial task is how to search for the next point of interest from the constructed GP model. Acquisition functions are exploited to determine where to next evaluate the GP model. Since our goal is to find a set of design parameters such that high efficiency is obtained, the objective function is defined as (29)

The automatic optimization strategy for the PA designs is accomplished by combining ADS with MATLAB or R. As is shown in Fig. 4, ADS is used to run the PA simulation so that training data is obtained. MATLAB or R is responsible for the Bayesian optimization since there are many related codes written in these two programming languages, which are available for public use. MATLAB or R starts the Bayesian optimization when the training data is exported from ADS.

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Fig. 4. Automatic optimization strategy.

Fig. 5. Matching network topology.

Fig. 6. Optimization process for the PA designs.

Similarly, ADS activates the simulation as soon as it receives new design parameters. Finally, the optimization strategy outputs the best design parameters to the users after the iterations finish. In this paper, the design parameters are the widths and the lengths of the matching network transmission lines. The simplified real frequency technique (SRFT) is exploited to determine the matching network topology and the initial guess for the design parameters [28], [29]. The S-parameters of the transistor are used as the inputs to the SRFT in order to generate this initial guess. As shown in Fig. 5, there are six steppedimpedance transmission lines and a bias line for both the input and output matching networks, resulting in 28 design parameters in total. The output targets in the optimization are the fundamental output power, and the harmonic and dissipated components described in Section II. It is important to note that it is the voltage and current waveforms at the current-generator plane that we are interested in optimizing, rather than the waveforms

Fig. 7. Fabricated 10 W PA designs. (a) EM-based BO with 50 training data points. (b) Circuit-based BO with 50 training data points. (c) Circuit-based BO with 200 training data points.

seen at the package plane. The objective function is defined as the root mean square (RMS) of the fundamental output power across the band (34) where denotes the number of the frequency points. The constraint function is the sum of the RMS of the harmonic and dissipated power (35) Harmonics greater than the fifth are neglected in this paper due to their minor impact upon efficiency improvement. As per (2)

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Fig. 8. Convergence for the 10 W PA designs.

Fig. 9. Simulated intrinsic drain waveforms at 2 GHz for the 10 W PA design using EM-based BO.

and (5), this paper optimizes the drain waveforms by maximizing (34) while minimizing (35), guaranteeing that high efficiency is achieved in a wide band. Since the 28-dimensional space is very high, it requires a vast number of training data to capture the characteristics of the PA system, leading to quite expensive computation during the optimization. In order to balance the model accuracy and the computational time, this paper uses sub-models to search for design parameters instead of using the whole model. A sub-model is constructed around the current point, representing a portion of the whole model. After finding a better point, a new sub-model is constructed and is then applied to predict the next point. In this way, the sub-models are able to find the optimum point for the whole model. However, it should be pointed out that there is a risk of the optimization converging on a local minimum, rather than the desired global minimum. Fig. 6 further describes the optimization process more specifically for the PA designs. First, we set the iteration number and apply the SRFT to obtain the initial guess for the design parameters. The sampling points are created within a 10% range of the current point using the Latin hypercube sampling technique [30]. By sweeping the sampling design parameters, ADS runs the simulation and exports the RMS of those in (34) and (35). With the available training data, the optimization algorithm builds the GP sub-models and predicts new design param-

Fig. 10. Compared measurements for 10 W PA designs. (a) Drain efficiency. (b) Output power. (c) Gain.

eters by maximizing the acquisition function in (33) using the DIRECT algorithm [31]. For the sake of good convergence, the optimization algorithm rejects predicted points which worsen performance and keeps the current best one. In order to avoid sub-optimal local minima in the optimization, the random seed is changed such that the sampling points and the sub-models are renewed at each iteration. The optimization algorithm repeats the above steps and finally outputs the optimal design parameters when the iterations are terminated. In this way, we apply Bayesian optimization to optimize a PA design automatically.

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Fig. 11. Measurement setup.

V. PRACTICAL PA OPTIMIZATION A. Broadband 10 W PA Design In order to demonstrate the validity of this design approach, we optimized the designs of broadband high-efficiency 10 W PA using circuit- and EM-based Bayesian optimization, respectively. Cree CGH40010F Gallium Nitride (GaN) high-electron mobility transistors (HEMTs) were used for the designs. In the circuit-based BO, the sub-models were built with the training data from circuit simulation. Similarly, in the EM-based BO, EM simulation supplied the training data for building the submodels, which are more accurate than those of the circuit simulation. Considering that the EM simulation requires expensive computational time, we used 50 training data points to build the GP sub-models in the EM-based BO. In order to test the sensitivity of the optimization to the number of training data, 50 and 200 training data points were used in the circuit-based BO. For comparison, the ADS simulated annealing optimizer with 1000 iterations was employed to optimize the PAs while keeping the same variable settings and objective functions. The transistor model is a critical part of the “black-box” modeling, affecting the deviation between the simulated results and measurements to a great extent. Clearly, if the model is not of sufficient accuracy, then the optimization process will not result in good performance upon measurement. Cree's dynamic load-line model has been shown in a large number of papers to be of good accuracy [10], [11], and, hence, was used for the designs. Additionally, the model in question gives access to the intrinsic current and voltage waveforms, as desired. The PA designs were implemented on Taconic RF35 substrate with 3.5 and a thickness of 1.52 mm. The iteration number was set to 20 and the initial design parameters of the matching networks of Fig. 5 were obtained using the SRFT, , where [5.75, 1.63, 15.30, 2.21, 27.91, 26.15, 2.09, 11.34, 1.57, 11.95, 1.83, 5.78, 1, 1] mm, and [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 20, 20] mm. The bounded range for the width in the matching networks was 0.7 mm 30 mm, corresponding to the characteristic impedance within 9 105 on the RF35 board. Following the optimization process shown in Fig. 6, the 10 W PAs were optimized from 1.5 to 2.5 GHz, with a step of 50 MHz. The optimization process ran on a computer featuring an Intel Core i7-3770 CPU @ 3.40 GHz with 16.0 GB RAM. After 20 iterations, the EM-based BO outputted the optimized parameters, =[5.07, 1.51, 15.38, 2.79, 22.69, 26.12, 2.16,

Fig. 12. Fabricated 30 W PA designs. (a) EM-based BO with 50 training data points. (b) Circuit-based BO with 50 training data points. (c) Circuit-based BO with 200 training data points.

11.19, 1.60, 10.63, 1.43, 5.96, 1.28, 1.11] mm, and [5.20, 5.29, 5.47, 4.42, 5.76, 6.24, 3.54, 7.90, 4.31, 4.03, 5.66, 4.94, 18.54, 15.46] mm. In the circuit-based BO with 50 training data points, the optimized design parameters were [4.77, 1.57, 18.24, 2.54, 28.58, 27.92, 2.19, 13.08, 1.46, 13.86, 1.42, 6.62, 1.41, 1.23] mm, and [5.26, 5.55, 5.68, 3.41, 7.67, 6.33, 4.25, 7.89, 4.98, 4.02, 5.43, 4.67, 18.89, 19.22] mm. As for the circuit-based BO with 200 training data points, we got the optimized parameters, [5.01, 1.60, 20.14, 3.02, 26.05, 28.62, 2.10, 12.62, 1.57, 12.81, 1.64, 4.97, 1.32, 1.03] mm, and [4.82, 4.55, 5.10, 2.96, 7.05, 7.16, 4.07, 9.80, 5.88, 4.46, 5.09, 5.37, 22, 21.04] mm. Fig. 7 shows the fabricated PAs which were optimized using the three approaches described above. The PAs were biased at a drain voltage of 28 V with a quiescent drain current of 70 mA. The convergence of the proposed optimization algorithm is shown in terms of a normalized error in Fig. 8. The

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Fig. 13. Convergence for the 30 W PA designs.

normalized errors drop considerably over the 20 iterations, indicating that the algorithm converges very quickly. It was observed that the normalized error reduced when the training data number was increased from 50 to 200. Therefore, increasing the training data number is helpful in obtaining better design parameters from accurate models. The simulated drain waveforms of the PA using EM-based BO, depicted in Fig. 9, show only a small amount of overlap, suggesting high performance. Fig. 10 shows the measurement results of the optimized PAs, together with comparison designs created using the SRFT and the ADS simulated annealing optimizer. These results were obtained with the measurement setup shown in Fig. 11, when an available input power of 28 dBm was provided across the band. The optimized PAs all showed large improvements compared with the initial design using the SRFT. The optimized PA using EM-based BO delivered drain efficiency above 60.0% from 1.5 to 2.5 GHz, with output power greater than 39.9 dBm and gain larger than 11.8 dB. The PA using circuit-based BO with 200 training data points showed better performance than that using 50 training data, corresponding to the lower normalized error of Fig. 8. It achieved greater than 60.8% drain efficiency over the entire band, with output power greater than 39.8 dBm and gain larger than 11.4 dBm. Although the ADS simulated annealing optimizer achieved a drain efficiency of greater than 61.4% over the band, the output power decreased to 39.1 dBm, with gain dropping down to 11.0 dB. It should be noted that the EM-based design provided superior output power and gain when compared with the other designs, particularly at the upper end of the frequency scale.

Fig. 14. Compared measurements for 30 W PA designs. (a) Drain efficiency. (b) Output power. (c) Gain.

B. Broadband 30 W PA Design We also applied the above approaches to optimize the designs of 30 W PA operating from 1.5 to 2.5 GHz. Cree CGHV40030F GaN HEMTs were used for the designs. Again, the Cree's dynamic load-line model was utilized in the ADS simulation. The SRFT provided the initial design parameters, [7.01, 1.44, 20.79, 3.07, 26.86, 30, 1.66, 20.29, 4.01, 17.61, 3.08, 3.66, 0.8, 0.8] mm, and [7, 7, 7, 7, 7, 7, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 15, 20] mm. As shown in Fig. 12, the first PA using EM-based BO had the dimensions of [5.51, 1.84, 11.71, 1.50, 19.14,

24.64, 1.67, 17.57, 3.50, 18.40, 2.63, 6.51, 1.03, 1.17] mm, and [3.37, 3.92, 5.65, 3.20, 11.79, 5.20, 3.34, 8.59, 8.92, 5.43, 8.28, 8.15, 20.21, 20.49] mm. The second PA using circuit-based BO with 50 training data points had the optimized parameters, [8.33, 1.59, 17.11, 2.61, 27.13, 28.98, 1.55, 19.85, 3.62, 18.30, 2.85, 5.90, 1.04, 1.22] mm, and [6.82, 7.41, 5.77, 6.60, 8.09, 6.96, 4.14, 7.60, 7.8, 5.77, 7.86, 7.12, 18.68, 15.59] mm. As for the last design using circuit-based BO with 200 training data points, the optimized parameters were,

CHEN et al.: BAYESIAN OPTIMIZATION FOR BROADBAND HIGH-EFFICIENCY POWER AMPLIFIER DESIGNS

Fig. 15. Simulated intrinsic drain waveforms at 2 GHz for the 30 W PA design using EM-based BO.

TABLE II COMPARISONS OF THE 30 W PA DESIGNS

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as minimize the harmonic and dissipated components, resulting in similar non-overlapping drain waveforms. The optimization algorithm builds the GP sub-models for the PA and utilizes an acquisition function to predict design parameters with which high efficiency is achieved. The 10 and 30 W PA designs were optimized using circuit-based BO and EM circuit-based BO. Measured results show that the 10 W PA using circuit-based BO with 200 training data points obtained better than 60% drain efficiency and greater than 39.8 dBm output power from 1.5 to 2.5 GHz. In the 30 W PA designs, EM-based BO performed much better than circuit-based BO, due to the higher power designs being more sensitive to simulation accuracy. The 30 W PA using EM-based BO operated at a drain efficiency of greater than 57%, with output power greater than 43.8 dBm across the band. Comparison results show that the proposed strategy greatly surpasses the ADS simulated annealing optimizer in terms of the gain and output power achieved across the band, with comparable efficiency shown with both methods. Moreover, it should be stressed that the performances of the optimized PAs also rely on the accuracy of the transistor models applied in the ADS simulation. ACKNOWLEDGMENT

The measurements are compared from 1.5 to 2.5 GHz. The cost time is the approximate average time for each optimization iteration.

[7.54, 1.58, 17.76, 3.70, 27.06, 28.52, 1.91, 19.93, 3.56, 16.64, 2.91, 5.75, 0.91, 1.26] mm, and [7.22, 6.04, 6.0, 6.56, 9.23, 6.17, 4.58, 7.86, 7.60, 5.39, 6.35, 5.45, 17.33, 17.33] mm. The algorithm convergence of the 30 W PA designs are shown in Fig. 13. The 30 W PAs were biased at a drain voltage of 50 V with a quiescent drain current of 95 mA, and were measured with 32 dBm available input power. As shown in Fig. 14, the optimized PA using EM-based BO obtained drain efficiency greater than 57.0% across the band, with output power greater than 43.8 dBm and gain larger than 11.6 dBm. As high power PAs have a smaller range of ideal harmonic impedances, circuit-based optimization designs show worse performances. The PA using the circuit-based BO with 200 training data gave a minimum drain efficiency of 51.5%, which was still better than that of using the ADS simulated annealing optimizer. The EM-based PA again showed significantly greater output power and gain than the other designs. The non-overlapping drain waveforms for the 30 W PA design using EM-based BO are shown in Fig. 15. Table II gives the comparison of the 30 W PAs using the above different methods. From the compared results, we can see that EM-based BO is more preferable than circuit-based BO in high power designs although it requires expensive computational time. VI. CONCLUSION A Bayesian optimization-based method is presented in this paper to design broadband high-frequency power amplifiers from 1.5 to 2.5 GHz. This method is implemented automatically by combining ADS with MATLAB or R programming. Its aim is to maximize the fundamental output power, as well

The authors would like to acknowledge the support of Cree, Inc. REFERENCES [1] S. C. Cripps, RF Power Amplifier for Wireless Communications, 2nd ed. Boston, MA, USA: Artech House, 2006. [2] P. Colantonio, F. Giannini, and E. Limiti, High Efficiency RF and Microwave Solid State Power Amplifiers. New York, NY, USA: Wiley, 2009. [3] P. Wright, J. Lees, J. Benedikt, P. J. Tasker, and S. C. Cripps, “A methodology for realizing high efficiency Class-J in a linear and broadband PA,” IEEE Trans. Microw. Theory Techn., vol. 57, no. 12, pp. 3196–3204, Dec. 2009. [4] S. C. Cripps, P. J. Tasker, A. L. Clarke, J. Lees, and J. Benedikt, “On the continuity of high efficiency modes in linear RF power amplifiers,” IEEE Microw. Wirel. Compon. Lett., vol. 19, no. 10, pp. 665–667, Oct. 2009. [5] M. Eron, B. Kim, F. Raab, R. Caverly, and J. Staudinger, “The head of the class,” IEEE Microw. Mag., vol. 12, no. 7, pp. S16–S33, Dec. 2011. [6] P. J. Tasker and J. Benedikt, “Waveform inspired models and the harmonic balance emulator,” IEEE Microw. Mag., vol. 12, no. 2, pp. 38–54, Apr. 2011. [7] Y. Y. Woo, Y. Yang, and B. Kim, “Analysis and experiments for high efficiency Class-F and inverse Class-F power amplifiers,” IEEE Trans. Microw. Theory Techn., vol. 54, no. 5, pp. 1969–1974, May 2006. [8] V. Carrubba, A. L. Clarke, M. Akmal, J. Lees, J. Benedikt, P. J. Tasker, and S. C. Cripps, “On the extension of the continuous class-F mode power amplifier,” IEEE Trans. Microw. Theory Techn., vol. 59, no. 5, pp. 1294–1303, May 2011. [9] V. Carrubba, A. L. Clarke, M. Akmal, J. Lees, J. Benedikt, S. C. Cripps, and P. J. Tasker, “The continuous inverse class-F mode power amplifier with resistive second-harmonic impedance,” IEEE Trans. Microw. Theory Techn., vol. 60, no. 6, pp. 1928–1936, Jun. 2012. [10] N. Tuffy, L. Guan, A. Zhu, and T. J. Brazil, “A simplified broadband design methodology for linearized high-efficiency continuous Class-F power amplifiers,” IEEE Trans. Microw. Theory Techn., vol. 60, no. 6, pp. 1952–1963, Jun. 2012. [11] K. Chen and D. Peroulis, “Design of broadband highly efficient harmonic-tuned power amplifier using in-band continuous Classmode transferring,” IEEE Trans. Microw. Theory Techn., vol. 60, no. 12, pp. 4107–4116, Dec. 2012. [12] S. Preis, D. Gruner, and G. Boeck, “Investigation of class-B/J continuous modes in broadband GaN power amplifiers,” in IEEE MTT-S Int. Microw. Symp. Dig., 2012, pp. 1–3.

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[13] J. W. Bandler, Q. S. Cheng, S. A. Dakroury, A. S. Mohamed, M. H. Bakr, K. Madsen, and J. Søndergaard, “Space mapping: The state of the art,” IEEE Trans. Microw. Theory Techn., vol. 52, no. 1, pp. 337–361, Jan. 2004. [14] S. Koziel, J. W. Bandler, and K. Madsen, “A space mapping framework for engineering optimization: Theory and implementation,” IEEE Trans. Microw. Theory Techn., vol. 54, no. 10, pp. 3721–3730, Oct. 2006. [15] Q. J. Zhang, K. C. Gupta, and V. K. Devabhaktuni, “Artificial neural networks for RF and microwave design—From theory to practice,” IEEE Trans. Microw. Theory Techn., vol. 51, no. 4, pp. 1339–1350, Apr. 2003. [16] J. E. Rayas-Sánchez, “EM-based optimization of microwave circuits using artificial neural networks: The state-of-the-art,” IEEE Trans. Microw. Theory Techn., vol. 52, no. 1, pp. 420–435, Jan. 2004. [17] L. Zhang, K. Bo, Q.-J. Zhang, and J. Wood, “Statistical space mapping approach for large-signal nonlinear device modeling,” in 36th Eur. Microw. Conf. Dig., Manchester, U.K., Sep. 2006, pp. 676–679. [18] S. Koziel, “Shape-preserving response prediction for microwave design optimization,” IEEE Trans. Microw. Theory Techn., vol. 58, no. 11, pp. 2829–2837, Nov. 2010. [19] C. M. Bishop, Pattern Recognition and Machine Learning. New York, NY, USA: Springer, Aug. 2006. [20] E. Brochu, V. M. Cora, and N. de Freitas, “A tutorial on Bayesian optimization of expensive cost functions, with application to active user modeling and hierarchical reinforcement learning,” Univ. British Columbia, Vancouver, BC, Canada, Tech. Rep., 2010. [21] C. E. Rasmussen and C. K. I. Williams, Gaussian Processes for Machine Learning. Cambridge, MA, USA: MIT Press, 2006. [22] J. Snoek, H. Larochelle, and R. P. Adams, “Practical Bayesian optimization of machine learning algorithms,” presented at the Neural Inform. Process. Syst., Lake Tahoe, CA, USA, 2012. [23] P. Chen and T. J. Brazil, “Gaussian processes regression for optimizing harmonic impedance trajectories in continuous Class-F power amplifier design,” in IEEE MTT-S Int. Microw. Symp. Dig., May 2015, pp. 1–3. [24] A. I. J. Forrester and A. J. Keane, “Recent advances in surrogate-based optimization,” Progr. Aerosp. Sci., vol. 45, pp. 50–79, 2009. [25] D. R. Jones, M. Schonlau, and W. J. Welch, “Efficient global optimization of expensive black box functions,” J. Global Optimization, vol. 13, pp. 455–492, 1998. [26] N. Srinivas, A. Krause, S. Kakade, and M. Seeger, “Gaussian process optimization in the bandit setting: No regret and experimental design,” presented at the Int. Conf. Machine Learning, Haifa, Israel, 2010. [27] P. Hennig and C. J. Schuler, “Entropy search for information-efficient global optimization,” J. Mach. Learning Res., vol. 13, pp. 1809–1837, 2012. [28] B. S. Yarman, Design of Ultra Wideband Power Transfer Networks. New York, NY, USA: Wiley, 2010. [29] B. S. Yarman and H. J. Carlin, “A simplified “real frequency” technique applied to broadband multistage microwave amplifiers,” IEEE Trans. Microw. Theory Techn., vol. 30, no. 12, pp. 2216–2222, Dec. 1982.

[30] M. D. McKay, R. J. Beckman, and W. J. Conover, “A comparison of three methods for selecting values of input variables in the analysis of output from a computer code,” Technometrics, vol. 21, no. 2, pp. 239–245, 1979. [31] D. E. Finkel, “Direct optimization algorithm user guide,” North Carolina State Univ., Raleigh, NC, USA, CRSC Tech. Rep. CRSC-TR03-11, Mar. 2003.

Peng Chen (S'15) received the B.E. degree in communication engineering and the M.E. degree in electronic engineering from Harbin Institute of Technology, Harbin, China, in 2010 and 2012, respectively. He is currently pursuing the Ph.D. degree in electronic engineering from the RF & Microwave Research Group, University College Dublin, Dublin, Ireland. His research interests include nonlinear device modeling and optimization algorithms applied to power amplifier design.

Brian M. Merrick (S'12–M'15) received the B.E. and Ph.D. degrees from University College Dublin (UCD), Dublin, Ireland, in 2010 and 2015, respectively. He is currently a postdoctoral researcher with the RF and Microwave Research Group, UCD. His research interests include device characterization and nonlinear modeling, and the design of high-efficiency, broadband power amplifiers.

Thomas J. Brazil (F'03) received the Ph.D. degree from the National University of Ireland, Dublin, Ireland, in 1977. He is head of the RF and Microwave Research Group, UCD. He holds the Chair of Electronic Engineering at the School of Electrical and Electronic Engineering, University College Dublin (UCD). His research interests include the fields of nonlinear modelling and characterization techniques at the device, circuit, and system level within high frequency electronics. Dr. Brazil was elected a Member of the Royal Irish Academy (RIA) in 2004. He is a serving member of IEEE MTT-S AdCom.

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Theory and Implementation of RF-Input Outphasing Power Amplification Taylor W. Barton, Member, IEEE, and David J. Perreault, Fellow, IEEE

Abstract—Conventional outphasing power amplifier systems require both a radio frequency (RF) carrier input and a separate baseband input to synthesize a modulated RF output. This work presents an RF-input/RF-output outphasing power amplifier that directly amplifies a modulated RF input, eliminating the need for multiple costly IQ modulators and baseband signal component separation as in previous outphasing systems. An RF signal decomposition network directly synthesizes the phase- and amplitude-modulated signals used to drive the branch power amplifiers (PAs). With this approach, a modulated RF signal including zero-crossings can be applied to the single RF input port of the outphasing RF amplifier system. The proposed technique is demonstrated at 2.14 GHz in a four-way lossless outphasing amplifier with transmission-line power combiner. The RF decomposition network is implemented using a transmission-line resistance compression network with nonlinear loads designed to provide the necessary amplitude and phase decomposition. The resulting proof-of-concept outphasing power amplifier has a peak CW output power of 93 W, peak drain efficiency of 70%, and performance on par with a previously-demonstrated outphasing and power combining system requiring four IQ modulators and a digital signal component separator. Index Terms—Base stations, Chireix, LINC, load modulation, outphasing, power amplifier (PA), signal component separator (SCS), transmission-line resistance compression network (TLRCN).

I. INTRODUCTION

O

UTPHASING architectures use phase-shift control of multiple saturated or switched-mode branch power amplifiers (PAs) to create a modulated radio frequency (RF) output. Interaction through a lossless non-isolating power combiner produces load modulation of the branch amplifiers, which in turn modulates the system output power. When realized with efficient saturated or switched-mode branch amplifiers, the outphasing approach has the potential to provide high operating efficiency over a wide range of output power levels, making it Manuscript received June 30, 2015; revised September 22, 2015; accepted October 23, 2015. Date of publication November 10, 2015; date of current version December 02, 2015. This paper is an expanded version from the IEEE MTT-S International Microwave Symposium, Phoenix, AZ, USA, May 17–22, 2015. T. W. Barton is with the Department of Electrical Engineering, The University of Texas at Dallas, Richardson, TX 75080 USA. (e-mail: taylor.barton@ utdallas.edu). D. J. Perreault is with the Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139 USA. (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2015.2495358

ideal for high peak-to-average power ratio (PAPR) signals such as those found in modern communications systems. Examples of this approach include Chireix power combining systems [1]–[5], and the multi-way lossless outphasing system [6]–[11] which improves upon the achievable operating efficiency of the Chireix system by providing nearly ideal resistive loading conditions to the branch PAs. Since its introduction by Chireix in 1935, a major limitation in the outphasing approach has been the need for signal component separation of the desired RF signal into multiple phase- and amplitude-modulated signals driving the branch PAs. For example, in an early commercial outphasing amplifier, Ampliphase, two sets of dynamic phase-modulating amplifiers were used to modulate the carrier signal by the (baseband) audio signal and drive the branch PAs [12]. This property has made outphasing systems less attractive compared to the Doherty approach with its ability to operate directly on a modulated RF input signal [13], [14]. The signal component separator (SCS) and the associated need for multiple baseband-to-RF upconverting paths incurs excessive complexity, cost, and power consumption to the outphasing system compared to power amplifiers that can operate directly on a modulated RF input. The digital signal decomposition requirement can also complicate any digital correction scheme. SCS approaches performing the required computation have been proposed in various domains, including analog baseband [15] and analog IF operating in feedback [16]–[18] or open-loop [19] topologies. The most common approach in modern outphasing systems, however, is to use some form of digital signal processing based on lookup tables or other means of computing the nonlinear relationship between the input signal and the phase-modulated branch PA drives [20]–[25]. As illustrated in the block-diagram comparison in Fig. 1, performing the signal component separator (SCS) in the RF domain instead of the digital domain allows for decoupled design of the digital and RF elements, reduced system complexity, and for the resulting outphasing system to be treated as a “black box” drop-in replacement for another PA. This work presents an RF-input/RF-output outphasing PA, shown in block diagram form in Fig. 2. An RF-domain signal decomposition network directly synthesizes the multiple branch PA drive signals from a modulated RF input signal, performing both the phase and amplitude modulation required for outphasing systems to control the output power over a wide range [3], [9]. This signal decomposition network (or RF-domain signal component separator) is based on use of a resistance compression network (RCN) terminated

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Fig. 2. Conceptual schematic of the four-way RF-input outphasing system, with example waveforms sketched assuming the PA is operating in the outphasing regime. The phasor relationship among the four branch voltages – is a result of the decomposition network structure. The non-isolating combining and decomposition networks are abstracted for simplicity.

Fig. 1. Comparison of signal component separation techniques for conventional outphasing systems and the RF-domain SCS proposed in this work. Baseband signals are indicated with black lines while RF paths are shown in red. The RF-input outphasing PA has reduced cost, complexity, and power consumption and can operate directly on a modulated RF input. (a) Digital SCS. (b) RF-domain SCS (this work).

with nonlinear elements. The resulting system is a true RF amplifier in the sense that its input is a modulated RF signal, and its output is an amplified version of that signal. This paper expands on the brief conference paper [26] with a complete analysis of the theory and development of this approach, and presents additional experimental data including modulated output spectrum and input impedance characterization of the 2.14-GHz prototype system. In Section II we derive the theoretical behavior of the RF decomposition network, and describe how a nonlinear termination network is used to implement mixed-mode phase- and amplitude-modulation of practical outphasing systems. Design of the nonlinear termination network and RF decomposition networks is discussed in Section III. Finally, the experimental system showing proof-of-concept operation at a 2.14 GHz carrier frequency with peak output power of 95 W is described in Section IV. II. SYSTEM THEORY Fig. 3 shows a simplified schematic of the proposed RF-input/RF-output system, in which a passive RF decomposition network performs signal separation of a modulated input to produce the four modulated signals required to drive the four branch PAs. The system consists of the decomposition network (based on a four-way transmission-line resistance compression network (TLRCN) terminated with nonlinear components), driver and branch PAs, and a lossless multi-way power combiner. A. Conceptual Overview In the outphasing operating mode, the function of the RF signal decomposition network is to convert amplitude modulation at the system input into relative phase modulation among the inputs to the four branch PAs. As can be seen from the struc-

ture in Fig. 3, the signal decomposition is related to the combining network through symmetry. Conceptually, the decomposition network's function can be thought of as being opposite of that of the combining network. That is, in the power combining network, phase-modulated signals interact to produce amplitude modulation at the output, whereas in the signal decomposition network, input amplitude modulation is converted to four phase-modulated drive signals. The four outphased drive signals are chosen such that the branch PAs “see” loading conditions that vary (nearly resistively) over some pre-determined range. Extending the conceptual symmetry argument, then, varying the decomposition network's loads over that same range of resistance values should (at least approximately) generate the desired outphasing relationship among the four port phases. The nonlinear loads ( in Fig. 3) are designed to vary as a function of input amplitude so that amplitude modulation at the input is converted “automatically” to phase modulation among the four PA drive signals. This inverse resistance compression network (IRCN) outphasing control strategy forms the basis of the RF signal decomposition in the outphasing regime. The implementation described in this work and used for the experimental prototype is based on an all-transmission-line approach as described for the power combining system in [10], and for resistance compression networks (RCNs) in [27], but we note that versions are also possible using discrete components, microstrip techniques, or a combination of those, related to the lumped-element [7], [8], microstrip with shunt reactive element [9], and all-transmission-line [10] variations of the four-way outphasing power combiner. Likewise, the approaches described in this work may be applied two-way (Chireix) outphasing, including its relatively wideband variations [4], [5]. The four-way outphasing architecture is selected as the basis for this work due to both its nearly-resistive loading conditions presented to the branch PAs (which lends itself to an intuitive understanding of the RF-input approach by arguments of symmetry) and because the impact of eliminating the multiple upconvering paths including mixers and filters is even greater in the four-way system compared to the conventional Chireix approach. B. Outphasing Operation An IRCN outphasing control law was originally introduced as one basis for selecting the input phases and for a

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Fig. 3. Simplified schematic of the new RF-input/RF-output outphasing system showing the transmission-line-based implementation used in the experimental – , given also by (1)–(4). prototype in this work. The vector diagram at upper left describes the relative phase relationship among the four branch signals

baseband-input, lumped-element four-way outphasing system [6]. This control law is based on the approximate relationship between the phase angles of a multi-way RCN and a corresponding multi-way power combining network with appropriate controls: the power combiner can be (approximately) derived from an RCN by applying the principle of time-reversal duality [6]. In essence, the direction of power flow in the power combining network is reversed by changing the sign of each reactance, resistance, and electrical length, replacing sources (approximated as negative resistors) with resistors (and vice versa). This transformation is illustrated for the lumped-element combiner of [6] in Fig. 4. An analogous inverse-RCN approach can be seen in the relationship between the transmission-line combining network [10] and transmission-line resistance compression network (TLRCN) [27]. As described in detail in [27], a TLRCN may be constructed as a binary tree of transmission-line sections, with the two branch lengths at the th branch point a deviation from a base length (typically or ). The ends of the final branches are typically terminated in identical loads, and a quarter-wave transmission line may also be employed before the initial branch point to provide impedance matching into the TLRCN. Examining the RF decomposition network of Fig. 3, we can see that it is based on a passive network (derived from a TLRCN) terminated with four varying (but equal) resistances . In the following analysis, we assume that the TLRCN terminating impedance is , neglecting any effects of the input impedance . In practice, as will be shown in Section III below, the terminating impedance can be designed to include effects of . The four output port voltages – can be found in terms of the input , terminating resistances , and network parameters through analysis of the decomposition network (1)–(2). These relationships are derived in the Appendix. Note that in (2), represents the impedance into the transmission-line pairs closest to the

Fig. 4. Dual relationship between RCN and combiner (shown here in lumped-element form) means that wide range output power control of the combiner system is possible through an IRCN control scheme.

nonlinear loads (see Fig. 3) and is a function of . From [27], will be purely resistive when is resistive

(1)

(2) The phases of the four port voltages are related as indicated in (1) and the vector diagram in Fig. 3, and can be shown to be related to the load resistance as in (3)–(4) where , , , and , with and

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Fig. 5. Plot of the port relationship from (1) when is varied, assuming is constant, and the decomposition network is designed with parameters , , , , and . Note that in practice, varies as a function of .

representing differences in base line lengths as illustrated in Fig. 3 (3) (4) The magnitudes and phases of the four voltages at the output of the RF decomposition network, – , are plotted as a function of load resistance in Fig. 5. Note that in this plot, is held constant. In practice, as will be described below, the value of will vary as a function of , and the magnitude relationship will therefore be modified from that shown in Fig. 5. Throughout this work we will assume that the PA output amplitudes are equal to each other. The further assumption that they are constant (in the outphasing operating mode) is enforced by both a limiter-based implementation of the nonlinear terminations and the saturating characteristics of the drivers and branch PAs, and will be examined in more detail in the next section. After amplification, the four branch PA outputs ( – ) (Fig. 3) are assumed to have the same outphasing relationship given by the vector diagram in Fig. 3 and with and from (3)–(4). The magnitudes – are furthermore assumed to be equal with value . In this case, the output power of the combining system is described by (5) [10] (5) is a system propNote that, although the expression for erty (and therefore unchanged from [10]), the selection of outphasing angles and is different in this work from that of the Optimal Susceptance (OS) control law in [10]. From (5) it can be seen that the output power of the amplifier system can be modulated by controlling either and (through control of ), the branch PA drive amplitude , or a combination of these methods.

Fig. 6. Plot of the theoretical loading impedances on the ports based on the IRCN (solid) and OS (dashed) control laws for the transmission-line system in this work, assuming a four-way transmission-line power combining as in [10] , , , , with values . and

The load impedances seen by the four branch PAs is found following the methodology in [10] but with the outphasing angles given by (3)–(4). In this analysis, the magnitudes of the four PA outputs – are assumed to be equal and to have a constant value ; that is, we ignore any amplitude variation in the PA drive signals due to variation in the amplitudes of – (the load impedances seen by the branch PAs do not depend on the value of , only on the relative phases of the four PA outputs). The resulting effective branch PA loading impedances (each including the effect of load modulation from the action of the other PAs) are shown in Fig. 6. Note that because the RCN and combiner networks are not exact duals, the actual combiner output power does not precisely track the (scaled) input power. However, this and other nonlinearities in the implemented system can be addressed through pre-distortion of the input signal [6], [11], [28]. C. Mixed-Mode Operation The above system analysis assumes that the branch PAs are operated in saturated or switched mode, with a constant-envelope output voltage and output power control achieved only through modulation of the effective load impedance seen by each PA. In principle, the output power of an outphasing system can be modulated in this way through phase-only control of the multiple signals driving the branch PAs. Practical implementations, however, use both phase and amplitude modulation of the signals driving the branch PAs for two reasons [3], [9]. First, as the system output power is reduced (by increasing the load resistance seen by each branch PA), the input power required to drive each PA into saturation is reduced as well. In this case, drive amplitude modulation can be used to improve efficiency of the overall RF lineup (and power-added efficiency [PAE]) while maintaining outphasing operation [9]. Second, and more importantly for many communications applications, amplitude modulation of the branch PA drive signals can be used to extend the system's output power range to include zero crossings. These two effects are summarized in Fig. 7.

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Fig. 7. Benefits of mixed-mode operation; (a) measured PAE of the inverse class F PAs used in this work showing PAE over load modulation; PAE is maintained by reducing drive amplitude as the loading impedance increases (reproduced from [9]), (b) theoretical efficiency of four-way outphasing (assuming branch PAs are implemented in class B) with (solid) and without (dashed) back-off control at low power levels.

Note that in Fig. 7(a), the individual final stage PAs are operated in compression (and driven into saturation) for most of the outphasing range, leading to flat power gain versus output voltage. However, at the highest output powers/lowest PA loading impedance (owing to load modulation), the drive amplifiers no longer drive the final stage hard enough to saturate it, so the PA comes out of compression and overall power gain increases slightly. Below the shown range, the drive amplitude to the PAs is reduced, and so efficiency is expected to decrease as shown in Fig. 7(b) due to this mixed-mode operation. In the pure outphasing mode (dashed lines in Fig. 7(b)), by contrast, the efficiency drops off in a near-vertical way as a result of operating outside the nominal range of the combiner. The combining network and associated control law is designed for operation over a fixed range (e.g., 10 dB as in Fig. 6), and outside this range the loading impedances of the branch PAs rapidly become highly reactive. Both Chireix and four-way outphasing systems are designed for a particular dynamic range over which the effective load impedance of the branch PAs is well-controlled, but present highly reactive loads in the limit as the output power goes to zero (resulting in problematic loading conditions for the branch PAs). In practical outphasing systems requiring accurate zerocrossings, therefore, the output power range can be extended by holding the outphasing angles constant at the phases corresponding to the lower extreme of the desired outphasing range, and backing off on the drive amplitudes to operate the branch PAs in a class-B or other non-saturated mode [3], [9]. This approach has the additional advantage that it does not rely on exact cancellation of the outputs of the multiple branch PAs to produce zero output power. In this work, we realize mixed-mode phase with amplitude modulation through the design of the termination networks at the RCN output ports. In the outphasing mode of operation, the effective loading resistance to the RCN varies over the desired range (i.e., the range of loading impedances that the branch PAs are designed to operate well over). This load resistance variation is a function of input drive amplitude, so that amplitude modulation of the RF input is decomposed into phase modulation for the four branch PA signals. Below the outphasing range, the

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Fig. 8. Nonlinear load element used to terminate the RCN: (a) equivalent schematic, and (b) effective input resistance at the fundamental (idealized diode and ON-resistance , assumed). with turn-on voltage

phases should be held constant at the value corresponding to the low end of the outphasing range, or in other words the effective load resistance seen by the individual PAs becomes fixed. Now amplitude modulation at the input produces amplitude modulation of the branch PA drives. Note that the port impedance derivation in the previous section assumes that the drive amplitudes – are equal, and this operating condition is also maintained in mixed-mode operation. D. Nonlinear Termination The amplitude to phase conversion of the decomposition network is produced by realizing its terminations as nonlinear networks whose effective resistance is a function of input power. That is, the variable resistances of Fig. 3 are implemented using nonlinear passive networks having an effective one-port impedance that varies as a function of the applied voltage. At the upper range of input power, the nonlinear loads behave as variable resistors, generating outphasing control angles corresponding to the IRCN control law. Below a threshold level the terminating resistance is fixed and the four signals are amplitude-modulated with the input signal, with the input signal split evenly among the four branches. The nonlinear load network used in this work is shown in Fig. 8. The implemented impedance variation of the load network is not optimized, but it has the general required characteristics to demonstrate the RF-input outphasing concept, namely that (in the high-power range) the resistance posed by the load network decreases as the power driving it increases. When the applied (sinusoidal) current driving the load network is sufficiently large, the voltage waveform across the load network will be a clipped version of the input current. As the input power is increased, the output voltage will remain at the clipped amplitude, but the fundamental component of the current will increase with input power. As a result, neglecting the effect of and any parasitic resistance, the effective input impedance of this network will be an inverse function of input power. When the parallel resistance is included, then, the input resistance will be limited to a value at low drive (drive levels insufficient to turn on the diodes). The resistor corresponds to an impedance-transformed version of the 50- impedance into the driver amplifiers ( , Fig. 3). Fig. 9 shows the simulated amplitude and phase relationships among the four branches when the nonlinear network in Fig. 8 is used to terminate the decomposition network. The

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Fig. 9. Simulated amplitude and phase of voltages at the output of the decomposition network, as a function of system input voltage. The mixed-mode outphasing and amplitude control can be seen: between a threshold voltage the outphasing angles are fixed and the amplitude of the branch voltages is proportional to the input voltage. Note that only the fundamental component of the amplitude is shown.

Fig. 10. Effective loading impedances seen by the four branch PAs in the RF-input/RF-output system ( , Fig. 3) as a function of system input voltage, when the outphasing angles resulting from the decomposition network are applied to the power combiner (simulated). The diode threshold voltage is . simulated as

mixed-mode outphasing and amplitude control can be clearly seen; below a threshold voltage the outphasing angles are fixed, and the amplitude of the branch voltages is proportional to the input voltage amplitude. Above that threshold, the four voltages – follow the IRCN control law. Similarly, the simulated port voltage amplitude (fundamental component only) shows the limiting effects of the diode termination. Note that these voltage signals approach square waves as the drive input level increases, i.e., there is significant additional harmonic content. The driver and RF stage amplifiers also have limiting characteristics, further enforcing constant-envelope behavior at the output of the branch PAs (e.g., the input of the power combining network). The effective load impedances of the four branch PAs, shown in Fig. 10, is simulated using the idealized diode-based model. III. IMPLEMENTATION This section describes the design and implementation of the RF decomposition network used for experimental validation of the approach, including the implementation of the TLRCN, and the nonlinear loading network. The experimental system is designed to operate at 2.14 GHz. A. Microstrip TLRCN The signal decomposition network is implemented as an alltransmission-line RCN [27], although alternative implementations including could be designed as in the related lumped-element [8] or microstrip [9] power combining networks. The layout (Fig. 11) is made up of curved microstrip segments; right angles and “T” junctions are avoided in order to most closely match the theoretical behavior of the network. The layout of this and other system components are not optimized for size, although more compact versions are possible by using e.g., serpentine layout. This network is implemented on a 1.52-mmthick Rogers RO4350 substrate.

Fig. 11. Layout of RF signal decomposition board implemented on a 1.52mm-thick Rogers RO4350 substrate. The board dimensions are 14.5 cm 14.2 is synthesized from the (50- ) cm. As indicated, the parallel resistance impedance into the driver stage using a quarter-wavelength impedance transformation.

The TLRCN component of the decomposition network is designed assuming that the nonlinear loads vary over an approximately 10–85 range, corresponding to the range that the combining network is designed to present to the branch power amplifiers. The layout therefore uses the same parameters as the power combining network [10], with characteristic impedances , and delta-electrical lengths and . (The original paper describing the transmission-line combiner [10] indicated values and in error; the lengths and were used in both the transmission-line combiner and TLRCN.) A secondary benefit of the TLRCN structure is that it provides a narrow-range resistive input impedance even when its load im-

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pedances ( , Fig. 3) vary. As in the corresponding combiner design, an impedance-transforming quarter-wave transmission line is included at the input port, with . Combined with the resistance compression behavior of the TLRCN, this impedance transformation establishes a nominally 50- input impedance to the power amplifier system. The simulated reflection coefficient at the input port has over the entire range of operation. B. Nonlinear Load Element The anti-parallel diode pair is implemented using Avago HSMS-286C detector diodes, which are available as a single packaged pair. Matching to reduce the effects of parasitic reactance is incorporated into the quarter-wavelength transmission line before the diode. For other choices of diodes or frequency, a more complicated impedance match may be necessary. The shunt resistance is designed to be 85 , and is generated by transforming the 50- input impedance of the following (driver) stage with a quarter-wavelength impedance transformer.

Fig. 12. Comparison of measured relative phases at the outputs of the decomposition network (grey), the full PA paths (black; branch PAs 50- terminated), and the ideal phase relationship calculated based on commanded power using the optimal susceptance control law [10] (dashed, top axis). Net phase shift has been removed from the plot for clarity. The mixed-mode behavior can be seen below around 7 dB input commanded power, below which the measured outphasing angles are held constant.

IV. EXPERIMENTAL SYSTEM A. Decomposition Network The decomposition network is characterized by measuring the phase relationship at its four output ports (ports A, B, C, D in Fig. 11) when the input power is varied. For this experiment, the decomposition network is first terminated (at reference plane D, Fig. 3) with 50- loads representing the input impedances to the PA drivers. The relative phases at the four output ports of the decomposition network ( – ) are shown in Fig. 12 (grey curves). This figure shows the relative phases among the four branches only; net phase shift has been removed from the plot for clarity. Next, the full RF paths are characterized up to reference plane E; for this measurement, the branch PAs are terminated in 50 and the relative phase of signals – at their outputs is characterized with system input power (Fig. 12, black curves). Note that the actual phase relationship into the combiner may vary if the PAs have load-modulation to phase-modulation nonlinearity. Static phase offsets are trimmed out using phase shift tuners (Aeroflex Weinchsel 980–4) in the four paths. The transition between outphasing control and drive modulation can also be seen near 7 dB normalized input power. The measured phase characteristics are compared to those calculated from the OS control law (which in principle yields more optimal performance than the IRCN control law), shown in Fig. 12 as dashed curves (and referring to the top axis). A close match can be observed between the phase relationships among the measured and theoretical control angles. At the same time, it can be seen by comparing the top and bottom axes that there is not a one-to-one correlation between the two scales, and that the input power range of the experimental system is approximately twice (in dB) that of the calculated power command range. This means that the output power is not a linear function of linear power (as will be shown in the system measurements below); this nonlinearity is related to the implementation of the nonlinear load network used in this work.

Fig. 13. Measured transmission coefficient (normalized) of each PA path (terminated by 50 ) as a function of system input power. The variation in AM/AM performance between the four paths was not corrected for in the system characterization.

The amplitude characteristics of all four ports are likewise measured over swept input power. This measurement, made into 50- loads only, reveals amplitude mismatch among the four branches, particularly at low drive levels (see Fig. 13). This imbalance was not corrected for in the system characterization. The resistance compression property of the decomposition network can be seen in Fig. 14, which shows the measured input impedance to the RF decomposition network ( in Fig. 3) over the swept power characterization of Fig. 12. The input reflection coefficient remains better than over the entire range of applied power. Furthermore, the impedance is nearly constant, with an improved 50-ohm match clearly possible if desired. B. RF-Input/RF-Output Outphasing System 1) Overview: A photograph of the complete system including (left to right) the decomposition network, phase shift tuners, two predriver stages, the inverse class F branch PAs, and the power combining network [10], is shown in Fig. 15. The input CW or W-CDMA signal is generated using a Rohde

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Fig. 14. Input reflection coefficient for the signal decomposition network as the input power is swept over the 20-dB range as in Fig. 12. This measurement in Fig. 3. The nearly constant corresponds to the reference plane indicated by ) is a result of the resistance compression input impedance (showing network used as the basis for the signal decomposition network.

& Schwarz SMJ100A vector signal generator, and is amplified by a pre-amplifier to reach the required input level before the signal decomposition network. The nature of the nonlinear loads in the decomposition network constrains the possible range of input powers to the system for a given design. Here, the decomposition network is designed for input powers up to 23 dBm, while a 50 dBm system output power is desired. After the RF-domain decomposition, phase-shift tuners are employed to trim out static phase offsets (these are largely due to mismatched delays in the driver amplifiers). The two driver amplifiers, based on demonstration boards for the Hittite HMC455 and Freescale MW7IC2020N parts respectively, have not been optimized for the system, and so are excluded from the efficiency characterization. In fact, as can be seen in the photograph, excess gain in the driver chain is adjusted for using fixed attenuators. This arrangement is due to the available driver stages and is clearly undesirable for a practical system. Note that the driver PAs have been replaced compared to the related work in [26], although efficiency performance is similar. The branch PAs are based on the CGH40025 device from CREE and the design in [14], and are the same PAs as used in the baseband-input work demonstrating the all-transmission-line multi-way outphasing power combiner [10]. The power combining network is likewise the same as used in [10], so that the performence of that baseband-input system can be directly compared to this work. Drain efficiency of the final-stage power amplifiers (which have approximately 10 dB gain [9]) is measured using an Agilent N6705A power supply and Rohde & Schwarz NRT power meter. A block diagram of the measurement setup is shown in Fig. 16.

Fig. 15. System photograph showing: (a) the testbench including instrumentation; (b) details of the RF decomposition network, drivers, and RF power stage.

Fig. 16. Block diagram of the measurement setup, with reference planes indicated based on the definitions in Fig. 3.

2) CW Measurements: A CW measurement of drain efficiency of the final RF power stage versus output power is shown in Fig. 17 (black curve). The power amplifier has a peak output power of 49.7 dBm and peak drain efficiency of 70%. Also shown (grey curve) is a system characterization in which the branch PA drive signals (corresponding to reference plane in Fig. 3) are generated using four separate IQ modulators with

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Fig. 18. CW characterization of the power amplifier. The inflection point at the transition between outphasing and amplitude modulation for output power control can be seen around an output power of approximately 44 dBm. Fig. 17. Measured outphasing power amplifier performance (black), and measured performance of a baseband-input system comprising the same branch PAs and power combining network [10]. The new RF-input PA has nearly identical performance but operates directly on a modulated RF signal with a simple passive network replacing the complex baseband signal processing setup of [10]. This variation occurs due to differences in the active devices, passive devices, interconnects and pcb manufacturing among the PA and driver chains of the four paths.

the Optimal Susceptance control law that selects outphasing angles such that the reactive component of the branch PA load impedance is minimized (reproduced from [10]). The same combiner and RF power stage are used for both measurements. Note that the inclusion of phase shift tuners compared to the initial prototype in [26] allows for static phase adjustment of the four paths and a slightly improved efficiency characteristic. The excellent match in the efficiency performance of these systems demonstrates the effectiveness of the RF signal decomposition network. The reduced peak power of the new system is likely due to a combination of the higher load susceptance associated with the IRCN law and the phase mismatch observed in Fig. 12. Compared to the system using four IQ modulators, this proof-of-concept RF-input/RF-output implementation has significant advantages in system complexity without degradation in peak efficiency. The RF-input/RF-output outphasing amplifier is also characterized in terms of CW input/output characteristics as shown in Fig. 18. The two regions of output power control, amplitude modulation and outphasing control, are apparent from this measurement. The clear “knee” between the two regimes, and the compressive behavior in the outphasing control region, indicate that the nonlinear termination for this design is not optimal. This and other nonlinearities can be addressed through pre-distortion of the input signal or further refinement of the nonlinear load characteristic used in the decomposition network. 3) Modulated Measurements: A preliminary characterization of the outphasing PA was performed using a W-CDMA input signal. The measured output spectrum, with no linearization applied, is shown in Fig. 19. For this measurement, the average output power was 24 W, and average drain efficiency of the final PA stage was . The measured output PAPR was 6.18 dB. A comparison to other works of related technology and power level is given in Table I. The evident nonlinearity of the RF-input outphasing PA may be attributed to several factors including the nonlinear

Fig. 19. Output spectrum of the RF-input outphasing PA when no linearization is applied, measured over a 40 MHz span for a 3.84 MHz W-CDMA signal.

TABLE I COMPARISON TO OTHER WORKS: W-CDMA PERFORMANCE.

overall AM-AM characteristic shown in Fig. 18, which is most likely caused by the non-ideal nonlinear termination element used in the implemented system. Improvements in this nonlinear characteristic, along with a complete characterization of the load-modulation-to-amplitude-modulation characteristics of the branch PAs, could improve the observed “knee” characteristic in Fig. 18. The linearity of outphasing systems has additionally been shown to be sensitive to amplitude, phase, and delay mismatch among the branches, and limited bandwidth of the combining network [31]–[33]. We note that a common linearization approach for outphasing systems (e.g., [32], [33]) treats the signal component separator, branch

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PAs, and power combining network as a “black box” model, and applies digital predistortion (DPD) based on the overall input-output characteristic of the system. Although linearization is outside the scope of this work, which focuses on the initial proof-of-concept demonstration of RF-input outphasing, we therefore expect that this architecture is compatible with conventional linearization techniques. Fig. 20. Three-port network forming the building blocks of both the transmission-line combining network and the TLRCN-based decomposition network.

V. CONCLUSION The RF signal decomposition network presented in this work exploits the relationship between resistance compression networks and lossless outphasing power combiners in order to create an RF-input/RF-output outphasing power amplifier. This approach eliminates the digital signal component separator and multiple IQ modulators required for prior outphasing system implementations. Advantages of the approach include reduced system cost and baseband signal processing complexity, and the ability to work with many existing calibration and digital pre-distortion schemes. The proof-of-concept prototype in this work is implemented using transmission-line techniques, and demonstrates the feasibility of this approach through CW measurements at 2.14 GHz. The system achieves a peak output power of 93 W and a peak drain efficiency of 70%, performance that is on par with the previously-demonstrated outphasing system [10] requiring four IQ modulators. The excellent match between these two systems demonstrates the effectiveness of the RF signal decomposition approach. This approach can be extended to a range of frequencies and implementation types including lumped element implementations as in [8], or microstrip versions [9]. Future development of this technique will focus on design of the nonlinear termination in the signal decomposition network to generate a more overall-linear characteristic.

ports. The voltage magnitudes are equal and given by (9), while the two port phases are given by (10)–(11) (9) (10) (11) When is as defined graphically in Fig. 20, then, this outphasing angle can be written as (12) To form the four-way decomposition network, the stage in Fig. 20 is “stacked” in a coporate combining structure. The behavior of the second stage is identical to the first, and it is loaded with a variable resistance ( in Fig. 3) that is a function of . This impedance is the input impedance to the first stage ( in Fig. 20) and can be calculated following the analysis in [27] to be

APPENDIX

(13)

This appendix gives the derivation of (1)–(4) relating the port voltages of the decomposition network when the terminating impedance varies. The three-port network shown in Fig. 20 can be thought of as the fundamental building block of both the transmission-linebased power combining network and the TLRCN. The port relationship of this network can be shown through transmission-line analysis to be: (6) where . When ports 1 and 2 are terminated resistively, , the port voltages can be written as

The relative angle resulting at the plane indicated by in Fig. 3 is obtained by substituting the expression for into (12), producing (3)) (14) as As shown in Fig. 3, we denote the segments closer to having differential electrical length , and the segment closer to the input as having differential electrical length . The port voltage magnitudes after the second stage (i.e., at the reference plane indicated by in Fig. 3) can be found by substituting the expression for into (9) (15)

(7) (8) In this application, the parameters of interest are the magnitude of port voltages and , and the relative phase between the

Substituting (15) into (9) yields the port voltage amplitude given in (1). REFERENCES [1] H. Chireix, “High power outphasing modulation,” Proc. IRE, vol. 23, no. 11, pp. 1370–1392, Nov. 1935.

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[2] D. Calvillo-Cortes, M. van der Heijden, M. Acar, M. de Langen, R. Wesson, F. van Rijs, and L. de Vreede, “A package-integrated Chireix outphasing RF switch-mode high-power amplifier,” IEEE Trans. Microw. Theory Techn., vol. 61, no. 10, pp. 3721–3732, Oct. 2013. [3] J. Qureshi, M. Pelk, M. Marchetti, W. Neo, J. Gajadharsing, M. van der Heijden, and L. de Vreede, “A 90-W peak power GaN outphasing amplifier with optimum input signal conditioning,” IEEE Trans. Microw. Theory Techn., vol. 57, no. 8, pp. 1925–1935, Aug. 2009. [4] M. van der Heijden, M. Acar, J. Vromans, and D. Calvillo-Cortes, “A 19 W high-efficiency wide-band CMOS-GaN class-E Chireix RF outphasing power amplifier,” in Proc. IEEE MTT-S Int. Microw. Symp. (IMS), Jun. 2011, pp. 1–4. [5] M. Pampin-Gonzalez, M. Ozen, C. Sanchez-Perez, J. Chani-Cahuana, and C. Fager, “Outphasing combiner synthesis from transistor load pull data,” in Proc. IEEE MTT-S Int. Microw. Symp. (IMS), May 2015, pp. 1–4. [6] D. Perreault, “A new power combining and outphasing modulation system for high-efficiency power amplification,” IEEE Trans. Circuits Syst. I: Reg. Papers, vol. 58, no. 8, pp. 1713–1726, Feb. 2011. [7] A. Jurkov, L. Roslaniec, and D. Perreault, “Lossless multi-way power combining and outphasing for high-frequency resonant inverters,” in Proc. Int. Power Electron. Motion Control Conf., Jun. 2012, vol. 2, pp. 910–917. [8] T. Barton, J. Dawson, and D. Perreault, “Experimental validation of a four-way outphasing combiner for MICROWAVE power amplification,” IEEE Microw. Wireless Compon. Lett., vol. 23, no. 1, pp. 28–30, Jan. 2013. [9] T. Barton and D. Perreault, “Four-way microstrip-based power combining for MICROWAVE outphasing power amplifiers,” IEEE Trans. Circuits Syst. I: Reg. Papers, vol. 61, no. 10, pp. 2987–2998, Oct. 2014. [10] T. W. Barton, A. S. Jurkov, and D. J. Perreault, “Transmission-linebased multi-way lossless power combining and outphasing system,” in Proc. IEEE MTT-S Int. Microw. Symp. (IMS), Jun. 2014, pp. 1–4. [11] A. Jurkov, L. Roslaniec, and D. Perreault, “Lossless multi-way power combining and outphasing for high-frequency resonant inverters,” IEEE Trans. Power Electron., vol. 29, no. 4, pp. 1894–1908, Apr. 2014. [12] A. Miller and J. Novik, “Principles of operation of the Ampliphase transmitter,” Broadcast News, no. 104, Jun. 1959. [13] W. Doherty, “A new high efficiency power amplifier for modulated waves,” Proc. IRE, vol. 24, no. 9, pp. 1163–1182, Sep. 1936. [14] A. Grebennikov, “A high-efficiency 100-W four-stage Doherty GaN HEMT power amplifier module for WCDMA systems,” in Proc. IEEE MTT-S Int. Microw. Symp. (IMS), Jun. 2011, pp. 1–4. [15] L. Panseri, L. Romano, S. Levantino, C. Samori, and A. Lacaita, “Lowpower signal component separator for a 64-QAM 802.11 LINC transmitter,” IEEE J. Solid-State Circuits, vol. 43, no. 5, pp. 1274–1286, May 2008. [16] A. Rustako and Y. Yeh, “A wide-band phase-feedback inverse-sine phase modulator with application toward a LINC amplifier,” IEEE Trans. Communications, vol. 24, no. 10, pp. 1139–1143, Oct. 1976. [17] D. Cox and R. Leck, “Component signal separation and recombination for linear amplification with nonlinear components,” IEEE Trans. Commun., vol. 23, no. 11, pp. 1281–1287, Nov. 1975. [18] B. Shi and L. Sundstrom, “A 200-MHz IF BiCMOS signal component separator for linear LINC transmitters,” IEEE J. Solid-State Circuits, vol. 35, no. 7, pp. 987–993, Jul. 2000. [19] B. Shi and L. Sundstrom, “A translinear-based chip for linear LINC transmitters,” in Proc. Symp. VLSI Circuits, Jun. 2000, pp. 58–61. [20] L. Sundstrom, “The effect of quantization in a digital signal component separator for LINC transmitters,” IEEE Trans. Vehicular Tech., vol. 45, no. 2, pp. 346–352, May 1996. [21] S. Hetzel, A. Bateman, and J. McGeehan, “A LINC transmitter,” in Proc.. IEEE Vehicular Tech. Conf., May 1991, pp. 133–137. [22] W. Gerhard and R. Knoechel, “LINC digital component separator for single and multicarrier W-CDMA signals,” IEEE Trans. Microw. Theory Techn., vol. 53, no. 1, pp. 274–282, Jan. 2005. [23] Y. Li, Z. Li, O. Uyar, Y. Avniel, A. Megretski, and V. Stojanovic, “High-throughput signal component separator for asymmetric multilevel outphasing power amplifiers,” IEEE J. Solid-State Circuits, vol. 48, no. 2, pp. 369–380, Feb. 2013.

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[24] T.-W. Chen, P.-Y. Tsai, D. De Moitie, J.-Y. Yu, and C.-Y. Lee, “A low power all-digital signal component separator for uneven multi-level LINC systems,” in Proc. European Solid-State Circuits Conf., Sep. 2011, pp. 403–406. [25] M. Heidari, M. Lee, and A. Abidi, “All-digital outphasing modulator for a software-defined transmitter,” IEEE J. Solid-State Circuits, vol. 44, no. 4, pp. 1260–1271, Apr. 2009. [26] T. Barton and D. Perreault, “An RF-input outphasing power amplifier with RF signal decomposition network,” in Proc. IEEE MTT-S Int. Microw. Symp. (IMS), May 2015, pp. 1–4. [27] T. Barton, J. Gordonson, and D. Perreault, “Transmission line resistance compression networks and applications to wireless power transfer,” IEEE J. Emerging Sel. Topics Power Electron., vol. 3, no. 1, pp. 252–260, Mar. 2015. [28] A. Jurkov and D. Perreault, “Design and control of lossless multi-way power combining and outphasing systems,” in Proc. Midwest Symp. Circuits Syst., Aug. 2011, pp. 1–4. [29] D. Calvillo-Cortes, M. van der Heijden, and L. de Vreede, “A 70 W package-integrated class-E Chireix outphasing RF power amplifier,” in Proc. IEEE MTT-S Int. Microw. Symp. (IMS), Jun. 2013, pp. 1–3. [30] J. Kim, J. Moon, Y. Y. Woo, S. Hong, I. Kim, J. Kim, and B. Kim, “Analysis of a fully matched saturated Doherty amplifier with excellent efficiency,” IEEE Trans. Microw. Theory Techn., vol. 56, no. 2, pp. 328–338, 2008. [31] T. Hwang, K. Azadet, R. Wilson, and J. Lin, “Linearization and imbalance correction techniques for broadband outphasing power amplifiers,” IEEE Trans. Microw. Theory Techn., vol. 63, no. 7, pp. 2185–2198, Jul. 2015. [32] P. Landin, J. Fritzin, W. V. Moer, M. Isaksson, and A. Alvandpour, “Modeling and digital predistortion of class-D outphasing RF power amplifiers,” IEEE Trans. Microw. Theory Techn., vol. 60, no. 6, pp. 1907–1915, Jun. 2012. [33] A. Aref, T. Hone, and R. Negra, “A study of the impact of delay mismatch on linearity of outphasing transmitters,” IEEE Trans. Circuits Syst. I: Reg. Papers, vol. 62, no. 1, pp. 254–262, Jan. 2015. Taylor W. Barton (S'07–M'12) received the Sc.B., M.Eng., E.E., and Sc.D degrees from the Massachusetts Institute of Technology (MIT), Cambridge, MA, USA, in 2012. In 2014, she joined The University of Texas at Dallas (UT Dallas), Dallas, TX, where she is currently an Assistant Professor. Prior to joining UT Dallas, she was a Postdoctoral Associate in the MIT Microsystems Technology Laboratories. Her research interests include high-efficiency RF, power, and analog circuit design, and classical control theory.

David J. Perreault (S'91–M'97–SM'06–F'13) received the B.S. degree from Boston University, Boston, MA, USA, and the S.M. and Ph.D. degrees from the Massachusetts Institute of Technology (MIT), Cambridge, MA, USA. In 1997, he joined the MIT Laboratory for Electromagnetic and Electronic Systems as a Postdoctoral Associate, and became a Research Scientist in the laboratory in 1999. In 2001, he joined the MIT Department of Electrical Engineering and Computer Science, where he is presently Professor and Associate Department Head. His research interests include design, manufacturing, and control techniques for power electronic systems and components, and in their use in a wide range of applications. He also consults in industry, and is co-founder of Eta Devices, a startup company focusing on high-efficiency RF power amplifiers. Dr. Perreault received the Richard M. Bass Outstanding Young Power Electronics Engineer Award, the R. David Middlebrook Achievement Award, the ONR Young Investigator Award, and the SAE Ralph R. Teetor Educational Award, and is co-author of seven IEEE prize papers.

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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 63, NO. 12, DECEMBER 2015

Hysteresis and Oscillation in High-Efficiency Power Amplifiers Jesús de Cos, Student Member, IEEE, Almudena Suárez, Fellow, IEEE, and José A. Garc´ıa, Member, IEEE

Abstract—Hysteresis in power amplifiers (PAs) is investigated in detail with the aid of an efficient analysis method, compatible with commercial harmonic balance. Suppressing the input source and using, instead, an outer-tier auxiliary generator, together with the Norton equivalent of the input network, analysis difficulties associated with turning points are avoided. The turning-point locus in the plane defined by any two relevant analysis parameters is obtained in a straightforward manner using a geometrical condition. The hysteresis phenomenon is demonstrated to be due to a nonlinear resonance of the device input capacitance under near optimum matching conditions. When increasing the drain bias voltage, some points of the locus degenerate into a large-signal oscillation that cannot be detected with a stability analysis of the dc solution. In driven conditions, the oscillation will be extinguished either through synchronization or inverse Hopf bifurcations in the upper section of the multivalued curves. For an efficient stability analysis, the outer-tier method will be applied in combination with pole-zero identification and Hopf-bifurcation detection. Departing from the detected oscillation, a slight variation of the input network will be carried out so as to obtain a high-efficiency oscillator able to start up from the noise level. All the tests have been carried out in a Class-E GaN PA with measured 86.8% power-added efficiency and 12.4-W output power at 0.9 GHz. Index Terms—Bifurcation, class-E, harmonic balance (HB), GaN, hysteresis, power amplifier (PA), stability, UHF.

I. INTRODUCTION

C

LASS-E power amplifiers (PAs) have been receiving increased attention due to their potential for simultaneously providing linear and efficient amplification when employed in bias- or load-modulation architectures [1]. However, it is not uncommon to observe instability phenomena in these amplifiers, some of which have been reported in [2] and [3]. Indeed, hysteresis can be found under near-optimum input-matching conditions, which gives rise to sudden transitions or jumps [2], [4], [5] between different sections of the power-transfer curve Manuscript received July 03, 2015; revised September 27, 2015; accepted October 13, 2015. Date of publication October 29, 2015; date of current version December 02, 2015. This work was supported by the Spanish Ministry of Economy and Competitiveness (MINECO) under Project TEC2014-60283-C3-1-R and Project TEC2014-58341-C4-1-R, with FEDER co-funding, the Parliament of Cantabria (12.JP02.64069) and by the Predoctoral Fellowship for Researchers in Training of the University of Cantabria and the Regional Ministry of Education of the Government of Cantabria. This paper is an expanded version from the IEEE MTT-S International Microwave Symposium, Phoenix, AZ, USA, May 17–22, 2015. The authors are with the Communications Engineering Department, Escuela Técnica Superior de Ingenieros Industriales y de Telecomunicación (ETSIIT), University of Cantabria, 39005 Santander, Spain (e-mail: [email protected]; [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2015.2492968

when either increasing or decreasing the input power. From a geometrical viewpoint, the hysteresis is due to the presence of turning points or infinite-slope points [5], [6] in the solution curve, which, in designs based on commercial harmonic balance (HB), have been detected [2], [4], [7] with the aid of an auxiliary generator (AG). However, there is little insight into the mechanism for the appearance of these turning points, often observed when approaching the intended operation conditions [2], [3]. In the GaN HEMT-based Class-E PA studied here, the nonlinear input capacitance resonates with the inductive input matching network, as will be demonstrated analytically. For an accurate prediction/suppression of the phenomenon, the outer-tier method presented in [8] will be adapted to the case of the PA with hysteresis, which will allow tracing the multivalued solution curves in an efficient manner, with no need for parameter switching [7], [9]–[11]. This method will also enable a direct calculation of the turning-point locus in terms of any practical analysis parameter, such as the gate bias voltage, the input matching capacitor, or the input power, by simply imposing a geometrical condition [8]. The observation of the hysteresis phenomenon studied in detail in [3] is often empirically associated with the onset of oscillations under a relatively small variation of the circuit parameters or element values. This paper expands [3] by studying the relationship between these two phenomena, apparently quite different, which will be done through a detailed analysis of the impact of the drain bias voltage on the turning-point locus. As will be shown, the turning-point locus, which at zero drain bias voltage is solely due to the input nonlinear capacitance, spreads over lower input power values. From certain , some discrete points of the locus reach zero input power and degenerate into free-running oscillations that coexist with a stable dc solution. As will be demonstrated in this work, under most input matching conditions, this oscillation cannot be detected with any standard stability analysis, as it coexists with a stable dc regime even for gate bias voltages above the conduction threshold. When injecting the input power, it will give rise to a stable self-oscillating mixer regime, coexisting with the stable periodic solution at the frequency of the input source. The oscillation will be extinguished either through synchronization [5], [12], for input frequencies near the free-running oscillation frequency, or through inverse Hopf-type bifurcations [5], [6], [12]. This paper expands [3] with a detailed analysis of the oscillatory solution and the mechanisms for the oscillation extinction. Synchronization of an oscillation with an injection source occurs at particular types of turning points, at which a local-global

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DE COS et al.: HYSTERESIS AND OSCILLATION IN HIGH-EFFICIENCY PAs

bifurcation takes place [5], [12], [13], also known as a limit cycle on saddle node in the Poincaré map. Therefore, these bifurcations will belong to the turning-point locus that is efficiently detected with the outer-tier method. Another contribution relative to [3] is the derivation of a methodology for the Hopf bifurcations, which will be carried out combining this outer-tier method with a zero-amplitude oscillation condition, imposed with the aid of a small-signal AG [2], [5], [11]. Since the Hopf bifurcations may take place in any section of the multivalued curves, the combination of this limit-oscillation condition with the outer-tier method is very advantageous since it avoids the need for a large-signal nonperturbing AG to sustain solutions in sections of the multivalued curve to which commercial HB does not converge by default. Another extension with respect to [3] will be the combination of the outer-tier methodology with pole-zero identification to obtain the whole evolution of the stability properties of the multivalued solution curve in a single sweep with no need to perform any parameter switching. The ease of application of the bifurcation detection methodologies will allow an in-depth investigation of the impact of the most relevant parameters, such as the gate bias voltage, the input matching capacitor, and the input power, on the global stability of the PA. This will provide insight into the various instability mechanisms observed in the PA and the relationships between them. A final contribution expanding [3] is the derivation of an oscillator design methodology based on a controlled selection of the element values that should turn the Class-E PA into a highly efficient oscillator [14], able to start up from the noise level. RF power oscillators may be of interest for the implementation of high-power density and fast response resonant dc/dc converters [15], wireless power transmission links [16], etc. This paper is organized as follows. Section II presents the study of the hysteresis using a high-efficiency Class-E PA demonstrator. The stability of the resulting multivalued curves is analyzed in Section III with the aid of the outer-tier method. In Section IV, the detected free-running oscillation is related to the hysteresis phenomenon. Finally, a high efficient RF power oscillator is presented. II. STUDY OF HYSTERESIS A. Class-E PA Demonstrator A PA at 900 MHz was designed in [3] with the aim of obtaining a very high value of power-added efficiency (PAE). Among many choices, the high efficiency of Class-E operation was exploited, minimizing the switching loss associated with the transistor output capacitance. A CGH35030F GaN on SiC HEMT from Cree Inc. was selected as the switching element due to the very low value of its on resistance times output capacitance product and high breakdown voltage (over 120 V). Initially, the transistor was experimentally characterized in an Arlon 25N substrate ( mm, m) for a typical drain bias voltage V, after verifying the peak value of the voltage waveform, [17], would stay below the process breakdown figure. The gate bias voltage was set slightly below pinch-off: V, while the output capacitance and off-state resistance were estimated

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Fig. 1. (a) Schematic of the Class-E PA demonstrator [3]. Values in the table are for Colcraft Air Core inductors and ATC 100B capacitors. (b) Simulated reflection coefficient of the output network and load–pull contours. (c) Photograph of the measurement setup.

from the measured parameter [3]. The measured values of on-state resistance, output capacitance, and off-state resistance at 900 MHz are 0.6 , 3.5 pF, and 5.1 k , respectively. An ideal dc voltage source, a capacitor, and a resistance were added to the already accurate and reliable Cree’s proprietary large-signal transistor model to finely adjust, respectively, the values of the gate threshold voltage, output capacitance, and off-state resistance in simulations to the measured device parameters. As a first approximation, the output network was designed based on the optimum or nominal conditions for a 50% switching duty cycle and maximum output power found by Raab [17],

(1) Unfortunately, the required inductance value in the classic Class-E output network may be too large to be obtained with commercially available coils, as their self-resonant frequency could be below the most significant higher order harmonics to be properly terminated [18]. One not uncommon solution for lumped-element Class-E implementations at UHF band [19] is to take advantage of a high- coil with a self-resonant frequency in between the second- and third-order harmonics [20] so that a high enough impedance (either inductive or capacitive) is presented. Here, a slightly different strategy was adopted. A smaller inductor, in the schematic of Fig. 1(a), was selected, with an associated smaller equivalent series resistance at dc, trying to minimize its contribution to the circuit conduction loss [21]. In addition, advantage was taken from its higher self-resonant frequency at about the fifth-order harmonic for properly terminating most of them. The optimum reactance value in (1) was adjusted with a section of microstrip transmission line, while the capacitor to ground allowed synthesizing the desired . The reflection coefficient of the resulting output network, , is represented in the Smith chart in Fig. 1(b), together with the simulated load–pull contours for drain efficiency (solid line) and output power (dashed line).

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TABLE I RF CLASS-E PAs IN THE LITERATURE

Fig. 2. PAE of the Class-E PA versus input power. Solid lines are the results of a default simulation in commercial HB. The curve is completed (dashed line) with the method described in Section II-C. Symbols are measurements.

The contours were obtained at the fundamental frequency with ideal terminations (open circuit) to other harmonics. A typical single low-pass section was used to match the input of the PA to increase the gain and thus the PAE. The experimental value of the input matching capacitor was 10 pF, a bit lower than the one used in simulations. A resistance was introduced in the gate biasing path to improve stability at lower frequencies. Although not included in the schematic for simplicity, a capacitor of 56 pF and a bank of high-valued capacitors (1, 10, and 100 nF and 1 and 10 F) were added in the gate and drain dc lines. The employed measurement setup is shown in Fig. 1(c). As can be seen, two low-pass filters with cutoff frequency at 1 GHz are included just before the power sensor to exclude any possible contribution of harmonics different than the fundamental to the output power. Table I includes the measurement results and a comparison with other RF Class-E PAs in the literature. In Fig. 2, the PAE of the amplifier is represented versus the input power . When increasing , a jump is observed for 10 dBm. When decreasing the input power there is no longer a jump at 10 dBm, but at a lower value of about 7 dBm. This behavior is evidence of hysteresis. Looking at the simulated curve, two turning points or infinite slope points are found, responsible for the undesired phenomenon. The multivalued curve has been traced with the method described in Section II-C. Note that default HB is unable to pass through the infinite slope points. Any other solution curve (output power, power gain, dc consumption, etc.) represented versus the input power will fold at the same values of as the curve in Fig. 2.

carried out short circuiting the transistor drain and source terminals, and modeling the transistor input with only its nonlinear gate-to-channel capacitance, as depicted in Fig. 3(a). The input matching network considered is the one in the original design in Fig. 1(a), but neglecting the impact of the parasitics in the lumped elements, the transmission line, and the RF choke. A describing function of the corresponding nonlinear charge will be used, assuming a sinusoidal input waveform . This allows formulating the circuit at the fundamental frequency,

(2) has been defined. Calculating where a complex function the derivatives of the real and imaginary part of (2) with respect to and , the Jacobian matrix is shown in (3) at the bottom of this page, where . The singularity condition is

(4) The expression of the input power (in dBm) is obtained squaring and adding the real and imaginary parts of (2),

B. Study of the Parametric Hysteresis The hysteresis phenomenon observed in the solution curve of Fig. 2 is caused by a nonlinear resonance of the device input capacitance (due to the gate-to-source and the input-reflected gate-to-drain Miller capacitances [29]) with the inductive impedance of the input network. An analytical study will be

(5) Results obtained with the analytical formulation (5) and with HB are compared in Fig. 3(b). As shown in the figure, the simplified analytical study of the input network is able to predict

(3)

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Fig. 4. Circuit used for obtaining the outer-tier admittance function

Fig. 3. (a) Circuit used to study the input network of the PA. (b) Comparison between the analytical result and HB simulation. The turning points have been marked.

.

Fig. 5. PAE of the Class-E PA versus input power for some values of the gate bias voltage. Solid lines are simulation results obtained with the outer-tier method. The dashed line superimposed is the turning-point locus. Symbols are measurements.

the existence of two turning points. Each of these two turning points fulfills the condition (4). Discrepancies come from contributions of the extrinsic parameters inside the transistor model, not considered when calculating the nonlinear charge in the frequency domain. C. Analysis Method The multivalued solution curves will be obtained by adapting the outer-tier method, developed in [8] for injection-locked oscillators, to the case of PAs. The input generator is suppressed using, instead, an AG [5], [11] at the gate terminal, which operates at the input frequency (Fig. 4). This enables the calculation of the outer-tier admittance function , where is the current through the AG at the fundamental frequency and is the AG amplitude. The admittance function will be combined with the Norton equivalent of the input network at the gate terminal, which can be calculated from its scattering matrix. The combination of both functions provides an outer-tier equation, which relates the gate voltage amplitude at the fundamental frequency (agreeing with ) and the input generator current , (6) where

To obtain a power-transfer curve, is swept, calculating the function at each sweep step. The input generator current enabling each voltage is determined with the outer tier equation given by (6). Note that the outer-tier (6) is combined with the full HB system, acting as an inner tier, so all the circuit variables are available at each sweep step. Therefore, relevant magnitudes such as the output power or

Fig. 6. Turning-point locus in the plane defined by the gate bias voltage and the input power. Square symbols are measurements (for the particular value V, it was also measured when decreasing ).

efficiency can be calculated in a straightforward manner. The outer-tier method provides the multivalued solution curves with no need of parameter switching unlike previous works [5], [30]. The method has been applied to complete the solution curve in Fig. 2 and to trace the whole one in Fig. 3 in simulation. It has also been used to analyze the impact of the gate bias voltage on the PAE curves (Fig. 5). It must be emphasized that here a complete description of the input network is considered, including full models of the passive components, the transmission line, and the RF choke. The evolution of the hysteresis region versus a relevant parameter , affecting the nonlinear resonance, can be efficiently investigated by tracing the turning-point locus in the plane defined by the particular parameter and the input power, following the method in [8]. One of these analysis parameters

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Fig. 7. Zero-level contours of the total conductance and susceptance obtained when introducing an AG at the gate terminal for V dBm. The intersections determine the three solutions in the correand sponding solution curve of Fig. 2. Note the multivalued nature of the contours.

is , already considered in the analysis of Fig. 5, and the other is the input matching capacitance . To obtain the turning-point locus one should consider the surface described by (6) on the plane defined by and . The turning-point locus is the set of points of satisfying zero partial derivative with respect to , i.e., the zero-level contour, (7) as a parameter The locus resulting from (7) when using has been superimposed on the solution curves of Fig. 5 via the dashed line. As can be seen, the locus passes through all the turning points of the solution curves. Fig. 6 shows the same turning-point locus represented in the plane defined by and . The hysteresis region decreases with and vanishes to zero near the pinch-off voltage . Measurement points are superimposed. To get some insight into the reasons for the observation of the phenomena in the lower range, one must take into account that in these subthreshold conditions the transistor gain increases with the excitation amplitude. As a result, the conductance function, when looking into the circuit nonlinear section from the AG terminals (Fig. 4), initially increases with the excitation amplitude and then decreases as expected in any physical device. Since the frequency of each coexisting solution agrees with the frequency of the input source, the phase shift between the driving source and the AG excitation voltage is a relevant variable. Fig. 7 shows the contour plots of total conductance and total susceptance equal to zero in the plane defined by the AG phase and amplitude, when the input power is set to 8 dBm. The total conductance/susceptance functions include contributions from both the linear and nonlinear sections of the PA at the observation node. There is a steady-state solution for each intersection of the two contour plots so three steady-state solutions , , and coexist for this value, in agreement with the results of Fig. 2. The high dependence of the total admittance function on the excitation amplitude gives rise to two zero susceptance contours and a bending of the zero conductance contour. This favors the occurrence of three intersections,

Fig. 8. Evolution of the turning-point locus versus the drain bias voltage, repand . This diagram illustrates the conresented in the plane defined by nection between the hysteresis and a free-running oscillation. The values in the upper axis correspond to the quality factor of the input network for each value in the label.

corresponding to the three solutions that coexist for the particular value. Next, the impact of the matching capacitance will be analyzed. In [3], the turning-point locus was represented in the plane defined by and for different values of . This allowed to suppress the hysteresis. The final measurements results for an experimental capacitor value of 8.2 pF are 85.4% of PAE, 16.1 dB of power gain, and 12.3 W of output power. Here, the turning-point locus is represented in the plane defined by and for different values of the drain bias voltage . For V, one obtains the small-size locus in Fig. 8, existing for capacitor values between 31.3 and 52.3 pF. This locus characterizes the hysteresis phenomenon that is solely due to the nonlinear input capacitance, as studied in Section II-B. For each constant value, the locus provides the input power values at which the hysteresis jumps are produced. When increasing , there is also an influence of the nonlinear transfer characteristic [29], and the locus expands over larger intervals of and . From a certain value, the locus decays to zero value and this will give rise to an oscillation phenomenon. For a detailed analysis, the typical drain bias voltage V will be considered, as this is the one selected for the high-efficiency design. The analysis versus will be extended to the quality factor of the input network . For estimating , the transistor has been represented by a resistance in series with a linear capacitance, whose values were obtained from the device small-signal input impedance at V below pinchoff when short circuiting the drain and source terminals. Despite neglecting the nonlinear nature of the device input capacitance, this approximation may be appropriate enough as long as the signal excursion does not take the gate-to-source junction into conduction, as described in [31]. In these conditions, the general definition of the quality factor is applied, (8)

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where and are, respectively, the resistance and reactance of the circuit and . The frequency of resonance is found for each value of , computing through a finite difference for calculating the derivative. An additional axis is included in Fig. 8 with the values of corresponding to each value in the label. Fig. 9(a) presents the turning-point locus for V. In the results presented so far and in [3], a model of the input matching capacitor, including the parasitics, is used. For those analysis using as a parameter, a lower value is selected, for which no hysteresis is found, and then an ideal capacitor is connected in parallel. In this way, the value of the capacitance can be varied continuously. As can be seen in Fig. 9(a), there are two capacitor values for which the turning-point locus reaches the axis (zero input power value). At these two particular points, and , the locus should degenerate into two free-running oscillations. An interesting fact is that the dc solution of the PA is stable for all the capacitor values considered in Fig. 9(a), as the device is biased below pinch-off. In measurements, the dc solution was found stable for all the capacitor values tested, even when biasing the transistor above pinch-off. In simulations, the dc solution only becomes unstable in a very reduced region when biasing the transistor above pinch-off for large capacitor values. Therefore, the oscillations in Fig. 9(a) cannot be detected with a small-signal stability analysis of the PA. The relationship between the hysteresis and the oscillations obtained in Fig. 9(a) will be investigated with a stability analysis methodology adapted to the case of multivalued solutions. III. STABILITY ANALYSIS THROUGH MULTIVALUED SOLUTIONS

THE

The application of a complementary stability analysis through multivalued solution curves is demanding since HB will converge to the default solution, usually corresponding to the one with the smallest output power, or will not converge at all. To cope with this problem, the outer-tier method will be combined with pole-zero identification [32], [33] and bifurcation detection [2], [5], [11], [30], [34], as explained in the following. A. Stability Analysis In the analysis of Fig. 4, the whole solution curve is traced suppressing the input source and using an AG to calculate the outer-tier admittance function considered in (6). The curve is then obtained by sweeping the AG amplitude in HB. The input power is calculated from using the Norton equivalent. Thus, turning points only result from the composition of any of the circuit state variables with the input power. In this way, the equivalent system (6) provides the same solutions that would be obtained with a suitably initialized HB system. Therefore, the stability can be analyzed with the AG connected to the circuit, instead of the driving source (Fig. 4). Note that unlike other previous methods the AG does not fulfill a nonperturbation condition. In the presence of this AG, a small-signal current source at the incommensurate frequency is introduced at a sensitive circuit node (the gate terminal). This source is used to linearize the circuit about the large-signal periodic regime at

Fig. 9. Synchronization with free-running oscillations. (a) Turning-point (solid line) and Hopf-bifurcation (dashed–dotted line) loci: input power versus the in free-running input matching capacitor value. (b) Output power versus W). (c) Autonomous frequency versus in free-runoperation ( values for which the autonomous frequency ning operation. Note that the is 0.9 GHz agree with the degenerate points of the turning-point locus ( W). Stable (unstable) sections in solid (dashed) line. Square symbols are mea). surements (attention was only paid to values close to

each HB sweep step with the conversion-matrix approach [35], [36]. The following calculation is performed: (9)

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Fig. 10. Comparison between the transfer function obtained in the original circuit with the one obtained using the circuit of Fig. 4.

small input power, this oscillation will give rise to a quasi-periodic regime. Therefore, when injecting input power, one may expect the occurrence of Hopf bifurcations, leading to a transition between the periodic and quasi-periodic regime or vice versa. In previous works [2], [5], [30], Hopf bifurcations are detected by introducing an AG at the oscillation frequency and solving the steady-state oscillation condition for oscillation amplitude tending to zero. Again, a problem arises when dealing with multivalued solution curves as the Hopf bifurcation may occur in the curve sections to which commercial HB does not converge by default. Here, the outer-tier method will be used to avoid the need of an extra AG to initialize/sustain these coexisting solutions. Let a Hopf bifurcation leading to the generation/extinction of an oscillation at the frequency be considered. The oscillation amplitude tends to zero at the bifurcation point so this bifurcation can be detected linearizing the circuit about the largesignal periodic solution at each HB sweep step with the conversion-matrix approach [35], [36]. A small-signal current source at is connected to a sensitive node of the circuit in Fig. 4. At each Hopf bifurcation, the following system of combined steady-state plus bifurcation equations must then be fulfilled: (10)

Fig. 11. Comparison between the Hopf-bifurcation locus obtained with the previous method and with the new method.

where is the gate node voltage and is the current of the small-signal source. The stability analysis is performed applying pole-zero identification [32], [33] to the function (9) obtained for each value. For the stability analysis to work properly, a difference with respect to [3] and [8] must be remarked: the filter should only stop the frequency of the input generator (0.9 GHz), allowing for a proper impedance termination at other harmonic mixing terms. For validation, the stability analysis has been applied to the solution point in Figs. 2 and 7. Note that it is a point to which the HB method converges by default, as gathered from the solid line simulation in Fig. 2. The transfer functions obtained with the original circuit and performing the topology change (suppression of the input source plus introduction of the outer-tier AG) are compared in Fig. 10. The results in the two different analysis conditions overlap. B. Hopf-Bifurcation Detection The degenerate points and in the turning-point locus of Fig. 9(a) evidence the existence of a free-running oscillation for some capacitor values. In the presence of a relatively

where is the sensitive node voltage and is the current of the small-signal source. System (10) is solved through optimization of and . Note that the standard AG-based procedure [11] would also require the optimization of the amplitude and phase of the extra AG that is used to achieve convergence to the upper section(s) of the solution curve, and therefore, it is a more demanding optimization process. Parameter switching in this extra AG would be needed for the calculation of the whole Hopf-bifurcation locus versus two relevant parameters, such as and . The Hopf-bifurcation locus obtained with (10) has been superimposed in the plane defined by and in Fig. 9(a). As can be seen, the Hopf locus is composed by three different sections. Section 1 corresponds to Hopf bifurcations in the lower sections of the multivalued curves. Section 2 corresponds to Hopf bifurcation in the upper sections of the multivalued curves and Section 3 to Hopf bifurcations obtained for capacitor values at which the solution curve is no longer multivalued. The accuracy of the Hopf-bifurcation locus calculated with (10) has been validated through comparison with the one obtained with the previous method [11], which, by default, can only detect Hopf bifurcations in the nonmultivalued sections of the curves. As shown in Fig. 11, the results of both methods are totally overlapped. In Section IV, the described approach will be applied for a detailed investigation of the relationship between the hysteresis and the oscillatory phenomena detected in Fig. 9(a). IV. RELATIONSHIP BETWEEN HYSTERESIS SELF-OSCILLATION

AND

The turning-point locus in Fig. 9(a) indicates the presence of free-running oscillations that cannot be detected with an ordi-

DE COS et al.: HYSTERESIS AND OSCILLATION IN HIGH-EFFICIENCY PAs

nary stability analysis of the dc solution. This is because the periodic solution at the input drive frequency is stable when the transistor is biased below pinch-off. The interval for which these oscillations exist will be analyzed using one of the two degenerate turning points at W as an initial value for a free-running oscillator analysis. Using an AG [5], the free-running oscillation curve has been traced versus at constant V, in Fig. 9(b). As can be seen, the solution curve exhibits a turning point at pF. For , there is no oscillatory solution. For , there are two coexisting steady-state oscillations for each value. The infinite slope point at implies that a real pole passes through zero at this particular capacitor value [5]. Therefore, the two sections of the oscillation curve must exhibit different stability properties. As has been verified with pole-zero identification [32], applied through the oscillation curve, the upper section of this curve is stable and the lower section is unstable. At each of the two points of the turning-point locus in Fig. 9(a) obtained for W, the PA solution degenerates into a free-running oscillation, having approximately the same frequency as the input generator (0.9 GHz). In fact, there are two capacitor values for which the free-running frequency agrees with this precise value, as gathered from Fig. 9(c). Each of them is responsible for one of the two degenerate points in the turning-point locus of Fig. 9(a). With the values considered in the measurements and under a full variation of , the dc solution was always stable so dc solutions were physically obtained in the whole bias voltage range going from 8 to 2.3 V. Despite this fact, a free-running oscillation coexists with each dc solution, which in measurements could only be observed by injecting input power up to a certain level and then decreasing this power to zero. The described situation prevents the detection of this oscillation when performing a stability analysis of the dc solution. As an example, Fig. 12(a) presents the closed oscillation curve obtained for pF versus . The oscillation amplitude does not decay to zero for any value so there are no Hopf bifurcations in dc regime. This is why this oscillation does not start up from the noise level. Arguably, the oscillation in Fig. 9(b) should arise at a Hopf bifurcation from the dc regime, obtained versus the gate bias voltage for some combinations of the capacitor and other circuit element values. Fig. 12(b) presents the variation of the dominant poles of the dc solution versus the gate bias voltage. The poles approach the imaginary axis, but do not cross this axis, which prevents the detection of the coexisting high amplitude oscillation of the PA. As already stated, to obtain this oscillation in measurements it was necessary to inject the circuit with enough input power from the driving source and then reduce to zero for a particular value of . Once oscillating, can be varied to obtain the measurement points. The measurement points obtained in this way are superimposed in Fig. 12(a). The reason why the input power is able to start the oscillation will be understood after a thorough stability analysis of the periodic solution curves obtained versus the input power. The impact of the free-running oscillation in Fig. 12(a) on the stability properties of the PA power-transfer curves will be analyzed considering variations in the capacitor , which di-

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pF in freeFig. 12. (a) Output power versus gate bias voltage for running operation. Stable (unstable) sections are in solid (dashed) line. Square symbols are measurements. (b) Stability analysis of the dc solution versus the gate bias voltage.

rectly affects the input matching and oscillation conditions, as gathered from Fig. 9. This capacitor will be varied from 12 to 23 pF. Fig. 13 presents the turning-point and Hopf-bifurcation loci, calculated with (7) and (10), respectively, in the plane defined by the input power and the capacitance . The values (starting at pF) that give rise to a free-running oscillation, as detected from the solution curve in Fig. 9(b), are indicated with a thick vertical line at W. For these capacitor values when increasing from zero, the oscillation associated will give rise to a self-oscillating mixing regime coexisting with the periodic stable solution. This quasi-periodic regime has never been observed experimentally when increasing the input power from zero. Once the circuit is operating in the upper section of a given periodic solution curve, it is observed when reducing the input power. There is then a transition from a periodic regime at to a self-oscillating mixer solution. This solution is mathematically extinguished at certain input power so it only exists in the lower input power range. Depending on the input frequency value, it can be extinguished in two different manners: through synchronization or through an inverse Hopf bifurcation. Synchronization will occur for capacitor values such that the free-running oscillation frequency is close enough to the fre-

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Fig. 13. Turning-point (solid line) and Hopf-bifurcation (dashdot line) loci repand . The capacitor values giving rise resented in the plane defined by to a free-running oscillation have been marked with a thick solid line. The values analyzed in Fig. 14 are marked.

quency of the input generator . Due to the similarity of the two frequencies, the input source will have a significant influence over the self-oscillation. Therefore, the synchronization will take place for rather low input power values. Inverse Hopf bifurcations will be obtained for capacitor values such that the free-running oscillation frequency is farther away from . Due to the larger frequency difference, a higher input power will be required for extinction of the oscillation. As described in the following, the parameter region for the occurrence of each of the two phenomena is easily determined from inspection of Fig. 13. As already stated, a stable free-running oscillation will exist for all the capacitor values in the thick solid line in Fig. 13. In the neighborhood of the degenerate point , the transition to periodic regime will take place when crossing the turning-point locus as the input power is increased. In fact, turning points do not always indicate jump phenomena, but may also correspond to synchronization (limit cycle on a saddle node in the Poincaré map), as described in [6] and [12]. As a general rule, turning points near the free-running oscillation, having no Hopf bifurcations in the neighborhood, will correspond to synchronization [5]. In the diagram of Fig. 13, this will be the case for values between 15.8 and 20.8 pF. Oscillation extinction through an inverse Hopf bifurcation takes place for a higher difference between and the original free-running value. In the diagram of Fig. 13, this occurs when Section 2 of the Hopf-bifurcation locus is crossed when increasing the input power. This is the case for capacitor values pF. It is important to emphasize that the free-running oscillation in Fig. 13 cannot be detected with a small-signal stability analysis. Section 1 of the Hopf locus corresponds to Hopf bifurcations in the lower section of the multivalued curves. Their implications on the circuit solution will be better understood when superimposing the Hopf-bifurcation locus on the power-transfer curves obtained for different values. Fig. 14(a) and (b) presents the power-transfer curves obtained for pF and pF, respectively. The turning-point locus obtained with (7) passes through all the infinite-slope points of the solution curves (marked in the figure with a ), as can be verified through simple inspection. On the

Fig. 14. Periodic solution curves of the PA: output power versus input power . The stable sections are highlighted. The turningfor different values of point (dashed line) and Hopf-bifurcation (dashdot line) loci, together with the pF. Square symbols are bifurcations points, have been included. (a) pF. (c) and pF. measurements. (b)

other hand, the Hopf locus obtained with (10) passes through all the Hopf bifurcaton points (marked with ), as will be validated later with pole-zero identification. The case of pF will be initially considered. The lower section of the power-transfer curve, up to the point , is stable. This is because, when injecting the input power, it emerges from a stable dc regime. At the Hopf bifurcation, a

DE COS et al.: HYSTERESIS AND OSCILLATION IN HIGH-EFFICIENCY PAs

quasi-periodic regime is generated, which should be extinguished from certain input power, due to the natural reduction of the negative resistance with the input amplitude. When the oscillation is extinguished, a jump takes place to the upper section of the periodic curve, with stable behavior. Now, reducing the input power, the circuit remains in the stable periodic solution up to the Hopf bifurcation , where an oscillation is generated. Note that when increasing the input power from zero, the self-oscillation [due to the existence of free-running solutions in Fig. 9(b)] is extinguished at this same bifurcation. However, because of the coexistence of the stable periodic solution with this oscillatory regime, it will be rare to observe this oscillation when increasing the input power from zero. The upper section of the periodic curve is unstable between the turning point and the Hopf bifurcation so the potential jump point is never reached physically. In the case of pF, when increasing from zero, the periodic solution curve will be stable up to the Hopf-bifurcation point . In a manner similar to the previous case, a transition to quasi-periodic regime will occur at this point and then to the upper section of the periodic curve, with stable behavior. When decreasing the input power, the upper section of the curve keeps stable up to the turning point , which is, in fact, a synchronization point. The reason for the different behavior is that the input frequency 0.9 GHz is quite close to the free-running oscillation frequency obtained for pF so the transition to quasi-periodic regime is through a loss of synchronization. For pF, there is no longer a free-running oscillation, as gathered from Fig. 9(b), so, as can be expected, there is no Hopf bifurcation in the lower section of the periodic solution curve in Fig. 14(c), in agreement with Fig. 13. The two turning points will give rise to jumps between different sections of the multivalued periodic curve (hysteresis). For pF, a regular curve showing gain expansion (with neither oscillation nor jumps) is obtained. As gathered from the bifurcation loci in Fig. 13, there can be Hopf bifurcations in the lower section of the curves (Section 1 of the Hopf-bifurcation locus) even when there are no free-running oscillations. The quasi-periodic regime generated at these points should exhibit a turning point when increasing the input power (as those reported in [5] and [11]) and be extinguished in a saddle-connection bifurcation in the Poincaré map [12]. This is a global bifurcation [12] that requires the presence of a saddle point such as those in the intermediate section of the multivalued solution curves. The saddle-connection bifurcation is also associated with co-dimension two bifurcations, at which the turning-point and the Hopf-bifurcation loci merge, such as the ones indicated with in Figs. 9(a) and 13. The accuracy of the Hopf-bifurcation detection has been validated with pole-zero identification. Fig. 15 shows the evolution of the critical poles of the solution curve corresponding to pF. The pole locus indicates that the lower section is stable up to dBm, where the poles cross to the right-hand side of the complex plane (RHP), giving rise to a Hopf bifurcation from periodic regime. The poles merge and split into two real poles, and for dBm, one of the real poles crosses to the left-hand side of the complex plane (LHP) at a turning point

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Fig. 15. Pole locus of the solution curve in Fig. 14(a) obtained for pF.

in the solution curve. This real pole crosses again to the RHP at dBm, giving rise to the second turning point in the solution curve. When further increasing the input power, the two real poles merge on the RHP and split into two pairs of complex-conjugate poles (associated with a same pair of Floquet multipliers [5], [6], [37]). At dBm, the poles cross to the LHP giving rise to an inverse Hopf bifurcation from which the periodic solution curve becomes stable. The pole analysis is in total agreement with the results of the bifurcation analysis in Figs. 13 and 14(a). The PA measurements for an input matching capacitor of 12 pF have been superimposed in Fig. 14(a). The capacitor value is significantly lower in measurements that the one used in simulations. As mention in Section II-A, the capacitor value that best matched the input of the PA in measurements was already lower than the one used in simulations. The shift in the capacitor value is attributed to modeling inaccuracies. One must also take into account that the value used in the simulations was a combination of a lower capacitor value and an ideal capacitor connected in parallel, to be able to vary the capacitance continuously, as explained in Section III-A. Even under this unavoidable accuracy limitations, the qualitative behavior and power levels are reproduced satisfactory. The measured spectra at different input power values are shown in Fig. 16. At low input power, the spectrum is periodic, as shown in Fig. 16(a). When continuously increasing the input power, a Hopf bifurcation is obtained at dBm, which gives rise to the quasi-periodic spectrum in Fig. 16(b). When further increasing the input power, the self-oscillation vanishes due to a turning point in the quasi-periodic solution curve so a jump takes place at dBm to the upper section of the periodic solution curve. Fig. 16(c) shows the spectrum obtained for dBm. Now, when reducing the input power, the PA keeps behaving in the periodic regime up to the input power dBm, at which the circuit undergoes a Hopf bifurcation. Below dBm, the circuit operates in a quasi-periodic regime [see Fig. 16(d)] that is never observed when increasing the input power from zero. The results are in total agreement with the two Hopf-bifurcation points that were detected with (10) and displayed in Figs. 13 and 14(a).

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Fig. 16. Sequence of output spectra measured for pF. (a) When dBm). increasing the input power from very low value it is periodic ( dBm). (c) Jump to the periodic (b) Jump to a quasi-periodic solution ( dBm). (d) Now, when decreasing the input power, a quasisolution ( periodic solution, resulting from the mixing with the free-running oscillation, is dBm). Synchronization with this last one is obtained observed ( reducing the input frequency. (e) Adler spectrum near synchronization ( GHz).

With the discrete capacitor values available during the experimental tests, it was not possible to observe a synchronization phenomenon with the input frequency GHz. This is because, for those capacitor values, the frequency of the free-running oscillation that coexists with the dc solution is too different from GHz. To validate the existence of the phenomenon, a small shift was applied to the input frequency, using, instead, the value GHz, together with the capacitor pF. With these parameter values, synchronization could be measured. The typical near-synchronization spectrum, with a triangular shape [38], is shown in Fig. 16(e). As previously shown, the input power is able to start an oscillation in the PA, which persists when reducing the power to zero, even when the dc solution is stable in the whole range considered. In Section IV-A, the above study will allow turning the PA into a highly efficient free-running power oscillator. A. High-Efficiency RF Class-E Power Oscillator In simulation, a shift of the pole locus in Fig. 12(b) to the right is observed when suppressing the 50- load of the input source. This gives rise to an interval of values for which the dc solution becomes unstable, allowing the oscillation to

Fig. 17. (a) Output power and efficiency of the RF Class-E power oscillator, represented versus the gate bias voltage. Square symbols are measurements. V. (b) Phase noise spectral density measured at

start up from the noise level. Fig. 17(a) presents the free-running oscillation curve obtained for the original capacitor value pF in the design of Fig. 1(a). Note that the oscillation persists in a large gate bias voltage interval. The Hopf bifurcation from the dc regime is subcritical [5], [12], [39] so the oscillation amplitude grows for decreasing values of . In measurements, the value of for which the oscillation starts up ( 2.8 V) agrees with the Hopf-bifurcation point obtained in simulation. The evolution observed versus is in total agreement with the predicted results. In comparison with other configurations, requiring an accurate synthesis of a feedback network [39], the oscillator topology is greatly simplified. Indeed, the feedback path is provided here by the device gate-to-drain capacitance . In Fig. 17(a), the efficiency variation has also been represented versus the gate bias voltage. A peak value as high as 86.4% was measured for V, staying above 80% for V. The gate bias voltage provides a simple way to control the oscillation frequency. For the voltage interval considered in Fig. 17(a), it varies between 0.826 and 0.98 GHz. Finally, the phase noise spectral density was captured for several oscillation frequencies and no noticeable difference was appreciated. In Fig. 17(b), it is represented at V. Phase noise values of 114.8 and 141.4 dBc/Hz were estimated for frequency offsets of 100 kHz and 1 MHz, respectively,

DE COS et al.: HYSTERESIS AND OSCILLATION IN HIGH-EFFICIENCY PAs

in the ranges reported in the literature for GaN HEMT based oscillators [40]. V. CONCLUSION An in-depth investigation of hysteresis in a Class-E PA has been presented, demonstrating that it is due to a nonlinear resonance of the transistor input capacitance with the inductive input matching network. The different set of circuit parameters and operating conditions that give rise to turning points in the solution curves are efficiently detected with an outer-tier method, under a geometrical condition for infinite slope. Under an increase of the drain bias voltage, the locus evolves so as to give rise to a free-running oscillation that for the most usual circuit element values cannot be detected with any standard stability analysis, even under an exhaustive variation of the bias voltages. Under input power injection, this oscillation will give rise to an undesired self-oscillating mixer regime, extinguished either through synchronization or inverse Hopf bifurcations. The Hopf bifurcations in the multivalued curves can be efficiently detected combining the outer-tier method with a limit-oscillation condition imposed with the aid of a small-signal AG. The great flexibility in the bifurcation analysis has enabled a thorough investigation of the circuit stability properties under extensive variations of bias voltages, input power, and circuit element values. In this way, it has been possible to modify the original PA design, close to the state-of-the-art for the UHF band so as to make a practical use of the oscillation originally associated with the degenerated turning points. It has been possible to obtain a high-efficiency Class-E oscillator with a slight variation of the input network, providing 154 MHz of frequency coverage with an efficiency figure above 80%. ACKNOWLEDGMENT The authors would like to thank M. N. Ruiz, University of Cantabria, for her assistance with measurements, J. Ma Salmón (retired) for kindly crafting the aluminum carriers for the PA, S. Pana, University of Cantabria, for her help with the fabrication of the prototype, and R. Baker, Cree Inc., for the support provided. REFERENCES [1] F. H. Raab et al., “Power amplifiers and transmitters for RF and microwave,” IEEE Trans. Microw. Theory Techn., vol. 50, no. 3, pp. 814–826, Mar. 2002. [2] S. Jeon, A. Suárez, and D. B. Rutledge, “Analysis and elimination of hysteresis and noisy precursors in power amplifiers,” IEEE Trans. Microw. Theory Techn., vol. 54, no. 3, pp. 1096–1106, Mar. 2006. [3] J. de Cos, A. Suárez, and J. A. Garc´ıa, “Parametric hysteresis in power amplifiers,” in IEEE MTT-S Int. Microw. Symp. Dig., 2015, pp. 1–4. [4] N.-Ch. Kuo et al., “DC/RF hysteresis in microwave pHEMT amplifier induced by gate current—Diagnosis and elimination,” IEEE Trans. Microw. Theory Techn., vol. 59, no. 11, pp. 2919–2930, Nov. 2011. [5] A. Suárez, Analysis and Design of Autonomous Microwave Circuits. Hoboken, NJ, USA: Wiley, 2009. [6] T. S. Parker and L. O. Chua, Practical Numerical Algorithms for Chaotic Systems. New York, NY, USA: Springer-Verlag, 1989. [7] E. Palazuelos, A. Suárez, J. Portilla, and F. J. Barahona, “Hysteresis prediction in autonomous microwave circuits using commercial software: Application to a Ku-band MMIC VCO,” IEEE J. Solid-State Circuits, vol. 33, no. 8, pp. 1239–1243, Aug. 1998.

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[8] J. de Cos and A. Suárez, “Efficient simulation of solution curves and bifurcation loci in injection-locked oscillators,” IEEE Trans. Microw. Theory Techn., vol. 63, no. 1, pp. 181–197, Jan. 2015. [9] D. Hente and R. H. Jansen, “Frequency-domain continuation method for the analysis and stability investigation of nonlinear microwave circuits,” Proc. Inst. Elect. Eng., vol. 133, no. 5, pt. H, pp. 351–362, Oct. 1986. [10] L. O. Chua and A. Ushida, “A switching-parameter algorithm for finding multiple solutions of nonlinear resistive circuits,” Int. J. Circuit Theory Appl., vol. 4, no. 3, pp. 215–239, Jul. 1976. [11] A. Suárez, J. Morales, and R. Quéré, “Synchronization analysis of autonomous microwave circuits using new global-stability analysis tools,” IEEE Trans. Microw. Theory Techn., vol. 46, no. 5, pp. 494–504, May 1998. [12] J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamic Systems, and Bifurcations of Vector Fields. New York, NY, USA: Springer-Verlag, 1983. [13] S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos. New York, NY, USA: Springer-Verlag, 1990. [14] J. Ebert and M. Kazimierczuk, “Class E high-efficiency tuned power oscillator,” IEEE J. Solid-State Circuits, vol. SSC-16, no. 2, pp. 62–66, Apr. 1981. [15] H. Hase, H. Sekiya, J. Lu, and T. Yahagi, “Resonant DC/DC converter with class E oscillator,” in IEEE Int. Circuits Syst. Symp., 2005, pp. 720–723. [16] A. N. Laskovski and M. R. Yuce, “Class-E oscillators as wireless power transmitters for biomedical implants,” in Int. Appl. Sci. Biomed. Commun. Tech. Symp., 2010, pp. 1–5. [17] F. H. Raab, “Idealized operation of the class E tuned power amplifier,” IEEE Trans. Circuits Syst., vol. CS-24, no. 12, pp. 725–735, Dec. 1977. [18] F. H. Raab, “Class-E, class-C, and class-F power amplifiers based upon a finite number of harmonics,” IEEE Trans. Microw. Theory Techn., vol. 49, no. 8, pp. 1462–1468, Aug. 2001. [19] J. A. Garc´ıa, R. Marante, and M. N. Ruiz, “GaN HEMT class E2 resonant topologies for UHF DC/DC power conversion,” IEEE Trans. Microw. Theory Techn., vol. 60, no. 12, pp. 4220–4229, Dec. 2012. [20] R. Negra and W. Bächtold, “Lumped-element load-network design for class-E power amplifiers,” IEEE Trans. Microw. Theory Techn., vol. 54, no. 6, pp. 2684–2690, Jun. 2006. [21] N. O. Sokal and A. Mediano, “Redefining the optimum RF class-E switch-voltage waveform, to correct a long-used incorrect waveform,” in IEEE MTT-S Int. Microw. Symp. Dig., 2013, pp. 1–3. [22] N. D. Lopez, J. Hoversten, M. Poulton, and Z. Popović, “A 65-W highefficiency UHF GaN power amplifier,” in IEEE MTT-S Int. Microw. Symp. Dig., 2008, pp. 65–68. [23] J. Cumana, A. Grebennikov, G. Sun, N. Kumar, and R. H. Jansen, “An extended topology of parallel-circuit class-E power amplifier to account for larger output capacitances,” IEEE Trans. Microw. Theory Techn., vol. 59, no. 12, pp. 3174–3183, Dec. 2011. [24] A. Al Tanany, A. Sayed, and G. Boeck, “Broadband GaN switch mode class E power amplifier for UHF applications,” in IEEE MTT-S Int. Microw. Symp. Dig., 2009, pp. 761–764. [25] T. B. Mader, E. W. Bryerton, M. Markovic, M. Forman, and Z. Popović, “Switched-mode high-efficiency microwave power amplifiers in a free-space power-combiner array,” IEEE Trans. Microw. Theory Techn., vol. 46, no. 10, pp. 1391–1398, Oct. 1998. [26] Y. Qin, S. Gao, P. Butterworth, E. Korolkiewicz, and A. Sambell, “Improved design technique of a broadband class-E power amplifier at 2 GHz,” in Eur. Microw. Conf., 2005, pp. 4–6. [27] H. G. Bae, R. Negra, S. Boumaiza, and F. M. Ghannouchi, “High-efficiency GaN class-E power amplifier with compact harmonic-suppression network,” in Eur. Microw. Conf., 2007, pp. 9–12. [28] M. P. van der Heijden, M. Acar, and J. S. Vromans, “A compact 12-watt high-efficiency 2.1–2.7 GHz class-E GaN HEMT power amplifier for base stations,” in IEEE MTT-S Int. Microw. Symp. Dig., 2009, pp. 657–660. [29] L. C. Nunes, P. M. Cabral, and J. C. Pedro, “AM/AM and AM/PM distortion generation mechanisms in Si LDMOS and GaN HEMT based RF power amplifiers,” IEEE Trans. Microw. Theory Techn., vol. 62, no. 4, pp. 799–809, Apr. 2014. [30] A. Suárez and R. Quéré, Stability Analysis of Nonlinear Microwave Circuits. Boston, MA, USA: Artech House, 2003. [31] S. Maas, The RF and Microwave Circuit Design Cookbook. Norwood, MA, USA: Artech House, 1998. [32] J. Jugo, J. Portilla, A. Anakabe, A. Suárez, and J. M. Collantes, “Closed-loop stability analysis of microwave amplifiers,” Electron. Lett., vol. 37, no. 4, pp. 226–228, Mar. 2001.

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[33] N. Ayllon, J. M. Collantes, A. Anakabe, I. Lizarraga, G. SoubercazePun, and S. Forestier, “Systematic approach to the stabilization of multitransistor circuits,” IEEE Trans. Microw. Theory Techn., vol. 59, no. 8, pp. 2073–2082, Aug. 2011. [34] S. Jeon, A. Suárez, and D. B. Rutledge, “Global stability analysis and stabilization of a class-E/F amplifier with a distributed active transformer,” IEEE Trans. Microw. Theory Techn., vol. 53, no. 12, pp. 3712–3722, Dec. 2005. [35] J. M. Paillot, J. C. Nallatamby, M. Hessane, R. Quéré, M. Prigent, and J. Rousset, “A general program for steady state, stability, and FM noise analysis of microwave oscillators,” in IEEE MTT-S Int. Microw. Symp. Dig., 1990, pp. 1287–1290. [36] V. Rizzoli, F. Mastri, and D. Masotti, “General noise analysis of nonlinear microwave circuits by the piecewise harmonic-balance technique,” IEEE Trans. Microw. Theory Techn., vol. 42, no. 5, pp. 807–819, May 1994. [37] J. M. Collantes, I. Lizarraga, A. Anakabe, and J. Jugo, “Stability verification of microwave circuits through Floquet multiplier analysis,” in Proc. IEEE Asia–Pacific Circuits Syst., 2004, pp. 997–1000. [38] R. Adler, “A study of locking phenomena in oscillators,” Proc. IEEE, vol. 61, no. 10, pp. 1380–1385, Oct. 1973. [39] S. Jeon, A. Suárez, and D. B. Rutledge, “Nonlinear design technique for high-power switching-mode oscillators,” IEEE Trans. Microw. Theory Techn., vol. 54, no. 10, pp. 3630–3640, Oct. 2006. [40] M. Horberg, L. Szhau, T. N. T. Do, and D. Kuylenstierna, “Phase noise analysis of a tuned-input/tuned-output oscillator based on a GaN HEMT device,” in Eur. Microw. Conf., 2014, pp. 1118–1121.

Jesús de Cos (S’15) was born in Santander, Spain. He received the Telecommunications Engineering degree and M.Sc. degree from the University of Cantabria, Santander, Spain, in 2010 and 2011, respectively, and is currently working toward the Ph.D. degree at the University of Cantabria. His research interests include stability analysis, bifurcation theory, and circuit simulation techniques applied to microwave circuits. Mr. de Cos was a finalist in the IEEE Microwave Theory and Techniques Society (IEEE MTT-S) International Microwave Symposium Student Paper Competition in 2015.

Almudena Suárez (M’96–SM’01–F’12) was born in Santander, Spain. She received the Electronic Physics and Ph.D. degrees from the University of Cantabria, Santander, Spain, in 1987 and 1992, respectively, and the Ph.D. degree in electronics from the University of Limoges, Limoges, France, in 1993. She is currently a Full Professor with the Communications Engineering Department, University of Cantabria. She coauthored Stability Analysis of Nonlinear Microwave Circuits (Artech House, 2003). She authored Analysis and Design of Autonomous Microwave Circuits (IEEE, 2009). Dr. Suárez is a member of the Technical Committees of the IEEE Microwave Theory and Techniques Society (IEEE MTT-S) International Microwave Symposium (IMS) and the European Microwave Conference. She was an IEEE Distinguished Microwave Lecturer (2006–2008). She has been a member of the Board of Directors of the European Microwave Association (EuMA) since 2012. She is the editor-in-chief of the International Journal of Microwave and Wireless Technologies.

José A. Garc´ıa (S’98–A’00–M’02) was born in Havana, Cuba. He received the Telecommunications Engineering degree from the Instituto Superior Politécnico “José A. Echeverría” (ISPJAE), Havana, Cuba, in 1988, and the Ph.D. degree from the University of Cantabria, Santander, Spain, in 2000. From 1988 to 1991, he was a Radio System Engineer with a high-frequency (HF) communication center, where he designed antennas and HF circuits. From 1991 to 1995, he was an Instructor Professor with the Telecommunication Engineering Department, ISPJAE. From 1999 to 2000, he was with Thaumat Global Technology Systems, as a Radio Design Engineer involved with base-station arrays. From 2000 to 2001, he was a Microwave Design Engineer/Project Manager with TTI Norte, during which time he was in charge of the research line on SDR while involved with active antennas. From 2002 to 2005, he was a Senior Research Scientist with the University of Cantabria, where he is currently an Associate Professor. During 2011, he was a Visiting Researcher with the Microwave and RF Research Group, University of Colorado at Boulder. His main research interests include nonlinear characterization and modeling of active devices, as well as the design of power RF/microwave amplifiers, wireless powering rectifiers, and RF dc/dc power converters.

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Digitally Assisted Analog/RF Predistorter With a Small-Signal-Assisted Parameter Identification Algorithm Hai Huang, Student Member, IEEE, Jingjing Xia, Anik Islam, Eric Ng, Student Member, IEEE, Peter M. Levine, Member, IEEE, and Slim Boumaiza, Senior Member, IEEE

Abstract—This paper proposes a digitally assisted analog/radio frequency predistorter (ARFPD) and a linear small-signal-assisted parameter identification algorithm suitable for the linearization of power amplifiers driven with wideband and carrier aggregated communication signals. It starts by describing the newly proposed finite-impulse-response assisted envelope memory polynomial (FIR-EMP) model which allows for reduction of hardware implementation complexity while maintaining good linearization capacity and low power overhead. Furthermore, a linear two-step small-signal-assisted parameter identification algorithm is devised to estimate the parameters of the two main blocks of the FIR-EMP model. Measurement results obtained by using the FIR-EMP predistorter demonstrate its excellent linearization capacity when used to compensate for distortion exhibited by gallium nitride Doherty power amplifiers driven by digitally modulated signals with a bandwidth up to 80 MHz. This confirms the potential of ARFPD as a very promising candidate for the linearization of small cell base stations power amplifiers while simultaneously reducing the power overhead compared to the popular digital predistortion technique. Index Terms—Analog/radio frequency predistortion (ARFPD), digital predistortion (DPD), envelope memory polynomial (EMP), linearization, small-signal assisted parameter identification (SSAPI).

I. INTRODUCTION

T

HE NEED TO provide higher data rates and increased capacity has driven modern wireless communication systems to shift towards highly dense networks composed of large numbers of small-cells using advanced modulation schemes. For carrier-aggregated signals with modulation bandwidths of up to 100 MHz, and high peak-to-average power ratios (PAPR), high efficiency power amplifiers (PAs) for radio frequency (RF) wireless front-ends often require advanced efficiency enhancement techniques such as envelope tracking [1] and Doherty [2]. Such techniques unavoidably introduce significant distortions,

Manuscript received July 02, 2015; revised September 27, 2015, October 21, 2015; accepted October 22, 2015. Date of publication November 09, 2015; date of current version December 02, 2015. This paper is an expanded version from the IEEE MTT-S International Microwave Symposium, Phoenix, AZ, USA, 17–22 May 2015. The authors are with the Emerging Radio Systems Group (EmRG), Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON, Canada N2L 3G1 (e-mail: [email protected]; [email protected]; [email protected]; [email protected]; [email protected]; [email protected]). Digital Object Identifier 10.1109/TMTT.2015.2495362

which require sophisticated linearization systems to compensate for both the static nonlinearity and memory effects in order to meet the linearity requirements. Given the significantly lower transmitted power of small-cell base stations (a few watts or less down from tens of watts in macro-cell base stations), the power overhead of the linearization system can no longer be neglected. Digital predistortion (DPD), as shown in Fig. 1(a) is a popular choice to compensate for the distortion exhibited in PAs. It consists of pre-adjusting the communication signal magnitude and phase in baseband by applying a nonlinear function which mimics the inverse nonlinear behaviour of the PA [3]–[5]. To compensate for in-band distortions and inter-modulation products produced by the dynamic nonlinear behaviour of the PA, the output signal of the DPD has a wider bandwidth (typically five times) than that of the input baseband signal. Hence, the DPD engine needs to operate at much higher clock rates compared to the original digital baseband signal, and the digitalto-RF converter needs much faster digital-to-analog converters (DACs) and wider instantaneous bandwidth. The power overhead of DPD is only a minor concern for high power macro-cell base stations. However, as the power overhead increases with the signal bandwidth and does not scale down with the PA output level, it becomes a significant factor for small-cell base stations with much lower transmitted power, compromising the practicality of DPD. Some attempts have been made to bring more of the signal processing in the predistorter to the analog domain [6]–[8]. The digital/RF architecture uses a digital processor to synthesize the predistortion function and applies it to the RF input signal through a vector multiplier. However, the predistortion engine is still implemented in the digital domain and its performance is limited due to the static polynomial nature of the predistortion function, which becomes insufficient in the presence of significant PA memory effects. Exploiting the inherent low power property of analog circuits, several works [9]–[14] have investigated fully analog predistortion solutions. In [9]–[12], static polynomials with nonlinearity orders of up to five are synthesized using analog circuits and applied directly to the intermediate frequency (IF) or RF signals. Although being truly lowpowered solutions, their practical adoption is hindered by the limited linearization capacity in regards to static nonlinearity and the lack of a viable solution to address the memory effects. In [13], [14], the concept of analog/RF predistortion (ARFPD), as shown in Fig. 1(b), is investigated. The pre-

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the performance of the proposed model and identification algorithm, followed by the conclusion in Section V. II. LINEAR FILTER ASSISTED ENVELOPE MEMORY POLYNOMIAL MODEL OVERVIEW In an ARFPD system, the generation of predistorted signals usually involves two steps: a) synthesis of a nonlinear function (e.g., memory polynomial (MP)) that is complementary to the distortion of the PA and b) application of the synthesized predistortion function output to the RF input signal to generate the required predistorted outputs. One popular approach to address the memory effects is to use the MP model whose conventional baseband representation is expressed as (1)

Fig. 1. Block diagram of (a) a conventional DPD system and (b) the ARFPD system.

distorted signal generated by the analog engine, which uses complex analog signal processing circuits capable of handling memory effects, is applied to the RF signal through vector multipliers. Compared to the conventional DPD as shown in Fig. 1(a), the ARFPD scheme eliminates the power hungry DPD engine and reduce the bandwidth requirement of the DAC and IQ modulator, at the cost of additional analog hardware such as the analog predistortion engine and the RF vector multipliers. An ARFPD system capable of linearizing PAs with up to 20 MHz modulated signals while consuming as little as 0.2 W of power has been reported [14]. The linearization capacity of the aforementioned works is still limited, however, due to the difficulty in designing a predistortion model of comparable linearization capacity to DPD using analog hardware. In [15], a study of the solutions presented in [13], [14] revealed their inability to handle the linear memory effects of PAs. Accordingly, a new finite-impulse-response filter assisted envelope memory polynomial (FIR-EMP) predistorter is proposed. Preliminary linearization results where the predistortion signal is computed in software confirms the validity of the FIR-EMP model. In this work, a two-step, small-signal-assisted parameter identification (SSAPI) algorithm is proposed to extract the coefficients of the FIR-EMP structure for which the conventional least square errors (LSE) technique cannot be used. A new ARFPD test bench including the key component RF vector multiplier is devised to realistically assess the performance of the FIR-EMP model and the SSAPI algorithm in the presence of actual analog hardware. This paper is organized as follows. Section II briefly reintroduces the FIR-EMP model proposed in [15]. Section III presents the proposed linear parameter identification algorithm of the cascaded FIR filter and EMP model. Section IV presents the ARFPD test bench and the experimental results used to verify

where and are baseband samples before and after the predistortion, are the model coefficients, is the nonlinearity order, and is the memory depth. Reformulating the MP of (1) in the continues time domain for the ARFPD scheme, can be expressed as

(2) (3) where is a nonlinear function corresponding to a memory term of order , and denotes the time delay. The block diagram corresponding to (2) is illustrated in Fig. 2(a). The envelope signals are generated by the envelope detector followed by analog delay elements (D), and the delayed RF inputs are generated using RF delay elements (RF-D). The many RF-D elements and vector multipliers required for this architecture would consume a large amount of physical space and increase the hardware complexity. To simplify the hardware implementation, attempts have been made to remove the dependency of the memory paths on receiving phase information from the preceding input signals by using the envelopes of the signals only. The EMP in [16] is one such approach. The baseband complex output is given by (4) where , and are defined in the same way as (1). A reformulation of (4) for ARFPD results in (5) The performance of the EMP predistorter is assessed using a wideband gallium nitride (GaN) Doherty PA. Measurement

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Fig. 3. AM/AM and AM/PM characteristics, measured and modelled using the EMP model of a GaN Doherty PA driven with a 20 MHz WCDMA signal at 2 GHz [15].

sate for the memory effects, both the amplitude and phase information of preceding signals are required [18]. To address the shortcomings of EMP, linear filter is added before the EMP engine [15]. As shown in the block diagram in Fig. 2(b), the linear filter is implemented as a finite impulse response (FIR) filter in digital baseband. The resultant signal from the linear filter is then predistorted using EMP to compensate for the static and dynamic nonlinearities. The advantages of the proposed FIR-EMP model in the ARFPD setup over the conventional MP model can be seen clearly by comparing Figs. 2(a) and (b). The FIR filter in the digital baseband can be clocked at a much lower speed than a full DPD, thus requiring lower power overhead, as it must only cover the bandwidth of the baseband signal rather than the typical five times factor imposed by a DPD. EMP is also much simpler to realize in analog hardware than the MP based predistorter as it does not require multiple RF delay elements and vector multipliers. Fig. 2. Block diagram of (a) the MP function (b) the proposed FIR filter assisted EMP when applied to the ARFPD.

III. FIR-EMP PARAMETER IDENTIFICATION ALGORITHM A. Challenges in Identifying the Parameters

results indicate that the performance of the EMP model is adequate when the signal bandwidth is limited to 20 MHz, but it significantly degrades as the modulation bandwidth extends beyond that. Such shortcomings of EMP model are attributed to its limited ability to model the linear memory distortion. To illustrate the point, the measured AM/AM and AM/PM plots of the GaN Doherty PA, and those predicted by EMP, are shown in Fig. 3. It is clear that the EMP model results have good agreement with the measured data at high input powers where the nonlinearity of the PA is more pronounced, but fails to predict the distortion at low powers where the linear memory distortion dominates (also where there is wider signal bandwidth). This limitation of EMP is a result of the simplification used to derive the EMP from the Volterra series. The simplification assumes flat behaviour by the fundamental and its harmonics [17], and that the passband of the PA is much larger than the RF signal bandwidth [18]. Wider modulation bandwidth signals challenge this narrowband assumption. To accurately model and compen-

In the proposed FIR-EMP scheme outlined in the previous section, the FIR filter block is implemented in the digital domain and the EMP block is implemented in the RF domain. The cascade of a linear filter and a highly nonlinear block makes identifying the respective coefficients a major challenge. The commonly used LSE algorithm, popular for identifying the coefficients of a single-block predistortion model (e.g., MP or low pass equivalent Volterra), cannot be used to identify the respective coefficients of such a two-block nonlinear system due to the lack of linear relationships between the coefficients and the output signals. One potential solution is to use a nonlinear optimization algorithm such as the quasi-Newton method but this can be computationally intensive and is not suitable for realtime applications. B. Proposed Identification Algorithm In this section, a small-signal-assisted parameter identification (SSAPI) algorithm is proposed to efficiently identify the

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Fig. 4. Training scheme for identifying the coefficients of the FIR-EMP predistorter.

coefficients of the FIR filter and the EMP block, respectively without resorting to nonlinear optimization. Fig. 4 depicts the training scheme for the FIR-EMP predistorter. During the predistorter training (inverse modelling), and are the input and output envelope of the predistorter respectively, and the following expression can be obtained Fig. 5. Steps of the proposed SSAPI algorithm for the FIR-EMP predistorter (a) FIR parameter identification using the forward model of the PA (b) EMP parameter identification using the intermediate output of the FIR filter.

(6) is the intermediate training data at the output of where the FIR filter block, is the order of the FIR filter, and are the coefficients of the FIR filter. Expanding (6) leads to the following expression

(7) generally According to (7), estimating the values of and requires an advanced nonlinear optimization algorithm, which is possible but impractical in terms of the required time and computation resources. In the proposed SSAPI algorithm, the basic principle is to use a small-signal to probe the linear memory effects of the nonlinear device, which avoids the static nonlinearity and the nonlinear memory effects associated with the device, and leaves the linear memory effects the dominant source of distortion. To illustrate this, assume that the magnitude of the output is small enough such that all of the higher order terms (e.g., ) can be approximated as zero. Equation (7) can be simplified to (8) can be absorbed by the FIR coefficients and the linear gain . With (8), coefficients of the FIR filter block are estimated using the LSE algorithm. In order to obtain the small-signal training data, and , one obvious approach is to operate the PA at a significant back-off region, where the linear memory effects dominate

Fig. 6. Modelling accuracy versus the number of iterations for the quasi-Newton nonlinear optimization and the proposed SSAPI algorithm.

and the nonlinearity of the PA can generally be neglected. However, this obvious approach has three limitations. First, the linear memory effects of the PA might change due to a shift in the PA's region of operation. Second, the small-signal stimulus requires a high dynamic range in the transmitter observation receiver and the recorded samples could be sensitive to measurement noise. Lastly, forcing the PA to operate in the small-signal region necessitates off-line training and is not suitable for field applications. In consideration of the aforementioned limitations, this obvious approach is deemed unsuitable for obtaining the smallsignal training data. To address such limitations, it is proposed that the small-signal training data (e.g., and ) can be deduced using the forward model of the PA (e.g., Volterra). As the small-signal training data are obtained using the forward model in the software without forcing the PA to operate at a significant back-off region, the aforementioned limitations are less

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Fig. 7. Block diagram of the ARFPD engine test bench and the PAs under test.

problematic. Fig. 5 summarizes the steps of the proposed SSAPI algorithm and the detailed algorithm is summarized below: 1) The forward model of the PA is estimated using and . 2) The small-signal training data are estimated by using a small-signal stimulus as the input to the forward model. 3) The coefficients of the FIR block, are estimated using the LSE algorithm based on and . 4) The intermediate training data are estimated according to (6) 5) The coefficients of the EMP model are estimated using the LSE algorithm based on and . C. Evaluation of the Proposed SSAPI Algorithm In order to assess the validity of the proposed parameter identification algorithm, coefficients of the FIR-EMP predistorter are estimated using 1) the quasi-Newton algorithm from the MATLAB nonlinear optimization toolbox and 2) the proposed SSAPI algorithm. The training data is the same test data used in Fig. 3. Out of the 50000 available points, 10000 points are used to train the proposed FIR-EMP model and the other 40000 points are used for model validation purpose. Fig. 6 compares the modelling normalized mean square error (NMSE) versus the number of iterations corresponding to the two algorithms. Note that each of the two algorithms takes approximately the same computation time per iteration. According to Fig. 6, the proposed SSAPI algorithm achieved an NMSE of dB and only requires one iteration. In contrast, the nonlinear optimization requires iterations to reach the same level of modelling accuracy. It is worth mentioning that the described SSAPI algorithm is specifically proposed for the FIR-EMP model and is fundamentally different from the well-known parameter identification algorithm used by the Hammerstein or Wiener models [19], [20]. The two-box Hammerstein or Wiener model that consists of a static nonlinearity and an FIR filter is typically trained by

Fig. 8. Photograph of the ARFPD measurement setup.

first identifying the static nonlinearity, either through a continuous wave (CW) test [19] or a moving average method [20], before the FIR block can be identified. However, in the case of the proposed FIR-EMP model, the linear and nonlinear memory effects modelled by the FIR and EMP blocks respectively, are coupled and cannot be separated for conventional CW testing or the moving average method. On the other hand, the proposed SSAPI algorithm begins by first identifying a PA forward model, which is then used to generate new sets of input-output signals at the small-signal, so that the FIR filter coefficients can be identified. The coefficients of the EMP block are then identified using typical LSE algorithms. IV. VALIDATION AND MEASUREMENT RESULTS To realistically assess the performance of the proposed FIR-EMP model in an ARFPD system, a digitally assisted ARFPD test bench is built. Its corresponding block diagram is shown in Fig. 7 and the photograph of the testbench is shown in Fig. 8. The test bench consists of five main parts: the digital signal processing (DSP) unit, IQ modulator, RF vector multiplier, PA under test and the transmitter observation receiver.

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Fig. 9. (a) AM/AM and (b) AM/PM characteristics for PA1 without predistortion (red) and with the proposed FIR-EMP in ARFPD test bench (blue) of a 30 MHz WCDMA signal.

The DSP unit synthesizes the predistortion function (i.e., FIR-EMP) and generates the corresponding signals in the digital baseband. Two Keysight N8241A arbitrary waveform generators (AWGs) are synchronized using the same sampling clock (625 MHz). AWG-1 sends the baseband analog in-phase and quadrature signals and to the transmitter (ADL5375) for up-conversion. AWG-2 generates baseband signals and and sends them to the RF vector multiplier (ADL5390) in order to apply the predistortion function to the incoming RF signal. The output of the PA under test is captured using a Keysight N9030A signal analyzer with a maximal observation bandwidth of 160 MHz. All the equipment is synchronized using a 10 MHz reference clock. Compared to a complete ARFPD system, the current digitally assisted ARFPD test bench implements the major RF building blocks (i.e., IQ modulator and RF vector multiplier) but uses an emulated predistortion engine. Although implementation of the predistortion engine in hardware is feasible, this function would require a dedicated integrated circuit design. As a proofof-concept evaluation, the described ARFPD test bench is used to evaluate the proposed FIR-EMP model at the system level. The proposed FIR-EMP model and the proposed SSAPI algorithm are evaluated in the ARFPD test bench described previously to linearize different PAs driven by various wideband and intra-band carrier-aggregated signals. Two PAs under test are used, consisting of: 1) A GaN push-pull PA with 85-W peak envelope power operating at a carrier frequency of 900 MHz (PA1) 2) A GaN Doherty PA with 20-W peak envelope power operating at a carrier frequency of 1.9 GHz (PA2) [21].

Fig. 10. (a) AM/AM and (b) AM/PM characteristics for PA2 without predistortion (red) and with the proposed FIR-EMP in ARFPD test bench (blue) of a 30 MHz WCDMA signal.

The nonlinearity order is found out to be 7 and the memory depth is found out to be 5 based on the PAs characteristics through iterative parameter sweeping. For comparison purposes, a DPD test bench is also built. This DPD test bench is identical to Fig. 7 but without the RF vector multiplier and AWG-2. Three predistortion test cases are designed: 1) using the MP model in the DPD setup 2) using the dynamic deviation reduction based Volterra series (DDR-Volterra) model [4] in the DPD setup 3) using the proposed FIR-EMP model in the ARFPD setup. The validity of the proposed FIR-EMP model is first assessed in the ARFPD test-bench to linearize PA1 and PA2, driven by two different wideband modulated signals: 1) A 20 MHz LTE signal with a PAPR of 8.9 dB 2) A 30 MHz 4-carrier 110011 WCDMA signal with a PAPR of 8.6 dB. Tables I summarize the linearization results for PA1 and PA2, respectively, corresponding to the different test cases. The PA distortions (AM/AM and AM/PM) corresponding to PA1 and PA2 driven under the 30 MHz signal are plotted in Figs. 9 and 10. The output spectra of PA1 and PA2 under the three test cases are plotted in Figs. 11 and 12. For PA1, the proposed FIR-EMP model in the ARFPD setup achieved an adjacent channel leakage ratio (ACLR) improvement of 20 dBc when linearizing a 20 MHz LTE signal. Compared with the MP model based DPD setup, up to 2.7 dB ACLR improvement is noticed.

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TABLE I SUMMARY OF THE LINEARIZATION PERFORMANCE OF PA1 AND PA2 DRIVEN BY WIDEBAND MODULATED SIGNALS

Fig. 11. Output spectra of PA1 driven with 30 MHz bandwidth signal.

Fig. 12. Output spectra of PA2 driven with 30 MHz bandwidth signal.

For PA2, the advantages of the proposed model are evident according to Table I. The ACLR measured using the proposed FIR-EMP are 4.6 dB better than the MP model based DPD for

Fig. 13. Output spectra of PA2 driven by 80 MHz signal.

the 30 MHz WCDMA signal. Linearization results from the DDR-Volterra model are provided as the baseline for comparison, and the FIR-EMP model in the ARFPD test bench achieves comparable linearization capacity. Fig. 12 shows the excellent linearization capacity of the proposed FIR-EMP model by comparing the spectra recorded for PA2. The proposed FIR-EMP test case has significantly lower in-band and out-of-band distortion compared to the spectra obtained using the MP-DPD. It achieves comparable linearization results to the sophisticated DDR-Volterra model based DPD setup. To further evaluate the performance of the proposed FIR-EMP model under newer 4G communication signals, a 40 MHz mixed standard carrier aggregated signal, consisting of a 15 MHz 3-carrier WCDMA signal and a 15 MHz LTE signal with a combined PAPR of 8.4 dB is synthesized. For PA1, the proposed FIR-EMP in the ARFPD test-bench achieves an ACLR of dBc, compared to an ACLR of dBc found using the MP in DPD. For PA2, the proposed FIR-EMP test case achieve an ACLR of dBc, compared to the MP test case which records an ACLR of dBc. Compared with the sophisticated DDR-Volterra model, the proposed FIR-EMP model achieves a similar level of linearization (i.e., about dBc ACLR).

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To further assess the performance of the proposed FIR-EMP under even wider bandwidths, an 80 MHz mixed-standard intraband carrier aggregated signal, consisting of a 20 MHz 4-carrier WCDMA signal and a 20 MHz LTE signal with a combined PAPR of 9.5 dB. As summarized in Table I, when compared with the MP test case, the proposed FIR-EMP model achieves a 4 dB improvement in the measured ACLR. Significant in-band distortion is observed in the MP-DPD case, which leads to a high error vector magnitude (EVM) of 3.5% while the proposed FIR-EMP model has a measured EVM of 1.4%. The output spectra are presented in Fig. 13. V. CONCLUSION In this paper, an ARFPD system using the FIR-EMP model along with a linear SSAPI algorithm has been presented. An ARFPD test bench, which incorporates major RF components, has been built to assess the validity of the proposed FIR-EMP scheme and the SSAPI algorithm. It has been demonstrated that the SSAPI algorithm can extract coefficients with excellent modelling accuracy for the cascaded blocks of the FIR-EMP in a single iteration. Measurement results have shown that the proposed FIR-EMP model using the SSAPI algorithm can successfully linearize multiple PAs driven with various wideband and carrier-aggregated signals of up to 80 MHz instantaneous bandwidth. Linearization performance comparable to a DDR-Volterra based DPD scheme indicates the viability of the proposed FIR-EMP model for implementing ARFPD modules capable of mitigating the distortions exhibited by PAs driven by communication signals with up to 80 MHz modulation bandwidth. This confirms the potential of ARFPD as a very promising candidate for the linearization of small-cell base station PAs, which would reduce the power overhead compared to using the popular digital predistortion technique. REFERENCES [1] S. Jin, K. Moon, B. Park, J. Kim, Y. Cho, H. Jin, D. Kim, M. Kwon, and B. Kim, “CMOS saturated power amplifier with dynamic auxiliary circuits for optimized envelope tracking,” IEEE Trans. Microw. Theory Techn., vol. 62, no. 12, pp. 3425–3435, Dec. 2014. [2] A. Mohamed, S. Boumaiza, and R. Mansour, “Doherty power amplifier with enhanced efficiency at extended operating average power levels,” IEEE Trans. Microw. Theory Techn., vol. 61, no. 12, pp. 4179–4187, Dec. 2013. [3] J. Kim and K. Konstantinou, “Digital predistortion of wideband signals based on power amplifier model with memory,” Electron. Lett., vol. 37, no. 23, pp. 1417–1418, Nov. 2001. [4] A. Zhu, J. Pedro, and T. Brazil, “Dynamic deviation reduction-based Volterra behavioral modeling of RF power amplifiers,” IEEE Trans. Microw. Theory Techn., vol. 54, no. 12, pp. 4323–4332, Dec. 2006. [5] B. Fehri and S. Boumaiza, “Baseband equivalent Volterra series for behavioral modeling and digital predistortion of power amplifiers driven with wideband carrier aggregated signals,” IEEE Trans. Microw. Theory Techn., vol. 62, no. 11, pp. 2594–2603, Nov. 2014. [6] S. Boumaiza, J. Li, M. Jaidane-Saidane, and F. Ghannouchi, “Adaptive digital/RF predistortion using a nonuniform LUT indexing function with built-in dependence on the amplifier nonlinearity,” IEEE Trans. Microw. Theory Techn., vol. 52, no. 12, pp. 2670–2677, Dec. 2004. [7] W. Kim, K. Cho, S. Stapleton, and J. Kim, “Baseband derived RF digital predistortion,” Electron. Lett., vol. 42, no. 8, pp. 468–470, Apr. 2006.

[8] W. Woo, M. Miller, and J. Kenney, “A hybrid digital/RF envelope predistortion linearization system for power amplifiers,” IEEE Trans. Microw. Theory Techn., vol. 53, no. 1, pp. 229–237, Jan. 2005. [9] T. Rahkonen, O. Kursu, M. Riikola, J. Aikio, and T. Tuikkanen, “Performance of an integrated 2.1 GHz analog predistorter,” in Proc. International Workshop on Integrated Nonlinear Microwave and Millimeter-Wave Circuits, Jan. 2006, pp. 34–37. [10] E. Westesson and L. Sundstrom, “Low-power complex polynomial predistorter circuit in CMOS for RF power amplifier linearization,” in Proc. ESSCIRC, Sep. 2001, pp. 486–489. [11] N. Mizusawa, S. Tsuda, T. Itagaki, and K. Takagi, “A polynomial-predistortion transmitter for WCDMA,” in Proc. IEEE Int. Solid-State Circuits Conf. Tech. Dig., Feb. 2007, pp. 350–608. [12] A. Kidwai and B. Jalali, “Power amplifier predistortion linearization using a CMOS polynomial generator,” in Proc. IEEE Radio Freq. Integr. Circuits Symp., Jun. 2007, pp. 255–258. [13] R. N. Braithwaite, “Memory correction for a WCDMA amplifier using digital-controlled adaptive analog predistortion,” in Proc. IEEE Radio and Wireless Symp., 2010, pp. 144–147. [14] F. Roger, “A 200 mW 100 MHz-to-4 GHz 11th-order complex analog memory polynomial predistorter for wireless infrastructure RF amplifiers,” in Proc. IEEE Int. Solid-State Circuits Conf. Tech. Dig., 2013, pp. 94–95. [15] H. Huang, A. Islam, J. Xia, P. Levine, and S. Boumaiza, “Linear filter assisted envelope memory polynomial for analog/radio frequency predistortion of power amplifiers,” in Proc. IEEE MTT-S IMS, May 2015, pp. 1–3. [16] O. Hammi, F. Ghannouchi, and B. Vassilakis, “A compact envelope-memory polynomial for RF transmitters modeling with application to baseband and RF-digital predistortion,” IEEE Microw. Wireless Compon. Lett., vol. 18, no. 5, pp. 359–36, May 2008. [17] C. C. Cadenas, J. R. Tosina, M. J. M. Ayora, and J. M. Cruzado, “A new approach to pruning Volterra models for power amplifiers,” IEEE Trans. Signal Process., vol. 58, no. 4, pp. 2113–2120, 2010. [18] E. G. Lima, T. R. Cunha, and J. C. Pedro, “PM-AM/PM-PM distortions in wireless transmitter behavioral modeling,” in Proc. IEEE MTT-S Int. Microw. Symp. Dig., 2011, pp. 1–4. [19] J. Pedro and S. Maas, “A comparative overview of microwave and wireless power-amplifier behavioral modeling approaches,” IEEE Trans. Microwave Theory Techn., vol. 53, no. 4, pp. 1150–1163, Apr. 2005. [20] T. Liu, S. Boumaiza, and F. Ghannouchi, “Augmented Hammerstein predistorter for linearization of broad-band wireless transmitters,” IEEE Trans. Microwave Theory Techn., vol. 54, no. 4, pp. 1340–1349, Jun. 2006. [21] H. S. A. Jundi and S. Boumaiza, “An 85-W multi-octave push-pull GaN HEMT power amplifier for high efficiency communication applications at microwave frequencies,” IEEE Trans. Microw. Theory Techn., vol. PP, no. 99, pp. 1–10, Sep. 2015. Hai Huang (S'15) received the B.A.Sc. degree in electrical and computer engineering from the University of Waterloo, Waterloo, Ontario, Canada, in 2013 and is currently working towards the Ph.D. degree at the University of Waterloo. His research interests include Analog/digital signal processing, analog and RF integrated circuits and linearization of RF power amplifiers.

Jingjing Xia received the B.Eng. and Ph.D. degree in electrical and electronics engineering from the Nanyang Technological University, Singapore, in 2008 and 2013, respectively and the M.A.Sc. degree in electrical and computer engineering from the University of Waterloo, Waterloo, ON, Canada in 2013. He is currently a research engineer in the Emerging Radio Research Group Lab., University of Waterloo. His current research interests include microwave and millimeter-wave transmitters as well as analog and digital predistortion techniques.

HUANG et al.: DIGITALLY ASSISTED ANALOG/RF PREDISTORTER WITH A PARAMETER IDENTIFICATION ALGORITHM

Anik Islam received the B.A.Sc. degree from the University of Waterloo, Waterloo, ON, Canada, in 2013 and is currently working towards an M.A.Sc. degree at the University of Waterloo. In 2014, he joined the Emerging Radio Systems Group at the University of Waterloo as a Research Associate. His research focuses on the construction and identification of nonlinear dynamic models for the predistortion of radio frequency power amplifiers.

Eric Ng (S’14) is currently pursuing the B.Sc. and M.Sc. in electrical engineering at the University of Waterloo, Waterloo, Canada. In 2014 he joined the Emerging Radio Systems group as an undergraduate student research assistant, working on hybrid predistortion techniques in RF power amplifiers. His research interests include digitally assisted analog RF front end design and ultra-low power transceiver architecture.

Peter M. Levine received the B.Eng. degree in computer engineering and the M.Eng. degree in electrical engineering from McGill University, Montreal, QC, Canada in 2001 and 2004, respectively, and the Ph.D. in electrical engineering from Columbia University, NY, USA in 2009. From 2009 to 2010, he worked as a Research Engineer in integrated circuit and sensor design for Ion Torrent, Guilford, CT, USA. In 2011, he joined the Department of Electrical and Computer Engineering at the University of Waterloo, Waterloo, ON, Canada as an Assistant Professor. His research interests include CMOS-integrated bio-

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chemical assays, integrated microsystems for clinical and environmental monitoring, and the design of precision analog/mixed-signal integrated circuits for sensor interfaces. He is an inventor or co-inventor on six issued U.S. patents. Prof. Levine has served as a technical program committee member for several conferences, including the IEEE/ACM International Symposium on Low Power Electronics and Design (ISLPED) and the IEEE Biomedical Circuits and Systems Conference (BioCAS). He was a recipient of the Intel Foundation Ph.D. Fellowship in 2005.

Slim Boumaiza (S'00–M'04–SM'07) received the B.Eng. degree in electrical engineering from the Ecole Nationale Ingnieurs de Tunis, Tunis, Tunisia, in 1997, and the M.S. and Ph.D. degrees from the Ecole Polytechnique de Montreal, Montreal, QC, Canada, in 1999 and 2004, respectively. He is currently an Associate Professor with the Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON, Canada, where he leads the Emerging Radio Systems Group, which conducts multidisciplinary research activities in the general area of RF/microwave and millimeter component and system design for wireless communications. His current research interests include RF/digital signal processing mixed design of intelligent RF transmitters; design, characterization, modeling and linearization of high-efficiency RF power amplifiers; and reconfigurable and software-defined transceivers.

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Digital Compensation for Transmitter Leakage in Non-Contiguous Carrier Aggregation Applications With FPGA Implementation Chao Yu, Member, IEEE, Wenhui Cao, Student Member, IEEE, Yan Guo, Student Member, IEEE, and Anding Zhu, Senior Member, IEEE

Abstract—In this paper, a generalized dual-basis envelope-dependent sideband (GDES) distortion model structure is proposed to compensate the distortion induced by transmitter leakage in concurrent multi-band transceivers with non-contiguous carrier aggregation. This model has a generalized structure that is constructed via first generating a nonlinear basis function that maps the inputs to the target frequency band where the distortion is to be cancelled, and then multiplying with a second basis function that generates envelope-dependent nonlinearities. By combining these two bases, the model keeps in a relatively compact form that can be flexibly implemented in digital circuits such as field programmable gate array (FPGA). Experimental results demonstrated that excellent suppression performance can be achieved with very low implementation complexity by employing the proposed model. Index Terms—Behavioral model, carrier aggregation, multi-band, power amplifiers, transmitter leakage suppression.

I. INTRODUCTION ON-CONTIGUOUS carrier aggregation (CA) technique [1] has been proposed to effectively combine multiple frequency bands to conduct high-speed data transmission in wireless communications. To support CA operation, high-efficiency concurrent multi-band transmitters are often deployed [2]. Due to nonlinear characteristics of RF power amplifiers (PAs), distortion is normally added into the transmit signal after amplification [3]. In multi-band operation, the distortion is usually located not only near the transmission bands, but also at the intermodulation frequencies. These intermodulation frequency bands, e.g., the third-order intermodulation (IM3) bands, sometimes can overlap with the receiver bands in the frequency-division duplex (FDD) mode, as illustrated in Fig. 1. Ideally, the duplexers shall have enough attenuation to avoid the distortion generated by the transmitter that falls into the receiver band. In practice, however, it is not easy to design such duplexers to meet

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Manuscript received June 29, 2015; revised September 02, 2015; accepted October 18, 2015. Date of publication November 11, 2015; date of current version December 02, 2015. This work was supported in part by the Science Foundation Ireland under the Principal Investigator Award Grant Number 12/IA/ 1267. This paper is an expanded version from the IEEE MTT-S International Microwave Symposium, Phoenix, AZ, USA, 17–22 May 2015. C. Yu is with the State Key Laboratory of Millimeter Waves, School of Information Science and Engineering, Southeast University, Nanjing 210096, China (e-mail: [email protected]). W. Cao, Y. Guo, and A. Zhu are with the School of Electrical and Electronic Engineering, University College Dublin, Dublin 4, Ireland (e-mail: [email protected]; [email protected]; [email protected]). Digital Object Identifier 10.1109/TMTT.2015.2495144

Fig. 1. Transmitter leakage in 3-carrier carrier aggregation scenario.

the requirement. Some intermodulation products can therefore leak to the receiver band and introduce serious spurious emission to the receiver, causing significant quality degradation of the received signal. Various compensation schemes have been proposed either in transmitter (Tx) or in receiver (Rx) to resolve the problem. Because of low cost and great accuracy, digital predistortion (DPD) [4]–[10] in the transmitter has been widely employed to remove the sideband distortion. In [4], C. Yu et al. proposed a full-bandwidth DPD method by treating the multiband signal including the sideband signal as a single signal to effectively remove the unwanted sideband distortion. In [5], [6], P. Roblin and J. Kim et al. proposed a frequency selective DPD method to successfully cancel the sideband separately by employing a large signal network analyzer (LSNA) to extract the device under test (DUT) information. In [7], S. A. Bassam et al. proposed a filtering-based sideband distortion modeling technique to inject the anti-phase sideband distortion for distortion suppression. To reduce complexity, M. Abdelaziz et al. in [8], [9] proposed simplified methods by only picking the modeling terms falling into the specified distortion bands. In [10], Z. Fu et al. proposed a sideband compensation scheme based on evaluating and minimizing the power spectral density (PSD) of PA output signal around the pre-specified frequency. The DPD-based sideband compensation methods work well in general but they require extra bandwidths to transmit the sideband information in multi-band transmitters, which is often not desirable in many applications.

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YU et al.: DIGITAL COMPENSATION FOR TRANSMITTER LEAKAGE

Instead of removing the distortion in Tx, some other compensation schemes [11]–[20] are realized in Rx. The main idea is to build a distortion model to generate the replica of the distortion that falls into the receiver band and subtract it from the received signal to obtain the original signal, as shown in Fig. 1. In [11], [12], A. Frotzscher et al. analyzed the impact on system performance in zero-IF receiver impaired by transmitter leakage. In [13], M. Kahrizi et al. proposed a digital method to suppress the second-order intermodulation (IM2) of Tx leakage in WCDMA direct-conversion receivers. M. Omer et al. in [14] created the replica of the sideband distortion by assuming that the frequency response of duplex filter is known, while A. Kiayani et al. in [17] proposed a method to estimate the transmitter leakage channel including both duplexer and PA. The same authors in [18] extended this method to deal with concurrent dual-band signal. In [19] and [20], H.-T. Dabag et al. proposed an all-digital cancellation technique to mitigate the receiver desensitization in uplink CA in cellular handsets. In [21], we proposed a novel dual-basis envelope-dependent sideband distortion model to characterize the transmitter leakage in the receiver band in concurrent dual-band transceivers. Experimental results showed that only a very small number of model coefficients with narrowband digital signal processing are required to achieve satisfactory cancellation performance. Due to limited space, in [21], only the basic concept and the verification of suppression of distortion in concurrent dual-band transceivers were given. In this paper, we provide a detailed analysis of transmitter leakage and give comprehensive derivations for the model development in more complex scenarios, such as 3-Carrier (3-C) CA applications. Based on the analysis, a generalized dual-basis envelope-dependent sideband (GDES) distortion model structure is then proposed to provide a uniform architecture to suppress various distortions that appeared in such systems. By employing the proposed model structure, different distortion components can be accurately characterized and compensated with the same digital circuit module. The distortion overlapping issue can also be easily resolved. Compared to the existing methods, the proposed model is in a compact format and can be easily extended to different scenarios without increasing much complexity. A generalized FPGA architecture with detailed hardware implementation is also given. The rest of the paper is organized as follows: In Section II, the transmitter leakage analysis focusing on the 3-C CA application is provided. A generalized model structure is then proposed in Section III with FPGA implementations given in Section IV. The experimental results for the different scenarios are provided in Section V, followed by a conclusion in Section VI.

II. TRANSMITTER LEAKAGE ANALYSIS With increasing demands for high data rates, carrier aggregation techniques will be widely employed in wireless cellular communications and the number of aggregated carriers will inevitably keep increasing in the future. As discussed earlier, the distortion generated in transmitters can leak to receiver bands

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and cause quality degradation of the received signals. This situation becomes worse when CA is employed. In this section, we take a 3-carrier CA scenario as an example to illustrate how the transmitter leakage is generated. A. 3-Carrier Carrier Aggregation Considering the frequency plan for LTE FDD mode [22] and the transmitter architecture employing CA techniques [23], three cases of frequency allocations might be assigned for three-carrier carrier aggregation. As shown in Fig. 2(a), in the first case, three bands are located at MHz (LTE band 5), MHz (LTE band 1), and MHz (LTE band 22). Since these three bands are spanned in a very large frequency range, multiple RF chains and power amplifiers may be employed. In this case, only the distortions near main carriers are our concern. The intermodulation products crossing the multiple bands may not cause severe problems. However, in the second case, shown in Fig. 2(b), if three bands are located at MHz (LTE band 3), MHz (LTE band 1), and MHz (LTE band 7), the intermodulation products will spread over to nearby receiver bands which can cause problems. For example, the upper 3rd-order intermodulation product generated from band 1 and 3 is located around 2510 MHz , which overlaps with the uplink band for LTE band 7 allocation (2500 MHz–2570 MHz). In the third case, shown in Fig. 2(c), three bands are located at MHz (LTE band 3), MHz (LTE band 2), and MHz (LTE band 1). In this case, all three bands are located over a frequency range of 400 MHz and thus it is possible to only employ one wideband PA to transmit this multi-band signal. Similar to the second case, the intermodulation products also affect receiver bands and in this case the situation becomes much more complex since not only the intermodulation products generated from two frequency bands, but also the ones generated from three frequency bands can affect receivers. For instance, one of the IM3 generated from these three bands are 1950 MHz , that overlaps with the uplink band for LTE band 1 allocation (1920 MHz–1980 MHz). B. Derivation for Tx Leakage Let's assume the aggregated input signal sented as

can be repre-

(1) where are the baseband representations of the signals located at the carrier frequencies . If the input signal passes through a nonlinear system, the output will contain many distortion products that can spread over multiple frequency bands. Here, to simplify the derivation, a memoryless polynomial model is taken for example, that is (2)

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From (3), we can see that the center frequency for each distortion item can be calculated from the main carrier frequencies, that is

(4) For example, the center frequency of the distortion at IM3 bands can be obtained from

(5) By using (5), the distortion at IM3 at the frequency can be expressed as

(6)

Fig. 2. 3-Carrier carrier aggregation allocation.

where and is the input and output, respectively and is the nonlinear order. Substituted (1) into (2), all the distortion can be obtained

Removing the carrier frequency, the baseband information can be represented as

(7) For better illustration, the distortion terms are listed below

.. .

(3)

(8)

From (8), we can see that the distortion is generated from combinations of the signals located at different bands. If we treat these signals at each band as independent inputs, constructing the distortion model is straightforward: simply generate each term by combining the baseband signals at different bands, as shown in Fig. 3. The disadvantage of this approach is that

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Fig. 3. Model structure based on picking terms for 3-C CA application.

the model complexity will increase quickly with the number of bands and the situation becomes worse when higher order nonlinearity and memory terms are included into the model.

can be divided into two sections as listed in Table I. Looking closely, we can find that the two parts of the modeling terms have distinct functionalities: the common part is related to the band of the distortion to be cancelled while the changing part depends on the envelope of the inputs only. We will explain this phenomenon in detail in next two sections. Nevertheless, based on this finding, in this work, we propose to decompose the model into two basis functions: the first basis function is to locate the frequency components in the target bands, denoted as Basis 1; and the second basis is to create an accurate mapping from the input to the output by using envelope dependent nonlinear terms, denoted as Basis 2. The model structure can be described as

(12)

III. PROPOSED MODEL To overcome the disadvantage of the existing models, a novel model structure is proposed in this section.

where

A. Model Basis Decomposition

As mentioned earlier, if the input signal passes through a nonlinear PA, the output will contain many distortion products that can spread over multiple frequency bands. To cancel transmitter leakage, we only concern the distortion that falls at the receiver frequency band, for example, the distortion at band in 3-C CA Case in Fig. 2(b). Because this frequency band is different from where the original input signals are located, to generate this distortion, we must “inter-modulate” inputs between two bands and thus generate the new frequency band. The basic description for the dual-band scenario can be found in [9]. For instance, as illustrated in Fig. 4(a), to generate the distortion at band, we can multiply two inputs from one band with the conjugate of the input from the other band

For better illustration, two special cases for IM3 in (5) are chosen. One is for the case in Fig. 2(b) where the IM3 is generated from LTE band 1 and 3 and the other is for the case in Fig. 2(c) where the IM3 is generated from all three bands, that is (9) Then, (7) can be transformed to (10), shown at the bottom of the page. Looking at (10), although the term combinations change with the order of nonlinearities, there are some “common” unchanged terms in each equation. To illustrate this, we can re-write (10) as (11), shown at the bottom of the page, where we can see that and appear in all the modeling terms, for each case, respectively. By separating the common parts from the changing parts in each term, the model

and

represent Basis 1 and 2, respectively.

B. Model Basis 1

(13) where is the conjugate operation. This term is corresponding to the carrier frequency change, i.e., . As shown in Fig. 3, (13) only generates the 3rd-order distortion.

(10)

(11)

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TABLE I CONVENTIONAL MODEL DECOMPOSITION

TABLE II PROPOSED MODEL DECOMPOSITION

For higher order distortion, we need to add in more terms, e.g., for the 5th order. To ensure the model output stay in the target band, these extra added terms should not “move” the band. In other words, they should only affect the frequency components within the target band, but not crossing the bands. For instance, is only used to weight in . In the frequency domain, is corresponding to the frequency , which indicates that multiplying this term does not change the carrier frequency. Therefore, from the frequency selection point of view, (13) is the key element that “selects” the target bands in the model construction. Follow the same logic, the band selection element for IM3 band in the 3-C CA case in Fig. 2(c) is (14) as illustrated in Fig. 4(b). In summary, Basis 1 of the above cases can be described as

(15) Based on the same idea, the distortion located at other frequency bands can also be constructed by simply changing the combination of the signal terms. C. Model Basis 2 To model high order nonlinearities, (15) can be multiplied with different high order terms as shown in Table I, which can be describe as Basis 2, that is

(16)

This polynomial extension is straightforward, but this operation will lead to considerable increase of the model complexity when strong nonlinear distortion is involved as discussed earlier. As mentioned in [24], [25] for the low-pass equivalent model, once the relationship between the input and output meets the requirement of odd parity and the mapping is located at the specified frequency band, it is not necessary to build the high-order

nonlinearities using conventional polynomials. Instead of using each individual envelope, in this work, we propose to construct the second basis function using the average envelope of the signal, that is

(17)

This structure keeps the even-parity, which satisfies the oddparity rule of the low-pass equivalent model construction, when multiplied with the Basis 1 function that satisfies the odd-parity. At the first glance, we may think the square root operations can be very complex in hardware implementation compared to the conventional polynomials. Surprisingly, with the assistance of coordinate rotation digital computer (CORDIC) technique [26] in FPGA, the complexity can be significantly reduced and becomes lower than that for the polynomials. We will discuss this in detail in Section IV D. Model Basis Re-Combination To simplify the model expression, we move the power operation out of the basis in (17) and re-define the terms inside the power operation as Basis 2. Thus the new model can be expressed as (18) is the basis deciding which band to be compenwhere sated, and is the basis for generating the high-order nonlinearities. represents the nonlinear order. In the dual-band and tri-band cases, specific examples are given in Table II. The derivation above is only for the memoryless nonlinear systems. To further characterize a wider range of nonlinear systems, memory effects need to be taken into account. To do so, the model can be constructed as

(19) where and is Basis 1 and Basis 2, respectively. again represents the nonlinear order and and represent the memory length for each basis, respectively.

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Fig. 6. Proposed model structure.

and then multiplied with the Basis 2 function respectively and finally combined together to form the full model. In summary, there are three basis functions used in the model for this case

(22)

Fig. 4. Basis 1 generation. (a) 3-C CA Case in Fig. 2(b). (b) 3-C CA Case in Fig. 2(c).

To generalize this procedure, we reformat the model as

(23)

Fig. 5. Even-spaced case for 3-C CA application.

E. The Generalized Model The model proposed above can be easily extended to general cases without structure changes. For instance, in the 3-C CA case, if the three carrier frequencies are evenly allocated, multiple intermodulation products may fall into the same frequency band, as shown in Fig. 5, where the carrier frequency MHz (LTE band 3), MHz (LTE band 2), MHz (LTE band 1) are evenly spaced, which leads that the distortion located at 2245 MHz can be generated from two different IM3 products. One is generated from two carriers, 1985 MHz and 2115 MHz, and the other from all three carriers, that is

(20) Because both distortion bands are located at the same frequency, the total distortion component should consist of two parts, which requires two different modeling terms. As discussed earlier, the frequency components can be easily selected with Basis 1 functions in the proposed model. In this case, we simply construct two Basis 1 functions to model the two IM3 products, i.e.,

(21)

is the basis for the th distortion band or where term to be compensated, and is the basis for modeling high-order nonlinearities. represents the nonlinear order and represent the memory length for each basis, respectively. We call this model the generalized dual-basis envelope-dependent sideband (GDES) distortion model. The model structure is illustrated in Fig. 6, where a frequency analysis block is added to select distortion components and bands before constructing the model. Compared to the existing solutions, this new model structure provides many advantages. Firstly, the signal processing bandwidth is only related to the baseband signals at each band, leading to the narrow bandwidth requirement. Secondly, because only one average envelope is involved, the number of model coefficients is significantly reduced and thus low-complexity implementation can be realized. Thirdly, the target band can be arbitrarily changed by replacing the terms in Basis 1 without significantly changing the model structure, which brings great flexibilities for future extension. IV. FPGA IMPLEMENTATIONS To evaluate the practical application of the proposed cancellation structure, the proposed model is implemented in FPGA and compared with the existing models in terms of resource consumption. A generalized FPGA implementation architecture for TX leakage suppression in 3-C CA application is also proposed in this section.

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Fig. 8. FPGA implementation for mode selection.

Fig. 7. PGA implementation architecture for (a) the existing model structure and (b) the proposed model structure.

A. FPGA Resource Consumption Comparison Two types of structures are employed to make a fair comparison. The first model is an existing model based on termspicking approach in the dual-band case as

(24) The second model is a typical example of the proposed model for the same dual-band scenario as

(25) The objective is to compare the resources consumption when the similar performance is achieved. Based on (24) and (25), two FPGA implementation architectures can be built as shown in Fig. 7. In Fig. 7(a), the common part can be implemented by employing two complex multipliers. To implement the changing part, four square operations and two adders are required to calculate and . Multiplexing technique can be employed to reuse the hardware resource and thus reduce resource consumption. Different orders of nonlinear terms are then fed into multiplication and combination module to construct all the possible combinations for the two inputs, e.g., . The different outputs will then be multiplied with the common part, and fed into memory structure (equivalent to the FIR structure). Finally, all these terms can be added together to construct the full distortion model. Since there are many possible combinations, a large number of multipliers are usually involved in this implementation.

In Fig. 7(b), the proposed structure mainly consists of three parts: Basis 1 generation, Basis 2 generation and the combination of these two bases including different orders and memory. Firstly, in Basis 1 generation, is equivalent to the common part in Fig. 7(a). Secondly, Basis 2 is generated in a different way from the conventional method. At the first glance, one may think more complex computation will be involved in the envelope calculation, since there is square root operation. However, by using CORDIC [26], this step becomes very simple with only shift and addition operations involved, which significantly reduces the implementation complexity. The details for the square root implementation are given in Appendix. Two CORDIC modules are employed to generate and , which take the I signal as one input and Q signal as the other input to calculate the . To reduce the resource consumption, multiplexing technique can also be employed, which is also discussed in Appendix. After this operation, we can continue to employ a CORDIC module to realize the implementation of . Then, the implemented function can be used to generate high order terms, combined with the Basis 1, and delayed and multiplied with different coefficients. Finally, all these terms can be added together to construct the full distortion model. In practice, the memory structure can be further simplified based on the practical requirement. For example, if memory terms are few, all the different memory structure can be added first and then delayed together, which will reduce the number of multipliers required. B. The Generalized Architecture for 3-C CA Application One big advantage of the proposed structure is that the envelope term is in a generalized format which can be easily extended to various multi-band cases. For instance, to extend from dual-band to tri-band, only one more CORDIC needs to be employed in the implementation. The detail of this implementation is given in Appendix. Furthermore, because the model is in a generalized structure, all the distortions located at different IM3 bands can be generated by using the same hardware block. It also allows multiplexing to be employed to save resources in FPGA. For instance, as illustrated in Fig. 8, the input may consist of three original inputs . To generate , we can simply select from branch 1 and select from branch 2 and

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Fig. 9. General FPGA implementation architecture for tri-band intermodulation product cancellation.

3. To generate and should be selected from different branches, respectively. The resource consumption for this module will be discussed in next section with a practical example. Based on the discussion above, the general FPGA implementation architecture for tri-band intermodulation product cancellation is shown in Fig. 9. In selection block, the input “mode” is used to select the cancellation band. For example, in the 3-C CA application, there are 9 options for the IM3 bands selection. With this operation, the distortion located at different bands can be cancelled by controlling the single variable of the mode. V. EXPERIMENTAL RESULTS To effectively validate the proposed method, a test bench was setup as shown in Fig. 10. In the transmit chain, the baseband signals with different carrier aggregation allocations are generated in PC by software MATLAB, then up-converted to RF frequency, and fed into a high power LDMOS PA operated at 2.14 GHz with average output power of 37.5 dBm. Due to the limitation of the platform, we conduct the test without a real duplexer but using a digital filter instead. In other words, the transmitter distortion at the receiver band is not attenuated by a duplexer before down-conversion. In our test, the full transmitter signal is fed into the receiver, then down-converted, sampled and finally demodulated back to the baseband. The sideband distortion is obtained by applying a digital filter on the received signal. The distortion suppression model was implemented in FPGA and can run in real-time, but the model extraction was conducted in MATLAB by using the standard least squares (LS) algorithm. Furthermore, in these tests, the receiver chain was considered being linear and had a fixed gain. Due to the bandwidth limitation of the platform, we only used 5 MHz signals at each band to conduct the “proof-of-concept” tests. A. 3-C CA Case 1: Fig. 2(b) In this test, the baseband signal combines two 5 MHz signals located at MHz and MHz and with peak-to-average power ratio (PAPR) of 7.8 dB. The sideband distortion is located at

Fig. 10. Test bench setup.

MHz. The model configuration in (25) is set as . Fig. 11 shows the measured power spectrum density with and without the transmitter leakage suppression. From Fig. 11, it can be clearly seen that 25 dB suppression can be achieved by employing the proposed model, which confirms the model accuracy. The signal processing bandwidth required is only 46 MHz that is corresponding up to 9th order nonlinearities with the two 5 MHz baseband signals, regardless of the frequency spacing. It is also worth mentioning that only 8 coefficients are required in this proposed model, which leads to a very low-complexity in practical implementations. The model was implemented in real hardware FPGA board. The measurement results from FPGA implementation are compared with the one from the simulation in Fig. 12, where we can see that the hardware performance is almost as good as that simulated in MATLAB. For the conventional model, to obtain the similar performance, 12 coefficients are required, that is, the model configuration in (24) is set as . The performance is also illustrated in Fig. 11. The FPGA resource utilization for this case is listed in Table III to compare the resource consumption. The implementation of Basis 1, , in both models are the same, which occupies 2068 slice LUTs and 2036 slice registers.

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TABLE III FPGA RESOURCE UTILIZATION COMPARISONS FOR THE CASE IN FIG. 2(B)

Fig. 11. Measured performance comparison for distortion suppression at IM3 band in 3-C CA case 1: Fig. 2(b).

Fig. 12. Measured performance for proposed method in distortion suppression at IM3 band in 3-C CA case 1: Fig. 2(b).

The differences are in the implementations of the step 2, 3 and 4, whose resource consumptions are listed in Table III in details Basis 2 of in the proposed algorithm is accomplished by using CORDIC, which saves 57% LUTs and 38% registers in contrast with that in step 2 in the conventional model. As mentioned earlier, the conventional algorithm requires 4 more coefficients than the proposed one based on the similar calibration performance, resulting in great amount hardware occupation in step 3 and 4 to implement coefficients multiplication. Since the memory structures of two models are identical, the resource usages for both approaches are the same in step 5. In summary, compared to those in the conventional model, the numbers of slice LUT and slice register used in the proposed model decrease by 3426 and 3309, respectively. As discussed in Section IV, multiplexing technique can be employed to further reduce the FPGA resource consumption. The simplified cases are illustrated in Table IV. In step 2, the generation block of and by CORDIC can be multiplexed, which is the same case as to obtain and by adders and multipliers in the conventional model In the final step 5, the summation with different memory consists of current terms and delayed terms can share one structure. Moreover, the resource consumption of step 4 in Table IV is dramat-

ically reduced in the low-cost implementation compared with that in Table III. This is because the specific mode of the multiplications between coefficients and input terms in step 4 is employed. When the multiplier model is set as constant coefficient model, the consumption will be calculated depended on fixed coefficient, which is normally less than common (parallel) multiplier mode. Therefore, both implementations for step 4 in Table IV employ fixed coefficient strategy to further save hardware dissipation. The difference of resource utilization between the proposed and the conventional method in the low-cost multiplexing implementation is smaller than the previous structure without simplification in Table III, but the proposed model still shows advantages over the conventional model. Furthermore, comparisons with other models published in the literature are also listed in Table V, in terms of suppression performance and hardware resource usage. From the results, we can see that our model can achieve great suppression performance with relatively low hardware resources. B. 3-C CA Case 2: Fig. 2(c) In this test, the baseband signal combines three 5 MHz signals located at MHz, MHz, MHz to form a 3-C CA signal. Although the scenario is changed compared to Part A, the model configuration is still set as with 8 coefficients. Fig. 13 shows the measured power spectrum density with and without the transmitter leakage suppression. In Fig. 13, two typical examples of IM3 distortion bands in 3-C CA are expected to be compensated: (1) the IM3 distortion generated from all three carriers, e.g., the target frequency is located at , as shown in Fig. 13(a); (2) the IM3 distortion generated from any two carriers, e.g., the target frequency is located at , as

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TABLE IV FPGA RESOURCE UTILIZATION MULTIPLEX FOR THE CASE IN FIG. 2(B)

TABLE V COMPARISONS OF THE IMD3 CANCELLATION IN THE DUAL-BAND SCENARIO

Fig. 13. Measured performance for distortion suppression at IM3 band in 3-C (2) target frequency CA case 2: Fig. 2(c). (a) target frequency .

shown in Fig. 13(b). From Fig. 13, it can be clearly seen that 2 dB suppression can be achieved for both cases by employing the proposed model. Also the measurement results from FPGA implementations perform as good as the ones from MATLAB. The FPGA resource utilizations for both cases are listed in Table VI. Compared to the resource utilization in Table IV, the consumptions in both cases listed in Table VI only increase slightly Also it can be easily seen that there is slight difference in FPGA resource utilization for both cases. The reason is that due to the different values of the coefficients in these two cases, the FPGA implementation will lead to slight different hardware occupations. Based on the results, it can be seen that the proposed methods will save more FPGA resources when more carriers involved. It is also worth mentioning that the resource consumptions for the selection module in Fig. 8 have also been investigated in this section. The FPGA resource utilization comparison is listed in Table VII Compared to the case without Mux implementation in Table VI, the one with Mux implementation only increases 96 slice LUTs which is insignificant. However, this module will largely enhance the flexibility to form a uniform structure to cancel any sideband distortion located in IM3 bands.

TABLE VI FPGA RESOURCE UTILIZATION FOR THE CASE IN FIG. 2(C)

TABLE VII FPGA RESOURCE UTILIZATION COMPARISON FOR THE SELECTION MODULE

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TABLE VIII FPGA RESOURCE UTILIZATION COMPARISON FOR SQUARE ROOT OPERATION

C. 3-C CA Case 3: Fig. 5 In this test, the baseband signal combines three 5 MHz signals located evenly at MHz, MHz, MHz. One of the sideband distortions is located at 2200 MHz, which can be generated from and , that is and also from all three carriers, that is, . Both distortion components will be overlapped with each other. The model configuration in (22)–(23) is set as , in which two memory parameters are simplified to one. Compared to the cases in Part A and B, the number of the coefficients will be doubled, that is, 16 coefficients, since there are two different basis 1 functions in the model. Fig. 14 shows the measured power spectrum density with and without the transmitter leakage suppression. From Fig. 14, it can be clearly seen that again 20 dB suppression can be also achieved by employing the proposed model. VI. CONCLUSION In this paper, a generalized dual-basis envelope-dependent sideband distortion model, which is further developed from the basic concept in [21], was proposed to model and suppress transmit leakage for non-contiguous CA applications. The proposed model structure provides great flexibility for dealing with different intermodulation products in a uniform structure, which has been validated by FPGA implementation. Experimental results demonstrated excellent model performance with very low model complexity, which provides a promising application in future carrier aggregation applications.

APPENDIX FPGA IMPLEMENTATION OF SQUARE ROOT OPERATION CORDIC is a technique that calculates the trigonometric functions of sine, cosine, magnitude and phase to a desired precision via iteratively rotating the phase of the complex number by multiplying it with a succession of constant values. In this Appendix, FPGA implementation for the square root operation of complex numbers employing CORDIC is provided. To find the magnitude of a complex number, , we can simply rotate it to have a phase of zero and then the magnitude of this complex number is just the real part since the imaginary part is zero. To do this in digital circuits using CORDIC, we first need to make sure its phase is less than degrees. This can be achieved by rotating the complex number by 90 degrees first if its phase is greater than 90 degrees: at the first step, we need to determine if the complex number has a positive or negative phase by looking at the sign of the value. If the phase is positive, rotate it by degrees otherwise by degrees. To rotate by degrees, swap and , and

Fig. 14. Measured performance for distortion suppression at IM3 band in 3-C CA case 3: Fig. 5.

change the sign of , i.e., ; to rotate by degrees, swap and , and change the sign of , i.e., . The phase of is now less than degrees, and we then further rotate the phase iteratively using CORDIC. Since the phase of a complex number is , the phase of “ ” is and likewise, the phase of “ ” is . To add phases, we can multiply by “ ” while to subtract phases, we can use “ ”. In the following iterations, we rotate the phase of the complex number using numbers of the form of “ ”, where is decreasing with powers of two after each iteration, starting with and thereafter , etc., until the phase goes to zero. The operations can be expressed as (A.1) is the real and imaginary part of the complex where and number, respectively, and represents th rotation. can have the value of or 1, which is used to determine the direction of the rotation depends on the sign of . represents the gain of each rotation, that is (A.2) To simplify the operation, the gain can be compensated together by using a scaling factor in the end of iterations, that is (A.3) Since the multiplies are powers of two, CORDIC can be implemented in binary arithmetic logic using just shifts and adds without using actual multipliers [26]. For instance, at each iteration, the real part is obtained via which is only involving shifting to right and adding with . A. Implementation of Since (A.4)

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One CORDIC module can be directly employed and reused, that is (A.5)

However, in this operation, the scaling factor for is , while the one for is . Therefore, both operations require multipliers. In order to reduce the number of multipliers, a new method is proposed below, that is

Then employing the CORDIC to calculate again, we can obtain (A.10) (A.6) To reduce complexity, the scaling factor of CORDIC and compensated later, that is

Finally, we can obtain

can be moved out

(A.7) where we can see that only two CORDICs are involved to conduct the square root operation. Because CORDIC module only uses adders and shifters, the FPGA resource consumed in the proposed approach is much less than that in the conventional polynomial implementation. Let's compare the resource consumption of with that of . At first glance, one may think the implementation of should be more complex than that of , since there is one extra square root operation. However, after careful investigation, the actual resource consumptions are totally different, as shown in Table VIII. The implementation of will require four complex multipliers and three adders. Due to the multipliers, the resource consumption will be costly, which will require 1172 slice LUTs and 1211 slice registers in FPGA. Even if the multiplexing technology is employed, e.g., and may share the same resources, the total resource consumption is still very high. On contrary, the implementation of will only require three CORDIC module, which only employs 495 slice LUTs and 726 slice registers, leading to 40% saving of the resource consumption. Also, if multiplexing is employed, and can share the same CORDIC module and thus only two CORDIC modules will be required, which will further reduce the resource consumption. In summary, because the multipliers will consume more resources than CORDIC, the total FPGA resources consumed for the implementation of is actually large than the one of . B. Implementation of Based on the implementation (A.7) of more input is added into CORDIC module. Firstly

, one (A.8)

then

(A.9)

(A.11) Although one more CORDIC is employed, it can be also multiplexed, which significantly reduces the total implementation cost. REFERENCES [1] M. Iwamura, K. Etemad, M.-H. Fong, R. Nory, and R. Love, “Carrier aggregation framework in 3GPP LTE-advanced [WiMAX/LTE update],” IEEE Commun. Mag., vol. 48, no. 8, pp. 60–67, Aug. 2010. [2] W. Chen, S. A. Bassam, X. Li, Y. Liu, K. Rawat, M. Helaoui, and F. M. Ghannouchi, “Design and linearization of concurrent dual-band Doherty power amplifier with frequency dependent power ranges,” IEEE Trans. Microw. Theory Tech., vol. 59, no. 10, pp. 2537–2546, Oct. 2011. [3] P. B. Kennington, High Linearity RF Amplifier Design. Norwood, MA, USA: Artech House, 2000. [4] C. Yu, M. Allegue-Martinez, Y. Guo, and A. Zhu, “Output-controllable partial inverse digital predistortion for RF power amplifiers,” IEEE Trans. Microw. Theory Tech., vol. 62, no. 11, pp. 2499–2510, Nov. 2014. [5] P. Roblin, S. K. Myoung, D. Chaillot, Y. G. Kim, A. Fathimulla, J. Strahler, and S. Bibyk, “Frequency selective predistortion linearization of RF power amplifiers,” IEEE Trans. Microw. Theory Tech., vol. 56, no. 1, pp. 65–76, Jan. 2008. [6] J. Kim, P. Roblin, D. Chaillot, and Z. Xie, “A generalized architecture for the frequency-selective digital predistortion linearization technique,” IEEE Trans. Microw. Theory Tech., vol. 61, no. 1, pp. 596–605, Jan. 2013. [7] S. A. Bassam, M. Helaoui, and F. M. Ghannouchi, “Channel-selective multi-cell digital predistorter for multi-carrier transmitters,” IEEE Trans. Commun., vol. 60, no. 8, pp. 2344–2352, Aug. 2012. [8] M. Abdelaziz, L. Anttila, J. R. Cavallaro, S. S. Bhattacharyya, A. Mohammadi, F. Ghannouchi, M. Juntti, and M. Valkama, “Low-complexity digital predistortion for reducing power amplifier spurious emissions in spectrally-agile flexible radio,” in Proc. 9th Int. Conf. Cognitive Radio Oriented Wireless Networks Commun. (CROWNCOM), Jun. 2–4, 2014, pp. 323–328. [9] M. Abdelaziz, L. Anttila, A. Mohammadi, F. Ghannouchi, and M. Valkama, “Reduced-complexity power amplifier linearization for carrier aggregation mobile transceivers,” in Proc. IEEE ICASSP, Florence, Italy, May 2014, pp. 3908–3912. [10] Z. Fu, L. Anttila, M. Abdelaziz, M. Valkama, and A. M. Wyglinski, “Frequency-selective digital predistortion for unwanted emission reduction,” IEEE Trans. Commun., vol. 63, no. 1, pp. 254–267, Jan. 2015.

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[11] A. Frotzscher and G. Fettweis, “Baseband analysis of Tx Leakage in WCDMA zero-IF receivers,” in Proc. IEEE Int. Symp. Control, Commun. Sig. Proc. (ISCCSP'08), 2008, pp. 129–134. [12] A. Frotzscher, M. Krondorf, and G. Fettweis, “On the performance of OFDM in zero-IF receivers impaired by Tx Leakage,” in Proc. IEEE Int. Conf. Commun. (ICC'09), Jun. 2009, pp. 1–5. [13] M. Kahrizi, J. Komaili, J. Vasa, and D. Agahi, “Adaptive filtering using LMS for digital TX IM2 cancellation in WCDMA receiver,” in Proc. IEEE Radio Wireless Symp., Orlando, FL, USA, Jan. 22–24, 2008, pp. 519–522. [14] M. Omer, R. Rimini, P. Heidmann, and J. S. Kenney, “A compensation scheme to allow full duplex operation in the presence of highly nonlinear microwave components for 4 G systems,” in Proc. IEEE MTT-S Int. Microw. Symp. Dig., Baltimore, MD, USA, Jun. 5–10, 2011, pp. 1–4. [15] M. Omer, R. Rimini, P. Heidmann, and J. S. Kenney, “All digital compensation scheme for spur induced transmit self-jamming in multi-receiver RF frond-ends,” in Proc. IEEE MTT-S Int. Microw. Symp. Dig., Montreal, QC, Canada, Jun. 17–22, 2012, pp. 1–3. [16] A. Kiayani, L. Anttila, and M. Valkama, “Modeling and dynamic cancellation of TX-RX leakage in FDD transceivers,” in Proc. IEEE Int. Midwest Symp. Circuits Syst. (MWSCAS), Aug. 2013, pp. 1089–1094. [17] A. Kiayani, L. Anttila, and M. Valkama, “Digital suppression of power amplifier spurious emissions at receiver band in FDD transceivers,” IEEE Signal Process. Lett., vol. 21, no. 1, pp. 69–73, Jan. 2014. [18] A. Kiayani, M. Abdelaziz, L. Anttila, V. Lehtinen, and M. Valkama, “DSP-based suppression of spurious emissions at RX band in carrier aggregation FDD transceivers,” in Proc. 22nd Eur. Sig. Proc. Conf. (EUSIPCO), Sep. 2014, pp. 591–595. [19] H.-T. Dabag, H. Gheidi, P. Gudem, and P. M. Asbeck, “All-digital cancellation technique to mitigate self-jamming in uplink carrier aggregation in cellular handsets,” in Proc. IEEE MTT-S Int. Microw. Symp. Dig., Seattle, WA, USA, Jun. 2013, pp. 1–3. [20] H.-T. Dabag, H. Gheidi, S. Farsi, P. Gudem, and P. M. Asbeck, “Alldigital cancellation technique to mitigate receiver desensitization in uplink carrier aggregation in cellular handsets,” IEEE Trans. Microw. Theory Tech., vol. 61, no. 12, pp. 4754–4765, Jan. 2013. [21] C. Yu and A. Zhu, “Modeling and suppression of transmitter leakage in concurrent dual-band transceivers with carrier aggregation,” in Proc. IEEE MTT-S Int. Microw. Symp. Dig., Phoenix, AZ, USA, May 2015. [22] “3rd Generation Partnership Project; LTE; Evolved Universal Terrestrial Radio Access (E-UTRA); Base Station (BS) Radio Transmission and Reception (Release 10),” Tech. Spec. 3GPP TS 36.104 V10.2.0 (2011-05), 3GPP, Sophia Antipolis Cedex, France, May 2011. [23] S. Bassam, W. Chen, M. Helaoui, and F. Ghannouchi, “Transmitter architecture for CA: carrier aggregation in LTE- Advanced systems,” IEEE Microw. Mag., vol. 14, pp. 78–86, Aug. 2013. [24] E. G. Lima, T. R. Cunha, H. M. Teixeira, M. Pirola, and J. C. Pedro, “Base-band derived Volterra series for power amplifier modeling,” in Proc. IEEE MTT-S Int. Microw. Symp. Dig., Boston, MA, Jun. 2009, pp. 1361–1364. [25] E. G. Lima, T. R. Cunha, and J. C. Pedro, “A physically meaningful neural network behavioral model for wireless transmitters exhibiting PM-AM/PM-PM distortions,” IEEE Trans. Microw. Theory Tech., vol. 59, no. 12, pp. 3512–3521, Dec. 2011. [26] J. E. Volder, “The CORDIC trigonometric computing technique,” IRE Trans. Electron. Compute., vol. EC-8, no. 3, pp. 330–334, Sep. 1959.

Chao Yu (S'09–M'15) received the B.E. degree in information engineering and M.E. degree in electromagnetic fields and microwave technology from Southeast University (SEU), Nanjing, China, in 2007 and 2010, respectively, and the Ph.D. degree in electronic engineering from University College Dublin (UCD), Dublin, Ireland, in 2014. He is currently an Associate Professor with the State Key Laboratory of Millimeter Waves, School of Information Science and Engineering, SEU. His research interests include RF power amplifiers modeling and linearization, high-speed ADC digital correction. He is also interested in antenna design, FPGA hardware implementation and RF wireless system design.

Wenhui Cao (S'15) received the B.E. degree in automation from Beijing University of Chemical Technology, Beijing, China, in 2013 and is currently working toward the Ph.D. degree in University College Dublin (UCD), Dublin, Ireland. She is currently with RF and Microwave Research Group, UCD. Her research interests include nonlinear behavioral modeling of RF power amplifiers, digital post-correction of high speed ADCs, and high performance field-programmable gate-array (FPGA) implementation methodologies.

Yan Guo (S'13) received the B.E. degree in information science and engineering from East China Jiaotong University, Nanchang, Jiangxi Province, China, in 2007, the M.E. degree in communication and information systems from Southeast University, Nanjing, China, in 2011, and is currently working toward the Ph.D. degree with University College Dublin (UCD), Dublin, Ireland. He is currently with the RF and Microwave Research Group, UCD. His research interests include spectrum sensing for cognitive radio, digital predistortion for RF power amplifiers, and field-programmable gate-array (FPGA) hardware implementations.

Anding Zhu (S'00–M'04–SM'12) received the B.E. degree in telecommunication engineering from North China Electric Power University, Baoding, China, in 1997, the M.E. degree in computer applications from the Beijing University of Posts and Telecommunications, Beijing, China, in 2000, and the Ph.D. degree in electronic engineering from University College Dublin (UCD), Dublin, Ireland, in 2004. He is currently a Senior Lecturer with the School of Electrical, Electronic and Communications Engineering, UCD. His research interests include high frequency nonlinear system modeling and device characterization techniques with a particular emphasis on Volterra-series-based behavioral modeling and linearization for RF power amplifiers (PAs). He is also interested in wireless and RF system design, digital signal processing, and nonlinear system identification algorithms.

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Coupling-Matrix-Based Design of High- Bandpass Filters Using Acoustic-Wave Lumped-Element Resonator (AWLR) Modules Dimitra Psychogiou, Member, IEEE, Roberto Gómez-García, Senior Member, IEEE, and Dimitrios Peroulis, Senior Member, IEEE

Abstract—This paper presents an original and simple coupling-matrix-based synthesis methodology for the design of a new class of bandpass filters (BPFs) that employ hybrid acoustic-wave-lumped-element resonator (AWLR) modules with improved out-of-band isolation (IS). The proposed BPFs feature quasi-elliptic-type frequency response—shaped by poles and transmission zeros (TZs) for an th-order transfer function, compact physical size, and high effective quality factors of the order of 1000. Despite the use of acoustic wave (AW) resonators, passbands exhibiting fractional bandwidths (FBWs) that are no longer limited by the electromechanical coupling coefficient of the constituent AW resonators are obtained. A coupling-matrix-based model of a multi-mode AW resonator is also reported. It facilitates the incorporation of high- and low-frequency spurious modes that are present in a realistic filter response so that they can be anticipated at the synthesis and simulation levels. For proof-of-concept validation purposes, two BPF prototypes at 418 MHz made up of commercially-available surface acoustic wave (SAW) resonators and surface mounted devices (SMD) were built and measured. They perform first(one pole and two TZs) and second-order (two poles and four TZs) transfer functions with measured passband insertion losses (IL) between 2.4–5.4 dB, between 1600–1900, 3-dB absolute ), bandwidths ranging from 0.52 to 1 MHz (i.e., 1.6–3.2 times and minimum IS levels between 25–46 dB. Index Terms—Acoustic wave (AW) filter, bandpass filter (BPF), enhancement, quasi-elliptic-type filter, RF/microwave filter, surface acoustic wave (SAW) filter, SAW resonator.

I. INTRODUCTION

E

MERGING wireless communication systems are more and more evolving towards multi-frequency and multi-standard communication services which in turn result in

Manuscript received June 29, 2015; revised September 28, 2015; accepted October 11, 2015. Date of publication November 18, 2015; date of current version December 02, 2015. This work was supported in part by the National Science Foundation under Award 1247893 and in part by the Spanish Ministry of Economy and Competitiveness under Project TEC2014-54289-R. This paper is an expanded version from the IEEE MTT-S International Microwave Symposium, Phoenix, AZ, USA, May 17–22, 2015. D. Psychogiou and D. Peroulis are with the School of Electrical and Computer Engineering, Birck Nanotechnology Center, Purdue University, West Lafayette, IN 47907 USA (e-mail: [email protected]; [email protected]). R. Gómez-García is with the Department of Signal Theory and Communications, University of Alcalá, Madrid 28871, Spain (e-mail: roberto.gomez. [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2015.2494597

a highly-congested frequency radio spectrum [1], [2]. A typical example of this trend is the UHF band (300–3000 MHz), which is currently exploited by numerous military and commercial applications sharing closely-spaced or even co-located frequency bands. In order to efficiently utilize this region of the electromagnetic (EM) spectrum without sacrificing receiver sensitivity, bandpass filters (BPFs) with increased selectivity, large out-of-band rejection, narrow fractional bandwidth (FBW), and low insertion loss (IL) need to be employed in the RF front-end module in order to properly preselect the desired band of frequencies [3], [4]. When size is of critical importance in these systems, RF BPFs using EM wave resonators (e.g., microstrip-line [5], lumped-element [6], [7], and waveguide [8] resonators) cannot adequately meet the aforementioned performance requirements due to the inversely proportional relationship between resonator size and unloaded quality factor . On the other hand, filtering topologies made up of acoustic wave (AW) resonators [e.g., surface acoustic wave (SAW) and bulk acoustic wave (BAW) type] exhibit high values (1000–10 000) in a highly miniaturized volume [9]–[13]. However, their FBW is inherently limited by the electromechanical coupling coefficient 0.05%–0.1%) of their structural materials. It is typically between 0.4–0.8 for conventional lattice or ladder AW resonator arrangements [11]. Furthermore, as an additional shortcoming to be mentioned, they require AW resonators of alternative impedances and resonant frequencies. This makes their response sensitive to manufacturing and tolerance variations. A number of bandwidth-enlargement techniques have been reported in the open technical literature to date. In [14]–[19], the development of piezoelectric materials with high is discussed. However, the frequency response of these BPFs is limited by increased IL (i.e., reduced ), temperature sensitivity, and unwanted spurious modes [17], [19]. In an alternative approach, all-AW BPFs with closely-spaced passbands are effectively combined to increase the BPF bandwidth [20]. Their frequency response is nevertheless constrained by fabrication tolerances and material properties variations, which result in excessive ripples within the passband leading to perceptible amplitude-distortion levels for in-band processed signals. A hybrid-technology BPF design concept in which AW resonators are effectively combined with lumped-element (LE) components is reported in [21] for bandwidth-broadening purposes. It allows the realization of large-FBW (up to 5 ) transfer func-

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tions whose passband preserves the high- (e.g., of 4000) characteristics of the constituent AW resonators. However, their RF response is limited by poor out-of-band isolation (IS) when large FBW transfer functions are actualized. In this paper, a novel acoustic-wave-lumped-element (AWLR) resonator module that comprises one AW resonator (two-terminal one-port type) and three LE resonators is reported. It permits the realization of high- BPFs with quasi-elliptic-type frequency response, , and IS levels that can be arbitrarily designed—without being constrained by the realizable FBW state—as opposed to the BPF architecture in [21]. A further relevant contribution of this work is the development of an original and simple coupling-matrix (CM)-based synthesis methodology for this class of BPFs. It facilitates the design of AW-resonator-based BPFs through conventional coupled-resonator filter design techniques and improves the flexibility of existing AW-filter synthesis methodologies. Preliminary results on this approach were first demonstrated in [22]. It is the intention of this work to further investigate this concept and present an in-depth theoretical analysis of its merits by expanding its applicability to higher-order BPF transfer functions. Furthermore, the CM-based model of a multi-mode AW resonator that facilitates the incorporation of spurious modes (high- and low-frequency ones) already at the theoretical design level is reported and validated through various synthesis examples. Lastly, new first- and second-order BPF prototypes are presented as proof-of-concept demonstrators. The content of this work is organized in the following manner. In Section II, the engineered BPF design concept that consists of AWLR modules with improved IS is introduced. The theoretical foundations of the CM-based synthesis technique are expounded through various BPF design examples. Moreover, the multi-mode CM-based model of two-terminal one-port AW resonators is also presented. In Section III, the design and experimental validation of BPF prototypes that feature first- and second-order transfer functions are reported as proof-of-concept demonstrators. Lastly, a summary of the major contributions and the most relevant conclusions of this work is provided in Section IV. II. THEORETICAL FOUNDATIONS The devised BPF concept is based on a new class of AWLR modules with improved IS that are synthesized through a hybrid combination of one high- resonant node , three lowresonant nodes ( and ), and one non-resonant node (N) as detailed in the coupling matrix diagram (CMD) in Fig. 1(a). Each AWLR module features a quasi-elliptic-type frequency response that is shaped by one pole in-between two transmission zeros (TZs) [see Fig. 1(a)]. The location of the pole is primarily defined by the resonant node whereas the TZs stem from the parallel combination of a passband resonance—created by node —and a stopband resonance—produced by the combination of nodes N and . Note that, in this configuration, the resonant nodes are only used to define the IS of the AWLR module as it will be further explained in this section. In the practical BPF developments of this work, two-terminal one-port type AW resonators (e.g., SAW or BAW type) are considered as highresonant elements whereas the rest of the low- resonant nodes

Fig. 1. (a) th-order AWLR BPF that comprises AWLR modules with improved IS. The characteristic response (S-parameters) of the single AWLR module with improved IS is also shown. (b) Circuit schematic of a realistic th-order BPF model that consists of two-terminal one-port type AW res, and impedance inverters (K-inv). onators, LE resonators

and coupling sections are realized by means of conventional LE components. This is illustrated in Fig. 1(b) for an example circuit schematic of an th-order BPF with quasi-elliptic-type response. The theoretical foundations of the AWLR-based BPF concept are described in this section starting from the detailed analysis of the AWLR module with improved IS. Its application to the synthesis of high-order bandpass filtering transfer functions is subsequently addressed. A. Acoustic Wave Resonator Modeling The circuit details of the two-terminal one-port type AW resonator [23] that is typically represented by the Butterworth Van-Dyke (BVD) model [see Fig. 2(a)], along with its corresponding frequency response—for an AW resonator example with H, fF, , and pF—are depicted in Fig. 2. Its transfer function consists of one series resonant frequency and one anti-series resonant frequency that can be specified using (1) [23, p. 864]. Note that these frequencies can be calculated from the geometrical and material properties of the AW resonator for a given resonator geometry as discussed in [11]. Such a frequency response can be synthesized from a CMD in which the parallel combination of one resonant node and one non-resonant node N is considered as depicted in Fig. 2(b). Its corresponding self-coupling coefficients and

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BANDPASS FILTERS

Fig. 2. AW resonator. (a) Butterworth Van-Dyke (BVD) circuit model [23]. (b) Equivalent CMD for the representation of one resonant and one antiresonant , (i.e., ), frequency with . (c) Synthesized S-parameters using the BVD model in and H, (a) for a two-terminal one-port type AW resonator with fF, , pF, , and the CMD in (b).

can be specified through (2) [24], [25] whereas the inter-node coupling coefficients and — for the example in Fig. 2—are obtained by fitting the synthesized CMD response to the one obtained by RF-measurements or EM-simulations assuming a FBW equal to . Note that and in (2) refer, respectively, to the FBW and of the series resonant branch [ , , in Fig. 2(a)] of the AW resonator that can be determined from (3), in which denotes the reference impedance of the two-port network. Fig. 2(c) illustrates a comparison between the simulated response that stems from the BVD circuit and the synthesized transfer function using the CMD in Fig. 2(b). As can be seen, they are in fairly-close agreement and, thus, validate the devised CMD for the two-terminal one-port type AW resonator

(1)

(2)

(3)

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Fig. 3. (a) CMD representation of a multi-mode AW resonator. The parallel cascaded resonant nodes represent the fundamental series resonant frequency ) and the spurious resonant frequencies (nodes ), respectively. (b) (node , , Example matrix of an AW resonator with five resonant nodes (nodes , , ) and one non-resonating node (node N). (c) RF-measured response for a commercially-available SAW resonator from Abracon Corp. (ASR418S2) , and synthesized response from a CMD with , , , , , (i.e., ), , , , and .

As an additional original contribution of this work, the CMD of the AW resonator can be further extended to include the undesired signal contributions of low- and high-frequency spurious modes. These modes are present in the measured frequency response and typically appear in a close proximity to the fundamental resonances ( , ), hence limiting the filter's performance. A generic multi-mode CMD is depicted in Fig. 3(a). In this scenario, the higher-order modes are taken into consideration by adding extra resonant nodes— - , where is the number of the existing spurious modes—in-parallel to the primary resonant node as for the case of representing multimode resonators in multi-band filter designs [24, Ch. 9], [26]. The self-coupling coefficients and the inter-node coupling coefficients can be calculated through (4), in which , , and are, respectively, the FBW, , and resonant frequency of each spurious resonance that can be derived from the RF-measured or EM-simulated response. In order to verify the aforementioned model, a comparison between the CM-synthesized and the RF-measured response of a commercially-available two-terminal one-port type AW resonator from Abracon Corp. (part ASR418S2) is depicted in Fig. 3. Note that the synthesized response was obtained from the CM in Fig. 3(b), in which one fundamental and four spurious modes are considered. As can be seen, a very close agreement is obtained

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among the two traces, hence successfully verifying the conceived multi-mode CMD for two-terminal one-port type AW resonators. Its applicability to the synthesis of bandpass transfer functions that take into consideration the multi-mode nature of AW resonators will be discussed in the next sections

(4) B. Acoustic-Wave-Lumped-Element Resonator Module Using as a reference the CMD in Fig. 2(b) and by readily adding a resonant node below the non-resonant node , is effectively decoupled from as shown in the examples in Fig. 4. It results in a high- passband that is located in-between two TZs with FBW (0.032% for the AW resonator of Figs. 2 and 3) that can be calculated through (3). In a practical RF design scenario, it can be implemented by adding an inductance in parallel to the parasitic capacitance of the AW resonator as shown in Fig. 1(b). It is apparent that for a given AW resonator topology the coupling coefficients , , , and are fixed. As such, the location (normalized frequency) of the out-of-band TZs can be only adjusted by modifying and as described in (5) that respectively correspond to altering the resonant frequency (through the variation of ) or its relevant , values—for the same resonant frequency as the high- resonant node—in relation to the series resonant branch , . A set of power transmission response examples that are synthesized using the aforementioned CMD for alternative levels of and are plotted in Fig. 4(b) and (c), respectively, to illustrate the aforementioned TZ control capability. The power transmission response dependence (IS and passband IL) on the finite of is also shown at the same figure. It can be observed that the IS at the location of the TZs only depends on ( that corresponds to ), which is practically defined by the of since the element of the AW resonator is considered lossless. As such, the resulting of the grouped resonator ( , ) is much higher than that of a conventional LE resonator in which both the inductive and capacitive resonator components feature a finite . Noteworthy is that even for a of the order of 100, the IS levels at the location of the TZs are over 45 dB. In addition, as can be seen in the inset of Fig. 4(a), the passband IL remains unchanged. This demonstrates the suitability of the AWLR module for the realization of high- BPFs with quasi-elliptic-type frequency response

Fig. 4. (a) CMD of the AWLR and detail of its power transmission response : 70, 70, and 31.4i (i.e., ). (b) Power for various levels of : 70, 70, and 31.4i (i.e., transmission response for various levels of ). The rest of the coupling coefficients are: , , (i.e., ), and . (c) Power : 55, 85, and 105. The rest of the transmission response for various levels of , , coupling coefficients are: (i.e., ), , and .

augmented to theoretically any value despite the finite of the AW resonator which typically limits the FBW in all-AW BPFs to 0.4–0.8 . As a trade-off to be mentioned, the referred FBW increase comes at the expense of reduced out-of-band rejection as typically observed in all-AW filters

(5) The FBW of the AWLR module can be further increased by inserting impedance inverters at its input/output ports, as illustrated in the CMD of Fig. 5(a). Its corresponding coupling coefficients can be specified though (6), in which is the designed FBW. Fig. 5(b) illustrates the synthesized response of the CMD in Fig. 5(a) for various sets of . As can be seen, the FBW of the obtained BPF response can be arbitrarily

(6)

C. Acoustic-Wave-Lumped-Element Resonator Module With Improved Out-Of-Band Isolation The out-of-band rejection levels of the AWLR with improved FBW can be arbitrarily increased by readily integrating

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Fig. 5. (a) CMD of the AWLR with impedance inverters at its input/output and accesses. (b) Power transmission response for various levels of , , (i.e., ), and .

two low- resonant nodes as illustrated in the CMD in Fig. 6(a). Note that both nodes need to resonate at the center frequency of the passband while featuring different inductance and capacitance values than those of the remaining CMD nodes as shown in the practical implementation circuit in Fig. 1(b). In this manner, the inter-node coupling coefficients that are adjacent to (i.e., , , and ) are scaled by a factor that represents the inductance scaling among the resonators as well as the nodes transformation in relevance to the CMD in Fig. 5(a). For a given inductance , it can be calculated using (7) which in turn results in a quasi-elliptic-type frequency response with significantly improved out-of-band IS as demonstrated in Fig. 6(b). A comparison between the synthesized response of the AWLR with improved IS and that of Fig. 5(a) is illustrated in Fig. 6(b) for various levels of . As can be seen, the decrease of produces an increase of the out-of-band rejection. The finite effect of the resonant nodes (with equal to ) is also shown through a comparison between the synthesized transfer function of the CMD in Fig. 6(a) for infinite and of 100. It can be observed that it comes at the expense of increased IL. However, the corresponding of the resulting passband is of the order of 2300 despite the use of low- resonant nodes with around 100. This corroborates the potential of this design approach for the actualization of high- BPF transfer functions despite the inclusion of the low- nodes for IS enhancement (7)

Fig. 6. (a) CMD and equivalent CM of the AWLR module with improved IS. 12.8 (b) Synthesized power transmission response for various levels of ( and 31.4i (i.e., infinite and 100). The values and 25.7) and , , , of the rest of the coupling coefficients are: . (c) Synthesized power transmission response of the AWLR and module with improved IS using the multi-mode model of the AW resonator for 1, 3, 6, and 9), , , , various levels of FBW ( , , and . Note that in all examples the is considered lossless. resonant node

D. Filter Synthesis with Incorporated Spurious Modes In the analysis detailed in Sections II-B and II-C, the utilized AW resonator is represented through the simplified CMD in Fig. 2(a) (i.e., only the fundamental modes are included) in

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order to expound the most relevant filter synthesis principles in a comprehensive manner. However, taking into consideration that the presence of spurious modes can severely affect the filter's performance, their prediction at the theoretical synthesis level becomes of critical importance. Various examples of synthesized transfer functions that stem from an expanded version of the CMD in Fig. 6(a), in which the spurious modes of the AW resonator are incorporated as parallel-cascaded resonant nodes - [see Fig. 3(a)], are demonstrated in Fig. 6(c). As can be seen, the impact of the spurious resonant modes becomes more prominent with the increase of FBW. In particular, when considering large FBW states, the spurious modes that are located in a close proximity to the fundamental modes might appear as in-band notches. Thus, although the FBW of the AWLR module with improved IS is not theoretically limited by the , it is however restricted in practice by the separation and magnitudes of the lower and upper closest-to-passband spurious modes. In addition, it should be noticed that broader FBWs can be realized by either suppressing the undesired spurious modes or by increasing their separation from the fundamental modes as reported by the authors in [27], [28]. However, such an investigation falls out of the scope of this work. E. Extension to Higher-Order Transfer Functions The AWLR concept with improved IS can be readily extended to the realization of higher-order BPF transfer functions by cascading in-series multiple AWLR modules ( for an th-order BPF response) as shown in the th-order CMD in Fig. 1(a) and its corresponding circuit schematic in Fig. 1(b). The devised CMD facilitates the synthesis of BPF transfer functions with and quasi-elliptic-type frequency response that is shaped by poles and 2 TZs. The obtained TZs can be located around the passband in a symmetric or in an asymmetric fashion. Note that each pair of TZs is controlled by the coupling coefficients and (frequency characteristics of the resonant node ) of each AWLR module as described in (5). In order to better illustrate the aforementioned functionalities, the synthesis of second-order transfer functions with symmetrically located TZs is considered. They stem from the CMD and its equivalent CM representation in Fig. 7(a). Note that, in this case, the coupling sections with normalized coefficients and tailor the BPF's FBW and power matching levels, respectively. Furthermore, the BPF's IS is controlled by as in the first-order transfer function in Fig. 6. An example of a synthesized second-order transfer function that realizes a 3-dB absolute bandwidth of 0.8 MHz (lossless case) and features symmetrically located TZs is depicted in Fig. 7(b) for various levels of . Note that, in this implementation, lossless resonant nodes are considered. As can be seen, the cascade of two AWLR modules with improved IS gives rise to spurious passbands that are symmetrically located around the BPF's center frequency. However, their intensity can be significantly mitigated by introducing a finite in the resonant nodes , which is typically the case in a practical BPF development in which LE resonators are considered. It is apparent that there is a tradeoff between passband IL and the magnitude of the spurious modes as observed in Fig. 7(b). However, in most realistic implementations, the use of resonant

Fig. 7. Second-order BPF using two series-cascaded AWLR modules with improved IS. (a) CMD and CM. (b) Frequency response of a second-order transfer function that stems from the CMD in (a) with 3-dB absolute bandwidth of 0.8 (lossless is conMHz and alternative levels of the of the resonator , sidered in these examples) using the following coupling coefficients: , , , (i.e., ), , and . The frequency response of a second-order BPF with similar bandwidth and of 1200 is also shown for comparison purposes.

nodes with offers a relatively good compromise in terms of the above parameters. Such an example is shown in Fig. 7(b), in which a second-order BPF response with of the order of 1200 and minimum IS of 55 dB is obtained by using nodes with of only 75, making the proposed BPF synthesis approach suitable for LE development. Alternative examples of synthesized transfer functions are plotted in Fig. 8. Note that, in all the cases, resonant nodes with finite ( and ) are considered. It can be observed in Fig. 8(a) that for the same levels of IS (e.g., 50 dB at 405 MHz) narrower bandwidth states feature lower levels of IL—which correspond to larger levels of . Furthermore, it should be further noticed that for the same bandwidth state the increase of IS (smaller ) comes at the expense of some IL deterioration as also shown in Fig. 8(a). Synthesized transfer

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Fig. 9. (a) Schematic circuit of the AWLR module with improved IS. (b) Manufactured prototype for the realization of a 3-dB absolute bandwidth of 1 MHz and minimum IS 25 dB. The utilized LE components are as follows: Johanson 251R14S110GV4T, Coilcraft 1206CS100, Coilcraft 165-05-A06, and SAW=Abracon ASR418S2.

Fig. 8. Second-order BPF using two series-cascaded AWLR modules with improved IS. (a) Frequency response for alternative levels of 3-dB absolute bandwidth (e.g., 0.46 and 0.8 MHz) and IS (e.g., 50 and 70 dB at 405 MHz) for symmetrically located (around the passband) double pairs of TZs . (b) Frequency response of a quasi-elliptic BPF with 0.8-MHz 3-dB absolute bandwidth (labelled as “BW in this figure”) and four symmet. Unless rically located (around the passband) TZs , , explicitly stated in the legend of each figure, , (i.e., ), (i.e., ), (i.e., ), , and . Note that for the synthesis of these transfer functions, resonators with realistic values of have been considered. The indicated 3-dB absolute bandwidth of the BPF refers to the bandwidth before the RF losses are added.

functions for different positions of symmetrically located TZs around the desired passband (located at 418 MHz) are also shown in Fig. 8(b). They have been obtained through AWLR modules that either feature symmetric [e.g., grey trace in Fig. 8(b)] or asymmetric [e.g., red and black trace in Fig. 8(b)] TZs [see Fig. 4(b)]. This demonstrates the controllability of TZs for improved IS realization. III. RF MEASUREMENTS AND DISCUSSION First- and second-order BPF prototypes have been designed, manufactured, and characterized in order to evaluate the practical usefulness of the proposed CM-based synthesis formalism for mixed-technology AWLR modules and its applicability to the realization of high- BPFs with quasi-elliptic-type frequency response. All filters prototypes have been implemented on a Rogers RO 4003C dielectric substrate with the following characteristics: dielectric permittivity , dielectric thickness 1.524 mm, dielectric loss tangent , and 35- m-thick Cu-cladding. They have

been designed for a center frequency of 418 MHz and a 50reference impedance. Note that, for the proposed implementation approach, external matching networks which would lead to increased IL and physical size are not required as opposed to conventional all-AW filter architectures. Commercially-available two-terminal one-port type SAW resonators (ASR418S21) from Abracon Corporation were employed as resonant nodes. Furthermore, for the realization of the low- resonant nodes and and their adjacent impedance inverters (coupling coefficients and ), LE components from Johanson Tech. and Coilcraft Inc. were utilized as listed in the captions of Figs. 9 and 11. The RF design of the BPF prototypes starts by defining the filter CM by using the design methodology described in Section II. Afterwards, the coupled-resonator approach in [24, pp. 215–216] is employed in order to specify the realistic impedance inverter values (90 -length-at- transmission lines) which are in turn implemented by their first-order -type LE lowpass equivalent circuit. Lastly, the final values of the LEs that need to be utilized in the actual BPF prototype are obtained through full-wave simulation analysis of the realistic filter geometry (landing pads for the LE components and RF excitation interface) using the EM solver of the Advanced Design Systems (ADS) software from Keysight Technologies. In the next subsections, the RF performance metrics of two—firstand second-order—BPF prototypes are discussed in terms of RF measurements and simulations. A. First-Order BPF Using AWLR Modules With Improved IS An example of an experimental BPF prototype that features a first-order quasi-elliptic-type frequency response with 3-dB absolute bandwidth of 1 MHz and minimum IS of 25 dB is illustrated in Fig. 9. Its LE components, along with its equivalent

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Fig. 10. (a) RF-measured, EM-simulated (multi-mode resonator model), and CM-synthesized (multi-mode resonator model) power transmission response of the first-order prototype in Fig. 9. (b) RF-measured, EM-simulated (multi-mode resonator model), and CM-synthesized (multi-mode resonator model) input power reflection response of the first-order prototype in Fig. 9.

schematic circuit, are also shown at the same figure. The RF performance of this filter assembly was experimentally evaluated in terms of S-parameters with an Agilent E8361A network analyzer. Its measured power transmission and reflection responses are shown in Fig. 10. Based on these curves, the measured RF performance parameters can be summarized as follows: 3-dB absolute bandwidth of 0.95 MHz, 2.4 dB (SMA connector loss and RF excitation interface are included), (SMA connector loss and RF excitation interface are included), , IS > 25 dB, and return loss (RL) 21.6 dB. A comparison between the RF-measured, EM-simulated, and the CM-synthesized response (multi-mode SAW resonator model) is also depicted in Fig. 10. As can be seen, all responses are in close agreement, thus successfully validating the suggested filter design concept. As discussed in Section II, the presence of spurious modes is attributed to the multi-mode nature of the SAW resonator as typically observed in all-AW resonator filters—as, for example, in [10]–[22]. B. Second-Order BPF Using AWLR Modules With Improved IS The realization of higher-order BPF transfer functions was experimentally validated through a second-order filter assembly. Its corresponding manufactured prototype, equivalent circuit model, and its actual commercially-available LE components are presented in Fig. 11. The RF-measured response of

Fig. 11. (a) Schematic circuit of a second-order BPF using the AWLR module with improved IS. (b) Manufactured prototype of the second-order BPF for the actualization of a 3-dB absolute bandwidth of 0.5 MHz and 50 dB. The utilized LE components are as follows: minimum IS Johanson 251R14S2R0BV4T, Coilcraft 0805HQ-39N, JoCoilcraft 0805CS-6N9, Johanson hanson 251R14S1R2BV4T, Coilcraft 0806SQ-6N9, 251R14S0R3BV4T//251R14S180JV4T, Johanson 251R14S0R5BV4T//251R14S160GV4T, Coilcraft 165-05-A06, and SAW=Abracon ASR418S2.

the second-order BPF prototype is plotted in Fig. 12. Its main characteristics can be summarized as follows: 3-dB absolute bandwidth equal to 0.52 MHz, 5.4 dB (SMA connector loss and RF excitation interface are included), (SMA connector loss and RF excitation interface are included), , IS > 46 dB, and 33 dB. As can be seen, it agrees well with the one obtained through EM simulations and CM synthesis, hence confirming the applicability of the conceived concept to the realization of higher-order transfer functions featuring high levels of and FBW that is no longer limited by the of the constituent AW resonators. IV. CONCLUSION This work has presented a new and straightforward CM-based RF-design approach that allows the realization of AW-resonator-based BPFs with the following features: 1) FBW that is no longer limited by the of the utilized AW resonators; 2) controllable levels of IS; 3) AW resonators of identical frequency response and impedance characteristics; and 4) of the order of 1000 for a compact physical size. The CMD of a multi-mode AW resonator has been extracted to allow for the incorporation of spurious modes already in the filter analytical synthesis and simulation stages. A new class of AWLR modules that enable the actualization of quasi-elliptic-type BPFs with controllable levels of IS has also been proposed. Its experimental usefulness and the underlying CMD synthesis approach have been verified through the design of two—first- and second-order—BPF prototypes at 418 MHz

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Fig. 12. (a) RF-measured, EM-simulated (multi-mode resonator model), and CM-synthesized power transmission response of the second-order prototype in Fig. 11. (c) RF-measured, EM-simulated (multi-mode resonator model), and CM-synthesized input power reflection response of the second-order prototype in Fig. 11.

that employ commercially-available SAW resonators and SMD components. For these circuits, transfer functions with passband IL between 2.4–5.4 dB were measured. They correspond to between 1650–1900, which are approximately 20–50 larger than in conventional LE filters for comparable physical size. The FBW enhancement of the aforementioned BPF prototypes was measured between 1.6–3.2 , which is 2–16 times larger than that of state-of-the-art all-AW BPFs which feature FBWs between 0.2–0.8 —as, for example, the ones in [11], [12], [15], [19], [29] 0.17-0.29 . As an added advantage to be emphasized, the conceived BPF design approach facilitates the realization of stopbands with continuous increase in the IS levels when considering frequencies away from the passband. Such a feature is not feasible in conventional all-AW-resonator BPFs (e.g., ladder type) [15], [31] as well as in the AWLR filter in [21], which typically suffer from decreased levels of IS. These RF performance merits highlight the potential of the engineered mixed-technology filter principle for the actualization of miniaturized highBPFs with quasi-elliptic-type filtering profile. REFERENCES [1] M. Rais-Zadeh, J. T. Fox, D. D. Wentzloff, and Y. B. Gianchandani, “Reconfigurable radios: A possible solution to reduce entry costs in wireless phones,” Proc. IEEE, vol. 103, no. 3, pp. 438–451, Mar. 2015.

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[2] R. Gómez-García, F. M. Ghannouchi, N. B. Carvalho, and H. C. Luong, “Advanced circuits and systems for CR/SDR applications,” IEEE J. Select. Emerging Topics Circuits Syst., vol. 3, no. 4, pp. 485–488, Dec. 2013. [3] W. J. Chappell, E. J. Naglich, C. Maxey, and A. C. Guyette, “Putting the radio in “Software-defined radio”: Hardware developments for adaptable RF systems,” Proc. IEEE, vol. 102, no. 3, pp. 307–320, Mar. 2014. [4] J. Shellhammer, A. K. Sadek, and W. Zhang, “Technical challenges for cognitive radio in the TV white space spectrum,” Inform. Theory Appl. Workshop, pp. 323–333, Feb. 8–13, 2009. [5] Z. Wang, J. R. Kelly, P. S. Hall, A. L. Borja, and P. Gardner, “Reconfigurable parallel coupled band notch resonator with wide tuning range,” IEEE Trans. Microw. Theory Techn., vol. 61, no. 11, pp. 6316–6326, Nov. 2014. [6] K. Zeng, D. Psychogiou, and D. Peroulis, “A VHF tunable lumpedelement filter with mixed electric-magnetic couplings,” presented at the IEEE Wirel. Microw. Tech. Conf., Cocoa Beach, FL, USA, Apr. 13–15, 2015. [7] Y. C. Ou and G. M. Rebeiz, “Lumped-element tunable bandstop filters for cognitive radio applications,” IEEE Trans. Microw. Theory Techn., vol. 59, no. 10, pp. 2461–2468, Oct. 2011. [8] D. Psychogiou and D. Peroulis, “Tunable VHF miniaturized helical filters,” IEEE Trans. Microw. Theory Techn., vol. 62, no. 2, pp. 282–289, Feb. 2014. [9] C. Campbell, Surface Acoustic Wave Devices for Mobile and Wireless Communications, 1st ed. Orlando, FL, USA: Academic Press, 1998. [10] R. Aigner, “SAW and BAW technologies for RF filter applications: A review of the relative strengths and weaknesses,” in Proc. IEEE Ultrason. Symp., Beijing, China, Nov. 2–5, 2008, pp. 582–589. [11] S. Gong and G. Piazza, “Design and analysis of Lithium-Niobate-based high electromechanical coupling RF-MEMS resonators for wideband filtering,” IEEE Trans. Microw. Theory Techn., vol. 61, no. 1, pp. 403–414, Jan. 2013. [12] S. Gong and G. Piazza, “An 880 MHz ladder filter formed by arrays of laterally vibrating thin film Lithium Niobate resonators,” in IEEE 27th Int. MEMS Conf., San Francisco, CA, USA, Jan. 26–30, 2014, pp. 1241–1244. [13] M. Pijolat, S. Loubriat, D. Mercier, A. Reinhardt, E. Defaÿ, C. Deguet, M. Aïd, S. Queste, and S. Ballandras, “LiNbO3 film bulk acoustic resonator,” in Proc. IEEE Int. Freq. Control Symp., Newport Beach, CA, USA, Jun. 1–4, 2010, pp. 661–664. [14] G. Endoh, O. Kawachi, and M. Ueda, “A study of leaky SAW on piezoelectric substrate with high coupling factor,” in Proc. IEEE Ultrason. Symp., Caesars Tahoe, NV, USA, Oct. 17–20, 1999, pp. 309–312. [15] T. Omori, Y. Tanaka, K. Hashimoto, and M. Yamaguchi, “Synthesis of frequency response for wideband SAW ladder type filters,” in Proc. IEEE Ultrason. Symp., New York, NY, USA, Oct. 28–31, 2007, pp. 2574–2577. [16] S. Gong and G. Piazza, “Multi-frequency wideband RF filters using high electromechanical coupling laterally vibrating lithium niobate MEMS resonators,” in Proc. IEEE 26th Int. MEMS Conf., Taipei, Taiwan, Jan. 20–24, 2013, pp. 785–788. [17] S. Gong and G. Piazza, “An 880 MHz ladder filter formed by arrays of laterally vibrating thin film Lithium Niobate resonators,” in Proc. IEEE 27th Int. MEMS Conf., San Francisco, CA, USA, Jan. 26–30, 2014, pp. 1241–1244. [18] M. Pijolat, S. Loubriat, D. Mercier, A. Reinhardt, E. Defaÿ, C. Deguet, M. Aïd, S. Queste, and S. Ballandras, “LiNbO3 film bulk acoustic resonator,” in Proc. IEEE Int. Freq. Control Symp., Newport Beach, CA, USA, Jun. 1–4, 2010, pp. 661–664. [19] H. Nakanishi, H. Nakamura, and R. Goto, “High-electromechanical-coupling-coefficient surface acoustic wave resonator on Ta2O5/Al/LiNbO3 structure,” Jpn. J. Appl. Phys., vol. 49, no. 7S, p. 07HD21, Jul. 2010. [20] J. Meltaus, V. P. Plessky, A. Gortchakov, S. Harma, and M. M. Salomaa, “SAW filter based on parallel-connected CRFs with offset frequencies,” in Proc. IEEE Ultrason. Symp., Honolulu, HI, USA, Oct. 5–8, 2003, pp. 2073–2076. [21] D. Psychogiou, R. Gómez-García, R. Loeches-Sánchez, and D. Peroulis, “Hybrid acoustic-wave-lumped-element resonators (AWLRs) for highbandpass filters with quasi-elliptic frequency response,” IEEE Trans. Microw. Theory Techn., vol. 63, no. 7, pp. 2233–2244, Jun. 2015. [22] D. Psychogiou, R. Gómez-García, and D. Peroulis, “Highbandpass filters using hybrid acoustic-wave-lumped-element resonators (AWLRs) for UHF applications,” presented at the IEEE MTT-S Int. Microw. Symp. Dig., Phoenix, AZ, USA, May 17–22, 2015.

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[23] J. D. Larson, III, R. C. Bradley, S. Wartenberg, and R. C. Ruby, “Modified Butterworth-Van Dyke circuit for FBAR resonators and automated measurement system,” in Proc. IEEE Ultrason. Symp., San Juan, Puerto Rico, Oct. 22–25, 2000, pp. 863–868. [24] J.-S. Hong, Microstrip Filters for RF/Microwave Applications, 2nd ed. Hoboken, NJ, USA: Wiley, 2011. [25] D. Swanson and G. Macchiarella, “Microwave filter design by synthesis and optimization,” IEEE Microw. Mag., vol. 8, no. 2, pp. 55–69, Apr. 2007. [26] J.-S. Hong, H. Shaman, and Y.-H. Chun, “Dual-mode microstrip openloop resonators and filters,” IEEE Trans. Microw. Theory Techn., vol. 55, no. 8, pp. 1764–1770, Aug. 2007. [27] H. Nakamura, H. Nakanishi, R. Goto, and K.-Y. Hashimoto, “Suppression of transverse-mode spurious responses for saw resonators on SiO2/Al/LiNbO3 structure by selective removal of SiO2,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 58, no. 10, pp. 2188–2193, Oct. 2011. [28] R. H. Olsson, J. Nguyen, T. Pluym, and V. M. Hietala, “A method for attenuating the spurious responses of aluminum nitride micromechanical filters,” J. Microelectromech. Syst., vol. 23, no. 5, pp. 1198–1207, Oct. 2014. [29] H. Wang, H. Zhong, Y. Shi, and K.-Y. Hashimoto, “Design of narrow bandwidth elliptic-type SAW/BAW filters,” Electron. Lett., vol. 48, no. 10, pp. 539–540, May 2012. [30] D. Morgan, Surface Acoustic Wave Filters: With Applications to Electronic Communications and Signal Processing, 2nd ed. San Diego, CA, USA: Academic Press, 2010. [31] O. Ikata, T. Miyashita, T. Matsuda, T. Nishihara, and Y. Satoh, “Development of low-loss band-pass filters using SAW resonators for portable telephones,” in Proc. IEEE Ultrason. Symp., Tucson, AZ, USA, Oct. 20–23, 1992, pp. 111–115. Dimitra Psychogiou (S'10–M'14) received the Dipl.-Eng. degree in electrical and computer engineering from the University of Patras, Patras, Greece, in 2008, and the Ph.D. degree in electrical engineering from the Swiss Federal Institute of Technology (ETH) Zürich, Switzerland, in 2013. Since 2013, she has been with Purdue University, where she is currently a Senior Research Scientist at the Department of Electrical and Computer Engineering, West Lafayette, IN, USA. In 2008, she joined the Wireless Communication Research Group (WiCR), University of Loughborough, Loughborough, U.K., as a Research Assistant. From 2009 to 2013, she was a Teaching and Research Assistant with the Laboratory of Electromagnetic Fields and Microwave Electronics (IFH), ETH Zürich. Her main research interests include RF design and characterization of reconfigurable microwave and millimeter-wave passive components, tunable filter synthesis, and frequency agile antennas.

Roberto Gómez-García (S'02–M'06–SM'11) was born in Madrid, Spain, in 1977. He received the Telecommunication Engineer and Ph.D. degrees from the Polytechnic University of Madrid, Madrid, Spain, in 2001 and 2006, respectively. Since April 2006, he has been an Associate Professor with the Department of Signal Theory and Communications, University of Alcalá, Alcalá de Henares, Madrid, Spain. He has been for several research stays in the C2S2 Department of the XLIM Research Institute (formerly IRCOM), University of

Limoges, France, Telecommunications Institute of the University of Aveiro, Portugal, the U. S. Naval Research Laboratory (NRL), Microwave Technology Branch, Washington, DC, USA, and Purdue University, West Lafayette, IN, USA. His current research interests include the design of fixed/tunable high-frequency filters and multiplexers in planar, hybrid and MMIC technologies, multi-function circuits and systems, and software-defined radio and radar architectures for telecommunications, remote sensing, and biomedical applications. Dr. Gómez-García is an Associate Editor for the IEEE TRANSACTIONS OF MICROWAVE THEORY AND TECHNIQUES, IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I: REGULAR PAPERS, and IET Microwaves, Antennas and Propagation. He is a Guest Editor of the IEEE JOURNAL ON EMERGING AND SELECTED TOPICS IN CIRCUITS AND SYSTEMS 2013 Special Issue on “Advanced Circuits and Systems for CR/SDR Applications”, the IET Microwaves, Antennas and Propagation 2013 Special Issue on “Advanced Tuneable/Reconfigurable and Multi-Function RF/Microwave Filtering Devices,” and the IEEE Microwave Magazine 2014 Special Issue on “Recent Trends on RF/Microwave Tunable Filter Design”. He is a reviewer for several IEEE, IET, EuMA, and Wiley Journals. He serves as a member of the Technical Review Board for several IEEE and EuMA conferences. He is also a member of the “IEEE MTT-S Filters and Passive Components” (MTT-8), “IEEE MTT-S Biological Effect and Medical Applications of RF and Microwave” (MTT-10), “IEEE MTT-S Wireless Communications” (MTT-20), and “IEEE CAS-S Analog Signal Processing” (ASP) Technical Committees.

Dimitrios Peroulis (S'99–M'04–SM’15) received the Ph.D. degree in electrical engineering from the University of Michigan at Ann Arbor, Ann Arbor, MI, USA, in 2003. Since August 2003, he has been with Purdue University, West Lafayette, IN, USA, where he is currently Professor of the Department of Electrical Engineering and the Deputy Director of the Birck Nanotechnology Center. His current research projects are focused on the areas of reconfigurable electronics, RF MEMS, and sensors in harsh environment applications. He has been a key contributor on developing very high quality ( > 1000) RF MEMS tunable filters in mobile form factors. Furthermore, he has been investigating failure modes of RF MEMS and MEMS sensors through the DARPA M/NEMS S&T Fundamentals Program, Phases I and II) and the Center for the Prediction of Reliability, Integrity, and Survivability of Microsystems (PRISM) funded by the National Nuclear Security Administration. Dr. Peroulis was a recipient of the National Science Foundation CAREER Award in 2008, the Outstanding Young Engineer Award of the IEEE Microwave Theory and Techniques Society (MTT-S) in 2014, the Outstanding Paper Award from the IEEE Ultrasonics, Ferroelectrics, and Frequency Control Society (Ferroelectrics section) in 2012. He has co-authored over 220 journal and conference papers. His students have received numerous Student Paper Awards and other student research-based scholarships. He is a Purdue University Faculty Scholar and has also received ten teaching awards including the 2010 HKN C. Holmes MacDonald Outstanding Teaching Award and the 2010 Charles B. Murphy Award, which is Purdue University's highest undergraduate teaching honor.

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Ultra-Miniature SIW Cavity Resonators and Filters Ali Pourghorban Saghati, Student Member, IEEE, Alireza Pourghorban Saghati, Student Member, IEEE, and Kamran Entesari, Member, IEEE

Abstract—This paper presents ultra-miniature substrate integrated waveguide (SIW) cavity resonators, and filters by employing ramp-shaped slots as interdigital capacitors (IDCs) to force the structure to operate in the first negative-order resonance mode. Additionally, a metal patch in the middle metal layer along with disconnected vias is used to increase the equivalent series capacitance of the resonator and accordingly the miniaturization factor. By applying this method to half-mode SIW (HMSIW) and quarter-mode SIW (QMSIW) resonators, 90%, and 95% of miniaturization is achieved, respectively, compared to conventional full-mode SIW resonators. Afterwards, a two-pole bandpass filter is proposed based on the presented QMSIW resonator. Also, by using a combination of HMSIW and QMSIW ultra-miniature resonators, two trisection filters with a controllable transmission zero on either side of the passband are presented. To the best of authors' knowledge, this is the first disclosure of simultaneous use of HMSIW and QMSIW resonators to achieve asymmetric filter response with an ultra-compact size. Index Terms—Bandpass filter, cavity filter, composite right/left handed (CRLH), miniaturization, substrate integrated waveguide (SIW).

I. INTRODUCTION

L

OW loss bandpass filters, constructed using compact high- resonators are one of the essential blocks of modern wireless communication systems. Ease of fabrication, high-power handling, high linearity, and integration compatibility of substrate integrated waveguide (SIW) cavity resonators make them a good candidate for high-performance microwave filters [1]. Despite their advantages, their use in compact microwave devices is hindered due to their large size. As a result, miniaturization techniques need to be employed to reduce the size of SIW filters, while maintaining the high performance characteristics [2]. Manuscript received June 26, 2015; revised September 14, 2015; accepted October 11, 2015. Date of publication November 11, 2015; date of current version December 02, 2015. This paper is an expanded version from the IEEE MTT-S International Microwave Symposium, Phoenix, AZ, USA, May 17–22, 2015. A. Pourghorban Saghati is with the Department of Electrical and Computer Engineering, Texas A&M University, College Station, TX 77843 USA (e-mail: [email protected]). A. Pourghorban Saghati was with the Department of Electrical and Computer Engineering, Texas A&M University, College Station, TX 77843 USA. He is now with Ossio Inc., Bellevue, WA 98004 USA (email: [email protected]). K. Entesari is with the Department of Electrical and Computer Engineering, Texas A&M University, College Station, TX 77843 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2015.2494023

The existing work in the area of miniature SIW filters includes loading the SIW resonator using defected ground planes (DGS) and ring gaps [3], [4], using complementary split-ring resonators to change the characteristic cutoff frequency of the SIW structure [5], forcing the SIW resonator to operate at lower-order modes (e.g., -1st mode) using metamaterial-inspired components [6], and cutting the SIW resonators on their fictitious magnetic walls to achieve half-mode SIW (HMSIW) or quarter-mode SIW (QMSIW) resonators [7]–[9]. Among these, the largest miniaturization factor belongs to the QMSIW with roughly 75% of size reduction. The miniaturization factor for the other methods such as the CSRR-loaded resonators, and the negative order resonance-mode ones is limited by the geometrical dimensions of the employed loading structures and the area available on the top/bottom walls of the SIW cavity. This paper proposes ultra-miniature HMSIW and QMSIW resonators in which the first negative order resonance is excited to further decrease the size of the resonators. The mentioned issue of size limitations for loading structures becomes more severe for the case of HMSIW/QMSIW resonators. Accordingly, based on the method first proposed in [10], ramp-shaped slots as inter-digital capacitors (IDC) on the top metal layer of the cavity structure are employed to efficiently use the available resonator area. Also, by employing an additional middle metal layer, a loading patch is employed to increase the capacitance value of the loading IDCs. Finally, disconnected via posts are inserted in the locations of maximum E-field distribution to increase the miniaturization beyond the limits defined by the size of the IDCs. Using these elements, 90% miniature HMSIW, and 95% miniature QMSIW resonators are achieved. The miniature QMSIW resonator was first introduced by the authors in [2], and was used toward the design of a two-pole filter operating at a center frequency of 690 MHz with an area of and a fractional bandwidth of 5.9%. Here, a more in-depth study on the miniaturization method is conducted. Also, the half-mode SIW version of the resonator is provided. Moreover, a combination of an HMSIW and two QMSIW resonators is uniquely employed to design two different trisection filters with controllable transmission zeros on either side of the passband. In addition to the miniaturization due to area reduction (HMSIW-QMSIW combination instead of three SIW resonators), frequency shift due to the loading IDC structure and disconnected vias results in 70% of size reduction in comparison with a normal full-mode SIW resonator. As a result, the entire area of the trisection filter consumes roughly 30% of the area for only one full-mode SIW cavity resonator at the operating frequency. The two trisection filters have midband frequencies of 912 and 754 MHz with total areas of , and , respectively. In comparison with the existing

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Fig. 1. (a) Res. I: Normal cylindrical SIW cavity resonator. (b) Res. II: Ring gap-loaded SIW cavity resonator (37% miniaturization). (c) Res. III: Ramp-shaped IDC loaded SIW cavity resonator (57% miniaturization). (d) Res. IV: IDC-loaded SIW cavity resonator employing a rectangular patch in an additional middle metal layer (66% miniaturization). (e) 3D cross-section view of Res. IV (and the simplified LC resonator model). (f) Res. V: IDC-loaded SIW cavity resonator loaded with floating patch and disconnected vias (73% miniaturization). (g) A-A' cross-section view of Res. V.

SIW-based trisection filters in literature [11]–[14], the proposed trisection filters are the first ones which are ultra-compact, while having controllable transmission zeros, to the best of authors' knowledge. II. RESONATOR DESIGN A. Full-Mode SIW Resonator Fig. 1 demonstrates the procedure used to achieve the miniaturized SIW cavity resonator. Res. I, shown in Fig. 1(a), is a conventional cylindrical SIW cavity resonator which its dimensions are determined based on the fundamental TM010 mode [15]. Based on a Rogers RT/Duroid 6010 ( , )1 dielectric layer with a thicknesses of 3.135 mm, is calculated to be 17.4 mm. As a result a fundamental TM010 mode exists around 2 GHz. For a fixed resonator size, inserting proper elements into the structure will reduce the resonance frequency. The miniaturization factor for a particular miniaturized resonator operating at a lowered frequency of is computed using Miniaturization factor 1Rogers

Corp.. Brooklyn, CT, USA.

(1)

where is the area of a conventional cylindrical SIW resonator, which fundamentally operates at and is the area of the proposed resonators. This miniaturization factor contribution for each element is mentioned in the caption of Fig. 1. 1) Miniaturization Elements: a) Capacitive Ring Gap: First, the SIW cavity resonator is loaded with a shunt via at the center [see Fig. 1(b)]. Afterwards, a ring slot is etched on the top wall to disconnect this wall from the bottom wall. The ring gap can be modeled as small series capacitance which loads the resonator and results in a lower resonance frequency. The capacitance value, as a function of physical dimensions, can be approximated based on the approach provided in [4]. The frequency down-shift due to this capacitive loading is mainly limited by the size of the annular gap. To better understand this limitation, the structure is simulated using commercial high frequency structure simulator (HFSS),2for various , and values, while is fixed to 0.75 mm, and the results are shown in Fig. 2(a). As can be seen, increasing the width and length of the ring gap results in higher miniaturization factors. However, these two dimensions are limited by the size of the cavity which is assumed to be fixed for all the resonators. Fine tuning of the resonance frequency is also feasible by adjusting the spacing value of the ring-gap . Considering 2Ansys

HFSS ver. 15, Ansys Inc.. Canonsburg, PA, USA, 2013.

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Fig. 2. Miniaturization factor of Res. II for different ring slot dimensions.

4 mm, 8 mm, and 0.75 mm, 37% miniaturization is achieved. b) Ramp-Shaped Interdigital Capacitor (IDC): Fig. 1(c) shows Res. III in which the ring slot on the top metal layer is replaced by ramp-shaped slot [10]. In this figure, is the total width of the ramp-shaped slot etched on the top metal wall of the cavity, while is the angle between the adjacent slots. Similar to Res. II, stands for the spacing value of the slot-gap, and its value remained 0.75 mm for Res. III, IV, and V. The cavity-wall vias and center via can be modeled as shunt inductors. Therefore, utilizing IDC, as an equivalent series capacitance, forces the SIW resonator to operate at resonance [6]. This is basically different from Res. II, where the fundamental resonance frequency is shifted down due to the capacitive loading effect of the annular gap, and as a result, the operating mode is quasi-TEM [4]. In order to observe the 1st, 0th, and resonances, Res. III is simulated as a two-port resonator, and the resonance peaks on are plotted and shown in Fig. 3(a). In this figure, the frequency is normalized to the fundamental TM010 resonance frequency. For this resonator, the zeroth and first negative order resonances happen at 0.8 and , respectively. In this case, increasing the series capacitive loading results in further shifting down the resonance frequency rather than the fundamental mode. Similar to traditional IDC structures, for a constant total area of the IDC, higher equivalent series capacitance values are achievable by increasing the number of fingers [16]. For the ramp-shaped configuration, assuming the total size of the IDC is constant, increasing the number of fingers is feasible by decreasing the angle between the adjacent slots . The effect of the ramp-shaped slot physical dimensions on the miniaturization factor is studied by simulating the resonator for various , and values, while the number of fingers are changed accordingly. The results are shown in Fig. 3(b). According to the available area on the cavity top-metal wall (for 17.4 mm), by decreasing from 50 to 30 , the maximum possible number of fingers is increased from 4 to 8, and consequently, higher miniaturization factors are achieved. However, further decreasing to lower than 30 means drastic reduction in the fingers' metal width . As a result, higher capacitance values cannot be achieved for values less than 30 , and the miniaturization factor drops for . Moreover, this trade-off between , and results in another bottleneck. Reduction in the metal width of each finger will reduce the quality factor

Fig. 3. (a) Resonance peaks on of Res. III, IV, and V shown in of Res. III for various number of Fig. 1. (b) Miniaturization factor and fingers for the IDC (solid lines are miniaturization factor and dashed lines ). are

of the IDC, and the resonator [16]. This is also shown in Fig. 3(b), where the unloaded quality factor of Res. III is plotted for each case. Therefore, the optimum values of , and are employed for this design. On the other hand, has small effect on the resonance frequency, and can be used for fine tuning. The spacing value has minor effect on the miniaturization factor of Res. III, while very large values of can cause the of the resonator to drop. This is mainly due to increased leakage loss from the top interdigital slot. By increasing from 0.75 to 1.75 mm, the resonance frequency only reduces by 3.1%, however, the value drops from 253 to 221. On the other hand, for 0.75 mm, the leakage loss form the top IDC slot is roughly constant, and neither the miniaturization factor, nor value change considerably. Therefore, considering 0.75 mm, and 15.5 mm, the miniaturization factor is roughly 57% for Res. III. c) Floating Metal Patch: To further increase the capacitive loading and thus the frequency shift, a floating metal patch is inserted in an additional middle metal layer beneath the rampshaped slot [Res. IV shown in Fig. 1(d)]. As can be seen in Fig. 3(a), by employing this metal patch, the resonance frequency is shifted down to a lower value compared to Res. III. To better demonstrate the capacitive loading effect of this floating patch, a 3D cross-section view of Res. IV is shown in Fig. 1(e). In this figure, the shunt capacitance to the ground (between the patch and the cavity bottom wall) and the two fringing capacitances (between the ramp-shaped slot edges and the patch) are named as , and , respectively, and stands for the equivalent series capacitance introduced by the ramp-shaped interdigital slot. For simplicity, the metal planes are assumed perfect electric conductors, and parasitics are excluded. As can be

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SIMULATED

Fig. 4. (a) Miniaturization factor of Res. IV for various widths and heights of the patch. (b) The effect of the patch openings and disconnected vias on the miniaturization factor for different heights of the patch.

seen, the patch increases the effective series capacitance as follows: (2) While should be minimized, needs to be maximized to increase the overall series capacitance and achieve more miniaturization. The effect of the size and location of the patch on shifting down the resonance frequency is studied by simulating the structure for various widths and heights for the patch, and the results are shown in Fig. 4(a). While can be used for fine adjustment, needs to be maximized to reduce , increase two values, and to achieve the highest miniaturization factor. However, this dimension is limited by the height of the standard substrate thickness used for the floating patch. Therefore, considering 7.5 mm for highest miniaturization, is chosen to be 2.5 mm, while is 0.635 mm, based on the availability of standard Rogers RT/Duroid 6010 substrate thicknesses and fabrication constraints. By using this structure, a miniaturization factor of 66% is achieved. d) Disconnected Vias: Disconnected vias are the last loading elements [see Fig. 1(f)] to increase the miniaturization factor. These capacitive disconnected via posts will further load the cavity and push the resonance frequency to even lower values [see Fig. 3(a)]. The loading effect of disconnected vias and their design considerations are well-studied in [17]. They need to be placed where the E-field distribution is maximum inside the cavity to have the highest loading effect. Fig. 1(f) and (g) show the top and 2D cross-section views of the final resonator (Res. V), respectively, in which the patch

TABLE I FACTOR OF THE RESONATORS SHOWN IN FIG. 1

and the disconnected vias are both inserted. The loading via posts are disconnected from the bottom wall of the cavity by using disk-slot openings. These openings are relatively small compared to wavelength at operating frequencies, and the leakage is negligible [17]. Also, capacitive via posts need to be disconnected from the floating metal patch to avoid shortening it to the top metal wall. This can be done by etching either circular disk- or triangular-shaped slots on the floating patch and around the vias. The opening slots on the floating patch should have minimum effect on the equivalent fringing capacitances between the patch and the ramp-shaped slot edges . In order to better study the effect of the opening slots on the miniaturization factor, the simple patch in Res. IV is replaced with a patch with triangular-shaped slots, and a patch with disk-shaped slots, respectively. Then, the two modified resonators are simulated for different heights of the patch and the results are compared to the original Res. IV in Fig. 4(b). As can be seen, etching the slots on the patch will slightly reduce the miniaturization factor of Res. IV, however, there is no significant difference between utilizing patch with diskor triangular-shaped slots. In this design, triangular slots are etched on the metal patch to disconnect it from the loading vias, and avoid shortening it to the top metal wall [see Fig. 1(f)–(g)]. Afterwards, disconnected vias are inserted, and the final resonator is also simulated for different heights of the patch. Inserting disconnected vias results in higher miniaturization factors compared to Res. IV for any height of the patch with triangular slots. By employing all the miniaturization elements, 73% of miniaturization is achieved. Ramp-shaped IDC has the most effect on miniaturization as it forces the resonator to operate at resonance mode. 2) Loss: To study the loss mechanism of the presented resonators, the unloaded quality factor is extracted from two-port s-parameters simulation, based on the approach in [18]. The top, middle, and bottom metal layers are all considered as copper (1 oz), and as mentioned before, both substrate layers are Rogers RT/Duroid 6010 ( , ) with different thicknesses of 2.5 mm and 0.635 mm. For Res. III to V, the two dielectric layers are bonded together using Rogers RO4450B pre-preg material ( , , 0.09 mm). Each single resonator is weakly coupled at the input/output ports, and simulated. The resulting unloaded quality factors are shown in Table I. The loss mechanism of a regular SIW cavity resonator (Res. I) has been investigated in literature [19]. Using a low-loss dielectric layer, the leakage loss from the apertures between the side-wall vias is negligible if the vias are placed close enough to each other [3]. Therefore, for such resonators, conductor loss

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Fig. 5. Magnitude of electric field distribution inside the resonators shown in Fig. 1 at the corresponding resonance frequency.

and dielectric dissipation have the main contribution to degradation. The -factor of a conventional rectangular SIW cavity resonator is reported 500 at the fundamental resonance frequency [3], while the and the of the employed dielectric material are 3, and 0.001, respectively. However, using high-permittivity dielectric materials such as Rogers 6010, with higher loss tangent of 0.0023, -factor drops to 312 for Res. I in this design. Moreover, other loss factors need to be considered carefully as different miniaturization elements are added to the resonator. As can be seen in Table I, Res. II has a lower value compared to Res. I. This is mainly because of leakage loss from the annular ring gap on the top metal wall. The leakage loss can be minimized by increasing the equivalent capacitance introduced by the ring-gap. This means that by increasing the miniaturization factor, the leakage loss decreases. To better discern this relation, the magnitude of E-field distribution is plotted for all resonators in Fig. 5. The center via post and the capacitive elements around it force the maximum E-field distribution to be around the capacitive elements. As this capacitive loading effect increases by inserting IDC, metal patch, and the disconnected vias, the operating frequency of the resonator is pushed down to lower values, and hence, the wavelength becomes larger. This means that the size of the resonator relative to its operating wavelength becomes smaller as miniaturization increases. As a result, the leakage loss decreases for resonators with higher miniaturization factors, and Res. III, IV, and V have larger values compared to Res. II. Based on this argument, Res. V is expected to have less radiation loss and better compared to Res. III, or IV. However, this resonator has another source of leakage which is the disk-slot openings on the bottom wall of the cavity. As a result, the is degraded compared to Res. III and IV. B. Half-Mode SIW Resonator The miniaturization method introduced in the previous subresonance of a regular section was based on exciting the SIW cavity, and shift that resonance down to the lowest possible value by loading the cavity. In order to design a more compact resonator, the proposed method is applied to a HMSIW cavity resonator (see Fig. 6). First, the regular SIW resonator (Res. I) is bisected on its fictitious magnetic wall. For a large diameter to height ratio of the cavity, the leakage from the open wall would be negligible, and the resonator will operate at roughly a same resonance frequency [7]. Then, all the above miniaturization elements are inserted to achieve a HMSIW resonator

Fig. 6. (a) Original HMSIW resonator. (b) Modified HMSIW resonator. (c), (d) Magnitude of magnetic field distribution inside the original and modified HMSIW resonators, respectively.

which operates at resonance. While, the frequency of operation remains approximately the same compared to Res. V [see Fig. 1(e)], the size is reduced by half. 1) Effect of the Center Via Position: Fig. 6(a) and (b) show the top view of two possible configurations for the miniaturized HMSIW cavity resonator. The difference between these two resonators is the place of the center via. As Res. V [see Fig. 1(f)] is bisected to achieve the HMSIW resonator, the center via can be either kept at the same position, or replaced by two other shunt vias at the two ends of the ramp-shaped slot [see Fig. 6(b)]. While the original HMSIW resonator is useful to achieve positive coupling, the modified HMSIW resonator enables negative coupling. This is very useful in filter design process, where cross-coupling between the resonators is needed. The magnitude of H-field distribution is plotted for the two resonators in Fig. 6(c) and (d). For the original HMSIW resonator, the magnetic field is maximum at the center and around the shunt via, while the E-field is maximum around the capacitive elements [see Fig. 6(c)]. As a result, by changing the shunt via position, the maximum of the magnetic field happens at the two ends of the ramp-shaped slot instead of the center of the cavity [see Fig. 6(d)]. By controlling the position of the

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FINAL DIMENSIONS (mm)

Fig. 7. (a) Ultra miniature QMSIW resonator. (b) Magnitude of magnetic field distribution inside the original and modified QMSIW resonators.

magnetic field concentration, it is possible to couple the resonators either positively or negatively (see Section III). However, changing the center via position slightly lowers miniaturization factor for the modified HMSIW resonator. Considering 11.75 mm, the miniaturization factor for the modified HMSIW resonator is 90%, while for the original HMSIW resonator, it is 92%. 2) Loss: The loss mechanism of the two HMSIW resonators is investigated by calculating the value based on the same approach described in the previous subsection. Using same substrate layers as before, values of 216 and 221 are achieved for the original and modified HMSIW resonators, respectively. The degradation is mainly contributed to the leakage loss from the open wall of the cavity, even though, the conductor loss would be less for HMSIW resonators compared to their SIW counterparts. C. Quarter-Mode SIW Resonator QMSIW resonator can be obtained by bisecting the HMSIW resonator on its fictitious magnetic wall [8]. The overall size of the QMSIW resonator is roughly 25% of its SIW counterpart [9]. Again, inserting all the above miniaturization elements inside the QMSIW resonator forces the structure to resonate at resonance mode. Therefore, an ultra miniature resonator can be achieved which has approximately the same resonance frequency as Res. V [see Fig. 1(e)], while its size is reduced by 75% [2]. Fig. 7(a) shows the top, middle, and bottom metal layers of the final ultra miniature QMSIW resonator. The shunt center via used in the SIW resonators is now placed on the corner of the resonator, and the ramp-shaped inter-digital slot, and the floating patch are precisely quarter of their SIW version counterparts. 1) Effect of the Corner Via Position: Similar to the HMSIW resonator presented in the previous subsection, it is possible

TABLE II ULTRA-MINIATURE QMSIW FILTER

OF THE

to control the magnetic field concentration inside the cavity to some degree by modifying the location of the shunt corner via. The magnitude of H-field distribution is shown in Fig. 7(b) for two QMSIW resonators. As can be seen, the magnetic field is concentrated around the corner via. By placing the shunt via on the other end of the ramp-shaped slot, the concentration of the H-field is modified. Again, altering the shunt via position results in slightly lower miniaturization factors. The dimensions of the final resonator are tabulated in Table II. Based on these dimensions, and using same dielectric layers, the resonance happens at 731 MHz. Compared to a full mode SIW resonator with a fundamental mode at 731 MHz, roughly 95% miniaturization is achieved for the original QMSIW resonator in Fig. 7(a) [2]. However, considering 11.75 mm, the miniaturization factor for the modified QMSIW resonator is 93%. 2) Loss: The loss mechanism of this resonator is studied based on the same approach used for the SIW and HMSIW resonators. The values are 186 and 189 at 731 MHz for the original and modified QMSIW resonators, respectively. Although the conductor loss would be less than the SIW and HMSIW versions of the resonator, because of two open walls of the cavity the values are degraded. Ultra compact size, relatively high , and capability of cross coupling of this resonator make it a suitable candidate for ultra miniature filter design. III. FILTER DESIGN AND IMPLEMENTATION The ultra miniature HMSIW, and QMSIW resonators, introduced in the previous section, are used to design and fabricate a two-pole bandpass filter, and two trisection filters with transmission zeros on either side of the passband. First, the design values of the low-pass prototype response is determined for each filter based on the target specifications. Afterwards, the required coupling coefficient matrices and external quality factors are calculated for each filter based on the design values achieved in the first step. Since the method is based on the coupled-resonators filter design, the next step is to establish the relationship between the coupling coefficient matrix and the physical dimensions of the coupled resonators. The coupling factor for synchronously tuned coupled resonators can be approximated using [20] (3) , and are the two split resonance frequencies where extracted from full-wave simulation of the coupled resonators with weakly-coupled input/output ports. The positive or negative sign of the coupling factor determines whether the resonators are positively or negatively coupled, respectively.

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Fig. 8. Top and bottom views of the miniaturized two-pole QMSIW filter. The 4 mm, 4.4 mm, 8.9 mm, parameter values are: 10.9 mm, and 18 mm.

The value is extracted from full-wave simulation of the singly loaded resonator using [20] (4)

Fig. 9. (a) Coupling factor of the two-pole filter as a function of the spacing values as a function of the L-shaped slot length. between the resonators. (b)

where is the simulated resonance frequency and the is the difference of the frequencies at which a phase shift of occurs in the phase response of the resonator. A. Two-Pole Bandpass Filter Fig. 8 shows the top, and bottom views of the two-pole bandpass filter using the proposed QMSIW resonator implemented with two Rogers RT/Duroid 6010LM substrates that are bonded together with Rogers RO4450B pre-preg material as described before [2]. The two-pole coupled-resonator filter is designed to operate at center frequency of 700 MHz. For an in-band return loss better than 20 dB with pass-band ripple of 0.01 dB and 3-dB bandwidth (FBW) of 6%, using the designed values of the low-pass Chebyshev prototype response, the required coupling factor is , and the external quality factor is . While the spacing between the two resonators ( , and ) is used to obtain the proper coupling, the L-shaped slot ( and ) is used at the input/output to adjust the required external quality factor. To better show the relationship between the physical dimensions and the required theoretical design values, the coupling factor as a function of the spacing between the resonators, and the value as a function of the L-shaped slot length is plotted in Fig. 9(a) and (b), respectively. The horizontal distance between the two resonators, , can be used for coarse adjustment of the coupling factor. However, the vertical distance, , can be utilized for fine tuning. As shown in Fig. 7(b), the H-field distribution inside the original QMSIW cavities are maximized around the shunt corner via. As decreases, and increases, the two shunt corner vias will become closer to each other, and as a result, higher coupling factors are achievable ( 4 mm, and 4.4 mm for ). For the external quality factor, the total length of the L-shaped slot needs to be adjusted accurately. In this design, value becomes close to 7.4 when is 9 mm and is 11 mm.

Fig. 10. Top (left) and bottom (right) views of the two-pole filter prototype.

Fig. 10 shows the top and bottom views of the fabricated prototype. First, the top and bottom metal walls are etched on the upper metalization side of the top substrate, and lower metalization side of the bottom substrate, respectively. Afterwards, the bottom-side metalization of the top substrate is completely removed, while the top-side metalization of the bottom substrate is etched to create the floating patch. The two substrate layers are then bonded to each other using Rogers pre-preg material, and finally, the plated via holes are drilled through both substrates [2]. The overall size of the presented QMSIW two-pole filter, excluding the microstrip feed lines, is , where is the wavelength in free space at the frequency of operation. Fig. 11(a) shows the measured and simulated narrow-band s-parameters responses of the proposed filter [2]. Also, the ideal synthesized response of the standard two-pole Chebyshev prototype is plotted for and [20]. As can be seen, good agreement between the theory, simulation, and measurement results is achieved. The return loss is better than 30 dB, while the measured in-band insertion loss is 2.1 dB. The measured 3-dB fractional bandwidth is 5.9%, which is almost the same as the designed value. The measured and simulated wide-band s-parameters response of the filter are shown in Fig. 11(b). Since the resonance mode of the QMSIW

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Fig. 12. Two possible single-unit trisection topologies.

TABLE III TRISECTION FILTERS SPECIFICATIONS AND REQUIRED DESIGN VALUES

Fig. 11. (a) Ideal, simulated, and measured narrow-band responses of the twopole filter. (b) Measured and simulated wide-band filter responses.

resonators is used to design the two-pole filter, there is a transmission zero occurred around the 0th-order resonance mode. Therefore, the first spurious harmonic does not appear up to the 1st resonance mode of the QMSIW resonators. This provides an out-of-band rejection better than 30 dB up to 2.1 GHz, which is almost three times the center frequency of the operating band. To the best of authors' knowledge, this is the most compact two-pole SIW-based bandpass filter, which also has improved upper stopband rejection. B. Trisection Filters In some applications high selectivity is required on solely one side of the passband [20]. Hence, for asymmetric bandpass filter response with minimum possible insertion loss, trisection filters can be used, which are capable of having transmission zero on either side of the passband that high selectivity is required [21]. The transfer function of a trisection filter can be expressed as [20] (5) (6) where is the ripple constant, is the frequency variable of the lowpass prototype filter, is the th transmission zero, and is the degree of the filter. It is noteworthy that since there is only one finite transmission zero in one-unit trisection filter, the other two will be placed at infinity in the domain. 1) Filter Synthesis: Fig. 12 shows two general topologies for one-unit trisection filter. Both are three-pole arrangements with cross-coupling between the first and the third resonators. Positive (dashed line) and negative (solid line) cross couplings are used in Trisection I and II topologies, respectively. As a result,

Trisection I topology has its transmission zero on the lower side of the passband, while for Trisection II, the transmission zero appears on the upper side of the passband. Although, the response of the trisection filter is basically asymmetrical, it is possible to keep the physical configuration of the filter symmetrical [20]. Therefore, for each topology in this design, the two coupling factors and and, also, the two external quality factors and are equal, respectively. Trisection I and II filters are designed to operate at midband frequencies of 920 and 760 MHz with out-of-band rejection 20 dB for frequencies 890 and 790 MHz, respectively. For both filters, the 3-dB fractional bandwidth is considered 4.4%, while the in-band return loss is better than 20 dB. Based on these specifications, the element values of the low pass prototype filters are first calculated based on the approach discussed in [20]. Afterwards, the required resonance frequency of each resonator ( , , ), the external quality factors, and the coupling matrix elements are extracted for both filters. The specifications and the required theoretical design values of both filters are summarized in Table III. For the Trisection I case is higher and is lower than the filter's midband frequency . For the Trisection II filter, however, is lower than its , while is higher. The general coupling matrix for both Trisection filters and are calculated based on the required specifications summarized in Table III

The two matrixes have close values, while the signs are reverse. This will guarantee mirrored frequency responses for the

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Fig. 13. Synthesized responses of the two trisection filters.

two filters compared to each other [21]. Using and the synthesized responses of two ideal trisection filters are shown in Fig. 13. The lumped-element equivalent circuits of the trisection filters are comprehensively discussed in [20] and the precise value of each lumped element can be extracted using , and . Based on the presented ultra-compact QMSIW and HMSIW resonators, two trisection filters are designed and implemented. 2) Filter Design: Figs. 14 and 15 show the top and bottom views of the two designed trisection filters. The two QMSIW resonators are the first and the third resonators of the topologies shown in Fig. 12, while the HMSIW resonator acts as the second resonator. For simplicity, the required resonance frequencies , , and are adjusted by finely tuning the radius of the cavities (R1, and R2), while miniaturization parameters are kept the same as tabulated in Table II. The two structures are excited using microstrip feed lines. However, to make enough room for SMA connectors, the distance between the input/output ports is increased to value by using additional microstrip lines. Similar to the two-pole filter and based on Fig. 9(b), the length of the L-shaped slots ( , ) at the input/output ports are adjusted to achieve the required value. As was shown in Figs. 6 and 7, it is possible to control the location of the maximum H-field distribution inside the cavities by changing the shunt corner via position. As a result, either positive or negative couplings can be achieved based on adjusting the location of the shunt via. When the two shunt vias of the two QMSIW resonators are close enough to each other, the concentration of the maximum of H-field distribution of the two resonators are in close proximity, and as a result, negative coupling can be achieved between the two resonators. However, by placing the shunt vias far from each other ( 11.75 mm), the concentration of maximum H-field distribution of the two cavities are far enough to make positive coupling between the two QMSIW resonators possible. In Trisection I configuration (see Fig. 14), the two QMSIW resonators are coupled to the HMSIW resonator negatively from the open-wall of the cavities where the shunt vias are placed. However, they are coupled to each other positively from their other open-wall where there are no shunt vias. On the other hand, for Trisection II configuration shown in Fig. 15, the two QMSIW resonators are coupled to each other negatively as their shunt vias are placed in the corner, and in close proximity to each other. However, the shunt vias of the HMSIW resonator are removed from its open edge, and instead, two of the previously disconnected vias are now connected to act as center shunt vias (see Fig. 15). This way the

Fig. 14. Top and bottom views of the designed Trisection I filter with a con19 mm, trollable transmission zero on lower side of the passband ( 17.4 mm, 4.35 mm, 3 mm, 7 mm, 9.5 mm, 1.36 mm, and 25.07 mm).

Fig. 15. Top and bottom views of the designed Trisection II filter with a con17.4 mm, trollable transmission zero on higher side of the passband ( 20 mm, 3.3 mm, 3.6 mm, 9 mm, 7.5 mm, 1.36 mm, and 25.07 mm).

undesired negative coupling between the HMSIW and QMSIW resonators is minimized, and the two QMSIW resonators are coupled positively to the HMSIW resonator from its open wall. The distance between the resonators ( and ) is used to adjust the required coupling values. In order to better show the cross-coupling behavior, each two resonators are weakly coupled at the input/output ports and simulated separately.

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Fig. 16. Inter-resonator coupling factors of the two trisection filters as a function of the spacing between the resonators.

Fig. 16 shows the relationship between the physical dimensions ( , and ), and the coupling matrix elements ( , , and ) for both trisection filters. For Trisection I topology, by increasing , lower coupling coefficient values are achievable between the QMSIW and the HMSIW resonators. However, increasing results in higher coupling coefficient values between the two QMSIW resonators in this filter. This is an evidence that the two coupling coefficients are out of phase [22]. Inversely, for Trisection II topology, increasing results in lower coupling coefficients, while for larger values, higher coupling factors are achievable. The final dimensions of the proposed filters are summarized in the caption of Figs. 14 and 15. 3) Fabrication and Experimental Results: Fig. 17(a) and (b) show the top and bottom views of the two fabricated trisection filters, respectively. The fabrication process is same as the two pole filter. The overall size of Trisection I prototype [see Fig. 17(a)], excluding the microstrip feed lines, is 39.4 mm 42.3 mm, which is equivalent to . Similarly, the size of Trisection II prototype is 41 mm 41.5 mm, which is equal to . The fabricated prototypes are measured using a two-port network analyzer (Agilent N5230A) after short-open-load-thru (SLOT) calibration. Fig. 18(a) and (b) show the simulated and measured narrow-band s-parameter responses of the two trisection filters, which are in reasonably good agreement with the ideal responses of the two filters shown in Fig. 13. The measured in-band return loss is better than 17 dB for both filters, while the insertion loss is 2.45 dB, and 2.1 dB for Trisection I and II filters, respectively. The midband frequencies are 912 MHz for Trisection I and 754 MHz for Trisection II, while the FBW is 4.2% for both prototypes, which is very close to the designed value.

Fig. 17. Top (left) and bottom (right) views of fabricated (a) Trisection I and (b) Trisection II prototypes.

Fig. 18. Measured and simulated narrow-band filter responses of: (a) Trisection I prototype and (b) Trisection II prototype.

POURGHORBAN SAGHATI et al.: ULTRA-MINIATURE SIW CAVITY RESONATORS AND FILTERS

TABLE IV COMPARISON OF RELATED WORKS

IN

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slight discrepancy in insertion loss between the measurement and simulation results corresponds to the effect of practical errors such as variations in via diameter, or soldering and SMA connector's loss, which were not considered in simulations. The quality factor error between the measured and simulated results of the proposed filters is less than 6%. Table IV compares the measured performance characteristics of the proposed two-pole and trisection filters with the previously presented works in literature. In order to perform a fair size comparison, filter sizes are computed relative to the air-wavelength at the center operating frequency for each filter. As can be seen, the proposed method achieves the highest miniaturization factor, while it meets similar or better performance specifications. V. CONCLUSION

Fig. 19. Measured and simulated wide-band filter responses of: (a) Trisection I prototype and (b) Trisection II prototype.

Fig. 19(a) and (b) show the simulated and measured wideband response of the two filters, respectively. Similar to the two pole filter, and as the resonance frequency is excited to design an ultra compact filter, a transmission zero occurs around the 0th resonance mode for both filters. Hence, a rejection level of 19 dB is achieved in the frequency range of 0.965–2 GHz and 0.8–1.5 GHz for Trisection I, and II filters, respectively. IV. DISCUSSION As can be seen in Figs. 11(a) and 18, the measured and simulated results of the proposed prototypes are relatively in good agreement. The frequency-shift error is less than 1.5%, which probably comes mainly from the dielectric constant tolerances. For the Rogers 6010 dielectric material, the reported tolerance of value is 2.45% over 10.2 from the datasheet.3 Moreover, 3RT/duroid

6010LM data sheet. [Online]. Available: www.rogerscorp.com

Ultra-miniature two-pole and trisection filters based on QMSIW and HMSIW resonators are introduced. The proposed trisection filters have controllable transmission zeros on either side of the passband. The maximum in-band loss for the two-pole and trisection filters is 2.1 and 2.45 dB, respectively. First negative order resonance is excited by using metamaterial inspired ramp-shaped interdigital capacitors on the top metal wall of the cavity. The equivalent series capacitance is increased by the aid of a floating metal patch, and disconnected via posts. By applying this method to half- and quarter-mode SIW resonators, roughly 90%–95% of miniaturization is achieved, compared to conventional SIW cavity resonators. To the best of authors' knowledge the proposed filters are the most compact SIW-based bandpass filters today. Also the combinational use of QMSIW-HMSIW to achieve an ultra-compact trisection response is proposed for the first time. REFERENCES [1] K. Entesari, A. Pourghorban Saghati, V. Sekar, and M. Armendariz, “Tunable SIW structures: Antennas, VCOs, filters,” IEEE Microw. Mag., vol. 16, no. 5, pp. 34–54, Jun. 2015. [2] A. Pourghorban Saghati, A. Pourghorban Saghati, and K. Entesari, “An ultra-miniature quarter-mode SIW bandpass filter operating at first negative order resonance,” in IEEE MTT-S Int. Microw. Symp. Dig., May 2015, pp. 1–3.

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[3] Y. L. Zhang, W. Hong, K. Wu, J. X. Chen, and H. J. Tang, “Novel substrate integrated waveguide cavity filter with defected ground structure,” IEEE Trans. Microw. Theory Techn., vol. 53, no. 4, pp. 1280–1287, Apr. 2005. [4] J. Martinez, S. Sirci, M. Taroncher, and V. Boria, “Compact CPW-fed combline filter in substrate integrated waveguide technology,” IEEE Microw. Wirel. Compon. Lett., vol. 22, no. 1, pp. 7–9, Jan. 2012. [5] Y. D. Dong, T. Yang, and T. Itoh, “Substrate integrated waveguide loaded by complementary split-ring resonators and its applications to miniaturized waveguide filters,” IEEE Trans. Microw. Theory Techn., vol. 57, no. 9, pp. 2211–2223, Sep. 2009. [6] Y. Dong and T. Itoh, “Substrate integrated waveguide negative order resonances and their applications,” IET Microw. Antennas Propag., vol. 4, no. 8, pp. 1081–1091, Aug. 2010. [7] V. Sekar and K. Entesari, “A novel compact dual-band half-mode substrate integrated waveguide bandpass filter,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2011, pp. 1–4. [8] Z. Zhang, N. Yang, and K. Wu, “5-GHz bandpass filter demonstration using quarter-mode substrate integrated waveguide cavity for wireless systems,” in Proc. IEEE Radio Wirel. Symp., Jan. 2009, pp. 95–98. [9] C. Jin and Z. Shen, “Compact triple-mode filter based on quarter-mode substrate integrated waveguide,” IEEE Trans. Microw. Theory Techn., vol. 62, no. 1, pp. 37–45, Jan. 2014. [10] A. Pourghorban Saghati, M. Mirsalehi, and M. Neshati, “A HMSIW circularly polarized leaky-wave antenna with backward, broadside, forward radiation,” IEEE Antennas Wirel. Propag. Lett., vol. 13, pp. 451–454, Mar. 2014. [11] L. Szydlowski, A. Jedrzejewski, and M. Mrozowski, “A trisection filter design with negative slope of frequency-dependent crosscoupling implemented in substrate integrated waveguide (siw),” IEEE Microw. Wirel. Compon. Lett., vol. 23, no. 9, pp. 456–458, Sep. 2013. [12] J. Martinez, S. Sirci, and V. Boria, “Compact SIW filter with asymmetric frequency response for C-band wireless applications,” in Proc. Int. Wirel. Symp., Apr. 2013, pp. 1–4. [13] P.-J. Zhang and M.-Q. Li, “Cascaded trisection substrate-integrated waveguide filter with high selectivity,” Electron. Lett., vol. 50, no. 23, pp. 1717–1719, 2014. [14] S. Sirci, J. Martinez, J. Vague, and V. Boria, “Substrate integrated waveguide diplexer based on circular triplet combline filters,” IEEE Microw. Wirel. Compon. Lett., vol. 25, no. 7, pp. 430–432, July 2015. [15] E. Arnieri and G. Amendola, “Analysis of substrate integrated waveguide structures based on the parallel-plate waveguide green's function,” IEEE Trans. Microw. Theory Techn., vol. 56, no. 7, pp. 1615–1623, Jul. 2008. [16] J. Hobdell, “Optimization of interdigital capacitors,” IEEE Trans. Microw. Theory Techn., vol. 27, no. 9, pp. 788–791, Sep. 1979. [17] A. Pourghorban Saghati and K. Entesari, “A reconfigurable SIW cavity-backed slot antenna with one octave tuning range,” IEEE Trans. Antennas Propag., vol. 61, no. 8, pp. 3937–3945, Aug. 2013. [18] D. Pozar, Microwave Engineering, 4th ed. Hoboken, NJ, USA: Wiley Global Education, 2011. [19] H. J. Tang, W. Hong, J.-X. Chen, G. Q. Luo, and K. Wu, “Development of millimeter-wave planar diplexers based on complementary characters of dual-mode substrate integrated waveguide filters with circular and elliptic cavities,” IEEE Trans. Microw. Theory Techn., vol. 55, no. 4, pp. 776–782, Apr. 2007. [20] J.-S. G. Hong and M. J. Lancaster, Microstrip Filters for RF/Microwave Applications. Hoboken, NJ, USA: Wiley, 2004. [21] C.-C. Yang and C.-Y. Chang, “Microstrip cascade trisection filter,” IEEE Microw. Guided Wave Lett., vol. 9, no. 7, pp. 271–273, Jul. 1999. [22] X.-P. Chen and K. Wu, “Substrate integrated waveguide cross-coupled filter with negative coupling structure,” IEEE Trans. Microw. Theory Techn., vol. 56, no. 1, pp. 142–149, Jan. 2008.

Ali Pourghorban Saghati (S'11) received the M.Sc. degree (honors) in electrical engineering from Ferdowsi University, Mashhad, Iran, in 2014. He is currently pursuing the Ph.D. degree in electrical and computer engineering at Texas A&M University, College Station, TX, USA. His research interests include miniaturized RF/microwave antennas and filters, reconfigurable multiband and broadband antennas, microwave interferometric chemical sensors for lab-on-chip applications. Mr. Pourghorban Saghati was a recipient of the Texas A&M University ECE Departmental Graduate Student Scholarship in Fall 2014.

Alireza Pourghorban Saghati (S'08) received the M.Sc. degree (honors) in electrical engineering from Urmia University, Urmia, Iran, in 2010 and the Ph.D. degree from Texas A&M University, College Station, TX, USA, in 2015. He is currently an RF/Antenna Engineer with Ossia Inc., Bellevue, WA, USA. His research interests include RF communication systems, RF energy harvesting, wireless power transfer, and wearable wireless devices. Dr. Pourghorban Saghati was a recipient of the Texas A&M University ECE Departmental Graduate Student Scholarship in Fall 2011. He was also a recipient of the Student Paper Award (honorable mention) at the Student Paper Competition presented at the 2013 IEEE AP-S International Symposium, Orlando, FL, USA.

Kamran Entesari (S'03–M'06) received the B.S. degree in electrical engineering from the Sharif University of Technology, Tehran, Iran, in 1995, the M.S. degree in electrical engineering from Tehran Polytechnic University, Tehran, Iran, in 1999, and the Ph.D. degree from The University of Michigan, Ann Arbor, MI, USA, in 2005. In 2006, he joined the Department of Electrical and Computer Engineering, Texas A&M University, College Station, TX, USA, where he is currently an Associate Professor. His research interests include microwave chemical/biochemical sensing for lab-on-chip applications, RF/microwave/millimeter-wave integrated circuits and systems, reconfigurable RF/microwave antennas and filters, and RF micro-electromechanical systems (MEMS). Prof. Entesari currently serves as an Associate Editor for the IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS (MWCL), and is on the Technical Program Committee (TPC) of the IEEE RFIC Symposium. He was a recipient of the 2011 National Science Foundation (NSF) CAREER Award. He was a co-recipient of the 2009 Semiconductor Research Corporation (SRC) Design Contest Second Project Award for his work on dual-band millimeter-wave receivers on silicon and the Best Student Paper Awards of the IEEE RFIC Symposium in 2014 (second place), IEEE Microwave Theory and Techniques Society (IEEE MTT-S) in 2011 (third place), and IEEE AP-S in 2013 (honorable mention).

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Design and Multiphysics Analysis of Direct and Cross-Coupled SIW Combline Filters Using Electric and Magnetic Couplings Stefano Sirci, Student Member, IEEE, Miguel Ángel Sánchez-Soriano, Member, IEEE, Jorge D. Mart´ınez, Member, IEEE, Vicente E. Boria, Senior Member, IEEE, Fabrizio Gentili, Associate Member, IEEE, Wolfgang Bösch, Fellow, IEEE, and Roberto Sorrentino, Fellow, IEEE

Abstract—In this paper, combline substrate integrated waveguide (SIW) filters using electric and magnetic couplings are thoroughly studied. Thus, a negative coupling scheme consisting on an open-ended coplanar probe is proposed and analyzed in detail. Several in-line 3-pole filters at C-band are designed, manufactured and measured showing how the presented approach can be used for implementing direct couplings while enabling an important size reduction and improved spurious-free band compared to conventional magnetic irises. A fully-packaged quasi-elliptic 4-pole filter is also designed at 5.75 GHz showing how the negative coupling structure can be used for introducing transmission zeros by means of cross-couplings between non-adjacent resonators. Finally, average and peak power handling capabilities of these filters have been also analyzed from a multiphysics point of view. Measured results validate the theoretical predictions confirming that combline SIW filters can handle significant levels of continuous and peak power, providing at the same time easy integration, compact size and advanced filtering responses. Index Terms—Cross-coupled filters, electric and magnetic mixed couplings, multiphysics analysis, power handling capabilities, quasi-elliptic filter, substrate integrated waveguide.

I. INTRODUCTION

S

UBSTRATE INTEGRATED WAVEGUIDE (SIW) has already demonstrated to be a successful approach for implementing microwave and mm-wave filters with high Q-factor, easy integration with planar circuits, and mass production manufacturing processes in PCB and LTCC technology [1]. HowManuscript received July 03, 2015; revised October 02, 2015; accepted October 11, 2015. Date of publication November 12, 2015; date of current version December 02, 2015. This work was supported in part by MINECO (Spanish Government) under projects TEC2013-47037-C5-1-R and TEC2013-48036-C3-3-R. This paper is an expanded version from the IEEE MTT-S International Microwave Symposium, Phoenix, AZ, USA, May 17–22, 2015. S. Sirci, M. A. Sánchez-Soriano, and V. E. Boria are with the iTEAM, Universitat Politècnica de València, Camino de Vera s/n, E-46022 Valencia, Spain (e-mail: [email protected]; [email protected]; [email protected]. es). J. D. Mart´ınez is with the I3M, Universitat Politècnica de València, E-46022 Valencia, Spain (e-mail: [email protected]). F. Gentili and W. Bösch are with the IHF, Graz University of Technology, 8010 Graz, Austria (e-mail: [email protected], [email protected]). R. Sorrentino is with the University of Perugia, 06100 Perugia, Italy (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2015.2495287

ever, other potential features that, combined with the former advantages, could be of huge interest in a wide range of wireless and mobile applications are a lively subject of research, like compactness, advanced filtering responses, and recently power handling capabilities. The realization of compact SIW filters has been approached from different perspectives. Several authors have proposed more compact alternatives to conventional SIW cavities by bisecting the resonator at quasi-perfect magnetic walls. Among the most relevant techniques that can be identified in the literature, there are folded [2], half-mode [3] and quarter-mode [4] SIW bandpass filters. Other approaches have focused on loading the SIW resonator with complementary split-ring resonators [5], dielectric rods [6] and more recently combline SIW filters, which were proposed as a translation of the well-known 3D coaxial resonator concept to a substrate integrated scheme [7]. Even with some trade-offs in terms of Q-factor or manufacturing complexity, most of the former approaches can obtain significant size reduction, but keeping fabrication and integration easiness (i.e., preferably single-layer batch-fabrication processes with solid bottom ground planes) that are usually of major importance from a practical point of view. At the same time, filtering functions including transmission zeros (TZs) at finite or imaginary frequencies are of great interest in many applications, enabling to achieve higher selectivity with a reduced footprint. In this sense, the use of crosscouplings between resonators is a well-known and extended technique for the introduction of TZs, based on the generation of multiple paths between the filter input and output, and therefore allowing for signal cancellation [8], [9]. Even if positive and negative couplings are generally required, magnetic coupling using irises between adjacent resonators has been the preeminent scheme, and the use of all inductive couplings has been already demonstrated for implementing linear-phase [10] and trisection [11] band-pass SIW filters. On the other hand, electric coupling mechanisms in SIW structures have been investigated by several authors. In [12] and [13], a negative coupling structure between SIW cavity resonators is proposed using a balanced microstrip line with a pair of plated via holes. However, in both structures, slots need to be etched at the top and bottom layers of the substrate, limiting the integration and packaging possibilities of the devices. In [14], a controllable mixed coupling is created using an embedded short-ended stripline com-

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bined with a wall iris at the expense of a multi-layer fabrication process that increases the complexity of the structure. On the other hand, grounded coplanar lines [15], microstrip lines [16] and oversized cavities [17] have been proposed as single-layer solutions, although some of the former structures are limited in terms of flexibility (i.e., coupling level or resonator positioning) or they require a larger area. Following this approach, the authors have recently proposed a solution for obtaining electric coupling in combline SIW resonators using a single-layer open-ended coplanar probe [18]. Lastly, even if higher power capacity is usually accepted as an advantage of SIW structures, power handling capabilities of SIW filters has not been broadly studied yet from a multiphysics perspective considering electrical, thermal and mechanical effects at the same time. In this work, the electric coupling structure proposed in [18] is studied in detail both for implementing direct and cross-couplings in combline SIW filters. As it is shown in the paper, this electric coupling scheme can be used to allow a further reduction of the filter size and increased bandwidth compared to conventional magnetic irises. Moreover, a fully packaged quasi-elliptic filter is designed, manufactured and measured. Finally, average and peak power handling capabilities of the device are theoretically studied and experimentally validated. The obtained results show that combline SIW filters can be a self-packaged, compact solution capable of incorporating both positive and negative couplings while keeping low-cost and batch-fabrication processes. The paper is structured as follows. In Section II, the negative coupling structure is presented and investigated. Section III provides the design, manufacturing and measurement of in-line three-pole combline SIW filters using the proposed negative coupling scheme. A comparison between magnetic and electric inter-resonator coupling is carried out, showing how the latter can be used to obtain more compact implementations while keeping the filter bandwidth. In Section IV, a fully packaged quasi-elliptic filter using a negative cross-coupling between non-adjacent resonators is presented, while the power handling capabilities of the filter are studied in Section V using a multiphysics approach to obtain the average and peak power capacities of the device. Finally, Section V presents the main conclusions. II. NEGATIVE COUPLING STRUCTURE A. Coaxial SIW Resonator The building block resonator to be considered for the design of the in-line and quasi-elliptic bandpass filters is a combline resonator implemented in SIW technology [7]. The inductive section is obtained by a metallic post, implemented by a metallized via-hole, connected to ground at one of its ends. At the other side, a metallic disk having a radius much higher than the post diameter is connected. Between this disk (which can have a square or a circular shape) and the top ground plane a small air gap is inserted, so generating a high capacitance towards ground (termed loading capacitance ), which represents the capacitive section of the coaxial resonator. Fig. 1 shows the layout of a coaxial SIW resonator, including its main design parameters.

Fig. 1. (a) 3D view and (b) top view of the coaxial SIW resonator including its main design parameters.

Such resonator can be modelled as a TEM-mode combline resonator embedded into the dielectric substrate. The TEM-mode resonant frequency is given by the condition , where the susceptance of the coaxial SIW resonator can be expressed as (1) where is the propagation constant of the TEM-mode and the thickness of the substrate. Then, the characteristic impedance of the coaxial resonator, and the ratio between the outer cavity side and the via diameter are obtained from [7] (2) (3) where is the resonator electrical length at the design frequency , that in our case is . The synthesis procedure starts by choosing the resonator slope parameter at the center angular frequency of the filter. The susceptance slope parameter for resonators having zero susceptance at is defined by [19] (4) The slope parameter has to be conveniently chosen as a trade-off between quality factor , compactness and physical feasibility of synthesized values of and . In order to increase component compactness, it is very important to set the inner via hole diameter to the minimum diameter allowed

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Fig. 2. Topology of the proposed electric coupling for coaxial SIW resonators.

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for Fig. 3. Coupling coefficient variation versus iris width mm, mm and mm. As the iris width increases, the total coupling decreases until it changes from electric to magnetic coupling and then increases again. In this figure, mm.

for the fabrication technology, as well as to keep as small as possible. This allows us to reduce radiation from apertures, thus helping to preserve a reasonable value for the resonator -factor. B. Negative Inter-Resonator Coupling The proposed solution to realize an electrical coupling between coaxial SIW resonators is based on a capacitive probe implemented by a high impedance coplanar line (CPW). The two ends of such a line penetrates into the head of the resonator capacitive patches, i.e., in the region with the highest intensity of electric field. A gap between the capacitive circular patch of the resonators and the probe is ensured. Part of the field is then collected by the probe and transferred to the adjacent resonator, so realizing an electric coupling. In absence of the probe described above, the main source of coupling would be due to the magnetic field inside the SIW cavities. For the considered structure, the sign of the magnetic coupling is opposite to the electrical one. Therefore in order to boost the effect of the probe and get higher values of coupling, the magnetic coupling must be minimized. Such condition can be achieved with a wall of via holes placed across the resonators, which strongly confine the magnetic field coupling. The probe can still be realized if the width of the CPW line is sufficiently smaller than the gap between the central via-holes realizing the wall, as shown in Fig. 2. Fig. 3 shows the total coupling vs. (obtained from the contribution of both electric and magnetic couplings), where is a generic -th resonator. Such trace was derived with a constant value for the insertion (i.e., mm) of the probe inside the head of the resonator. For increasing values of , the wall becomes more similar to a coupling iris with reference to classical waveguide structures. The curve shows that as the iris opens up, the total coupling starts to decrease until a certain point after which it starts to rise again. This effect can be explained by considering that when is minimum, the iris is completely closed and we are in the condition of minimum magnetic coupling between the two resonators. Therefore, the major contribution to the coupling is given by the probe (i.e., electric coupling). When starts to increase, the magnetic coupling between the two resonators is not negligible anymore and it starts to counteract the effect of the elec-

Fig. 4. Coupling coefficient variation versus CPW probe dimensions: conductor width , spacing and insertion on capacitive disks. Red line is the mm, mm and mm). The simulation baseline (i.e., mm. post-wall iris width is

trical coupling, until they reach the same magnitude and the total coupling collapses to zero . From this point on, if is increased the magnetic coupling starts to prevail, and the effect of the electric probe is not visible anymore. This analysis demonstrates that, in order to obtain electrical coupling between the two resonators, it is not sufficient to implement the probe described above, but it is also necessary to minimize the magnetic coupling by means of a post-wall iris. The insertion of the probe inside the head of the resonators is the main parameter to control the magnitude of the coupling . The behaviour of vs. for the structure of Fig. 2 is shown in Fig. 4, which considers two resonators implemented on a substrate with and thickness mm. As expected, becomes stronger as the insertion within the head of the resonator is increased. Clearly, also depends on and . The behaviour of vs. and is also reported in Fig. 4. Nevertheless, the contribution of these parameters has a lower impact on the coupling magnitude. Thus, we can settle these values, and controlling the coupling by means of . A main advantage of the proposed electric coupling is to allow increasing direct inter-resonator coupling, especially for strongly loaded coaxial SIW resonators. As a way of comparison, the coupling strength capabilities of the magnetic and electric coupling schemes (Figs. 5 and 6) are compared. First, in

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Fig. 5. (a) Coupling coefficient variation versus the relation between and the SIW cavity side . (b) Inter-resonator the post-wall iris width coupling system based on post-wall iris, showing design parameters.

Fig. 5, the coupling provided by a post-wall iris is depicted for two different values of slope parameter. As it is shown, by increasing the slope parameter of such structures, the magnetic coupling is strongly reduced between coaxial SIW resonators. That variation of , from 0.029 to 0.034, corresponds to diminish the SIW cavity side from 15 mm to 11.6 mm while of the capacitive disks increases from 0.825 pF to 0.95 pF. Both coaxial SIW resonators resonate in all cases at the same frequency, that is 5.5 GHz. Now, by applying the proposed electric coupling for the same pair of coaxial resonators, it is possible to see how higher coupling values are easily implementable in more compact structures. Fig. 6 depicts the inter-resonator coupling values that can be obtained using the proposed electric CPW probe, and below the scheme of that solution is shown with its main design parameters. It is worth mentioning that the insertion of the coupling of the capacitive patches, thus probes modifies the value of their sizes have to be slightly modified to meet specifications in terms of frequency. The proposed coupling scheme presents different advantages: single layer implementation, accurate control of the coupling level and it is well suited for tunable cross coupling using tuning elements, which can be easily mounted on the top metal layer.

III. THREE-POLE IN-LINE SIW FILTER WITH ELECTRIC COUPLING As it has been demonstrated in the previous Section II, the proposed electric coupling is an efficient approach for ensuring higher couplings between coaxial SIW resonators, and this is

Fig. 6. (a) Coupling coefficient variation versus electric coupling probe mm and mm. (b) Interinsertion . Other parameters are: resonator coupling system created at the top metal layer of the SIW resonators, showing design parameters.

especially true when the resonator compactness has to be increased. The CPW probe used to obtain an electric coupling between coaxial SIW resonators can generate high values of coupling if the insertion of the probe inside the capacitive disks is opportunely chosen, independently of the SIW cavity size. Indeed, if the building block resonator is designed with a higher slope parameter , the SIW cavity dimensions can be strongly reduced to compensate for the needed higher capacitive contribution of while maintaining the same resonant frequency, as deduced from (1)–(4). This circuit area reduction also leads to shift up the first spurious mode of the SIW cavity, widening the stopband bandwidth, so that, an improvement in terms of size and filter response can be really achieved. In order to validate the aforementioned statements three third-order coaxial SIW filters having center frequency 5.5 GHz, passband bandwidth of 250 MHZ (that corresponds to 4.6%) and return losses better than 15 dB have been designed. The main difference between those filters shown in Fig. 7 is the coupling configuration used to couple resonators: filter in Fig. 7(a) presents magnetic couplings based on post-wall iris, meanwhile filters in (b) and (c) are based on the proposed electric coupling. In particular, the filter shown in Fig. 7(c) is designed to present a higher resonator slope parameter (which leads to a small size cavity) in order to demonstrate the improved design characteristics added by using the electric coupling. It should be noted that this size reduction is incompatible with the use of the magnetic coupling scheme, since a smaller cavity leads to lower coupling values limiting the maximum achievable passband bandwidth. In this context, the electric coupling provides a higher design flexibility in order to fulfil requirements in terms of bandwidth, size and rejection

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Fig. 9. Comparison of three simulated responses with same in-band characteristics but different stop-band behaviour.

Fig. 7. Structure of the (a) magnetic-coupled, (b) electric-coupled and (c) compact electric-coupled coaxial SIW filters and main design dimensions.

Fig. 8. Multipath coupling diagram for the three-pole in-line coaxial SIW filter based on (a) magnetic (i.e., filter of Fig. 7(a)) and (b) electric coupling system (i.e., filters of Figs. 7(b)–(c)).

band. Fig. 8 shows the coupling schemes of such three-pole coaxial SIW filters with magnetic and electric couplings. The chosen dielectric substrate in these designs is now the 1.524 mm-thick Rogers R4003 with permittivity . So, the resonator electrical length corresponds to 18.9 , i.e., 0.05 , where is the guided wavelength at 5.5 GHz. In the first two filters, the coaxial SIW resonators have been designed to present S that gives a loading capacitance of fF while . By using both values and choosing a diameter of mm for the inner via hole, the SIW resonator cavity size is mm (i.e., and ) whilst the square patch side is 4.2 mm with an air gap of 0.24 mm between the patch and the ground plane. The final structure of those coaxial SIW filters in Figs. 7(a) and (b) have a footprint of 15 45 mm , i.e., and . When the coaxial SIW resonator has S, and become now 950 fF and 89.4 , respectively. The resonator cavity size consequently diminishes down to mm , i.e., and ,

having a square disk side of 4.8 mm and an air gap of 0.24 mm. Finally, the compact electric coupling based filter shows a footprint of 11.6 34.8 mm , i.e., and . The value of inter-resonator coupling for all filters are while the external coupling coefficient is , as it is shown in Fig. 8. Fig. 9 shows the simulation results of the three aforementioned filters. As it can be seen, the filter frequency responses above the passband show a higher order spurious band, which is due to the excitation of the mode of the SIW cavity. The best stopband performance is obtained by the filter of Fig. 7(c), as expected, with a wide stopband of up to 8.5 GHz with more than 25 dB of rejection. In particular, this filter presents the same level of insertion losses ( dB at 5.5 GHz for all filters) with a 40% of total size reduction compared to the other two coaxial SIW filters of Figs. 7(a)–(b) and a 70% of area reduction with respect to a standard -mode SIW filter centered at 5.5 GHz. It should be noted that this passband bandwidth along with such a compact circuit area could not be implemented by using the magnetic coupling based on post-wall iris. The reason is that, as shown in Fig. 5, the maximum coupling values between two coaxial SIW resonators with slope parameters S coupled by a magnetic coupling scheme results less than 0.03, which is below the values needed for the third-order filter considered (see Fig. 8). Table I gives the relation between unloaded quality factor and miniaturization degree of a coaxial SIW resonator implemented in 1.524 mm-thick Rogers R4003, when its slope parameter is increased. Those values have been compared to the area and of a standard SIW cavity resonator centered at 5.5 GHz. As Table I shows, the coaxial SIW topology allows high miniaturization of SIW structures with moderate degradation of . A photograph of the filter prototypes of Fig. 7(b) and (c) is shown in Fig. 10, while the simulated and measured responses of these filters are shown in Figs. 11 and 12, respectively. Measurements for both designs have validated the proposed concept, showing good insertion losses (i.e., 1.57 dB and 1.97 dB at , respectively), and return losses better than 11 dB for both filters. The measured response of filter prototype of Fig. 7(b) undergoes a frequency shift of 1.2% towards lower frequency, from

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TABLE I VERSUS MINIATURIZATION FOR SIW CAVITY RESONATORS IMPLEMENTED IN ROGERS R4003 RESONATING AT 5.5 GHZ (UNIT: MM)

Fig. 13. Multipath coupling diagram for the cross-coupled filter.

response, which is not possible for an iris-based magnetic coupling. IV. FOUR-POLE CROSS-COUPLED SIW FILTER A. Filter Design

Fig. 10. Photography of the proposed three-pole in-line coaxial SIW filters S, and (b) S. based on electric coupling, where (a)

Fig. 11. Simulated (dashed line) and measured (solid line) wideband responses S (Fig. 7(b)). of the proposed three-pole in-line SIW filter with

Fig. 12. Simulated (dashed line) and measured (solid line) wideband responses of the proposed three-pole in-line coaxial SIW filter with S (Fig. 7(c)).

5.5 GHz to 5.43 GHz (see Fig. 11). For the compact three-pole filter of Fig. 7(c), the measured response has been shifted up to 5.9 GHz, as it can be observed in Fig. 12. These frequency deviations have been caused by an increase of the square patch air gap during fabrication process. The simulation results have taken into account such a variation in the air gap. Among others, the advantage of using such coupling scheme is that tuning devices can be opportunely used to create a reconfigurable filter

In order to further demonstrate the proposed coupling solution, its application on a 4-pole narrow-band filter with a quasielliptic frequency response is now considered. The coupling scheme of the filter is given in Fig. 13. The coupling between resonators 1 and 4, termed , has opposite sign compared to all the inter-resonator couplings. This configuration is particularly interesting because it improves the selectivity generating TZs located both above and below the filter passband. The filter center frequency is chosen to be 5.75 GHz with an equi-ripple fractional bandwidth FBW of 2% (114 MHZ), which results in a simulated 1-dB bandwidth of 94 MHZ % . The TZs are set at 5.63 and 5.87 GHz, respectively, corresponding to the center frequencies of adjacent filters in a multiplexer application with contiguous channels. In this design, the slope parameter of the combline SIW resonator is chosen to be S, while the substrate presents and thickness mm. As it was previously mentioned, the resonator electrical length corresponding to substrate thickness is 46.5 , i.e., , where is the guided wavelength at 5.75 GHz. This gives a loading capacitance of fF while the characteristic coaxial impedance is . By taking both previous values and choosing a diameter of mm for the metallic via hole implementing the coaxial topology, the resonator structure can be optimized with EM full-wave simulations, by adjusting the size of the loading capacitive disk and the gap that separates it from the top metal layer. The resonators size is mm (i.e., ) whilst the capacitive disk radius is 0.915 mm with an air gap of 0.15 mm between the disk and the ground plane. The final structure of the filter presents a very compact footprint of 21.2 21.2 mm , which corresponds to 63% of area reduction compared to a quasi-elliptic four-pole filter based on -mode SIW resonators and implemented in the same dielectric substrate. The input-output coupling is realized by means of coplanar waveguide-to-SIW transition with 90 bend slots, which are etched from the metal on top of the first (last) cavity, see Fig. 14. The value of the can be easily controlled by modifying the dimensions of the probe. The coupling coefficients are and . Fig. 14 shows the geometric configuration of the 4-pole crosscoupled filter, including the proposed electric cross-coupling and some main filter dimensions. The coupling between the SIW

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TABLE II LAYOUT DIMENSIONS OF THE DESIGNED FILTER (UNIT: MM)

Fig. 14. Layout of the cross-coupled SIW filter assembled on a carrier substrate. Open-ended CPW line provides the electric coupling.

resonators 1 and 4 and the input/output ports are realized by means of CPW current probes that are etched on the top metal layer. The decreases with increasing size of ground plane openings that are created at the end of the CPW line. The filter dimensions are given in Table II. From simulations, the minimum insertion loss is 2.2 dB and the two TZs are located at 5.63 and 5.87 GHz providing 35 dB and 27 dB of minimum rejection, respectively.

Fig. 15. Side views of the vertical CPW-CPW transition that allows SMD assembly of the packaged filter on a carrier substrate.

B. Vertical Transition In Fig. 14, below the SIW filter substrate, it can be seen a host board with two isolated coplanar lines which were implemented on a 1.524 mm-thick Rogers R4003. In fact, the considered four-pole filter has been designed for allowing surface mounting device (SMD) assembly considering a PCB fabrication process. In order to enable SMD packaging of the filter, connection must be provided to the filter input and output. This kind of self-packaged solution for coaxial SIW filters, which provides access to the input/output ports through castellated plated via holes, was originally proposed in [20] showing promising results. This solution offers potential advantages in terms of design flexibility, low loss and enabling the SMD integration of the device. The proposed system is illustrated in Fig. 15, where a scheme of the vertical transition structure is shown. The bottom layer will interface between the carrier board and the packaged filter through a vertical pseudo-CPW structure. Since the CPW structure has both signal and ground on the same plane, the connection of the device to the host board is simple. In fact, the device can be easily placed and soldered onto the carrier substrate. The diameter and spacing of the transition half-a-hole vias are the most important design parameters for controlling the EM performance [20]. C. Experimental Results The designed filter has been fabricated on a 3.175 mm-thick Rogers TMM4 substrate using a standard single-side PCB process. The diameter and center-to-center pitch of the external via holes are 0.6 mm and 1.1 mm, respectively. A photograph of the filter prototype is shown in Fig. 16 while Fig. 17 shows the frequency responses of the cross-coupled SIW filter. It is worth mentioning that simulated and measured -parameters include the vertical transition for connecting input/output ports. The measured 1-dB bandwidth is 102.5 MHZ that corresponds to 1.8%, while the band-

Fig. 16. Photography of the filter prototype assembled on its substrate carrier.

Fig. 17. Simulated (dashed line) and measured (solid line) wideband responses of the proposed SIW filter.

width at dB corresponds to 200 MHZ. The S-parameters of the fabricated filter prototype were measured with an Agilent E8364B PNA series network analyzer, and a TRL calibration was performed using a home-made CPW cal-kit. The frequency shift of 70 MHZ % between simulations and results is due to the fabrication tolerances which, however, can be corrected in the filter design process. The minimum

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COMPARISON

OF

TABLE III CROSS-COUPLED FILTERS

IN

SIW TECH.

IL has increased up to 3.6 dB due to fabrication issues of the vertical transitions, resulting in an estimated Q-factor of 225, being 320 the simulated resonator . The measured return losses are better than 25 dB. The upper stop-band is in very good agreement with simulations up to 12 GHz, being the attenuation always better than 30 dB, as shown in Fig. 17. Table III shows the comparison between this work and other cross-coupled SIW filters shown in the references, where it can be observed the high compactness degree obtained with the proposed solution.

Fig. 18. 3D Electric Field distribution for a SIW Combline cavity.

From the Newton's Law of cooling, the generated heat is equal to the total heat delivered to the environment by means of convection and/or thermal radiation. Thus, this energy balance can be written as

V. MULTIPHYSICS STUDY FOR THE POWER HANDLING CAPABILITY EVALUATION OF SIW COMBLINE FILTERS In this section the power handling capability (PHC) of the SIW combline resonator is studied in detail. Two different kind of studies are addressed: a) Average Power Handling Capability (APHC), where it is assumed that a CW signal is applied to the circuit and the electro-thermo-mechanical coupling is analyzed in order to determine the maximum temperature and thermal stress of the circuit as a function of the input signal power. And b) Peak Power Handling Capability (PPHC), in such a case pulsed signals are applied to the circuit and the corona discharges are examined as a function of the input signal power and pressure. As an example of analysis, the PHC study is focused on the quasi-elliptic filter presented in Section IV. A. Average Power Handling Capability For moderated CW signal powers (1–5 W) high temperatures can be achieved in planar circuits due to self-heating, which limits the APHC [22]–[24]. Planar circuits present three loss mechanisms: conductive, dielectric and radiation losses. They are linearly proportional to the input power, but only the two former loss mechanisms produce heat in the circuit, so that they can be defined as the internal heat sources of the structure. In particular, dielectric loss is treated as a volumetric heat source whereas conductive loss as a surface heat source. In pure planar technologies as microstrip, the gradient of temperature due to self-heating is computed by determining the conductor and dielectric losses, then, the heat flow distribution in the microstrip cross section is derived to finally obtain the temperature rise that defines the maximum working input power [22], [23], [25]. In SIW technology, due to its large aspect ratio , and the fact that conductive losses are equal both in top and bottom planes, the whole heat source can be assumed to be homogeneous in a differential region , consequently providing a homogeneous temperature in this volumetric region. This assumption is also favoured by the use of via holes conforming the SIW, which propagate the heat between the top and bottom layers.

(5) where (6) being the loss factor of the structure and the input signal power. is any external heat source (such as solar radiation), is the temperature in the surroundings, and are the surface layers exposed to convection and radiation boundary conditions, respectively, and and are the convection and radiation coefficients. The values and depend on the external conditions of each layer, i.e., if there is a heat sink attached, natural or forced convection, emissivity, etc. From (5), the maximum temperature can be computed for a given and if the environment conditions ( and ) are known. An expected conclusion from this equation is that, if is kept, the bigger the surface , the lower the is, and therefore, the higher the APHC. For the SIW combline resonators, the electric-magnetic field distribution which defines the heat source pattern is different to that presented by standard SIW rectangular cavities, as seen in Fig. 18. However, the large aspect ratio as well as the use of the outer via holes and the inner conductor, make the temperature in the SIW combline cavity nearly homogeneous, and therefore, (5) can be used as a first order approximation. For the APHC analysis of the filter, firstly, the power loss per resonator is computed from the equivalent lumped element circuit whose behaviour is modeled by the coupling matrix shown in Fig. 13. GHz and % are used for such a computation. As seen from Fig. 19, the total highest power loss is found at the inband corners, at 5.68 and 5.82 GHz, with . In particular, resonator #2 presents the highest level of losses, so that it is expected that this resonator limits the APHC. Equation (5) can be used in order to calculate the average temperature in the whole circuit. For W at 5.82 GHz, assuming natural convection with

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TABLE IV THERMO-MECHANICAL PROPERTIES OF TMM 4

Fig. 19. Power loss in each resonator per watt from the equivalent lumped el. ement circuit model.

Fig. 21. Maximum equivalent Von-Mises Stress as a function of GHz and assuming natural convection on the circuit with

Fig. 20. Thermal profile of the filter presented in Section IV. 5.82 GHz with natural convection around the circuit with C. and

W/m

C and

W/m

W at C

C, with a whole circuit area of mm and neglecting thermal radiation, the average temperature in the circuit is found to be 176 C. ANSYS Multiphysics is used in order to accurately obtain the thermal profile for such an example. Fig. 20 shows its thermal profile where the hottest spot is found in resonator #2, as predicted, with a value of 205 C. The simulated average temperature in the circuit is very close to the computed value according to (5). The APHC is limited by that which creates such a thermal gradient leading to exceed the glass transition temperature of the substrate or, that which generates a thermal stress able to destroy (or deform) the circuit. The minimum of those values limits the APHC. For the electro-thermo-mechanical coupling needed to evaluate the thermal stress, ANSYS Multiphysics is used again. Table IV summarizes the thermo-mechanical parameters required for the study. It should be remarked that the thermal conductivity in the substrate both in SIW and SIW coaxial cavities is not a critical parameter for the reduction of the gradient of temperature as it is in microstrip technology. The yield strength point gives the maximum stress that a material can afford before permanent deformation. It defines the transition between the linear mechanical behaviour (elastic behaviour) of the material and the non-linear one. Fig. 21 shows the maximum equivalent stress (Von-Mises) as a function of at the frequency where losses are the highest

. At 5.82 C.

(5.82 GHz) and for two different load cases (bottom of the circuit is fixed or unfixed). Obviously, when the bottom is fixed the stress produced is higher and the elastic limit is reached for lower power levels. The maximum stress happens in the metal, both in layers and the via holes, whereas the stress provoked in the substrate is much lower. From these figures, it can be concluded that W in order to keep the circuit in safety ranges of applied power. It should be noted that for this circuit, due to the high value of , APHC is limited by thermal stress. With respect to the deformation produced in the circuit while the CW signal is applied, in the case of the bottom is fixed, deformation is insignificant (maximum deformation m for W). In the case when the bottom is unfixed, although the maximum deformation is still low, it can produce a small frequency shift in the transfer function for high (maximum deformation m for W). B. Peak Power Handling Capability The SIW combline resonator presents an important density of electric field through the air, between the loading capacitive disk and the top layer ground. Thus, this resonator can be susceptible to present corona discharges for high power applied signals. The situation is different for standard SIW technology, since the electric field is mainly distributed through the dielectric and the critical areas for air ionization are the slot edges of the coplanar line feeding the SIW cavities [1]. In order to evaluate any possible corona discharge, the maximum voltage (and consequently, the expected maximum electric field) of the SIW combline filter should be found as a function of the input signal power. From the equivalent lumped element circuit, the voltage and current in each resonator of the filter can be computed as (7) (8)

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threshold (peak value) can be determined by following the rule [31] (13)

Fig. 22. Scheme of the SIW combline resonator where the current and voltage distributions are shown at resonance frequency.

where is the generator voltage, the normalized external quality factor, is the reference impedance and is the normalized impedance/admittance matrix defining the filter network [19]. Once the equivalent voltages/currents are known, the stored energy can be found as (9) where is the available power at the input port and BW is the absolute bandwidth of the filter in rad/s. At resonance, the stored energy by every resonator of the equivalent lumped element network should be the same as that associated to the distributed resonators [26], [27]. Fig. 22 shows the scheme of a combline resonator where the voltage and current standing waves are also plotted at resonance. From the standing waves the stored energy by the distributed resonator can be calculated as [28], [29] by integrating the standing waves (in form of sinusoidal functions) along the resonator. Thus, by making the peak voltage in the SIW combline resonator can be found at the capacitive patch as (10) where (11) It should be noted that for the case is small, the SIW combline resonator behaves as a lumped element resonator, and therefore, the values found with (10) are the same as those obtained with (7). The air ionization is a phenomenon linked to the electric field strength rather than to the voltage [27], [30]. So, the electric field strength must be estimated in the capacitive patch of the resonators forming the filter. Although the electric field distribution along the air gap is not evident, as a fast approximation the maximum electric field in each resonator can be computed as (12) where is the annular gap of the resonator . For high pressure regime (pressures mbar), the air ionization breakdown

where is the pressure in torr and is the operation frequency in GHz. At this point, from (12) and (13) the PPHC can be analytically computed in filters based on combline resonators for high pressure regime. For low pressure regime, the continuity equation describing the electron density evolution must be solved. This arduous task must be done numerically, in this work the software tool AURORASAT™ SPARK3D® is employed. This tool uses the real electromagnetic field distribution of the device under test in order to solve the continuity equation, and provides the power breakdown threshold of the device from some input parameters such as pressure, kind of gas (air or nitrogen) or temperature. As a validation example, the PPHC is computed for the quasi-elliptic filter by using the equations derived in the previous lines and by using SPARK3D. The input parameters are GHz (where the voltage is maximum, which happens at the capacitive patch of resonator #2; this frequency coincides with the frequency of maximum losses) and mbar. From the derived equations, PPHC is analytically calculated as 7.3 W whereas from SPARK3D is 11.2 W. If the maximum electric field strength of the structure is simply taken from an electromagnetic tool (such as HFSS or CST; note that a normalization could be needed depending on the software used), and by applying the rule (13), the obtained PPHC is 0.9 W, which is a value considerably lower than those previously obtained. From these results, it can be concluded that taking the maximum electric field from the EM simulation results, which is indeed a strategy commonly used for waveguides or coaxial resonators, gives a very conservative limit for PPHC in SIW combline resonators. This is due to the fact that the maximum electric field values are very concentrated around the capacitive patch edges, in a region involving just some microns, which is not enough to alter the electron density. Additionally, some field singularities could appear in the resolution of the field around such corner edges. Another conclusion is that the approximation made in (12) gives a reasonable value of electric field strength in order to determine the PPHC. Fig. 23 shows the Paschen curves of the filter for each resonator, obtained from SPARK3D at the frequency where losses and voltage magnification are maximum. Resonator #2 is limiting the PPHC, as expected. The critical pressure is around 5–10 mbar, where PPHC is just 0.6 W. So, it is presumed that in a low pressure regime corona limits PHC rather than the thermo-mechanical effects. An interesting effect has been also detected in this filtering structure: due to the sharp shape of the first (and fourth) resonator corners (see Fig. 24), it is found that there is a high concentration of electric field density around those corners, providing higher values of electric field strength than those of resonator #2. Thus, resonator #1 may limit the PPHC of the filter even though the voltage in this resonator is lower than that in resonator #2 at the frequency of analysis. However, after fabrication, those corners are rounded, as seen in Fig. 24(b), leading to a reduction of the electric field density around them. Fig. 24(c) shows the simulated Paschen Curves for

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Fig. 24. Zoom in of the resonator #1. (a) Layout. (b) Fabricated. (c) Simulated Paschen Curves comparison between the sharp and rounded corner cases.

Fig. 23. Simulated Paschen Curves for the resonators involved in the filter under test. (a) Critical pressure region. (b) The whole pressure range. In this GHz and C. simulation,

the first resonator when the corners are sharped and rounded. As deduced from this figure, rounding the corners can considerably increase PPHC in this filter topology. In Fig. 23 the Paschen Curve of resonator #1 corresponds to the rounded corner case. Obviously, for both cases the filter response remains constant. C. APHC and PPHC Measurements In order to validate the calculated and simulated results, high power measurements have been performed at the European High-Power RF Space Laboratory (Valencia, Spain). Fig. 25 shows a schematic diagram of the employed test-bed. Several methods have been used for the corona discharge detection: third harmonic detection, nulling of the forward/reverse power at the operation frequency, electron probe and by visual inspection by recording the circuit with a video camera. The applied signal to the filter has been a pulsed signal with a carrier frequency of 5.75 GHz (frequency where the voltage magnification and losses are maximum in the measured filter), a pulse width of 20 s and a duty cycle of 1%. These pulsed signal characteristics avoid any self-heating effect in the device, whereas the pulse width is wide enough to assume that the pulse breakdown threshold converges to the CW one. The PPHC has been evaluated for different pressures in order to obtain the Paschen Curves of the device. In Fig. 23 the measured data can be also observed. For all scenarios corona breakdown has firstly appeared in resonator #2, as expected. There is a reasonable good agreement (especially at

lower pressures) with the simulated results what validates the theoretical prediction and the study done. The maximum difference between the measured and simulated breakdown field levels has been of 45%, which has been found for a pressure of 600 mbar. Fig. 26 shows the capture from the video camera at the moment of a corona discharge has occurred. As seen, the spark is uniformly originated along the annular slot. With respect to the APHC measurement, a CW signal at the same frequency has been applied to the circuit at ambient pressure ( mbar) and temperature. The temperature has been measured by means of thermocouples attached to the resonators in regions where their impact is low. The circuit was suspended so that natural convection can be assumed on all faces. The thermal steady-state was reached after around 5 minutes the signal is switched on. The measured temperatures for the different CW applied signal power samples have been close to the analytically calculated and simulated values, with differences lower than 20%. Up to 5 W there were no evidences of any rupture point in the circuit, however W should be avoided since temperatures higher than 150 C were measured. Furthermore, for W a frequency shift started being noticed in the measured response as well as a considerable increase of losses. After switching on/off the applied signal, the circuit could recover its original electromagnetic performance, although probably with a slight permanent material deformation. The CW applied power was increased up to obtain the complete failure of the device. The circuit was finally destroyed by a continuous corona discharge which occurred for W. This value is lower than the one measured at ambient pressure for the pulsed signal case and shown in Fig. 23. This can be due to the following reasons: the air temperature was much higher because of self-heating, which reduces the corona breakdown threshold for high pressure regime and, because corona breakdown thresholds are normally lower for the CW case than for

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Fig. 25. Scheme of the testbed configuration used for corona breakdown detection.

the power handling measurements. They also acknowledge Val Space Consortium for its contribution—Laboratories funded by the European Regional Development Fund—A way of making Europe. We would like also to thank the “Lab-STICC Computing Platform” at the University of Brest (France) for their support in order to perform the multiphysics simulations. REFERENCES Fig. 26. Capture of a corona discharge at the second resonator of the filter under test.

the pulsed signal case, unless a very wide pulsed signal width is used. VI. CONCLUSION In this paper the design of SIW combline resonator filters with advanced performances has been investigated. For this aim, different coupling configurations involving magnetic and electric coupling mechanisms have been proposed and studied in detail. It has been demonstrated that the proposed electric coupling configuration provides a high flexibility in filter design, which allows us to design very compact filters by keeping a reasonable level of losses, as well as to increase the maximum achievable passband bandwidth in SIW coaxial technology. Additionally, it has been proposed such a filter where the magnetic and electric coupling schemes has been arranged in order to design a very compact quasi-elliptic narrowband bandpass filter, presenting a very selective response with a wide rejection band. The power handling capability (both average and peak) has been also studied for such filtering structures from a multiphysics point of view. As it has been shown, these filters can afford moderate levels of power in spite of their small circuit area and narrow band. All concepts have been validated by the simulation and measurement of some fabricated proof-of-concept filtering devices. High power measurements have been also carried on, which have verified the proposed multiphysics study. ACKNOWLEDGMENT The authors would like to thank M. Reglero and M. Taroncher for their valuable help and discussions with the realization of

[1] X.-P. Chen and K. Wu, “Substrate integrated waveguide filters: Practical aspects and design considerations,” IEEE Microw. Mag., vol. 15, no. 7, pp. 75–83, Nov. 2014. [2] N. Grigoropoulos, B. Sanz-Izquiredo, and P. Young, “Substrate integrated folded waveguides (sifw) and filters,” IEEE Microw. Wireless Compon. Lett., vol. 15, no. 12, pp. 829–831, Dec. 2005. [3] Y. Wang, W. Hong, Y. Dong, B. Lui, H. Tang, J. Chen, X. Yin, and K. Wu, “Half mode substrate integrated waveguide (hmsiw) bandpass filter,” IEEE Microw. Wireless Compon. Lett., vol. 17, no. 4, pp. 265–267, Apr. 2007. [4] C. Jin and Z. Shen, “Compact triple-mode filter based on quarter-mode substrate integrated waveguide,” IEEE Trans. Microw. Theory Tech., vol. 62, no. 1, pp. 37–45, Jan. 2014. [5] Y. D. Dong, T. Yang, and T. Itoh, “Substrate integrated waveguide loaded by complementary split-ring resonators and its applications to miniaturized waveguide filters,” IEEE Trans. Microw. Theory Tech., vol. 57, no. 9, pp. 2211–2223, Sep. 2009. [6] L.-S. Wu, L. Zhou, X.-L. Zhou, and W.-Y. Yin, “Bandpass filter using substrate integrated waveguide cavity loaded with dielectric rod,” IEEE Microw. Wireless Compon. Lett., vol. 19, no. 8, pp. 491–493, Aug. 2009. [7] J. D. Mart´ınez, S. Sirci, M. Taroncher, and V. E. Boria, “Compact CPW-Fed combline filter in substrate integrated waveguide technology,” IEEE Microw. Wireless Compon. Lett., vol. 22, no. 1, pp. 7–9, Jan. 2012. [8] R. Levy, “Filters with single transmission zeros at real or imaginary frequencies,” IEEE Trans. Microw. Theory Tech., vol. MTT-24, no. 4, pp. 172–181, Apr. 1976. [9] J. Thomas, “Cross-coupling in coaxial cavity filters-A tutorial overview,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 4, pp. 1368–1376, Apr. 2003. [10] X. Chen, W. Hong, T. Cui, J. Chen, and K. Wu, “Substrate integrated waveguide (SIW) linear phase filter,” IEEE Microw. Wireless Compon. Lett., vol. 15, no. 11, pp. 787–789, Nov. 2005. [11] J. D. Mart´ınez, S. Sirci, and V. E. Boria, “Compact substrate integrated waveguide filter with asymmetric frequency response for c-band wireless applications,” in Proc. IEEE MTT-S Int. Wireless Symp. (IWS), Beijing, China, Apr. 2013, pp. 1–4. [12] X. P. Chen and K. Wu, “Substrate integrated waveguide cross-coupled filter with negative coupling structure,” IEEE Trans. Microw. Theory Tech., vol. 56, no. 1, pp. 142–149, Jan. 2008.

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[13] G. H. Lee, C. S. Yoo, J. G. Yook, and J. C. Kim, “Siw quasi-elliptic filter based on LTCC for 60-GHz application,” in Proc. 4th Eur. Microw. Integ. Circuits Conf., Sep. 2009, pp. 204–207. [14] K. Gong, W. Hong, Y. Zhang, P. Chen, and C. J. You, “Substrate integrated waveguide quasi-elliptic filters with controllable electric and magnetic mixed coupling,” IEEE Trans. Microw. Theory Tech., vol. 60, no. 10, pp. 3071–3078, Oct. 2012. [15] B. Potelon, J. Favennec, C. Quendo, E. Rius, C. Person, and J. Bohorquez, “Design of a substrate integrated waveguide (SIW) filter using a novel topology of coupling,” IEEE Microw. Wireless Compon. Lett., vol. 18, no. 9, pp. 596–598, Sep. 2008. [16] W. Shen, W. Y. Yin, X. W. Sun, and L. S. Wu, “Substrate-integrated waveguide bandpass filters with planar resonators for system-on-package,” IEEE Trans. Compon. Packag. Manufact. Technol., vol. 3, no. 2, pp. 253–261, Feb. 2013. [17] F. Zhu, W. Hong, J. X. Chen, and K. Wu, “Cross-coupled substrate integrated waveguide filters with improved stopband performance,” IEEE Microw. Wireless Compon. Lett., vol. 22, no. 12, pp. 633–635, Dec. 2012. [18] S. Sirci, F. Gentili, J. D. Mart´ınez, V. Boria, and R. Sorrentino, “Quasi-elliptic filer based on SIW combline resonators using a coplanar line cross-coupling,” in Proc. IEEE MTT-S Int. Microw. Symp. Dig., Phoenix, AZ, USA, May 2015, pp. 1–4. [19] J. S. Hong, Microstrip Filter for RF/Microwave Applications, 2nd ed. Hoboken, NJ, USA: Wiley, Feb. 2011. [20] S. Sirci, J. Mart´ınez, R. Stefanini, P. Blondy, and V. Boria, “Compact SMD packaged tunable filter based on substrate integrated coaxial resonators,” in Proc. IEEE MTT-S Int. Microw. Symp. Dig., Tampa Bay, FL, USA, Jun. 2014, pp. 1–4. [21] J. Lee, E. J. Naglich, H. Sigmarsson, D. Peroulis, and W. J. Chappell, “Tunable inter-resonator coupling structure with positive and negative values and its application to the field-programmable filter array (FPFA),” IEEE Trans. Microw. Theory Tech., vol. 59, no. 12, pp. 3389–3400, Dec. 2011. [22] K. C. Gupta, R. Garg, I. J. Bahl, and P. Bhartia, Microstrip Lines and Slotlines, 2nd ed. Boston, MA, USA: Artech House, 1996. [23] M. Sanchez-Soriano, Y. Quere, V. Le Saux, C. Quendo, and S. Cadiou, “Average power handling capability of microstrip passive circuits considering metal housing and environment conditions,” IEEE Trans. Compon., Packag., Manufact. Technol., vol. 4, no. 10, pp. 1624–1633, Oct. 2014. [24] M. Sanchez-Soriano, M. Edwards, Y. Quere, D. Andersson, S. Cadiou, and C. Quendo, “Mutiphysics study of rf/microwave planar devices: Effect of the input signal power,” in Proc. 15th EuroSime, Apr. 2014, pp. 1–7. [25] I. Bahl and K. Gupta, “Average power-handling capability of microstrip lines,” IEE J. Microw. Opt. Acoust., vol. 3, no. 1, pp. 1–4, 1979, UK. [26] C. Ernst and V. Postoyalko, “Prediction of peak internal fields in directcoupled-cavity filters,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 1, pp. 64–73, Jan. 2003. [27] M. Yu, “Power-handling capability for rf filters,” IEEE Microw. Mag., vol. 8, no. 5, pp. 88–97, Oct. 2007. [28] R. E. Collin, Foundations for Microwave Engineering. Hoboken, NJ, USA: Wiley, 2007. [29] M. Sánchez-Soriano, E. Bronchalo, and G. Torregrosa-Penalva, “Parallel-coupled line filter design from an energetic coupling approach,” IET Microw., Antennas, Propag., vol. 5, no. 5, pp. 568–575, Apr. 2011. [30] R. J. Cameron, C. M. Kudsia, and R. R. Mansour, Microwave Filters for Communication Systems. Hoboken, NJ, USA: Wiley-Interscience, 2007. [31] W. Woo and J. DeGroot, “Microwave absorption and plasma heating due to microwave breakdown in the atmosphere,” Phys. Fluids, vol. 27, no. 2, pp. 475–487, 1984. Stefano Sirci (S'14) received the B.S. and M.S. degrees (with distinction) in electronic engineering from the University of Perugia, Perugia, Italy, in 2006 and 2009, respectively. In 2009, he received the M.S. degree in efficient modal computation in arbitrarily shaped waveguides by BI-RME Method with the Polytechnic University of Valencia, Valencia, Spain, where he is currently working toward the Ph.D. degree. From 2010 to 2015, he has been with the Microwave Application Group (GAM) at the Institute of Telecommunications and Multimedia Applications (iTEAM) at the Polytechnic

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University of Valencia. His working is focused on emerging technologies for reconfigurable microwave components with emphasis on designing, fabrication and measurement of tunable microwave SIW filters, in PCB and LTCC technologies.

Miguel Ángel Sánchez-Soriano (S'09–M'13) was born in Yecla (Murcia), Spain, in 1984. He received the Telecommunications Engineer degree (with a Special Award) and the Ph.D. degree in electrical engineering from the Miguel Hernandez University (UMH), Spain, in 2007 and 2012, respectively. In 2007 he joined the Radiofrequency Systems Group, UMH, as a research assistant. He was a Visiting Researcher with the Microwaves Group headed by Prof. Jia-Sheng Hong at Heriot–Watt University, Edinburgh, U.K., in 2010. In January 2013 he joined the LabSTICC group, Université de Bretagne Occidentale, Brest, France, as a Postdoctoral Researcher, where he worked for 2 years. Since January 2015, he is a “Juan de la Cierva” research fellow at the “Grupo de Aplicaciones de Microondas” (GAM), Polytechnic University of Valencia, Spain. His research interests cover the analysis and design of microwave planar devices, especially filters and their reconfigurability, and the multiphysics study of high frequency devices. Dr. Sánchez-Soriano was the recipient of the runner-up HISPASAT award to the Best Spanish Doctoral Thesis in New Applications for Satellite Communications, awarded by the Spanish Telecommunication Engineers Association (COIT/AEIT), and the Extraordinary Ph.D. award from the Miguel Hernndez University. He serves as a reviewer for various journals and conferences, including the IEEE TRANSACTIONS ON MICROWAVES, THEORY AND TECHNIQUES, the IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS and the IET Microwaves, Antennas and Propagation.

Jorge D. Mart´ınez (M'09) was born in Murcia, Spain. He received the degree in telecommunication engineering and the Ph.D. degree from Polytechnic University of Valencia (UPV), Valencia, Spain, in 2002 and 2008, respectively. He is currently Associate Professor at the School of Telecommunication Engineering of the Polytechnic University of Valencia (UPV) since 2012. He joined the Department of Electronics Engineering of the UPV in 2002 as a Research Fellow, and became Assistant Professor in 2009. During 2007 he was a Research Visitor at XLIM, CNRS and University of Limoges, France, where he worked on the design and fabrication of RF MEMS components under the advice of Prof. Pierre Blondy. He is a Researcher of the I3M R&D institute at UPV, where he actively collaborates with the Microwave Applications Group (GAM). At I3M premises, he is now the Technical Responsible of the Laboratory for High Frequency Circuits Fabrication (LCAF) of the UPV, focused on Low Temperature Co-fired Ceramics (LTCC) and other related multi-layered technologies. His current research interests are focused on emerging technologies for reconfigurable microwave components with emphasis on tuneable filters and RF MEMS, and the design and fabrication of advanced microwave filters in planar and substrate integrated waveguide technologies, as well as the application of multi-layer fabrication technologies to RF/microwave and millimetre-wave applications.

Vicente E. Boria (S'91–A'99–SM'02) was born in Valencia, Spain. . He received the Ingeniero de Telecomunicacin degree (first-class honors) and the Doctor Ingeniero de Telecomunicacin degree from the Polytechnic University of Valencia, Valencia, Spain, in 1993 and 1997, respectively. In 1993 he joined the Departamento de Comunicaciones, Polytechnic University of Valencia, where he has been Full Professor since 2003. In 1995 and 1996, he was holding a Spanish Trainee position with the European Space Research and Technology Centre, European Space Agency (ESTEC-ESA), Noordwijk, The Netherlands, where he was involved in the area of EM analysis and design

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of passive waveguide devices. He has authored or co-authored 10 chapters in technical textbooks, 125 papers in refereed international technical journals, and over 175 papers in international conference proceedings. His current research interests are focused on the analysis and automated design of passive components, left-handed and periodic structures, as well as on the simulation and measurement of power effects in passive waveguide systems. Dr. Boria has been a member of the IEEE Microwave Theory and Techniques Society (IEEE MTT-S) and the IEEE Antennas and Propagation Society (IEEE AP-S) since 1992. He is member of the Editorial Boards of the IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, Proceeding of the IET (Microwaves, Antennas and Propagation), IET Electronics Letters and Radio Science. Since 2013, he serves as Associate Editor of IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS. He is also a member of the Technical Committees of the IEEE-MTT International Microwave Symposium and of the European Microwave Conference.

Fabrizio Gentili (GSM'12–A'14) was born in Foligno, Italy. He received the Master Laurea degree (with distinction) in electronic engineering and the Ph.D. degree from the University of Perugia, Perugia, Italy, in 2010 and 2014, respectively. His doctoral dissertation concerned innovative solutions for RF and microwave filters. In 2009, he carried out his Master thesis on photonic nanoantennas with the University of Bristol, Bristol, U.K. In March 2010, he joined RF Microtech, where his research concerned the design of antennas and passive microwave components. Since April 2014, he has been a Post-Doctoral Researcher with the Institute of Microwave and Photonic Engineering, Graz University of Technology, Graz, Austria.

Wolfgang Bösch (F’13) received the engineering degrees from the Technical University of Vienna, Vienna, Austria, and Technical University of Graz, Austria. He received the M.B.A. (with distinction) at Bradford University School of Management, U.K., in 2004. He joined the Graz University of Technology, Austria, in March 2010 to establish a new Institute for Microwave and Photonic Engineering. Previously he was the CTO of the Advanced Digital Institute in the U.K., a not-for-profit organization to promote research activities. He has also been the Director of Business and Technology Integration of RFMD UK. For almost 10 years he has been with Filtronic plc as CTO of Filtronic Integrated Products and Director of the Global Technology Group. Prior to joining Filtronic, he held positions in the European Space Agency (ESA) working on amplifier linearization techniques, MPR-Teltech in Canada working on MMIC technology projects and the Corporate R&D group of M/A-COM in Boston, MA, USA, where he worked on advanced topologies for high efficiency power amplifiers. For four years he

was with Daimler-Chrysler Aerospace in Germany, working on T/R Modules for airborne radar. He has published more than 80 papers and holds 4 patents. Dr. Bösch is a Fellow of the IET. He was a Non-Executive Director of Diamond Microwave Devices (DMD) and the Advanced Digital Institute (ADI). Currently he is a Non-Executive Director of VIPER-RF (U.K.).

Roberto Sorrentino (LF'90) is a Professor at University of Perugia, Perugia, Italy, where he was the Chairman of the Electronic Department, Director of the Computer Center (1990–1995), and Dean of the Faculty of Engineering (1995–2001). His research activities have been concerned with various technical subjects, but mainly with numerical methods and CAD techniques for passive microwave structures and the analysis and design of microwave and millimetre-wave circuits including filters and antennas. In recent years he has been involved in the modelling and design of Radio Frequency Microelectromechanical Systems (RF-MEMS) and their applications on tuneable and reconfigurable circuits and antennas. He is the author or co-author of more than 150 technical papers in international journals and 200 refereed conference papers. He has edited a book Numerical Methods for Passive Microwave Structures (IEEE Press, 1989) and co-authored four books: Advanced Modal Analysis (with M. Guglielmi and G. Conciauro) (Wiley, 2000); RF and Microwave Engineering (in Italian) (with G. Bianchi) (McGrawHill, 2006); Electronic Filter Simulation and Design (with G. Bianchi) (McGrawHill, 2007); RF and Microwave Engineering, (with G. Bianchi) (J. Wiley, 2010). Dr. Sorrentino 1990 he became a Fellow of the IEEE for contribution to the modelling of planar and quasi-planar microwave and millimetre-wave circuits. He has received several international awards and recognitions: in 1993 the IEEE MTT-S Meritorious Service Award, in 2000 the IEEE Third Millennium Medal, in 2004 the Distinguished Educator Award from IEEE MTT-S, in 2010 the Distinguished Service Award from the European Microwave Association, in 2012, together with S. Bastioli and C. Tomassoni, the Microwave prize for the paper “A New Class of Waveguide Dual-Mode Filters Using TM and Nonresonating Modes.” In 2015 he was awarded the Microwave Career Award from the IEEE MTT-Society. He has been active within the IEEE MTT Society. From 1984 through 1987 he was the Chairman of the IEEE Section of Central and South Italy and was the founder of the local MTT/AP Chapter that he chaired from 1984 to 1987. From Jan. 1995 through April 1998 he was the Editor-in-Chief of the IEEE MICROWAVE AND GUIDED WAVE LETTERS. From 1998 to 2005 he has served on the Administrative Committee of the IEEE Microwave Theory and Techniques Society. He was elected again in MTT AdCom for the term 2011–2013. He is also a member of Technical Committees MTT-15 on Field Theory and MTT-1 on Computer-Aided Design, which he chaired in 2003–04. He served the International Union of Radio Science (URSI) as Vice Chair (1993–1996) then Chair (1996–1999) of the Commission D (Electronics and Photonics). Since 2007 he is the President of the Italian Commission of URSI. In 2002 he was among the founders and first President of the Italian Electromagnetic Society (SIEm) that he chaired until 2008. From 1998 to 2005 he was a member of the High Technical Council of the Italian Ministry of Communications. In 1998 he was one of the founders of the European Microwave Association (EuMA) and was its President till 2009. In 2007, he founded RF Microtech, a spin-off company of the University if Perugia dealing with RF MEMS, microwave systems and antennas.

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Exact Design of a New Class of Generalized Chebyshev Low-Pass Filters Using Coupled Line/Stub Sections Evaristo Musonda, Graduate Student Member, IEEE, and Ian C. Hunter, Fellow, IEEE Abstract—A method for the design of a new class of distributed low-pass filters enables exact realization of the series short-circuited transmission lines, which are normally approximated via unit elements in other filter realizations. The filters are based upon basic sections using a pair of coupled lines, which are terminated at one end in open-circuited stubs. The approach enables realization of transmission zeros at the quarter-wave frequency, hence giving improved stopband performance. A complete design theory starting from a distributed generalized Chebyshev low-pass prototype filter is presented. A design example demonstrates excellent performance in good agreement with theory. Index Terms—Distributed low-pass filters, generalized Chebyshev, meander line, selectivity, TEM.

I. INTRODUCTION

L

OW-PASS filters are often needed in microwave systems to “clean up” spurious responses in the stopband of coaxial and dielectric resonator filters. The most important driving factors are compact size, sharp roll-off, and wide stopband. Some of the recent works have addressed some of these problems [1], [2]. Although it is relatively easy to obtain theoretical circuit models, the challenge in practical low-pass filters lies in achieving good approximation using real transmission-line components. There exist many realizations for low-pass filters. One popular type is the stepped impedance low-pass filter consisting of interconnections of commensurate lengths of transmission lines of alternating low and high impedance [3]. This type of filter has low selectivity for a given network order because the transmission zeros are all at infinity on the real axis in the complex plane. In order to increase selectivity, transmission zeros may be placed at finite frequencies using distributed generalized Chebyshev low-pass prototype filters [4]. The problem is that there is no direct realization of the series short-circuited stubs associated with this prototype filter. In the existing physical realization [5], the series short-circuited stubs are approximated by short lengths of the high-impedance transmission line (forcing those transmission zeros at a quarter-wave frequency to move Manuscript received June 24, 2015; revised September 15, 2015; accepted October 11, 2015. Date of publication October 29, 2015; date of current version December 02, 2015. This work was supported in part by the Beit Trust, in part by The University of Leeds, in part by RS Microwave Inc., in part by Radio Design Limited, and in part by The Royal Academy of Engineering. This paper is an expanded version from the IEEE MTT-S International Microwave Symposium, Phoenix, AZ, USA, May 17–22, 2015. The authors are with the Institute of Microwave and Photonics, School of Electronic and Electrical Engineering, University of Leeds, LS2 9JT Leeds, U.K. (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2015.2492969

Fig. 1. Proposed layout of meander-like low-pass filter: (a) composed of a section of high-impedance parallel coupled lines short circuited by a low-impedance open-circuited stub at alternate ends and (b) graphical line equivalent circuit.

to infinity on the real axis), while the shunt series foster is realized exactly as an open-circuited stub of double unit length. The approximation involved results in relatively poor stopband rejection. As an expansion to the work described in [6], this paper presents two solutions in which the series short-circuited stubs are exactly realized within the equivalent circuit of the filter. In Section II, the synthesis techniques for the two physical realizations have been developed. In the previous paper, only the equivalent circuit for the second low-pass filter physical realization was known and the element values were obtained via optimization in a circuit simulator. In this revised and expanded paper, the synthesis is developed and presented together with the required canonical low-pass circuit forms and corresponding transmission zeros that the transfer functions may realize. The procedure for different low-pass filter degrees is included with the required circuit transformations, which was a significant piece of work. Design examples are included to illustrate the synthesis technique. II. DESIGN THEORY In Fig. 1, the general physical layout is given for the proposed method. The structure consists of a middle section of high-impedance coupled lines terminated at every alternate end in a low-impedance open-circuit stub forming a “meander-like” structure, as in Fig. 1. All the transmission lines are of commensurate length. Grounded decoupling walls

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Fig. 2. Derived equivalent circuit transformations (*may be a hanging node).

must be utilized to eliminate coupling between the open-circuited stubs. In this work it is shown how a general Chebyshev transfer function may be used to implement two alternative realizations

arising from Fig. 1 via a series of derived circuit transformations and one of the earlier transformation derived by Sato in [7, Table I]. The synthesis of distributed low-pass filter networks is based on work done in [8]. Fig. 2 shows the derived equiv-

MUSONDA AND HUNTER: EXACT DESIGN OF A NEW CLASS OF GENERALIZED CHEBYSHEV LOW-PASS FILTERS

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TABLE I 7 -DEGREE LOW-PASS FILTER SYNTHESIZED ADMITTANCE VALUES

Fig. 4. Graphical representation of the equivalent circuit of Fig. 3 after transformation of the 3 -degree basic sections.

Fig. 3. Generalized Chebyshev distributed low-pass prototype.

alent-circuit transformations and the required admittance relationships. The next two sections describe how these transformations were used to derive the equivalent circuit for the two possible physical realizations from their canonical low-pass filter derivatives.

Fig. 5. Basic section containing a pair of coupled line and a stub and its equivalent circuits.

A. Physical Realization I The first physical realization realizes the equivalent circuit for the general Chebyshev distributed network given in Fig. 3. By using the synthesis technique given in [8], the network of Fig. 3 may be synthesized directly in the distributed domain from an ( odd) degree Chebyshev transfer function with pairs of symmetrically located transmission zeros and a single transmission zero at a quarter-wave frequency . simply refers to an -deIn this work, gree low-pass filter with number of transmission zeros at some general frequency in the complex plane, number of transmission zeros at quarter-wave frequency (i.e., ), and number of real axis half transmission zero pairs at infinity (i.e., ). Where exists, these transmission zeros may either be symmetrically pure imaginary frequency pairs (i.e., ) or in general paraconjugated pairs on the complex plane (i.e., ) is always even. Therefore, in general, the dissuch that tributed network of Fig. 3 is of the form . Using circuit transformation I on each of the 3 -degree sections, Fig. 3 may be transformed into Fig. 4. It is then clear from Fig. 4 that each of the 3 -degree sections is just the equivalent circuit of a pair of two parallel coupled lines with one end terminated in an open circuited stub, as depicted in Fig. 5. The overall network after the transformation is illustrated in Fig. 6. This is equivalent to Fig. 1(a), but with every second coupling between the parallel coupled lines section removed [i.e., couplings , , removed in Fig. 1(b)], such that the structure is composed of cascaded 3 -degree basic sections of Fig. 5, as shown in Fig. 6.

Fig. 6. Physical layout for generalized Chebyshev distributed low-pass prototype filter of physical realization I. TABLE II 7 -DEGREE LOW-PASS FILTER IMPEDANCE VALUES TRANSFORMATION II (A)–(C) IN 50- SYSTEM

AFTER

1) Design Example: A 7 -degree low-pass filter was designed using the techniques described above with cutoff frequency at 1 GHz, 20-dB minimum passband return loss with pairs of finite transmission zeros at and (2.18, 1.72, and 2.18 GHz), and a single quarterand electrical length at wave transmission zero

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Fig. 8. Physical layout of the striplines for the general meander-like low-pass filter with allowed coupling between parallel lines of the adjacent basic sections.

Fig. 7. Circuit and HFSS simulation response for example I.

the cutoff frequency, . The element values are shown in Table I corresponding to the circuit of Fig. 3 where symmetry is assumed for the element values. Using circuit transformation I, the circuit was transformed to the final form of Fig. 4 with the element values shown in Table II. All the element values are clearly realizable. Fig. 7 shows the circuit simulation of the design example. In this realization I, is approaching practical limits for realizable element values. Reducing the electrical length at the cutoff frequency further causes the impedance values of the high- and low-impedance lines to become unrealizably high and low, respectively. However, in reality the practical stopband bandwidth is perturbed due to high-order modes and spurious couplings between the basic sections, as shown by the HFSS simulation in Fig. 7 with small resonance peaks around . The decoupling walls do not give exact circuit realization for realization I. In the second physical realization, however, some of the couplings are allowed between basic sections. B. Physical Realization II—“Meander-Like” Low-Pass Filter A more general realization is achieved by using the layout of Fig. 1. The only difference with the previous physical realization I is that, in the general case, physical realization II, all the couplings between high-impedance coupled lines of Fig. 1 are allowed. The structure is built from the basic 3 -degree section of Fig. 5 by adding a parallel line to the parallel coupled lines section and an open-circuited stub at one end to form an interconnect each time to increase the network degree by 2. The stripline layout for physical realization II is given in Fig. 8 and its derived equivalent circuit is shown in Fig. 9 with the unit element impedance values named sequentially from input to output. This realization is optimal since an -degree filter requires commensurate length transmission lines. At the quarter-wave frequency, all the series short-circuited stubs become open circuited while all the open-circuited stubs become short circuited so that the alternate ends of the parallel coupled lines are shorted to ground. Thus, the meander-like low-pass filter of Fig. 8 has at least one transmission zero at the quarter-wave frequency. The other transmission zero pairs may exist at infinity on the real axis or as symmetrical pure imag-

Fig. 9. Graphical representation of the equivalent circuit of Fig. 8 for a meander-like low-pass filter.

inary frequency pair or, in general, as paraconjugated pairs on the complex plane due to multipath in the structure. It is now shown how the meander-like low-pass filter network of Figs. 8 and 9 may be synthesized from suitable low-pass filter networks and then using appropriate circuit transformation to transform the canonical low-pass filter network forms to a meander-like low-pass filter. The canonical low-pass filter network forms were obtained by the synthesis method in [8] and then applying cascaded synthesis. The 3 , 5 , 7 , and 9 -degree meander-like low-pass filter are examined next, as depicted in Fig. 10. The 3 -degree filter is simply a trivial case corresponding to circuit transformations I, as shown in Fig. 10 (I). In this case, a 3-0-3 or 3-2-1 low-pass filter may be realized. There are two possible cases for the 5 -degree filter, namely, a 5-0-4 and 5-2-2 low-pass filter. For the first case of Fig. 10 (II), a 5-0-4 low-pass filter has a single real axis half transmission zero pair at infinity and four transmission zeros are at a quarter-wave frequency . Beginning with the canonical network form, step 1 is to split the transmission lines into two equal parts between ports 2 and 4. In step 2, transformation III is carried out on each of the branches 3,2,4 and 2,4,5 respectively. Finally in step 3, two separate transformations II are carried out on each of the three port subnetworks of 1,3,5 and 3,5,6 to derive the final equivalent circuit, as illustrated in Fig. 10 (II). The second meander-like low-pass filters, the 5-2-2 low-pass filter in Fig. 10 (III and IV), have a single pair of symmetrical finite frequency transmission zeros , a single real axis half transmission zero pair at infinity , and two transmission zeros at the quarter-wave frequency . For an asymmetrical 5-2-2 case of Fig. 10 (III), step 1 utilizes Sato’s transformation [7, Table I] to eliminate branch 1,2 and in turn creates branches 1,3 and 1,5. In Step 2, Sato’s transformation is used again to eliminate branch 2,3 and creates branch

MUSONDA AND HUNTER: EXACT DESIGN OF A NEW CLASS OF GENERALIZED CHEBYSHEV LOW-PASS FILTERS

Fig. 10. Derived network transformation for

and

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meander-like low-pass filters.

3,5. In step 3, transformation III is applied on branch 1,5,6 and two sequential transformations III are applied on branch 1,3,5. The final equivalent circuit is obtained by application of transformation II on a three-port subnetwork of 4,6,7, as illustrated in Fig. 10 (III). For the symmetrical 5-2-2 low-pass filter of Fig. 10 (IV), step 1 splits the inductor between node 5 and 7 such that the admittances of the outermost inductors in branches 1,2 and 7,8 are identical. In step 2, transformation IV is carried out on the two-port network between nodes 2 and 7, and finally, two separate transformations II are carried out on three-port subnetworks 1,9,10 and 9,8,10, respectively, to obtain the final symmetrical form, as illustrated in Fig. 10 (IV). Note that a negative sign on in transformation IV should be taken for realizable impedance values. For a 7 -degree filter, one possible realization derived is a 7-2-5 low-pass filter of Fig. 10 (V) with a single pair of symmetrical finite frequency transmission zero pair and all the remaining five transmission zeros at the quarter-wave frequency , which is now illustrated. From the canonical low-pass filter form, transformation I is applied on the two-port network between nodes 2 and 7 in step 1. This is followed by transformation V again on the same two port network between nodes 2 and 7 in step 2. In step 3, two separate transformation III are then applied on branches 3,2,6 and 8,7,9 and finally, in step 4, three separate transformation II are applied on three port subnetworks of 1,3,5, 3,5,8, and 5,8,9, respectively, to obtained the final form of the meander-like low-pass filter of Fig. 10 (V). For a 9 -degree filter, two derivative low-pass filter networks were examined whose core subnetworks were derived from a 5 -degree network discussed above. The first one is a 9-0-8 filter with a single real axis half transmission zero pair at infinity and all the remaining eight transmission zeros at a quarter-wavelength frequency

. Beginning with the canonical low-pass filter in Fig. 10 (VI) in step 1, a two-port network between nodes 2 and 8 is replaced by a derived circuit for a 5-0-4 circuit as explained above [see Fig. 10 (II)]. In step 2, two separate transformations III are then applied to branches 3,2,7 and 5,8,9. This is followed by two separate transformations II, which are applied on three-port subnetworks of 1,3,5 and 7,9,10, respectively, to give the final equivalent circuit, as illustrated in Fig. 10 (VI). The second 9 -degree low-pass filter is a 9-2-6 low-pass filter with a single symmetrical pair of finite frequency transmission zeros , a single real axis half transmission zero pair at infinity , and all remaining six transmission zeros at a quarter-wave frequency . Beginning with the canonical low-pass filter form in Fig. 10 (VII) in step 1, a two-port network between nodes 2 and 9 is replaced by a derived circuit for a 5-2-2 circuit, as explained above [see Fig. 10 (III or IV)]. In step 2, two separate transformations III are then applied to branches 3,2,6 and 8,9,10, respectively. This is followed by two separate transformations II, which are applied on three-port subnetworks of 1,3,8 and 6,10,11, respectively, to give the final equivalent circuit shown in Fig. 10 (VII). Note that a positive sign on in transformation IV should be taken for realizable impedance values. Multiple solutions do exist depending on the transformations used. Impedance levels are within positive realizable values as long as the electrical length at the cutoff is chosen to be around as the two examples will show. Moving further away form , either direction tends to lead to extreme element’s impedance values, some of which may assume negative values arising from the formulas used in some of the cases of Fig. 2. As its canonical circuit form, the meander-like low-pass filter is relatively unaffected by small changes in the impedances values because it requires an optimal number of elements . Thus, small mismatch in the impedance values only slightly degrades the passband return loss.

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Fig. 10. (Continued.) Derived network transformation for

and

1) Design Example I: A 7 -degree (7-2-5) meander-like low-pass was designed with a symmetrical pair of finite frequency transmission zero at (1.625 GHz) and five transmission zeros at a quarter-wave frequency , 20-dB minimum passband return loss and electrical length of at a cutoff frequency of 1 GHz. The synthesized element values for the canonical low-pass filter is shown in Table III [assuming symmetry with impedance values assigned

meander-like low-pass filters.

sequentially from left to right of Fig. 10 (V)]. Using the technique as explained in Section II-B and Fig. 10 (V) by a sequence of circuit transformations, the meander-like element values were then obtained as shown in Table IV. The circuit simulation shown in Fig. 11 validates the synthesis process. 2) Design Example II: An experimental 9 -degree meander-like low-pass filter was designed with cutoff frequency at 1 GHz, 20-dB minimum return loss, and . The stop-

MUSONDA AND HUNTER: EXACT DESIGN OF A NEW CLASS OF GENERALIZED CHEBYSHEV LOW-PASS FILTERS

Fig. 10. (Continued.) Derived network transformation for

and

band insertion loss was defined to be above 70 dB between 1.3 and 2.7 GHz and this was achieved by placing a symmetrical transmission zero pair at (1.294 GHz), a single real axis half transmission zero pair at infinity and six transmission zeros at quarter-wave frequency

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yielding a 9-2-6 low-pass filter of Fig. 10 (VII). The synthesized element values for the canonical 9 -degree low-pass filter are shown in Table V. These values were transformed to the meander-like circuit with the element values shown in Table VI.

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Fig. 10. (Continued.) Derived network transformation for

and

TABLE III 7 -DEGREE CANONICAL LOW-PASS FILTER IMPEDANCE VALUES

The low-pass filter is then realized using rectangular bars or striplines. The technique by Getsinger [9], [10] was used to determine the initial physical dimensions. The final optimized dimensions are given in Table VII. The nomenclature used in Table VII corresponds to Figs. 13 and 14. Fig. 12 shows good correspondence between the measured and theoretical simulation using HFSS.

meander-like low-pass filters.

TABLE IV 7 -DEGREE MEANDER-LIKE LOW-PASS FILTER IMPEDANCE VALUES

The overall length of the low-pass filter realization is three times the electrical length at the cutoff frequency. High-order modes do exist in the structure that potentially could worsen the stopband response, especially with relatively larger groundplane spacing. The effect is to shorten the effective stopband frequency window as the design example shows in Fig. 12. The choice of the ground-plane spacing affects the spurious resonances within the filter structure, which in this case appeared

MUSONDA AND HUNTER: EXACT DESIGN OF A NEW CLASS OF GENERALIZED CHEBYSHEV LOW-PASS FILTERS

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Fig. 11. Circuit simulation of a 7-2-5 meander-like low-pass filter in example II B (1). TABLE V SYNTHESIZED 9 -DEGREE CANONICAL LOW-PASS FILTER IMPEDANCE VALUES

Fig. 13. Diagram showing the layout of the fabricated 9 -degree meander-like low-pass filter. Dimension shown are as given in Table VII. TABLE VI SYNTHESIZED 9 -DEGREE MEANDER-LIKE LOW-PASS FILTER IMPEDANCE VALUES

TABLE VIII IMPROVED 9 - DEGREE LOW-PASS FILTER OPTIMIZED DIMENSIONS (IN MILLIMETERS)

TABLE VII 9 - DEGREE LOW-PASS FILTER OPTIMIZED DIMENSIONS (IN MILLIMETERS)

Fig. 14. Physical hardware of the fabricated 9 -degree “meander-like” lowpass filter (top cover removed).

Fig. 12. Comparison of simulated response of the synthesized, HFSS, and measurement of meander-like low-pass filter.

above 2.6 GHz. The insertion loss is fairly low across the passband with a peak at 0.3476 dB at the cutoff frequency in the

measured response, as depicted in Fig. 15. The slight discrepancy in the insertion loss between the simulated and measurement results in Fig. 15 is due to a slight mismatched response, as evident from the return-loss plot in Figs. 12 and 16. Improvement in the stopband response may be achieved by reducing the ground-plane spacing from mm to mm at the expense of slightly increased insertion loss (Fig. 15). Fig. 16 shows HFSS simulations for different ground-plane spacing versus the ideal circuit response. Clearly

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Fig. 15. Comparison of insertion losses between HFSS simulations for mm and mm and measured response with mm.

Fig. 16. Comparison of optimized equivalent-circuit simulation and HFSS simulations of meander-like low-pass filter with ground-plane spacing of 15 and 25 mm.

the stopband performance matches very well with the prediction for mm. Table VIII shows the corresponding optimized physical dimensions. Notice that much smaller ground-plane spacing is limited by realizability of the physical dimensions as the dimensions of the low-pass filter are proportional to the ground-plane spacing. C. Comparison A 9 -degree meander-like low-pass filter was compared to other low-pass filter realizations. To achieve the same selectivity, a 9 -degree generalized Chebyshev low-pass filter would be required while a 15 -degree stepped-impedance low-pass filter would be required as depicted in Fig. 17 with electrical length at the cutoff frequency of 1 GHz. Thus, for the same selectivity, the proposed structure requires a much fewer number of filter elements than the stepped-impedance low-pass filter. Although the generalized Chebyshev low-pass filter may be designed with the same degree as the meander-like low-pass filter, its stopband performance is much poorer in its physical realization, as shown in Fig. 17, because the series short-circuited stubs are approximated by high-impedance transmission lines [3]. Furthermore, both the generalized Chebyshev and stepped-impedance low-pass filters’ effective stopband response is much worse in practice because it is difficult to realize ideal commensurate transmission-line elements and often discontinuities, high-order modes, and mode

Fig. 17. Circuit simulation comparison of 9 -degree meander-like low-pass filter with a 9 -degree generalized Chebyshev low-pass filter and 15 -degree stepped-impedance low-pass filter.

Fig. 18. Circuit insertion-loss simulation comparison of 9 -degree meanderlike low-pass filter with a 9 -degree generalized Chebyshev low-pass filter and 15 -degree stepped impedance low-pass filter.

conversion occurs within the filter structure [11]. These reduce the effective stopband width of practical low-pass filters to as much as half of the predicted width! Even though effective stopband width may be widened by using a lower electrical length at cutoff frequency, it is often limited by element realization as the variations in element values tend to be extreme. By utilizing relatively smaller ground-plane spacing, as described in Section II-B, the proposed low-pass structure offers superior stopband performance. Fig. 18 shows the circuit-level insertion-loss analysis of the three low-pass filters being compared above with the same ground-plane spacing of 25 mm assuming copper conductors in air. It is quite obvious that the stepped-impedance low-pass filter fairs worse because of the highest number of unit elements required to achieve the selectivity. The generalized Chebyshev low-pass filter passband insertion compares well with the proposed meander-like low-pass filter with the losses increasing towards the cutoff frequency. The proposed structure has an optimal number of unit elements equal to the degree of the network regardless of the number of finite frequency transmission zeros. The generalized Chebyshev low-pass filter, on the other hand, requires 12 unit elements to achieve the selectivity requirements. Thus, the proposed meander-like low-pass filter is much more compact with low insertion loss than the other two low-pass filters. The meander-like low-pass filter has a

MUSONDA AND HUNTER: EXACT DESIGN OF A NEW CLASS OF GENERALIZED CHEBYSHEV LOW-PASS FILTERS

high achievable roll-off rate of 246.7 dB/GHz with an achievable relative stopband bandwidth of 0.883 [12] and could be advantageous where a much deeper out-of-band rejection is required. III. CONCLUSION An exact design technique for realizing generalized Chebyshev distributed low-pass filters using a coupled line/stub without approximating the series short-circuited stubs has been demonstrated. The physical realization I has a simple equivalent circuit; however, it requires isolation walls to eliminate coupling between basic sections. Since a single basic section may realize a pair of finite frequency transmission zero, a maximum of pairs of symmetrically located transmission zeros is achievable. A more general meander-like structure, physical realization II, with an optimal number of elements and simple physical layout of transmission lines, has also been presented. Its physical realization does not require decoupling walls between the parallel coupled line section, and hence, is easier to construct. However, only certain forms of transfer functions are realizable as described above. Synthesis of a few realizations up to 9 -degree together with the required transmission zeros locations of their canonical forms have been illustrated. A low-pass filter design example utilizing the later physical realization was fabricated and measurement results showed good agreement with theory. Comparison with other low-pass filter realizations reviewed that the proposed low-pass filter has a much higher roll-off rate and deeper effective stopband. REFERENCES [1] H. M. Jaradat and W. M. Fathelbab, “Selective lowpass filters realizing finite-frequency transmission zeros,” in IEEE Radio Wireless Symp., 2009, pp. 252–255. [2] C. J. Chen, C. H. Sung, and Y. D. Su, “A multi-stub lowpass filter,” IEEE Microw. Wireless Compon. Lett., vol. 25, no. 8, pp. 532–534, Aug. 2015. [3] I. Hunter, Theory and Design of Microwave Filters. Stevenage, U.K.: IET, 2001. [4] J. D. Rhodes and S. Alseyab, “The generalized Chebyshev low-pass prototype filter,” Int. J. Circuit Theory Appl., vol. 8, pp. 113–125, 1980. [5] S. A. Alseyab, “A novel class of generalized Chebyshev low-pass prototype for suspended substrate stripline filters,” IEEE Trans. Microw. Theory Techn., vol. MTT-30, no. 9, pp. 1341–1347, Sep. 1982. [6] E. Musonda and I. Hunter, “Design of generalised Chebyshev lowpass filters using coupled line/stub sections,” in IEEE MTT-S Int. Microw. Symp. Dig., 2015, pp. 1–4.

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[7] R. Sato, “A design method for meander-line networks using equivalent circuit transformations,” IEEE Trans. Microw. Theory Techn., vol. MTT-19, no. 5, pp. 431–442, May 1971. [8] E. Musonda and I. Hunter, “Synthesis of general Chebyshev characteristic function for dual (single) bandpass filters,” in IEEE MTT-S Int. Microw. Symp. Dig., 2015, pp. 1–4. [9] W. J. Getsinger, “Coupled rectangular bars between parallel plates,” IRE Trans. Microw. Theory Techn., vol. MTT-10, no. 1, pp. 65–72, Jan. 1962. [10] M. A. R. Gunston, Microwave Transmission-Line Impedance Data. London, U.K.: Van Nostrand, 1972. [11] R. J. Cameron, C. M. Kudsia, and R. R. Mansour, Microwave Filters for Communication Systems: Fundamentals, Design, and Applications. Hoboken, NJ, USA: Wiley, 2007. [12] J. Wang, L. J. Xu, S. Zhao, Y. X. Guo, and W. Wu, “Compact quasielliptic microstrip lowpass filter with wide stopband,” Electron. Lett., vol. 46, pp. 1384–1385, 2010.

Evaristo Musonda (GSM’13) received the B.Eng degree (with distinction) from The University of Zambia, Lusaka, Zambia, in 2007, the M.Sc. degree in communication engineering (with distinction) from The University of Leeds, Leeds, U.K., in 2012, and is currently working toward his Ph.D. degree at The University of Leeds. In early 2008, he joined Necor Zambia Limited, an ICT company, prior to joining the country’s largest mobile telecommunication services provider, Airtel Zambia, in June 2008, where he was involved in core network planning, optimization, and support roles for three years. He is currently involved in research for new microwave filters synthesis techniques for digital wireless communication systems at The University of Leeds. His research interests include microwave filters and network synthesis.

Ian Hunter (M’82–SM’94–F’07) received the B.Sc. degree (first-class honors) and Ph.D. degree from Leeds University, Leeds, U.K., in 1978 and 1981, respectively. Early in his career, he was with Aercom, Sunnyvale, CA, USA, KW Engineering, San Diego, CA, USA, and Filtronic, Shipley, U.K., where he was involved with the development of broadband microwave filters for electronic warfare (EW) applications. From 1995 to 2001, he was with Filtronic Comtek, where he was involved with advanced filters for cellular radio. He currently holds the Royal Academy of Engineering/Radio Design Ltd. Research Chair in Microwave Signal Processing with the School of Electronic and Electrical Engineering, The University of Leeds, Leeds, U.K., where he currently leads a team involved with the research of new microwave filters for mobile communications systems. He has authored Theory and Design of Microwave Filters (IEE Press, 2001). Prof. Hunter is a Fellow of the IET and the U.K. Royal Academy of Engineering. He was general chair of 2011 European Microwave Week, Manchester, U.K. He is the chair of the 2016 European Microwave Conference, London, U.K.

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Propagating Waveguide Filters Using Dielectric Resonators Cristiano Tomassoni, Member, IEEE, Simone Bastioli, Member, IEEE, and Richard V. Snyder, Life Fellow, IEEE

Abstract—In this paper a new class of propagating waveguide in-line pseudoelliptic filters exploiting dielectric resonators is presented. The basic structure is a singlet, which is implemented by a mode dielectric resonator placed into a rectangular waveguide above cutoff. Couplings are controlled by a proper positioning of the puck. The fundamental propagating mode of the waveguide is exploited to both excite and bypass the resonator so as to obtain bypass coupling capability, allowing the generation of transmission zeros. Higher order filters are obtained by cascading singlets through quarter-wave or half-wave waveguide sections. The quarter-wave section behaves as an admittance inverter, while the half-wave section behaves as a resonator, the latter resulting in filters which combine dielectric and cavity resonators. Thanks to this combination, unique performances such as wide bandwidth and sharp transition bands can be obtained. To validate the proposed method a third-order filter with 2.3% fractional bandwidth (FBW) and a fifth-order filter with 8.15% FBW have been designed and manufactured, thus demonstrating the approach feasibility. Index Terms—Bandpass filters, dielectric resonators, elliptic filters, rectangular waveguide, transmission zeros (TZs).

I. INTRODUCTION

T

HE dramatic increasing of communication market demands for compact light filters with even more higher performances. High permittivity dielectric resonators are widely employed because of their compactness and superior performance in terms of Q-factor and temperature stability [1]. Their application ranges from very narrowband dielectric-loaded cavity filters for satellites and cellular base-stations, to highly stable oscillators [2], [3]. Most common dielectric-loaded cavity filters exploit the fact that the field is mainly confined within the high-permittivity dielectric puck to reduce ohmic losses. For this reasons pucks are generally suspended in a metallic enclosure. They can be axially located along the enclosure [4]–[7], or mounted in a planar configuration [8], [9]. Filter poles are obtained by exploiting the fundamental resonant mode or higher order mode in combination with its degenerate mode to obtain dual-mode filters [6], [7], the Manuscript received July 01, 2015; revised October 01, 2015; accepted October 11, 2015. Date of publication November 13, 2015; date of current version December 02, 2015. This paper is an expanded version from the IEEE International Microwave Symposium, Phoenix AZ, May, 17–22, 2015. C. Tomassoni is with the Electronic and Information Engineering Department (DIEI), University of Perugia, 06125 Perugia, Italy (e-mail: tomassoni@diei. unipg.it). S. Bastioli and R. V. Snyder are with RS Microwave, Butler, NJ 07405 USA (e-mail: [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2015.2495284

latter allowing for pseudoelliptic responses while maintaining an in-line configuration. Pseudoelliptic filters exploiting mode have been lately obtained in an in-line configuration [10] by using pucks with orthogonal orientation to realize cross-coupling among nonadjacent resonators by exploiting different polarizations of the waveguide evanescent modes. The in-line topology is in fact convenient for mechanical and size considerations and in the last years several filters exploiting nonresonating modes have been proposed in order to obtain pseudoelliptic responses without using folded cross-coupled architectures. As an example, the nonresonating mode technique has been used in [11] to cascade transverse magnetic (TM) dualmode cavies, in [12] where the TM dual-mode cavities have been loaded by dielectric pucks in order to reduce the size, as well as in [13] by using dual-post resonators in propagating waveguide. A new class of in-line filters with dielectric pucks properly located in propagating rectangular waveguide has been proposed in [14]. The basic structure is a singlet, which is implemented by a mode dielectric resonator placed into a rectangular waveguide above cutoff. The fundamental propagating mode of the waveguide is exploited to both excite and bypass the resonator so as to obtain bypass coupling capability, allowing the generation of transmission zeros. Specifically, singlets having the same coupling amplitude in input and output (with no control of the source to load coupling) have been proposed in [14], where higher order filters have been obtained by cascading multiple singlets through nonresonating quarter-wave waveguide sections. This paper significantly extends the above idea by introducing new singlet configurations with a noticeably increased capability in term of coupling control. By properly positioning the dielectric pucks with respect to the waveguide, an independent control of input and output couplings is now possible. A more advanced technique to obtain a precise control of source to load coupling by using a capacitive post is also shown. Furthermore, a new filter configuration exploiting such singlets is proposed where the singlets are cascaded through half-wave waveguide sections. The half-wave waveguide sections behave as additional resonators, thus increasing the filter order. The strong bypass coupling of the singlet and the weak coupling between cavities and dielectric pucks allow for the design of wideband filter having transmission zeros very close to the pass-band edges, thus resulting in extremely sharp transition bands. This strong coupling allows wideband filters, while the weak coupling between cavities and dielectric puck together with the strong bypass allows transmission zeros very close to the filter band resulting in extremely sharps transition bands.

0018-9480 © 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

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Fig. 1. Dielectric puck in rectangular waveguide. (a) Three-dimensional view and (b) top view and coupling pattern.

This configuration overcomes the typical problem of limited bandwidth capability of dielectric filters while maintaining the high performance in terms of temperature stability of dielectric based structures. Detailed design procedure for the exact evaluation of coupling coefficients are introduced for both structures using quarter-wave and half-wave waveguide sections. Finally, a new experimental result of a fifth-order filter is presented to show the feasibility of filters which combine dielectric and cavity resonators.

Fig. 2. Singlet composed by a dielectric puck in rectangular waveguide. Comparison between full-wave response (continuous dark lines) and coupling matrix response (dotted red lines). In the figure inset, the topology and the relevant coupling matrix as well as 3-D sketch of the singlet are shown. The modal E-field and modes (yellow arrows) and modal H-field (green arrows) for are drawn. The waveguide is a WR90, while the dielectric puck has a radius mm, a height mm, and a relative permittivity .

II. SINGLET The singlet structure is here used as basic building block for the design of higher order filters. According to Fig. 1, the singlet consists of a dielectric puck suspended within a propagating waveguide. The coupling paths are illustrated in Fig. 1(b): the propagating waveguide mode excites the dielectric resonant mode, resulting in sequential couplings and . Part of the power carried by the fundamental mode bypasses the resonator and creates the input-to-output coupling . In the following the mechanisms of the couplings and the way to control them are explained in detail for the basic singlet structure (Section II-A), and for a more complex singlet structure exploiting a capacitive post as coupling section (Section II-B). A. Basic Configuration Let us first consider the case where the dielectric puck resonator is centered with respect to the waveguide. With reference to Fig. 2, for symmetry reasons related to and modal field distributions, the resonant mode is not excited and the most of the power carried by the bypasses the resonator and creates a strong source-to-load coupling. The simulated S parameters confirm that no poles are present in the response and about 80% of the power bypasses the puck ( ). In the inset of Fig. 2 the coupling matrix representation of the singlet is also shown and its response (dotted lines) is compared to the full-wave response (continuous lines). The extraction of the coupling matrix from the response is obtained by optimizing the coupling matrix response. To excite the resonant mode it is necessary to break the symmetry of the structure. This can be done in two ways: by rotating the puck as shown in Fig. 3, or by shifting the puck as shown in Fig. 4. In both cases, first-order pseudoelliptic responses with one pole and one transmission zero are obtained. Observe that the transmission zero is located below the pole when the puck is rotated, while it is located above the pole if the puck is offset. This is due to the fact that in the case of a rotation , while in the case of a shift as can be easily understood considering the field distribution shown in

Fig. 3. As in Fig. 2 but with the dielectric puck rotated around the -axis of an . angle

Fig. 4. As in Fig. 2 but the puck is no longer centered to the waveguide, and mm. the puck offset is

the figure insets. The control of and amplitude is carried out by using the rotation angle (or the offset): the larger the angle (or the shift) the stronger the coupling. Note that in both shift and rotation cases, because of the high source to load coupling, the response actually is closer to a

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Fig. 6. Comparison between full-wave and coupling matrix response of (a) and (b) puck shifted with mm and centered puck rotated of . rotated of

Fig. 5. As in Fig. 2 but the puck is shifted and rotated. The puck offset is mm (as that of Fig. 4), while the puck rotation is (as that of Fig. 3).

stop-band filter. For this reason, a fractional bandwidth (FBW) reported in figure insets is referred to a FBW of the stop-band. As can be noted, the input-to-output coupling is stronger in the case of rotation than in the case of shift ( instead of ). This is due to the fact that the field of the is higher in the center of the waveguide and is more influenced by a centered puck. In some applications the fact that the amplitude of and are the same is a limitation. To overcome this limitation a shifted and rotated puck is considered. For the estimation of the coupling matrix when shift and rotation are combined, we consider a sort of superposition property. The scattering superposition is applied to the denormalized coupling coefficients (Appendix I)

(1) Here the superscript indicates that the coupling coefficient is referred to the singlet with rotated puck (no shift), the superscript is referred to the singlet with shifted puck (no rotation), while the superscript , is referred to the singlet where the puck is both shifted and rotated. Note that the superposition property has not been applied to the direct input-to-output coupling. This is due to the fact that this coupling is mainly dependent on the puck position with respect to the center of the waveguide. Formulas have been tested in Fig. 5 where the response of a dielectric rotated 25 (as in Fig. 3) and shifted 3.8 mm (as in Fig. 4) is shown. In this case the coupling matrix has been evaluated by applying the superposition property (1) to the scattering matrices of Figs. 3 and 4. Although the superposition property is just an approximation, Fig. 5 shows that the approximation is quite accurate. Obviously, by inverting (1) it is possible to design a singlet having prescribed and

(2)

Let us suppose to design a singlet with and . According to (2) this leads to and . The singlet of Fig. 4 having mm, realizes the desired , while the singlet of Fig. 6(a) having realizes the desired . This leads to a structure with a dielectric puck shifted of mm and rotated of . The expected coupling matrix for this structure has been calculated applying the scattering superposition property (1) to those in Figs. 4 and 6(a). In Fig. 6(b) the response of the calculated coupling matrix is plotted along with the full-wave response, showing an excellent agreement. The main limitation of the present structure is that there is no control on source-to-load coupling. To overcome this limitation it is possible to use additional coupling sections. As an example irises at the input and output of the singlet can be used to control the source-to-load coupling. This leads to a very simple structure where couplings are still controlled by shifting and rotating the dielectric. Unfortunately, irises decrease also the coupling of the dielectric to source and load, and this structure can be used just in the case where no strong couplings are needed (as in the case of the manufactured filter in Section IV-B). B. Singlet With Posts Another possible coupling section can be realized by a capacitive post. As shown in Fig. 7, we consider a singlet realized by a dielectric puck and a capacitive post in propagating waveguide. The post is placed at a distance and a shift with respect to the dielectric resonator. Let us consider the case where the dielectric is centered ( ) to the waveguide. This configuration guarantees a complete control of couplings. In fact, in contrast with the singlet without post, in this case the coupling between dielectric resonator and input and output is different ( ) due to the presence of the post, and there is no necessity of combining shift and rotation of the dielectric puck. To illustrate the features of this structure let us consider a nonrotated puck ( ) and a post centered with respect to the waveguide ( ). According to Fig. 7, the symmetry of the electric field of the centered post does not allow the excitation of the resonant mode. In Fig. 8, the response of such a structure as a function of the post height is shown. As expected, there are no resonances, and the power flowing from input to output is due to the fundamental mode that bypasses the resonator: the higher the post the lower the . Of course, when the post height tends to zero, the value of tends to those of Fig. 2.

TOMASSONI et al.: PROPAGATING WAVEGUIDE FILTERS USING DIELECTRIC RESONATORS

Fig. 7. Singlet composed by a dielectric puck and a metallic capacitive post. (a) Front view, (b) top view, and (c) 3-D view. In (c) the -field for waveguide mode and puck resonant mode as well as the E-field in the transverse section of the waveguide in correspondence of the post is shown.

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Fig. 9. Singlet composed by a puck and a post. Responses of the singlet for different values of (continuous lines) compared to the coupling matrix response calculated for different FBW (dotted lines). In the figure inset the structure and the electric field distribution are shown.

Fig. 8. Singlet with centered post and nonrotated dielectric puck. Transmission coefficient as a function of the post height.

Once the distance is fixed, all the coupling parameters can be independently controlled: the post height mainly controls , the rotation angle mainly controls , while the post offset mainly controls . Observe that is chosen so that the post is close enough to influence the dielectric field. To show the design procedure let us implement a singlet having , and different from zero. To obtain we fix the post height to 7.5 mm. Different curves have been obtained in Fig. 9 by varying from 0 to 60 , resulting in different values of the coupling between load and resonator. For each the position of the post has been selected so that . This value has been obtained by exploiting the field perturbation due to the presence of the post, as shown in the figure inset in the case of . In fact, because of the radial nature of the field around the post, the field in the left and right side of the post contribute to the excitation of the resonant mode with different sign. In this case, the position of the post is chosen so that the sum of all contributions is zero, thus leading to . By increasing , a negative coupling is obtained, while decreasing the coupling becomes positive. This is clearly shown in Fig. 10, where mm produces a positive coupling [Fig. 10(c)] while mm produces a negative coupling [Fig. 10(d)], being in this specific case mm the position for which the coupling is zero [Fig. 10(b)]. As can be noted from Fig. 9, the difference between fullwave responses and equivalent matrix responses increases ap-

Fig. 10. (a) Singlet and relevant dimensions. Response for the singlet with the mm (b), mm (c), and mm (d). post in position

proaching 9.5 GHz. This is due to a spurious resonance of the post appearing above 9.5 GHz. This spurious resonance also influences responses of Fig. 8. The higher the post height, the lower the spurious frequency. Another possible singlet configuration is the one in Fig. 11(a), where the offset (instead of the rotation) is exploited to control : the higher the the higher the is instead still controlled by the post position , as in the case of the centered puck. In Fig. 12 some responses of the above singlet structure have been obtained. Different stop-bands have been obtained by varying the offset and readjusting the post offset in order to obtain . Finally, a generalized singlet configuration is shown in Fig. 11(b) where the dielectric resonator is both rotated and shifted. In that case both offset and rotation contribute to . is instead still controlled by the post position . In Fig. 13 the response of a singlet having both and equal zero is shown. Note that the rotation is chosen so that its contribution to eliminates the contribution of the shift , thus leading to . Starting from this point, by increasing ,we obtain , while decreasing we obtain .

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Fig. 14. Three singlets cascaded through admittance inverters and . In the figure, the path connecting source to resonator 3 (res, 3) avoiding all other resonators is shown (red dotted line). From this path it is possible to calculate of Fig. 16. the admittance related to

Fig. 11. (a) Noncentered puck configuration and (b) noncentered rotated puck configuration.

Fig. 15. Singlets cascaded through a quarter wave length.

Fig. 12. Noncentered puck resonator. Responses obtained for different values . of puck shift . All responses have

Fig. 16. Canonical equivalent circuit of three pole pseudoelliptic filter. Formulas allow the evaluation of admittance inverters starting from those of Fig. 14.

Fig. 13. Response of the structure illustrated in the figure inset with puck radius 3.25 mm and pack height 3 mm. The relative dielectric constant is 30.

III. SINGLET CASCADED THROUGH QUARTER-WAVE WAVEGUIDE SECTIONS A. Design Procedure Higher order filters can be obtained by cascading singlets through quarter wave transmission line lengths, as shown in Fig. 15. An important property of such a structure is that the transmission zero of each singlet is preserved exactly in the same position after the cascade. In other words, each singlet controls its own zero, allowing for a modular design and a precise positioning of each transmission zero. A quarter wave length behaves like as a unitary admittance inverter. This means that the cascade of three singlets

can be represented with the equivalent circuit of Fig. 14 with and equal 1. The coupling matrix associated to this equivalent circuit is a 9 9 matrix. In fact in this circuit, 7 nodes are present: three resonant nodes and four nonresonating nodes, as will be illustrated later on in the example of Fig. 17. Nonresonating nodes can be removed, leading to a 5 5 coupling matrix and the relevant equivalent circuit of Fig. 16. The procedure to find the -inverter connecting resonant node to resonant node is very easy and involves the path connecting node to node that avoids all other resonant nodes. The same procedure applies for the evaluation of coupling involving source and load. As an example the path related to is illustrated in Fig. 14 (red dotted line). The formula consists in the product of all encountered -inverter values pertaining to the singlets divided by the product of all -inverters values (with changed sign) used to connect the singlet. Referring to the example of Fig. 14, the inverter pertaining to the singlet are

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Fig. 18. Singlet exploited in the manufactured filters. The waveguide is a WR137. Puck dielectric constant is 35.62. Puck diameter 8.89 mm. Thickness of low-permittivity dielectric holding the puck is 2 mm.

Fig. 17. Coupling matrix obtained cascading three singlets. The highlighted submatrices are the coupling matrices of the relevant singlets. Nodes 2, 3, 5, and 6 are nonresonating nodes. Nonresonating nodes corre. spond to sources and loads of cascaded singlets.

,

and , those related to the cascade are , thus resulting in

and

(3) This formula can be easily found by considering that the cascade of three admittance inverters , and is still an admittance inverter of value , as demonstrated in the Appendix II As a filter synthesis example, let us consider the coupling matrix (4) to design a 3pole-3zero filter with 2% FBW and central frequency 5.78 GHz. To synthesize the coupling matrix (4), the response of the equivalent circuit of Fig. 14 has been first optimized. Then the associated coupling matrix of Fig. 17 has been evaluated from the circuit parameters by exploiting formulas in Appendix I. Finally formulas in Fig. 16 has been applied to remove the nonresonating nodes from the coupling matrix of Fig. 17, obtaining matrix (4)

(4) To realize the filter we first design each singlet. As is evident from Fig. 17 the design of only two singlets is required as first and third singlets are equal. Singlets of Fig. 17 have been implemented by using the structure of Fig. 18. In the singlet design, the low-permittivity dielectric holding the high permittivity dielectric puck and the tuning metal disk are also taken into account. The tuning metal disk is held by low-permittivity stick and is used to tune the resonant frequency by varying its distance to the puck. Note that, according to the coupling matrix, singlets have slightly different resonant frequency. In this case the tuning disk is also used to obtain the different resonant frequencies in singlets having identical pucks. The singlets of Fig. 17 have been designed and their responses are shown in Fig. 19 along with the relevant coupling matrix responses. Note that the reference plane of the input and output

Fig. 19. Implementation of (left) singlets 1 and 3 (left) and (right) singlet 2 of Fig. 17. Comparison between coupling matrix responses (dotted lines) and full-wave responses (continuous lines).

ports have been chosen in order to match the phase of the coupling matrix response. As can be seen, because of the dispersive behavior of the waveguide, the matching of the phase is not as good as the amplitude, and the port distance has been chosen in order to minimize much as possible the differences in the filter band. With reference to Fig. 17, a unitary coupling ( ) connects singlets. This unitary coupling corresponds to a unitary -inverter that can be implemented by a waveguide length of 90 . At the frequency of 5.78 GHz, this corresponds to a waveguide length of 19.41 mm. Considering the reference planes position, this leads to a distance of 30.25 mm between the puck centers, as reported in Fig. 20 where the response of the whole filter is also shown. Note that the full-wave simulation of the filter has been obtained just cascading the three singlets and no further optimization has been required, demonstrating the high modularity of the method. As mentioned before, another advantage is that the transmission zeros of the filter are the same of that of the cascaded singlets, thus allowing a very precise control of the transmission

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Fig. 20. Third-order filter with three transmission zeros in the upper stop-band obtained cascading the structures of Fig. 19. Comparison between coupling matrix response (dotted lines) and full-wave response (continuous lines). The transmission zero at higher frequency is a double-zero.

Fig. 22. Equivalent circuit of doublets cascaded through half-wave lengths. (a) Third-order filter. (b) Fifth-order filter.

Fig. 21. Third-order filter with a FBW of 2.3%. Comparison between measurements (dotted lines) and full-wave analysis (continuous lines).

zero position. In the filter of Fig. 20 the first and last singlet are identical and each of them produces a transmission zero exactly at 9.06 GHz, resulting in a double zero. For this reason the filtering response shows two transmission zeros only, but one of them is a double zero.

resonators, thus increasing the filter order. The half-wave section can be substituted by a lumped resonator so as to obtaining the more standard equivalent circuit of Fig. 22(b). Impedance inverter values change according to the equations in Fig. 22. Note that the presence of regular half-wave resonators (without source-to-load couplings) allows transmission zeros at infinity. Let us consider a first example where the coupling matrix (5) has been implemented by using two identical singlets with capacitive posts, exploiting the capability of such a singlet to produce different input and output coupling values. Coupling matrix (5) has been extracted from the equivalent circuit of Fig. 22(b), derived from that of Fig. 22(a), and the desired filter response has been obtained by optimization.

B. Experimental Result The manufactured filter design starts form that of Fig. 20, but the distance between puck centers has been increased of 1.65 mm (about 8 ) increasing the bandwidth from 2% to 2.3%. The mismatching in the filter band has been compensated by increasing the rotation of puck 2 from 47 to 56 . leaving the puck 1 in the same position. The modified filter has then been manufactured and in Fig. 21 measurements have been compared to full-wave simulations, showing an excellent agreement. The manufactured filter has high tuning capability: resonant frequencies are tuned by the metal disk while couplings are tuned by rotating pucks. IV. SINGLET CASCADED THROUGH HALF-WAVE WAVEGUIDE SECTIONS A. Design Procedure In contrast with the previous configuration where quarter wave waveguide sections are used, a different technique consists of cascading singlets by means of half-wave sections. With reference to Fig. 22(a), half-wave sections behave as additional

(5) As in the previous example a modular design approach has been followed by first designing individual singlets. In Fig. 23 the comparison between full-wave and equivalent circuit response of the singlet is shown. Design parameters for the equivalent circuit have been calculated by using equations in Appendix I and the formulas of Fig. 22 for . This value of is due to the fact that, for the physical realizability of the structure, the two singlets have been cascaded by adding a wave length section. In fact, as already explained in the previous example, the position of the reference planes are taken so as to obtain the best phase matching. In this case, because of reference plane positions, the cascade of singlets through a half-wave length would lead to unfeasible overlapped pucks. In the resulting filter, shown in Fig. 24, the distance between puck centers along the longitudinal direction is 53.25 mm. After the cascade a minor optimization is needed. According to Fig. 22, the final optimized parameters are: mm, post height 9.25 mm, puck rotation 37 , while a moderate tuning of

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Fig. 23. Comparison between coupling matrix response (dotted lines) and fullwave simulation (continuous lines) for the singlet with metal post sketched in mm, post height is 9.7 mm, post radius is the figure inset. Puck shift mm and mm. 1.5 mm, and, according to symbols in Fig. 7, Fig. 25. Response of fifth-order filter. Nominal response (continuous lines) compared to the response obtained by detuning the first and last cavity of 15 MHz and to the response obtained by detuning the central cavity of 15 MHz (dotted lines).

Fig. 24. Third-order filter with a double transmission zero. Comparison between coupling matrix response (dotted lines) and full-wave response (continuous lines). In the figure the nonoptimized response (continuous lines) obtained just cascading the singlet of Fig. 23 is also shown.

the frequency has been carried out by varying the position of the tuning metal disks. The values of parameters and are instead those of Fig. 23 as they were not changed during the optimization.

Fig. 26. Filter of order 5 with (a) double transmission zero and (b) relevant equivalent circuit.

B. Experimental Result A fifth-order filter implementing the coupling matrix (6) with 8.15% FBW centered at 6.26 GHz has been designed and manufactured. Coupling matrix (6) has been extracted from the equivalent circuit of Fig. 26(b) and the filtering response has been obtained by optimization.

Fig. 27. Manufactured fifth-order filter.

(6) According to Fig. 26, the filter has been implemented by using three cavities and two identical singlets realized with resonant pucks. A double transmission zeros appears in the filtering function because of the two identical singlets. In this case irises have been used instead of posts to control the source to load coupling in singlets. This configuration overcomes the typical problem of limited bandwidth capability of dielectric filters while maintaining the high performance in terms of temperature stability of dielectric based structures. This is illustrated in

Fig. 25 where the lower cut-off of the filter is shown in case of resonators detuned of 15 MHz. As is evident, in the case of the detuned cavities the position of the lower cut-off does not change and the return loss remains above 15.5 dB. The filter has been designed starting from the design of the singlet by exploiting formulas in Appendix I and in Fig. 26(b). The filter is in WR137, its length is 108 mm, and its weight is 300 grams. In any case, this is only a prototype and mass and envelope have not been optimized here.

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V. CONCLUSIONS

Fig. 28. Comparison between simulation (dotted lines) and measurement (continuous lines) for the fifth-order manufactured filter.

In this paper a new class of in-line pseudoelliptic filters using dielectric pucks in propagating waveguides has been presented. The singlet configuration has been extensively analyzed and described by means of several examples. The precise and independent positioning of transmission zeros, the modularity property, as well as the wide pass-band capability, of these structures have all been demonstrated. Detailed design procedure for higher order filter employing quarter-wave or half-wave sections between dielectric resonators have been proposed. In particular the configuration with quarter wave sections allows for simple modular design of narrow band filters where each singlet individually controls its transmission zero. On the other hands, half-wave sections introduce additional cavity resonators which allow for design of wide band filters having transmission zero very close to the (temperature stable) pass-band edges. Both design techniques have been successfully demonstrated by the experimental results of two prototype filters. APPENDIX I Admittance inverter are related to the normalized coupling matrix elements in the following way:

Fig. 29. Measurements of the fifth-order manufactured filter at three different C, and C. temperatures: room temperature,

where FBW represents the Fractional Bandwidth. In the case of the coupling between two synchronous resonators:

where and resonators.

are the resonant frequencies of the coupled APPENDIX II

Fig. 30. (Top) Two nodes connected by three j-inverters. The three j-inverters are equivalent to the j-inverter in the figure bottom. The equivalence is obtained by the equation reported in the figure.

In Fig. 27 the photograph of the manufactured filter is shown, while the comparison between full-wave simulations and measurement is shown in Fig. 28. Here the measurement has been extended to 8 GHz to show the out-of-band behavior. As can be seen, spurious resonances appear at 7.3 GHz. In any case they are still far enough from the passband to be easily removed by a simple low-pass filter. The filter has a band of 510 MHz and a very sharp transition band at the lower cutoff: an attenuation of 10 dB is obtained within 6–7 MHz. Finally, in order to show the temperature stability, the filter has been measured in a temperature range of 125 C and the relevant responses are shown in Fig. 29. As can be seen, in all cases the return loss is higher than 15 dB.

To demonstrate the formula of Fig. 30 let us consider the transmission matrix of a -inverter of value (7) By exploiting the property of the transmission matrices, the transmission matrix of the cascade of the three -inverters of Fig. 30 can be written as

The resulting transmission matrix value .

is that of a -inverter of

REFERENCES [1] C. Wang and K. A. Zaki, “Dielectric resonators and filters,” IEEE Microw. Mag., vol. 8, no. 5, pp. 115–127, Nov. 2007.

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[2] S. J. Fiedziuszko and S. Holmes, “Dielectric resonators raise your high- ,” IEEE Microw. Mag., vol. 2, no. 3, pp. 50–60, Sep. 2001. [3] R. R. Mansour, “Filter technologies for wireless base stations,” IEEE Microw. Mag., vol. 5, no. 1, pp. 68–74, Mar. 2004. [4] S. B. Cohn, “Microwave bandpass filters containing high- dielectric resonators,” IEEE Trans. Microw. Theory Techn., vol. MTT-16, no. 4, pp. 218–227, Apr. 1968. [5] W. H. Harrison, “A miniature high- bandpass filter employing dielectric resonators,” IEEE Trans. Microw. Theory Techn., vol. MTT-16, no. 4, pp. 210–218, Apr. 1968. [6] S. J. Fiedziuszko, “Dual-mode dielectric loaded cavity filters,” IEEE Trans. Microw. Theory Techn., vol. MTT-30, no. 9, pp. 1311–1316, Sep. 1982. [7] K. A. Zaki, C. Chen, and A. E. Atia, “Canonical and longitudinal dual mode dielectric resonator filters without iris,” IEEE Trans. Microw. Theory Techn., vol. MTT-35, no. 12, pp. 1130–1135, Dec. 1987. [8] J.-F. Liang and W. D. Blair, “High- TE01 mode DR filters for PCS wireless base stations,” IEEE Trans. Microw. Theory Techn., vol. 46, no. 12, pp. 2493–2500, Dec. 1998. [9] H. Rafi, R. Levy, and K. Zaki, “Synthesis and design of cascaded trisection (CT) dielectric resonator filters,” in Proc. 27th Eur. Microw. Conf., 1997, vol. 2, pp. 784–791. modedielec[10] S. Bastioli and R. S. Snyder, “Inline pseudoelliptic tric resonator filters using multiple evanescent modes to selectively bypass orthogonal resonators,” IEEE Trans. Microw.Theory Techn., vol. 60, no. 12, pp. 3988–4001, Dec. 2012. [11] C. Tomassoni, S. Bastioli, and R. Sorrentino, “Generalized TM dualmode cavityfilters,” IEEE Trans. Microw. Theory Techn., vol. 59, no. 12, pp. 3338–3346, Dec. 2011. [12] L. Pelliccia, F. Cacciamani, C. Tomassoni, and R. Sorrentino, “Ultracompact high-performance filters based on TM dual-mode dielectricloaded cavities,” Int. J. Microw. Wireless Techn., pp. 151–159, Apr. 2014. [13] C. Tomassoni and R. Sorrentino, “A new class of pseudoelliptic waveguide filters using dual-post resonators,” IEEE Trans. Microw.Theory Techn., vol. 61, no. 6, pp. 2332–2339, Jun. 2013. [14] C. Tomassoni, S. Bastioli, and R. S. Snyder, “Pseudo-elliptic in-line filters with dielectric resonators in propagating waveguide,” in Proc. IMS2015, Int. Microwave Symp., Phoenix, AZ, USA, May 17–22, 2015. Cristiano Tomassoni (M’15) was born in Spoleto, Italy. He received the Laurea degree and Ph.D. degree in electronics engineering from the University of Perugia, Perugia, Italy, in 1996 and 1999, respectively. His dissertation concerned the mode-matching analysis of discontinuities involving elliptical waveguides. In 1999, he was a Visiting Scientist with the Lehrstuhl für Hochfrequenztechnik, Technical University of Munich, Munich, Germany, where he was involved with the modeling of waveguide structures and devices by using the generalized scattering matrix (GSM) technique. From 2000–2007, he was a Postdoctoral Research Associate with the University of Perugia. In 2001, he was a Guest Professor with the Fakultät für Elektrotechnik und Informationstechnik, Otto-von-Guericke University, Magdeburg, Germany. During that time, he was involved with the modeling of horn antennas having nonseparable cross sections by using hybrid methods combining three different techniques: the finite-element method, mode-matching technique, and generalized multipole technique. He was also involved in the modeling of low-temperature co-fired ceramics by using the method of moments. He studied new analytical methods to implement boundary conditions in the transmission-line matrix method, and he modeled aperture antennas covered by dielectric radome by using spherical waves. Since 2007, he has been an Assistant Professor with the University of Perugia. His main area of research concerns the modeling and design of waveguide devices and antennas. His research interests also include the development of reduced-size cavity filters, reconfigurable filters, and printed reconfigurable antenna arrays. Dr. Tomassoni was the recipient of the 2012 Microwave Prize presented by the IEEE Microwave Theory and Technique Society.

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Simone Bastioli (S'10–M'11) received the Master's and Ph.D. degrees in electronic engineering from the University of Perugia, Perugia, Italy, in 2006 and 2010, respectively. In 2005, he was an Intern with Ericsson AB, Mölndal, Sweden, where he was involved with waveguide filters and transitions for RF applications. In 2006, he joined the University of Perugia under a scholarship funded by the Italian Space Agency (ASI). In 2009, he was with RF Microtech Srl, Perugia, Italy, where he was responsible for the design of advanced microwave filters for private and European Space Agency (ESA)-funded projects. In 2010, he joined the RS Microwave Company Inc., Butler, NJ, USA, where he is currently Acting Chief Engineer involved with reduced-size multimode cavity filters, advanced high-power evanescent-mode filters, as well as dielectric resonator and lumped-element filters. His research activities have resulted in more than 20 publications in international journals and conferences. He has four patent applications pending. Dr. Bastioli is a member of the MTT-8 Filters and Passive Components Technical Committee. He was the recipient of the 2012 IEEE Microwave Prize. He was the recipient of the Best Student Paper Award (First Place) of the IEEE Microwave Theory and Techniques Society (MTT-S) International Microwave Symposium (IMS), Atlanta, GA, USA, in 2008, and the Young Engineers Prize of the European Microwave Conference, Amsterdam, The Netherlands, also in 2008. He was the recipient of the Hal Sobol Travel Grant presented at the IEEE MTT-S IMS, Boston, MA, USA, in 2009.

Richard V. Snyder (LF'05) received the B.S. degree from Loyola-Marymount University, Los Angeles, CA, USA, the M.S. degree from the University of Southern California (USC), Los Angeles, and the Ph.D. degree from the Polytechnic Institute, New York University, New York, NY, USA. He is President of RS Microwave, Butler, NJ, USA, which was founded in 1981. He teaches and advises at the New Jersey Institute of Technology. He is a Visiting Professor with The University of Leeds, Leeds, U.K. He has authored or coauthored 117 papers and three book chapters. He holds 21 patents. His interests include electromagnetic (EM) simulation, network synthesis, dielectric and suspended resonators, high-power notch and bandpass filters, and active filters. Dr. Snyder served the IEEE North Jersey Section as Chairman and 14-year Chair of the IEEE Microwave Theory and Techniques–Antennas and Propagation (MTT–AP) Chapter. He chaired the IEEE North Jersey Electron Device Society and Circuits and Systems chapters for ten years. He served as General Chairman for IMS2003, Philadelphia, PA, USA. He will be Emeritus Chair of IMS2018, Philadelphia, PA, USA. He was elected to the Administrative Committee in 2004, where he served as Chair of the TCC and liaison to the European Microwave Association. He served as an IEEE MTT Society Distinguished Lecturer (2007–2010), as well as continuing as a member of the Speakers Bureau. He was an Associate Editor for the IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES (T-MTT), during which time he responsible for most of the submitted filter papers. He is a member of the American Physical Society, the American Association for the Advancement of Science, and the New York Academy of Science. He was the IEEE MTT Society President in 2011. He has been a Reviewer for the IEEE T-MTT, the IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, the Progress in Electromagtnetic Research Symposium, and IET Microwave. He served seven years as chair of MTT-8 and continues in MTT-8/TPC work. He is the organizer of the annual IWS Conference in China and continues as a member of the IWS EXCOM. He was a two-time recipient of the Region 1 Award. He was the recipient of the IEEE Millennium Medal in 2000.

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Self-Biased Y-Junction Circulators Using Lanthanum- and Cobalt-Substituted Strontium Hexaferrites V. Laur, G. Vérissimo, P. Quéffélec, Senior Member, IEEE, L. A. Farhat, H. Alaaeddine, E. Laroche, G. Martin, R. Lebourgeois, and J. P. Ganne

Abstract—In this paper, we propose the application of polycrystalline lanthanum- and cobalt-substituted strontium hexaferrites in the realization of self-biased circulators. These materials present a high anisotropy field, dependent on the substitution rate, which makes it possible to reach operating frequencies in the millimeter-wave range. A first demonstrator was successfully designed and realized using a 20% rate of substitution Sr La Fe Co O . This circulator showed insertion losses of 1.79 dB and an isolation level of 28.1 dB at 41.4 GHz without magnets. Performances can be significantly improved by applying a low magnetic field H Oe . According to the literature, increasing the substitution rate makes it possible to increase the anisotropy field, and thus, the internal field. Consequently, a 30% substituted strontium hexaferrite was tested. It appears that the anisotropy field was not higher in this case. However, magnetic losses are much lower and enabled us to halve insertion losses of the self-biased circulator (0.87 dB at 41 GHz). Index Terms—Ceramics, circulators, ferrites, millimeter wave measurements, rectangular waveguide, Y-junction.

I. INTRODUCTION

C

IRCULATORS are still very important microwave components in modern telecommunication systems. These three-port nonreciprocal devices are genereally used to allow full-duplex communications (transmission and reception at the same time) with a single antenna. Isolators (one of the port connected to a matched load) are also used to protect the transmission equipment, especially amplifiers, from parasitic radiations or impedance mismatch. However, in spite of much progress over recent decades, these devices remain quite costly, heavy, and bulky, which limits their integration in telecommunication systems, especially in future millimeter-wave satellite front-ends at Q-band. Manuscript received June 30, 2015; revised August 17, 2015 and October 21, 2015; accepted October 22, 2015. Date of publication November 13, 2015; date of current version December 02, 2015. This work was supported by the French DGCIS in the framework of MM-WIN (Advanced millimeter-wave interconnects) European Euripides project. This paper is an expanded version from the IEEE MTT-S International Microwave Symposium, Phoenix, AZ, USA, May 17–22, 2015. V. Laur, G. Vérissimo, and P. Quéffélec are with Lab-STICC, University of Brest, Brest, 29290 France (e-mail: [email protected]). L. A. Farhat, H. Alaaeddine, E. Laroche, and G. Martin are with Chelton Telecom & Microwave, Villebon-sur-Yvette, 91140, France. R. Lebourgeois and J. P. Ganne are with Thales Research & Technology, Palaiseau, 91120 France. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2015.2495218

Consequently, filter-diplexers or switches are sometimes preferred for duplexing applications as they provide a better means of integration. Thus, new technologies need to be developed to decrease the size of circulators and be competitive with passive (planar diplexer) and active (MMIC switches) technologies. The bulkiness of circulators can be reduced in two main ways: using planar technologies (microstrip for example) and/or removing permanent magnets through the use of preoriented materials. The use of hard ferrites, whose uniaxial particles have been oriented during pressing, is the most classical solution to avoid using magnets [1]–[6]. Demonstrators in the Ku [6] and Ka [3], [4] bands have been realized on this principle. However, the published performances of these circulators are often corrected [2], [5] and, thus, do not correspond to the performances “as-measured” due to the difficulties encountered in the modeling of such devices and in the control of magnetic ceramics properties. Ferromagnetic nanowires [7] or soft ferrite nanowires [8], embedded in porous dielectric substrates, were also studied to design self-biased circulators. Nevertheless, these technologies have not reached maturity and need to be improved in order to be integrated in telecommunication systems. In a previous paper, presented during the 2015 IEEE International Microwave Symposium [9], we proposed to use lanthanum and cobalt doped strontium hexaferrites to realize millimeter-wave circulators. It is of particular interest that we obtained insertion losses of 1.79 dB and an isolation level of 28.1 dB at 41.4 GHz without magnets by using Sr La Fe Co O hexaferrites, here called La Co -SrM. We also observed that a low external magnetic field allowed performances to be significantly improved. As a consequence, we concluded that a material with a higher anisotropy field should make it possible to get lower insertion losses. According to the literature, increasing the substitution rate makes it possible to increase the anisotropy field. Consequently, a 30% substituted strontium hexaferrite was tested. In this paper, in Section III-A., we will first make a recap of the results obtained using La Co -SrM hexaferrites. Then, in Section III-B. we will show that using a higher substitution rate Sr La Fe Co O enabled us significantly improve the performances of the mm-wave self-biased circulator. These results will be discussed and compared with those of the literature. II. CHARACTERIZATION AND SIMULATION METHODS In this study, we used polycrystalline preoriented hexaferrites to design and realize self-biased circulators at millimeter-

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wave frequencies. Strontium hexagonal ferrites with a magnetoplumbite structure exhibit a very high anisotropy field of about 19 kOe and a high remanence to saturation ratio, making it possible to realize mm-wave self-biased circulators. This material is the ferrite the most used for such applications in the literature [1]–[6]. It has allowed the successful realization of selfbiased circulators up to 30 GHz. Some experimental demonstrations around 40 GHz have also been carried out. However, performances at this frequency in self-biased working mode are slightly degraded because of the proximity to the natural (without an applied magnetic field) gyromagnetic resonance frequency (FMR). In order to reach a working frequency of 40 GHz, two solutions can be considered: applying an external magnetic field in order to shift FMR at higher frequencies or using materials with higher anisotropy fields. Lanthanum and cobalt substitutions make it possible to increase the anisotropy field of strontium hexaferrites. Sr La Fe Co O which will be called La Co -SrM was therefore used in this work. The preparation route is based on a conventional ceramic process. First, powder with the targeted composition is prepared starting from SrCO , La O and Co O raw materials and by using solid-state reaction. Then, the hexaferrite powder is magnetically oriented and pressed before sintering. The magnetostatic properties of (La,Co)-SrM hexaferrites were studied through Superconductive Quantum Interference Device (SQUID) measurements (Quantum Design MPMS XL). These measurements enabled us to investigate the magnetization saturation level of the samples and the squareness of the hysteresis loops. Ansys HFSS software was used to model the circulators. This electromagnetic (EM) software integrates Polder's model [10] which makes it possible to predict the permeability spectra of magnetized ferrites from their saturation magnetization , . However, this internal field and magnetic losses model is well-suited to the case of saturated ferrites and therefore needs to be modified in the case of ferrites in their remanent state, where the magnetization level to be considered is (1) is the remanent magnetization along z-axis and is the relative remanent level that will be measured using SQUID measurement. Contrary to saturated soft ferrites, the internal field in preoriented hexaferrites in their remanent state is not mainly governed by an applied magnetic field but rather by anisotropy and demagnetizing fields. In our case, the internal field is calculated by the following equation:

where

(2) is the internal magnetic field along z-axis, the where applied magnetic field, the anisotropy field and the demagnetizing coefficient calculated by using Aharoni equations [11]. A previous version of a 40-GHz Y-junction rectangular waveguide circulator integrating spinel ferrites was used to test La Co -SrM materials. EM simulations were performed to optimize the dimensions of the La Co -SrM pucks for a self-biased working mode at 40 GHz (Fig. 1).

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Fig. 1. Simulation model of the self-biased circulator in rectangular waveguide technology integrating La Co -SrM hexaferrite pucks.

Fig. 2. Measurement setup used for the microwave characterization of the circulators.

Then, hexaferrite pucks were machined by keeping their c-axis (direction of the magnetization) perpendicular to the plane of the pucks. These flat cylinders were glued to the center of the Y-junction circulator. Circulators were measured with a Vector Network Analyzer (Rhode&Shwarz ZVA67) in the 40–60 GHz for the first circulator and between 35 and 50 GHz for the second one (Fig. 2). Thru-Reflect-Line (TRL) calibration procedure was performed in order to shift the reference plane after the coaxial-to-waveguide transitions. Self-biased circulators were measured in isolator mode (a load was connected to one of the ports). An external magnetic dc field, applied using an electromagnet, was also used to observe the behavior of the circulator as a function of the applied biasing field. The static magnetic field was measured with a gaussmeter during the measurement. III. CHARACTERIZATION AND SIMULATION RESULTS OF MATERIALS AND DEVICES A. Results Using La Co

-SrM

La Co -SrM preoriented ceramics were synthesized by the process described in part II. Pure strontium hexaferrites were synthesized using the same process in order to compare their static magnetic properties. Fig. 3 presents M(H) hysteresis loops of a 20% substituted SrM Sr La Fe Co O and of a nonsubstituted one. We observed a slight increase of the coercive field of doped SrM

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Fig. 3. M(H) hysteresis loops measured with a SQUID magnetometer on par-SrM materials (along the allelepiped samples made of SrM and La Co mm mm mm c-axis). Dimensions of the samples: SrM and La Co -SrM mm mm mm .

TABLE I DIELECTRIC AND MAGNETIC PROPERTIES OF La Co

Fig. 4. Internal field of a La Co -SrM cylinder as a function of its aspect ratio without an applied external magnetic field.

-SrM HEXAFERRITES

hexaferrites compared with the nonsubstituted ones H Oe and H La Co -SrM Oe). Moreover, the La Co -SrM cycle presents a higher squareness: the remanent magnetization reaches 90% of the saturation one RRL while this value is only 85% of the saturation magnetization for a nonsubstituted SrM material. Even without magnets, magnetic dipoles remain well aligned along the c-axis (direction perpendicular to the plane of the sample in our case) proving the strong potential of La Co -SrM ceramics for the design of self-biased circulators. The properties of La Co -SrM ceramics, slightly refined compared to [9], are given in Table I. Saturation magnetization and squareness values were extracted from SQUID measurements. The other values were at first approximated by using published results [8], [12], [13], and then refined by using retro-simulations of measurements. The dielectric constant value was also measured by coaxial line measurements in the 1–18 GHz frequency band that gave a slightly lower value of permittivity than the one given in [8]. This material presents a higher anisotropy field than pure SrM but its magnetic losses near resonance remain quite high. Equation (2) enabled us to calculate the internal field of a La Co -SrM cylinder as a function of its aspect ratio (height divided by radius). It appears that the internal field is much lower than the anisotropy field because of the high magnetization level of this material (Fig. 4). A previous constructed rectangular waveguide structure, optimized for spinel ferrites at 50 GHz, was modified to test the La Co -SrM materials. The evolution of the internal field was taken into account for the simulations. The optimized dimensions of La Co -SrM disks are a radius of 0.87 mm and a height of 0.2 mm. These dimensions lead to a demagnetizing factor of . By using (1) and (2), we calculated the and self-magnetization of the disks along z axis their internal field Oe. Polder's model thus allows us to obtain an approximate value of the permeability spectra (Fig. 5). The ferrite disk shows a

Fig. 5. Calculated real and imaginary parts of the permeability spectra of La Co -SrM disks ( mm and mm) without an applied field.

Fig. 6. Simulated S-parameters of the self-biased circulator integrating La Co -SrM hexaferrite pucks.

self-FMR (without applied field) at 49.1 GHz. Even if the broadening of magnetic losses due to dispersion in magnetic moments inside the sample is not taken into account here, this high value of FMR appears to be sufficient to design a self-biased circulator at around 40 GHz. Fig. 6 presents the simulated S-parameters of the self-biased circulator integrating La Co -SrM disks. A maximum isolation level Iso dB appears at 41.3 GHz while insertion losses are minimum at 42.2 GHz IL dB . However, return losses remains moderate in the operating band (RL dB at 42.2 GHz). The simulated performances appear to be sufficient to experimentally demonstrate the potential of La Co -SrM materials, and thus it was decided to realize this structure as a first proof of concept. The circulator is shown in Fig. 7. This Y-junction circulator was realized by using WR-19 rectangular waveguides.

LAUR et al.: SELF-BIASED Y-JUNCTION CIRCULATORS USING LANTHANUM- AND COBALT-SUBSTITUTED STRONTIUM HEXAFERRITES

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Fig. 9. Measured (solid lines) and simulated (dashed lines) S-parameters of the -SrM hexaferrites with an applied self-biased circulator integrating La Co biasing field of 2100 Oe. Fig. 7. Photograph of the circulator in rectangular waveguide technology (in-SrM pucks integrated into the circulator). sert: internal view of La Co

isolation and return losses were 16.5 dB and 24.6 dB, respectively. One should note that isolation remained above 15 dB from 42.58 to 56.06 GHz (more than 13 GHz) resulting in a relative bandwidth of 27.3%. However, insertion losses reached 3 dB from 47.62 GHz and thus limit the working frequency band of the device to 11.2% (42.58–47.62 GHz). Comparisons between simulation and measurement were in a good agreement. One should note that the parameters of the ferrite were kept the same for this simulation (cf. Table I) and that only the internal field was modified. The overestimation of the relative bandwidth seems again to be due to the inhomogeneity of the internal field not taken into account in the simulation. B. Results Using La Co

Fig. 8. Measured (solid lines) and simulated (dashed lines) S-parameters of -SrM hexaferrites without an the self-biased circulator integrating La Co applied biasing field.

Impedance matching is achieved through the change of sections of the WR-19 waveguide near the Y-junction. La Co -SrM disks were glued at the center of the circulator. Measured performances of the circulator in the 40–60 GHz frequency band without an applied dc field are shown in Fig. 8. Insertion losses are the lowest dB at 41.4 GHz. At this frequency, isolation is 28.1 dB. However, at the same time, return losses remain low RL dB and limit the performances of the device. The circulator demonstrates a 15 dB . A very good bandwidth of 3 GHz RBW dB agreement was demonstrated between the simulated and measured S-parameters (Fig. 8). However, the simulated fractional bandwidth appears to be slightly higher than the measured one. This phenomenon could be due to the inhomogeneity of the internal field (spatial dispersion of the magnetic moments in the polycrystalline hexaferrite disks), which is not taken into account in the simulation. This device was placed into an electromagnet to study the effect of an external biasing field (applied perpendicularly to the plane of the ferrite pucks) on its performances. Measured S-parameters when a 2100-Oe magnetic field was applied to the circulator are presented in Fig. 9. In this case, minimal insertion losses of 1.23 dB were observed at 43.2 GHz. At the same time,

-SrM

We demonstrated above that a low static magnetic field allows us to significantly improve the performances of a La Co -SrM-based circulator. Now, Grössinger et al. demonstrated in [12], [13] that anisotropy field increases as lanthanum and cobalt rate increases in Sr La Fe Co hexaferrites at room temperature. As can be seen in (2), increasing the anisotropy field could make it possible to increase the internal field without applying an additional external magnetic field. As a consequence, we undertook to replace the La Co -SrM disks by hexaferrites with a higher rate of substitution. Thus, Sr La Fe Co hexaferrites, here called La Co -SrM, were selected. Ferrite disks with the same dimensions as those made from La Co -SrM, were machined and glued in the circulators. The circulator was then measured between 35 and 50 GHz, first without an applied field, and then with increasing biasing field using an electromagnet. Fig. 10 presents the measured S-parameters of the La Co -SrM-based circulator without an applied biasing field. No increase in frequency was observed, as expected for a material with a higher anisotropy field. However, a significant decrease of insertion losses was demonstrated. Thus, minimum insertion losses of 0.87 dB at 41 GHz were measured. At this frequency, an isolation level of 16.5 dB together with return losses of 12.6 dB were demonstrated. This circulator also presents a 15 dB bandwidth of 1.3 GHz RBW . dB Retro-simulations using Ansys HFSS enabled us to extract the properties of La Co -SrM hexaferrites. A good agreement between measurements and simulations was achieved

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TABLE III MEASURED PERFORMANCES OF La Co -SrM-BASED CIRCULATORS WITH AND WITHOUT AN APPLIED BIASING FIELD

Fig. 10. Measured (solid lines) and simulated (dashed lines) S-parameters of -SrM hexaferrites without an the self-biased circulator integrating La Co applied biasing field.

TABLE II DIELECTRIC AND MAGNETIC PROPERTIES OF La Co

Relative bandwidth calculated for Isolation level less than

15 dB.

-SrM HEXAFERRITES

Fig. 12. State of the art. “As-measured” insertion losses of hexaferrite-based circulators as a function of frequency.

As observed earlier, the measured bandwidth is significantly lower than that predicted by simulations, probably because of the broadening of FMR losses linked to a slight spatial inhomogeneity of the internal field. Fig. 11. Measured (solid lines) and simulated (dashed lines) S-parameters of -SrM hexaferrites with an apthe self-biased circulator integrating La Co plied field of 1600 Oe.

with the parameters listed in Table II (Fig. 10). It appears that the decrease of insertion losses is mainly related to the strong decrease of magnetic losses for this composition ( about three times lower than that of La Co -SrM). We also observed that the anisotropy field is quite similar to that of La Co -SrM, which is consistent with the similar working frequencies in both cases but not in agreement with previous published studies concerning this family of ferrites [12], [13]. Additional material characterizations will have to be performed to explain this difference of behavior compared to the literature. This circulator was placed in an electromagnet in order to investigate its behavior with an increasing biasing field. The best performances were achieved for an applied 1600-Oe magnetic field. In these conditions, insertion losses of 0.21 dB were measured at 42.9 GHz. At the same time, isolation and return losses were 41.3 and 25.6, respectively. Isolation level remained lower than 15 dB between 41.5 and 45.1 GHz leading to a relative bandwidth of 9.7%. One should note that, in contrast to La Co -SrM, insertion losses were kept quite low in this bandwidth, with a maximum value of 0.78 dB. Simulated S-parameters were once again in good agreement with the measured performances (Fig. 11).

C. Discussion The measured performances of La Co -SrM-based circulators are listed in Table III. A self-biased operating mode was demonstrated by using La Co -SrM hexaferrites. When La Co -SrM were used, insertion losses without applied biasing field were significantly decreased due to lower magnetic losses . In both cases, a low external magnetic field made it possible to generally improve performances except for the isolation level of La Co -SrM-based circulator which was decreased. We are now working on the optimization of the Y-junction in order to improve the self-biased performances of the circulator. Fig. 12 allows us to compare our results with those found in the literature. Only “as-measured” performances are presented [1]–[4], [6], [14]–[17], i.e., external tuning or post-treatments (feed lines or removal of connector losses) are not considered. This figure presents measured insertion losses of hexaferritebased circulators as a function of frequency. The circulator designed by Wang et al. [6] is distinguished from other results by its very low frequency of operation which is, to our knowledge, the lowest one achieved for a self-biased circulator. Circulators made of preoriented hexagonal ferrite composites have also been realized [16], [17], but these technologies still need to progress and mature in order to provide lower insertion losses. The other results show operating frequencies between 24 and 40 GHz. In this context, our performances are remarkable owing

LAUR et al.: SELF-BIASED Y-JUNCTION CIRCULATORS USING LANTHANUM- AND COBALT-SUBSTITUTED STRONTIUM HEXAFERRITES

to the low level of insertion losses and the high frequency of operation. Such high working frequencies seem to be unreachable using pure SrM materials below FMR.

IV. CONCLUSION This work concerns the modeling and the characterization of a self-biased circulator around 40 GHz. The use of lanthanum-cobalt substituted strontium hexaferrites made it possible to increase the operating frequency of the circulator. Static properties were measured to confirm the increase of squareness (remanent magnetization) and anisotropy field compared to a nonsubstituted SrM. A circulator was realized in rectangular waveguide technology and characterized using Sr La Fe Co O preoriented ferrites. Without magnets, insertion losses of 1.79 dB and isolation of 28.1 dB were measured at 41.4 GHz. The application of a low magnetic field noticeably improves the performances of the device. The use of lanthanum-cobalt doped SrM with a higher substitution rate Sr La Fe Co O decreased insertion losses signifidB at 41 GHz). cantly without an applied field (IL We are convinced that we can improve the performances of these self-biased circulators. A new Y-junction specifically designed for La Co -SrM materials will soon be developed. In parallel, planar circulators will be realized and characterized in order to demonstrate the high potential of these materials for the design of integrated self-biased circulators.

REFERENCES [1] M. A. Tsankov and L. G. Milenova, “Design of self-biased hexaferrite waveguide circulators,” J. Appl. Phys., vol. 73, no. 10, pp. 7018–7020, May 1993. [2] S. A. Oliver, P. Shi, W. Hu, H. How, S. W. McKnight, N. E. McGruer, P. M. Zavracky, and C. Vittoria, “Integrated self-biased hexaferrite microstrip circulators for millimeter-wavelength applications,” IEEE Trans. Microw. Theory Techn., vol. 49, no. 2, pp. 385–387, Feb. 2001. [3] X. Zuo, H. How, S. Somu, and C. Vittoria, “Self-biased circulator/ isolator at millimeter wavelengths using magnetically oriented polycristalline strontium M-type hexaferrite,” IEEE Trans. Magn., vol. 39, no. 5, pp. 3160–3162, Sep. 2003. [4] N. Zeina, H. How, C. Vittoria, and R. West, “Self-biasing circulators operating at Ka-band utilizing M-type hexagonal ferrites,” IEEE Trans. Magn., vol. 28, no. 5, pp. 3219–3221, Sep. 1992. [5] B. K. O'Neil and J. L. Young, “Experimental investigation of a selfbiased microstrip circulator,” IEEE Trans. Microw. Theory Techn., vol. 57, no. 7, pp. 1669–1674, Jul. 2009. [6] J. Wang, A. Yang, Y. Chen, Z. Chen, A. Geiler, S. M. Gillette, V. G. Harris, and C. Vittoria, “Self-biased Y-junction circulator at Ku band,” IEEE Microw. Wireless Components Lett., vol. 21, no. 6, pp. 292–294, Jun. 2011. [7] M. Darques, J. Medina, L. Piraux, L. Cagnon, and I. Huynen, “Microwave circulator based on ferromagnetic nanowires in an alumina template,” Nanotechnology, vol. 21, pp. 145208.1–145208.4, 2010. [8] J. Wang, A. Geiler, P. Mistry, D. R. Kaeli, V. G. Harris, and C. Vittoria, “Design and simulation of self-biased circulators in the ultra high frequency band,” J. Magn. Magn. Mater., vol. 324, pp. 991–994, 2012.

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[9] V. Laur, G. Vérissimo, P. Quéffélec, L. A. Farhat, H. Alaaeddine, J. C. Reihs, E. Laroche, G. Martin, R. Lebourgeois, and J. P. Ganne, “Modeling and characterization of self-biased circulators in the mm-wave range,” in Proc. IEEE Int. Microwave Symp., 2015. [10] D. Polder, “On the theory of ferromagnetic resonance,” Phil. Mag., vol. 40, pp. 99–115, Jan. 1949. [11] A. Aharoni, “Demagnetizing factors for rectangular ferromagnetic prims,” J. Appl. Phys., vol. 83, no. 6, pp. 3432–3434, 1998. [12] R. Grössinger, J. C. Tellez Blanco, F. Kools, A. Morel, M. Rossignol, and P. Tenaud, “Anisotropy and coercivity of M-type Ba and Sr-ferrites containing La and Co,” in Proc. Int. Conf. Ferrites, 2000, pp. 428–430. [13] R. Grösssinger, C. Tellez Blanco, M. Küpferling, M. Müller, and G. Wiesinger, “Magnetic properties of a new family of rare-earth substituted ferrites,” Phys. B: Condensed Matter, vol. 327, pp. 202–207, Apr. 2003. [14] P. Shi, H. How, X. Zuo, S. A. Oliver, N. E. McGruer, and C. Vittoria, “Application of single-crystal scandium substituted barium hexaferrite for monolithic millimter-wavelength circulators,” IEEE Trans. Mag., vol. 37, no. 6, pp. 3941–3946, Nov. 2001. [15] J. A. Weiss, N. G. Watson, and G. F. Dionne, “New uniaxial-ferrite millimeter-wave junction circulators,” in Proc. IEEE Int. Microwave Symp., 1989, pp. 145–148. [16] C. Blengeri, T. Casad, A. Abburi, D. N. McIlroy, W. J. Yeh, and J. L. Young, “Fabrication of bulk, self-bias barium ferrites for microwave circulator applications,” J. Mater. Sci. Eng., vol. 5, pp. 314–318, 2011. [17] T. Boyajian, D. Vincent, S. Neveu, M. Leberre, and J. Rousseau, “Coplanar circulator made from composite magnetic material,” in Proc. IEEE Int. Microwave Symp., 2011. V. Laur, photograph and biography not available at the time of publication.

G. Vérissimo, photograph and biography not available at the time of publication.

P. Quéffélec, (M’99–SM’07) photograph and biography not available at the time of publication.

L. A. Farhat, photograph and biography not available at the time of publication.

H. Alaaeddine, photograph and biography not available at the time of publication..

E. Laroche, photograph and biography not available at the time of publication.

G. Martin, photograph and biography not available at the time of publication.

R. Lebourgeois, photograph and biography not available at the time of publication.

J. P. Ganne, biography and photograph not available at the time of publication.

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A 2.45 GHz Phased Array Antenna Unit Cell Fabricated Using 3-D Multi-Layer Direct Digital Manufacturing Thomas P. Ketterl, Member, IEEE, Yaniel Vega, Nicholas C. Arnal, John W. I. Stratton, Student Member, IEEE, Eduardo A. Rojas-Nastrucci, Student Member, IEEE, María F. Córdoba-Erazo, Student Member, IEEE, Mohamed M. Abdin, Student Member, IEEE, Casey W. Perkowski, Paul I. Deffenbaugh, Kenneth H. Church, Member, IEEE, and Thomas M. Weller, Senior Member, IEEE

Abstract—This paper reports on the design, fabrication and characterization of a 3-D printed RF front end for a 2.45 GHz phased array unit cell. The printed unit cell, which includes a circularly-polarized dipole antenna, a miniaturized capacitive-loaded open-loop resonator filter and a 4-bit phase shifter, is fabricated using a direct digital manufacturing (DDM) approach that integrates fused deposition of thermoplastic substrates with micro-dispensing for deposition of conductive traces. The individual components are combined in a passive phased array antenna unit cell comprised of seven stacked substrate layers with seven conductor layers. The measured return loss of the unit cell is dB across the 2.45 GHz ISM band and the measured gain is dBi including all components. Experimental and simulation-based characterization is performed to investigate electrical properties of as-printed materials, in particular the inhomogeneity of printed thick-film conductors and substrate surface roughness. The results demonstrate the strong potential for fully-printed RF front ends for light weight, low cost, conformal and readily customized applications. Index Terms—Additive manufacturing, dipole antenna, direct digital manufacturing, open loop resonator filter, switched-line phase shifter, 3-D printing.

I. INTRODUCTION

A

DDITIVE MANUFACTURING (AM) is a technology that is maturing from a cost-effective rapid prototyping solution to one suitable for low volume production in a diverse array of fields that includes RF and microwave design. As reported in [1], the AM market has grown to over 3000 organizations with an estimated $9.46 billion for printed and thin film electronics. In the microwave field, frequency selective surManuscript received July 02, 2015; revised September 22, 2015, October 21, 2015, October 23, 2015; accepted October 23, 2015. Date of publication November 11, 2015; date of current version December 02, 2015. This work was supported in part by US Air Force Research Laboratoryunder contract #FA865014-C-2421. The material was assigned a clearance of CLEARED on 18 Feb 2015 (Case Number: 88ABW-2015-0603). The work was also supported by the National Science Foundationunder grant #ECCS-1232183. This paper is an expanded version from the IEEE MTT-S International Microwave Symposium, Phoenix, AZ, USA, 17–22 May 2015. T. P. Ketterl, Y. Vega, N. C. Arnal, J. W. I. Stratton, E. A. Rojas-Nastrucci, M. F. Cordoba-Erazo, M. M. Abdin, and T. M. Weller are with the Department of Electrical Engineering, University of South Florida, Tampa, FL 33620 USA (e-mail: [email protected]). C. W. Perkowski, P. I. Deffenbaugh, and K. H. Church are with Sciperio Inc., Orlando, FL 32826 USA. Digital Object Identifier 10.1109/TMTT.2015.2496180

faces, electrically-small antennas and RF MEMS devices are among the demonstrated applications [2]–[10]. While there are numerous AM processes, including a variety of all metal and all plastic methods, in this work the focus is on a multi-material approach that integrates fused deposition of thermoplastics with micro-dispensing of conductive pastes. This integrated direct digital manufacturing (DDM) process enables the realization of multi-layer, high frequency structural electronic designs in a single build. Conceptually, the approach merges the flexible 3-D design capability afforded by low temperature co-fired ceramic (LTCC) technology with the large area format achievable with multi-layer printed circuit boards (PCBs). The feature sizes currently achievable with DDM are equivalent to those of PCBs, with m minimum layer thickness and 50–100 m line widths on smooth surfaces, though the arbitrary volumetric design capability is specific to DDM. With the integration of chip and packaged semiconductor devices, printed electronic systems are realizable. This paper reports on the demonstration of components of a 2.45 GHz RF front-end that are fabricated using the DDM approach. These components comprise a unit cell of a phased array antenna (PAA) (Fig. 1) which is the first known demonstration of an AM-produced multi-layer microwave circuit. One of the presented components is a 2.45 GHz circular polarized (CP) antenna consisting of a pair of crossed-dipole elements that fits on a 6 6 cm 3-D-printed substrate. Another CP crosseddipole antenna on a 10 10 cm substrate is introduced that includes a high impedance surface (HIS) to isolate the antenna from the back ground plane, and consists of four metal layers, five substrate layers and thru conductive vias. A second component is a square open-loop resonator 2.45 GHz band-pass filter that is miniaturized using discrete capacitive loading. Finally, a multi-bit phase shifter using packaged MMIC switches is demonstrated. The printed designs use acrylonitrile butadiene styrene (ABS) thermoplastic as the substrate and DuPont CB028 thick-film Ag paste for the conductors. Preliminary results of this work are presented in [6] and are expanded in this paper. The 3-D fabrication process described in Section II now includes a detailed review of selected dielectric and conductive materials used in additive manufacturing. The section also includes DC and RF analysis of

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KETTERL et al.: 2.45 GHZ PHASED ARRAY ANTENNA UNIT CELL

Fig. 1. Phased array antenna (PAA) unit cell fabricated with direct digital manufacturing (DDM). The front-end consists of a phase shifter, band-pass filter, balun and antenna (on bottom of stack). The unit cell dimensions are 6 cm in length and width, with a height of 5.2 mm.

the conductive material used in this investigation in order to provide an understanding of the high frequency performance of the individual components described in following sections. Section III expands on the design and testing of the printed CP antennas introduced in [6] by providing return loss and radiation pattern measurements for antennas that include lumped element phase shifters in the feed network and a new HIS layer design that provides more bandwidth and is more compatible with DDM processing. A new filter topology that is miniaturized using a DDM-printed coupling capacitor is described in Section IV, along with an analysis of surface roughness effects on filter performance. Section V adds the design and analysis of a printed multi-bit shifter to the switched-line phase shifter design introduced in [6] and a detailed analysis of the phase shifter performance has been added. A major contribution to the material in [6] is presented in Section VI, which describes the first results for the PAA unit cell. II. 3-D FABRICATION Numerous additive manufacturing methods are applicable for RF/microwave applications. Fused deposition modeling (FDM), stereolithography and different jetting techniques are used to form polymer structures that can act as substrates and packaging. For (thick or thin) films such as conductive interconnects, micro-dispensing, ink-jet, aerosol jet and selective laser structuring are among the available approaches. In this work a DDM printing system that integrates micro-dispensing and fused deposition is used. Details of the DDM fabrication approach and various materials that are compatible with DDM are described in this section. A. Multi-Material Micro-Dispensing/Fused Deposition Fabrication Approach An nScrypt 3-Dx-300 printing system is the primary fabrication tool used in this work. This tool combines a micro-dispensing head with picoliter control for depositing pastes

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Fig. 2. ABS-CB028 printing process: (1) 0.2 mm thick ABS on a 90 C bed, (2) CB028 antenna elements, (3) 3 mm ABS antenna substrate, (4) CB028 ground plane with vias, (5) 0.5 mm ABS microstrip substrate, and (6) CB028 microstrip feedline. The photograph at the bottom shows the CB028 line edge quality; each tick mark is 400 um [6].

with viscosities ranging from 1.0 to 1.0e6 cP, with a fused deposition system that uses tip orifices down to 12.5 m. Both deposition systems are on a common gantry with 2 m position accuracy. The printing process used for the circularly-polarized dipole antenna (Section III) is illustrated in Fig. 2. It consists of 3 FDM steps to deposit ABS (UltiMachine) for a base layer, a substrate layer for the antenna elements, and a substrate layer for the feedline. There are also 3 micro-dispensing steps to deposit CB028 for the antenna elements, an intervening ground plane layer and the microstrip feedline. The printing bed temperature is held at 90 C which allows the CB028 to be cured in place. No additional steps to smooth the ABS surfaces are required to obtain excellent line edge quality (see bottom of Fig. 2). With the described fabrication method, the main limiting factor to edge definition is the tendency of the CB028 silver paste to flow laterally in a somewhat non-uniform fashion as the surface topography of the ABS varies. CB028 is a particle flake loaded thixotropic material, and its time dependent shear thinning feature implies that the material will move from a thick state to a thin state and then back again to a thick state. If a surface is perfectly smooth, a thixotropic material will still be micro shaped along the edges due to surface tension. The range of viscosity for CB028 is from 15 000 to 30 000 cP, and because this is not extremely high the effects of surface tension will have an impact on edge definition. For the ABS surface roughness typical of this work, it is found that line width variations can be controlled to within m, independent of nominal line width. Accordingly, minimum line dimensions on the order of 100 m are possible to achieve with an optimized process, without noticeable variation in the characteristic impedance of the lines. To improve yield, a minimum line width of m has been followed in this work. On smoother substrates such

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TABLE I RF MATERIAL PROPERTIES OF FDM-COMPATIBLE MATERIALS

TABLE II TENSILE STRENGTH OF FDM-COMPATIBLE MATERIALS

TABLE III HEAT DEFLECTION TEMPERATURE (HDT) OF FDM COMPATIBLE MATERIALS

TABLE IV BULK DC CONDUCTIVITY OF CB028 SILVER PASTE

C. DC Properties of Conductive Material The material used for conductive lines in this work is DuPont CB028. This is a thick-film paste that consists of silver flakes in a polymer matrix. When cured, the solvent in the paste evaporates and the polymer shrinks, drawing the flakes into contact. Typical film thickness in this work is m. One basic parameter which controls the conductivity of CB028 is the temperature at which it is cured. Table IV shows four key data points on the DC conductivity of CB028 measured using a four point probe and van der Pauw [18] equations on a 10 mm square patch. As shown in the table the nominal DC conductivity for the CB028 films used in this work is 2.62e6 S/m. D. RF Properties of Conductive Material

as Kapton, line dimensions down to 25 achieved.

m are consistently

B. Properties of Dielectric Materials Material selection is critical when using 3-D printing to manufacture functional devices. Several material property areas are examined herein, including the RF dielectric properties, strength and heat deflection temperature (HDT). The RF material properties of ABS, polycarbonate (PC), and ULTEM™ (polyetherimide (PEI), Stratasys ULTEM 9085) are similar to one another [13] but the loss tangent of polylactic acid (PLA) is higher [12]. A summary is provided in Table I. The tensile strength of ABS, PC, ULTEM™ and PLA is compared using the ASTM D638 standard (Table II). Measured data of maximum tensile strength is obtained using a digital pull tester of the actual materials used in the phased array antenna unit cell (see Section VI). PC and ULTEM tensile strength from Stratasys is stated as bulk, i.e., not printed, which is slightly stronger than as-printed. The heat deflection temperature (HDT) of a given material (Table III) must fulfill end use and manufacturing requirements. Softening occurs as a material passes its HDT and internal stresses introduced by the non-uniform cooling of the layers, when relieved by softening can cause warping. For instance, the HDT of ABS is 88 C @ 1.8 MPa so for the purposes of this paper, 90 C is the maximum process temperature used in order to achieve good results. PLA is not a good choice because of its low HDT. ABS, with an HDT temperature of 88 C, is selected for this work due to its printability, moderate temperature range, and low dielectric loss.

FDM printing generates relatively rough surfaces and the curing process of the micro-dispensed conductive paste results in an inhomogeneous particle distribution on the micron scale. Due to these features of the printed materials, the effective RF conductivity of the silver paste can be substantially different from the DC values shown in Table IV and can also be spatially dependent. Since conventional methods used to measure the electrical conductivity of printed traces provide an averaged value of the electrical resistivity, a measurement technique that combines the ability to spatially resolve variations in conductivity and surface relief is desirable. These variations can affect the performance of the printed structures particularly for high frequency applications. Near-Field Microwave Microscopy (NFMM) has proven to be an important tool to image electromagnetic properties of homogenous and uniform bulk insulators [19], conductors [20], [21] and semiconductors [22] with subwavelength resolution. Recently, NFMM has also been used to image the electrical resistance of resistors fabricated using micro-dispensing [23]. Advantages of using NFMM to characterize printed samples are that variations in conductivity and topography of a sample can be tracked with spatial resolution that is about the size of the sensing tip. Additionally, NFMM is a non-contact, non-destructive technique and provides the electromagnetic properties in the microwave frequency regime rather than DC values. NFMM systems commonly utilize a resonant technique for sensing changes in material properties. The basic components in this type of instrument consist of a source and a resonator terminated in a sensing element which can be an aperture or a conductive tip whose size is smaller than the wavelength at the operating frequency. The material under test (MUT) is placed in close proximity to the probe tip at a distance smaller than the tip

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Fig. 4. Cross-section SEM micrograph of (a) CB028 interconnect and (b) bim [6]. nary matrix after image processing. The silver flake size is

Fig. 3. Conductivity (a) and topography (b) images of CB028 over an area of 100 m 100 m obtained using the NFMM.

size in order for the resonator to be sensitive to the MUT properties. Changes in the resonant properties of the probe can be correlated with the material properties by calibrating the NFMM using samples with known material properties [24], [25]. Herein, a dielectric resonator-based NFMM operating at 5.73 GHz is used for imaging simultaneously the electrical conductivity and topography of CB028 on glass. Design, experimental setup and a lumped element circuit model of the NFMM used in this work are described in [23], [26], [27]. The NFMM is calibrated using samples with known electrical conductivity in order to correlate the measured Q with . The scanning is performed at a tip-sample distance of 3 m in steps of 2 m. Fig. 3(a) and (b) show the electrical conductivity and topography images obtained, respectively. The distribution in Fig. 3(a) indicates that the conductivity varies between 0.6e6 S/m and 2e6 S/m. Higher conductivity regions are observed over thinner areas in the topography. The conductivity variation observed in the NFMM data can be understood using image processing to analyze cross-sectional SEM micrographs of CB028 films. A typical micrograph for a 25.19 m thick sample is shown in Fig. 4(a). An intensity histogram for the sample can be used to isolate the silver flakes from the polymer matrix and convert the micrograph to a binary matrix (Fig. 4(b)), and from there the silver flake density distribution can be determined. Fig. 5 shows the measured silver ink particle density as a function of the sample height for films of several thicknesses.

Fig. 5. Silver particle density versus distance from bottom of film for CB028 films of varying thickness.

The results confirm that the conductive layer is not homogenous. Furthermore, this data shows particle settling, where the density decreases as a function of distance from the bottom of the film. Also, thicker samples (40 m–50 m) show lower density for the top layer, when compared with thinner samples (20 m–40 m). The results of the cross-section analysis and NFMM imaging confirm the inhomogeneous nature of the micro-dispensed CB028 films, and the reduction in silver particle density to % near the upper 5–8 um can explain the differences between the measured DC conductivity (2.6e6 S/m) and the range of conductivities observed in the NFMM images (0.6e6 to 2.0e6 S/m). This inhomogeneity will extend to the edges of printed lines where high RF current densities exist, thus contributing to an effective RF conductivity that must be accounted for in circuit design and numerical electromagnetic simulation. This effect, combined with surface roughness effects, is discussed in more detail in the following sections. It is noted that although the NFMM characterization data applies to GHz, the extracted values of conductivity are expected to remain stable at lower frequencies as long as the skin depth is much less than the conductor thickness. This conclusion is supported by results for several demonstration circuits tested in the 2–6 GHz frequency range.

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III. CIRCULARLY-POLARIZED DIPOLE ANTENNA In this section 3-D printed antennas are described to demonstrate the multilayer DDM process. Tight control of the antenna and substrate dimensions is required in order to achieve the correct resonant frequency and operation bandwidth. The manufacturing process also includes the fabrication of via sections that connect the antennas through one or more layers to the bottom feed layer, as well as buried vias that connect the bottom layer to the internal ground plane. The antennas presented in this study are circular polarized (CP) designs consisting of a pair of crossed-dipole antenna elements. To provide circular polarization, two arms of one dipole are fed by a 0–180 network and each is connected through a 90 phase shift section to a neighboring arm of the second dipole to accomplish the quadrature phase between the two elements. The antennas are required to be low profile with a thickness of less than 4 mm, and include a ground plane to separate the bowtie elements on top of the substrate and the signal feed layer fabricated on the bottom surface. The feed layer will also include the individual front-end components for the unit cell described in Section VI. Since placing an antenna in close proximity to a ground plane (much less than ) generally degrades the overall performance [28], a high impedance surface (HIS) layer will be used in one design to mitigate the ground effects and achieve high directivity in the broadside direction [29]. The two variations of the CP antenna described herein are shown in Fig. 6 and denoted as Design 1 (without an HIS layer) and Design 2 (with an HIS layer). Design 1 is a simpler geometry that requires fewer printing steps and provides a baseline for the radiation efficiency determination, and particularly the impact of the HIS layer used in the more complex Design 2. Both designs use lumped element pi network phase shifters to implement the 90 phase shift sections between antenna arms. A surface mount balun provides the 0–180 phase for the differential feed. Each bowtie element is designed to have a 50 input impedance, including the 90 lumped phase shifter. The resonant frequency, besides being dependent on the bowtie length and via height, is very sensitive to the antenna via diameter and a value of 0.8 mm is needed to achieve the required frequency of 2.45 GHz. Simulations and tuning of the antenna models were performed in Ansys HFSS. Substrate-scalable Modelithics models of Johanson L-07C series inductors and R07S series capacitors with a 0402 body style were used in simulations to achieve the proper phase shift at the design frequency. Fig. 7 shows a CAD model of the bowtie elements and the feed layer, along with location of the components that are added after the printing process. Design 1 has a ground plane that only covers the area directly underneath the feed components and is designed to have minimal effect on the antenna radiation pattern while still providing a ground to the feed network components. Fig. 8 shows the CAD model of the simulated antenna and a stack up of the printed layers. The phase shifter element values are pF and nH for the capacitor and inductor, respectively. The data are given in Fig. 9, showing close correlation between measured and simulated

Fig. 6. Two types of 3-D printed crossed-bowtie antennas: Design 1 without HIS (top); and Design 2 with HIS (bottom) [6].

Fig. 7. CAD model of the crossed-bowtie antenna element (top) and the stack-up of the printed ABS and CB028 layers (bottom) for the design without the HIS (Design 1) [6].

results; the slight frequency offset in the measured data is most likely due the fact that the antenna via diameter is not exactly 0.8 mm. The antenna includes a surface mount U.FL connector which connects to the input of the balun component. The simulation includes the balun component and also the microstrip feed line. Simulated and measured radiation patterns are also shown in Fig. 9, demonstrating an axial ratio of less than 2 dB with a measured gain of dBi at 2.45 GHz. These results compare well to the simulated axial

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Fig. 8. CAD model of the crossed-bowtie antenna element (top) and the stack-up of the printed layers for the design with HIS (bottom) [6].

ratio of 0.6 dB and gain of dBi. The gain and radiation efficiency of the antenna are not strongly dependent on the effective conductivity of the CB028 silver paste as simulation results show that the efficiency is reduced by % as the conductivity changes by an order of magnitude from 1e7 S/m to 1e6 S/m (Table V). The broadband characteristic of the antenna results in the low sensitivity to the silver film conductivity, in contrast to the behavior of Design 2 and the narrowband filter described in the following section. Based on the NFMM characterization presented earlier, the assumed CB028 conductivity in the simulations is 1e6 S/m. To compare the performance of the printed antenna to an antenna of the same design fabricated using conventional printed circuit board (PCB) materials, simulations of a CP antenna design using 0.5 oz. copper clad Rogers Duroid for the substrate and conductive material were also performed. The simulated return loss comparisons are shown in Fig. 9. Even though the PCB antenna provides about a 30% larger bandwidth, the gain and efficiency at the design frequency of 2.45 GHz, shown in Table V, are comparable to the printed antenna design. For Design 2, a high impedance surface layer is included in the design and requires an additional CB028 and ABS layer in the printing process. Also, the ground plane covers the entire substrate. A high impedance surface is generally composed of periodic and identical elements arranged in a single layer and has a bandlimited response [30]–[32]. A HIS layer consisting of square conductive patches that are capacitively coupled is used in this design, as shown in Fig. 10(top). The HIS layer was optimized using Ansys HFSS to achieve a minimum bandwidth of 100 MHz centered at 2.45 GHz. Over this bandwidth the phase of the reflection coefficient is within with a magnitude near unity, as excited using a Floquet port. A very narrow gap between the HIS patches is required to achieve a bandwidth close to 100 MHz, while keeping within the overall

Fig. 9. Comparison between measured and simulated data for antenna Design 1: return loss (top) and radiation patterns (bottom). The return loss of the antenna using copper clad graph also includes the simulated Duroid for the substrate. For the pattern plot: solid line—simulated horizontal cut; dashed line—measured horizontal cut; dash-dotted line—simulated vertical cut; dotted line—measured vertical cut.

TABLE V ANTENNA DESIGN 1 GAIN AND EFFICIENCY AT 2.45 GHZ AS A FUNCTION OF SIMULATED PRINTED SILVER CONDUCTIVITY. A COMPARISON TO A SIMULATED ANTENNA USING CONVENTIONAL PCB MATERIALS IS ALSO INCLUDED

substrate thickness constraints which are equivalent to . The required gap spacing between the HIS plates is 300 m, and the length and width of each square patch is 9.7 mm. The cross section of the antenna is shown in Fig. 10 (bottom). The phase shifter values in this case are 10 pF and 0.5 nH for the capacitor and inductor, respectively. The measured for Design 2 is given in Fig. 11 and shows an operational bandwidth shift from 2.45 GHz to GHz. Through simulation it was found that the HIS performance is highly sensitive to variations in the antenna via diameter, the HIS patch size and the gap spacing between patch elements.

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Fig. 10. CAD model of the crossed-bowtie antenna element (top) and the stack-up of the printed ABS and CB028 layers for the design with an HIS (bottom) [6].

Therefore the frequency shift is most likely due to these dimensional tolerances in the printing process. To reduce the frequency shift, tighter control of the gap width between the HIS plates and the diameter of the printed vias that connect the antenna elements to the feed layer is required. Simulation show that a mm change in the HIS gap spacing corresponds to a MHz shift in the operational frequency. A shift of 120 MHz was observed when the diameter of the printed vias was also varied mm. The differences seen in the measured and simulated out-of-band may be due to surface wave effects, which can be difficult to predict accurately in electrically-large HIS structures. Radiation pattern measurements at frequencies across the measured bandwidth show that a best case axial ratio of 2.1 dB is obtained at 2.53 GHz with a measured gain of dBi (Fig. 11, bottom). Assuming the HIS layer introduced no additional loss, the dBi gain of Design 1 would be expected to increase to approximately 0.5 dBi with the change to a more uni-directional pattern due to the HIS. This 5.4 dB gain reduction contributed by the HIS layer is equivalent to an efficiency factor of %, which is at least 3 dB worse than the % typically achieved with low profile, HIS-backed antennas that use high quality, copper-clad commercial laminates; the 3 dB degradation is similar to the results obtained for the insertion loss of DDM filters presented in the following section, when compared to PCB filters on copper-clad laminates. The gain and efficiency compare well to the efficiency predicted in simulation which are dBi and 31%, respectively. IV. MINIATURIZED OPEN-LOOP RESONATOR FILTER The performance of microstrip band-pass filters is examined in this section in order to further assess the impact of the effective RF conductivity of the CB028 film, as well as the ABS

Fig. 11. Measured and simulated data for antenna Design 2: (top) and radiation patterns (bottom). For the pattern plot: solid line - simulated horizontal cut; dashed line - measured horizontal cut; dash-dotted line - simulated vertical cut; dotted line - measured vertical cut.

substrate surface roughness on the high frequency characteristics of DDM circuits. The filter topology is comprised of square open loop resonators (SOLR) which are often used in communications systems due to their compact size [35]. SOLR filters have been miniaturized to an area of 20% that of a conventional SOLR filter by loading the resonators with surface mount capacitors [34]. Herein, four versions of a 2.45 GHz 10% bandwidth SOLR filter that is loaded with series capacitors are presented. Filters 1–3 use only discrete chip capacitors across the gaps in the resonators while Filter 4 uses a new DDM-enabled design approach to increase coupling between adjacent resonators. All filters use 18–20 m-thick CB028 conductors on the front side and for the ground plane. A. Filter Designs A photograph of Filters 1–3 is given in Fig. 12 along with an outline drawing of Filter 2; all three filters have similar dimensions, with the minimum feature size being the 240 m spacing

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Fig. 13. Top: Illustration of metal-insulator-metal overlay capacitor used to increase coupling between adjacent resonators; Bottom: Outline drawing of Filter 4 (in mm) with dashed lines indicating the MIM capacitor locations [6].

Fig. 12. Top: Band-pass Filters 1–3 printed using CB028 Ag paste; Bottom: Outline drawing of Filter 2 (in mm) [6].

between resonators. Each filter is also printed on a 32 mil-thick substrate, with ABS used for Filters 1 and 2 and Rogers 4003c microwave laminate used for Filter 3. The resonators of each filter are loaded with ATC 600S (0603 body style) 0.5 pF capacitors for miniaturization. In order to achieve greater miniaturization of the filter footprint the value of the loading capacitors placed across the resonator gaps must be increased. Numerical electromagnetic simulations reveal that the maximum value that can be used for the loading capacitors is approximately 0.7 pF, as larger values result in such small resonator dimensions that effective input/output tapping (which controls the external quality factor) cannot be obtained. A further consequence of the reduced resonator dimensions is that the coupling region between adjacent resonators is shortened, thus requiring significantly reduced resonator spacing. For the 0.7 pF design, the required spacing is 70 m as compared to the 240 m used for the designs with 0.5 pF capacitors. As noted above, on relatively rough surfaces such as the printed ABS, feature sizes at this scale cannot be consistently realized using micro-dispensing. To circumvent this problem an alternative approach to achieving the necessary coupling coefficient was developed [14]. The new approach uses 3-D-printed metal-insulator-metal overlay capacitors that bridge adjacent resonators and are formed by depositing a thin, localized layer of ABS on top of the filter and printing the top capacitor plates with silver paste (Fig. 13). Using numerical electromagnetic simulations it is found that using an ABS insulator thickness m and a resonator spacing m, the required resonator coupling coefficient is achieved with a total top plate width of m and length

m. The approximate coupling capacitance with these dimensions is 0.18 pF using the parallel plate approximation. B. Analysis of Filter Performance The measured and simulated S-parameters for the four filters are plotted in Fig. 14 and a summary of key parameters is given in Table VI. The simulations were performed using Ansys HFSS with and for the ABS substrate and and for the Rogers 4003c substrate. Keysight Advanced Design System was also used in order to include the discrete chip capacitors using Modelithics ATC600S substrate-scalable models. For Filters 1–3 it is assumed that the actual values of the capacitors are 0.45 pF due to the 10% tolerance because a frequency shift was observed in the measurements. As indicated in the table, Filter 4 achieves the greatest miniaturization factor (21% the size of a conventional filter with no capacitive loading) due to the use of 0.7 pF chip capacitors and the overlay MIM capacitors. It can also be observed in Fig. 14 that the out-of-band rejection of Filter 4 is approximately 10 dB lower than that of Filters 1–3. This difference is attributed to the MIM capacitor loading approach and the smaller footprint of the resonators, as simulations of a similar geometry that assumed 70 m resonator spacing and no overlay capacitors predict a 5 dB reduction in the out-of-band rejection. Finally, a filter identical to Filter 3 but using 0.5-oz. copper instead of the CB028 conductor demonstrates a measured insertion loss of 1.5 dB. An important difference among the filters is the surface roughness (Ra) of the ABS substrate and the corresponding impact on the pass-band insertion loss. The roughness for Filter 1 is 7.1 m versus 4.9 m Filter 2, with the improvement coming from the use of a smaller diameter FDM head and other adjustments in the printing parameters. Although there

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Fig. 15. Profilometer Scan Over a Typical FDM ABS Substrate (Left) and Cross Section of a CB028 Filter on ABS Showing Ink Valleys (Right) [6].

Fig. 14. Simulated (solid lines) and measured (markers) data for Filters 1–4 (starting clock-wise from upper left).

TABLE VI PARAMETERS FOR FILTERS 1–4. C—CHIP CAPACITOR VALUE; IL—PASS-BAND INSERTION LOSS; RA—SURFACE ROUGHNESS; BW–3-DB BANDWIDTH; AR—AREA REDUCTION COMPARED TO FILTER WITH NO CAPACITIVE LOADING; —EFFECTIVE RF CONDUCTIVITY OF CB028 FILM

Fig. 16. Switched-line phase shifters (left—PCB, right—DDM) [6].

maximum conductivity remains below the bulk DC value for CB028 (2.6e6 S/m) due to the edge effects and inhomogeneous silver flake distribution discussed in Section II.C. V. MULTI-BIT PHASE SHIFTER

are also minor geometrical differences between these filters and the 3-dB bandwidth increased, numerical electromagnetic simulation data confirm that the primary reason for improved insertion loss is an increase in the effective RF conductivity of the CB028 film due to the reduction in surface roughness. This conclusion is further supported by simulation studies on Filter 3, which has a narrower 3-dB bandwidth than Filter 2 but lower surface roughness and slightly improved insertion loss. The surface roughness in the filter simulations is represented by adjusting the conductivity of the CB028 film to match measured filter performance, and assuming the conductors to be on a perfectly flat surface. (An alternative, more computationally expensive approach of representing the surface profile of the ABS in the simulation model is discussed in Section V). A profilometer scan of a representative sample is shown in Fig. 15 (left) illustrating the filament-like characteristic of the FDM print as well as relatively deep ( m) periodic valleys between filaments. Fig. 15 (right) is an SEM micrograph of a filter cross-section which demonstrates how the CB028 paste seeps into the valleys, creating points of high current concentration and lowering the effective conductivity. Table VI lists the RF conductivity values for the silver paste that produced simulation results equal to the measured insertion loss, showing a range from 0.6e6 to 1.2e6 S/m for the different Ra values. It is important to use common profilometer settings and scan lengths in order to consistently measure surface roughness for multiple samples of these filament-like materials. The

A multi-bit 2.45 GHz phase shifter design which is integrated as part of the phased array unit cell is described in this section. The performance of the design closely matches that of an identical circuit fabricated using a high quality commercial microwave laminate. In addition, a detailed analysis of the loss is performed to study the impact of the filament-like surface of the ABS substrate. The results demonstrate the close correlation between modeled and simulated insertion loss that is achievable using full-wave simulation of the non-planar surface and accurate values for the CB028 conductivity. A. Phase Shifter Design Two versions of a single-bit 45 switched-line phase shifter are presented; one fabricated using the described DDM process and one using a conventional PCB (copper-clad Rogers 4003c) process (Fig. 16). The Skyworks AS179-92LF SPDT SC-70 is used to switch between the thru- and delay-states on both circuits. The switches and surface mount inductors and capacitors are attached using H20E, an Ag nanoparticle conductive epoxy. The measured insertion loss in the delay state of the DDM and PCB circuits at 2.45 GHz is 1.55 dB and 1.25 dB, respectively (Fig. 17). This loss includes that of the switches and surface mount components ( dB total) and the interconnect lengths, where the latter differs by 0.3 dB. As shown in Section V.B. this difference is explained by the lower conductivity of the CB028 paste compared to copper, and the roughness of the ABS surface. For the phased array unit cell, a 4-bit design combining highpass low-pass and switched-line sections is used (Fig. 18). The least significant bits (45 and 22.5 ) are implemented using the switched-line approach to take advantage of the simplicity

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Fig. 17. of thru- and delay-states of phase shifters. Solid lines depict the thru-state and dotted lines the delay sate.

Fig. 18. DDM 4-bit high pass/low pass, switched line phase shifter [6].

and manufacturability of the design. The 180 and 90 bits are implemented using a high-pass low-pass approach in order to minimize the footprint. MA-COM MASWSS0115 SPDT RF switches are used in these bits. The insertion loss of the 16 states of the 4-bit phase shifter is shown in Fig. 19(left), showing an average state insertion loss of 5.8 dB at 2.45 GHz; the total contribution from the switches is dB. The phase shift of the individual states is given in Fig. 19 (right). A 2.45 GHz power sweep on a DDM test fixture that includes a MASWSS0115 SPDT switch yields a 1 dB compression point of dBm, which is within the switch specifications and indicates that the power handling capability is not limited by the DDM fabrication approach.

Fig. 19. Measured results for the 16 states of the 4-bit phase shifter: magnitude (top) and phase (bottom). The S21 plot shows that the insertion loss from dB for all 16 phase states. The phase shift plot shows 2.4 to 2.5 GHz is about the 22.5 relative phase difference between the 16 phase states at 2.45 GHz.

B. Analysis of Phase Shifter Performance To understand the difference in the measurements of the single-bit switch-line phase shifter using the two technologies, EM simulations of CB028-on-ABS (DDM) and copper-on-RO4003C (PCB) microstrip lines are performed using Ansys HFSS. The cross section of the microstrip lines used in the simulations are shown in Fig. 20(a) and (b). The microstrip line lengths are identical to those in the phase shifters ( mm) however the switches and capacitor pads are excluded. Although both conductive materials are assumed to be flat on the top surface, the CB028 is made to conform to the eggshell (filament-like) surface on the bottom. The eggshell surface is similar to that in Fig. 15. The conductivity of CB028 is selected to be 1e6 S/m, which is in the range measured using NFMM (Fig. 5(a)). Simulated surface current density plots at 3 GHz are shown in Fig. 20(c) and (d). As expected for this frequency, the current is concentrated at the edges of the copper

Fig. 20. Cross sections of microstrip lines simulated in HFSS for (a) copper on RO4003C (PCB) and (b) CB028 on ABS (DDM). Surface current density for (c) PCB and (d) DDM.

and CB028 traces. However, for the DDM circuit high current density is also observed in the valleys. The simulated of the DDM and PCB microstrip lines is shown in Fig. 21. The predicted losses are higher for the CB028/ABS circuit. In particular, at 2.45 GHz the difference

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Fig. 21. Simulated

for the PCB and DDM microstrip lines.

Fig. 23. Measured return loss of the 2.45 phased array unit cell showing a redB for all 16 phase states across the entire 2–3 GHz turn loss of less than frequency band.

Fig. 22. Printed unit cell in an anechoic chamber during antenna pattern measurements. The unit cell with control board is shown on the right and the linearly polarized transmit antenna can be seen on the left. The center insert shows a front view of the unit cell front end with Arduino controller and wire interface board.

is 0.32 dB, in close agreement with the measurement data presented above. VI. PHASED ARRAY UNIT CELL The printing process used for the phased array unit cell is the same as used for the circularly-polarized dipole antenna (Section III) but with 14 total steps. The process consists of 7 FDM steps to deposit ABS for a base antenna layer, a dielectric separation to the HIS, a HIS-ground separation, and 4 substrate heights for the various circuits. No post-processing is required to smooth the ABS. There are also 7 micro-dispensing steps to deposit CB028 for the antenna elements, the HIS, the ground, the antenna feed, and 3 additional substrate heights. Fig. 22 shows the unit cell used for the return loss and radiation pattern measurements. The phase shifts were controlled using an Arduino microprocessor. A 6 6 cm unit cell for a 2.45 GHz phased array antenna was assembled by integrating the individual components described in the preceding sections; namely, the circular-polarized HIS-backed dipole antenna, a square open-loop resonator filter and a 4-bit phase shifter. A reduced-size Rat-Race hybrid coupler is also inserted between the filter and antenna feed points, acting as a balanced-to-unbalanced transformer (balun) to provide the required 0 –180 differential feed for the antenna. The coupler design is adopted from [35]. As illustrated Fig. 1 a different substrate thickness is used for each of the four circuit components and the required topography is realized by varying the number of ABS layers deposited in different regions of the top surface. A transition with a 45 slope is used at the boundary

Fig. 24. Measured radiation patterns of the 2.45 GHz phased array unit cell. The vertical and horizontal gain pattern plots are shown.

between different substrate thicknesses and the width of the deposited CB028 trace is varied to maintain a 50 characteristic impedance. The filter design used in the unit cell is that of Filter 2 (see Section IV). Return loss measurements of the unit cell referenced to the input of the phase shifter are shown in Fig. 23 at the 16 phase states. Again, a resonant frequency shift occurred from 2.45 to 2.53 GHz, as observed with the HIS antenna in Section III Radiation pattern measurements at 2.45 GHz in the vertical and horizontal direction to obtain the axial ratio and maximum gain in the broadside direction are given in Fig. 24. The measured 2.53 GHz gain of the unit cell varies from dBi to dBi over all phase shifter states. VII. CONCLUSION The work presented herein demonstrates the potential of direct digital manufacturing for realizing high quality, light weight and conformal microwave structural electronics. By utilizing the multi-layer and multi-material capability of the DDM process, complex 3-D printed electronic systems can be produced when combined with pick-and-place assembly

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of packaged and surface mount devices. The assemblies can have buried conductors, local variations in substrate thickness and both distributed and lumped elements that are additively manufactured. Furthermore, the minimum layer thickness and conductor feature size of the DDM process are sufficient for circuit design at least in the lower microwave frequency bands. The materials characterization and analysis indicate that thermoplastic substrates produced via FDM have surface roughness features that remain a challenge, and the impact of transmission loss of the relatively low conductivity of micro-dispensed thick-film conductors can be magnified by the roughness of the surfaces they are printed upon. Compared to typical high-performance copper-clad microwave laminates, the degradation in transmission loss is marginal in low-Q circuits. However, as expected the loss effects are more substantial in narrow-band, high-Q circuits such as the HIS-backed dipole antenna and band-pass filters. Continuing research will address improvements in surface roughness and conductivity of the printed conductive materials which are necessary to make DDM fabrication competitive with state of the art PCB technology and viable for mm-wave applications. Improvements in surface roughness may be achieved using localized and/or global in-situ post-processing using mechanical, thermal or other means. REFERENCES [1] R. Das and P. Harrop, Printed, Organic & Flexible Electronics Forecasts, Players and Opportunities 2012–2022, Business Report. [2] B. Sanz-Izquierdo and E. A. Parker, “3-D printing technique for fabrication of frequency selective structures for built environment,” Electron. Lett., vol. 49, no. 18, pp. 1117–1118, Aug. 2013. [3] I. T. Nassar and T. M. Weller, “An electrically-small, 3-D cube antenna fabricated with additive manufacturing,” in Proc. IEEE Topical Conf. Wireless Sensors Sensor Networks (WiSNet), 2013, pp. 58–60. [4] A. M. N. Al-Mobin, R. Shankar, W. Cross, J. Kellar, K. W. Whites, and D. E. Anagnostou, “Advances in direct-write printing of RF-MEMS using M3-D,” in Proc. IEEE MTT-S Int. Microw. Symp. (IMS), 2014, pp. 1–4. [5] P. I. Deffenbaugh, R. C. Rumpf, and K. H. Church, “Broadband microwave frequency characterization of 3-D printed materials,” IEEE Trans. Components, Packaging Manufacturing Technol., vol. 3, no. 12, pp. 2147–2155, Dec. 2013. [6] N. Arnal, T. Ketterl, Y. Vega, J. Stratton, C. Perkowski, P. Deffenbaugh, K. Church, and T. Weller, “3-D multi-layer additive manufacturing of a 2.45 GHz RF front end,” in IEEE MTT-S Int. Microw. Symp. (IMS), 2015, pp. 1–4. [7] J. A. Paulsen, M. Renn, K. Christenson, and R. Plourde, “Printing conformal electronics on 3-D structures with aerosol jet technology,” in Proc. Future Instrum. Int. Workshop (FIIW), 2012, pp. 1–4. [8] L. Min, C. Shemelya, E. MacDonald, R. Wicker, and X. Hao, “Fabrication of microwave patch antenna using additive manufacturing technique,” in Proc. USNC-URSI Radio Sci. Meeting (Joint With AP-S Symp.), 2014, pp. 269–269. [9] L. Min, C. Shemelya, E. MacDonald, R. Wicker, and X. Hao, “3-D printed microwave patch antenna via fused deposition method and ultrasonic wire mesh embedding technique,” IEEE Antennas Wireless Propagat. Lett., vol. 14, pp. 1346–1349, 2015. [10] L. Min, X. Yu, C. Shemelya, E. MacDonald, and X. Hao, “3-D printed multilayer microstrip line structure with vertical transition toward integrated systems,” in Proc. IEEE MTT-S Int. Microw. Symp. (IMS), 2015, pp. 1–4. [11] M. Liang, “Three-dimensionally printed/additive manufactured antennas,” in Handbook of Antenna Technologies, Apr. 7, 2015, pp. 1–30. [12] T. Nakatsuka, “Polylactic acid-coated cable,” Fujikura Tech. Rev., pp. 39–45, 2011, Rev. 40. [13] D. Espalin, D. Muse, E. MacDonald, and R. Wicker, “3-D printing multifunctionality: Structures with electronics,” Int. J. Adv. Manuf. Tech., vol. 72, no. 5, pp. 963–978, Mar. 2014.

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[14] N. Arnal, T. Ketterl, T. Weller, G. Wable, T. Hue, W. Garon, and D. Gamota, “3-D digital manufacturing and characterization of antennas integrated in mobile handset covers,” in Proc. IEEE 16th Annual Wireless Microw. Technol. Conf. (WAMICON), Jun. 2015, pp. 1–5. [15] B. M. Tymrak, M. Kreiger, and J. M. Pearce, “Mechanical properties of components fabricated with open-source 3-D printers under realistic environmental conditions,” Materials & Design, vol. 58, pp. 242–246, 2014. [16] J. E. Mark, Physical Properties of Polymers Handbook, 2nd ed. New York, NY, USA: Springer Science, 2007, p. 489. [17] A. Bagsik, V. Schoeppner, and E. Klemp, “FDM part quality manufactured with ultem *9085,” in Proc. 69th Ann. Tech. Conf. Soc. Plastics Engineers (ANTEC), 2011, pp. 1294–1298. [18] L. J. Van der Pauw, “A Method of Measuring Specific Resistivity and Hall Effect of Discs of Arbitrary Shape,” Philips Research Reports, 12.1, Feb. 1958, vol. 13, pp. 1–9, no. 1. [19] M. Tabib-Azar, D. P. Su, A. Pohar, S. R. LeClair, and G. Ponchak, “0.4 um spatial resolution with 1 GHz ( cm) evanescent microwave probe,” Rev. Sci. Instrum., vol. 70, pp. 1725–1729, 1999. [20] A. Imtiaz, T. Baldwin, H. T. Nembach, T. M. Wallis, and P. Kabos, “Near-field microwave microscope measurements to characterize bulk material properties,” Appl. Phys. Lett., vol. 90, p. 243105, 2007. [21] M. Córdoba-Erazo, E. Rojas-Nastrucci, and T. Weller, “Measurement of electrical conductivity of direct digital printed conductive traces using near-field microwave microscopy,” in Proc. 42nd Int. Symp. Microelectron. (IMAPS), 2014, pp. 898–904. [22] J. C. Weber, J. B. Schlager, N. A. Sanford, A. Imtiaz, T. M. Wallis, L. M. Mansfield, K. J. Coakley, K. A. Bertness, P. Kabos, and V. M. Bright, “A near-field scanning microwave microscope for characterization of inhomogeneous photovoltaics,” Rev. Sci. Instrum., vol. 83, pp. 083702–083702-7, 2012. [23] M. F. Cordoba-Erazo and T. M. Weller, “Noncontact electrical characterization of printed resistors using microwave microscopy,” IEEE Trans. Instrum. Meas., vol. 64, no. 2, pp. 509–515, Feb. 2015. [24] V. V. Talanov, A. Scherz, and A. R. Schwartz, “A microfabricated near-field scanned microwave probe for noncontact dielectric constant metrology of low-k films,” in Proc. IEEE MTT-S Int. Microw. Symp. Dig., 2006, pp. 1618–1621. [25] V. V. Talanov, A. Scherz, R. L. Moreland, and A. R. Schwartz, “Noncontact dielectric constant metrology of low-k interconnect films using a near-field scanned microwave probe,” Appl. Phys. Lett., vol. 88, no. 19, p. 192906, May 2006. [26] M. F. Cordoba-Erazo and T. M. Weller, “Liquids characterization using a dielectric resonator-based microwave probe,” in Proc. 42nd Eur. Microw. Conf. (EuMC), 2012, pp. 655–658. [27] M. F. Cordoba-Erazo, E. A. Rojas-Nastrucci, and T. Weller, “Simultaneous RF electrical conductivity and topography mapping of smooth and rough conductive traces using microwave microscopy to identify localized variations,” in Proc. IEEE 16th Ann. Wireless Microwave Technol. Conf. (WAMICON), 2015, pp. 1–4. [28] B. A. Munk, Frequency Selective Surfaces: Theory and Design. New York, NY, USA: Wiley, 2000. [29] O. Luukkonen, C. Simovski, G. Granet, G. Goussetis, D. Lioubtchenko, A. V. Raisanen, and S. A. Tretyakov, “Simple and accurate analytical model of planar grids and high-impedance surfaces comprising metal strips or patches,” IEEE Trans. Antennas Propag., vol. 56, no. 6, pp. 1624–1632, Jun. 2008. [30] F. Costa, A. Monorchio, and G. Manara, “An equivalent-circuit modeling of high impedance surfaces employing arbitrarily shaped FSS,” in Proc. Int. Conf. Electromagn. Adv. Appl. (ICEAA), 2009, pp. 852–855. [31] S. R. Best and D. L. Hanna, “Design of a broadband dipole in close proximity to an EBG ground plane,” IEEE Antennas Propag. Mag., vol. 50, no. 6, pp. 52–64, Dec. 2008. [32] G. Bianconi, F. Costa, S. Genovesi, and A. Monorchio, “Optimal design of dipole antennas backed by a finite high-impedance screen,” Progr. Electromagn. Res. C, vol. 18, pp. 137–151, 2011. [33] H. Jia-Sheng and M. J. Lancaster, “Couplings of microstrip square open-loop resonators for cross-coupled planar microwave filters,” IEEE Trans. Microw. Theory Tech., vol. 44, no. 11, pp. 2099–2109, Nov. 1996. [34] L. Ledezma and T. Weller, “Miniaturization of microstrip square open loop resonators using surface mount capacitors,” in Proc. IEEE 12th Ann. Wireless Microw. Technol. Conf. (WAMICON), 2011, pp. 1–5. [35] M. M. Abdin, J. Castro, W. Jing, and T. Weller, “Miniaturized 3-D printed balun using high-k composites,” in Proc. IEEE 16th Ann. Wireless Microw. Technol. Conf. (WAMICON), 2015, pp. 1–3.

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Thomas P. Ketterl (S'98–M'01) received the B.S. degree in ocean engineering from Florida Atlantic University, Boca Raton, FL, USA, in 1994 and the M.E. and Ph.D. degrees from the University of South Florida, Tampa, FL, USA, in 2000 and 2006, respectively. From 2001 to 2010, he was a Research Engineer with the Center of Ocean Technology at the University of Florida, St. Petersburg, FL, USA. Since 2011, he has been working as a Research Associate with the University of South Florida's Department of Electrical Engineering. His research interests include electronic hardware design for medical applications, 3-D printing of RF circuits and antennas, and RF MEMS.

Yaniel Vega received the B.S. degree in electrical engineering from the University of South Florida, Tampa, FL, USA, in 2012, where he is currently pursuing the M.S.E.E. degree in RF/microwave engineering. Before joining the Wami group in 2014 he worked for Space Machine and Engineering Co. His current work is focused on the Direct Printing of 3-D Structural RF Electronics.

Nicholas C. Arnal received the B.S. and M.S. degrees in electrical engineering in 2014 and 2015, respectively, from the University of South Florida, Tampa, FL, USA. During this time he worked as a graduate research assistant for Dr. Thomas Weller and performed research in the area of RF/microwave circuits produced using additive manufacturing. He now works as an RF Engineer at Lockheed Martin Space Systems in Denver, CO, USA.

John Stratton received the B.S.E.E. degree (high honors) in May 2014 from the University of South Florida, Tampa, FL, USA, where he is currently pursuing the M.S.E.E. degree, focusing on RF/microwave engineering, under the guidance of Dr. Thomas Weller. His Master's thesis is related to the direct printing of 3-D structures with embedded RF circuits.

Eduardo A. Rojas Nastrucci received the B.S. degree in electrical engineering from the Universidad de Carabobo, Valencia, Venezuela, in 2009, and the M.S. E.E. degree from the University of South Florida, Tampa, FL, USA, in 2014, where he is currently pursuing the Ph.D. degree with the WAMI group. His doctoral research is focused on additive manufactured microwave circuits and antennas. He worked as Assistant Professor from 2011–2012 at Universidad de Carabobo. Specifically, his work is oriented in developing new structures, materials, and techniques with the objective of developing 3-D printed devices with improved performance.

María F. Córdoba-Erazo (S'11) received the B.S. degree in engineering physics from Universidad del Cauca, Colombia, in 2005 and the M.S. degree in electrical engineering from University of Puerto Rico at Mayagüez in 2009. Currently, she is working toward the Ph.D. in electrical engineering at University of South Florida, Tampa, FL, USA.

Ms. Córdoba-Erazo has been recipient of the IEEE MTT-S Graduate Fellowship in 2015, the ARFTG Roger Pollard Memorial Student Fellowship in Microwave Measurement in 2015 and the DOE-UPRM Scholarship in 2008.

Mohamed Mounir Abdin received the B.Sc. degree in electrical engineering from Arab Academy for Science and Technology (AAST), Cairo, Egypt, in 2010. Prior to joining the WAMI Research Center, University of South Florida, Tampa, FL, USA, in 2013, he worked for three years as a Process Engineer at a leading MEMS Foundry called Innovative Micro Technology (IMT), Santa Barbara, CA. Currently he is exploring the possibilities of designing RF/MW Systems using additive manufacturing.

Casey W. Perkowski is currently pursuing the B.S. degree in mechanical engineering at the University of Central Florida, Tampa, FL, USA. He has been an employee at Sciperio Inc., Orlando, FL, USA, since 2013 where he has worked done research in additive manufacturing techniques for both electrical and mechanical applications.

Paul I. Deffenbaugh received the UTEP Ph.D. degreee collaborating with Dr. Weller and his team at the WAMI Research Center, University of South Florida, Tampa, FL, USA, (electromagnetics group) in 2014, making measurements of 3-D printed RF/microwave devices. He worked at nScrypt, Inc., Orlando, FL, USA, designing and building 3-D printing equipment. For two years from 2011–2013 he conducted fundamental research in the 3-D printing of RF parts at the W.M. Keck Center for 3-D Innovation in El Paso. His research interests are 3-D printing and its applications in microwave electromagnetics. He currently works at Sciperio, Inc., Orlando, FL, USA, producing RF circuits using high precision 3-D printing equipment.

Kenneth H. Church received the B.S. degree in physics and electrical engineering in 1988 and 1989, respectively, and the M.S. and Ph.D. degrees in electrical engineering in 1991 and 1994, respectively, from Oklahoma State University, OK, USA. His areas of research include laser-materials interactions, RF materials and designs, antennas and 3-D printed electronics. He currently holds professional positions at Sciperio and nScrypt, Inc., Orlando, FL, USA. He is also a Research Professor with the University of Texas at El Paso, TX, USA.

Thomas M. Weller (S'92–M95–SM'98) received the B.S., M.S., and Ph.D. degrees in electrical engineering in 1988, 1991, and 1995, respectively, from the University of Michigan, Ann Arbor, MI, USA. From 1988 to 1990 he worked at Hughes Aircraft Company, El Segundo, CA, USA. He joined the University of South Florida, Tampa, FL, USA, in 1995 where he is currently Professor and Chair in the Electrical Engineering Department. His current research interests are in the areas of RF/microwave applications of additive manufacturing, development and application of microwave materials, and integrated circuit and antenna design.

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A Reconfigurable K-/Ka-Band Power Amplifier With High PAE in 0.18- m SiGe BiCMOS for Multi-Band Applications Kaixue Ma, Senior Member, IEEE, Thangarasu Bharatha Kumar, Student Member, IEEE, and Kiat Seng Yeo, Senior Member, IEEE

Abstract—This paper presents a high power efficient broad-band programmable gain amplifier with multi-band switching. The proposed two stage common-emitter amplifier, by using the current reuse topology with a magnetically coupled transformer and a MOS varactor bank as a frequency tunable load, achieves a 55.9% peak power added efficiency (PAE), a peak saturated power of 11.1 dBm, a variable gain from 1.8 to 16 dB, and a tunable large signal 3-dB bandwidth from 24.3 to 35 GHz. The design is fabricated in a commercial 0.18- m SiGe BiCMOS technology and measured with an output 1-dB gain compression point which is better than 9.6 dBm and a maximum dc power consumption of 22.5 mW from a single 1.8 V supply. The core amplifier, excluding the measurement pads, occupies a die area of 500 m 450 m. -band, Index Terms—Current reuse, dual band, -band, power added efficiency (PAE), SiGe BiCMOS, transformer coupled load, tunable amplifier, variable gain amplifier (VGA).

I. INTRODUCTION

I

N THE RECENT decade, the rising demand in short-range high-speed wireless communication systems have nurtured the development of radio frequency (RF) integrated circuit design for the diversified -band (18–27 GHz) and -band (26.5–40 GHz) applications such as 24 GHz industrial scientific and medical (ISM) band gigabit-per-second wireless systems [1], wireless sensor network [2], point-to-point communication (18–23 GHz) [3], local multipoint distribution service (27.5–29.5 GHz) [4], and short-range (22–29 GHz) automotive radar applications for anti-collision detection [5], [6]. The power amplifier (PA) design often involves the tradeoff between the efficiency and linearity. This limitation can be mitigated by using several design techniques such as the stacked Manuscript received June 19, 2015; revised September 29, 2015; accepted October 11, 2015. Date of publication November 11, 2015; date of current version December 02, 2015. This work was supported in part by the Exploit Technologies Pte. Ltd. (ETPL), Singapore and Nanyang Technological University (NTU), Singapore. This paper is an expanded version from the IEEE MTT-S International Microwave Symposium, Phoenix, AZ, USA, May 16–23 2015. K. Ma is with the School of Physical Electronics, University of Electronic Science and Technology of China, Chengdu 610054, China (e-mail: kxma@ieee. org). T. B. Kumar and K. S. Yeo are with the Singapore University of Technology and Design, 138682 Singapore (e-mail: [email protected]; [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2015.2495129

amplifier design proposed in [7] that supports a large signal swing to increase the output power by alleviating the high frequency device's low at the cost of large supply voltage. An alternative design technique is the switched mode PA in which the circuit operation adapts dynamically based on instantaneous characteristics (amplitude, phase, frequency) of the input signal such as the class E in [8] and class in [9] that minimizes power in the amplifying transistors by avoiding overlap between the current and voltage waveforms by using the digital ON/OFF switches. However, such designs require special linearization techniques to reduce the nonlinearities introduced by the output harmonics of the switching distorted waveforms. In contrast, PA design is also based on continuous power control such as adaptive biasing technique implemented in [10] and by using load impedance modulation technique of the Doherty PA in [11]. However, these PA design techniques involve large dynamic range complex circuitry that consumes additional dc power. An implementation technique to enhance PA efficiency as well as linearity is by reducing the losses involved in the interconnects and passive components by using distributed structure equivalents in physical layout such as Wilkinson couplers [12] and the thin-film micro-strip lines (MSL) [13] as the power splitter/ combiner between multiple PA stages, the substrate-shielded coplanar waveguide (CPW) structures [14], the transmission line transformers (TLT) [3], and the substrate-shielded MSL [6], [15]. However, these distributed structures occupy a large die area. The amplifier power efficiency can be improved by using various current-reused topologies [16] such as the capacitive-coupling [17], the inter-stage LC series resonance, and the transformer-coupling. The transformer-based LC tank has been already proposed in the design of various transceiver building blocks such as the voltage controlled oscillator (VCO) [18], low noise amplifier (LNA) [19], and Class-F PA [20]. The work in [17] presents an inductor load based current-reused LNA at -band with an efficiency of up to 37%. In this paper, a SiGe BiCMOS based -/ -band digitally controlled variable gain amplifier (DVGA) with multiple frequency tunable bands is proposed, designed and verified by on-wafer measurement. This work is extended from [21] to include the physical implementation details of the loaded tank circuit, together with a detailed analysis of its quality factor enhancement, and henceforth the resulting improvement in the overall amplifier PAE of 55.9% and the linearity performance. The proposed design improves power efficiency by simultane-

0018-9480 © 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

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Fig. 1. Circuit schematic of (a) the proposed reconfigurable multi-band amplifier and (b) half circuit equivalent.

Fig. 2. Hybrid- small signal half circuit equivalent of the proposed reconfigurable multi-band amplifier.

ously reducing the overall dc power consumption using the current reuse technique and improving the amplifier linearity by using a loaded tank circuit's enhanced . The proposed design provides a variable gain control, frequency-band switching, wideband small signal gain flatness, low power consumption, improved linearity, and high PAE. This paper is organized as follows. Section II describes the detailed analysis of the proposed amplifier circuit. The detail implementation of the frequency tunable load is explained in Section III. Section IV discusses about the load tank circuit's -factor enhancement resulting in improvement of proposed amplifier's linearity and PAE performance. The design analysis is verified in Section V by on-wafer measurement with the performance comparison of this work against the state-of-the-art -band amplifiers. Finally, the paper conclusion is provided in Section VI. II. CIRCUIT ANALYSIS The circuit schematic of the proposed multi-band tunable amplifier is a fully differential two-stage ac cascaded and dc stacked common emitter amplifier as shown in Fig. 1(a). The first stage is a DVGA with a four bit digital gain control and the second stage is a frequency tunable amplifier. The block depicted as the frequency tunable load is the tank circuit that consists of an integrated 2-coil spiral transformer

and the varactor bank. The inductors and the transformer used in the proposed differential circuit are chosen with center tap configuration to significantly improve the die area utilization. The capacitors provide the ac ground for second stage differential amplifier. The circuit in Fig. 1(a) is symmetric and can be folded along the vertical axis of symmetry as shown in Fig. 1(b). By replacing the transistors with the hybrid- model of the and transistors and re-arranging the circuit components in Fig. 1(b), the small signal equivalent half-circuit of the proposed tunable amplifier is obtained as shown in Fig. 2. A. Variable Gain Amplifier Stage Analysis The output power of the proposed tunable amplifier can be adjusted by varying the gain of the first stage amplifier using the four digital bits . Based on Figs. 2 and 3, the amplifier gain of first stage is given as (1) where transconductance , early voltage , the commonemitter forward current gain , and the output resistance's degradation factor due to transistor saturation with are indicated for the transistor pair , the constant coefficients of the estimated

MA et al.: RECONFIGURABLE K-/Ka-BAND POWER AMPLIFIER WITH HIGH PAE

linear gain function to 3), the digital gain control configuration as received from the digital controller or the digital baseband ( 0 to 3), and which is the dc current corresponding to the amplifier minimum gain when all the digital control bits are reset V . The gain control based on the base bias current variation of the first stage amplifier in the stacked structure mainly affects the output resistance and does not significantly alter the transconductance of the HBT pair [17]. From the variable gain control bias circuit shown in Fig. 3, the mirrored variable base biasing currents through the nodes ( 1 and 2) has to be properly matched to avoid offset errors in the first stage differential amplifier. Unlike voltage biasing of amplifiers, the current biasing circuit provides a gain control along with the power down capability. The maximum limited input signal level at and nodes provides a small voltage fluctuation at the drain of the PMOS current mirror transistors which continues to operate in the strong saturation region by generating almost same bias currents. Hence the induced nonlinearity effect due to input signal on the input transistor's bias currents is very minimal.

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Fig. 3. Variable gain control base biasing circuit.

B. Frequency Tunable Amplifier Stage Analysis The second stage amplifier gain from Fig. 2 is based on the fixed biasing transconductance of the transistor pair [21] and frequency tunable load impedance as (2) From Fig. 4(a), the load impedance of the second stage amplifier is determined by a high -factor transformer with the primary coil which is magnetically coupled to an LC tank circuit built by using the transformer secondary coil and the varactor bank . This load impedance is connected in parallel to the output matching network and the influence of the tank circuit on output matching is described in the following section. The transformer used in the load circuit can be represented as a T-network based on [22] and also the varactor bank can be modeled as a series combination [23] of the capacitor and varactor loss as shown in Fig. 4(b). By using loop analysis of the network in Fig. 4(b), we obtain the load impedance as (3) shown at the bottom of the page. 1) Varactor Bank Q-Factor: The varactor bank, as viewed from the transformer secondary coil [shown in Fig. 4(a)], consists of the parallel connected variable capacitors with equivalent impedance . The equivalent lumped circuit model of the varactor bank impedance as determined by [23] is shown in Fig. 5. The varactor bank impedance consisting of identical varactors is given by (4)

Fig. 4. (a) Tunable load (transformer and MOS-varactor bank) with output matching network. (b) T-section model of transformer with MOS-varactor.

Fig. 5. Varactor bank with equivalent lumped circuit model.

From (4), the varactor bank

-factor is (5)

(3)

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Fig. 6. Simulation plots of output matching by tuning the tank circuit load with

Based on (5) it is deduced that by connecting any number of varactors in parallel for the tunable tank circuit, the -factor contribution from the varactor bank is almost fixed. 2) Transformer Secondary Coil Q-Factor: The transformer secondary coil's -factor is given as

varied together from 0 V to 1.8 V

.

By assuming a negligible effect of the large shunt bias resistors and on the small signal analysis, the overall multi-band tunable amplifier gain is determined by the gain product of the cascaded stages as (12)

(6) 3) Overall Tank Circuit Q-Factor: For the tunable load impedance transfer function as given in (3), we can deduce that (7) (8) where is the angular resonant frequency and is the overall tank circuit -factor. By re-arranging (8), the overall tank -factor is given as (9) The overall tank -factor [24] based on the individual tors of the inductance and the varactor bank is given by

-fac(10)

By using (5) and (6) in (10) we get (11) The overall tank -factor as determined by (9) is the same as (11). Furthermore, the -factor of second-stage amplifier response in (2) is mainly determined by transformer secondary coil and a single identical varactor of the varactor-bank. Hence, the overall -factor of the second stage amplifier load is obtained by considering the mutual magnetic coupling due to the in-phase currents of the transformer primary coil and the induced current from the secondary coil shunted with the varactor bank. This enables the design to be scalable in frequency with a voltage controlled tuning range.

From (12), we can infer that the frequency response of the overall proposed amplifier gain is a function of the four bit digital gain control configuration as well as the tunable varactor control voltage . C. Impedance Matching Analysis The amplifier input and output terminals are matched to differential impedance by using T-networks as shown in Fig. 1(a). The intermediate matching network which is also the first stage amplifier's load is L-network and its passive component values, including the inductor and de- resistors , are optimized for better amplifier gain flatness. Based on the amplifier circuit topology, the output return loss is mainly determined by the output matching network as well as the load tunable tank circuit. By using the frequency band selection bits of the load tank circuit, an adaptive output return loss is achieved as shown in Fig. 6. This allows the output return loss to be frequency band reconfigurable unlike the input return loss which is almost unaffected by the tank circuit tuning. The bandwidth for both the frequency bands are governed by the output matching network's loaded -factor as well as the tank -factor. III. FREQUENCY TUNABLE LOAD DESIGN The frequency tunable load in the second stage amplifier consists of a 2-coil center tap transformer and a MOS varactor bank connected to the secondary coil as shown in Fig. 7. The primary and secondary coils of the transformer are built on the same plane with edge coupling to avoid formation of a broadside coupled parasitic capacitance between the coils. Hence it shifts the tank circuit self-resonance to a higher frequency. The transformer coils are oriented in non-inverting mode [22] and are implemented by using the top metal layer (with thickness

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Fig. 7. Transformer layout (a) 3D view and (b) top view with interface to the varactor bank.

Fig. 8. EM simulation plot of the designed transformer's primary and secondary coil inductance along with the coupling coefficient against the standalone inductance.

) as supported of 2.81 m and sheet resistance of 10.5 m in the fabrication process to achieve a high -factor. The transformer's primary outer coil size is 85 m, the secondary coil size is 105 m, the uniform coil width is 8 m, and the coil spacing is 2 m (shown in Fig. 7). The transformer is designed and optimized using the Agilent ADS Momentum 2.5D EM simulator in RF mode to estimate the desired primary and secondary coil inductance over the entire operating frequency range as shown in Fig. 8. The transformer design does not include any kind of shielding structures. When compared to the scheme with a standalone inductive load, the transformer by using a magnetic coupling coefficient provides an enhanced -factor that increases the effective secondary coil inductance as given by (13) The transformer in the proposed design has turns ratio of 2:1 which is also evident in Fig. 7. Hence the ratio of primary coil inductance to secondary coil inductance by assuming almost equal sized coils is 4:1. This assumption is also validated by the inductance plot obtained from the EM simulation as shown in Fig. 8.

The work in [18] claims that for a same area constraint, there is no -improvement for transformer tank resonator as compared to a standalone inductor tank resonator which is not completely agreeable for the planar transformer with in-phase current orientation. Since in this work [18], the limitations such as reduction of the coil inductance by increasing its width and spacing as well as the loss contributions of the tank circuit capacitors are neglected. Moreover, due to the increased effective coil inductance by the magnetic coupling, the length of the coil can be reduced to provide the same inductance value as a standalone inductor in the required frequency range. This reduces the resistive loss associated with the transformer coil and eventually enhances the -factor due to the transformer coupled tank circuit as compared to the standalone load inductor. The varactor bank is parallel-connected MOS varactors that are operating in the accumulation mode with the gate-source tuning voltage ranging from 0.9 to 0.9 V to traverse across the to value, respectively. To avoid negative external tuning voltages at the varactor source/drain terminals , the varactor gate voltage is level-shifted to 0.9 V through the secondary transformer's center tap as shown in Fig. 7(b). This ensures a positive external voltage ranging from 0 to 1.8 V to be used as the varactor tuning voltage with the capacitance tuning characteristics as shown in Fig. 9(a). The simulation plots in Fig. 9(a) and (b) are obtained for identical varactors connected in parallel against the same varactor tuning voltage . From Fig. 9(a), the equivalent capacitance adds up as the number of identical varactors in parallel increases. An interesting observation noticed in the varactor bank -factor plot, shown in Fig. 9(a), is the equivalent -factor of the varactor bank which is unaffected by any number of parallel connected varactors . This behavior agrees with (5) as described in Section III. This is one of the merits of this proposed design and the amplifier operating frequency range can be easily reconfigured based on the number of varactors in parallel as shown by the intrinsic tank frequency plot in Fig. 9(b). As the number of varactors in the varactor-bank increases, the main design trade-off taken into consideration is the shrinking of the tunable frequency range due to the increased tank minimum capacitance value which is limited by .

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Fig. 10. Simulated single-ended open circuit (self-inductance) and varactor bank loaded tank -factor for two versions of the transformer primary coil size and the MOS varactor length as m m and m m .

Fig. 9. Simulation plots at 30-GHz frequency of the designed varactor's (a) capacitance and quality factor and (b) intrinsic tuned tank frequency.

The variation [23]of the varactor capacitance tuning voltage ( 1, 2, etc.) is defined as

by the

(14) is the minimum capacitance value of varactor, is the varactor tuning range, is the range of gate bias at which has a maximum variation for , determines the normalized bias voltage range. From (3), (7), (12) and (14) we can infer that by changing using a corresponding varactor tuning voltage ( 1, 2, etc.), the center frequency of the overall amplifier frequency response can be tuned. where,

IV.

-FACTOR ENHANCEMENT

As evident from the simulation plot in Fig. 10, the loaded tank -factor is enhanced under two conditions namely, A. Loaded Tank Q-Enhancement From

to

The loaded tank -factor curves from to in Fig. 10 are obtained by reducing the transformer size of the primary outer coil from 94 to 85 m and the secondary coil

Fig. 11. Microphotograph of proposed multi-band amplifier with tunable load m , Total area with I/O pads: m ). (Core area:

size from 114 to 105 m as well as by concurrently decreasing the MOS varactor-bank's channel length from 650 to 500 m. From Fig. 10, the curves from to are upshifted both along the frequency as well as the peak value. Both these observations can be illustrated by considering the simultaneous reduction of the tank circuit component dimensions ( and ) from to that results in a frequency upshift due to the decreased product according to (7) as well as an increased peak value by the resulting decreased resistive losses and as discussed in (9) and (13).

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Fig. 13. Large signal measurement plot of the proposed tunable amplifier at “11”). 29.5 GHz frequency, maximum gain setting, and band #2 (

ering the fact that the peak of the loaded resonant tank -factor is positioned within the pass-band of the amplifier's interested frequency range. Hence we can mitigate the complicated tank circuit analysis by neglecting the high-order effects of transformer secondary coil loaded by the capacitive varactor bank [19]. V. EXPERIMENTAL RESULTS

Fig. 12. Measured -parameter variation based on (16 steps), band (2 steps) (a) gain and (b) return loss and isolation. switch based on

B. Loaded Tank Q-Enhancement By Band-Select Input VSW From “00” to “11” Configuration From Fig. 10, we also observe that, for either of the curves or , the frequency upshifts for band-select input configuration switching from “00” to “11” as well as the peak value is enhanced. This can be analytically justified by considering the intrinsic tank frequency characteristics and the MOS varactor bank's -factor as shown in Fig. 9(b) and (a), respectively for an increase in the voltage from 0 to 1.8 V. Both these -factor enhancements simultaneously improves the proposed amplifier's PAE, linearity and the peak gain performance by reducing the tank circuit losses which are also evident from the on-wafer measurement results. The choice of the proposed transformer coil dimensions and the varactor bank aspect ratios are mainly determined by consid-

The proposed -band frequency tunable DVGA is implemented in a 0.18- m SiGe BiCMOS process from Tower Jazz Semiconductors. The microphotograph of the proposed amplifier in the fabricated wafer is shown in Fig. 11 which occupies an overall die area of 0.89 mm 0.81 mm including the on-wafer probing pads. The proposed design performance is experimentally verified by using on-wafer probing with the Agilent E8364B PNA network analyzer that supports a 4-port calibration and mixed mode scattering parameter measurement by avoiding the use of any balun. The proposed amplifier consumes a total dc current ranging from 9.9 to 12.5 mA for the maximum to minimum gain variation, respectively during its normal operation mode V and during the power down mode V dissipates a dc current of 106 A from a single 1.8 V supply voltage. The gain reduction with an increase in the bias current is due to the transition of first stage amplifying transistors from active region (maximum gain) towards saturation region (minimum gain). The measurement setup consists of wafer probe station with two RF GSSG probes for probing the amplifiers' differential input and output, along with a 7-pin dc probe that provides a 4-bit digital gain control signal along with a 2-bit frequency band selection input, and individual dc probes for supply voltage V , the base bias circuit constant current A , and the power down mode control as marked in Fig. 11. The digital pins namely , and are applied with dc voltages of either 0 V (for bit “0”) or 1.8 V (for bit “1”).

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Fig. 15. Measured stability factors of the proposed amplifier design for the maximum gain and band #1 condition.

Fig. 14. Measured linearity performance over the two bands “0000”) (a) proposed design with maximum gain ( PAE.

of the and (b)

The variable gain control using the four gain control bits of the proposed amplifier is verified by the measured -parameters shown in Fig. 12(a) and (b). Additionally, Fig. 12 indicates the frequency band switching functionality of the proposed amplifier that is achieved by providing a same voltage to pins (together depicted as ). By providing option for dual-band switching, the center frequency of the gain response can be changed. The small-signal gain's 3-dB bandwidth can support -band by selecting band#1 ( “00”) and -band using band#2 selection ( “11”). Additionally, a 0.75 dB small signal gain flatness is achieved for a frequency ranging from 22.67 to 30.2 GHz across both the frequency bands. The high transformer coupled load along with the current reuse topology of the proposed design provides a high gain and an improved linearity performance together with low dc power consumption. This results in an output 1-dB gain compression point ) of 9.6 dBm for the band#2 ( “11”), and the maximum gain condition ( “0000”) at a measured frequency of 29.5 GHz as shown in Fig. 13. The measured and PAE (with a 11.1 dBm peak saturated power and 55.9% peak PAE) of the proposed tunable amplifier over the two switchable frequency bands based on

Fig. 16. Simulated (dashed line) and measured (solid line) gain of proposed “00”). design for maximum/minimum gain conditions band#1 (

and maximum gain setting ( “0000”) are shown in Fig. 14(a) and (b), respectively. Both these plots indicate that the linearity and PAE performance are improved for band#2 ( “11”) by considering the tank circuit load enhancement as illustrated in Fig. 10. Although, the peak output power in both the configurations is comparative by only about 1.9 dB difference as well as the amplifier performance with “00” configuration is also comparable with the state-of-the-art performance to support dual band reconfigurability. Hence the configuration of “00” is necessary which also highlights the merit of this dual-band amplifier design. Based on this proposed power down method, there is a possibility to turn on the input transistors, under power down mode by a large input signal power level of at least 8 dBm. This signal level is much larger than the input point of the proposed amplifier design under normal dc bias condition. Hence by providing the same limitation on the input power

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TABLE I PERFORMANCE SUMMARY OF WIDEBAND K-/KA-BAND DRIVE POWER AMPLIFIERS

Fig. 17. Simulated load voltage and load current waveforms at 28 GHz with “00” configuration for band #1 against input power sweep from 35 to 10 dBm (step = 1 dB).

Fig. 18. Simulated load voltage and load current waveforms at 30 GHz with “11” configuration for band #2 against input power sweep from 35 to 10 dBm (step = 1 dB).

level as boundary condition we can still achieve the power down using the proposed method. The stability factors ( and ) extracted from measured S-parameters shown in Fig. 15 indicates that the proposed amplifier has unconditional stability over the operating frequency range. The difference between the simulation and measurement results as shown in Fig. 16 for the maximum and minimum gain condition can be attributed to the transistor and varactor model inaccuracy at such high frequencies. The simulation load voltage and load current waveforms at each of the band based on configuration for input power sweep indicates that the proposed dual band amplifier design operates in linear region as shown in Figs. 17 and 18 for a large

input power level of 10 dBm which is close to the input point. The performance of the proposed multi-band amplifier is consolidated in Table I and compared with the state-of-the-art -band monolithic amplifier designs. By using dc current reuse topology along with a high frequency tunable transformer coupled load and a variable gain control option, the PAE and the overall amplifier performance is improved as compared to other works in Table I. It is also evident that the amplifier's linearity performance ( and ) in other works are mainly achieved by using a larger supply voltage (increased headroom) and also high dc power consumption that supports the large signal drive capability.

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Although the proposed amplifier design has enhanced PAE performance as compared to the state-of-the-art works, the high linearity performance becomes a hard limit and a major concern in power amplifier specifications and reconfigurable devices. VI. CONCLUSION This paper presents a high power efficient broadband DVGA with reconfigurable dual-band switching capability to support -band (18–27 GHz) satellite communication, short range 24 GHz ISM (22–29 GHz) automotive radar system and -band (26.5–40 GHz) applications. In this work, the tunable loaded tank circuit -factor enhancement along with the variable gain control, and the frequency-band switching of the proposed amplifier, together with their resulting improvement on PAE and linearity performance are theoretically analyzed and experimentally verified. ACKNOWLEDGMENT The authors would like to thank the Tower Jazz Semiconductors Inc., Newport Beach, CA, USA, for providing fabrication service of the design. The authors would also like to thank W. Yang of Nanyang Technological University (NTU), Singapore for assisting in the on-wafer measurement of the proposed design. REFERENCES [1] T. Tokumitsu, “K-band and millimeter-wave MMICs for emerging commercial wireless applications,” IEEE Trans. Microw. Theory Techn., vol. 49, no. 11, pp. 2066–2072, Nov. 2001. [2] I. Gresham et al., “Ultra-wideband radar sensors for short-range vehicular applications,” IEEE Trans. Microw. Theory Techn., vol. 52, no. 9, pp. 2105–2122, Sep. 2004. [3] C.-W. Kuo, H.-K. Chiou, and H.-Y. Chung, “An 18 to 33 GHz fullyintegrated darlington power amplifier with guanella-type transmissionline transformers in 0.18 m CMOS technology,” IEEE Microw. Wirel. Compon. Lett., vol. 23, no. 12, pp. 668–670, Dec. 2013. [4] M. K. Siddiqui, A. K. Sharma, L. G. Callejo, and R. Lai, “A high power and high efficiency monolithic power amplifier for LMDS applications,” IEEE Trans. Microw. Theory Techn., vol. 46, no. 12, pp. 2226–2232, Dec. 1998. [5] FCC, Washington, DC, USA, “First report and order, revision of part 15 of the commission's rules regarding ultra wideband transmission systems ET Docket 98–153,” 2002. [6] J.-W. Lee and S.-M. Heo, “A 27 GHz, 14 dBm CMOS power amplifier using 0.18 m common-source MOSFETs,” IEEE Microw. Wirel. Compon. Lett., vol. 18, no. 11, pp. 755–757, Nov. 2008. [7] J.-H. Chen, S. R. Helmi, and S. Mohammadi, “A fully-integrated Ka-band stacked power amplifier in 45 nm CMOS SOI technology,” in Proc. IEEE Topical Meet. Silicon Monolithic Integr. Circuits RF Syst., Jan. 2013, pp. 75–77. [8] C. Cao, H. Xu, Y. Su, and O. K. Kenneth, “An 18-GHz, 10.9-dBm fully-integrated power amplifier with 23.5% PAE in 130-nm CMOS,” in Proc. 31st Eur. Solid-State Circuits Conf., Sep. 2005, pp. 137–140. [9] S. Y. Mortazavi and K.-J. Koh, “A class F-1/F 24-to-31 GHz power amplifier with 40.7% peak PAE, 15 dBm OP 1 dB, and 50 mW Psat in 0.13 m SiGe BiCMOS,” in Int. Solid-State Circuits Conf. Tech. Dig., San Francisco, CA, USA, Feb. 2014, pp. 254–255. [10] N. -. Kuo, J.-C. Kao, C.-C. Kuo, and H. Wang, “K-band CMOS power amplifier with adaptive bias for enhancement in back-off efficiency,” in IEEE MTT-S Int. Microw. Symp. Dig., Baltimore, MD, USA, Jun. 2011, pp. 1–4. [11] E. Kaymaksut and P. Reynaert, “Transformer-based uneven Doherty power amplifier in 90 nm CMOS for WLAN applications,” IEEE J. Solid-State Circuits, vol. 47, no. 7, pp. 1659–1671, Jul. 2012. [12] K. Kim and C. Nguyen, “A 16.5–28 GHz 0.18- m BiCMOS power amplifier with flat 19.4 1.2 dBm output power,” IEEE Microw. Wirel. Compon. Lett., vol. 24, no. 2, pp. 108–110, Feb. 2014.

[13] P.-C. Huang, J.-L. Kuo, Z.-M. Tsai, K.-Y. Lin, and H. Wang, “A 22-dBm 24-GHz power amplifier using 0.18- m CMOS technology,” in IEEE MTT-S Int. Microw. Symp. Dig., Anaheim, CA, USA, May 2010, pp. 248–251. [14] A. Komijani, A. Natarajan, and A. Hajimiri, “A 24-GHz, 14.5-dBm fully integrated power amplifier in 0.18- m CMOS,” IEEE J. SolidState Circuits, vol. 40, no. 9, pp. 1901–1908, Sep. 2005. [15] P. J. Riemer, J. S. Humble, J. F. Prairie, J. D. Coker, B. A. Randall, B. K. Gilbert, and E. S. Daniel, “Ka-band SiGe HBT power amplifier for single chip T/R module applications,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2007, pp. 1071–1074. [16] V. Giammello, E. Ragonese, and G. Palmisano, “A transformer-coupling current-reuse SiGe HBT power amplifier for 77-GHz automotive radar,” IEEE Trans. Microw. Theory Techn., vol. 60, no. 6, pp. 1676–1683, Jun. 2012. [17] T. B. Kumar, K. Ma, and K. S. Yeo, “A Ku-band variable gain LNA with high PAE in 0.18 m SiGe BiCMOS technology,” IEEE Microw. Wirel. Compon. Lett., submitted for publication. [18] H. Krishnaswamy and H. Hashemi, “Inductor- and transformer-based integrated RF oscillators: A comparative study,” presented at the IEEE Custom Integr. Circuits Design Conf., San Jose, CA, USA, Sep. 2006. [19] Y. Xiaohua and N. M. Neihart, “Analysis and design of a reconfigurable multimode low-noise amplifier utilizing a multitap transformer,” IEEE Trans. Microw. Theory Techn., vol. 61, no. 3, pp. 1236–1246, Mar. 2013. [20] K. K. Sessou and N. M. Neihart, “An integrated 700–1200-MHz class-F PA with tunable harmonic terminations in 0.13- m CMOS,” IEEE Trans. Microw. Theory Techn., vol. 63, no. 4, pp. 1315–1323, Apr. 2015. [21] T. B. Kumar, K. Ma, and K. S. Yeo, “A low power programmable gain high PAE K-/Ka-band stacked amplifier in 0.18 m SiGe BiCMOS technology,” in IEEE MTT-S Int. Microw. Symp. Dig., Phoenix, AZ, USA, May 2015, pp. 1–4. [22] J. R. Long, “Monolithic transformers for silicon RF IC design,” IEEE J. Solid-State Circuits, vol. 35, no. 9, pp. 1368–1382, Sep. 2000. [23] K.-H. Tsai and S.-I. Liu, “A 104-GHz phase-locked loop using a VCO at second pole frequency,” IEEE Trans. Very Large Scale Integr. (VLSI) Syst., vol. 20, no. 1, pp. 80–88, Jan. 2012. [24] L. Li, P. Reynaert, and M. Steyaert, “Design and analysis of a 90 nm mm-wave oscillator using inductive-division LC tank,” IEEE J. SolidState Circuits, vol. 44, no. 7, pp. 1950–1958, Jul. 2009. [25] J.-L. Kuo and H. Wang, “A 24 GHz CMOS power amplifier using reversed body bias technique to improve linearity and power added efficiency,” in IEEE MTT-S Int. Microw. Symp. Dig., Montreal, QC, Canada, Jun. 2012, pp. 1–3. [26] P. C. Huang, Z. M. Tsai, K. Y. Lin, and H. Wang, “A 17–35 GHz broadband, high efficiency pHEMT power amplifier using synthesized transformer matching technique,” IEEE Trans. Microw. Theory Techn., vol. 60, no. 1, pp. 112–119, Jan. 2012. Kaixue Ma (M'05–SM'09) received B.E. M.E. degree from Northwestern Polytechnolgical University (NWPU), China, and the Ph.D. degree from Nanyang Technological University (NTU), Singapore. From August 1997 to December 2002, he was with China Academy of Space Technology (Xi'an), where he was Group Leader of millimeter-wave group for space-borne microwave and millimeter-wave components and subsystems of satellite payload and VSAT ground station. From September 2005 to September 2007, he was with MEDs Technologies as an R&D Manager and project leader, where he provides design services and product development. From September 2007 to March 2010, he was with ST Electronics (Satcom & Sensor Systems) as R&D Manager, Project Leader, and Technique Management Committee of ST Electronics. From 2010 to 2013, he was a Senior Research Fellow and millimeter-wave IC team leader for 60 GHz Flagship Chipset project. From 2013 to the present, he is a full Professor with the University of Electronic Science and Technology of China (UESTC). As a PI/Technique Leader, he did projects with fund more than $12 million (excluding projects done in China). His research interests include RFIC Design, satellite communication, software defined radio, microwave/millimeter-wave circuits and system using CMOS, MEMS, MMIC, and LTCC. He filed 10 patents and authored/co-authored over 140 journal and conference papers. He is review board of over 10 international Journals. He gave invited talks or keynote addresses over 20 times. Dr. Ma was a recipient of Best Paper Awards from IEEE SOCC2011, IEEK SOC Design Group Award, Excellent Paper Award from International Confer-

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ence on HSCD2010, Chip Design Competition Bronze Award from ISIC2011, and Special Mention Award of Emerging Technology, Singapore Inforcomm Technology Federation for the development of the Singapore Next Generation Wi-Fi Chipset 2012 and Named in Precious China “Thousand Young Talent Program” in 2012.

Kiat Seng Yeo received the B.Eng. (EE) and Ph.D. (EE) degrees from Nanyang Technological University (NTU), Singapore, in 1993 and 1996, respectively. He is currently an Associate Provost (Graduate Studies and International Relations) at Singapore University of Technology and Design (SUTD) and Member of Board of Advisors of the Singapore Semiconductor Industry Association. Professor Yeo is a widely known authority in low-power RF/millimeter-wave IC design and a recognized expert in CMOS technology. He has secured over $30 million of research funding from various funding agencies and the industry in the last three years. Before his new appointment at SUTD, he was Associate Chair (Research), Head of Division of Circuits and Systems, and Founding Director of VIRTUS of the School of Electrical and Electronic Engineering, NTU. He has published 6 books, 5 book chapters, over 400 international top-tier refereed journal and conference papers, and holds 35 patents. Dr. Yeo served in the editorial board of the IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES and holds/held key positions in many international conferences as Advisor, General Chair, Co-General Chair and Technical Chair. He was a recipient of the Public Administration Medal (Bronze) on National Day 2009 by the President of the Republic of Singapore and was also a recipient of the Distinguished Nanyang Alumni Award in 2009 for his outstanding contributions to the university and society.

Thangarasu Bharatha Kumar (S'12) received the B. E. (E&C) degree from Ratreeya Vidyalaya College of Engineering (RVCE), Bangalore, India, which is affiliated with the Visvesvaraya Technological University (VTU), in 2002, the M.Sc. degree from German Institute of Science and Technology (GIST), Singapore, (a joint master's degree programme by NTU, Singapore and Technische Universitaet Muenchen (TUM), Germany), in 2010, and the Ph.D. (EE) degree from NTU, Singapore, in 2015. From January 2010 to August 2015, he was with VIRTUS, IC Design Centre for Excellence, NTU, Singapore, as a Research Associate where he worked on SiGe HBT and CMOS-based reconfigurable amplifiers for microwave and millimeter wave RF integrated circuit design. He is now a researcher with Singapore University of Technology and Design (SUTD), Singapore. His research interests include RF and millimeter-wave reconfigurable integrated circuit design. He has authored/coauthored over 25 journals and conference papers. Dr. Kumar was a recipient of the DAAD scholarship during his M.Sc. study.

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A Broadband GaN pHEMT Power Amplifier Using Non-Foster Matching Sangho Lee, Student Member, IEEE, Hongjong Park, Student Member, IEEE, Kwangseok Choi, Student Member, IEEE, and Youngwoo Kwon, Senior Member, IEEE

Abstract—Non-Foster matching is applied to design a multi-octave broadband GaN power amplifier (PA) in this paper. The bandwidth limitation from high-Q interstage matching is overcome through the use of negative capacitor, which is realized with a negative impedance converter (NIC) using the cross-coupled GaN FETs. For high power operation over the entire bandwidth, the natural interstage matching is optimized for the upper subfrequency band and the lower subfrequency band is compensated for by the negative capacitance presented by non-Foster circuit (NFC). Detailed analysis is presented to understand the frequency and power limits of NIC circuits for PA applications. Two negative impedance matched PAs (NMPAs) are fabricated with 0.25- m GaN pHEMT process. The implemented PA with combining shows the output powers of 35.7–37.5 dBm with the power added efficiencies of 13–21% from 6 to 18 GHz. combining PA achieves over 5 W output power from The 7 to 17 GHz. The NFC boosts the efficiencies and power below 12 GHz to achieve broadband performance without using any lossy matching or negative feedback. To our knowledge, this is the first demonstration of NIC-based broadband amplifiers with multi-watt-level output power. Index Terms—GaN, negative capacitance, negative impedance converter, non-Foster circuit, power amplifier (PA).

I. INTRODUCTION

A

WATT-LEVEL power amplifier (PA) with multi-octave bandwidth is required for broadband applications such as electronic warfare system. GaN device is suitable for this application due to its high power density and high voltage operation, which results in relatively large load impedance. The distributed amplifier (DA) is a commonly used topology for multi-octave PA. The input and output capacitances are absorbed into the artificial transmission line to overcome the frequency limitation. However, DAs suffer from small gain and requires a relatively large die area. The reactive matched PAs (RMPAs) are also widely used as multi-octave PAs. RMPAs utilize a multiple-stage design to realize high gain. However, it has the bandwidth (BW) problem coming from Bode–Fano criterion [1], [2]. To achieve Manuscript received July 01, 2015; revised August 26, 2015; accepted October 01, 2015. Date of publication November 17, 2015; date of current version December 02, 2015. This work was supported in part by the Electronic Warfare Research Center at the Gwangju Institute of Science and Technology, by the Defense the Acquisition Program Administration, and the Agency for Defense Development. This paper is an expanded version from the IEEE MTT-S International Microwave Symposium, Phoenix, AZ, USA, May 17–22, 2015. The authors are with the School of Electrical Engineering and Computer Engineering, Institute of New Media and Communications, Seoul National University, Seoul 151-742, Korea (e-mail: [email protected]). Digital Object Identifier 10.1109/TMTT.2015.2495106

broadband characteristics, lossy matching and negative feedback method are used to lower the Q-factor. This results in low efficiency and requires large chip size and has difficulty in achieving the required gain flatness over a wide bandwidth. Reconfigurable matching concept has also been proposed for multi-stage PAs to overcome the bandwidth limitation coming from Bode–Fano criteria in the interstage matching [3], [4]. However, the overall PA efficiency may be degraded due to the switch loss. Moreover, the linearity and power handling capability of the switch may limit its use for multi-watt-level PAs. A potential alternative for wideband matching is the use of a non-Foster circuit (NFC). Typical examples of non-Foster components are the negative inductors and negative capacitors. On the Smith chart, S-parameter traces of the non-Foster components move in counterclockwise direction as the frequency increases. The first non-Foster circuit using the transistors was proposed by Linvill in 1954 [5]. The NFC was used to compensate for the parasitic effects of various circuits such as filters, varactors, and VCOs [6]. For example, the negative slope of the reactance versus frequency is used to overcome the limitation of the antenna size and Q-factor at 800 MHz [7]. The gain-bandwidth enhancement of DA has been demonstrated using the negative capacitance in [8]. However, its application was limited to small-signal operation. Although the non-Foster matching is effective in cancelling out the reactance over a broad bandwidth, there are three major challenges using non-Foster circuit, noise, stability and power handling capability. Due to the power handling issues, little work has been presented to demonstrate a broadband PA using non-Foster circuit. In this work, two-stage GaN power amplifiers have been developed using NFC for broadband operation ranging from 7 to 17 GHz. The non-Foster circuit realized with the cross-coupled GaN FETs is applied to the interstage matching to cancel out the large input capacitance of the power-stage FETs over multi-octave bandwidth. This paper is an extended version of our previous work [9], which was the first demonstration of negative impedance converter (NIC) based broadband amplifiers with watt-level output power. This paper presents more detailed small-signal analysis to understand the high frequency limitation of the NIC. In addition, the large-signal behavior of the NIC is analyzed by using the full nonlinear GaN FET models. The combined results of small- and large-signal analyses are used to find the optimum transistor size and bias points to extend the operation frequency and power range of the NIC. This paper is organized as follows. Section II presents the overall design concept of the negative impedance matched PA

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Fig. 1. Block diagram of the two-stage PA with non-Foster matching network.

(NMPA), the operation principle of the NFC, the frequency and power limits of NFC, and the detailed NFC-based PA circuit design methodology. In Section III, the measurement results of the two GaN PAs are presented including the updated results with higher output power. The power and power added efficiency (PAE) enhancement with NFC are also explained using the comparison data. II. TWO-STAGE GAN PA WITH NFC A. NFC Operation Principle and Circuit Design A simplified block diagram of the two-stage GaN PA with the proposed non-Foster circuit is shown in Fig. 1. The unit FET size of the PA is 6 125 m, which has a maximum available gain (MAG) of 12 dB at 18 GHz. The GaN FET with a size of m shows a cut-off frequency of 21.7 GHz, an of 74.6 GHz, and a transconductance of 227 mS/mm at 28 V drain bias. The load-pull measurement on a 6 125 m FET cell shows a maximum output power density of 2.8 W/mm, a PAE of 41.6%, and a power gain of 9.3 dB at 15 GHz under continuous wave conditions. Even though the transistor performance merits do not match those of the state-of-the-art GaN transistors [17], [18], [21], the concept of NIC-based PA can be proven by comparing the PA performance with and without NICs. To achieve overall gain higher than 15 dB, a two-stage design is required, in which case the bandwidth limitation often comes from the high-Q interstage matching rather than the output matching. For wide bandwidth, lowering the Q-factor of interstage matching network is essential. Since Q-factor is the ratio between the stored energy and power loss, it can be reduced by increasing the power loss and decreasing the stored energy. The example of the former is the RMPA with lossy matching and the latter is - resonance matching. But, - resonance reduces the stored energy only over a narrow bandwidth. On the other hand, non-Foster matching can reduce the stored energy over a broad bandwidth. In this work, the NFC is employed in the interstage matching to cancel out the large input capacitance of the power-stage FETs, lowering the Q-factor of interstage matching. Output matching is realized with a conventional two-section matching network. The output powers from each FET are combined through a Wilkinson power combiner to achieve W over the target frequency range of 6–18 GHz. In theory, the addition of NFCs in the output matching network can further improve the power BW. However, the power handling capability

Fig. 2. Simulated interstage impedance matching with NFC.

of NFC has to scale with the RF power, which results in the excessive dc power consumption from the NFC and degrades the PAE of the overall PA. Therefore, in this work, NFC is employed in the interstage matching circuit only. One of the key practical issues with NFC is the limited operating frequency. The bandwidth limitation comes from the self-resonance. The self-resonating frequency (SRF) is limited by the of the device. 6 125 m GaN FET used as the unit transistor in the NFC has a gate length of 0.25 m and a of 21.7 GHz. As will be shown in the next subsection, the SRF is limited to GHz, which is not high enough to cover the entire bandwidth up to 18 GHz. Therefore, the interstage matching network is optimized separately for two subfrequency regions. The natural interstage matching is optimized for the upper subfrequency band above 11 GHz, where the negative capacitance is not available. The impedance mismatch in the lower subfrequency band below 11 GHz is compensated for by the negative capacitance presented by NFC. To better understand the benefit of NFC in the interstage matching, the input impedance of the power stage is simulated together with the optimum load impedance of the driver-stage FET in Fig. 2. The optimum driver-stage impedance moves along a constant-g circle in a counterclockwise direction as the frequency increases. The input impedance of the power stage is highly capacitive due to the large input gate capacitance of 1.4 pF. It is thus very difficult to provide optimum impedance matching across the entire bandwidth. Upper frequencies above 11 GHz are matched using an inductive line and shunt stubs. The impedance mismatch in the lower frequency subband is mitigated by employing a negative shunt capacitance of pF, which basically reduces the Q-factor of the input impedance of the power stage impedance from 10.30 to 1.62 at 6 GHz and from 4.39 to 0.78 at 8 GHz. In this way, the same natural matching circuit consisting of the inductive line and the shunt inductance can be used to match the lower subband frequencies below 11 GHz as well. B. Frequency and Power Limitation of the NFC The non-Foster circuit used in the interstage matching is based on the Linvill's NIC [Fig. 3(a)]. The NIC is composed

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(a)

(b)

Fig. 4. Reduced equivalent circuit of the NIC.

Fig. 3. (a) Circuit of Linvill's NIC and (b) the simplified equivalent circuit of the NIC.

of the cross-coupled FETs with the loaded capacitor. The main operation of the NIC is to invert the polarity of to an effective capacitance, . The coefficient, , is a function of frequency. However, the NIC cannot generate the negative capacitance in the low condition. For example, high-frequency operation or large signal-operation leads to low gain conditions. In this case, NIC operates just like normal inductor. For analysis, it is useful to represent the NIC with a simplified equivalent circuit of a series resistor and either negative capacitance or inductance , depending on the frequency, as shown in Fig. 3(b). Small-signal characteristics of the NIC can be understood from a simple analysis using and . With the two identical transistors, the input impedance, , and the can be expressed by the following equations [10]:

(1) (2) is . The equivalent circuit shown in Fig. 4 is where derived from the first equation. The equivalent circuit of NIC is composed of a complicated combination of resistors, inductors, and capacitors. As a result, the input impedance is a strong function of frequency. At frequencies higher than the transistor cut-off frequency, , NIC cannot convert the loaded capacitor to negative capacitance. However, as can be seen from (2), the SRF is much lower than due to the additional capacitances and inductances. For example, SRF is only 11.6 GHz even if is 21.7 GHz for a 6 125 m GaN FET ( pF and pF). Fig. 5 shows the simulated S-parameter of the NIC using the simplified equivalent circuit of Fig. 4 and the full FET model provided by the foundry. The equivalent circuit of the intrinsic FET model contains the low-frequency dispersion effect with the thermal and trap subcircuits [11]and the equations for , and are based on the Angelov model.

Fig. 5. Simulated S-parameters of the NIC using the full device model and the reduced equivalent circuit.

The full device model simulation predicts an SRF of 13 GHz while the simplified model shows an SRF of 11.6 GHz. The difference between the two results comes from and other parasitic effects not accounted for in the simplified equivalent circuit. The detailed circuit schematic of NFC is shown in Fig. 6. The cross coupled FETs used in the NFC are 6 125 m GaN FETs. The resistor , and are used to prevent instability. helps to reduce the equivalent series resistance, , due to the impedance inversion effect of the cross-coupled pair. The simulated frequency-dependent reactance of the NFC is plotted in Fig. 7. The reactance decreases as the frequency increases up to 11 GHz, which clearly shows non-Foster characteristics. The equivalent capacitances of the NFC in this frequency range are to pF. The equivalent series resistance varies between 4.4 and 11.4 . Above 11 GHz, where the self-resonance occurs, the positive reactance slope is observed and the circuit follows Foster's theorem. In this case, the NFC is represented with a series combination of a resistance and a positive inductance as shown in Fig. 3(b). Another limitation in NFC operation may come from the power handling capability in the PAs. The NFCs cease to

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(a)

Fig. 6. Detailed schematic of the proposed NIC.

(b) Fig. 8. (a) Simulation results of the power division ratio between the NIC and power stages. (b) Simulated susceptance of the NIC versus injected RF power.

(a)

(b)

Fig. 7. Simulated (a) reactance of the NIC as a function of frequency and (b) equivalent capacitance or inductance.

show negative impedance when they are driven with large RF power. As shown in Fig. 1, NFC shares the same node as the power-stage FETs. The RF power from the driver stage is divided into three paths with a different division ratio depending on the operating frequencies. Fig. 8(a) shows the simulated

power division ratio into the NFC versus the power FETs as a function of frequency. As the frequency decreases, more power is delivered to the NFC than to the power stages, which eventually reduces the loop gain in the NFC below a threshold level required to generate the negative impedance. To show the power handling capability, we have simulated the large-signal response of the NFC with 15 V drain voltage [Fig. 8(b)]. The negative susceptance, which is required to cancel out the positive susceptance due to the large power-stage input capacitance, decreases rapidly as the power increases. If the output power is 5 W and the power gain of the main stage is 3 dB, then the expected power delivered to the NFC is 1 W at 6 GHz. It is sufficient to cease the effect of NFC. Combining the results of Fig. 8(a) and (b), it is predicted that the low frequency operation of the NFC is vulnerable to large-signal operation. So, it is expected that the effective frequency range of the NIC in our PA is limited to 6–11 GHz, corresponding to the previously mentioned “low-frequency subband.” C. Detailed NFC Design for Broadband PAs Key design parameter is the value of the load capacitance, , in the NFC [see Fig. 3(a)], since it determines in Fig. 3(b). Larger results in a larger negative capacitance, which allows the compensation of larger input transistor capacitance. This means that a smaller number of NFCs are required to compensate for the given power-stage transistors. The dc power consumption of the NFC can be reduced in this way. However,

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(a)

(a)

(b) Fig. 9. Simulated (a) power handling capability of the NFC and (b) SRF with various unit transistor size.

(b)

SRF is inversely proportional to and one needs to carefully select and considering the required bandwidth. The transistor size used in the NFC determines . The transistor size also determines the power handling capability of the NFC. Fig. 9 shows the simulated power handling capability of the NFC with the various transistor sizes. The negative susceptance represents the effect of the NFC and the power capability can be determined by the input power when the susceptance crosses zero. The power limit of the NFC improves with the transistor size. This can be understood from the load seen by the cross-coupled transistors in the NFC. Each transistor has the output load composed of the and the other transistor, which presents relatively low impedance. Due to the large bias voltage of the GaN transistors, the power limitation of the NFC arises from the current clipping rather than the voltage clipping. Larger transistors provide higher current driving capability and thus improved power handling capability. However, one cannot increase the transistor size indefinitely since it will negatively impact the high-frequency operation limit of the transistors and their cut-off frequencies. To find the optimal transistor size for SRF, we have calculated SRF as the transistor size is varied in Fig. 9(b). and the unit gate finger width are fixed at 1.5 pF and 125 m, respectively, and the number of gate fingers is increased from 2 to 8. The simulation is repeated for two drain bias voltages, 8 and 15 V. As shown in Fig. 9(b), it is clear that the optimal SRF can be achieved with 6 125 m transistors at both 8 and 15 V bias conditions. In this work, a transistor size of 6 125 m is used together a value of 1.5 pF. The resulting is 1.27, and SRF is around 11.6 GHz.

Fig. 10. Simulated negative susceptance of NFC versus the input power at various (a) gate bias and (b) drain bias.

The side effect of using larger transistors in NFC is the increased power consumption. The NFCs employed for antenna matching have employed Class-C or Class-B biasing to avoid the dc power consumption under small-signal operation [12]. However, a similar biasing may not be applicable for large signal operation as in PAs. In an attempt to find the optimum bias points, the power handling capability of the simple NFC is simulated by sweeping the gate and drain biases at 8 GHz in Fig. 10. The large-signal transistor model employed in this work predicts the PA power performance with reasonable accuracy. However, it has limited accuracy in predicting the bias dependence of the PA. The modeling accuracy can be improved by using more sophisticated GaN FET models [13], [14]. As shown in Fig. 8, the NFC used in the interstage matching should present the negative susceptance up to dBm input power to cover the frequency range down to 6 GHz. Fig. 10(a) clearly shows that Class-B biasing provides insufficient power limit. In this work, Class A–AB biasing is used. Unlike the case of the gate bias, the drain bias can be reduced to 8 V without impacting the power handling capability as shown in Fig. 10(b). This can be understood from the fact that the current clipping is the main limiting mechanism rather than voltage clipping, and that the transistor transconductance peaks around 6–10 V and degrades slightly as the drain bias is increased. At high drain bias, GaN power transistors can show degradation due to self-heating [15], [16]. In this work, a drain bias of 8 V and 15

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(a) Fig. 12. Measured small-signal gain of NIC.

combined PA with and without the

(b) Fig. 11. (a) Fabricated chip photograph and (b) block diagram of PA with non-Foster matching network.

combined

V are employed for the cross-coupled transistors used in the NFC. III. MEASUREMENT RESULTS Two PAs are designed with non-Foster matching network and fabricated using a commercial 0.25- m GaN pHEMT foundry process. Both PAs are based on a two-stage design with the NFC employed in the interstage matching circuit. The first PA combines the output powers from two power FETs, each with a transistor size of 6 125 m, using a Wilkinson combiner to achieve an output power of 36–37 dBm. A single NFC consisting of the cross-coupled FETs with the same unit transistor size is used to cancel out the input capacitance of two power FETs. NIC and interstage matching for this PA are designed for optimum power performance in the lower subfrequency band from over 6 to 10 GHz. The second PA is designed to achieve higher output power by combining the output powers of four 6 125 m GaN FETs. It consists of two parallel PA chains, each with two power FETs combined using a shared output matching network. Wilkinson coupler is employed to combine the output powers from each PA chain. The expected output power is 1–2 dB higher instead of 3 dB with power combining due to the insertion and mismatch losses of the on-chip broadband Wilkinson coupler. The interstage matching for the second PA is optimized to show more pronounced NFC effect in a slightly shifted frequency range with focus on 8–12 GHz. For testing, the PA chips are mounted on 5-mm-thick Au-plated Cu carrier with eutectic bonding to mitigate self-heating. On-wafer probing using ground-signalground (GSG) probes (the Infinity probes from Cascade Microtech) is used to measure both small-signal and large-signal

Fig. 13. Measured return losses of

combined PA with and without the NIC.

characteristics. Continuous wave signal is used to measure the power characteristics. A. PA With

Combining

Fig. 11 shows the die photograph and the block diagram of the fabricated PA chip with two-FET combining. As shown in Fig. 11(b), a single NFC cancels out the input capacitance of two power FETs. Fig. 12 shows the measured small-signal gain with and without the NIC. The drain bias voltage to the PA is 28 V while that to the NIC is set to 15 V for this measurement. To show the effect of NIC on the return losses, and are also measured in Fig. 13 with NIC turned on and off. There is very little change in the return losses when NIC is turned on. The effect of NIC on the noise performance is also measured in Fig. 14. At the frequencies where the overall gain improves with NIC, the noise figure also improves. More meaningful improvement can be observed in the power characteristics shown in Fig. 15. Since NIC-based interstage matching circuit is designed to provide the optimum load impedance to the driver stage in the low-frequency subband, the output power and PAE improves by up to dB and %, respectively, between 6 and 11 GHz when NIC is used. At 8 GHz, the output power is increased from 36 to 37.3 dBm and the PAE is improved by 4.5%. The peak PAE of 13–21% and the output power of 35.7–37.5 dBm are achieved across the

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Fig. 14. Measured noise figure of

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 63, NO. 12, DECEMBER 2015

combined PA with and without the NIC.

(a)

(b)

Fig. 15. Measured output power and PAE of the NIC.

combined PA with and without

Fig. 16. (a) Fabricated chip photograph and (b) block diagram of PA with NFC.

combined

6–18 GHz frequency bandwidth. The overall PAE degradation due to the power consumption of NIC is estimated to be %. B. Parallel Combined PA With

Combining

comThe die photograph and the block diagram of the bining PA are shown in Fig. 16. For this PA, the drain bias to the power FETs is 28 V while that to the NFC FETs is reduced to 8 V based on the analysis presented in the previous section. Fig. 17 represents the measured small-signal gain with and without NIC. Similar to the result of the combining PA, increases in the low-frequency subband from 7 to 12 GHz with the NIC. The gain improvement is more pronounced at slightly higher frequencies in this design since the interstage circuit is further optimized to achieve better matching near 8–12 GHz. The gain improvement up to 3.9 dB can be observed at 11 GHz. The measured power characteristics with and without NIC are shown in Fig. 18. Unlike the case of combining PA which showed the power improvement ( dB) only up to GHz, this circuit showed significant power improvement ( dB) up to 12 GHz. Over a slightly shifted frequency range of 7 to 17 GHz, the output power higher than 5 W is achieved. The lower frequency limit for this design is around 7 GHz, below which no power improvement is observed with the NIC. The PAE degradation due to the power consumption of NIC is estimated to be less than 0.5%. Fig. 19 compares the power sweep characteristics at 10 GHz between the two PA circuits. With NIC, the output power is increased by as much as 2.1 dBm from 36.1 to 38.2 dBm and

Fig. 17. Measured small-signal gain of NIC.

combined PA with and without the

the PAE is improved by 4.5% in combining PA while the improvement is limited to 0.66 dBm and 1.6% for combining PA. This is again attributed to the further optimized interstage network at this frequency. The output power increase in combining PA compared with PA is 1–2 dB from 7 to 17 GHz. At the band edges, the output power improvement is limited due to the increased loss of the power combiner. The measured PAE of the combining PA is also lower than the PA due to the power combiner loss. Table I compares the performance of the PA of this work with the state-of-the-art DA and RMPA using GaN pHEMTs. This work is an extended version of our previous work [9], which is the first demonstration of the NMPA. Even though the measured

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TABLE I PERFORMANCE COMPARISON TABLE OF GAN BROADBAND PAS

Fig. 18. Measured output power of

combined PA with and without the NIC.

The bandwidth limitation due to high-Q interstage matching has been mitigated through the use of a shunt negative capacitance. To guarantee the high power operation over the entire bandwidth, natural interstage matching is optimized for the upper subfrequency band and the lower subfrequency band is compensated for by the negative capacitance presented by NFC. Detailed analysis is performed to understand the frequency limitation of NIC approach, which shows that high-frequency limit comes from the self-resonance and the low-frequency limit from the power handling capability. The fabricated combining PA shows output powers higher than 5 W from 7 to 17 GHz. At frequencies, where NFC is optimized for interstage matching, the power improvement by 2.1 dBm and PAE improvement by 4.5% have been achieved. This work demonstrates that non-Foster matching can provide a new perspective in designing the broadband PAs. REFERENCES

Fig. 19. Measured power sweep characteristics of

and

PAs at 10 GHz.

power and PAE do not match the state-of-the-art results due to the limited device performance, this work shows that NIC can be an effective method to realize a broadband PA in a small die area without lossy matching or feedback. IV. CONCLUSION In this work, two-stage GaN PAs with non-Foster circuit have been developed for multi-octave broadband power applications.

[1] R. M. Fano, “Theoretical limitations on the broadband matching of arbitrary impedances,” J. Franklin Inst., vol. 249, no. 1, pp. 57–83, 1950. [2] R. M. Fano, “Theoretical limitations on the broadband matching of arbitrary impedances,” J. Franklin Inst., vol. 249, no. 2, pp. 139–154, 1950. [3] S. Park, J. Woo, U. Kim, and Y. Kwon, “Broadband CMOS stacked RF power amplifier using reconfigurable interstage network for wideband envelope tracking,” IEEE Trans. Microw. Theory Techn., vol. 63, no. 4, pp. 1174–1185, Apr. 2015. [4] U. Kim, K. Kim, J. Kim, and Y. Kwon, “A multi-band reconfigurable power amplifier for UMTS handset applications,” in Proc. IEEE RF Integr. Circuits Symp. Dig., May 2010, pp. 175–178. [5] J. G. Linvill, “Transistor negative impedance converters,” in Proc. IRE, Jun. 1953, vol. 41, no. 6, pp. 725–729. [6] Q. Wu, S. Elabd, T. K. Quach, A. Mattamana, S. R. Dooley, J. McCue, dBc/Hz FOMT P. L. Orlando, G. L. Creech, and W. Khalil, “A wide tuning range Ka-band VCO using tunable negative capacitance and inductance redistribution,” in Proc. IEEE RF Integr. Circuits Symp. Dig., Jun. 2013, pp. 199–202. [7] O. O. Tade, P. Gardner, and P. S. Hall, “Antenna bandwidth broadening with a negative impedance converter,” Int. J. Microw. Wirel. Techn., vol. 5, no. 3, pp. 249–260, Jun. 2013. [8] A. Ghadiri and K. Moez, “Gain-enhanced distributed amplifier using negative capacitance,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 57, no. 11, pp. 2834–2843, Nov. 2010. [9] S. Lee, J. Kim, H. Park, and Y. Kwon, “A 6–18 GHz GaN pHEMT power amplifier using non-foster matching,” in IEEE MTT-S Int. Microw. Symp. Dig., May 2015.

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[10] Q. Wu, T. Quach, A. Mattamana, S. Elabd, S. R. Dooley, J. J. McCue, P. L. Orlando, G. L. Creech, and W. Khalil, “Design of wide tuning-range mm-wave VCOs using negative capacitance,” in Proc. IEEE Compound Semiconductor Integr. Circuit Symp., Oct. 2012, pp. 1–4. [11] O. Jardel, F. De Groote, T. Reveyrand, J.-C. Jacquet, C. Charbonniaud, J.-P. Teyssier, D. Floriot, and R. Quéré, “An electrothermal model for AlGaN/GaN power HEMTs including trapping effects to improve large-signal simulation results on high VSWR,” IEEE Trans. Microw. Theory Techn., vol. 55, no. 12, pp. 2660–2669, Dec. 2007. [12] S. E. Sussman-Fort and R. M. Rudish, “Non-Foster impedance matching of electrically-small antennas,” IEEE Trans. Antennas Propag., vol. 57, no. 8, pp. 2230–2241, Aug. 2009. [13] A. Raffo, V. Vadalà, D. M. M. Schreurs, G. Crupi, G. Avolio, A. Caddemi, and G. Vannini, “Nonlinear dispersive modeling of electron devices oriented to GaN power amplifier design,” IEEE Trans. Microw. Theory Techn., vol. 58, no. 4, pp. 710–718, Apr. 2010. [14] H. Jang, P. Roblin, and Z. Xie, “Model-based nonlinear embedding for power-amplifier design,” IEEE Trans. Microw. Theory Techn., vol. 62, no. 9, pp. 1986–2002, Sep. 2014. [15] S. Nuttinck, E. Gebara, J. Laskar, and H. M. Harris, “Study of selfheating effects, temperature-dependent modeling, and pulsed load-pull measurements on GaN HEMTs,” IEEE Trans. Microw. Theory Techn., vol. 49, no. 12, pp. 2413–2420, Dec. 2001. [16] L. Ardaravicius, A. Matulionis, J. Liberis, O. Kiprijanovic, M. Ramonas, L.-F. Eastman, J.-R. Shealy, and A. Vertiatchikh, “Electron drift velocity in AlGaN/GaN channel at high electric fields,” Appl. Phys. Lett., vol. 83, no. 19, pp. 4038–4040, Nov. 2003. [17] C. Campbell, T. Lee, V. Williams, M. Kao, H. Tserng, P. Saunier, and T. Balisteri, “A wideband power amplifier MMIC utilizing GaN on SiC HEMT technology,” IEEE J. Solid-State Circuits, vol. 44, no. 10, pp. 2640–2647, Oct. 2009. [18] J. J. Komiak, K. Chu, and P. C. Chao, “Decade bandwidth 2 to 20 GHz GaN HEMT power amplifier MMICs in DFP and no FP technology,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2011, pp. 1–4. [19] V. Dupuy, E. Kerherve, N. Deltimple, J.-P. Plaze, P. Dueme, B. MalletGuy, and Y. Mancuso, “A 39.7 dBm and 18.5% PAE compact X to Ku band GaN travelling wave amplifier,” in Proc. 57th IEEE Int. Midwest Symp. Circuits and Systems, Aug. 2014, pp. 611–614. [20] R. Santhakumar, B. Thibeault, H. Masataka, S. Keller, Z. Chen, U. K. Mishra, and R. A. York, “Two-stage high-gain high-power distributed amplifier using dual-gate GaN HEMTs,” IEEE Trans. Microw. Theory Techn., vol. 59, no. 8, pp. 2059–2063, Aug. 2011. [21] U. Schmid, H. Sledzik, P. Schuh, J. Schroth, M. Oppermann, P. Bruckner, F. van Raay, R. Quay, and M. Seelmann-Eggebert, “Ultra-wideband GaN MMIC chip set and high power amplifier module for multi-function defense AESA applications,” IEEE Trans. Microw. Theory Techn., vol. 61, no. 8, pp. 3043–3051, Aug. 2013. [22] Y. Niida, Y. Kamada, T. Ohki, S. Ozaki, K. Makiyama, N. Okamoto, M. Sato, S. Masuda, and W. Watanabe, “X-Ku wide-bandwidth GaN HEMT MMIC amplifier with small deviation of output power and PAE,” in Proc. IEEE Compound Semiconductor Integr. Circuit Symp., Oct. 2014, pp. 1–4. [23] G. Mouginot, Z. Ouarch, B. Lefebvre, S. Heckmann, J. Lhortolary, D. Baglieri, D. Floriot, M. Camiade, H. Blanck, M. Le Pipec, D. Mesnager, and P. Le Helleye, “Three stage 6–18 GHz high gain and high power amplifier based on GaN technology,” in IEEE MTT-S Int. Microw. Symp. Dig., May 2010, pp. 1392–1395. [24] E. Kuwata, K. Yamanaka, H. Koyama, Y. Kamo, T. Kirikoshi, M. Nakayama, and Y. Hirano, “C-Ku band ultra broadband GaN MMIC amplifier with 20 W output power,” in Asia-Pacific Microw. Conf. Proc., Dec. 2011, pp. 1558–1561. Sangho Lee (S'13) was born in Suwon, Korea, in 1986. He received the B.S. degree in electrical engineering from Seoul National University, Seoul, Korea, in 2011, and is working toward the Ph.D. degree in electrical and computer engineering at Seoul National University. His research activities include millimeterwave/RF integrated circuits and system design for wireless communication and radar, especially high-power and broadband PA design.

Hongjong Park (S'13) was born in Incheon, Korea, in 1988. He received the B.S. degree in electrical and computer engineering from Seoul National University, Seoul, Korea, in 2012, and is working toward the Ph.D. degree in electrical and computer engineering at Seoul National University. His research interests include large-signal modeling of GaN HEMT and millimeter-wave GaN MMICs.

Kwangseok Choi (S'15) was born in Seoul, Korea, in 1986. He received the B.S. and M.S. degree in electrical engineering from Sogang University, Seoul, Korea, in 2008, and 2010 respectively, and is currently working toward the Ph.D. degree in electric and computer engineering at Seoul National University. From 2010 to 2013, he was with Gigalane, Suwon, Korea, as a Research Engineer. From 2013 to 2014, he was with the System Integrated Circuit Laboratory, LG Electronics, Seoul, Korea, as a Junior Research Engineer.

Youngwoo Kwon (S'90–M'94–SM'04) was born in Seoul, Korea, in 1965. He received the B.S. degree in electronics engineering from Seoul National University, Seoul, Korea, in 1988, and the M.S. and Ph.D. degrees in electrical engineering from The University of Michigan at Ann Arbor, Ann Arbor, MI, USA, in 1990 and 1994, respectively. From 1994 to 1996, he was with the Rockwell Science Center, as a Member of Technical Staff, where he was involved in the development of millimeterwave monolithic integrated circuits (ICs). In 1996, he joined the faculty of the School of Electrical Engineering, Seoul National University, where he is currently a Professor. He is a coinventor of the switchless stage-bypass power amplifier architecture “CoolPAM.” He cofounded Wavics, a power amplifier design company, which is now fully owned by Avago Technologies. In 1999, he was awarded a Creative Research Initiative Program by the Korean Ministry of Science and Technology to develop new technologies in the interdisciplinary area of millimeter-wave electronics, MEMS, and biotechnology. He has authored or coauthored over 150 technical papers in internationally renowned journals and conferences. He holds over 20 patents on RF MEMS and power amplifier technology. Dr. Kwon has been an Associate Editor for the IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES. He has also served as a Technical Program Committee member of various microwave and semiconductor conferences including the IEEE International Microwave Symposium, RF Integrated Circuit Symposium, and the International Electron Devices Meeting. Over the past years, he has directed a number of RF research projects funded by the Korean Government and U.S. companies. He was the recipient of a Presidential Young Investigator Award from the Korean Government in 2006.

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Generalized Stability Criteria for Power Amplifiers Under Mismatch Effects Almudena Suárez, Fellow, IEEE, Franco Ramírez, Member, IEEE, and Sergio Sancho, Member, IEEE

Abstract—Potential instability of power amplifiers (PAs) under mismatch effects is analyzed, with emphasis on the ease and generality of application of the stability criteria. The methodology is based on the evaluation of a large-signal version of the factor, considering mismatch effects in the fundamental frequency and three relevant sidebands: the baseband, the lower sideband and the upper sideband. This requires an outer-tier scattering-type conversion matrix of order 3 3 to be obtained, with the rest of sideband equations acting as an inner tier. It is taken into account that the circuit behaves nonlinearly with respect to the termination at the fundamental frequency. The consideration of three sidebands will enable the prediction of the two major forms of large-signal instability: incommensurable oscillations and frequency divisions by two. The analysis is preceded by an evaluation of the circuit own stability properties (proviso) under open and short circuit terminations at the sidebands, for all possible values of the termination at the fundamental frequency. Three different factors can be defined between any two ports of the scattering matrix. The analysis of the relationships between these factors and their continuity properties will allow the derivation of a single number able to characterize the PA potential instability for each fundamental-frequency termination. Results have been exhaustively validated with independent circuit-level simulations based on pole-zero identification and with measurements, using a variable output load and loading the PA with an antenna. Index Terms—Antenna mismatch, bifurcation, stability analysis.

I. INTRODUCTION

I

NSTABILITY of power amplifiers (PAs) under termination conditions other than 50 , usually due to antenna mismatch [1]–[4], can give rise to severe malfunctioning, as reported in many previous works [5]–[11]. Furthermore, some applications impose stable operation even under highly reflective loads [6], [8]. The stability analysis under output mismatch is involved since it must be carried out under unknown termination impedances. To be precise, the practical stability analysis of a periodic solution with harmonic components , where goes from to , is based on the introduction of Manuscript received July 02, 2015; revised September 17, 2015; accepted October 11, 2015. Date of publication November 18, 2015; date of current version December 02, 2015. This work has been supported in part by the Spanish Government under contract TEC2014-60283-C3-1-R and in part by the Parliament of Cantabria (12.JP02.64069). This paper is an expanded version from the IEEE MTT-S International Microwave Symposium, Phoenix, AZ, USA, May 17–22, 2015 The authors are with the Communications Engineering Department, University of Cantabria, 39005 Santander, Spain (e-mail: [email protected]; [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2015.2494578

a perturbation at the positive frequency [12]–[15], which will give rise, through mixing effects, to the sideband frequencies . The aim is to predict the reaction of the periodic solution to small perturbations, so the circuit will be linearized about this solution and its frequency response will be obtained by sweeping . Under mismatched conditions, the frequency-dependent load impedance will exhibit unknown values at and , where . However, some considerations can be made. In the PA, the harmonic amplitudes are generally significant at the device output terminals, but quite low at the final 50 termination of the output network [16]–[23]. For instance, in a Class-E amplifier [16], [17] a nearly sinusoidal fundamental-frequency current flows through the output series resonator, so the impedance at the fundamental frequency is the most influential one. As stated in [17], the load network may include a low-pass or a band-pass filter to suppress harmonics of the switching frequency at the final output 50 load [19], [20]. On the other hand, in a class-F amplifier [21]–[23] the output network forces the output voltage to be ideally sinusoidal and additional resonators are added to tune the harmonic components. The mismatch effects occur after the PA output network, at the reference plane indicated in Fig. 1(a), so, in general, they will have a negligible effect at harmonic frequencies , where . Taking all the above into account, the approach in [9]–[11] assumes a bandpass filtering action of the PA output network, such that the particular values of the load impedances at frequencies other than the fundamental frequency and its lower and upper sidebands, and , have a negligible impact on the stability properties. With this in mind, the analysis of mismatch effects is limited to the three frequencies , at which the termination impedances may take any value. Then, a two-tier conversion matrix analysis is carried out [10], [11]. The outer-tier system is based on a 2 2 scattering-type matrix at the two mismatched sideband frequencies and , defined at the PA termination plane. The inner-tier system accounts for the rest of sideband frequencies, whose termination impedance values should have a negligible impact on the stability properties. Thus, they can be arbitrarily terminated in 50 . The two sideband frequencies and act as two virtual ports, which has enabled the extension of the Rollet stability criteria [24], [25] to large-signal operation under output mismatch effects [10]. However, [10] assumed a particular (matched) termination condition at the fundamental frequency . The generalization to arbitrary terminations implies some analysis difficulties, since any change of leads to a different steady-state solution, which must be calculated with harmonic

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Fig. 1. Power amplifier under output mismatch effects. The transistor is an , Avago ATF-50189, and the element values are , , , , and . In the modified PA, the output inductor is . (a) Circuit schematic. (b) Sketch of the termination impedances (replacing the original 50 load) at the analysis frequencies, including harmonics, in a solid line, and sidebands, in a dashed line. (c) Photograph.

balance (HB). Practical use and interpretation of data resulting from multiple amplitude and phase sweeps in require a judicious technique. In this sense, [11] proposed the calculation of a large-signal factor, obtained from the outer-tier scattering-type matrix at and , and the use of constantcontours, traced on the Smith chart corresponding to (with respect to which the circuit behaves nonlinearly). A limitation of this method lies in the fact that only particular values of the perturbation frequency are considered, though the stability analysis of a periodic regime at , must take into account all the values between 0 and . In fact, an upper frequency higher than will be necessary to detect the subharmonic resonance leading to a frequency division by 2, which is one of the main forms of large-signal instability [26]. In view of this problem, one of the objectives here will be derivation of a new analysis method accounting for this whole interval of perturbation frequencies. In [11], a preliminary investigation including the baseband termination in the set of relevant mismatched terminations was

presented. This relied on the calculation of a 3 3 outer-tier scattering matrix at the three sideband frequencies , and . However, the three-sideband analysis in [11] was only used for a final validation of the results obtained with the 2 2 scattering matrix, due to the difficulties involved in the evaluation of the large-signal for three possible combinations of two sidebands, , and , considering, in each case, all possible values of the complex reflection coefficient at the remaining sideband, denoted as . Furthermore, the evaluation of each large-signal must be carried out for each fundamental-frequency termination and each perturbation frequency , which will lead to prohibitive computational cost, unless some useful mathematical properties are identified. This work will present a thorough methodology for the stability analysis of PAs under mismatch effects that is mathematically consistent for all the possible values of the perturbation frequency . It will be derived from an in-depth investigation of the relationships between the different factors that can be defined in a three-sideband analysis, and a detailed study of their frequency dependences. The aim will be to obtain a single real quantity defining the PA potential stability properties in the whole perturbation-frequency interval, for each termination at . Unlike the two-sideband case, the analysis at accurately deals with situations in which the dangerous frequency intervals in and are close to or comprise this frequency. Therefore, it should enable a prediction of frequency divisions by two, often encountered in unstable PAs [27], [28]. This work will also take into account the need to verify the fulfilment of a proviso, with identical meaning to Rollet's proviso [29], [30] in a small-signal analysis, ensuring the observability of mismatched-induced instabilities from the output reference plane. This will require verification of the circuit stability under both open and short circuit terminations at the three relevant sidebands for all the possible values of the fundamentalfrequency termination . The analysis strategy, based on polezero identification, will take advantage of the continuity of the circuit equations, in order to avoid an unmanageable amount of data of difficult interpretation. The methods will be illustrated by means of its application to a PA at with 80% efficiency at 22 dBm output power. The paper is organized as follows. Section II presents the calculation of the three-sideband scattering matrix. Section III describes the potential instability analysis at three sidebands. Section IV presents a validation based on the calculation of stability circles. Section V proposes a new global stability parameter that is exhaustively validated with measurements. II. CALCULATION OF THE THREE-SIDEBAND SCATTERING MATRIX The stability analysis of a periodic solution at relies on the introduction of a perturbation at a frequency , to obtain the frequency response of the circuit linearized about this solution [12]. This will give rise to the mixing frequencies , where goes from to [12]–[15], [31], [32]. The opposite frequencies , though not considered in the analysis, will also exist and their components will be complex-conjugates of those at . In the case of a stability anal-

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output network) are only relevant at , , and . Fig. 1(b) shows a sketch of the analysis frequencies and the termination impedances at the output reference plane, with the harmonic components in a solid line and the sideband frequencies in a dashed line. For each termination at the fundamental frequency ,a full HB analysis is carried out considering harmonic terms. Next, the circuit is linearized about the resulting steady-state solution with the conversion-matrix approach [31]–[33]. The circuit's linearized equations are decomposed into an outer-tier system at and an inner-tier system at the rest of the frequencies , where , terminated in . The outer-tier system is formulated at the circuit's output reference plane [Fig. 1(a)] by means of 3 3 impedance matrix , later transformed into a scattering matrix. The matrix is obtained through the simultaneous conversion-matrix analysis of three circuits, terminated in at , in open circuit at , and , and in at the rest of the frequency components, as shown in Fig. 2(b). Each circuit will contain an independent small-signal current source at one of the sidebands . Then, the parameters of a 3 3 impedance matrix are obtained from the three respective circuits, as

(1)

Fig. 2. Two-tier conversion-matrix analysis. For each termination at , the perturbed circuit is represented with a 3 3 scattering matrix, calculated at the PA output terminals, as shown in Fig. 1. (a) Three circuit replicas used for . (b) Sketch of the outer-tier the calculation of the 3 3 impedance matrix scattering matrix and load impedances at the three sideband frequencies with mismatch effects.

ysis under output mismatch effects, and taking into account the low-pass characteristic of the output network, the mismatched conditions at the output reference plane [Fig. 1(a)] can be restricted to the fundamental frequency and the three frequencies , and . These mismatched frequencies are respectively terminated in the arbitrary reflection coefficients at each perturbation frequency [Fig. 1(a)]. The load impedances at the rest of the harmonic frequencies and sideband frequencies , where , should have no impact on the stability properties and can be arbitrarily terminated in . Note that the analysis method takes into account all the harmonic and sideband frequencies without any restrictions. The sole assumption is that mismatch effects (at the reference plane, after the

The above calculation is performed with a full conversion matrix approach, taking into account all the sideband frequencies , where goes from to . Note that we will have a different impedance matrix for each termination at and each perturbation frequency . The system is linear with respect to the terminations at the sideband frequencies, but nonlinear with respect to the termination at . Thus, a harmonic-balance analysis must be performed for any variation of the termination at . The (3 3) impedance matrix in (1) can be transformed into a (3 3) matrix of scattering type , which will relate reflected and incident power waveforms at the three sidebands

(2) where the asterisk denotes complex conjugation. This scattering matrix will allow a generalization of Rollet's criteria [24], [25] to predict potential instability under mismatch effects. The PA will be potentially unstable under these effects if for any pair of terminations at the sidebands , at the sidebands or at the sidebands , it exhibits negative resistance when looking into the circuit output at , or , respectively. This verification must be performed for every passive termination at and every perturbation frequency . However, the

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analysis described will only be able to detect the circuit instability under fulfilment of the Rollet proviso [29], [30], [34], [35], which must be adapted here to the problem of three mismatched sideband frequencies. To fulfil the proviso, the circuit terminated in at must be stable on its own, or equivalently, it must not exhibit any poles on the right-hand side of the complex plane (RHP) when the three sidebands are in open and short circuit conditions. The proviso must be verified for each passive termination at , with the three sideband frequencies , and in all possible combinations of short-circuit and open-circuit terminations. Indeed, short-circuit terminations facilitate the detection of unstable series resonances, which might not be observable from the analysis reference plane, whereas open-circuit terminations facilitate the detection of unstable parallel resonances. The verification of the proviso can be carried out with pole-zero identification [8], [15], fully applicable under open/short circuit terminations, since the load remains fixed at real impedance values at all the sideband frequencies , given by zero, near infinite or 50 . In fact, any complex-impedance (with a non-zero imaginary part) must physically vary with , so pole-zero identification should not be applied under constant complex termination impedances at the sideband frequencies. The pole-zero identification will be carried out versus variations in the termination at . A double sweep in the amplitude and phase of provides disconnected circles, which impedes taking advantage of the continuity properties of the harmonic-balance system. Indeed, this set of nonlinear algebraic equations is continuous with respect to all of its variables and parameters [12], [14]. Thus, it will also exhibit a continuous dependence on the load reflection coefficient at the fundamental frequency . The analysis can be carried out following a single spiral curve, depending on a single parameter , which will define both the amplitude and phase of the reflection coefficient . For a smaller step, and higher values of , the Smith chart will be covered in a finer way. Additionally the unit circle can be considered for a detailed analysis of the effect of purely reactive impedances. The analysis of the Rollet proviso will be applied to the Class-E PA in Fig. 1(a), with specified output power 22.5 dBm and efficiency 80% at and . The original values of the output inductor and load resistance are and . The resistance is implemented through an L-C matching section, terminated in 50 (Fig. 1). The analysis has been carried out with harmonic terms. This number of harmonic terms will be considered through the whole manuscript, for both the circuit-level simulations and the two-tier conversion-matrix analysis, based on in. Fig. 3(a) shows the spiral considered in the Smith Chart. Fig. 3(b) evidences that the circuit does not fulfil the proviso. This figure shows the variation of the real part of the dominant poles versus the parameter when using short-circuit terminations at the sidebands. When these sidebands are short-circuited, the circuit is unstable even under a 50 termination at . Note, however, that it is stable when fully matched, that is, when operating under a 50 final-termination load at all the harmonic and sideband frequencies. With

Fig. 3. Application of the proviso to the original PA in Fig. 1, following the , (a) Spiral spiral curve curve considered, traced on the Smith chart. (b) Pole evolution versus the paunder short-circuit terminations at the relevant sidebands. rameter in

the spiral curve, advantage is taken of the continuity of the circuit equations for an undemanding analysis. To improve the robustness of the circuit under mismatch-induced instability, some modifications have been performed in the output network. The output inductor has been changed to and the new load resistance, also implemented with an L-C section, is . When repeating the analysis of the proviso through the spiral curve , the circuit is stable under open and short circuit terminations at the three relevant sidebands, as shown in Fig. 4. Therefore, the potential instability analysis described in the next section will be applicable. III. POTENTIAL INSTABILITY ANALYSIS THREE-SIDEBANDS

AT THE

The works [36] and [37] demonstrate an extension of Rollet's analysis to three-port linear networks, which is based on the sequential definition of three different two-port networks. In each case, the two ports are taken from those of the original threeport network, under a variable passive termination in the remaining port. In [11], this procedure is adapted to the three-band stability analysis under mismatch effects. Under a termination at any of the three sideband frequencies , the 3 3 matrix in Fig. 2 can be reduced to a 2 2 matrix [36], [37]. Three different 2 2 matrixes can be defined. The first matrix is , at the virtual ports at and , depending on . The second matrix is , at the

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virtual ports and , depending on trix is , at the virtual ports . Using (2), the matrix

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. The third maand , depending on is obtained as

(3) where the subindex stands for reduced matrix. An analogous calculation is carried out for the other two matrixes and . For each of the three 2 2 matrixes, six large-signal equivalents of the factor [38] can be defined. This will be done using the same expressions as in [38], but considering, in each case, the two virtual ports of the reduced matrix instead of the two physical ports 1 and 2. The factors and , calculated from , respectively provide the distance to the stability circle in the and planes at each value. Analogous factors and , calculated from , and and , calculated from , will also be considered. In each case, the and factors provide the same stability information. Thus, the conditional stability analysis can be carried out in terms of three factors: , and , globally denoted as factors. This three-sideband analysis is demanding since each factor depends on (agreeing in each case with the reflection coefficient inside the parentheses), together with and the perturbation frequency . Due to this complexity, the three-band analysis was used in [11] only for validation purposes, under two specific values. In the following, the properties of matrix (2) and the three factors will be studied in order to simplify the analysis methodology. A. Consideration of all Possible Passive Values of Let any of the three factors , and be considered, which for simplicity will be denoted , where 1, 2 and 3 may correspond to any of the three sidebands . The terminations at Port 1, Port 2 and Port 3 will be denoted as , and , respectively. A potentially unstable case will be assumed. By definition, corresponds to the distance from the centre of the Smith chart to the stability circle, which must be evaluated for all the passive values of . Let the set of values providing be denoted as . Then, for any , there will be a set of loads, denoted by , such that for any the input reflection coefficient when looking into Port 1, , fulfils . The set , which will include passive loads, is delimited by a stability circle in , expressed as . Now a reduction of the 3 3 scattering matrix to Port 1 and Port 3, depending on , will be considered, performing the analysis in terms of the factor . Because the first analysis port (Port 1) is the same as in the previous case, for any load connected to Port 2 and connected to Port 3 we will have . Thus, condition must be fulfilled for any pair of loads . Therefore, if there are values such that , there must be values such that .

Fig. 4. Application of the proviso to the modified PA with and , following the spiral curve in Fig. 3(a). (a) Under open circuit terminations at the relevant sidebands. (b) Under short-circuit terminations.

Next, the connection of a passive load to Port 1, where , and the load to Port 2 will be assumed. By Kirchoff's laws, the reflection coefficient when looking into Port 3 will necessarily fulfil . In an analogous manner, when connecting the passive loads to Port 1 and to Port 3, the reflection coefficient when looking into the Port 2 will fulfil . One can conclude that if any of the factors , and is smaller than one for some passive values of the reflection coefficient within the brackets, the other two will also be smaller than one for certain passive values of the reflection coefficient on which they depend. Therefore, to determine whether the amplifier is potentially unstable under mismatch effects it will be sufficient to evaluate exhaustively one of the factors for all the possible passive values of its corresponding . B. Relationship Between the Three Passivity Boundary

Factors at the

Let particular terminations at the two sidebands , given by , be assumed. Then, it will be possible to write (4) The above relationships can be combined with (2) to obtain the input reflection coefficient at the baseband, given by . This provides the following expression, depending on and the scattering parameters (5) where the parameters and , depending only on the scattering parameters, are given by

(6)

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Fig. 5. Formation of the limit set

in the

plane.

The amplifier will be unconditionally stable under mismatch effects if for any pair of values of and , fulfilling and . For notation simplicity, the circles delimiting the passivity boundaries in each of the two planes will be denoted and . To determine the images of the passive regions and , one can take into account that for each constant value of , (5) defines a bilinear transformation [17] in the other parameter . In an analogous way, for each constant value of , (5) defines a bilinear transformation in the other parameter . Thus, the image of the circle , given by , will be the boundary of the images of all the passive loads , so all the images are either inside or outside the transformed circle . The same applies for the bilinear transformation in terms of , depending on . Applying a similar reasoning, the images of the two circles and in the plane, obtained through (5), form a global boundary of the images of all the possible passive combinations of and . This can be rigorously demonstrated as follows. First, let us consider all the pairs fulfilling: (7) where the function

is given by (5). Solving for

one obtains (8)

Now the following set

will be defined: (9)

The above mapping can give rise to values fulfilling either or . In particular, application of the mapping to the passivity boundary , , denoted as , will provide a set of circles (see Fig. 5), depending on the phase (10) For each , the whole region is mapped either inside or outside the circle , which constitutes a frontier between points belonging or not to the set for that value. When performing this operation , the boundary of the region is constituted by points belonging to the circles. These points will agree with those in the whole set of stability

circles traced in the plane for , . The factor provides the distance [28] to the stability circle in the plane for each . Because the set of circles , constitutes the boundary of the points such that , it will be sufficient to evaluate the factor through the circle to determine the potential instability properties. In fact, a relevant function will be the one providing the minimum value of when evaluated through . The resulting value will be denoted as . From the analysis of the mapping in (8), when evaluating through a circle , where , the minimum will be larger than and smaller than the one obtained for any other magnitude . However, when using instead of the passivity boundary , one must be aware that the three factors will provide different potential stability predictions, as the analysis is not exhaustive and the evaluation of each of the three factors will leave out some regions of , and . For the potential stability analysis, the three parameters , and will be initially considered, where it has been taken into account that (in agreement with the properties discussed in subsections and ) the minima resulting from and should be identical, although obtained for a different phase in each case. The parameters and respectively agree with the minimum distance to the stability circle in the and planes under phase variations in . In order to obtain the minimum distance to the stability circle in the plane, the parameter , agreeing with , must also be considered. Note that factors provide the distance to the stability circle in Smith chart corresponding to the “source” termination. The analysis of the three parameters , and has been applied to the PA in Fig. 1 operating at 0.8 GHz. In an initial study, a load describing a spiral curve, , has been considered. The analysis procedure is as follows. At each and for each perturbation frequency , the phase of the reflection coefficient is swept from 0 to 360 , in a fine step, evaluating the factors , and at each step. Note that harmonic components are taken into account in the calculation of the 3 3 scattering matrix that enables the determination of these factors. This is the number considered for all the analyses presented in this work. For each , only the minimum values versus are kept, agreeing with the parameters , and , where the frequency dependence of these parameters is indicated explicitly. The results obtained for four particular values in the spiral curve are shown in Fig. 6. As expected, the minima of and are overlapped for all the values. The three parameters , and provide the same information on the potential instability of the PA, in agreement with the derivations in subsections and . Indeed, the three parameters are either larger or smaller than 1 in the same intervals of perturbation frequency . They cross unity at exactly the same frequency values [see the expanded view in Fig. 6(d)].

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Fig. 7. Frequency variation of the parameter for going from 0 to 1, in steps of 0.1. The termination considered at the fundamental fre, in Fig. 6(c). The number of harmonic compoquency is . The parameter , agreeing with provides nents is at each . the minimum

Fig. 6. Variation versus the perturbation frequency the minima of the three , and with , for five particular values factors . (a) of . The number of harmonic components considered is , (b) , (c) , (d) , and (e) . An expanded view is shown in Fig. 6(d) to show the simultaneous crossing through 1.

For illustration, Fig. 7 presents the values taken by the parameter versus the perturbation frequency , for going from 0 to 1, in steps of 0.1. The termination considered at the fundamental frequency is , in Fig. 6(c). As can be seen, the parameter , agreeing with provides the minimum value at each . Identical results are obtained when analyzing the other two factors and . C. Frequency Variation of the Parameters

,

and

For the stability analysis of a periodic regime at one should consider variations in the perturbation frequency

between 0 and a value larger than , to enable the detection of frequency divisions by 2. In Fig. 6, the parameters , and have been evaluated in the whole frequency range 0 to . The frequency is an offset with respect to dc, and . Therefore, the information obtained for the higher frequency values should be redundant. Indeed, when increasing , the parameter provides an “image” of the predictions by the parameter at lower frequencies. This is very clear in the analyses of Fig. 6(a) and Fig. 6(c). The frequency variation observed in Fig. 6 is in agreement with the stability properties of periodic solutions. In fact, the poles of periodic solutions, agreeing with the Floquet exponents, are not univocally related to the Floquet multipliers, which do define the stability properties of periodic solutions in a unique manner [29]–[31]. Equivalent poles, associated with the same pair of complex-conjugate Floquet multipliers, are symmetrically located about the spectral lines of the harmonic frequencies of the original periodic regime , that is, they are distributed as . Therefore, the two bands with observed in the analysis in Fig. 6 are linked and correspond to the same potential instability, at and . Note that the poles at and are symmetrically located about , and may tend to this value under variation of a circuit parameter [26], [41]. From Fig. 6, one can expect potential frequency divisions by 2 when the fundamental frequency is terminated at the values considered in Fig. 6(a) to Fig. 6(d). However, the region of subharmonic impedances leading to this division is expected to be small, since the values of and are close to 1. The potential frequency division by two predicted in Fig. 6 has been validated with an independent simulation. A small signal current source at is introduced into the circuit at the output reference plane [Fig. 8(a)]. At , the circuit is loaded, in each case, with one of the values considered in Fig. 6. Instead of using a modified conversion-matrix approach as in [33], [42], a harmonic balance analysis at is carried out. It is taken into account that there must be a phase relationship between the subharmonic current source and the input generator, due to the coherency of the two signals. The phase of the subharmonic source is set to zero (phase origin). Then, the phase of the input source is swept, using the

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Fig. 9. Comparison of the results obtained with the new potential-stability analysis, using the three factors , and , with those obtained using the single factor considered in [11].

the subharmonic load

Fig. 8. Validation of the capability to predict frequency divisions by 2. (a) In(b) Bounddependent simulations using a small-signal current source at aries of passive loads at the subharmonic frequency giving rise to frequency values considered in Fig. 6. (c) Spectrum of the subhardivisions for three monic solution obtained with an independent HB simulation for and .

small-signal current source to calculate the input admittance at the subharmonic component at each phase step. The opposite admittance values fulfill a limit condition for frequency division by 2, with subharmonic amplitude tending to zero, and provide the boundary in the Smith chart corresponding to the subharmonic load. The points of this boundary correspond to flip bifurcations [26], [41]. To obtain the frequency-division boundary in the Smith chart at , the reflection coefficient associated to must be calculated. The above method has been applied for the values considered in Fig. 6(b), (d) and (e), corresponding to , and . The division boundary, obtained with the technique in Fig. 8(a), has been traced in Fig. 8(b) for the three cases. It only intersects the Smith chart for and . The passive loads enabling the frequency division are inside the division boundary. This division region is small, in agreement with the quantitative predictions of Fig. 6. This correspondence is found, despite the fact that the two types of analysis are fundamentally different, since the subharmonic current source in Fig. 8(a) has a phase relationship with the input generator. The capability to obtain frequency divisions for passive loads within the boundaries obtained in Fig. 8(a) has also been validated with an independent HB simulation. For

and , one obtains the spectrum of Fig. 8(c). The results of the three-band analysis have been compared in Fig. 9 with that obtained when using the single factor considered in [11], for which the analysis is restricted to the lower and upper sidebands and . This two-band factor should agree with the one obtained with , when imposing a particular termination at baseband, such as , which was considered in [11] and also here. Therefore, it has more limited prediction capabilities. As an example, in Fig. 9, corresponding to the fundamental-frequency termination in Fig. 6(d), the two-sideband method predicts stable behavior, whereas the three-sideband one predicts potential instability. To extend the method to mismatch effects at higher harmonic terms one should consider all possible sets of harmonic impedance terminations, and obtain an M-port scattering matrix for each combination of harmonic impedances, where is the total number of mismatched sidebands. All the factors defined between any two ports of the M-port scattering matrix will provide the same information on the potential instability, under the condition that the reflection coefficients of the termination loads at all the other ports describe a unit circle. Such computational effort will not be worth in most cases due to the filtering action of the output network. The three-sideband stability analysis will be validated with measurements, in Section V, and with independent simulations through pole-zero identification, in the next section. Verification through simulation enables a high accuracy, under the certainty that the passive and active component models are identical. This validation will rely on the calculation of stability circles in the plane corresponding to the baseband termination . The predictions obtained with these circles will be compared with the results of an accurate pole-zero identification at circuit level [15], [28], [39]. IV. STABILITY CIRCLES IN THE THREE-SIDEBAND ANALYSIS In this section, the use of stability circles when considering three sideband frequency terminations (besides the fundamental-frequency termination ) is presented and applied for an independent validation of the new outer-tier methodology. Selecting particular sets of values with different stability properties would require a demanding implementation of a frequency dependent load , exhibiting the values at the corresponding frequencies. Instead, a simple passive network will be considered here, which under

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Fig. 10. Variation of the real part of the dominant pair of complex-conjugate , at constant input power poles versus the inductor , with .

TABLE I REFLECTION COEFFICIENT OF THE R-L LOAD AT THE BIFURCATION POINT

modification of an element value should give rise to different stability conditions of the PA. Next, the values exhibited by the load at the four frequencies will be calculated to check the consistency with the potential instability analysis. The load will consist of an inductor in series with a resistor , which fits commonly used antenna models. When connected to the amplifier output (replacing the nominal 50 load) and under variations of the inductor , at constant , it gives rise to different stability conditions, as predicted by the pole-zero identification method. Fig. 10 presents the variation of the real part of the dominant pair of complex-conjugate poles versus the inductor , at constant input power . As gathered from Fig. 10, the PA is stable for , and unstable for . The circuit exhibits a Hopf bifurcation at the inductor value . The first validation will be carried out at the Hopf bifurcation point obtained for . The poles crossing the imaginary axis have the critical frequency , as obtained from the pole-zero identification. At the baseband, lower sideband, fundamental and upper sideband frequencies given by , , and , the R-L load exhibits the reflection coefficients shown in Table I. Next, the outer-tier matrix in (2) will be used to obtain the stability circles in the Smith chart, when the perturbation frequency varies in the interval from to about the critical value . At the fundamental frequency , the load exhibits the reflection coefficient . For this particular , the stability circles will be obtained reducing the matrix to a 2 2 matrix at the sideband frequencies and , depending on the termination . This reduced matrix will be expressed as . At each the 2 2 matrix is calculated for the precise value exhibited by the series R-L load at .

Fig. 11. Stability conditions at (bifurcation point in Fig. 10). (a) Stability circles for traced in the plane for values corresponding to those exhibited by the R-L load in the frequency into about the critical value terval . For perturbation frequencies such that , the stability circle is traced in solid (dashed) line. The variation of the exhibited by the R-L load in the same frequency interval has also been repre, calculated sented. (b) Total admittance function with the three-sideband outer-tier analysis and with a full conversion-matrix approach in HB, using 7 harmonic terms.

The stability circles obtained from the matrix are traced in the plane , for perturbation frequencies from to [Fig. 11(a)]. For perturbation frequencies such that , the stability circle is traced in solid line. When , the circle is traced in a dashed line. This allows distinguishing between the potentially unstable and stable regions. The circle obtained for the critical perturbation frequency is traced in a bolder line. The variation of the reflection coefficient exhibited by the series R-L load through the interval to has also been represented. Around the critical frequency , the load values are located, as expected, in the potentially unstable region. Next, the bifurcation condition at will be validated. At this frequency, the R-L load exhibits the coefficient , shown in Table I. Setting the reflection coefficient at the baseband frequency to and using the matrix one obtains at the upper sideband frequency the input reflection coefficient . This value fully agrees with the inverse of the reflection coefficient exhibited by the R-L load at the upper sideband frequency, i.e.

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(see Table I). Thus, the bifurcation condition is fulfilled, in total consistency with the results of pole-zero identification. As an additional validation, the total admittance function , calculated with the three-sideband outer-tier analysis has been compared with the one obtained with a full conversion-matrix approach in commercial harmonic balance, using 7 harmonic terms. For the full conversion-matrix approach, a small-signal current source is introduced in parallel with the output R-L load to calculate the total admittance function, as the ratio between the source current and the node voltage. Results are shown in Fig. 11(b). As can be seen, the curves for both the real and imaginary parts are overlapped and display a bifurcation point at , where the real and imaginary parts of the total admittance are equal to zero. Next, inductor values in the unstable and stable ranges predicted by the pole-zero identification will be considered. From Fig. 10, for , the amplifier is unstable. The stability circles are calculated for the new reflection coefficient , exhibited by the modified load , at . They have been traced in the Smith chart [Fig. 12(a)] for the values exhibited by the new R-L load in the perturbation-frequency interval to , which includes the frequency of the dominant pair of complex-conjugate poles at . The stability circle at has been traced in a bolder line and the unstable region corresponds to the outside of this circle, where the exhibited by the R-L load is located. This indicates, as expected, potential instability for this baseband termination. Next, the input admittance at the upper sideband is calculated using and . This allows the evaluation of the impedance-type transfer function , analogous to the transfer function usually chosen for pole-zero identification [8], [15] [Fig. 12(b)]. This function has been compared with the one obtained through the full conversion matrix approach in harmonic balance (with 7 harmonic terms), obtaining a full overlap of both the amplitude and phase. The impedance exhibits a clear resonance at the frequency of the dominant poles, with a positive phase slope that indicates unstable behavior, in total agreement with the pole-zero analysis in Fig. 10. Next value is , in the stable region predicted by the pole analysis of Fig. 10. Most of the stability circles obtained under variations of about the frequency of the dominant poles at , lie outside the Smith chart [Fig. 13(a)]. The circle corresponding to this precise frequency value has been traced in bolder line and indicates absolute stability. The impedance transfer function [shown in Fig. 13(b)], obtained with the three-sideband outer tier analysis, is fully overlapped with the one resulting from a full conversion-matrix approach in HB, using 7 harmonic terms. It has a negative phase slope, in agreement with the stable behavior predicted by pole-zero identification. V. DEFINITION OF A GLOBAL STABILITY PARAMETER As has been shown, the potential stability properties exhibit a multi-parameter dependence, changing with the fundamental-

Fig. 12. Stability conditions for . (a) Stability circles for traced in the plane for values corresponding to those exhibited by the R-L load about the frequency of the dominant poles . For perturbation frequencies such that , the stability circle is traced in solid (dashed) line. The variation of the exhibited by the R-L load in that frequency interval has also been represented. calculated with the three(b) Impedance function sideband outer-tier analysis and with a full conversion-matrix approach in HB, using 7 harmonic terms.

frequency termination , the perturbation frequency and the terminations at the three sideband frequencies. In view of this complexity, the goal will be the derivation of a single quantity, globally accounting for the stability properties at each fundamental-frequency termination . The three parameters , and , with their crossings through 1, provide the same information regarding the conditional or unconditional stability properties. However, the actual parameter values are interesting since they contain useful information on the stability margin. Indeed, at each perturbation frequency they provide the minimum distance to the stability circles in the respective planes , and . The analysis will be initially particularized to . In fact, this parameter (as well as the other two parameters and ) will vary with the perturbation frequency and with the fundamental-frequency termination . This is because the scattering matrix in (2) depends on this termination, which affects the steady-state solution about which the circuit is linearized. The double dependence will now be emphasized with the explicit notation . The parameter (as well as and ) is continuous in the frequency , due to the continuity of the scattering matrix, as evidenced by the results of Fig. 6. On the other hand, continuity with respect to is ensured by the smooth

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Fig. 14. Contour plots of and in the Smith chart. The and contours at the limit of potential instability, corresponding to , agree in the two cases.

Fig. 13. Stability conditions for . (a) Stability circles for traced in the plane for values corresponding to those to exhibited by the R-L load in the frequency interval about the frequency of the dominant poles . The exhibited by the R-L load in that frequency interval has also variation of the calculated been represented. (b) Impedance function with the three-sideband outer-tier analysis and with a full conversion-matrix approach in HB, using 7 harmonic terms.

behavior of the set of nonlinear algebraic equations composing the HB system. Taking into account these continuity properties, a global stability parameter, associated with , may be defined (11) which corresponds to the minimum value taken by in the perturbation-frequency interval. The above parameter contains the full information on the potential instability conditions at each particular termination . Identical parameters and can also be defined for the lower and upper sidebands. To gather the whole information on the impact of the fundamental-frequency termination on the potential stability properties, the analysis set-up in Fig. 2(a) must be used. A double sweep must be carried out in the amplitude and phase of (or a spiral sweep), performing, at each sweep step, a large-signal small-signal analysis to obtain the impedance matrix . This matrix, depending on both and , is transformed to a scattering matrix and exported to in-house software to calculate the parameters , and . Then, their variation with can be evaluated through contour plots traced in the Smith chart. When using these single numbers to characterize the potential stability properties, information on the most dangerous perturbation frequencies is lost, but can be easily recov-

Fig. 15. Measurement test-bench. A triple-stub tuner has been used as output load in the first measurement campaign to identify load values in the stable and unstable regions of the Smith Chart. It was later substituted by a microstrip patch antenna (Rogers 4003C).

ered through inspection of the frequency plots used in Fig. 6, obtained with an undemanding spiral sweep applied to , as done in Fig. 6. The above global analysis has been applied to the modified PA in Fig. 1, at the nominal operation point, with output power and efficiency 80%. Fig. 14 shows the contour plots of and in the Smith chart. At the limit of potential instability, corresponding to and , the contours agree in the two cases. When moving rightwards from these two contours, the two parameters decrease continuously from 1, but in a different manner. The parameter decreases faster than . The simulations in Fig. 14 have been validated with exhaustive measurements. The measurement test-bench is shown in Fig. 15. Initially, a triple stub tuner has been connected to the PA output. Multiple positions of the tuner have been tested. For each position, both the PA output spectrum and the input impedance exhibited by the tuner about the fundamental frequency have been measured. The tuner input impedance has been characterized with a network analyzer. These exhaustive tests have provided the results shown in Fig. 16. The impedance plots corresponding to stable behavior are marked with squares in Fig. 16(a). The corresponding ensemble of output spectra is shown in Fig. 16(b) and evidences stable behavior in all cases. The impedance plots corresponding to unstable behavior are marked with circles in Fig. 16(a). The measured output spectrum corresponding to each termination load is shown

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Fig. 17. PA behavior when connected to a patch antenna. (a) Antenna fabricated on Rogers 4003C (b) Measurement of the antenna VSWR. (c) Measured variation of its input reflection coefficient in the Smith chart. (d) Spectrum received by the log-periodic antenna demonstrating the unstable behavior of the PA.

Fig. 16. Exhaustive measurements with a triple stub tuner, where multiple positions of the tuner have been tested. (a) Impedance plots for the different positions of the tuner, corresponding to the curves A to Q, measured in a 40 MHz span. Stable and unstable points are marked with squares and circles, respectively. (b) Waterfall representation of the spectra measured for the stable loads. (c) The same representation for the unstable loads. (d) and (e) Projection of the measured spectra in (b) and (c), respectively.

in Fig. 16(b), in the case of stable loads, and in Fig. 16(c), in the case of unstable loads. These representations allow noting the output-power variation with the termination load. In Fig. 16(d) and Fig. 16(e), the output spectra are projected on the frequency—power plane, which, in the case of the unstable loads evidences undesired spectral components due to the PA self-oscillation. Very good agreement is found when comparing the experimental results in Fig. 16 with the stability predictions based on the contour plots of and in Fig. 14. On the other hand, the oscillation frequency is most usually within the regions of lowest values detected in Fig. 6. It should be emphasized that the contour plots in Fig. 14 inherently contain the information on the circuit linearized response versus a perturbation at an incommensurate frequency , as gathered from their definition in (11). The results obtained with the contour plots in Fig. 14 and the exhaustive experimental characterization in Fig. 16 have also been validated in conditions close to those in real applications. The PA has been connected to a patch antenna fabricated on Rogers 4003C, shown in Fig. 17(a). The VSWR of the manufactured antenna has been characterized and its lowest value is obtained at 787 MHz, instead of the PA operation frequency 800 MHz [Fig. 17(b)]. Fig. 17(c) shows the variation of its input reflection coefficient in the Smith chart.

Fig. 18. PA behavior when a directional coupler is inserted between the PA output and the antenna. (a) Input impedance of the subsystem composed by the cascade connection of the directional coupler and the antenna. (b) Frequency variation of the measured VSWR. (c) Measured spectrum showing a stable behavior.

For the stability characterization of the PA loaded with the patch antenna, the transmitted signal is received by a general purpose log-periodic broadband antenna, connected to a network analyzer. See the details of the measurement test bench in Fig. 15. By performing the measurement without a directional coupler, power splitter or analogous devices, used to take a sample of the output spectrum, one can be sure that the only loading effects of the PA are those coming from the antenna input impedance. Taking into account the contour plots in Fig. 14, from a simple inspection of the antenna input impedance in Fig. 17, one can anticipate that the PA loaded with this antenna will be unstable.

SUÁREZ et al.: GENERALIZED STABILITY CRITERIA FOR POWER AMPLIFIERS UNDER MISMATCH EFFECTS

Indeed, when connecting the antenna to the PA output, an oscillation is obtained, shown in Fig. 17(d). In the next experiment, a directional coupler will be inserted between the PA output and the antenna. Before that, the input impedance of the subsystem composed by the cascade connection of the directional coupler and the antenna has been measured, obtaining the plot displayed in Fig. 18(a). The measured VSWR is shown in Fig. 18(b). From inspection of the plot in Fig. 18(a), located in the stable region of the Smith chart, according to the contour plots in Fig. 14, the PA should be stable. This is confirmed by the spectrum measured in Fig. 18(c), which shows a stable behavior. The three-sideband analysis followed by the contour plots provides an easy-to-apply methodology for the detection and suppression of instabilities due to mismatch effects. VI. CONCLUSION A general application method for the prediction of potential instability in power amplifiers under mismatch effects has been presented. It is based on the extraction of an outer-tier scattering matrix at the three sideband frequencies with impact on the stability properties, which in most cases will correspond to the baseband and the lower and upper frequency sidebands. With the inclusion of the baseband, the analysis is more accurate and complete, and enables the prediction of common instabilities, occurring around the input frequency divided by 2. The termination at the fundamental frequency affects the steady-state solution and hence the outer-tier matrix, which is based on a linearization of the circuit about this solution. The complexity associated to the multiparameter dependence is resolved with a detailed analysis of the properties of the three different factors that can be associated to the 3 3 matrix. Form these analysis, three new parameters have been defined, able to provide global information on the potential instability properties. Contours plots of these parameters enable a simple identification of the fundamental-frequency terminations leading to potential instability and provide valuable information to devise a stabilization procedure. REFERENCES [1] D. Qiao, D. Cho, Y. Zhao, T. Hung, D. Kimball, M. Li, and P. Asbeck, “Antenna impedance mismatch measurement and correction for adaptive CDMA transceivers,” in Proc. IEEE MTT-S Int. Microw. Symp., 2005, pp. 783–786. [2] A. van Bezooijen, C. Chanlo, and A. van Roermund, “Adaptively preserving power amplifier linearity under antenna mismatch,” in Proc. IEEE MTT-S Int. Microw. Symp., 2004, pp. 1515–1518. [3] A. Keerti and A. H. Pham, “RF Characterization of SiGe HBT Power Amplifiers Under Load Mismatch,” IEEE Trans. Microw. Theory Tech., vol. 55, no. 2, Feb. 2007. [4] W. Karoui and W. T Parra, “A protection circuit for HBT RF Power Amplifier under load mismatch conditions,” in Proc. Circuits Syst. TAISA Con., Joint 6th Int. IEEE Northeast Workshop, Jun. 22–25, 2008, pp. 241–244. [5] S. Dellier, R. Gourseyrol, J. Collantes, A. Anakabe, G. SoubercazePun, and K. Narendra, “Stability analysis of microwave circuits,” Proc. 2012 IEEE 13th Ann. WAMICON,, pp. 1–5, Apr. 15–17, 2012. [6] K. Narendra, E. Limiti, C. Paoloni, J. M. Collantes, R. Jansen, and S. Yarman, “Vectorially Combined Distributed Power Amplifiers for Software-Defined Radio Applications,” IEEE Trans. Microw. Theory Tech., vol. 60, no. 10, Oct. 2012.

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[7] J. F. Imbornone, M. Murphy, R. S. Donahue, and E. Heaney, “New insight into subharmonic oscillation mode of GaAs power amplifiers Under Severe Output Mismatch Condition,” IEEE J. Solid State Circuits, vol. 32, pp. 1319–1325, Sep. 1997. [8] A. Anakabe et al., “Automatic pole-zero identification for multivariable large-signal stability analysis of RF and microwave circuits,” in Proc. Eur. Microw. Con. (EuMC), Paris, 2010, pp. 477–480. [9] A. Suárez, F. Ramírez, and S. Sancho, “Stability analysis of power amplifiers under mismatching effects,” in Proc. 2013 IEEE MTT-S Int. Microw. Symp., Seattle, WA, USA, Jun. 2013, pp. 1–3. [10] A. Suárez, F. Ramírez, and S. Sancho, “Stability Analysis of Power Amplifiers Under Output Mismatch Effects,” IEEE Trans. Microw. Theory Tech., vol. 62, no. 10, pp. 2273–2289, Oct. 2014. [11] A. Suárez, F. Ramírez, and S. Sancho, “Stability criteria for power amplifiers under mismatch effects,” in Proc. 2015 IEEE MTT-S Int. Microw. Symp., Phoenix, AZ, USA, May 2015, pp. 1–4. [12] V. Rizzoli and A. Neri, “State of the art and present trends in nonlinear microwave CAD techniques,” IEEE Trans. Microw. Theory Tech., vol. 36, pp. 343–356, Feb. 1988. [13] V. Rizzoli and A. Lipparini, “General Stability Analysis of Periodic Steady-State Regimes in Nonlinear Microwave Circuits,” IEEE Trans. Microw. Theory Tech., vol. 33, no. 1, pp. 30–37, 1985. [14] R. Quéré, E. Ngoya, M. Camiade, A. Suarez, M. Hessane, and J. Obregon, “Large signal design of broadband monolithic microwave frequency dividers and phase-locked oscillators,” IEEE Trans. Microw. Theory Tech., vol. 41, pp. 1928–1938, Nov. 1993. [15] J. Jugo, J. Portilla, A. Anakabe, A. Suárez, and J. M. Collantes, “Closed-loop stability analysis of microwave amplifiers,” IEE Electron. Lett., vol. 37, pp. 226–228, Feb. 2001. [16] N. O. Sokal and A. D. Sokal, “Class E-A New Class of High Efficiency Tuned Single-Ended Switching Power Amplifiers,” IEEE J. Solid-State Circuits, vol. SC-10, no. 3, pp. 168–176, Jun. 1975. [17] F. H. Raab, “Idealized Operation of the Class E Tuned Power Amplifier,” IEEE Trans. Circuits Syst., vol. 24, no. 12, pp. 725–735, Dec. 1977. [18] K. Chen and D. Peroulis, “Design of Highly Efficient Broadband Class-E Power Amplifier Using Synthesized Low-Pass Matching Networks,” IEEE Trans. Microw. Theory Tech., vol. 59, no. 12, pp. 3162–3173, Dec. 2011. [19] M. Franco and A. Katz, “Class-E Silicon Carbide VHF Power Amplifier,” in Proc. IEEE/MTT-S Int. Microw. Symp., Jun. 3–8, 2007, pp. 19–22. [20] S. Jeon, A. Suárez, and D. B. Rutledge, “Analysis and elimination of hysteresis and noisy precursors in power amplifiers,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 3, pp. 1096–1106, Mar. 2006. [21] A. Grebennikov, “Load Network Design Technique for Class F and Inverse Class F PAs,” High Freq. Electron., pp. 58–76, May 2011. [22] S. D. Kee, I. Aoki, A. Hajimiri, and D. Rutledge, “The class-E/F family of ZVS switching amplifiers,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 6, pp. 1677–1690, Jun. 2003. [23] R. A. Beltran, “Class-F and inverse class-F power amplifier loading networks design based upon transmission zeros,” in Proc. IEEE MTT-S Int. Microw. Symp. (IMS), Jun. 1–6, 2014, pp. 1–4. [24] J. M. Rollett, “Stability and power-gain invariants of linear twoports,” Ins. Radio Engineers Trans. Circuit Theory, vol. 9, pp. 29–32, 1962. [25] R. E. Collin, Foundations for Microwave Engineering, 2nd ed. New York, NY, USA: Wiley, 2001. [26] J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields. New York, NY, USA: Springer-Verlag, 1990. [27] S. Mons, J.-C. Nallatamby, R. Queré, P. Savary, and J. Obregon, “A unified approach for the linear and nonlinear stability analysis of microwave circuits using commercially available tools,” IEEE Trans. Microw. Theory Tech., vol. 47, no. 12, pp. 2403–2409, Dec. 1999. [28] A. Anakabe, J. M. Collantes, and J. Portilla et al., “Analysis and elimination of parametric oscillations in monolithic power amplifiers,” in Proc. IEEE MTT-S Int. Microwave Symp. Dig., Seattle, WA, Jun. 2002, pp. 2181–2184. [29] W. Struble and A. Platzker, “A rigorous yet simple method for determining stability of linear N-port networks [and MMIC application],” in Proc. Gallium Arsenide Integrated Circuit (GaAs IC) Symp. Tech. Digest, 1993, pp. 251–254. [30] W. Struble and A. Platzker, “Rigorous determination of the stability of linear n-node circuits from network determinants and the appropriate role of the stability factor K of their reduced two-ports,” Proc. Int. Workshop Integr. Nonlinear Microw. Millimeterwave Circuits, pp. 93–107, Oct. 5–7, 1994.

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[31] J. M. Paillot, J. C. Nallatamby, M. Hessane, R. Quéré, M. Prigent, and J. Rousset, “A general program for steady state, stability, FM noise analysis of microwave oscillators,” in Proc. IEEE MTT-S Int. Microw. Symp., 1990, pp. 1287–1290. [32] V. Rizzoli, F. Mastri, and D. Masotti, “General noise analysis of nonlinear microwave circuits by the piecewise harmonic balance technique,” IEEE Trans. Microw. Theory Tech., vol. 42, pp. 807–819, May 1994. [33] L. Pantoli, A. Suárez, G. Leuzzi, and F. Di Paolo, “Complete and systematic simulation tools for frequency divider design,” IEEE Trans. Microw. Theory Tech., vol. 56, no. 11, pp. 2442–2452, Nov. 2008. [34] D. Woods, “Reappraisal of the unconditional stability criteria for active 2-port networks in terms of S parameters,” IEEE Trans. Circuits Syst., vol. 23, no. 2, pp. 73–81, Feb. 1976. [35] R. W. Jackson, “Rollet proviso in the stability of linear microwave circuits—A tutorial,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 3, pp. 993–1000, Mar. 2006. [36] J. F. Boehm and W. G. Albright, “Unconditional stability of a threeport network characterized with S-parameters,” IEEE Trans. Microw. Theory Tech., vol. 35, no. 6, pp. 582–586, Jun. 1987. [37] E. L. Tan, “Simplified graphical analysis of linear three-port stability,” IEE Proc. Microw. Ant. Propag., vol. 152, no. 4, pp. 209–213, Aug. 2005. [38] M. L. Edwards and J. H. Sinsky, “A new criterion for linear 2-port stability using geometrically derived parameters,” IEEE Trans. Microw. Theory Tech., vol. 40, no. 12, pp. 2303–2311, Dec. 1992. [39] J. M. Collantes, I. Lizarraga, A. Anakabe, and J. Jugo, “Stability verification of microwave circuits through Floquet multiplier analysis,” Proc. 2004 IEEE APCCAS, pp. 997–1000, 2004. [40] F. Bonani and M. Gilli, “Analysis of stability and bifurcations of limit cycles in Chua's circuit through the harmonic-balance approach,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 46, pp. 881–890, Aug. 1999. [41] A. Suárez, Analysis and Design of Autonomous Microwave Circuits. Hoboken, NJ, USA: IEEE-Wiley, Jan. 2009. [42] F. Di Paolo and G. Leuzzi, “Bifurcation synthesis by means of Harmonic Balance and Conversion Matrix,” in Proc. Eur. Gallium Arsenide Appl. Symp., Munich, Germany, Oct. 2003, pp. 521–524. Almudena Suárez (M'96–SM'01–F'12) was born in Santander, Spain. She received the Electronic Physics and Ph.D. degrees from the University of Cantabria, Santander, Spain, in 1987 and 1992, respectively, and the Ph.D. degree in electronics from the University of Limoges, Limoges, France, in 1993. She is currently a Full Professor with the Communications Engineering Department, University of Cantabria. She co-authored Stability Analysis of Nonlinear Microwave Circuits (Artech House, 2003) and

authored Analysis and Design of Autonomous Microwave Circuits (IEEE-Wiley, 2009). Prof. Suárez is a member of the Technical Committees of the IEEE Microwave Theory and Techniques Society (IEEE MTT-S) International Microwave Symposium (IMS) and the European Microwave Conference. She was an IEEE Distinguished Microwave Lecturer from 2006 to 2008. She is a member of the Board of Directors of the European Microwave Association. She is the Editor-in-Chief of the International Journal of Microwave and Wireless Technologies (Cambridge University Press). She was the co-chair of IEEE Topical Conference on RF Power Amplifiers (PAWR) in 2014 and 2015.

Franco Ramírez was born in Potosí, Bolivia. He received the degree in electronic systems engineering degree from the Military School of Engineering (EMI), La Paz, Bolivia, in 2000 and the Ph.D. degree in communications engineering from the University of Cantabria, Santander, Spain in 2005. From 1999 to 2000 he worked for Ericsson de Bolivia Telecomunicaciones, where he was involved in several projects related with GSM and TDMA technologies. At present he is an Associate Professor at the Communications Engineering Department of the University of Cantabria. His research interests include phase noise, stability and the development of nonlinear techniques for the analysis and design of autonomous microwave circuits.

Sergio Sancho was born in Santurce, Spain, in 1973. In 1997 received the degree in physics from Basque Country University, Bizkaia, Spain. In 1998 he joined the Communications Engineering Department of the University of Cantabria, Spain, where he received the Ph.D. degree in electronic engineering in February 2002. Currently, he works at the University of Cantabria, as an Associate Professor of its Communications Engineering Department. His research interests include the nonlinear analysis of microwave autonomous circuits and frequency synthesizers, including stochastic and phase-noise analysis.

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Highly Efficient and Multipaction-Free P-Band GaN High-Power Amplifiers for Space Applications Natanael Ayllon, Member, IEEE, and Pier Giorgio Arpesi

Abstract—In this paper, the authors report upon the development of multipaction-free P-band (UHF) GaN high-power amplifiers (HPAs) with target RF output power values of 140 W and power-added efficiency beyond 70%. Initially, two different 80-W class single-ended power modules were designed, manufactured, and tested using GaN devices from two different manufacturers. Load–pull techniques were used in both designs to achieve the best tradeoff in terms of RF output power, efficiency, and stability. Secondly, two identical power modules have been combined in a balanced architecture in order to obtain the required level of RF output power. Multipaction analyses and tests have been carried out to guarantee reliable operation in space. The HPAs have been characterized over temperature from 15 C to 55 C in pulsed and constant-wave conditions, showing negligible drifts over temperature and multipaction-free operation. RF output power in excess of 180 W at 70% drain efficiency is also demonstrated. Index Terms—Balanced amplifier, GaN, high efficiency, high-power amplifier (HPA), multipaction, satellite, stability.

I. INTRODUCTION

B

IOMASS is the 7th European space-borne Earth Explorer mission. The overall objective of the mission is to reduce the uncertainty in the worldwide spatial distribution of the forest biomass and to monitor its dynamics from space in order to improve current assessments and future projections of the global carbon cycle [1]. Since the spacecraft is planned to be launched in 2020, pre-developments for the critical parts are currently ongoing. The main instrument of the spacecraft is a P-band (UHF) fully polarimetric synthetic aperture radar (SAR) that is also used for performing interferometry [2]. Preliminary system studies revealed the need to produce an RF output power in excess of 100 W (50 dBm) at the output of the RF amplifier [1]. However, although most of the required passive microwave devices such as filters, switches, and couplers are already commercial off-the shelf, no commercial product is available for the highpower amplifier (HPA) function. Due to the carrier frequency at 435 MHz, a vacuum tube device would be very large and heavy for its accommodation on the spacecraft, and therefore,

Manuscript received June 30, 2015; revised September 11, 2015; accepted October 10, 2015. Date of publication October 30, 2015; date of current version December 02, 2015. This paper is an expanded version from the IEEE MTT-S International Microwave Symposium, Phoenix, AZ, USA, May 17–22, 2015. N. Ayllon is with the European Space Agency, ESA-ESTEC, Noordwijk 2200 AG, The Netherlands (e-mail: [email protected]). P. G. Arpesi is with the Time and Frequency Department, Selex-ES, 20014 Nerviano, Milan, Italy (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2015.2493550

solid-state technologies are considered for amplifying the radar signal. There are few semiconductor technologies qualified for high RF power operation in space. For years, GaAs has been the workhorse for this type of applications. However, the required RF output power calls for more powerful semiconductor technologies since the use of GaAs processes would require complex power combination schemes and more challenging thermal management. GaN technology instead seems to be better suited for this application. As an example, the work in [3] and [4] demonstrates the capabilities of GaN technology to meet these requirements. The need to operate RF hardware at this frequency and RF power levels in space makes the system very prone to suffer from Multipaction and Corona discharges, as explained in [5]–[7]. These phenomena are widely discussed in the literature for the design of filters, diplexers, and waveguides. In this paper, the work in [4] is expanded with a deep investigation on multipaction discharge in the design of solid-state power amplifiers (SSPAs). To the authors’ knowledge, it is the first time such analysis and research is reported. This paper is organized as follows. Section II describes, in a more detailed manner than in [4], the design of 80-W GaN power modules by using RF power transistors from two different manufacturers. Simulated and measured results of the RF power modules are given and compared. Section III tackles the design of two high-power sections for the SSPA, where multipaction phenomenon is widely discussed. Section IV describes the manufacturing and test results of the SSPA. This paper ends with conclusions in Section V. II. DESIGN, MANUFACTURE, AND TEST OF POWER MODULES Two manufacturers were selected among the different suppliers with commercially available space qualified GaN transistors. United Monolithic Semiconductors (UMS) offer an 80-W device (CHK080A) in a ceramic–metal-flange package, using the space qualified 0.5- m gate-length GaN HEMT on an SiC process with 65% typical power-added efficiency (PAE) at 435 MHz. Similarly, Mitsubishi Electric offer an unmatched 80-W space qualified device (MGF0849GS) using a 0.7- m gate-length GaN HEMT on an SiC process with 66% typical PAE at 435 MHz. Both transistors are well suited for space applications and present a mean time to failure 10 h. Based on the manufacturers’ data sheets and nonlinear models of the power devices, the design of the power modules has been carried out. The modules are series tuned switch mode amplifiers, where the active device behaves like a switch operated by the gate–source voltage. Nevertheless, they are not

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Fig. 3. Detailed schematic of the RF power module based on dual-gate and dual-drain GaN HEMT device from Mitsubishi (MGF0849GS).

Fig. 1. Detailed schematic of the RF power module based on dual-gate–dualand is drain GaN HEMT device from UMS (CHK080A). Location of shown. Fig. 4. Layout of the RF power module based on GaN HEMT device from Mitsubishi (MGF0849GS). TABLE I SUMMARY OF SIMULATED POWER MODULE CHARACTERISTICS

Fig. 2. Layout of the RF power module based on GaN HEMT device from UMS (CHK080A). The dual-gate–dual-drain matching is illustrated.

true class-E, as neither the drain voltage nor the drain current is zero at the switching instant [4], [8]. Two single-stage single-ended circuits have been designed relying on CHK080A and MGF0849GS GaN HEMT devices from UMS and Mitsubishi, respectively. Load–pull simulations have been performed trading off RF output power, stability, and dc-to-RF efficiency and reliability. Indeed, the latter is of fundamental importance in space applications due to the fact that the SSPAs are expected to work nominally after several years of continuous operation without the need for maintenance and while suffering the stressful and hazardous conditions of space (i.e., radiation, ageing, and temperature variations). Therefore, more relaxed operating conditions are established by design, also called derating, where GaN HEMT devices are operated at around 75% of their absolute electrical maximum ratings and below a given junction temperature value ( ). By doing so, the risk of failure and degradation over time is minimized with a price to pay on RF performances, particularly on the maximum achievable PAE and RF output power. Concerning the design of the power module based on the UMS GaN transistor, input and output matching networks with a dual-gate–dual-drain configuration have been implemented (Fig. 1). Two relatively large series resistors at input minimize the interactions between the two paths at the operating frequency, also preventing low-frequency oscillations. As shown in Fig. 1, series impedances to each drain before the two paths are joined together on the output tuning capacitances minimizes the interaction under nominal, even operation of the two drain paths. Resistor prevents asynchronous operations in the form of odd-mode oscillations.

The layout of this design is shown in Fig. 2. A Rogers RT6002 substrate has been used with a thickness of 0.762 mm. The design of the power module based on the Mitsubishi GaN transistor is shown in Fig. 3. A low-frequency stabilization network is implemented by a combination of parallel and series losses in the signal path (i.e., series resistors on the gate signal path). Matching networks are of a series tuning type with an L–C filter at both the input and output. The layout of this version is shown in Fig. 4. The same substrate from Rogers has been used, achieving a similar layout size (11.5 cm 5 cm). The two manufactured boards were tested and results were reported in [4]. A summary table is reported here again for convenience (Table I). In general, both designs are able to achieve the required levels of output power, yet the power module based on the UMS GaN device presents higher levels of efficiency. As can be observed, the UMS nonlinear model underestimates the real performances of the transistor. To confirm this point, different GaN devices from the same batch were assembled in the same board, obtaining negligible drifts in the RF performances. Instead, the nonlinear model of the Mitsubishi GaN HEMT device appears to be more precise and is able to predict more accurately the actual RF performances. The stability of the linear and nonlinear regimes was analyzed from the very early stages of the design by using automatic pole-zero identification techniques described in [9] and

AYLLON AND ARPESI: HIGHLY EFFICIENT AND MULTIPACTION-FREE P-BAND GaN HPAs FOR SPACE APPLICATIONS

Fig. 5. Balanced architecture of the high-power final stage of the SSPA.

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Fig. 7. Thermal flow diagram used for the calculation of the junction temperatures on the GaN HEMT devices.

irrespective of the VSWR tolerance of the active devices. Stability analyses by using automatic pole-zero identification techniques [9], [10] were also performed in this balanced design, confirming once more the stable operation of the HPA. A. Thermal Management

Fig. 6. Photograph of the wireline coaxial coupler. Input and output ports are also shown in the photograph.

[10]. Unconditional stability was achieved by using stabilization resistors on the gate ( ) and inter-branch resistors between the drains of the transistor ( ). Following the method described in [11], a value of was calculated. No oscillations were observed in the manufactured amplifiers. III. DESIGN OF THE HPA The SSPA performance depends essentially on the characteristics of its RF high-power section. In this case, a 50matched balanced architecture by using quadrature couplers for the power splitting and combining functions is adopted with two identical 80-W class GaN HEMT power modules in parallel (Fig. 5). Therefore, the development of the single-stage single-ended amplifiers in Figs. 1 and 3 is of fundamental importance in order to achieve the required levels of RF output power and efficiency while reserving a stable behavior. The balanced architecture with quadrature couplers is widely implemented in space-borne SSPAs as the architecture offers inherently good return losses at input and output interfaces and enhances the linear and nonlinear stability thanks to the isolation between branches, preventing undesirable loops with Gain 0 dB. In particular, the design is based on 3-dB 90 Wireline quadrature coaxial couplers produced by Sage Laboratories, St. Louis, MO, USA. These coaxial couplers consist of a pair of wire center conductors (twisted up to three turns per inch) surrounded by a continuous dielectric insulator and shielded by a drawn or extruded outer jacket. The resultant construction has the physical attributes of a semi-rigid coaxial cable and the electrical performance of a precision TEM mode parallel coupled line coupler with low insertion loss and high directivity. Typical insertion loss at 435 MHz is 0.25 dB with 20-dB return losses over an octave bandwidth. A photograph of this coupler is shown in Fig. 6. An output isolator is normally introduced downstream to the output coupler in order to present a constant load impedance to the amplifier, stable behavior, and enhanced robustness against any voltage standing-wave ratio (VSWR) mismatch conditions

In addition to the electrical derating rules described previously, a derating rule for maximum junction temperature ( ) is also applied for space-borne SSPAs. In this case, and based on MTTF tests performed on both GaN HEMT devices, a maximum of 175 C was established as a requirement. An analysis has been made based on thermal resistances of the different layers where the devices are mounted (Fig. 7). The HPAs are mounted onto 2.5-mm-thick aluminum metal carriers using a Rogers RT/Duroid 6002 substrate with a thickness of 0.762 mm. The carriers are mounted onto a 13-mm-thick baseplate as part of the SSPA package, and finally, the SSPA package is assembled onto a final baseplate on the mounting panel of the spacecraft. Based on this assembly, a simple thermal calculation can be done by using (1), where is the temperature of the mounting baseplate, is the thermal resistance of the packaged transistor given by the manufacturer, is the peak power dissipated, is the thermal resistance of the mounting assembly, and is the averaged dissipated power over the area of the HEMT packaged transistor, (1) Based on the measured RF performances, the thermal calculation in (1) indicates maximum values of 160 C and 126 C for the UMS and Mitsubishi GaN devices, respectively, when operating in the CW mode, and values of 137 C and 108 C when operated in pulsed conditions (60- s pulse-width, 12% duty cycle). These values are well below the maximum derated value considered for a reliable operation in space. B. Multipaction, Corona, and Passive Intermodulation When designing high RF power devices, the following phenomena can typically occur [7]: • multipaction breakdown; • ionization breakdown, also known as corona discharge; • thermal related high-power breakdown; • passive intermodulation (PIM). As described in [5], multipaction breakdown is an RF vacuum breakdown mechanism in which secondary electron emission in resonance with an alternating electric field leads to exponential electron multiplication due to the growth of free electron space charge between two surfaces (metallic or dielectric). Corona is an electrical discharge brought on by the ionization of a gas or

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Fig. 9. Cross section of the connection from RF FET and microstrip. The critical area for multipaction breakdown is represented by a dashed circle.

Fig. 8. Simplified top view diagram of the HPA. Five critical points are identified in dashed circles.

fluid surrounding a conductor that results in the generation of plasma. If the ionized region continues to grow until it reaches another conductor at a lower potential, a low-resistance conductive path between the two will be formed, resulting in an electric arc. Contrary to multipaction, Corona discharge needs the presence of air or fluid, which only occurs in low-pressure environments. Thermal related breakdown could also appear if a device dissipates heat. Most of the materials used for manufacturing high-power RF hardware release gas when they are heated up (outgassing). If not properly vented, the released air cannot escape and creates locally an increase in the atmospheric pressure that can eventually lead to a Corona discharge. Finally, PIM are intermodulation products generated by passive hardware such as filters, isolators, switches, and waveguide components when they are operated under multicarrier or digitally modulated signals. It is of particular interest in satellite transponders since the nonlinearities produced in the transmit chain can lie within the frequency range of the receive chain. Nevertheless, the SSPA is per se a nonlinear device, and hence, PIM generated by the SSPA is well below the typical intermodulation produced by the amplifier itself. Amongst all high RF power phenomena described, multipaction is in the present case the most critical breakdown effect that needs to be analyzed since hermetically sealed devices are used to prevent Corona discharges and the housing of the SSPA includes sufficient venting holes to minimize outgassing and thermal breakdown related issues. A simplified top view schematic of the HPA is shown in Fig. 8, where five critical areas prone to trigger multipaction discharge are identified due to the existing gaps between two metallic surfaces. All these points are downstream to the two power modules, which is the only area of the SSPA where high RF voltages and currents are present. The five points are, from left to right, as follows: 1) connection from RF field-effect transistor (FET) to microstrip; 2) tuning capacitors between RF transmission line and ground; 3) transition from power module to output coupler; 4) transition from output coupler to microstrip; 5) transition from output microstrip to coaxial connector. 1) Connection From RF FET to Microstrip: A simplified drawing of the RF FET assembly is shown in Fig. 9, where a

dashed circle highlights the critical area around the transistor’s drain lead. In particular, the critical point is the gap between the drain lead and the microstrip metallic surface, whose proximity can lead to multipaction [5]. On one hand, the analysis based on the parallel-plate model is, in this case, not rigorous since it is not representative of the actual geometry of the assembly, leading to very low discharge thresholds [5]. On the other hand, another necessary condition for the multipaction discharge is the presence of RF alternating fields. In the present case, due to the adopted class-E design approach, the time-domain drain-voltage waveform remains positive during the full operation cycle, and therefore, the electric field has the same direction at any given time. Should the HPA present slightly negative voltages, the supply voltage applied to the drain line biases the electric field with respect to RF ground (chassis). This tends to stop the initiation of an electron avalanche regardless of the value of the secondary electron-emission yield (SEY) of the surface material [12]. Thus, this area is considered multipaction free. 2) Tuning Capacitors Between Transmission Line and Ground: Two chip capacitors are connected in parallel to the 50- transmission line on the output matching network of each power module (Figs. 2 and 4). The peak voltage on each capacitor spans ideally from 130 to 50 V, which is the range corresponding to the 80 W of RF output power into the 50- load, with 40-V drain supply voltage offset. Due to the dimensions of each capacitor (type CDR14), the gap between the microstrip and the ground metallization is only 1.6 mm, which leads to a frequency distance product of 0.7 GHz mm at 435 MHz. Due to this product value and to the predicted voltage swing, this gap is at risk of multipaction breakdown since it is inside the Hatch and Williams multipaction susceptibility area for aluminum metallic plates [5]. Fig. 10 shows the Hatch and Williams multipaction susceptibility zone for aluminum parallel plates extracted from [5], where some measured points on test samples confirm the validity of such a theory. One way of overcoming multipaction issues in the final design is to increase the distance between the RF signal path and the ground metallic path. This can be done by replacing the chip capacitors by meandered open stubs of a given length sufficiently separated from the ground path. For instance, a frequency distance product of 3.2 GHz mm gives a distance of 7.4 mm at 435 MHz. This distance gives a threshold of 170 W of RF power, which brings more than 3-dB margin to the present case. 3) Transition From Power Module to Output Coupler: The two power modules are connected to a 90 quadrature coaxial coupler that is physically assembled into a different silver-plated metallic carrier. A simplified drawing of the gap

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Fig. 12. 3-D structure and manufactured test sample for multipaction verification of a connection between two microstrip lines.

Fig. 10. Multipaction susceptibility zone for parallel plates. Dashed lines represent the Hatch and Williams theoretical curves. Solid line represents the boundaries for the design of RF hardware susceptible to multipaction breakdown.

Fig. 13. Detail of the inner conductor coaxial coupler connected to the microstrip. A resin with unknown SEY is used to prevent discharges. Fig. 11. Cross section of the transition from power module to output hybrid coupler.

between two interconnected microstrip lines is illustrated in Fig. 11. A gap of 0.5 mm between the two metal carriers is defined, which is guaranteed by using a calibrated 0.3-mm spacer during the module assembly inside the SSPA. The two parts are connected by using a 3.8-mm-wide SnPb ribbon. For the multipaction analysis, two different substrate thicknesses are considered, 0.762 and 1.524 mm. The parallel-plate analysis might lead to erroneous results in this case since the SEY of the silver-plated copper metallic surfaces is different than the one for aluminum. Therefore, a specific multipaction analysis has been done by Aurorasat, Valencia, Spain. A 3-D model of the structure has been created with CST Microwave Studio in order to calculate the S-parameters and extract the electromagnetic (EM) fields of the structure. The EM fields are then imported to SPARK3D, which is an evolution of the FEST3D software tool from Aurorasat able to determine the multipaction breakdown level also in microstrip structures. Results of these analyses indicate margin levels of 18 dB over the nominal RF power (80 W). Indeed, due to the small distance between the substrates and between the two carriers, electrons that travel from the ribbon to the mounting plate are not likely to do it without impacting the lateral walls, breaking a possible resonance and leading to the absorption of electrons on the lateral walls. Nevertheless, threshold results are very dependent on SEY values. Therefore, in order to confirm simulated results, a representative test jig of a connection between two microstrip lines (Fig. 12) has been designed, manufactured, and tested in the Eu-

Fig. 14. 3-D structure and manufactured test sample for multipaction verification of a connection between output coupler and microstrip lines.

ropean Space Agency–Val Space Consortium (ESA-VSC) European High Power RF Laboratory, Valencia, Spain. The test was conducted with the device-under-test (DUT) operated at 435 MHz, 5 10 mbar of pressure, temperature of 50 C, 60- s pulse width with 12% duty cycle, and up to an RF power of 1.5 kW (maximum available RF power). Prior to the test, a bake-out of 18 h was performed at 60 C for outgassing purposes. The DUT did not present any discharge event up to 1.5 kW, confirming a multipaction margin level of at least 12.76 dB by means of test. 4) Transition From Output Coupler to Microstrip: The wireline coaxial coupler described in Fig. 6 is soldered to the microstrip lines. As one can observe in Fig. 13, the output of this coupler is covered by a protective resin, which aims to prevent any discharge. It is worth noticing that the SEY of this resin is not known, and therefore, a rigorous analysis cannot be done by simulation. Again, a test sample (Fig. 14) has been designed, manufactured, and tested in the same facility.

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Fig. 16. Manufactured test sample for multipaction verification of a transition from output microstrip to coaxial connector.

TABLE II SUMMARY OF MULTIPACTION ANALYSIS AND TEST CAMPAIGN Fig. 15. Cross section of the transition from output microstrip to coaxial connector. Critical gaps for multipaction breakdown are shown.

Test conditions and bake-out were the same as for the DUT of Fig. 12. A multipaction discharge was detected at a power of 1375 W, establishing in this case a margin of 9.38 dB since the nominal RF output power at this point is 160 W (two parallel power modules of 80 W). 5) Transition From Output Microstrip to Coaxial Connector: A simplified drawing of a microstrip to coaxial connector transition is described in Fig. 15. The possibility to cover the gap between the connector and the carrier by means of a dielectric made of 0.25-mm-thick Duroid substrate (referred to as Duroid 2 in Fig. 15) has been considered to prevent discharges around the surface of the wall. Once more, two substrate thicknesses (referred as Duroid 1 in Fig. 15) of 0.762 and 1.524 mm were analyzed with and without a Duroid filling plate on the connector side. SEY of aluminum was taken into account for the multipaction analysis. Similarly to the analysis performed for the transition from the power module to output coupler, CST Microwave Studio has been used to obtain the EM fields of the 3-D structure and the fields have been imported to SPARK3D for the multipaction analysis up to a maximum simulated power of 10 kW. Results are the following. • Case 1: 0.762-mm Duroid substrate with filling plate 10 kW ( 18-dB margin). • Case 2: 0.762-mm Duroid substrate without filling plate 10 kW ( 18-dB margin). • Case 3: 1.524-mm Duroid substrate with filling plate 3 kW (12.77-dB margin). • Case 4: 1.524-mm Duroid substrate without filling plate 1.6 kW (10.04-dB margin). The reason behind the different results for both substrate thicknesses is the resulting geometry of the overall structure that does not allow sustained electron resonance trajectories between different zones in the connector. Electrons easily escape from the connector region entering the free space where they are lost. The use of the filling plate allows an extra margin of 3 dB in the case of the thicker substrate due to the fact that the gap distance is reduced, which does not allow electrons to gain enough kinetic energy.

Although a margin of 18 dB is found out in the analysis with SPARK3D, a test sample has been also designed, manufactured, and tested in the ESA-VSC laboratories in order to verify the results (Fig. 16). Test conditions and bake-out were the same as for the DUT of Fig. 12. No multipaction phenomenon was observed up to the maximum available RF power of 1.5 kW, giving a threshold margin of at least 9.76 dB by means of test. The multipaction critical areas of the proposed HPA have been described and carefully analyzed. Results of these analyses and tests have been the rationale for the adopted design approach in order to prevent multipaction discharge. Table II summarizes the main results for the five critical areas identified. IV. MANUFACTURING AND TESTING OF GaN HPAs Based on the design considerations described in the previous paragraphs, two different balanced GaN HPAs have been manufactured and tested over temperature in the range from 15 C to 55 C and in pulsed conditions (60 s, 12% duty cycle). The photographs and measurement results of the HPAs are reported in [4]. Nevertheless, the main RF performances are reported here again for completeness. Fig. 17 reports RF performances of the balanced HPA based on the UMS GaN devices. It delivers more than 18 dB of linear

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as multipaction, Corona discharge, and thermal handling effects for this type of equipment. Critical areas for multipaction discharge have been identified and analyzed in detail by means of theoretical curves, specific simulation tools, and dedicated tests campaigns on several assemblies. These analyses have been used to implement the required changes in the design in order to prevent electrical discharges while operating in space. ACKNOWLEDGMENT

Fig. 17. Measured pulsed RF output power and drain efficiency from 15 C V, to 55 C of the UMS balanced HPA. Bias condition is mA.

Fig. 18. Measured RF output power and drain efficiency from 55 C of the Mitsubishi balanced HPA. Bias condition is mA.

20 C to V,

gain, an RF output power of 180 W, and a drain efficiency exceeding 65% when operated at ambient temperature. A very good stability over temperature is obtained for the nominal operating point (2.5-dB output compression). Similarly, Fig. 18 shows measured RF performances obtained from the balanced HPA based on the Mitsubishi GaN devices. It reports at ambient temperature more than 150 W of RF output power with 19 dB of linear gain and 66% of drain efficiency when operated in saturation. The variation of the RF performances over temperature (from 20 C to 55 C) around the operating point is negligible. V. CONCLUSIONS Two different 80-W class P-band GaN power modules have been designed, manufactured, and tested with GaN HEMT devices from UMS and Mitsubishi. The design approach has traded-off RF performances such as efficiency, RF output power, and derating considerations for a reliable operation in space. Using the 80-W class power modules, two different balanced HPAs have been designed, manufactured, and tested, demonstrating its feasibility to cover the future needs for the biomass mission. A dedicated part of the paper has provided an in-depth analysis on high RF power phenomena in space such

The authors would like to thank all the ESA-VSC personnel for their dedication and professionalism during the Multipaction test campaign and D. Raboso for his expert support on this particular field. REFERENCES [1] “Report for mission selection: Biomass,” ESA Commun. Production Office, Noordwijk, The Netherlands, ESA SP-1324/1, May 2012, vol. 3. [2] J.-S. Lee and E. Pottier, Polarimetric Radar Imaging: From Basics to Applications. Rochester, NY, USA: CRC, 2009, pp. 5–22. [3] A. Katz, B. Eggleston, and J. MacDonald, “GaN SSPA for UHF space applications,” in IEEE MTT-S Int. Microw. Symp. Dig., 2013, pp. 1–4. [4] N. Ayllon and P. Arpesi, “P-band GaN high power amplifiers for spaceborne radar applications,” in IEEE MTT-S Int. Microw. Symp. Dig., May 2015, pp. 1–4. [5] A. Woode and J. Petit, “Diagnostic investigations into the multipactor effect, susceptibility zone measurements and parameters affecting a discharge,” ESA/ESTEC, Noordwijk, The Netherlands, Working Paper 1556, Nov. 1989. [6] R. Woo, “Final report on RF voltage breakdown in coaxial transmission lines,” Jet Propulsion Lab., Pasadena, CA, USA, Tech. Rep. 32-1500, Oct. 1970. [7] M. Yu, “Power handling capability for RF filters,” IEEE Microw. Mag., vol. 8, no. 5, pp. 88–97, Oct. 2007. [8] J. Vidkjaer, “Series-tuned high efficiency RF power amplifiers,” in IEEE MTT-S Int. Microw. Symp. Dig., 2008, pp. 73–76. [9] A. Anakabe, N. Ayllon, J. M. Collantes, and A. Mallet, “Automatic pole-zero identification for multivariable large-signal stability analysis of RF and microwave circuits,” in Proc. IEEE Eur. Microw. Conf., 2010, pp. 477–480. [10] J. Jugo, J. Portilla, A. Anakabe, A. Suárez, and J. M. Collantes, “Closed-loop stability analysis of microwave amplifiers,” IEEE Electron. Lett., vol. 37, no. 4, pp. 226–228, Feb. 2001. [11] N. Ayllon, J. M. Collantes, A. Anakabe, I. Lizarraga, G. Soubercaze-Pun, and S. Forestier, “Systematic approach to the stabilization of multi-transistor circuits,” IEEE Trans. Microw. Theory Techn., vol. 59, no. 8, pp. 2073–2082, Aug. 2011. [12] O. A. Ivanov, M. A. Lobaev, V. A. Isaev, and A. L. Vikharev, “Suppressing and initiation of multipactor discharge on a dielectric by an external DC bias,” Phys. Rev., Special Topic Accel. and Beams, vol. 13, 2010, Art. ID 022004. Natanael Ayllon (M’13) received the B.Sc. degree in telecommunications engineering, M.Sc. degree in electronics engineering, and Dr.-Ing. degree in microwave engineering from the University of the Basque Country (UPV/EHU), Bilbao, Spain, in 2005, 2007, and 2011, respectively. From 2006 to 2007, he was a Research Engineer with the Electricity and Electronics Department, UPV/EHU, where he was involved with linear and nonlinear stability analysis of microwave active circuits. From 2007 to 2011, he was with Thales Alenia Space, the Centre National d’Études Spatiales (CNES), and UPV/EHU, where he was involved in microwave integrated circuit (MIC)/monolithic microwave integrated circuit (MMIC) design, linear and nonlinear stability analysis, and manufacture and measurement techniques of such circuits. Since 2011, he has been with the European Space Agency, ESA/ESTEC, Noordwijk, The Netherlands, where he is currently the Principal responsible for high-power amplifier [solid-state power amplifiers (SSPAs) and traveling-wave tube amplifiers (TWTAs)] and transmit/receive module development activities for space-borne applications.

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Pier Giorgio Arpesi received the Laurea degree (cum laude) in electronic engineering from the University of Pavia, Pavia, Italy, in 1990 He then joined the Space Department, Siemens Telecomunicazioni S.p.A., Milan, Italy, as a Microwave Engineer involved with the design and development of ultra-low-noise amplifiers at L- and S-band for on-board receivers. In 1996, he joined the Laben S.p.A., Alenia Aerospazio Group, Milan, Italy, where he was responsible for the design of low-noise extremely high-frequency (EHF) receivers

(44-GHz frequency) in the frame of the SICRAL program. He was also involved in the preliminary study of space radiometers up to 100 GHz for the Planck satellite mission. In 2000, he joined Siemens I.C.N., Milan, Italy, where he was in charge of the development of Ku-band synthesizers in the frame of a 60-GHz low-capacity radio link for micro-cell applications. Since 2001, he has been with the Time and Frequency Department, Selex-ES, Milan, Italy, where he is currently a Project Leader on several space programs related to frequency synthesizer units and solid-state power amplifiers in the HF, VHF, and UHF frequency bands. He is currently the Head of the Time and Frequency Group within the Space Engineering Section, Selex-ES.

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A Highly Efficient LTE Pulse-Modulated Polar Transmitter Using Wideband Power Recycling Hao-Shun Yang, Member, IEEE, Chun-Wei Chang, Student Member, IEEE, and Jau-Horng Chen, Member, IEEE

Abstract—This paper presents a wideband power recycling technique for pulse-modulated polar transmitters (PMPTs). The technique allows unwanted out-of-band modulation spurs in PMPTs to be rectified and recovered back to the power supply for efficiency improvement. By configuring the power amplifiers as a balanced amplifier with dual-phase digital pulse-width modulation, the odd modulation spurs can be extracted directly from the isolation port of the output-combining quadrature coupler. Using the proposed architecture, the prototype transmitter achieved 59.1% drain efficiency at an output channel power of 26.2 dBm using a 10-MHz bandwidth long-term evolution 16-quadrature amplitude modulation test signal at 836.5 MHz. After output signal restoration by a surface-acoustic-wave filter, an output power level of 24.8 dBm and 42.8% drain efficiency were achieved while passing the spectral and receive-band-noise requirements without using any digital pre-distortion techniques. Index Terms—Long-term evolution (LTE), polar transmitters, power amplifier linearization, power amplifiers (PAs), rectifier.

I. INTRODUCTION

R

ECENT communication standards such as long-term evolution (LTE) utilize single-carrier frequency division multiple access (SC-FDMA) to achieve improved spectral efficiency, which leads to signals with increased peak-to-average power ratios (PAPRs). Therefore, the inherent low-efficiency characteristic in LTE transmitters is inevitable without using any efficiency enhancement schemes or linearization techniques [1]. The envelope elimination and restoration (EER) architecture proposed in [2] used a highly efficient supply modulator to modulate the power supply of a radio-frequency (RF) nonlinear power amplifier (PA) to achieve high-efficiency linear power amplification. In [3], the modified EER architecture called pulse-modulated polar transmitter (PMPT) was proposed, which pulse modulated the input phase-modulated signal with the envelope information using delta-sigma or pulse-width modulation (PWM). This kind of polar transmitter has no low-pass filter requirement in the envelope signal path

Manuscript received July 01, 2015; revised August 15, 2015; accepted September 25, 2015. This work was supported in part by the Ministry of Science and Technology, Taiwan, under Grants MOST 103-2221-E-002-271 and MOST 103-3113-E-002-005. This paper is an expanded version from the IEEE MTT-S International Microwave Symposium, Phoenix, AZ, USA, May 17–22, 2015. The authors are with the Department of Engineering Science and Ocean Engineering, National Taiwan University, Taipei, Taiwan (e-mail: d98943005@ntu. edu.tw; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2015.2484349

Fig. 1. Block diagram of the dual-phase PMPT with a Wilkinson combiner.

and, hence, simplifies the time alignment between the envelope and phase signals. However, the pulsing mechanism in PMPTs creates lots of out-of-band quantization noise or modulation spurs at both sides of the desired modulated signal in the frequency domain [4], [5]. Although multi-phase PWM can cancel or suppress the modulation spurs [6], [7], a significant portion of the out-of-band modulation spurs is out-of-phase and wasted as heat in the isolation resistor of the Wilkinson power combiner, as shown in Fig. 1. A power-recycling technique in outphasing PAs was proposed in [8], [9] to enhance the efficiency while maintaining sufficient isolation between both PAs. A 180 hybrid coupler was used to extract the original wasted power from its difference port. By replacing the isolation resistor load in the 180 hybrid coupler with an RF-dc rectifier, the otherwise wasted power can be converted back to dc power to assist in supplying the PAs. Unlike outphasing transmitters, the wasted power from the isolation resistor in the PMPTs shown in Fig. 1 occupies a wide frequency range. To avoid excessive signal distortion in PMPTs under wideband recycling, an additional circulator or isolator was added between the PA and output reconstruction band-pass filter (BPF) in [10], which is shown in Fig. 2. For cost and mass production considerations in mobile applications, it would be desirable to eliminate the need for circulators or isolators under power recycling for the PMPTs. In [11], a narrowband power-recycling PMPT was realized experimentally and showed promising results. In this paper, the theory of the power-recycling PMPT operation is presented and discussed with detailed measurement results. Moreover, a quadrature coupler with a compact wideband RF-dc rectifier at its isolation port is proposed to address those needs and realize a simple and wideband power-recycling PMPT system. II. TWO-WAY PWM USING THE QUADRATURE COUPLER The block diagram of the two-way PMPT using an output-combining quadrature coupler is shown in Fig. 3. Compared with the previous Wilkinson power combiner shown

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operation can be obtained by substituting and in (3) and (4) using (1). Therefore, the output voltage at the combination port is given by

Fig. 2. Block diagram of the power-recycling PMPT using a circulator.

(5) and the output voltage at the isolation port

is given by (6)

Fig. 3. Block diagram of the two-way PMPT using a quadrature combiner.

Equations (5) and (6) imply that, as the quadrature coupler is injected with two single-phase PWM RF input signals, the desired signal and all of the modulation spurs ideally fall into the combination port with no power going to the isolation port . B. Dual-Phase PWM Operation

in Fig. 1, the additional isolation port of the quadrature coupler can be used to aggregate the part of reflected power due to load mismatch [12]. Under pulse modulation operation with the quadrature combiner, the two input constant-envelope signals with quadrature phase difference are pulse modulated with the respective PWM signals and . Under single-phase operation, is equal to . For dual-phase operation, the respective PWM pulse trains can be expressed as

The output voltages at the combination port and isolation port of the quadrature coupler for the dual-phase PWM operation can be obtained by substituting and in (3) and (4) using (1) and (2), respectively. Therefore, the output voltage at the combination port is given as

(7) (1) (2) where , , is the duty cycle of the PWM pulse trains and is the PWM sampling angular frequency. Furthermore, the pulsed constantenvelope RF signals in the upper and lower signal paths are amplified by a pair of highly efficient nonlinear PAs with nonlinear complex gain and then sent to the input ports and of the quadrature coupler and eventually combined at port . The scattering matrix of the 3-dB quadrature coupler is also shown in Fig. 3 under the assumption of all matched ports with reciprocal and lossless properties for ease of analysis [13]. As a result, the output voltage at the combination port can be expressed as

From (7), it can be seen that the intermodulation terms of and will be cancelled when is an odd integer as follows: for for Moreover, the output voltage at the isolation port

(8) is given by

(9) From (9), it can be seen that the intermodulation terms of and will be cancelled when is an even integer as follows:

(3) where and are the amplitude and angular frequency of the RF carrier signal, respectively. Moreover, the output voltage at the isolation port can be expressed as (4) A. Single-Phase PWM Operation and isolation The output voltages at the combination port port of the quadrature coupler for the single-phase PWM

for for

(10) The advantage of dual-phase PWM becomes obvious by examining (8) and (10). The modulation spurs associated with the pulse modulation at the output combination port happen only at the even multiples of the PWM sampling frequency. The closest modulation spurs to the RF carrier are pushed away so the out-of-band filtering becomes easier. In addition, the amplitude of modulation spurs decreases rapidly as increases. Ideally, the residual modulation spurs at the odd multiples of the

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Fig. 4. Simulated and measured output spectra for a 10-MHz BW LTE under the single-phase and dual-phase PWMs. signal with a 62.5-MHz

Fig. 5. Simulated and measured output spectra for a 10-MHz BW LTE under the single-phase and dual-phase PWMs. signal with a 62.5-MHz

PWM sampling frequency end up at the isolation port . Therefore, the odd modulation spurs can be completely extracted directly from the isolation port of the output-combining quadrature coupler under ideal circumstances. However, any asymmetry in the gain between the upper and lower signal paths of the RF PAs and any deviation of the amplitude and phase in the quadrature coupler will result in part of the odd modulation spurs ending up at the combination port . Measurements were performed using single-phase and dual-phase signals at the two input ports of a Mini-Circuits RPQ-820 quadrature coupler. The measured output spectra at the combination and isolation ports are compared with the simulation of the dual-phase signal with identical ideal PAs in Figs. 4 and 5, respectively. III. RECYCLING POWER FROM SINGLEAND DUAL-PHASE PWMS The spurs of the combined pulse-modulated RF signal at the output port can be removed by bandpass filtering and has been verified in [14]. The BPF can usually be realized by a surfaceacoustic-wave (SAW) filter readily available in commercial mobile phones in the form of a duplexer. Because only the in-band signal can pass through the output SAW filter, the majority of modulation spurs will be reflected back to the quadrature coupler. The reflected modulation spurs will eventually arrive at

Fig. 6. Measured results of a commercially available coupler.

3

3-dB quadrature

Fig. 7. Calculated the transmission from isolation port to combination port under different return loss of the PA output ports.

the isolation port of the quadrature coupler. To understand how much power can be recycled from the isolation port between single-phase and dual-phase operations, the quadrature coupler under the condition of the two terminated input ports can be adopted for analysis. A signal path from the combination port to the isolation port of the inputs-terminated quadrature coupler is created as derived in [15]. Under the assumption of all matched ports with reciprocal and equal power-splitting properties for the 3-dB quadrature coupler, the derivation result can be simplified to (11) where is the transmission coefficient from the combination port to the isolation port with the two input ports terminated to a predetermined impedance. The reflection coefficient can be derived from the predetermined impedance. The parameters and imbalance of the RPQ-820 quadrature coupler were measured and shown in Fig. 6 for calculating . By substituting the parameters in (11) with the measurement results of the quadrature coupler, is obtained and shown in Fig. 7 with four different values of PA output reflection coefficient. As the output impedance of the PAs approaches

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Fig. 8. Circuit schematic of the designed compact wideband RF-dc rectifier.

50 , less recycling power from the modulation spurs will arrive at the isolation port. In reality, the balanced PA used in this work has approximately 3-dB output return loss over the frequency band. Therefore, the total power of the spurs reflected from the SAW filter at the combination port will be attenuated by 4 dB at the isolation port. Even though the amount of reflected spurs at the combining side are almost double for single-phase operation as compared to the dual-phase one, the recycled power at the isolation port for single-phase operation is 3 dB lower than that of dual-phase operation. The power difference is mainly resulted from the unbalanced energy distribution in the modulation spurs. By summing the total odd-spur power under pulse modulation, it is approximately 80% of the desired in-band signal power and is 4.7 times higher than the total even-spur power [6].

Fig. 9. Magnitude of input impedance between the Coilcraft choke and the of the designed RF-dc rectifier. Murata chip ferrite bead, and the measured

IV. WIDEBAND RF-DC RECTIFIER IMPLEMENTATION The overall power transformation efficiency of an RF-dc rectifier can be defined as the ratio of dc power assisting in supplying to the available RF input power , namely (12) where

is the reflection coefficient at the input of a rectifier, denotes the power reflection due to impedance mismatch, and represents the rectifier intrinsic efficiency. The term can be improved by using diodes with lower forward voltages, such as Schottky barrier diodes. For PMPT applications, the RF-dc rectifier is required to have wide input-matching characteristic to avoid degradation of system linearity from reflection of wide-spreading recycled spurs. Moreover, the wideband input matching has to be maintained over a wide range of input power for recycling different power levels of the modulation spurs at different frequencies. The broadband microwave rectifier using a high impedance inductor proposed in [16] with over two decades of bandwidth (BW) is suitable for the PMPT systems. The rectifier used a Coilcraft 4310LC-132KEB wideband bias choke to suppress RF signals and eliminate the requirement of an input matching network. However, the size of the wideband bias choke is too large to be used in modern mobile devices and the output dc voltage of such single-diode rectifier is too low. To overcome those drawbacks, the half-wave voltage-doubling circuit [17] and Murata BLM15HD182SN1B chip ferrite bead are adopted as shown in Fig. 8. The output voltage of this dual-diode rectifier shown in Fig. 8 is doubled as compared with that of the single-diode rectifier in [16]. A pair of commercially available Avago HSMS-286F zerobias RF Schottky barrier diodes is adopted to improve the and is depicted as and in Fig. 8. To achieve similar low

Fig. 10. Measured power transformation efficiency of the designed compact RF-dc rectifier over a wide input power range across a wide frequency range.

dc resistance and high ac impedance characteristics as the wideband bias choke, a surface-mount device (SMD) 0402 compact chip ferrite bead is adopted. The input ac impedances of both high ac impedance devices are compared over a wide frequency range shown in Fig. 9. Compared with the bias choke, the ferrite bead can achieve higher ac impedance over the desired frequency range for recycling the modulation spurs. For the measurement of input return loss, the input power is swept from 7 to 16 dBm and the measured return loss is better than 17 dB over one decade of bandwidth. In addition, of the designed RF-dc rectifier was measured and shown in Fig. 10. It can be seen, over 40% and 50% are achieved at around 10-dBm and 14-dBm input power, respectively. The peak of the designed RF-dc rectifier is over 70% in the low-frequency region. V. MEASUREMENT RESULTS All circuits including the RF PA in Fig. 11 for the prototype of the power-recycling PMPT were developed on two-layer FR-4 printed circuit boards (PCBs) as shown in Fig. 12. The Avago ATF-511P8 enhancement-mode pseudomorphic HEMT (pHEMT) was used to design the RF PAs as shown in Fig. 11.

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Fig. 11. Circuit schematic of the designed overdriven class-C RF PA.

Fig. 12. Developed PCB of power-recycling balanced PMPT with a SAW filter.

Fig. 14. Measured output spectra after SAW filter of single/dual-phase PMPTs with and without recycling using a 10-MHz BW LTE signal at 836.5 MHz.

Fig. 13. Measurement setup of the proposed power-recycling balanced PMPT.

The output wire-wound choke inductor and the input shunt resistor can be regarded as the drain and gate biasing components to ensure the PA's efficiency and stability. The large decoupling capacitors are used to create a low ac impedance path to ground to avoid residual RF signal feeding back to the drain of the PAs to ensure stability. A Mini-Circuits RPQ-820 3-dB quadrature coupler was used for configuring the RF PAs as a balanced PA, which provides better isolation, insertion loss, and imbalance performance as shown in Fig. 6. Operating at a supply voltage of 3.6 V and with a continuous-wave (CW) test signal at 836.5 MHz, the balanced PA with two overdriven class-C RF PAs based on the design used in [6] is able to deliver a saturated output power close to 30 dBm with drain efficiency over 70%. The output band-pass filter used in this work was a Taiyo Yuden FAR-F5KA-836M50-D4DF SAW filter with an average insertion loss of 1.4 dB over the passband and an out-of-band attenuation ranging from 30 to 60 dB. The difference of the RF-dc rectifiers between the previous work [11] and this work is the supported bandwidth. The wideband RF-dc rectifier with dual-phase operation used in this work leads to less reflected modulation spurs appearing at the output of the RF PAs, which ensures stability. The measurement setup and implementation of the proposed power-recycling PMPT is shown in Fig. 13. An additional Schottky diode was used between the output of the RF-dc rectifier and the supply to avoid reverse current. The calculated pulsed constant-envelope RF signals were generated digitally and loaded into a two-channel arbitrary waveform generator to directly drive the pair of PAs. Therefore, the RF phase and envelope signals can be completely synchronized.

Fig. 15. Measured output wideband spectra after SAW filter of single-phase and dual-phase power-recycling PMPTs with a 10-MHz BW LTE signal at 836.5 MHz.

Fig. 16. Measured RxBN of the single-phase and dual-phase power-recycling PMPTs using a 10-MHz bandwidth LTE 16-QAM signal at 836.5 MHz.

A 10-MHz channel bandwidth LTE 16-quadrature amplitude modulation (QAM) signal at 836.5 MHz was used to evaluate the performance of the transmitter. A 62.5-MHz PWM sampling frequency was chosen to prevent the output modulation spurs from falling into the receive bands. For an LTE mobile transmitter, the maximum allowable adjacent channel leakage ratios (ACLRs) as defined in [18] at the frequency offsets of 7.5, 12.5, and 10 MHz are 33 dBc , 36 dBc

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TABLE I COMPARISON OF RECENTLY REPORTED EFFICIENCY-ENHANCED LTE PA SYSTEMS AND A COMMERCIAL LTE PA PRODUCT FOR MOBILE APPLICATIONS

Specification of LTE 130 dBm/Hz

33

, and 30 dBc for measured bandwidths of 3.84, 3.84, and 9 MHz, respectively. The measured output spectra after the output SAW filter of the proposed power-recycling PMPT under single-phase and dual-phase operations are shown in Fig. 14. At an output power level of 24.8 dBm, only the dual-phase operation can pass all the ACLR requirements of LTE. The single-phase operation failed ACLR specification due to a great portion of odd modulation spurs reflecting from the SAW filter back to the PAs. The ACLRs under dual-phase operation with power recycling are only deteriorated by less than 1 dB as compared to those without power recycling. The overall drain efficiency of the RF PAs can be defined as (13) where is the RF output power, is the dc power consumption, is the supply voltage of 3.6 V used in this work, and is the power-supply current. The efficiency under single-phase operation was only 36.2%, but the efficiency under dual-phase operation was increased to 42.8%. Because the output SAW filter can be replaced by the duplexer already in commercial mobile devices, a 1.4-dB insertion loss of the SAW filter was de-embedded to obtain the actual PA efficiency. The average output power before the SAW filter is 26.2 dBm and the efficiencies under single-phase and dual-phase operations were increased to 49.9% and 59.1%, respectively. The PA efficiency improvement by using the power recycling for single-phase and dual-phase operations is 8% and 19%, respectively. Fig. 15 compares the measured output wideband spectra after the output SAW filter of the transmitter for both operations. The dual-phase PWM technique can suppress the odd-order out-of-band spurs at output significantly. As a result, the dual-phase operation can pass the stringent out-of-band spurious emission, as defined in [18]. In addition, the requirement of receive band noise (RxBN) is generally kept below 130 dBm/Hz after output signal attenuation by the duplexer to avoid desensitizing the receiver. To measure the RxBN, the receive-band Taiyo Yuden FAR-F5KA-881M50-D4DB SAW

36/

30 dBc

Using digital pre-distortion

Requirement of

filter for LTE band-V downlink was used at the output of the transmitter. As shown in Fig. 16, both operations can pass the RxBN requirement but the margin for dual-phase operation is larger. The RxBN can be further reduced by improving the symmetry of the pair of PAs to completely eliminate the output odd-order spurs. Table I compares recently reported efficiency-enhanced LTE PAs for mobile systems and a commercial LTE PA. The efficiency of the proposed transmitter is the highest one and is more than two times better than that of the commercial standalone PA with similar RxBN performance. VI. CONCLUSION A balanced PMPT using wideband power-recycling technique with high efficiency has been demonstrated for linear amplification in LTE mobile applications. By using dual-phase PWM, the odd modulation spurs of the transmitter can be directly recycled at the isolation port of the quadrature coupler without being wasted as heat or transmitted at the output, which increases the efficiency and eases spur filtering and signal restoring. The output power and efficiency of the transmitter tested by a 10-MHz channel bandwidth LTE 16-QAM signal at 836.5 MHz are 26.2 dBm and 59.1%, respectively. Moreover, excellent RxBN of 132.4 dBm/Hz was achieved while passing the spurious emission and ACLR requirements without the need of any pre-distortion. REFERENCES [1] C. Nader, P. N. Landin, W. V. Moer, N. Bjorsell, and P. Handel, “Performance evaluation of peak-to-average power ratio reduction and digital pre-distortion for OFDM based systems,” IEEE Trans. Microw. Theory Techn., vol. 59, no. 12, pp. 3504–3511, Dec. 2011. [2] L. R. Kahn, “Single-sideband transmission by envelope elimination and restoration,” Proc. IRE, vol. 40, no. 7, pp. 803–806, Jul. 1952. [3] Y. Wang, “An improved Kahn transmitter architecture based on delta-sigma modulation,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2003, pp. 1327–1330. [4] T.-P. Hung, J. Rode, L. E. Larson, and P. M. Asbeck, “Design of H-bridge class-D power amplifiers for digital pulse modulation transmitters,” IEEE Trans. Microw. Theory Techn., vol. 55, no. 12, pp. 2845–2855, Dec. 2007. [5] J.-H. Chen, H.-S. Yang, and Y.-J. E. Chen, “A multi-level pulse modulated polar transmitter using digital pulse-width modulation,” IEEE Microw. Wireless Comp. Lett., vol. 20, no. 5, pp. 295–297, May 2010.

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. YANG et al.: HIGHLY EFFICIENT LTE PULSE-MODULATED POLAR TRANSMITTER USING WIDEBAND POWER RECYCLING

[6] J.-H. Chen, H.-S. Yang, H.-C. Lin, and Y.-J. E. Chen, “A polar-transmitter architecture using multiphase pulsewidth modulation,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 58, no. 2, pp. 244–252, Feb. 2011. [7] H.-S. Yang, J.-H. Chen, and Y.-J. E. Chen, “A polar transmitter using interleaving pulse modulation for multimode handsets,” IEEE Trans. Microw. Theory Techn., vol. 59, no. 8, pp. 2083–2090, Aug. 2011. [8] R. Langridge, T. Thornton, P. M. Asbeck, and L. E. Larson, “A power re-use technique for improved efficiency of outphasing microwave power amplifiers,” IEEE Trans. Microw. Theory Techn., vol. 47, no. 8, pp. 1467–1470, Aug. 1999. [9] X. Zhang, L. E. Larson, P. M. Asbeck, and R. A. Langridge, “Analysis of power recycling techniques for RF and microwave outphasing power amplifiers,” IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process., vol. 49, no. 5, pp. 312–320, May 2002. [10] Y.-S. Jeon, H.-S. Yang, and S. Nam, “A power re-use technique for improved efficiency of pulsed oscillating amplifiers,” IEEE Microw. Wireless Comp. Lett., vol. 16, no. 10, pp. 567–569, Oct. 2006. [11] H.-S. Yang, C.-W. Chang, Y.-J. E. Chen, and J.-H. Chen, “A dual-phase pulse-modulated polar transmitter with high efficiency and linearity using power recycling,” in IEEE MTT-S Int. Microw. Symp. Dig., May 2015, pp. 1–3. [12] C.-W. Chang, Y.-J. E. Chen, and J.-H. Chen, “A power-recycling technique for improving power amplifier efficiency under load mismatch,” IEEE Microw. Wireless Comp. Lett., vol. 21, no. 10, pp. 571–573, Oct. 2011. [13] D. M. Pozar, Microwave Engineering, 2nd ed. New York, NY, USA: Wiley, 1998. [14] D. Seebacher, W. Bosch, P. Singerl, and C. Schuberth, “Highly efficient carrier bursting RF transmitter employing direct band pass filter connection,” in Proc. IEEE Eur. Microw. Conf., Oct. 2013, pp. 692–695. [15] H. Jeon et al., “A triple-mode balanced linear CMOS power amplifier using a switched-quadrature coupler,” IEEE J. Solid-State Circuits, vol. 47, no. 9, pp. 2019–2032, Sep. 2012. [16] D. Wang, M.-D. Wei, and R. Negra, “Design of a broadband microwave rectifier from 40 MHz to 4740 MHz using high impedance inductor,” in Proc. IEEE Asia–Pacific Microw. Conf., Nov. 2014, pp. 1010–1012. [17] D. L. Waidelich and C. H. Gleason, “The half-wave voltage-doubling rectifier circuit,” Proc. IRE, vol. 30, no. 12, pp. 535–541, Dec. 1942. [18] 3rd Generation Partnership Project Tech. Specification Group, “User Equipment (UE) Radio Transmission and Reception (FDD),” Valbonne, France, Rep. 3GPP TS 36.101, 2014. [19] J.-L. Woo, S. Park, U. Kim, and Y. Kwon, “Dynamic stack-controlled CMOS RF power amplifier for wideband envelope tracking,” IEEE Trans. Microw. Theory Techn., vol. 62, no. 12, pp. 3452–3464, Dec. 2014. on HBT Doherty power [20] D. Kang et al., “Impact of nonlinear amplifiers,” IEEE Trans. Microw. Theory Techn., vol. 61, no. 9, pp. 3298–3307, Sep. 2013. [21] R. Wu et al., “High-efficiency silicon-based envelope-tracking power amplifier design with envelope shaping for broadband wireless applications,” IEEE J. Solid-State Circuits, vol. 48, no. 9, pp. 2030–2040, Sep. 2013. [22] Skyworks Inc., “Power amplifier module,” Woburn, MA, USA, SKY77752 Data Sheet, Aug. 15, 2013 [Online]. Available: http:// www.skyworksinc.com/uploads/documents/SKY77752_201823B.pdf

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Hao-Shun Yang (S'09–M'15) received the Ph.D. degree in electronics engineering from National Taiwan University, Taipei, Taiwan, in 2014. In 2006, he was with Compal Communication, Taipei, Taiwan, as a Hardware Engineer, where he was involved with the design of cellular phones. Since 2014, he has been a Postdoctoral Researcher with the Department of Engineering Science and Ocean Engineering, National Taiwan University, Taipei. His research interests include power amplifier and analog/RF integrated-circuit design. Dr. Yang was the recipient of Second Runner-Up and Best Originality of the 2002 Macronix (MXIC) Golden Silicon Awards. He was a recipient of the Outstanding and Excellent Design Awards of the Chip Implementation Center Workshop in 2002 and 2003, respectively.

Chun-Wei Chang (S'15) received the B.S. degree in electrical engineering from National Taipei University of Technology, Taipei, Taiwan, in 2007, the M.S. degree in electrical engineering from National Chung Cheng University, Chiayi, Taiwan, in 2009, and the M.S. degree in engineering science and ocean engineering from National Taiwan University, Taipei, in 2011, where he is currently working toward the Ph.D. degree. From 2011 to 2014, he was a Design Engineer with Richwave Technology, Taipei, Taiwan, where he was involved with the design of RF components and CMOS FM receivers. In 2014, he returned to National Taiwan University, Taipei, where he is currently with the Department of Engineering Science and Ocean Engineering. His research interests include analog/RF integrated-circuit design.

Jau-Horng Chen (M'09) received the B.S. degree in electrical engineering from National Taiwan University, Taipei, Taiwan, in 2001, and the M.S. and Ph.D. degrees in electrical and computer engineering from the Georgia Institute of Technology, Atlanta, GA, USA, in 2002 and 2006, respectively. From 2006 to 2008, he was a Design Engineer with Freescale Semiconductor, Tempe, AZ, USA, where he was involved with designing dc-dc converters and predistortion linearizers for cell phone power amplifiers (PAs). In 2008, he joined National Taiwan University, Taipei, Taiwan, where he is currently an Associate Professor with the Department of Engineering Science and Ocean Engineering. He holds five U.S. patents. His research interests include analog/RF integrated-circuit design and high-efficiency PAs.

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A Transformer-Based Poly-Phase Network for Ultra-Broadband Quadrature Signal Generation Jong Seok Park, Student Member, IEEE, and Hua Wang, Senior Member, IEEE

Abstract—This paper presents a transformer-based poly-phase network to generate fully differential quadrature signals with low loss, compact area, and high-precision magnitude and phase balance over an ultra-wide bandwidth. A fully differential high-coupling 8-port folded transformer-based quadrature hybrid serves as the basic building block for the poly-phase unit stage to achieve significant size reduction and low loss. Multiple poly-phase unit stages can be cascaded to form the multistage poly-phase network to substantially extend the quadrature signal generation bandwidth. The designs of the high-coupling transformer-based quadrature hybrid, the poly-phase unit stage, and the multistage transformer-based poly-phase network are presented with the closed-form design equations in this paper. As a proof-of-concept design, a 3-stage transformer-based poly-phase network is implemented in a standard 65 nm bulk CMOS process with a core area of 772 m 925 m. Measurement results of this poly-phase network over 3 independent samples demonstrate that the output In-Phase and Quadrature (I/Q) magnitude mismatch is less than 1 dB from 2.8 GHz to 21.8 GHz with a passive loss of 3.65 dB at 6.4 GHz. The measured output I/Q phase error is less than 10 from 0.1 GHz to 24 GHz. The effective Image Rejection Ratio (IRR) based on the measured I/Q balancing is more than 30 dB from 3.7 GHz to 22.5 GHz. The 3-stage transformer-based poly-phase network design achieves high-quality quadrature signal generation over a first-ever one-decade bandwidth together with low-loss and compact area. Index Terms—Broad band, CMOS, poly-phase, quadrature generation, transformer.

I. INTRODUCTION

Q

UADRATURE signal generation plays a critical role in many RF, mm-wave, and mixed-signal circuits and systems. Popular circuit block examples include In-Phase/Quadrature (I/Q) vector modulator-based phase rotator [1], Doherty power amplifier [2], and balanced amplifier [3], all of which employ the quadrature signal generation blocks as their key components. As the system examples, Hartley and Weaver receivers [4] require quadrature Local Oscillator (LO) signals and/or quadrature signal combining networks for image rejections. Moreover, in many wireless communication and radar systems, the beam former structures, e.g., Butler Manuscript received July 03, 2015; revised September 24, 2015, October 18, 2015; accepted October 24, 2015. Date of publication November 18, 2015; date of current version December 02, 2015. This paper is an expanded version from the IEEE MTT-S International Microwave Symposium, Phoenix, AZ, USA, 17-22 May 2015. The authors are with the School of Electrical and Computer Engineering Department, Georgia Institute of Technology, Atlanta, GA 30308 USA (e-mail: [email protected]; [email protected]). Digital Object Identifier 10.1109/TMTT.2015.2496187

matrix [5], phased-array transceiver [6], and circular/elliptical polarized antenna [7], also rely on quadrature signal generation. Passive networks are commonly used for quadrature generation due to their superior linearity, zero power consumption, and frequency scalability. Passive quadrature generation networks are often evaluated by their passive loss, bandwidth, I/Q magnitude and phase balance, and robustness against the process variations. The RC-CR pairs and RC-CR poly-phase filters have been widely used due to their simplicity [4]. However, the RC-CR pairs suffer from inherent signal loss and narrow bandwidth, fundamentally due to the resistive components in the signal paths. Moreover, this RC-CR based approach is sensitive to the source impedances and load terminations, particularly limiting its use at mm-wave frequencies. By cascading multiple RC-CR stages, the RC-CR poly-phase networks can extend the quadrature generation bandwidth and improve the process variation robustness but at the expense of further signal loss [8], posing a direct trade-off between signal loss and bandwidth. On the other hand, transmission line couplers [3] can generate I/Q output signals with input/output matching at RF and mm-wave frequencies. However, the required transmission lines often occupy a substantial chip area, making on-chip integration challenging. In addition, L-C resonance based quadrature all-pass filter is also reported for I/Q generation [9]. Transformer-based quadrature generations are recently gaining an increasing interest. A one-stage singled-ended transformer-based 3 dB quadrature hybrid with its magnetic coupling coefficient k of 0.707 is reported at RF frequency (2 GHz) [10] and is later extended to mm-wave frequencies [11], [5]. This scheme offers low loss, high precision I/Q balancing, input/output matching, and a compact footprint even at the low RF frequency range. To further reduce the area, a fully differential folded transformer-based 3 dB quadrature hybrid is recently reported [12], which generates fully differential quadrature signals within only one inductor footprint by exploiting magnetic coupling enhancement of the differential mode operation. Transformer-based quadrature generation networks typically achieve 20% fractional bandwidth mainly limited by the I/Q magnitude mismatches. Although this bandwidth can be sufficient for many narrow-band applications, it cannot support wideband systems, such as broadband radars [13], hyperspectral imagers [14], or wideband antenna mode formers [15]. To address these challenges, we propose a transformer-based poly-phase network to suppress I/Q magnitude/phase mismatches and achieve ultra-broadband operation with low loss and a compact form factor [16]. This paper presents the complete circuit analysis, design equations, full simulation

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PARK AND WANG: TRANSFORMER-BASED POLY-PHASE NETWORK

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results, and extended measurement results to demonstrate the proposed transformer-based poly-phase network. In Section II, the circuit analysis, design equations, and graphic summary of the simulation results for high-coupling transformer-based quadrature hybrid are presented. Compared with the conventional quadrature hybrid design [10], it achieves a smaller required inductance and a wider bandwidth. The high-coupling transformer-based quadrature hybrid is then extended to a fully differential 8-port folded transformer design, which serves as the building block for the poly-phase unit stage. Section III shows the complete theoretical analysis of the multi-stage transformer-based poly-phase network. In particular, the resulting I/Q magnitude mismatch versus the number of poly-phase stages is thoroughly presented with the analytical design equations and compared with 3-D electromagnetic (EM) simulation results. These results demonstrate the fundamental basis of why cascading multiple transformer-based poly-phase unit stages can suppress the I/Q magnitude mismatch and substantially extend the bandwidth. As a proof-of-concept demonstration, in Section IV, we present a 3-stage transformer-based poly-phase network design example implemented in a 65 nm CMOS process with design details and simulation results. In Section V, complete measurement results on 3 independent samples are presented to demonstrate the robustness and repeatability of the proposed transformer-based poly-phase network. II. TRANSFORMER-BASED QUADRATURE SIGNAL GENERATION The schematic of the transformer-based quadrature hybrid [10] is shown in Fig. 1(a). Here, we will perform circuit analysis on this hybrid structure. We will also derive the complete and general design equations for an arbitrary coupling coefficient k, based on which, we will propose the high-coupling transformer-based quadrature hybrid. When driven only at the input port (IN), this transformerbased network utilizes both inductive and capacitive couplings to achieve matched quadrature output signals at the through port (THRU, ) and the coupled port (CPL, 0 ), shown in Fig. 1(a). The inductive coupling coefficient and the capacitive coupling coefficient are defined in (1) and (2), respectively. and indicate the mutual inductance and mutual capacitance, and the quantity C is defined as . (1) (2) For the even-mode operation , a virtual open-circuit condition exists along the symmetric line in Fig. 1(a), and a positive magnetic coupling is achieved. Thus, the equivalent even-mode half-circuit consists of an C-L-C pi-network with the even-mode inductance and the even-mode capacitance , shown in Fig. 1(b). The even-mode characteristic impedance and propagation velocity are given in (3) and (4), and the even-mode voltages at all the nodes are shown in (5) and (6). Note that and

Fig. 1. (a) Transformer-based quadrature hybrid schematic and its (b) evenmode half-circuit and (c) odd-mode half-circuit.

are the input and output voltages for the other and identical even-mode half circuit, which is not shown in Fig. 1(b) (3) (4)

(5) (6) In the odd-mode operation , a virtual ground is established along the symmetric line in Fig. 1(a), and the magnetic coupling is negative. Therefore, the odd-mode inductance equals , and the odd-mode capacitance equals , shown in the odd-mode halfcircuit in Fig. 1(c). The odd-mode characteristic impedance , propagation velocity , and the voltages at all the nodes are shown in (7)–(10). Note that and are the input and output voltages for the other and identical odd-mode half circuit, which is not shown in Fig. 1(c) (7) (8)

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(9) (10)

The transformer-based quadrature hybrid can be treated as a one-section synthetic coupled transmission line. For the desired transverse electromagnetic mode (TEM) propagation, the even-mode and odd-mode propagation velocities should equal to avoid dispersions [3]. Therefore, the capacitive coupling and the inductive coupling should be identical based on (4) and (8). Therefore, the 4-port S-parameters of the transformer-based quadrature hybrid can be obtained by the (11)–(15). Due to the symmetry, is the input impedance of any port with the other 3 ports loaded with defined in (19) (11) (12) (13) (14) (15) To achieve quadrature signal generation, the equivalent coupled transmission line should behave as a quarter-wave line at the frequency [3]. At this frequency, assume that the IN-port is excited by a source voltage of , the CPLport and THRU-port outputs are given as (16) (17) Therefore, the excitation at the IN-port will result in quadrature signals at the CPL-port and THRU-port. The complete design parameters for a transformer-based quadrature generation network can be uniquely specified by the (18)–(20) at the frequency (18) (19) (20) Based on (16)–(20), it is clear that the coupling coefficient k is an essential design parameter for the transformer-based quadrature hybrid, since it determines the output magnitudes of the CPL-port and the THRU-port as well as the required inductance and capacitance at the frequency .

It is of particular interest to investigate the transformer-based quadrature hybrid with equal output amplitudes and a 90 phase difference at the CPL-port and the THRU-port at the frequency . Based on (16) and (17), the coupling coefficient k should be 0.707 to achieve such 3 dB quadrature hybrid at . The result of such a special case matches the design guidelines presented in [10]. However, the requirement of directly limits the geometric design freedom and the footprint of the transformer structure. To address this limitation, we will next propose and demonstrate a 3 dB transformer-based quadrature hybrid using a highcoupling (high-k) transformer. This approach obviates the need of enforcing and allows a high-k transformer with a more compact footprint and lower loss. Based on (16) and (17), for , the magnitude is larger than the magnitude at . On the other hand, at a very low frequency (e.g., near dc), it is clear that (open-circuit) and (short-circuit) based on Fig. 1(a). Therefore, if we design a transformer-based 3 dB quadrature hybrid with , there exists at least one frequency value between dc to , at which the 3 dB quadrature hybrid relationship is achieved. On the other hand, if k is smaller than 0.707, then at both dc and . The existence of the frequency value for 3 dB quadrature hybrid relationship is not mathematically guaranteed from dc to . To illustrate this high-k design concept, Fig. 2 shows the calculated magnitude/phase responses based on (11)–(15) for a transformer-based 3 dB quadrature hybrid design with , and , where the frequency and inductance are normalized values. With , the CPL-port signal is greater than the THRU-port signal at . The 3 dB quadrature hybrid relationship is achieved at (Fig. 2(a)). Note that the return loss is more than 15 dB from dc up to a normalized frequency of 1.25. The phase mismatch is lower than 3 up to , and is only 10 at the normalized frequency of 1.33. In contrast, a conventional 3 dB quadrature hybrid with at the frequency requires an inductor L of 130, which is larger than our high-k transformer design ( and ). Therefore, our high-k design allows a significant transformer size reduction. Fig. 3 summarizes the normalized inductance values to achieve the 3 dB quadrature hybrid operation at a given frequency for different coupling k values. The required inductance values are normalized to the value in the conventional quadrature hybrid design with . As the coupling coefficient k increases, the required inductance decreases, achieving a substantial transformer size reduction. Besides size reduction, our proposed high-k transformer-based quadrature hybrid also enables wideband operation. To demonstrate this aspect, we will analyze the output I/Q magnitude/phase mismatches versus frequency as follows. Assuming the port 1 is the input port of the quadrature hybrid (Fig. 1(a)), based on the 4-port S-parameters design equations of the transformer-based quadrature hybrid (11)–(15), the

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Fig. 3. Calculated inductance for different coupling k to achieve 3 dB quadrature hybrid at a fixed given frequency . The inductance value is normalized . to the conventional hybrid design with

Fig. 2. Simulated (a) magnitude and (b) phase responses for the high-k transand . former-based 3 dB quadrature hybrid with

magnitude and phase responses of the CPL-port THRU-port can be derived and shown below

and the

(21) (22)

Therefore, the output I/Q magnitude and phase mismatches can be defined in (23) and (24)

(23) (24)

Fig. 4(a) and 4(b) show the simulated output I/Q magnitude and phase mismatches versus frequency of the high-k transformer-based 3 dB quadrature hybrid for different k values based on the (21)–(24). The design with and serves as the reference with the 3 dB quadrature hybrid operation at . The input matching is shown in Fig. 4(c). The required inductances of the transformer-based 3 dB quadrature hybrid for different coupling k values are summarized in Fig. 3. The quarter-wave length frequency for each coupling k is denoted in Fig. 4(c). Based on Fig. 4(a), although the transformer-based quadrature hybrid achieves equal power dividing only at one frequency point, a high-k design provides one additional frequency point where excellent I/Q magnitude matching can be achieved. Within these two frequency points, a trade-off exist for the I/Q magnitude mismatch and matching bandwidth by adjusting the k value. Therefore, the I/Q matching bandwidth can be substantially extended. Note that a high-k design actually offers one more frequency point at high-frequency with good I/Q magnitude matching. However, this frequency point cannot be used in practice due to the substantial I/Q phase degradation. For example, the transformer design with achieves an I/Q 2 dB magnitude mismatch over a normalized bandwidth of 100% compared to a normalized bandwidth of 60% for the conventional design , shown in Fig. 4(a). In addition, the normalized bandwidth for I/Q phase mismatches below 5 increases from 126% for design with to 170% for design with (Fig. 4(b)). At the same time, the input matching bandwidth ( dB) extends from 130% to 174% after changing k from 0.707 to 0.75. These results demonstrate that a higher coupling coefficient k directly extends the bandwidth of the transformer-based quadrature hybrid. In practice, this high-k transformer-based quadrature hybrid design is limited by the achievable coupling coefficient k and the acceptable in-band I/Q magnitude mismatch. In this paper, we choose the coupling coefficient to achieve a compact transformer-based 3 dB quadrature hybrid at Grad/s, and it is further utilized as a basic building block in our proposed transformer-based poly-phase network.

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Fig. 5. Block diagram of the proposed multistage transformer-based poly-phase network with N stages.

Fig. 6. Schematic of a transformer-based poly-phase unit stage.

poly-phase network scheme, which can suppress the I/Q magnitude/phase mismatches and achieve high-quality quadrature signals over an ultra-wide bandwidth. Different from conventional RC-CR poly-phase network, our transformer-based scheme has no resistive component in the signal paths. This aspect ensures its unique low-loss during multi-stage cascading. A. Multistage Transformer-Based Poly-Phase Network Fig. 5 shows the block diagram of our proposed multistage transformer-based poly-phase network with N stages. It consists of one fully differential transformer-based quadrature hybrid as the 1st stage and N-1 stages of transformer-based poly-phase unit stage as the following cascaded stages. The 1st stage generates fully differential I/Q signals from a differential input. The cascaded N-1 transformer-based poly-phase unit stages then suppress the I/Q magnitude/phase mismatches from the 1st stage and substantially extend the I/Q generation bandwidth. B. A Transformer-Based Poly-Phase Unit Stage Fig. 4. Calculated (a) output I/Q magnitude mismatches, (b) I/Q phase misof the transformer-based 3 dB quadrature matches, and (c) input matching . The calculations are based on hybrids for different coupling k with (11)–(22).

III. TRANSFORMER-BASED POLY-PHASE NETWORK SCHEME Although our proposed high-k transformer approach increases the bandwidth for the I/Q generation, it still exhibits trade-off with in-band I/Q magnitude mismatch, limiting the useful quadrature operation bandwidth in practice. In this section, we will introduce a multistage transformer-based

The schematic of a transformer-based poly-phase unit stage is shown in Fig. 6. It consists of four single-ended transformerbased 3 dB quadrature hybrids and has 4 inputs and 4 outputs. Both inputs and outputs are 4 fully differential I/Q signals, making this poly-phase unit stage cascadable to realize the multistage poly-phase network configuration shown in Fig. 5. The proposed transformer-based poly-phase unit stage in Fig. 6 employs four single-ended transformer-based 3 dB quadrature hybrids, which are arranged in such a way that the 4-output are generated by proper signal combining between the differential input I-signals ( or ) and the differential input Q-signals ( or ). The four possible combinations (2 2) of the differential input I/Q

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Fig. 8. Summary of the transformer-based poly-phase scheme.

Fig. 7. Calculated magnitude response of the THRU-path and CPL-path together with their Common-Mode (CM) and Differential-Mode (DM) output signals based on (25) and (26). These results are based on a transformer, and . based quadrature hybrid with

signals result in the four outputs. For example, the output 0 ( or ) signal is generated by in-phase combining the input 0 signal through the CPL-path of the transformer hybrid A with 0 phase shift and input 90 signal through the THRU-path of the transformer hybrid B with phase shift. Therefore, when the input I/Q signals have magnitude/phase mismatches, the transformer-based poly-phase unit stage will average out such mismatches. The operation principle of the poly-phase unit stage is demonstrated as follows by circuit analysis and analytical design equations. The magnitudes of the I (CPL-path) and Q (THRU-path) outputs of a transformer-based quadrature hybrid with , and are shown in Fig. 7. The THRU-port is lagging 90 behind the CPL-port and the normalized frequency of the 3 dB quadrature hybrid operation is 0.54 (Fig. 2(a) and (b)). Note that the I/Q phase mismatch is below 10 from dc to a normalized frequency of 1.33 (Fig. 2(b)). Thus, we will focus on I/Q magnitude mismatch in the following discussions, since it is often the dominant mismatch compared with the I/Q phase mismatch in transformer-based quadrature hybrids. Considering the CPL-path and THRU-path outputs ( and ), we can define the Common-Mode (CM) output and Differential-Mode (DM) output in (25)–(26) and plot them in Fig. 7. Note that the CM output has its magnitude variation of less than 3 dB from low-frequency (near dc) to a normalized frequency of 1.4 (Fig. 7), achieving an ultra-broadband flat frequency response. Within the frequency bandwidth where the I/Q 90 phase relationship holds, the complex I/Q outputs ( and ) can be represented by the CM and DM outputs in (27)–(28)

Fig. 8 summarizes the in-phase combining of the transformerbased poly-phase network at the Nth stage of the poly-phase unit stage. For the Nth unit stage, the differential I/Q outputs are derived and further expressed using CM and DM outputs in (29)–(32), within the frequency bandwidth where the I/Q 90 phase relationship holds

(29)

(30)

(31)

(32)

and denote the input I and Q magnitudes, while the output I and Q magnitudes are represented by and . Therefore, based on (29)–(32), the output I/Q magnitude mismatches of the Nth stage output are given as (33)

(25) (26) (27) (28)

C. The Cascaded Multistage Poly-Phase Network Behavior Next, we will investigate the cascaded multistage transformer-based poly-phase network behavior in particular the suppression on the I/Q magnitude and phase mismatches.

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errors due to electromagnetic simulation inaccuracy and device modelling errors in practice

(36) (37)

Fig. 9. Calculated I/Q magnitude mismatch suppression versus the number of stages of the multistage transformer-based poly-phase network based on (26) and (35).

Based on (33), by passing the I/Q signals through a transformer-based poly-phase unit stage, the I/Q magnitude mismatches can be suppressed within the frequency range where holds for the unit stage. For an N-stage transformer-based poly-phase network, the resulting I/Q magnitude mismatch at the network output can be expressed in (34) (34) where represents the I/Q magnitude mismatch due to the 1st stage transformer-based quadrature hybrid and is the mismatch suppression effect by the following stages of transformer-based poly-phase unit stages. If the 1st stage and the following unit stages adopt the same differential transformer-based quadrature hybrid design, they present the same Differential-Mode output component DM . Thus, the total output I/Q magnitude mismatch of the N-stage transformer-based poly-phase network is thus given by (35)

For the input I/Q phase errors of the Nth-stage transformer-based poly-phase unit stage in Fig. 6, we add phase error term at the differential input Q signals. Therefore, the input differential I/Q signals are denoted as , and for the Nth-stage unit stage. Based on the proposed N-stage transformer-based poly-phase network shown in Figs. 5 and 8, the differential input I/Q signals of the 2nd-stage poly-phase network are generated from the 1st-stage differential transformer-based 3 dB quadrature hybrid. Specifically, the differential I outputs ( and ) are generated through the two CPL-paths and the differential Q outputs ( and ) are generated from the two THRU-paths in the 1st stage hybrid shown in Fig. 8. Therefore, if identical transformer-based quadrature hybrids are used in the 1st stage and the following N-1 unit stages, thus equals . The output I/Q phase error at the Nth-stage transformer-based poly-phase unit stage outputs is derived in (38)–(44), as shown at the bottom of the next page. It is of particular interest to investigate the I/Q phase mismatch suppression at the normalized frequency above 1, where I/Q phase mismatch becomes more significant (Fig. 2). The magnitude of defined in (26) is small at the normalized frequency above 1 and at . Therefore, . Furthermore, as the number of stages of the transformer-based poly-phase network increases, I/Q magnitude mismatches are suppressed based on (34)–(35), and then in Fig. 9. Therefore, and at the normalized frequency above 1. Therefore, the (44) can be further expressed as

(35) Fig. 9 summarizes the calculated I/Q magnitude mismatch versus the number of stages of the transformer-based poly-phase network based on (26) and (35) for a transformer-based quadrature hybrid design with , and . The I/Q magnitude mismatch is largely suppressed as the number of stages increases in Fig. 9. Next, we will investigate the I/Q phase mismatches suppression by the proposed multistage transformer-based poly-phase network. We assume that the unit poly-phase stage (Fig. 6) is composed of four identical phase-mismatched transformer-based 3 dB quadrature hybrids. An effective phase error is added at the THRU-path of each hybrid output (270 ), while the CPL-path phase response remains as 0 , shown in (36)–(37). This effective phase error captures the phase

(45) The (45) shows that the quadrature phase mismatch due to the phase error of the transformer-based quadrature hybrid is also largely suppressed by the N-stage poly-phase network, as a result of the quadrature amplitude mismatch suppression. This directly reduced the output I/Q phase mismatches and extends the quadrature operation bandwidth. In summary, the proposed transformer-based poly-phase network suppresses both magnitude and phase mismatches of the I/Q signals and achieves an ultra-broadband operation.

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IV. A TRANSFORMER-BASED POLY-PHASE NETWORK DESIGN EXAMPLE In this section, we will present a proof-of-concept 3-stage transformer-based poly-phase network design ( Grad/s) with its design process and simulation results to demonstrate the proposed concept. The 3-stage transformer-based poly-phase network system architecture is shown in Fig. 10. A fully differential 8-port folded transformer-based quadrature hybrid serves as the 1st stage to generate the differential I/Q signals [12]. The same hybrid design is also employed in the transformer-based poly-phase unit stage, which is composed of two identical hybrid designs to process and generate differential quadrature signals. Two poly-phase unit stages are cascaded after the 1st stage to form the 3-stage poly-phase network. The design of the fully differential 8-port folded transformer-based 3 dB quadrature hybrid [12] with Grad/s is explained as follows (Fig. 11). Two single-ended transformer-based quadrature hybrids (TRF1 and TRF2) are first implemented by following the design equations in Section II, and the hybrid structure is modeled using 3-D EM simulations. The differential operation allows folding these two single-ended transformer-based quadrature hybrids (TRF1

Fig. 10. Implementation of the 3-stage transformer-based poly-phase network Grad/s). (

and TRF2) into only one-inductor foot print. The two separate single-ended transformer-based quadrature hybrids (TRF1 and TRF2) are first arranged as shown in Fig. 11 to ensure identical current flow directions, when being excited by differential signals. Therefore, folding TRF1 and TRF2 together can be achieved for significant size reduction. Moreover, this folded transformer exploits the positive magnetic coupling of

(38)

(39)

(40)

(41)

(42)

(43)

(44)

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Fig. 11. The 8-port folded transformer-based quadrature hybrid to generate a fully differential I/Q signals within one inductor footprint.

between the two single-ended transformer hybrids (TRF1 and TRF2), resulting in a larger effective inductance L). Such magnetic enhancement allows the further size reduction as well as low loss operation at the desired differential mode. Note that this magnetic coupling is simply the result of folding two transformer hybrids together, and it is different from the magnetic coupling k in designing the transformer-based quadrature hybrid itself in Section II. The parasitic ground capacitances of the physical transformer can be absorbed in the in Fig. 1 and the parasitic inter-winding capacitance can be absorbed in the in Fig. 1. Extra Metal-Oxide-Metal (MOM) capacitors are added to achieve the desired the capacitive coupling in Fig. 11. Fig. 12 shows the simulated I/Q magnitude and phase of the differential folded transformer-based quadrature hybrid. The coupling coefficient k of each transformer hybrid is 0.82 at 6.8 GHz. The input is driven differentially by a differential 100 input port (port1) and the other 6 ports are each terminated with a single-ended 50 load. Since the differential input power is equally dividing into four single-ended ports, the fundamental power dividing loss is 6 dB. The simulated passive loss due to the transformer-based quadrature hybrid structure is thus 0.4 dB (Fig. 12(a)). The I/Q magnitude mismatch is less than 1 dB from 5.8 GHz to 7.6 GHz and the I/Q phase mismatch is less than 5 from 0.1 GHz to 19 GHz for this one-stage differential transformer-based quadrature hybrid. The input matching is below dB from 0.1 GHz to 28 GHz and the isolation is below dB from 0.1 GHz to 26 GHz. The corresponding port definitions are shown in Fig. 11. Based on Fig. 6, a direct implementation of the transformerbased poly-phase unit stage requires four single-ended transformer-based 3 dB quadrature hybrids. Since the inputs and the outputs of the coupler A/B and the coupler D/C have differential relationship (Fig. 6), thus two folded differential transformer-based quadrature hybrids can equivalently replace four single-ended quadrature hybrids to achieve a substantial size reduction. Fig. 13 demonstrates the transformer-based poly-phase unit stage (Fig. 6) based on combining two differential 8-port folded transformer-based quadrature hybrids. Differential 100 micro-strip transmission lines are added for signal routing and parallel in-phase power combining. Due to the parallel combining at the 4 outputs, their impedance values are differential 50 , i.e., single-ended 25 , resulting in a non-perfect but

Fig. 12. Simulated (a) magnitude and (b) phase responses of the differential 8-port folded transformer-based quadrature hybrid based on full 3-D EM modelling. The port definitions are shown in Fig. 11.

Fig. 13. Transformer-based poly-phase unit stage implemented using two 8-port folded transformer-based 3 dB quadrature hybrids. The meander lines for phase-matched routing are not shown for simplicity. The equivalent schematic is shown in Fig. 6.

acceptable output matching of dB. The reflected signals at the 4 outputs are absorbed by the termination resistors at the isolation ports of the transformer hybrids without affecting the input matching. The total simulated passive loss of this poly-phase unit stage is 0.6 dB based on 3-D EM modeling. The additional meander lines for phase-matched signal routing are not shown for simplicity. Finally, we implement a 3-stage transformer-based poly-phase network (Fig. 5) with its 3-D EM model shown in Fig. 14(a). The magnitude and phase responses are simulated based on the 3-D EM modelling and shown in Fig. 14(b) and (c), respectively. The input (port1) is driven differentially by a differential 100 port and the 4 outputs (port2-port5) are each

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Fig. 15. Simulated output magnitude and phase mismatches for each stage in the example 3-stage transformer-based poly-phase network.

Fig. 14. (a) Full 3-D EM model of the proposed 3-stage transformer-based poly-phase network. (b) Simulated magnitude and (c) phase responses of the proposed 3-stage transformer-based poly-phase network based on full 3-D EM modelling. The port numbers are defined in Fig. 14(a).

terminated with a single-ended 50 port (Fig. 14(a)), and the theoretical loss of the poly-phase network is 6 dB due to the 1:4 power dividing. Based on 3-D EM modeling, the simulated passive loss is only 3.1 dB for the 3-stage transformer-based poly-phase network at 6.8 GHz (Fig. 14(b)). The simulated I/Q magnitude mismatch is lower than 1 dB from 2.9 GHz to 27 GHz, and the I/Q phase mismatch has its maximum value of 5 at 26 GHz. The input matching is below dB from 0.7 GHz to 24.5 GHz. The I/Q magnitude and phase mismatches at the outputs of the 1st stage and the 2nd stage are also simulated based on the

full 3-D EM models and plotted in Fig. 15. The simulated I/Q magnitude mismatch is below 1 dB from 5.8 GHz to 7.6 GHz at the 1st stage output (including the input signal pads and signal distribution lines). The simulated 1 dB I/Q magnitude mismatch at the 2nd stage output is satisfied from 4 GHz to 12.5 GHz and 20 GHz to 27 GHz. At the output of the 3rd stage, the simulated 1 dB I/Q mismatch bandwidth is from 2.9 GHz to 27 GHz. It is clear that cascading more transformer-based poly-phase stages directly suppresses the I/Q magnitude mismatch and extend the I/Q generation bandwidth. Note that the I/Q magnitude mismatch below 2.9 GHz cannot be efficiently suppressed, since the I/Q magnitude mismatch suppression condition, i.e., , cannot be satisfied in this low frequency range. This also aligns well with our theoretical derivations (Section III). The simulated I/Q phase mismatch is within 5 from 0.1 GHz to 12.5 GHz at the 1st stage output and from 0.1 GHz to 24 GHz for the 2nd stage output. This 5 I/Q phase mismatch bandwidth is further extended to 0.1 GHz to 26 GHz at the 3rd stage output. Therefore, cascading more transformer-based poly-phase stages also suppresses the I/Q phase mismatch and extend the I/Q generation bandwidth. In summary, these simulation results verify that our proposed multi-stage transformer-based poly-phase network achieves high-quality low-loss differential quadrature signal generation over an ultra-wide (one-decade) bandwidth.

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TABLE I COMPARISON OF STATE-OF-THE-ART SILICON-BASED QUADRATURE GENERATION SCHEME

Fig. 17. Measurement setup to characterize the 3-stage transformer-based poly-phase network. Fig. 16. Chip microphotograph of the proof-of-concept 3-stage transformerbased poly-phase network design.

The EM simulated insertion loss is approximately 1 dB/stage. This is mainly due to the finite quality factor of the transformers (0.4 dB), the phase-matched transmission line loss for a signal routing (0.2 dB), and non-perfect output matching (0.4 dB). The insertion loss increases at the high frequency due to the quality factor degradation (skin effect) at the high frequency. However, this insertion loss result including the routing parasitic is much lower than a typical RC-CR based poly-phase network, since this transformer-based poly-phase network does not require any explicit resistive components in the RF signal paths. V. MEASUREMENT RESULTS The proof-of-concept 3-stage transformer-based poly-phase network design is implemented in a standard 65 nm bulk CMOS process with a low resistivity substrate cm (Fig. 16) [16]. A differential 8-port folded transformer-based quadrature hybrid ( and m) serves as the 1st stage network. The same quadrature hybrid is also utilized to realize the two transformer-based poly-phase unit stages, and each unit stage occupies 277 m 772 m including the signal routings (Fig. 16). The core chip area of the 3-stage transformer-based poly-phase network is only 772 m 925 m, demonstrating a very compact foot print. Since the passive network has one differential input (differential port 1) and two differential outputs (ports 2 to 5), on-chip 50

terminations are implemented at all the ports and controlled by a digital code to facilitate the testing. By selectively terminating the unused ports with high-precision 50 on-chip termination resistors, the 6-port 3-stage transformer-based polyphase network thereby can be characterized by a 4-port vector network analyzer (Rohde & Schwarz ZVA 24). Three independent CMOS chip samples are measured, and the measurement results are summarized in Fig. 18. Fig. 18(a) shows the typical S-parameter measurements of one sample. Since the theoretical loss of this passive network is 6 dB due to the 1:4 power splitting, the measured passive loss of the 3-stage transformer-based poly-phase network is only 3.65 dB at 6.4 GHz. The 3 dB magnitude bandwidth is from 2.3 GHz to 18 GHz. Both results closely match the 3-D EM simulation results shown in Fig. 14(b). The measured input matching is below dB from 0.5 GHz to 21.3 GHz. The measured I/Q magnitude mismatch for one sample is within 1 dB from 2.8 GHz to 21.8 GHz. In Fig. 18(b), this measured result is compared with 3-D EM simulation result and the calculated result based on theoretically derived close-form design equation (35). Close agreement is achieved among these three results. The slight difference between the calculated I/Q magnitude mismatch and measured I/Q magnitude mismatch is mainly due to the finite Q of the transformer and the micro-strip transmission line magnitude/phase offsets. The measured I/Q magnitude mismatch results for all the 3 independent CMOS samples are summarized in Fig. 18(c). An

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Fig. 18. (a) Measured magnitudes response and (b) simulated, measured, and calculated I/Q magnitude mismatch of the 3-stage transformer-based poly-phase network. (c) Meausred I/Q magnitude mismatches of 3 independent samples. One differential 100 input and four single-ended 50 outputs are used for (a), (b) and (c). (d) Measured phases and (e) measured and EM simulated output I/Q phase mismatch. (f) Meausred I/Q phase mismatches of 3 independent samples. (g) The calculated IRR based on the measured 3 independent samples. The port definitions are shown in Fig. 16.

ultra-wide bandwidth is consistently achieved, showing the robustness of the proposed transformer-based poly-phase network design. The maximum variation of I/Q magnitude mismatch of independent 3 samples from 2.9 GHz to 21 GHz is below 0.5 dB. The measured maximum variation of the passive loss of in-

dependent 3 samples is 0.3 dB with the average passive loss of 3.65 dB at 6.4 GHz. Next, the typical measured differential output quadrature phase responses are shown in Fig. 18(d). The measured differential I/Q phase mismatch is compared with the 3-D EM

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simulation in Fig. 18(e). This measured maximum I/Q phase imbalance is within 10 from low-frequency up to 24 GHz. The measured I/Q phase mismatch matches well with 3-D EM simulation up to 20 GHz, and the slightly smaller bandwidth of the measured phase result is mainly due to the additional parasitic capacitances in practice. The measured phase mismatches of the 3 independent CMOS chip samples are summarized in Fig. 18(f). The maximum variation of I/Q phase mismatch of independent 3 samples from 0.1 GHz to 21.5 GHz is below 5 , also showing the robustness of the proposed transformer-based poly-phase network design. The Image Rejection Ratio (IRR) is often used to evaluate the quality of the quadrature signals to include both I/Q magnitude and phase mismatches [4], [18]. The IRR can be defined as

the high-precision and ultra-wideband quadrature generation of the proposed network and thus validate the theoretical analysis and the derived close-form design equations. The measured passive loss of the 3-stage poly-phase network is 3.65 dB at 6.4 GHz. The measured output I/Q magnitude mismatches is below 1 dB from 2.8 GHz to 21.8 GHz and the measured I/Q phase imbalance is lower than 10 from 0.1 GHz to 24 GHz. An effective Image-Rejection-Ratio (IRR) of more than 30 dB from 3.7 GHz to 22.5 GHz and more than 20 dB from 2.7 GHz to 24 GHz are achieved. The proof-of-concept 3-stage transformer-based poly-phase network design achieves high-quality quadrature generation with low loss and a first-ever one-decade bandwidth. Measurement results on 3 independent CMOS chip samples exhibit consistent performance and show the robustness of the proposed transformer-based poly-phase network design.

(46) ACKNOWLEDGMENT Fig. 18(g) shows the calculated image rejection ratio based on the measured 3 independent CMOS chip samples. The calculated IRR is more than 30 dB from 3.7 GHz to 22.5 GHz with peak IRR of 67.2 dB at 5.71 GHz. For dB, I/Q magnitude mismatch and I/Q phase mismatch should be below 1 dB and 10 , respectively [18] and the calculated IRR is more than 20 dB from 2.7 GHz to 24 GHz. In summary, these measurement results demonstrate that our proposed 3-stage transformer-based poly-phase network achieves high-quality quadrature signal generation with low-loss (3.65 dB at mid-band), a compact area, and a first-ever one-decade bandwidth. Note that such a low-loss and ultra-wideband quadrature generation cannot be achieved by conventional RC-CR poly-phase networks due to their severe signal losses in high-order implementations. VI. CONCLUSION In this paper, a transformer-based poly-phase network is proposed and demonstrated to achieve high-quality quadrature signal generation with low-loss, compact size, and an ultra-wide bandwidth. We first present a high-k transformer-based quadrature hybrid design with the complete circuit analysis and design equations. Such a high-k transformer-based quadrature hybrid achieves substantial size reduction and bandwidth extension compared with the convention transformer-based hybrid design with . The I/Q magnitude and phase mismatches are also analyzed for high-k transformer hybrids with analytical equations. Next, we introduce the proposed multistage transformer-based poly-phase network by cascading multiple transformer-based poly-phase unit stages, which are based on the high-k transformer-based quadrature hybrids. The behavior of such multistage transformer-based poly-phase network is studied. In particular, the suppressions of the I/Q magnitude and phase mismatches by cascading multiple poly-phase stages are analyzed, formulated by close-form equations, and demonstrated based on simulations. As a proof-of-concept, a 3-stage transformer-based poly-phase network is implemented in a standard 65 nm bulk CMOS process with a core area of 772 m 925 m. Simulations based on the 3-D EM modeling verify

The authors acknowledge Toshiba Corporation for foundry service and the members of Georgia Electronics and MicroSystem (GEMS) Lab for technical discussions. They thank T. Chi, T.-W. Li, and M.-Y. Huang from GEMS Lab for measurement support. They thank Mr. T. W. Dalrymple and Mr. T. Quach at Airforce Research Lab (AFRL) for helpful technical inputs. They also acknowledge Rohde & Schwarz and Keysight for providing measurement equipment. REFERENCES [1] J. Park et al., “A K-band 5-bit digital linear phase rotator with folded transformer based ultra-compact quadrature generation,” in Proc. IEEE Radio Freq. Integrated Circuits Symp. Dig., Jun. 2014, pp. 75–78. dBm transformer-based digital Doherty polar [2] S. Hu et al., “A power amplifier fully integrated in bulk CMOS,” in Proc. IEEE Radio Freq. Integrated Circuits Symp. Dig., Jun. 2014, pp. 235–238. [3] D. M. Pozar, Microwave Engineering, 4th ed. New York, NY, USA: Wiley, 2011. [4] B. Razavi, RF Microelectronics, 2nd ed. Englewood Cliffs, NJ, US: Prentice Hall, 2012. [5] J. Park et al., “An ultra-broadband compact mm-wave butler matrix in CMOS for array-based MIMO systems,” in Proc. IEEE Custom Integr. Circuit Conf. Dig., Sep. 2013, pp. 1–4. [6] S. Jeon et al., “A scalable 6-to-18 GHz concurrent dual-band quadbeam phased-array receiver in CMOS,” IEEE J. Solid-State Circuits, vol. 43, no. 12, pp. 2660–267, 3-Dec. 2008. [7] C. Balanis, Antenna Theory Analysis and Design. New York, NY, USA: Wiley, 2005. [8] F. Behbahani et al., “CMOS mixers and polyphase filters for large image rejection,” IEEE J. Solid-State Circuits, vol. 36, no. 6, pp. 873–887, Jun. 2001. [9] S. Kim et al., “An improved wideband all-pass I/Q network for millimeter-wave phase shifters,” IEEE Trans. Microw. Theory Tech., vol. 60, no. 11, pp. 3431–3439, Nov. 2012. [10] R. C. Frye et al., “A 2-GHz quadrature hybrid implemented in CMOS technology,” IEEE J. Solid-State Circuits, vol. 38, no. 3, pp. 550–555, Mar. 2003. [11] M. Tabesh et al., “60 GHz low-loss compact phase shifters using a transformer-based hybrid in 65nm CMOS,” in Proc. IEEE Custom Integr. Circuit Conf. Dig., Sep. 2011, pp. 1–4. [12] J. Park et al., “A fully differential ultra-compact broadband transformer based quadrature generation scheme,” in Proc. IEEE Custom Integr. Circuit Conf. Dig., Sep. 2013, pp. 1–4. [13] K. Koh et al., “An X- and Ku- band 8-element phased-array receiver in 0.18 m SiGe BICMOS technology,” IEEE J. Solid-State Circuits, vol. 43, no. 6, pp. 1360–1371, Jun. 2008. [14] R. Han et al., “A 260 GHz broadband source with 1.1 mW continuouswave radiated power and EIRP of 15.7 dBm in 65 nm CMOS,” in Proc. IEEE Int. Solid-State Circuits Conf. Dig., Feb. 2013, pp. 138–139.

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[15] W. Cao et al., “Multi-frequency and dual-mode patch antenna based on electromagnetic band-gap (EBG) structure,” IEEE Trans. Antennas Propag., vol. 60, no. 12, pp. 6007–6012, Dec. 2012. [16] J. Park et al., “A transformer-based poly-phase network for ultra-broadband quadrature signal generation,” in Proc. IEEE MTT-S Int. Microw. Symp. (IMS), May 2015, pp. 1–4. [17] K. Stadius et al., “Multitone fast frequency-hopping synthesizer for UWB radio,” IEEE Trans. Microw. Theory Tech., vol. 55, no. 8, pp. 1633–1641, Aug. 2007. [18] W. Lin et al., “1024-QAM high image rejection E-band sub-harmonic I/Q modulator and transmitter in 65-nm CMOS process,” IEEE Trans. Microw. Theory Tech., vol. 61, no. 11, pp. 3974–3985, Nov. 2013.

Jong Seok Park (S'13) received the B.S. degree in electrical and electronic engineering (highest honors) from Yonsei University, Seoul, South Korea, in 2012. He is now pursuing the Ph.D. degree in electrical and computer engineering at the Georgia Institute of Technology, Atlanta, GA, USA. His current research interests include novel EM structure, RF and mm-wave circuits, and sensors for biomedical applications. Mr. Park was the recipient of a study abroad scholarship from KFAS in 2012. He was also the recipient of the Analog Device Inc. Outstanding Student Designer Award in 2014, a co-recipient of the RFIC Best Student Paper Award (1st Place) in 2014, and recipient of the Catalyst Foundation, IBM, and Intel CICC student scholarship award in 2015.

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Hua Wang (M'05–SM'15) received the B.S. degree from Tsinghua University, Beijing, China, in 2003, and M.S. and Ph.D. degrees in electrical engineering from the California Institute of Technology, Pasadena, CA, USA, in 2007 and 2009, respectively. He was with Guidant Corporation during the summer of 2004, working on accelerometer-based posture monitoring systems for implantable biomedical devices. In 2010, he joined Intel Corporation, where he worked on the next generation energy-efficient mm-wave communication link and broadband CMOS Front-End-Module for Wi-Fi systems. In 2011, he joined Skyworks Solutions. His work at Skyworks included the development of SAW-less integrated filter solutions for low-cost cellular-standard Front-End-Module. In spring 2012, he joined the School of Electrical and Computer Engineering at Georgia Institute of Technology as an assistant professor. He currently holds the Demetrius T. Paris Junior Professorship of the School of Electrical and Computer Engineering. He is generally interested in innovating mixed-signal, RF, and mm-Wave integrated circuits and systems for communication, radar, and bioelectronics applications. Dr. Wang received National Science Foundation (NSF) CAREER Award in 2015, Roger P. Webb ECE Outstanding Junior Faculty Member Award in 2015, and Lockheed Martin Dean's Excellence in Teaching Award in 2015. He was the award recipient of the 46th IEEE DAC/ISSCC Student Design Contest Winner in 2009 based on his work of “An Ultrasensitive CMOS Magnetic Biosensor Array for Point-Of-Care (POC) Microarray Application.” He was also a co-recipient of the IEEE Radio Frequency Integrated Circuits Symposium (RFIC) Best Student Paper Award (1st Place) as the students' Ph.D. advisor in 2014. Dr. Wang is an Associate Editor of the IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS (MWCL). He is currently a Technical Program Committee (TPC) Member for IEEE Radio Frequency Integrated Circuits Symposium (RFIC), IEEE Custom Integrated Circuits Conference (CICC), and IEEE Biopolar/BiCMOS Circuits and Technology Meeting (BCTM). He is a member of Sigma Xi, the IEEE Solid-State Circuits Society (SSCS), the IEEE Microwave Theory and Techniques Society (MTT-S), the IEEE Circuits and Systems Society (CAS), and the IEEE Engineering in Medicine & Biology Society (EMBS). He serves as the Chair of the Atlanta's IEEE CAS/SSCS joint chapter, which won the IEEE SSCS Outstanding Chapter Award in 2014.

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Optimized Design of Frequency Dividers Based on Varactor-Inductor Cells Mabel Pontón, Member, IEEE, and Almudena Suárez, Fellow, IEEE

Abstract—This paper presents an in-depth analysis of a recently proposed frequency divider by two, which is based on a parallel connection of varactor-inductor cells, in a differential operation at the subharmonic frequency. The analytical study of a single-cell divider enables the derivation of a real equation governing the circuit at the frequency-division threshold. This equation is used for a detailed investigation of the impact of the circuit elements on the input-amplitude threshold and the frequency bandwidth. Insight provided by the analytical formulation enables the derivation of a thorough synthesis methodology for multiple-cell dividers, usable in harmonic balance with an auxiliary generator at the divided frequency. Two different applications of this topology are demonstrated: a dual-phase divider and a dual-band frequency divider. The former is obtained by using Marchand balun to deliver 180 phase-shifted signals to the two dividers. On the other hand, the dual-band divider is based on a novel configuration which combines cells with parallel varactors and cells with series varactors. Departing from the optimization procedure of the single-band divider, a simple synthesis method is presented to center the two division bands at the desired values. The techniques have been applied to three prototypes at 2.15 GHz, 1.85 GHz, and 1.75 GHz/3.95 GHz, respectively. Index Terms—Dual-band frequency division, dual-phase generation, frequency dividers, phase noise.

I. INTRODUCTION HE works [1], [2] propose a frequency divider topology based on the use of two parallel nonlinear transmission lines (NLTLs) connected through back to back diodes [Fig. 1(a)]. The two NLTLs behave like a reflective distributed resonator, since the odd-mode subharmonic oscillation terminates in a virtual ground at both ends, so the output signal is extracted from internal cells by means of a buffer [1], [2]. The subharmonic component is sustained by the gain exhibited by the varactors under the pump signal at and, in this manner, a standing wave [1], [2] is formed through the distributed resonator. This divider configuration exhibits zero static-power consumption [2], [3], which is an interesting quality since, in practical applications, the frequency divider usually consumes a significant portion of the frequency synthesizer power [1]–[3]. Another advantage comes from the absence of a free-running oscillation, which in injection-locked

T

Manuscript received July 02, 2015; revised September 30, 2015, October 20, 2015; accepted October 24, 2015. Date of publication November 17, 2015; date of current version December 02, 2015. This work was supported by the Spanish Ministry of Science and Innovationunder project TEC2014-60283-C3-1-R and by the Parliament and University of Cantabria under the project Cantabria Explora 12-JP02-640.69.This paper is an expanded version from the IEEE MTT-S International Microwave Symposium, Phoenix, AZ, USA, May 17–22, 2015. The authors are with the Departamento de Ingenier´ıa de Comunicaciones, Universidad de Cantabria, Santander 39005, Spain (e-mail: [email protected]; [email protected]). Digital Object Identifier 10.1109/TMTT.2015.2495348

Fig. 1. Multicell frequency divider. (a) Schematic of a multicell divider, enabling an odd-mode subharmonic oscillation. The number in the notation refers to the order of the back-to-back diode pairs. There is a total of pairs. (b) Photograph of the prototype built in Rogers 4003C substrate ( mm). In the different prototypes, individual signals are extracted with impedance transformers (as in the photograph) or with a source-follower buffer based on the transistor NE3210S01. (c) Auxiliary generator (AG) used to simulate and optimize the divider in HB. It is connected between the nodes and in the schematic of (a).

dividers [4]–[6], gives rise to undesired mixer like regimes [6], [7] outside the division band. In addition, the absence of an oscillation enables lower phase-noise spectral density at large offset frequency from the carrier [1], [2], [8]. The works [1], [2] have demonstrated that a synchronous propagation of the pump and subharmonic signals is beneficial for the energy transfer from the pump to the subharmonic signal. This requires a minimization of the dispersion effect, which is achieved through the use of an additional capacitor connected between the middle node of the back-to-back diodes and ground (Fig. 1). The capacitor decreases the average capacitance at , but does not directly affect the odd harmonics of the subharmonic signal, due to the circuit symmetry. The analysis in [1], [2] departs from a continuous transmission-line model [9], which is followed by several corrections accounting for dispersion and mismatch at the pump frequency, among other effects. An alternative investigation is presented in this work. It is based on a detailed circuit-level analysis of the new divider topology, carried out in two different ways: analytically [10], in the case of a single-cell divider, and through harmonic balance (HB), complemented with an auxiliary-generator technique [6], [7], in the case of multiple cells. Using the analytical formulation, a single equation, governing the global behavior of frequency divider at the division threshold, is derived, which will enable an understanding of the impact of each divider element

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on the input-sensitivity curve. With this insight, an optimization procedure, intended for HB simulators and applicable to dividers with multiple cells, will be developed. Novel applications of the divider based on varactor-inductor cells will be investigated. One of them is a dual-phase divider, based on the use of two of these dividers, together with a Marchand balun [11] for a simple generation of in-phase and quadrature signals. Possible applications include quadrature modulation and quadrature down conversion [12]. The Marchand balun provides two signals with 180 phase shift, which are introduced in the differential frequency dividers. Then the frequency division inherently gives rise to a 90 phase shift [12] between equivalent nodes of the two divider circuits. A dual-band frequency divider, based on the use of two different types of differential inductor-varactor cells, is also investigated. One section is composed of cells having the varactors in a parallel connection, whereas the other section is composed of cells having the varactors in a series connection. Unlike previously presented dual-band frequency dividers [13], there is no oscillation in the absence of an input signal. This avoids undesired self-oscillating mixer regimes below the division threshold and between the division bands. The dual-band design will allow coping with the major limitation of this novel kind of frequency dividers, which is the frequency bandwidth. As will be shown, the two coexistent division bands can be tuned, and even preset, with a simulation procedure that relies on the properties revealed by the analytical formulation. In this way, the designer can take advantage of the two interesting characteristics of this novel kind of dividers, which are the zero static power consumption and the low phase-noise spectral density [1], [2]. The paper is organized as follows. Section II presents the analytical study of a single-cell divider, with a detailed investigation of the impact of each element of the circuit topology. Section III describes a dual-phase divider, based on the use of a Marchand balun. Section IV presents the synthesis of a dual-band frequency divider. II. ANALYSIS OF THE DIVISION THRESHOLD The dependence of the input-amplitude division threshold on the various circuit elements and parameters will be studied in the two cases of a single-cell divider and a multicell divider. A. Single-Cell Divider For the analytical formulation of a single-cell divider, the varactor diode will be modeled by a nonlinear capacitor in series with a loss resistor [Fig. 2(a)]. Limiting the analysis to the subharmonic and input frequencies, and , the voltage waveform across the nonlinear capacitor will be approximated with the following truncated Fourier series: (1) where is the subharmonic frequency and the phase origin is taken at . Assuming a moderate input amplitude, it will be possible to model the varactor capacitance with a first-order Taylor series [1], [2]. Replacing the waveform (1) into , one obtains the current entering the nonlinear capacitor, in time domain. The two-sided

Fig. 2. Single-cell frequency divider. (a) Full topology. (b) Equivalent circuit at the subharmonic frequency . (c) Equivalent circuit at the input frequency .

Fourier-series expression of this current has the component at and the component at , which are given by (2) The ratio between the current and voltage provides the input admittance function, , exhibited by the nonlinear capacitor at the subharmonic frequency (3) , the nonAs gathered from (3), under a pump signal at linear capacitance will exhibit negative conductance at provided that the condition is fulfilled. To formulate the divider equations, one should take into account the symmetry properties of the circuit topology. Assuming an odd mode subharmonic oscillation (180 phase shift between the two branches), the middle points and are virtual short circuits at the subharmonic frequency [Fig. 2(a)], which leads to the schematic of Fig. 2(b) at the subharmonic frequency. Applying Kirchoff's laws to this equivalent circuit, one obtains (4) where . On the other hand, as gathered from Fig. 2(a), the point is a virtual open circuit at the input frequency . Taking also into account the input equivalent network at , shown in Fig. 2(c), one obtains the following equation at the input frequency: (5) where and are the amplitude and phase of the input source (considering a two-sided spectrum),

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and . and the capacitor only affect the (5), at . Dividing both terms of (4) by and using the definition of in (3), one obtains Note that

(6) agrees with the total-admittance function The function at the subharmonic component , calculated at node 2 of the equivalent circuit in Fig. 2(b). It is the addition of and the admittance of the series branch composed by and . Fulfillment of condition (6), , implies the existence of a self-sustained subharmonic oscillation, due to the energy flow from the input pump at to the subharmonic signal [1]. The frequency division by 2 is enabled by the negative conductance at and the resonance effects inherent to the complex equation (6). Dividing the two terms in (6) by one obtains the following relationship: (7) , Now, dividing all the terms of (7) by one obtains an alternative expression for the subharmonic-oscillation condition (8)

From inspection of (10), the voltage does not depend on . For a fixed varactor model, it depends on the inductor and the input frequency , so it can be expressed as . Next, expression (10) will be replaced into (5), imposing also the limit frequency-division condition . Solving for , one obtains a single real equation governing the circuit behavior at the division threshold

(11) where the subindex “ ” indicates that the input voltage is calculated at the division threshold. As gathered from (11), the expression for the input-amplitude threshold is composed by two factors. The middle-point capacitor only affects the second factor. Provided that the inductor fulfils , it will be possible to choose so as to minimize the input-amplitude threshold. Indeed, the second factor in (11), composed by the addition of two squared terms, will achieve a minimum at the capacitor value (12) which will lead to the following expression for the input-amplitude threshold: (13) On the other hand, from inspection of (11), the threshold decreases with the amplitude , which has the following expression, derived from (10):

where is the total admittance function between the diode terminals, given by (9) (14) is the voltage component at the input freand quency. The bar stresses the fact that this voltage has a phase value , unlike the subharmonic voltage , where the phasereference is established. Note that the total varactor-admittance function includes the effect of the loss resistance . Equation (8) agrees with the total-admittance function at the subharmonic component , calculated at node 1 of the equivalent circuit in Fig. 2(b). The use of a frequency-division condition in terms of the varactor admittance (including ) will facilitate the extension of this condition to multiple cells, presented later in this section. The limit condition for frequency-divider operation (division threshold) corresponds to a subharmonic amplitude tending to zero . This agrees with the condition for a flip bifurcation [6], [7], [14]. Splitting (6) [or, equivalently, (8)] into real and imaginary parts, one can calculate the voltage at in the presence of a frequency division, which will be denoted as . This is given by

(10)

where . The magnitude will exhibit a minimum if the following condition is satisfied:

(15) , The above condition, fulfilled at the given frequency agrees with in (10)(a). This condition enables an optimum operation of the diodes at the subharmonic frequency, as they behave as pure negative resistances, without any additional reactive component. The frequency agrees with center of the division band. Indeed, at constant , and because of the second squaring operation under the root in (14), the frequency response will be nearly symmetrical about . For illustration, the varactor diode SMV1231 [15] has been considered. At the bias voltage V, the parameters of the approximate model are (F) and (F/V). In a first design, the desired central frequency is GHz. The inductor value resulting from the condition (15) is nH. The corresponding input-sensitivity curve is obtained with (11). As

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Fig. 3. Input-sensitivity curves for two different values, centering the division band about two different frequencies. The input-amplitude values are . The sensitivity curves rereferred to a positive-frequency spectrum are traced in solid line in the two cases. sulting for an optimum capacitor

shown in Fig. 3, the inductor nH centers the division band about GHz for any value. This inductor fulfils , so it is possible to select the capacitor pF that minimizes the input-amplitude threshold at GHz. Due to the increased sensitivity with respect to the input signal under the resonance condition (12), the capacitor enables a broader division bandwidth (Fig. 3). This is studied in detail in Section II-C. As a second example, the same two-stage design method has been applied for a different central frequency GHz, observing the same performance (Fig. 3). The impact of the diode parameters and has also been analyzed. From a simple inspection of (10) the voltage amplitude at the input frequency is inversely proportional to , so according to (11) the input-amplitude threshold will decrease with . On the other hand, the capacitance affects (10)(a) and also the condition for a minimum in given by (15). For a given , a variation of will shift the center of the division band, , determined by (15). Provided that (12) is also fulfilled, a lower threshold will be obtained for smaller , as gathered from (13). However, one should take into account that both and depend on the particular bias voltage of the varactor diode. In the case of the diode SMV1231 [15], both and decrease with , in the whole range, going from 0 V to 15 V. Fig. 4(a), presents the analysis of the input-amplitude threshold versus the inductor , for different values of . The lowest threshold is obtained for V, providing the highest . The impact of on the input-sensitive curves is shown in Fig. 4(b). As expected, the lowest input-amplitude threshold and broadest division bandwidth is obtained for V which will be the value considered in this work. B. Multicell Divider A multicell divider, such as the one considered in Fig. 1(a), will be investigated. Initially, the study will be carried out using the model at the two frequencies and . The frequency-division condition (8) can be generalized to a multicell divider, which is done by means of an equivalent circuit analogous to the one in Fig. 2(b). The circuit total admittance is calculated at the node located between the first inductor and the rest of the varactor-inductor structure, at the

Fig. 4. Influence of the parameters of the diode model. (a) Variation of the input-amplitude threshold (in a positive-frequency spectrum) with the inductor at the constant input frequency GHz. (b) Input-sensitivity curve with the bias voltage , choosing, in each case, the inductor value that provides GHz. the minimum input-amplitude threshold at

subharmonic frequency sive equation:

. This provides the following recur-

(16) , with to , are the diode subharmonic adwhere mittance functions and is the number of back-to-back varactor pairs existing in the multicell divider, indexed as shown in Fig. 1(a). The admittance functions are defined as (17) Note that for , one has [see (7)–(9)]. In the above expression is the voltage component at across the nonlinear capacitor . The bar stresses the fact that it is a complex magnitude. Equation (16) agrees with the flip bifurcation condition of the multicell divider. Combining (17) with (16), one obtains a complex equation of the form (18) which depends on the whole set of second harmonic voltages at , calculated under the limit condition for frequency

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division . These voltages provide the negative resistances that should compensate the passive impedances exhibited by the circuit at , depending only on and . Using the first-order capacitance model and the two analysis frequencies and under the condition , the phasors will depend linearly on the input voltage , since the diode capacitance at is simply . A different expression will exist for each phasor, having the general form (19) The replacement of (19) in (16) provides a complex nonlinear equation in and , which can only be accurately resolved in a numerical manner. Because the flip-bifurcation (18) does not explicitly depend on , one may expect a behavior analogous to that of a single cell, regarding the two design parameters and . That is, the variation of will shift the division band and the variation of will modify the sensitivity to the input signal and, therefore, the division threshold. However, as gathered from (16), the optimum values of and for a desired central frequency will depend on the number of cells and should be optimized for each . Note that when implementing a multicell configuration, divisions by higher order will not be usually observed, due to the loading effects of the -varactor cells, which are tuned for frequency division by 2, instead of higher order divisions. Initially, a multicell divider with back-to-back varactor pairs will be analyzed [Fig. 1(a) and (b)], as this is the same number considered in [1], [2]. The impact of the number of will be studied later in this section. For a realistic analysis and design, harmonic balance (HB) is used, together with an auxiliary generator (AG) [6], [7]. The AG is needed because HB does not enable a direct optimization of frequency dividers. Even when setting the fundamental frequency to , the HB simulation will converge by default to a solution with zero value at all the odd harmonics of , since it contains a homogeneous subsystem at these frequency components [7]. The use of an AG at prevents this default convergence [6], [7]. The voltage AG is connected in parallel at a sensitive location, for instance between the nodes of a varactor diode in one of the innermost divider cells [Fig. 1(c)]. It contains an ideal bandpass filter centered at , to avoid any influence at frequencies different from . Due to the rational relationship with the input frequency, both the AG amplitude and its phase [or the phase of the input source] must be calculated in order to fulfil a nonperturbation condition. This condition is given by the zero value of the ratio between the AG current and voltage at , expressed as , where the phase origin is taken between the AG terminals. In commercial HB, this condition is solved through optimization, with the pure HB system, with as many harmonics as desired, as an inner tier. After convergence, the voltage component at , between the AG nodes, will agree with the AG value. Using this property, the division boundary will be obtained by setting the AG amplitude to a very small value . Taking into account the insight provided by the analytical study, the optimization procedure will be the one indicated in the flowchart of Fig. 5. It will start with the calculation of the inductor that minimizes the input-amplitude threshold at the

Fig. 5. Flowchart indicating the steps to be taken for the optimized design of the frequency divider.

desired central frequency and solving

. This is done by doing

(20) under the condition . Note that (20) is equivalent to (18) of the simplified formulation. Because (20) is complex, it contains two real equations in three unknowns, which provides a curve in the plane defined by and . To center the division band, is swept, solving the complex equation (20) in terms of at each step. The value providing the minimum is chosen. For illustration, the method will be applied to the divider shown in Fig. 1(a). In all the HB analyses presented hereafter, full diode models (including parasitics) and harmonic terms will be considered. The model used for the varactor diode SMV1231 is the one provided by the manufacturer [15]. Fig. 6(a) presents the results obtained when setting the AG frequency to the desired central value of the division band: , where GHz. Three different values of have been considered, but the inductor nH provides the minimum in the three cases, in agreement with the analytical study of the single cell. Next, the inductor is kept fixed at nH, performing a sweep in the capacitor and solving at each sweep step (Fig. 5). The minimum is obtained for pF [Fig. 6(b)]. The effect of varying the two parameters and on the bandwidth is analyzed by tracing the input-sensitivity curve in the plane defined by and . The frequency is swept, solving the complex equation in terms of at each sweep step. Fig. 6(c) shows the sensitivity curves obtained for different pairs of values . For each value, the sensitivity curve gets centered about a different frequency . Once

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Fig. 7. Measurement test-bench. (a) Sketch. (b) Photograph.

Fig. 6. Optimization of the multicell divider based on the diode SMV1231 in harmonic terms. (a) Fig. 1(a) by means of HB-AG simulations with Selection of the inductor value that minimizes the input- amplitude threshold GHz. (b) Further minimization at the desired central frequency through a proper selection of the additional capacitor . (c) Input-sensitivity nH at GHz and for curves for the optimum inductor GHz. In a different inductor value, which centers the band about each case, the input-amplitude threshold is minimized through an independent analysis versus .

the divider is centered about the desired frequency , the capacitor can be used to reduce the input-amplitude threshold. In agreement with the analytical study, variations of this capacitor do not shift the operation band. The sketch and picture of the measurement setup are shown in Fig. 7. It is based on the use of the Agilent 90804A Digital Storage Oscilloscope and the E4446A PSA spectrum analyzer (with phase noise measurement personality). The circuit is injected using the Rhode & Schwarz SMT06 signal generator. In this particular case, the divided solutions have been measured with two Agilent 1134A differential probes, which enable flexibility to test the differential waveforms at various circuit nodes. Measurement points have been superimposed in Fig. 6(a) to 6(b) with good agreement.

Now the impact of the inductor-varactor cells will be investigated. Initially, the first-order model has been considered. The central frequency is set to GHz. Then the inductor that minimizes the input-amplitude threshold at GHz is calculated numerically using the flip-bifurcation condition (18) for different values. Fig. 8(a) presents the resulting input-sensitive curves. A different is obtained for each , but the division band is centered about in all cases. For each , the division threshold is further reduced through a proper selection of the capacitor , as shown in Fig. 8(a). Fig. 8(b) presents the same analysis, using the HB-AG method with full diode models and harmonic terms. Each sensitivity curve corresponds to the and obtained following the flowchart of Fig. 5. As expected, for moderate input-amplitude levels, there is very good agreement between the results obtained with (16) and with HB. As shown in Fig. 8(a) and (b), there is a reduction of the division bandwidth when increasing . To investigate this effect, the variation of through the flip-bifurcation loci obtained for different has been analyzed in Fig. 8(c). The phase-shift interval with high sensitivity to decreases with , which is due to an earlier saturation effect in the nonlinear function in that governs the phase shift dependence: . Therefore, for given input amplitude, the fulfillment of the resonance condition at , required for the frequency division, is limited to a smaller interval. Despite this reduction of the frequency band, the increase in can be interesting for certain applications, since it enables higher subharmonic amplitude through the divider circuit, as was demonstrated in [9]. Indeed, for a higher , the subharmonic gain increases [1], [2] due to the cooperative effect of more varactor diodes. This is demonstrated in Fig. 9, which compares the resonance near the subharmonic

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Fig. 9. Resonance near the subharmonic frequency, responsible for the frevalues. A more negative conductance quency division by 2, for different (responsible for the subharmonic amplification) is obtained for higher .

Fig. 8. Influence of the number of back-to-back diode pairs on the frequency-division band. (a) Through the numerical solution of (16), based on a first-order model of the diode. (b) Using the HB-AG method with full diode harmonic terms. (c) Variation of the phase shift between models and the input source and the subharmonic voltage through the flip-bifurcation loci in (b).

frequency, responsible for the frequency division by 2, for different values. As can be seen, a more negative conductance (responsible for the subharmonic amplification) is obtained for higher . The higher frequency selectivity is also noted, in consistency with Fig. 8(c). C. Frequency Bandwidth The analysis of the frequency bandwidth will initially be carried out using the analytical expression (11), valid for one cell. Then the multicell divider with diode pairs will be studied with the HB-AG method. The impact of the additional capacitor is analyzed solving (11) for , in terms of and , which provides (21)

Sweeping at constant and , two different curves are obtained, respectively corresponding to the positive and negative sign before the root operation. In Fig. 10(a), the two curves have been traced (in solid and dashed lines) for different values and the inductor resulting from the minimization of the input-amplitude threshold at GHz. Division by two is obtained inside the region delimited by the two curves. For each , the edges of the maximum frequency bandwidth are given by the condition in (21), which is satisfied for a different at each side, due to the frequency dependence of . The curve versus exhibits an infinite slope at each of the two points fulfilling that condition. When setting the input amplitude to the global minimum at GHz, the two infinite slope points merge into a single one and solution curve degenerates into a point, obtained for the optimum capacitor value [see (7)]. As increases from this value, the two sections in (21) form a closed curve that later becomes an open curve. This is because for large , the minus sign before the denominator root gives rise to a (discarded) negative capacitor. As shown in Fig. 10(a), below certain value division is no longer possible, due to insufficient subharmonic gain of the nonlinear capacitances. On the other hand, for too large , this capacitor no longer has an impact on the divider operation, which justifies the open curves in the representation of Fig. 10(a). For a particular capacitor value , there is a constant curve such that its upper section is tangent to the straight line [Fig. 10(a)]. The particular value of this curve corresponds to the minimum threshold in the plane . On the other hand, the capacitor values providing the maximum frequency excursion for each do not differ too much [Fig. 10(a)]. The maximum bandwidth is obtained for a value that approximates the one resulting from the threshold-minimization procedure in Section II-A, for which a single point is obtained in the representation of Fig. 10(a), indicated as . Therefore, the minimization of the division threshold at a particular frequency should also enable a near maximum frequency bandwidth. The above analytical results have been validated in the multicell divider with diode pairs [Fig. 1(a)], using a HB simulation with harmonic terms. The frequency division

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the presence of noise sources. The AG, which uses the pure HB system as an inner tier, enables control of the subharmonic voltage, so the partial derivatives with respect to and , denoted as and , can be calculated through finite differences [8], [16]. The partial derivative is obtained through increments in , while keeping the frequency and phase constant at their original values, , the ones fulfilling . In turn, the partial derivative is obtained through increments in , while keeping the frequency and amplitude constant at their original values, . An analogous procedure is carried out to calculate . In the phase-noise analysis, amplitude noise from the input source will be neglected, considering only the input phase noise . The phase noise of a divider by is expected to follow up to a certain offset frequency, usually beyond the region of influence of the circuit flicker noise. Thus, only whitenoise sources will be considered. The circuit contains several white noise sources but they will all be modeled with a single equivalent current noise source. An example of the derivation of this kind of model is presented in [8]. The complex equivalent noise source, denoted as , is connected in parallel with the AG [8]. Taking into account the effect of the circuit noise sources, the total phase perturbation the observation node can be expressed as [8], [17]. In turn, the subharmonic amplitude undergoes an increment with respect to the steady-state value . The time-varying phase and amplitude gives rise to an instantaneous complex frequency that can be expressed [8], [17] Fig. 10. Variation of the frequency bandwidth with the additional capacitor for different values of the input amplitude . (a) Analytical calculation. Frequency division is obtained inside each curve or pair of curves resulting from diode pairs cell (21). (b) HB-AG analysis of the multicell divider with divider in Fig. 1. Measurements have been superimposed.

loci have been traced in the plane defined by for several values [Fig. 10(a)]. Each locus is obtained by solving the equation . The analysis have been carried out for the optimum inductor value nH, resulting from the simulation in Fig. 6(a). In good qualitative agreement with the analytical formulation, the division band degenerates to a point when is fixed to the global minimum input-amplitude threshold [Fig. 10(b)]. The corresponding value agrees with the one providing the minimum when sweeping at constant nH. Measurements are superimposed. D. Phase Noise Phase noise is a relevant characteristic of the frequency-divided solution. To calculate this solution at given input amplitude and frequency , one should solve the nonperturbation condition in terms of the AG amplitude and input phase, , as done in [10]. Once the nonperturbation condition is fulfilled, the voltage at the subharmonic frequency agrees with the AG voltage at the connection nodes, so one can write . For an understanding of the phase-noise behavior, the outer-tier function will be linearized about the divided steady-state solution in

(22) Then the phase-noise spectral density can be estimated with the following expression, derived in [7], [8]: (23) where indicates the cross product between real and imaginary parts. The varactor based divider will usually exhibit low frequency sensitivity, so it will be possible to approach the above equation with (24) where is the angle of and is the angle of . For low frequency sensitivity, the divider will follow the divided phase noise of the input source up to certain offset frequency, from which the circuit white noise sources will dominate. This will give rise to a transition from a spectrum closely following that of the input source to a flat spectrum. The transition will occur at the offset frequency for which the two terms in (24) have an identical magnitude. Assuming a low noise input source, the frequency will be larger for a higher magnitude , since this means a higher sensitivity to the phase of the input source. It will also decrease with the subharmonic amplitude and for angles close to an odd multiple of .

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Fig. 11. Phase-noise analysis of the multicell divider with diode pairs. Comparison between the phase noise spectra obtained with the approximate expression (24) and with the conversion-matrix approach. Measurements have been superimposed.

TABLE I PHASE NOISE CORNER FREQUENCY

The above conclusions have been validated with a detailed phase-noise analysis based on the conversion-matrix approach [18], [19] and with measurements. For the analysis with the conversion-matrix approach, the circuit is linearized about the periodic regime obtained with the AG, which is provided as an initial guess to the large-signal small-signal analysis of the commercial software. The analyses have been performed for several input frequencies, comparing the offset frequencies and the denominator of the second term of (14) in Table I. In Fig. 11, the phase-noise spectrum of the subharmonic component, extracted with an impedance transformer, is compared with the spectrum of the input source. III. DUAL-PHASE DIVIDER The use of two frequency dividers based on differential varactor-inductor cells, together with a balun, should enable the implementation of a dual-phase divider, with application in the generation of in-phase and quadrature signals [12], [20]. A planar Marchand balun [11]will be used here, which is based on two sections of coupled transmission lines, having an electrical length of 180 at the central operation frequency , as shown in Fig. 12. Initially, an analytical study of the configuration will be performed, using single-cell dividers [Fig. 12(a)]. Next, the practical case of a multicell divider with diode pairs will be studied [Fig. 12(b)–(c)], by means of numerical simulations and measurements. In the simpler case of ideal transmission lines, the admittance matrix describing the Marchand balun at is the following: (25) where the currents and voltages at the three ports are defined as shown in Fig. 12(a). For generality, we will consider different

Fig. 12. Dual-phase signal generator based on two varactor-based frequency dividers, connected through a Marchand balun. (a) Currents and voltages at the three ports of the Marchand balun. (b) Schematic. (c) Photograph of the protomm). type built in Rogers 4003C substrate (

voltage and current values at the inputs of the two dividers. This will be the case if one of the dividers is detuned with respect to the other. The analysis as a phase shifter requires full consideration of the nonlinear behavior with respect to the subharmonic components, so the components of the diode current will be given by (2), with . The matrix (25) provides the following relationships at the input frequency :

(26) where the prima indicates variables referring to Divider B in Fig. 12. At the subharmonic frequency, each divider is terminated in virtual short circuits, so their individual subharmonic components fulfill (27) where corresponds to the same impedance already defined in (4). Note that the phase origin is taken at the subharmonic component of the voltage across the varactor diode in the Divider A, so is a phasor of the form: . Applying Kirchoff's laws at the input frequency , under consideration of (26)(b) and (26)(c), one obtains

(28)

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Replacing alternatively (28)(a) and (28)(b) into (26)(a), the following equations are derived:

(29) where and . The difference between the voltage and current values at the two diodes is due to their different bias voltages. In the approximate model (29) each divider is coupled to the other only at the input frequency . To analyze the phase shifting capabilities, one should determine the phase of the subharmonic voltage since the phase of is zero. The two nonlinear equations in (29) can only be resolved numerically, but they can provide an intuition on the impact of on the phase shift. With this aim, the diode in Divider A is modeled with . In turn the diode in Divider B, undergoing the biasing variations, is modeled with . For a rough analysis of the impact of the coupling effects, one can define an equivalent current source (30) And solving (29)(b) for

one obtains (31)

where the following parameters with frequency dimension have been introduced and . Expression (31) will be replaced into (27)(b) considering the capacitance model to obtain the current component . This leads to (32) At a constant , all the impedance terms will be constant too, so varying the parameters will necessary give rise to a variation in and . From (26)(b) and (26)(c), one has , so it is possible to obtain the following relationship: (33) Because the biasing is varied in Divider B, one can expect the subharmonic amplitude to experience larger variations in this divider. Equation (33) indicates that the subharmonic oscillation may be extinguished in Divider B but not in the other, since, even when , this equation can provide . Of course, this condition will delimit the operation interval. For same bias voltage in the two dividers, one will have and , and due to the circuit symmetry, (33) will provide the solution (34) Then, the two dividers are ruled by a same equation (35)

Fig. 13. Variation of the subharmonic amplitudes versus the reverse bias voltage applied to the varactors of Divider B. The cases of a single-cell divider diode pairs are compared. and a multicell divider with

Due to the relationship (34), equivalent nodes of each divider will exhibit a 90 phase shift. This is indicated in Fig. 12(b). For instance, signals at the upper node of cell in Divider B and at the upper node of the same cell in divider A will exhibit a 90 phase shift. Signals at the lower node of cell in Divider B and at the lower node of the same cell in Divider A will also exhibit a 90 phase shift. On the other hand, upper and lower nodes of any cell in any of the two dividers will exhibit a 180 phase shift. Fig. 13 presents the numerical analysis of a dual-phase signal generator based on the use of two one-cell dividers. It shows the variation of the subharmonic amplitudes in the two dividers when changing the bias voltage of Divider B. The analysis demonstrates the coupling between the two dividers since the amplitude in Divider A varies with this bias voltage. A practical dual-phase generator based on two multicell dividers with diode pairs has also been analyzed by means of two AGs, connected in a differential manner, at the central cell of each divider [Fig. 12(b)]. The amplitude variations are superimposed in Fig. 13 and exhibit the same qualitative behavior. In the two cases, the amplitude of Divider B undergoes the most significant variation, as this bias voltage directly affects the performance of the diodes in Divider B, whereas those in Divider A are affected by this bias voltage only through coupling effects. This gives rise to the amplitude imbalance observed in Fig. 13. With this hyperabrupt diode the amplitude is quite sensitive to the varactor bias voltage, even in the case of a single (uncoupled) divider. The aim here is to present a proof of concept, though a more careful consideration of this aspect might be needed for some applications. In the case of the one-cell divider, the section comprised between the flip bifurcation and the turning point of the divided solution curve is unstable, as has been verified with pole-zero identification [21]. In the range (2.27–2.48 V), both the nondivided solution and the divided one located in the upper section of the curve are stable. Therefore, the divider will exhibit a small hysteresis interval, which is a common phenomenon in frequency dividers [7]. Fig. 14 presents the experimental waveforms between equivalent terminals of the two dividers for two different values of the varactor bias voltage. Fig. 14(a) shows a phase shift of 90 , for equal bias voltages, and Fig. 14(b) shows a phase shift of 54 , under detuning. The measured variation of the phase shift with the varactor bias voltage is presented in Fig. 15. When increasing the reverse bias voltage in one of the

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A. Series-Varactor Cell Initially, an analytical study of the series-varactor cell (Fig. 16) will be carried out. Taking into account the symmetry properties of the structure, the nodes and will be virtual short circuits at the subharmonic frequency, in analogous manner to the case of the original cell. Thus, at the circuit will be governed by the equation (36)

Fig. 14. Measured differential waveform for two different varactor bias voltages. (a) Phase shift 90 (b) Phase shift 54 .

Fig. 15. Measured variation of the phase-shift between the two divider circuits with the reverse bias voltage applied to the varactors of Divider B.

and has the same expression as where in (2). As gathered from the above equation, the dual cell exhibits an inductive effect which is four times that in the original cell (5). One obtains the same formal expression (14) for , though the definition of is different and given by . The different amplitude function will be emphasized with the notation . For a same value the minimum of will be obtained for a lower frequency than in the case of the original cell. To reduce the division threshold at a particular input frequency , one may choose an additional capacitive element , as in the case of the parallel cell, or an additional inductive element . In both cases, this additional element will be connected between the middle node of the parallel inductors and ground. In the case of a capacitive element , the equation governing the divider at the division threshold is the formally identical to (11), but replacing with . In the case of an additional inductor , the equation at the subharmonic component agrees with (36). However, the equation at the input frequency is different from (11). This equation, and the inductor that minimizes the input-amplitude threshold for are given by

(37) For

, one should use an additional capacitor

.

B. Dual-Band Divider

Fig. 16. Schematic of the series-varactor cell for frequency division at the lower band.

dividers, the phase shift decreases, though there is a near flat region in the middle. This detuning could only be performed in one sense, since the original (equilibrium) operation point corresponds to near zero varactor-bias voltage. IV. DUAL-BAND FREQUENCY DIVIDER The possibility to implement a dual-band frequency divider using an extension of the reflective topology will be investigated in this section. This will rely on the combination of the original cell, based on the parallel connection of the varactor diode, with a series-varactor cell, in which the diodes are in a series connection (Fig. 16).

The basic configuration of the dual-band divider consists of a series-varactor cell embedded between two parallel varactor cells, as shown in Fig. 18. In view of expressions (4) and (36), for given values of and , one can expect the parallel-varactor divider to operate at higher frequencies than the series-varactor one, due to the lower inductive effect. At these higher frequencies, the effect of the series-varactor cell will be initially neglected, since the impedances exhibited by its associated varactors and inductors will be low and high, respectively. Thus, in the higher frequency band, the configuration in Fig. 17 can be simplified as two parallel-varactor cells, responsible for the division at the higher frequency band. Their inductor and additional capacitor have been optimized according to the procedure described in Section II, imposing the central frequency GHz. The optimum values resulting from a HB-AG simulation with full diode models and harmonic terms are nH and pF. Next, the lower frequency division band will be considered. It is initially assumed that the components of two outermost cells can be neglected at this low frequency, so the circuit in

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Fig. 19. Influence of capacitor on the division bandwidth for fixed nH. (a) Sensitivity curves at the lower frequency band for intermediate and optimized values of . (b) Sensitivity curves at the upper frequency band. Measurements are superimposed. Fig. 17. Dual-band frequency divider. (a) Schematic. (b) Photograph of the mm). prototype built in Rogers 4003C substrate ( Output signals are extracted with a source-follower buffer based on the transistor NE3210S01.

Fig. 20. Variation of the subharmonic amplitude versus the input frequency in V. Measurements each of the two division bands, obtained for constant have been superimposed. Fig. 18. Input-sensitivity curves of the two dividers based on a series-varactor cell and two parallel-varactor cells optimized in HB in a separate manner, with harmonic components. The results are compared with those obtained harwhen simulating the full divider configuration in Fig. 17 with monic components.

Fig. 17 simplifies to a single series-varactor cell. For this single cell, the inductor is kept at nH, which centers the lower division band at GHz. Then the analytical expression (12) for the capacitor is used as an initial guess for the HB-AG optimization with 20 harmonic terms. The final capacitor value is pF. Fig. 18 presents the result of the individual analyses of the parallel-varactor divider (neglecting the series-varactor cell) and the series-varactor divider (neglecting the two parallel varactor cells). This result can be compared with the one obtained when performing a HB-AG simulation of the full divider in Fig. 17, taking into account the coupling between the two types of cells. The number of harmonic terms is in the three cases. To analyze the lower frequency band of the dual divider, the AG is connected in differential manner between the nodes and , corresponding to the series-varactor cell. To analyze the upper frequency band, the AG is connected in differential manner between the nodes and , of the parallel-varactor subcircuit [Fig. 17(a)]. The coupling tends to separate the bands but gives rise to a reduction

of the division thresholds, attributed to the presence of a higher number of varactor diodes in the two cases. As shown in Fig. 18, under coupled conditions the two division bands are centered about GHz and 3.97 GHz, respectively. Then the additional capacitors and of the two types of cells can be separately calculated to maximize the division bandwidth about each frequency. The resulting values are pF for the lower division band and pF for the upper division band. The corresponding input-sensitivity curves are shown in Fig. 19(a) and (b), where they can be compared with the ones obtained with a common , having an intermediate magnitude: pF. Measurements have been superimposed for both the original and optimized values. The output signal is extracted with a source-follower buffer based on the transistor NE3210S01. The solution curves in terms of the subharmonic amplitude have been calculated for the element values nH and pF in the series-varactor cell, and nH and pF, in the parallel-varactor cells. Results are shown in Fig. 20, where they can be compared with the measurement points. At V, the two division bandwidths are MHz and MHz at the low and high-frequency band respectively. Fig. 21(a) and (b) show the measured divided-solution waveforms obtained with the dual-band divider

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Fig. 21. Measured divided-solution waveforms obtained with the dual-band GHz. (b) GHz. divider. (a)

Fig. 23. Global operation of the dual-band frequency divider, analyzed in the and . (a) Effect of the variation of the to tune the plane defined by to tune the upper frelower frequency band. (b) Effect of the variation of quency band. Fig. 22. Phase-noise spectrum at the central frequencies of the two coexistent division bands. Each spectrum is compared with that of the input source. MeaGHz, in the lower surements are superimposed in the two cases. (a) GHz, in the higher division band. division band. (b)

at GHz and at GHz, respectively, both exhibiting a pronounced frequency division. Finally, the phase-noise spectrum at each of the two coexistent frequency-division bands, with respective input frequencies GHz and GHz, has been calculated and compared with the spectrum of the input source at each of the two frequencies. The results are shown in Fig. 22. The measured spectra are superimposed with good agreement. The respective corner frequencies are different, which can be attributed to differences in the three main magnitudes affecting the corner: and . C. Pre-Setting of the Two Division Bands

Fig. 24. Duplicated circuit for the optimization procedure. (a) Copy of the cir. (b) Copy cuit operating at the central frequency of the lower division band . of the circuit operating at the central frequency of the upper division band The two copies are simultaneously optimized with two AGs at and , in order to fulfill (38).

The possibility to center the two division bands at specified frequency and has been investigated. Due to the coupling effect, one cannot center one band without affecting the other. This is shown in the analysis of Fig. 23, with measurement superimposed. Variations in enable a large shift of the lower (upper) division band, with a smaller undesired shift in the upper (lower) band. To circumvent this problem, an optimization procedure has been developed, based on the simultaneous optimization of two identical copies of the circuit, with identical element values and (Fig. 24). The first circuit copy operates at the desired central frequency of the lower division band, , and is analyzed with an AG at , with an input-source phase . This AG is connected between the nodes of the series-varactor cell [Fig. 24(a)]. The second

circuit copy operates at the desired central frequency of the upper division band, , and is analyzed with an AG at , with an input-source phase . This AG is connected at one of the two parallel-varactor cells [Fig. 24(b)]. The two copies of the circuit are simultaneously analyzed with two-tone HB, at the two fundamental frequencies and , with 0 intermodulation order, since each circuit operates at a different frequency. Because the intermodulation order is 0, the analysis frequencies are the harmonics of and the harmonics of , so the computational cost is bearable. Because the aim is to preset the division threshold, the amplitude of the two AGs is set to

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Fig. 26. Use of conditions (38) to center the two division bands at the speciGHz and GHz. (a) Variation of two of fied frequencies , when decreasing . (b) Validation with an the optimization variables, independent analysis of the two division bands.

Fig. 25. Flowchart indicating the steps to be taken for the optimized design of the dual-band frequency divider.

very small value . Then the two circuits (with common design values) are simultaneously optimized to fulfil (38) with the pure two tone HB system as an inner tier. The initial values of the elements and are those resulting from the separate optimizations of the series-varactor cell and the parallel-varactor cell . On the other hand, the input sensitivity will be slightly different in each division band, so the input source should have different amplitude in each of the two copies of the circuit. The first (second) copy, operating at will have input amplitude . The initial values of and will correspond to those resulting from the initial separate optimization of the series-varactor divider and parallel-varactor divider, given by and , respectively. The complex system (38) is over-dimensioned, as it composed by two complex equations in six optimization variables, which should facilitate the convergence. The system forces the divider to operate at the two specified frequencies and . To actually center the two division curves about these values, one should reduce the division threshold and as much

as possible. This can be done by sweeping down the higher of the two magnitudes from the one obtained with the separate optimization (either or . System equation (38) is optimized at each sweep step. The different stages of the design procedure are indicated in the flowchart of Fig. 25. As an example, this procedure has been applied to center the two division bands at GHz and GHz. Fig. 26(a) shows the variation of the optimization elements that exhibit the largest variation when decreasing . The actual centering of the two division bands about and is demonstrated with an independent simulation of the divider, when operating at each of the two division bands [Fig. 26(b)]. As can be seen, with the simultaneous optimization it has been possibly to accurately center the “merged” dual-band divider at the specified frequencies and . V. CONCLUSION A design methodology for a recently proposed frequency-divider configuration based on varactor-inductor cell has been proposed. The method derives from an initial analytical study of a single-cell divider, which provides insight into the impact of the various circuit elements on the input-amplitude threshold and the frequency bandwidth. The inductors of the divider topology enable the shift of the frequency-division band and an additional capacitor enables the reduction of the input-amplitude threshold. With a higher number of cells, the two element types still enable these two separate actions, as has been verified with a full harmonic balance analysis, using an auxiliary generator at the divided frequency. Two different applications have been demonstrated: a dual-phase divider, based on the use of a Marchand balun, and a dual-band frequency divider,

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based on a novel configuration in which a series-varactor cell is embedded between two parallel-varactor cells. A simple synthesis method is presented to center the two division bands at the desired values. The techniques have been applied to three prototypes at 2.15 GHz, 1.85 GHz, and 1.75 GHz/3.95 GHz, respectively. REFERENCES [1] W. Lee and E. Afshari, “Low-noise parametric resonant amplifier,” IEEE Trans. Circuits Syst. I, vol. 58, no. 3, pp. 479–492, Mar. 2011. [2] W. Lee and E. Afshari, “Distributed parametric resonator: A passive CMOS frequency divider,” IEEE J. Solid-State Circuits, vol. 45, no. 9, pp. 1834–1844, Sep. 2010. [3] H. R. Rategh and T. H. Lee, “Superharmonic injection-locked frequency dividers,” IEEE J. Solid-State Circuits, vol. 34, no. 6, pp. 813–821, Jun. 1999. [4] R. Quere, E. Ngoya, M. Camiade, A. Suérez, M. Hessane, and J. Obregón, “Large signal design of broadband monolithic microwave frequency dividers and phase-locked oscillators,” IEEE Trans. Microw. Theory Techn., vol. 41, pp. 1928–1938, Nov. 1993. [5] A. Suárez, J. C. Sarkissian, R. Sommet, E. Ngoya, and R. Quere, “Stability analysis of analog frequency dividers in the quasi-periodic regime,” IEEE Microw. Guided Wave Lett., vol. 4, no. 5, pp. 138–140, May 1994. [6] A. Suárez and R. Quéré, Stability Analysis of Nonlinear Microwave Circuits. Boston, MA, USA: Artech House, 2003. [7] A. Suárez, Analysis and Design of Autonomous Microwave Circuits. Hoboken, NJ, USA: Wiley, 2009. [8] F. Ram´ırez, M. Pontón, S. Sancho, and A. Suárez, “Phase-noise analysis of injection-locked oscillators and analog frequency dividers,” IEEE Trans. Microw. Theory Techn., vol. 56, no. 2, pp. 393–407, Feb. 2008. [9] S. Qin, Q. Xu, and Y. E. Wang, “Nonreciprocal components with distributedly modulated capacitors,” IEEE Trans. Microw. Theory Techn., vol. 62, no. 10, pp. 2260–2272, Oct. 2014. [10] M. Pontón and A. Suárez, “Analysis of a frequency divider by two based on a differential nonlinear transmission line,” in IEEE MTT-S Int. Microw. Symp. Dig., Phoenix, AZ, USA, 2015, pp. 1–3. [11] S. A. Kian and I. D. Robertson, “Analysis and design of impedancetransforming planar Marchand baluns,” IEEE Trans. Microw. Theory Techn., vol. 49, no. 2, pp. 402–406, Feb. 2001. [12] L. Zhang and H. Wu, “A double-balanced injection-locked frequency divider for tunable dual-phase signal generation,” in Proc. IEEE Radio Frequency Integrated Circuits (RFIC) Symp., San Francisco, CA, USA, 2006. [13] V. Arana, A. Suarez, and P. Dorta, “Dual-band frequency divider based on oscillation control,” in IEEE MTT-S Int. Microw. Symp. Dig., Fort Worth, TX, USA, Jun. 2004, vol. 3, pp. 1501–1504. [14] J. Guckehnehimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. New York, NY, USA: Springer-Verlag, 1983. [15] [Online]. Available: [Online]. Available: http://www.skyworksinc. com/uploads/documents/SMV123x_Series_200058V.pdf [16] F. Ram´ırez, E. de Cos, and A. Suárez, “Nonlinear analysis tools for the optimized design of harmonic-injection dividers,” IEEE Trans. Microw. Theory Techn., vol. 51, no. 6, pp. 1752–1762, Jun. 2003.

[17] K. Kurokawa, “Noise in synchronized oscillators,” IEEE Trans. Microw. Theory Techn., vol. 16, no. 4, pp. 234–240, Apr. 1968. [18] J. M. Paillot, J. C. Nallatamby, M. Hessane, R. Quere, M. Prigent, and J. Rousset, “A general program for steady state, stability, and FM noise analysis of microwave oscillators,” in IEEE MTT-S Int. Microwave Symp. Dig., Dallas, TX, USA, 1990, pp. 1287–1290. [19] V. Rizzoli, F. Mastri, and D. Masotti, “General noise analysis of nonlinear microwave circuits by the piecewise harmonic-balance technique,” IEEE Trans. Microw. Theory Techn., vol. 42, no. 5, pp. 807–819, May 1994. [20] Y. Park, S. Chakraborty, C.-H. Lee, S. Nuttinck, and J. Laskar, “Wideband CMOS VCO and frequency divider design for quadrature signal generation,” in IEEE MTT-S Int. Microw. Symp. Dig., Fort Worth, TX, USA, Jun. 2004, vol. 3, pp. 1493–1496. [21] J. Jugo, J. Portilla, A. Anakabe, A. Suárez, and J. M. Collantes, “Closed-loop stability analysis of microwave amplifiers,” Electron. Lett., vol. 37, no. 4, pp. 226–228, 2001. Mabel Pontón (S'08–M'11) was born in Santander, Spain. She received the telecommunication engineering degree from the University of Cantabria, Santander, Spain, in 2004, and the Masters degree in information technologies and wireless communications systems and the Ph.D. degree, both from the University of Cantabria in 2008 and 2010, respectively. In 2006, she joined the Communications Engineering Department, University of Cantabria. From 2011–2013 she was with the Group of Electronic Design and Applications (EDA) at the Georgia Institute of Technology, Atlanta, GA, USA, as a Postdoctoral Research Fellow. Her research interests are focused on the nonlinear analysis and simulation of radiofrequency and microwave circuits, with emphasis on phase-noise, stability, and bifurcation analysis of complex oscillator topologies.

Almudena Suárez (M'96–SM'01–F'12) was born in Santander, Spain. She received the electronic physics and Ph.D. degrees from the University of Cantabria, Santander, Spain, in 1987 and 1992, respectively, and the Ph.D. degree in electronics from the University of Limoges, Limoges, France, in 1993. She is currently a Full Professor with the Communications Engineering Department, University of Cantabria. She coauthored Stability Analysis of Nonlinear Microwave Circuits (Artech House, 2003) and authored Analysis and Design of Autonomous Microwave Circuits (IEEE-Wiley, 2009). Prof. Suárez is a member of the Technical Committees of the IEEE Microwave Theory and Techniques Society (IEEE MTT-S) International Microwave Symposium (IMS) and the European Microwave Conference. She was an IEEE Distinguished Microwave Lecturer from 2006 to 2008. She is a member of the Board of Directors of the European Microwave Association. She is the Editor-in-Chief of the International Journal of Microwave and Wireless Technologies. She was the Cochair of IEEE Topical Conference on RF Power Amplifiers (PAWR) in 2014 and 2015.

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GaN Microwave DC–DC Converters Ignacio Ramos, Student Member, IEEE, María N. Ruiz Lavín, Student Member, IEEE, José A. García, Member, IEEE, Dragan Maksimović, Fellow, IEEE, and Zoya Popović, Fellow, IEEE

Abstract—This paper presents the design and characterization of dc–dc converters operating at microwave frequencies. The converters are based on GaN transistor class-E power amplifiers (PAs) and rectifiers. Three topologies are presented, which are: 1) a PA and synchronous rectifier, requiring two RF inputs; 2) a PA and self-synchronous rectifier with a single RF input; and 3) a power oscillator with a self-synchronous rectifier with no required RF inputs. The synchronous 1.2-GHz class-E converter reaches a maximum efficiency of 72% at 4.6 W. By replacing the RF input at the rectifier gate with a specific termination, a self-synchronous circuit demonstrates 75% efficiency at 4.6 W, with a maximum output power of 13 W at 58% efficiency. In the third topology, the PA is replaced by a power oscillator by providing correct feedback for class-E operation, resulting in a circuit requiring no RF inputs. This oscillating self-synchronous dc–dc converter is demonstrated at 900 MHz with an efficiency of 79% at 28 V and 12.8-W output power. Self-synchronous class-E transistor rectifier operation is analyzed theoretically in the time domain and validated with harmonic-balance simulations using an improved nonlinear model for a GaN HEMT. The simplified theoretical analysis provides a useful starting point for high-efficiency self-synchronous power rectifier design, which can, in turn, be extended to high-efficiency oscillating power inverter design. Index Terms—GaN, high-efficiency power amplifiers (PAs), high-frequency dc–dc converters, microwave rectifiers, RF circuits, switching PAs, ultrahigh-speed electronic circuits, VHF and UHF technology.

I. INTRODUCTION

T

HE SWITCHING speed of dc–dc converters has been increasing over the past five years, e.g., [1]–[3], with a goal of reduced size, faster transient response, and increased power density, which result from reduced values and sizes of passive Manuscript received June 30, 2015; revised September 04, 2015; accepted October 01, 2015. This work was supported in part by the Office of Naval Research under the Defense Advanced Research Projects Agency (DARPA) Microscale Power Conversion (MPC) Program under Grant N00014-11-1-0931, in part by the Advanced Research Projects Agency-Energy (ARPA-E), U.S. Department of Energy under Award DE-AR0000216, and in part by the Spanish Ministry of Economy and Competitiveness (MINECO) under Project TEC201129126-C03-01 and Project TEC2014-58341-C4-1-R with FEDER support. This paper is an expanded version from the IEEE MTT-S International Microwave Symposium, Phoenix, AZ, USA, May 17–22, 2015. I. Ramos, D. Maksimović, and Z. Popović are with the Department of Electrical, Computer and Energy Engineering, University of Colorado at Boulder, Boulder, CO 80309-0425 USA (e-mail: [email protected]; [email protected]; [email protected]). M. N. Ruiz Lavín and J. A. García are with the Department of Communications Engineering, University of Cantabria, 39005 Santander, Spain (e-mail: [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2015.2493519

TABLE I HIGH-FREQUENCY DC–DC CONVERTERS COMPARISON

components (inductors and capacitors). With increasing voltages and power densities enabled by wide-bandgap semiconductors such as GaN, monolithic integration towards a chipscale power supply becomes a possibility [4]. Higher switching frequencies are accompanied by reduced efficiency and attainable power levels since the losses in both passive and active components increase with frequency. In addition, parasitic reactances in the active devices and packages limit switching frequencies, as described in [1]. Table I presents an overview of high-frequency dc–dc converters and their respective efficiencies reported in the literature. In [5], a 30-MHz 200-W dc–dc converter operating at up to 200 V is demonstrated. A 23-W 87% efficient boost converter switching at 110 MHz is implemented using LDMOS technology in [6]. In [7], an integrated low-power four-phase buck converter is implemented in a 90-nm CMOS process with switching frequencies of 100–317 MHz. An off-chip air-core inductor is used in this case, resulting in efficiencies from 80% to 87%. In [3], a 100-MHz switching frequency buck converter is integrated together with its drive circuitry on a single 2.3 mm 2.3 mm chip in the TriQuint (Qorvo) 150-nm GaN on a SiC D-mode pHEMT process. This converter exhibits an efficiency of over 90% at 7 W. Two greater than 70% efficient class-E converters operating at 780 MHz and 1 GHz were demonstrated in [8] and [9]. Packaged and die 400-nm GaN HEMT devices from CREE were combined with high- coils and capacitors in hybrid circuit implementations. Wide-bandgap semiconductor devices, and in particular GaN HEMTs, enable high operating voltages at high frequencies, in contrast to circuits based on Si CMOS. Although very high power densities at the circuit level can be achieved with CMOS at lower frequencies (e.g., [6] and [7]), higher frequencies converters offer the potential for completely distributed implementations and fully monolithically integrated power supplies. Over two decades ago, as high as 64% efficiency was obtained with GaAs devices in a circuit based on transmission lines only, operating at 4.5 GHz at sub-watt power

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Fig. 2. Circuit schematic for class-E converter consisting of a class-E PA and rectifier coupled through a resonant network.

(2)

Fig. 1. Block diagram of high-frequency class-E dc–dc converter. (a) Synchronous topology, (b) self-synchronous topology with a single RF input at the inverter input, and (c) oscillating self-synchronous topology with no RF inputs.

[10], with both a power amplifier and a power oscillator as the inverter stage, and a dual-diode rectifier stage. Recently, a 1.2-GHz GaN converter demonstrated 75% efficiency at 5 W [11]. In this paper, we extend the concepts from [11] to two types of self-synchronous dc–dc converters implemented with GaN microwave transistors in hybrid circuits using a combination of distributed and lumped elements. The designs are based on a resonant class-E converter, first introduced in [12]. Fig. 1 illustrates the different converter topologies developed in this work, which are: (a) a synchronous topology; (b) a self-synchronous topology with a single RF input at the inverter input; and (c) a oscillating self-synchronous topology with no RF inputs. This paper is organized as follows. Section II presents the design and measured results for the well-known synchronous operation [9], [11], [12], implemented with GaN devices at 1.2 GHz. Section III develops a simplified theoretical analysis, as well as nonlinear harmonic-balance simulations of self-synchronous rectifiers using microwave GaN transistors. The measured results at 1.2 GHz are shown to be comparable to the synchronous version, but eliminate an entire RF part of the circuit. Section IV presents a slightly lower frequency converter (900 MHz) with no RF inputs. In this circuit, the inverter is an RF oscillator, and the rectifier is self-synchronous. The efficiency of this converter reaches nearly 80% with over 10 W of output dc power. II. SYNCHRONOUS CLASS-E OPERATION Well-known class-E PA design equations for the maximum frequency of operation and the class-E load presented at the virtual drain of the device are given by [13] (1)

where is the total output capacitance seen at the drain, is the input drive frequency (or switching frequency), and is the maximum dc current for a drain biasing voltage . Using the estimated value of pF for the T2G6001528-Q3 pseudomorphic HEMT (pHEMT) from TriQuint Semiconductor, V and A in (1), a maximum switching frequency of approximately 1.5 GHz is obtained. In order to account for additional parasitic capacitance and operate the class-E PA without sacrificing too much output power while maintaining a high switching frequency, a more conservative operating frequency of 1.2 GHz is chosen. The impedance to be synthesized by the matching network is calculated to be from [13]. As described in [14], the rectifier provides the correct value of and the reactances presented to the amplifier and the rectifier can be combined into one, resulting in . To synthesize at and provide an open circuit at and , the approach of [8] is adopted. The parasitic capacitance of a series inductor in Fig. 2 provides an approximately open circuit at and when the self resonance (SRF) is between the two harmonics, while a series capacitor tunes the impedance at the fundamental. To maintain a flat low circuit profile, only passive components with a maximum thickness of 2 mm are used. With this restriction, inductors from Coilcraft’s 0603HP series and capacitors from ATC’s 600L and 600S series are chosen. The inter-stage network is simulated using NI/AWR Microwave Office (MWO) with high-frequency models for the passive components provided by Modelithics. The design is implemented on a 30-mil Rogers RO4350B substrate, and a photograph of the prototype is shown in Fig. 3. The converter is characterized as shown in Fig. 4. The PA is biased at a quiescent current of 10 mA for input voltages ranging from 12 to 27 V, and the rectifier is pinched off. is implemented using a BK Precision 8500 electronic dc load in a constant voltage mode enforcing output voltages ranging from 10 to 27 V. All the measurements are performed with dBm. The phase shift is adjusted for synchronous operation. Fig. 5 shows the efficiency and output power as a function of output voltage for 13, 17, and 27 V. The efficiency of the converter is defined as

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Fig. 6. Simplified intrinsic model of a GaN HEMT. Diodes modeled as open circuits for self-synchronous analysis.

and

are

Fig. 3. Photograph of class-E converter prototype. The left side of the circuit is the class-E inverter and the right side is a synchronous rectifier. They are nH and coupled through the reactive network consisting of pF.

Fig. 7. Simplified switch model for class-E self-synchronous conditions. The and . is assumed switch is assumed to be ideal with is approximated as a sinusoid. The to be an ideal class-E waveform and is found under these conditions. unknown impedance

Fig. 4. Setup used to characterize the class-E converter prototype. The output voltage is enforced by the electronic load while the current is allowed to be set by the converter itself.

As expected, the output power in Fig. 5 increases with input voltage, while the efficiency of the converter decreases with increasing input and output voltage. III. SELF-SYNCHRONOUS RECTIFIER ANALYSIS AND OPERATION A number of recent publications show experimentally that at microwave frequencies, a transistor rectifier can be operated without the need of an RF input, referred to as self-synchronous operation [15]–[18]. This is mainly enabled by the drain-to-gate feedback capacitance . In a rectifier, the transistor operates in the third quadrant of its I–V curve [17], which is usually not taken into account in commercial nonlinear transistor models, making simulation impossible or unreliable. A. Theoretical Analysis of Self-Synchronous Rectifier

Fig. 5. Measured converter efficiency (red) and output power (blue) plotted as a function of output voltage for input voltages of 13, 17, and 27 V.

–

(3)

The goal of this analysis is to determine the theoretical value of the gate impedance that satisfies self-synchronous class-E rectification. Fig. 6 shows a simplified intrinsic model for an HEMT transistor [19]. When the transistor is pinched off, the two diodes can be approximated as open circuits. This is true when the dynamic load line keeps and below the forward-bias knee value. To investigate a class-E self-synchronous rectifier, the idealized circuit shown in Fig. 7 is considered. It assumes a sinusoidal input current source driving an ideal switch. The input current includes a negative dc term representing the rectified dc output current. The conditions for soft-switching class-E rectifier operation are , , and . For

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simplicity, the class-E time-reversed waveform [14], [20] is assumed across the switch, which can be expressed using the formulation in [13] as

(4)

represents the equivalent output capacitance when where the switch is off. The constants and are found as in [13] to be 1.862 and 32.48 , respectively. In addition to the classic class-E boundary conditions, for the rectifier to operate selfsynchronously, the voltage across should be less than the turn-off voltage of the transistor during the interval and greater than the turn-on voltage of the transistor during the interval . A simple approximation for is the following:

Fig. 8. RF–DC efficiency contours (red) and dc output power contours (blue) obtained in a load–pull simulation preformed at the gate port of a class-E selfsynchronous rectifier using an improved nonlinear GaN HEMT model [21]. ReV bias, , and an input power sults are obtained under a of 33 dBm (2 W). Impedance points a)–d) correspond to the impedance at the gate port for the dynamic load lines presented in Fig. 9.

(5) , and on for . From where the switch is off for Fig. 7, the current through capacitor can be written as (6) Kirchoff’s current law results in (7) When the switch is off, following (4)–(7), we obtain

B. Nonlinear Model Simulations

(8) When the switch is on, the voltage across the switch is 0, but the voltage across is not, hence the voltages across and are the same and (6) significantly simplifies. Following the previous procedure, during the interval , is found to be (9) The unknown load can now be found from the voltage and . It is easier to start with the interval when the switch is on. Since the current from (9) lags the voltage from (5) by , it is safe to assume that has to be inductive. To find the required equivalent inductance that imposes a class-E self-synchronous rectification, the current–voltage relationship is

(10) Solving for

which is the inductance required to resonate and in parallel. The value in (11), however, would short the output capacitance during the OFF-state, leading to a zero voltage across the switch. Resonating at a slightly higher frequency would ensure a finite and the desired class-E operation. Therefore, the idealized theoretical analysis gives the designer a starting point for choosing the gate termination for class-E synchronous rectification.

, (11)

To validate the above simplified analysis, ADS simulations of a semi-ideal class-E rectifier using harmonic balance are performed. An improved 8 75 m GaN HEMT model presented in [21] that accurately models , , , and the third quadrant of the transistor’s I–V curve is used in the simulations. The model used in the simulations does not correspond to the GaN HEMT used in the design of the class-E converter shown in Fig. 3. The simulation involves ideal bias-tees and an ideal tuner presenting an open circuit at , , , and and the impedance given by (2) at for pF and GHz. The dc load is set equal to 90 and the transistor is biased in pinch off with V. A load–pull was performed at the gate port of the rectifier to find the impedance that achieves maximum RF–dc convertion efficiency and maximum output power for an input power of 33 dBm (2 W). The optimum impedance is found to be approximately , which represents the reactance of a 11.9-nH inductor at 1.2 GHz. Fig. 8 shows the dc output power (blue) and efficiency (red) contours resulting from the simulated load–pull. The maximum efficiency is 66.7% with a dc output power of 31.14 dBm. Fig. 9 shows the dynamic load line for the respective impedance points a)–d) marked in Fig. 8. The contours and the dynamic load lines clearly illustrate how the performance of the rectifier diminishes as the equivalent reactance presented to the input of the GaN HEMT fails to approximately resonate . Impedance a) in Fig. 8 is the

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Fig. 10. Simulated nonlinear capacitance as a function of 75 m GaN HEMT model [21] used in Section II.

for the 8

Fig. 9. Simulated dynamic load line (red) corresponding to impedance points a)–d) in Fig. 8. The blue line shows the I–V curves for the quiescent bias V .

optimum impedance that minimizes power dissipation by approximating an ideal diode, as shown in Fig. 9(a). When the transistor is off and the voltage swings positively, the transistor should block the voltage and operate on the region along the axis. To ensure this, swings deeper into the pinch-off region as increases. As decreases toward 0 due to the resonant nature of the output network, increases and approximates the operating (I–V) characteristics of an ideal conducting diode near the axis in the third quadrant. As the impedance gets farther away from the equivalent reactance necessary to approximately resonate , more power is dissipated because the transistor momentarily conducts when the switch should be off, as shown in Fig. 9(b)–(d). The performance degrades as the impedance resonates and below , as in Figs. 8(d) and 9(d). Thus, the impedance presented to the gate should resonate at a slightly higher frequency than , as discussed in Section III-A and (11), as well as to account for nonlinearities of and . For the simulated design, is highly nonlinear with a profile plotted in Fig. 10. also varies as a function of from a minimum of pF at V to a maximum of 0.47 pF at V. Using the maximum value of those two capacitances and the equivalent inductor presented by the optimum impedance, the resonant frequency is pF

pF

nH

GHz (12)

which is only slightly larger than the switching frequency of 1.2 GHz. It is important to note that as the two nonlinear capacitances change with , the presented impedance will always resonate at a higher frequency than the switching frequency. Fig. 11 shows the time-domain waveforms at the intrinsic drain and at the intrinsic gate of the transistor for varying input powers (4–34 dBm) when the gate impedance is at point a) in Fig. 8. The waveforms show approximate class-E current and voltage waveforms at the intrinsic drain minimizing current and

Fig. 11. Time-domain waveforms of class-E rectifier. Voltage and current waveforms at: (a) intrinsic gate and (b) intinsic drain. Waveforms are shown for input powers varying from 0 to 35 dBm in dB steps.

voltage overlap as well as the corresponding voltage and current across the input capacitor . The voltage simulated in Fig. 11(a) approximates the sinusoidal voltage assumed in (5). Fig. 12 shows the dynamic load lines for the corresponding power levels of Fig. 11, which approximate behavior of an ideal diode. C. Class-E DC–DC Converter With Self-Synchronous Rectifier In order to implement a self-synchronous rectifier in the class-E converter, a load–pull is performed at the gate port

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Fig. 12. Simulated dynamic load line (red) and I–V curves of quiescent bias (blue) for class-E self-synchronous rectifier for an input power range of 0–35 resonating equivalent input capacitance at 1.22 GHz. As expected, dBm with the transistor minimizes power dissipation and approximates an ideal diode.

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Fig. 14. Comparison between the impedance presented by the rectifier’s input matching network EM simulated (brown) and the ideal 2.07-nH inductor (blue) required to resonate the 8.5-pF input capacitance of the T2G6001528 transistor model. The figure shows the impedance of the matching network closely follows the impedance of the ideal inductor around the switching frequency.

Fig. 15. Photograph of class-E converter with the rectifier operating self-synchronously. The RF port at the gate of the rectifier is removed and the input matching network is modified to present the optimum impedance to the rectifier. The size of the circuit board is 5.6 cm 6 cm. Fig. 13. Impedance constellation and efficiency contours produced by a load–pull performed at the gate port of the rectifier for maximum efficiency for a dc output voltage of 17 V. The Smith chart is normalized to 50 .

of the rectifier for maximum efficiency at an input voltage of 13, 17, and 27 V. The optimum impedance is not significantly affected by the output voltage. The results for 17 V are plotted in Fig. 13 with the optimum impedance found to be approximately at the connector reference plane. A length of transmission line and an 8-pF shunt capacitor to ground are used to present this impedance to the transistor. The equivalent input capacitance of the transistor is estimated using a nonlinear model to be 8.5 pF. Following the theory presented in this paper, the impedance that the matching network of the rectifier presents to the input of the transistor should resonate the 8.5 pF a little bit above the switching frequency of 1.2 GHz. Fig. 14 plots an electromagnetic (EM) simulation of this impedance and the impedance of an ideal 2.07-nH inductor necesary to resonate the 8.5 pF at 1.2 GHz. Fig. 14 clearly shows the impedance of the matching network follows that of the inductor, supporting the theory. A prototype of a self-synchronous converter is shown in Fig. 15. The converter is characterized following the previously described procedure without the need of a second RF driver for the rectifier. Fig. 16 shows the efficiency and output power as a function of output voltage for 13, 17, and 27 V. The results are

Fig. 16. Measured self-synchronous classconverter efficiency (red) and output power (blue) as a function of output voltage for input voltages of 13, 17, and 27 V.

improved compared to those of Fig. 5. The converter is the most efficient at 13-V input voltage and at lower output voltages in general, achieving an efficiency above 70% for output voltages

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Fig. 18. Photograph of oscillating self-synchronous class-E dc–dc converter. Fig. 17. Circuit schematic for self-oscillating self-synchronous classconverter.

dc–dc

ranging from 11 to 17 V, with a maximum efficiency of 75% and 4.6 W compared to the 72% efficiency of the converter from Section II. The improvement can be attributed to a shift in the value of the passive components used in the resonator, specifically the inductors that have a 5 tolerance.

the class-E oscillating inverter with some modifications. Substituting the current source in Fig. 7 by to account for the dc current supplied to the inverter, (4) becomes

(13)

while (8) becomes IV. OSCILLATING SELF-SYNCHRONOUS OPERATION CLASS-E CONVERTER

OF

Turning the PA of the converter into a free-running power oscillator becomes a logical highly desirable step toward a self-driving microwave frequency resonant dc–dc converter, as in Fig. 1(c), eliminating the RF input. A similar MOSFET 2-MHz converter was published in [22] using a class-E oscillator design procedure introduced in [23]. The converter achieved 78.9% under 1.55-W output power using a feedback inductor to force the oscillation of the class-E inverter. In [10], a sub-watt 4.6-GHz class-E oscillator was demonstrated with a diode rectifier. In this section, we demonstrate the architecture of Fig. 1(c) in a class-E GaN dc–dc converter operating around 900 MHz. In Fig. 17, the circuit schematic for the implemented oscillating self-synchronous class-E converter, based on the CGH35030F packaged GaN HEMT from Cree Inc., is presented. The change to a higher power device and lower frequency allows for higher output power and efficiency and demonstrates feasibility of the approach. The design procedure is very similar to the one described in Section I and is described in [9]. In order to interconnect the inverting and rectifying devices, an inductor and two capacitors are employed. Harmonic terminations at and are achieved as previously discussed through the self-resonance of , while the choice of allows for reactance adjustment at the fundamental. An open-circuit stub , a high-value capacitor to ground , and a length of transmission line are combined in order to synthesize the required gate impedance condition at the fundamental to operate the rectifier self-synchronously. The simplified theoretical analysis from Section III can be applied to

(14) The remaining equations remain unchanged. However, solving for and results in 1.862 and 32.48 , respectively. These correspond to the time-reversed waveforms of the class-E rectifier as in [13]. Since (11) remains unchanged, the conclusions obtained from Section III apply to the class-E oscillator as well. Hence, the impedance presented to the gate of the transistor should correspond to an equivalent reactance capable of resonating at a frequency slightly above the switching frequency to ensure the desired class-E soft-switching operation. For that reason, a gate matching network mirroring that of the self-synchronous rectifier was implemented in Fig. 17. A photograph of the oscillating self-synchronous converter is shown in Fig. 18. The oscillator gate biasing voltage is used to initiate the oscillation by increasing the voltage above pinch-off. Once the oscillation starts, the voltage is lowered to a value approximately equal to that of the self-synchronous rectifier, where the maximum efficiency can be obtained [24]. The converter is characterized in a modified setup of the one shown in Fig. 4; the main difference is the absence of any RF input source. The electronic load providing a constant dc output voltage is changed to a passive 50- load due to lower frequency oscillations produced by the electronic load. The rectifier was biased in pinch off 4.0 V, while the bias of the oscillator was increased until an oscillation is produced at around 3 V. Fig. 19 shows efficiency and dc output power for input voltages of 28, 22, and 17 V, as a function of output voltage.

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Fig. 19. Measured performance of oscillating self-synchronous class-E dc–dc converter. Converter efficiency (red) and output power (blue) plotted as a function of output voltage for input voltages of 17, 22, and 28 V.

The oscillating self-synchronous converter can only operate as a buck converter since the oscillations subside when the output voltage becomes higher than the input voltage, and hence, more attention was given to higher input voltages. The converter is 79% efficient at an input voltage of 28 V and an output power of 12.8 W. As expected, output power is directly proportional to input voltage, but efficiency is maintained above 70% for an input voltage range of 11–28 V. Output voltage control can be accomplished by frequency modulation (FM) through the oscillator’s gate biasing voltage, due to the input capacitance variation with in a GaN HEMT, as shown in Section III. This dependence can be exploited to control the output voltage of the converter for varying loads. When V, the frequency of oscillation starts around 920 MHz, and increases as the voltage decreases. At V, the oscillation disappears, reaching a frequency of 1040 MHz. The FM control is possible thanks to the detuning of the resonant interconnecting network, as is typical of class E converters. Fig. 20 shows efficiency and output power as a function of when the output voltage is controlled through to be 22, 17, and 12 V. FM presents a viable alternative for open or closed loop output voltage control, however, performance of the converter degrades at higher loads and lower voltages.

V. DISCUSSION AND CONCLUSION In this paper, a series of microwave dc–dc converters that operate around 1 GHz switching frequency with efficiencies greater than 70% at greater than 5-W output power have been demonstrated. A loss budget for the oscillating self-synchronous converter has been given in Table II. The losses were estimated from simulations since it is difficult to measure the separate sub-circuits at gigahertz frequencies. The simulations were performed for V, V, a dc load of 24 ,

Fig. 20. Measured performance of control through for oscillating self-synchronous converter. Input voltage is 28 V while output voltage is adjusted to 12, 17, and 22 V.

TABLE II ESTIMATED LOSSES BASED ON SIMULATION

and an operating frequency of 950 MHz. The converter was 80% efficient and the losses were distributed, as shown in Table II. The biggest contributor to the dissipated power is the transistor’s resistance for both the PA and the rectifier. Most of the losses in the passive elements came from power dissipated in the inductors. Estimated losses for the 1.2-GHz class-E converter from Fig. 15 showed a similar distribution. For the first time, an in-depth theoretical analysis of the operation of class-E self-synchronous transistor rectifiers has been derived. The idealized theoretical analysis has been validated with harmonic-balance simulations using an improved GaN HEMT nonlinear model. The procedure to design a self-synchronous rectifier by resonating the equivalent input capacitance slightly above the switching frequency provides the designer with a useful starting point for the design of a microwave dc–dc converter and self-synchronous rectifiers. The analysis has been validated for transistor rectifiers other than class-E, with some examples shown for a class-B circuit in [16] and a class F circuit in [15]. Finally, the analysis has been extended to the

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design of a oscillating self-synchronous class-E dc–dc converter. A oscillating self-synchronous Buck converter with no RF inputs has been demonstrated and characterized. The converter maintains an efficiency above 70% for input voltages of 11–28 V across a load of 50 .

ACKNOWLEDGMENT The authors would like to thank TriQuint Semiconductors (now Qorvo), as well as CREE Inc., for transistors donations. The authors also wish to thank Dr. T. Reveyrand for his advice regarding measurements and nonlinear modeling.

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[19] P. Cabral, J. Pedro, and N. Carvalho, “Nonlinear device model of microwave power GaN HEMTs for high power-amplifier design,” IEEE Trans. Microw. Theory Techn., vol. 52, no. 11, pp. 2585–2592, Nov. 2004. [20] N. Sokal, “Class E-A new class of high-efficiency tuned single-ended switching power amplifiers,” IEEE J. Solid-State Circuits, vol. SSC-10, no. 3, pp. 168–176, Jun. 1975. [21] O. Jardel et al., “A new nonlinear HEMT model for ALGaN/GaN switch applications,” in Eur. Microw. Integr. Circuits Conf., Sep. 2009, pp. 73–76. [22] H. Hase et al., “Resonant DC/DC converter with class E oscillator,” in IEEE Int. Circuits Syst. Symp., 2005, vol. 1, pp. 720–723. [23] H. Hase et al., “Novel design procedure for MOSFET class E oscillator,” in 47th Midwest Circuits Syst. Symp., Jul. 2004, vol. 1, pp. I-33–6. [24] S. Jeon, A. Suarez, and D. Rutledge, “Nonlinear design technique for high-power switching-mode oscillators,” IEEE Trans. Microw. Theory Techn., vol. 54, no. 10, pp. 3630–3640, Oct. 2006.

REFERENCES [1] D. Perreault et al., “Opportunities and challenges in very high frequency power conversion,” in 24th Annu. IEEE Appl. Power Electron. Conf. and Expo., Feb. 2009, pp. 1–14. [2] J. Hu et al., “High-frequency resonant SEPIC converter with wide input and output voltage ranges,” IEEE Trans. Power Electron., vol. 27, no. 1, pp. 189–200, Jan. 2012. [3] Y. Zhang, M. Rodriguez, and D. Maksimovic, “100 MHz, 20 V, 90% efficient synchronous buck converter with integrated gate driver,” in IEEE Energy Conv. Congr. and Expo., Sep. 2014, pp. 3664–3671. [4] R. Foley et al., “Technology roadmapping for power supply in package (PSiP) and power supply on chip (PwrSoC),” in IEEE Appl. Power Electron. Conf. and Expo., 2010, pp. 525–532. [5] J. M. Rivas et al., “A very high frequency DC–DC converter based resonant inverter,” in IEEE Power Electron. Specialists on a class Conf., 2008, pp. 1657–1666. [6] R. C. N. Pilawa-Podgurski et al., “Very-high-frequency resonant boost converters,” IEEE Trans. Power Electron., vol. 24, no. 6, pp. 1654–1665, Jun. 2009. [7] P. Hazucha et al., “A 233-MHz 80%–87% efficient four-phase DC–DC converter utilizing air-core inductors on package,” IEEE J. Solid-State Circuits, vol. 40, no. 4, pp. 838–845, Apr. 2005. [8] J. A. Garcia, R. Marante, and M. N. Ruiz, “GaN HEMT class E resonant topologies for UHF DC/DC power conversion,” IEEE Trans. Microw. Theory Techn., vol. 60, no. 12, pp. 4220–4229, Dec. 2012. [9] J. A. García et al., “A 1 GHz frequency-controlled class E DC/DC converter for efficiently handling wideband signal envelopes,” in IEEE MTT-S Int. Microw. Symp. Dig., 2013, pp. 2–5. [10] S. Djukic, D. Maksimovic, and Z. Popović, “A planar 4.5-GHz DC–DC power converter,” IEEE Trans. Microw. Theory Techn., vol. 47, no. 8, pp. 1457–1460, Aug. 1999. [11] I. Ramos et al., “A planar 75% efficient 1.2-GHz DC–DC converter with self-synchronous rectifier,” in IEEE MTT-S Int. Microw. Symp. Dig., May 2015. [12] J. Józwik and M. K. Kazimierczuk, “Analysis and design of class E DC/DC converter,” IEEE Trans. Ind. Electron., vol. 37, no. 2, pp. 173–183, Apr. 1990. [13] T. Mader et al., “Switched-mode high-efficiency microwave power amplifiers in a free-space power combiner array,” IEEE Trans. Microw. Theory Techn., vol. 46, no. 10, pp. 1391–1398, Oct. 1998. [14] D. C. Hamill, “Time reversal duality and the synthesis of a double class E DC–DC converter,” in IEEE Power Electron. Specialists Conf., 1990, pp. 512–521. [15] M. Roberg et al., “High-efficiency harmonically-terminated diode and transistor rectifiers,” IEEE Trans. Microw. Theory Techn., vol. 60, no. 12, pp. 1–9, Dec. 2012. [16] M. Litchfield et al., “High-efficiency X-band MMIC GaN power amplifiers operating as rectifiers,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2014, pp. 1–4. [17] T. Reveyrand, I. Ramos, and Z. Popović, “Time-reversal duality of high-efficiency RF power amplifiers,” IET Electron. Lett., vol. 48, pp. 1607–1608, 2012. [18] M. N. Ruiz and J. A. García, “An E-pHEMT self-biased and self-synchronous class-E rectifier,” in IEEE MTT-S Int. Microw. Symp. Dig., May 2014, pp. 1–4.

Ignacio Ramos (S’12) received the B.S. degree in electrical engineering from the University of Illinois at Chicago, Chicago, IL, USA, in 2009, the M.S. degree from the University of Colorado at Boulder, Boulder, CO, USA, in 2013, and is currently working toward the Ph.D. degree at the University of Colorado at Boulder. From 2009 to 2011, he was with the Power and Electronic Systems Department, Raytheon IDS, Sudbury, MA, USA, during which time he was involved in power systems for radars, dc–dc converters, and renewable energy systems. His research interests include high-efficiency microwave power amplifiers, RF and microwave dc–dc converters, radar systems, wireless power transmission, and wireless propagation.

María N. Ruiz Lavín (S’12) was born in Santander, Spain, in 1983. She received the Telecommunication Engineering degree and M.sC degree from the University of Cantabria (UC), Santander, Spain, in 2010 and 2013, respectively, and is currently working toward the Ph.D. degree at the University of Cantabria. She is currently with the Department of Communications Engineering (DICOM), University of Cantabria. Her research interests include high-efficiency microwave power amplifiers, rectifiers, oscillators, and dc/dc converters.

José A. García (S’98–A’00–M’02) was born in Havana, Cuba, in 1966. He received the Telecommunications Engineering degree from the Instituto Superior Politécnico “José A. Echeverría” (ISPJAE), Havana, Cuba, in 1988, and the Ph.D. degree from the University of Cantabria, Santander, Spain, in 2000. From 1988 to 1991, he was a Radio System Engineer with a high-frequency (HF) communication center, where he designed antennas and HF circuits. From 1991 to 1995, he was an Instructor Professor with the Telecommunication Engineering Department, ISPJAE. From 1999 to 2000, he was with Thaumat Global Technology Systems, as a Radio Design Engineer involved with base-station arrays. From 2000 to 2001, he was a Microwave Design Engineer/Project Manager with TTI Norte, during which time he was in charge of the research line on software-defined radios (SDRs) while involved with active antennas. From 2002 to 2005, he was a Senior Research Scientist with the University of Cantabria, where he is currently an Associate Professor. During 2011, he was a Visiting Researcher with the Microwave and RF Research Group, University of Colorado at Boulder. His main research interests include nonlinear characterization and modeling of active devices, as well as the design of RF/microwave power amplifiers, wireless powering rectifiers, and RF dc/dc converters.

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Dragan Maksimović (M’89–SM’04–F’15) received the B.S. and M.S. degrees in electrical engineering from the University of Belgrade, Belgrade, Serbia, in 1984 and 1986, respectively, and the Ph.D. degree from the California Institute of Technology, Pasadena, CA, USA, in 1989. From 1989 to 1992, he was with the University of Belgrade. Since 1992, he has been with the Department of Electrical, Computer, and Energy Engineering, University of Colorado at Boulder, Boulder, CO, USA, where he is currently a Professor and Director of the Colorado Power Electronics Center (CoPEC). He has coauthored over 250 publications and the textbook Fundamentals of Power Electronics (Springer, 2001). His current research interests include mixed-signal integratedcircuit design for control of power electronics, digital control techniques, as well as energy-efficiency and renewable energy applications of power electronics. Dr. Maksimović currently serves as an associate editor for the IEEE TRANSACTIONS ON POWER ELECTRONICS and as an editor for the IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN POWER ELECTRONICS. He was the recipient of the National Science Foundation (NSF) CAREER Award in 1997, the IEEE TRANSACTIONS ON POWER ELECTRONICS Prize Paper Award in 1997, the IEEE PELS Prize Letter Awards in 2009 and 2010, the University of Colorado Inventor of the Year Award in 2006, the IEEE PELS Modeling and Control Technical Achievement Award in 2012, the Holland Excellence in Teaching Award in 2004 and 2011, the Charles Hutchinson Memorial Teaching Award in 2012, and the 2013 Boulder Faculty Assembly Excellence in Teaching Award.

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Zoya Popović (S’86–M’90–SM’99–F’02) received the Dipl.Ing. degree from the University of Belgrade, Serbia, Yugoslavia, in 1985, and the Ph.D. degree from the California Institute of Technology, Pasadena, CA, USA, in 1990. Since 1990, she has been with the University of Colorado at Boulder, Boulder, CO, USA, where she is currently a Distinguished Professor and holds the Hudson Moore Jr. Endowed Chair with the Department of Electrical, Computer and Energy Engineering. In 2015, she was named the Distinguished Research Lecturer of the University of Colorado at Boulder. From 2001 to 2003 and in 2014, she was a Visiting Professor with the Technical University of Munich, Munich, Germany, and the ISAE, Toulouse, France, respectively. Since 1991, she has graduated 50 Ph.D. students and currently leads a group of 15 doctoral students and 4 Post-Doctoral Fellows. Her research interests include high-efficiency transmitters for radar and communication, low-noise and broadband microwave and millimeter-wave circuits, antenna arrays, wireless powering for batteryless sensors, and medical applications of microwaves such as microwave core-body thermometry and traveling-wave magnetic resonance imaging (MRI). Prof. Popović was the recipient of the 1993 and 2006 IEEE Microwave Theory and Techniques Society (IEEE MTT-S) Microwave Prize for the best journal paper and the 1996 URSI Issac Koga Gold Medal. In 1993, she was named a National Science Foundation (NSF) White House Presidential Faculty Fellow. In 1997, Eta Kappa Nu students chose her as a Professor of the Year. She was the recipient of a 2000 Humboldt Research Award for Senior U.S. Scientists from the German Alexander von Humboldt Stiftung. She was elected a Foreign Member of the Serbian Academy of Sciences and Arts in 2006. She was also the recipient of the 2001 Hewlett-Packard (HP)/American Society for Engineering Education (ASEE) Terman Medal for combined teaching and research excellence. In 2013, she was named an IEEE MTT-S Distinguished Educator.

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Common-Base/Common-Gate Millimeter-Wave Power Detectors Ayssar Serhan, Estelle Lauga-Larroze, and Jean-Michel Fournier

Abstract—The principle of two common base/gate millimeter-wave power detectors is analyzed and validated by experimental results. The detectors have been designed for automatic level control and built-in-test millimeter-wave applications. Closed-form expressions are derived for the transfer characteristic as well as for the noise behavior of each detector. The circuits are fabricated in a BiCMOS 55 nm ( 320 GHz/370 GHz) process from STMicroelectronics. Each detector occupies an area of 80 80 m and exhibits a relatively high input impedance at 60 GHz. Measurements show a detection dynamic range larger than 38 dB and a flat response over the 50–66 GHz bandwidth, for both detectors. Common-base detector shows a wider linear detection range than that of the common-gate one. Theoretical computation and computer simulation show that, for square-law detection, the minimum detectable input power (for SNR 10 dB) is around 41 dBm for the common-gate detector against 50 dBm for the common-base one. In their nominal bias conditions, the detectors' power consumption, under 1.2 V supply voltage, is 90 W for low input power and it increases to about 800 W for 8.5 dBm input power. These performances are beyond the current state-of-the-art of millimeter-wave detectors. Index Terms—Bipolar, CMOS, detectors, millimeter waves, RFIC.

I. INTRODUCTION

I

N THE PAST few years, the feasibility of high-performance millimeter-wave (mmWave) fully integrated transceivers has been widely demonstrated in both CMOS and BiCMOS technologies [1], [2]. This growth has created a large demand for mm-wave built-in-self-test (BIST) and automatic level control (ALC) solutions. In fact, test cost reduction is one of the main challenges that has to be solved while switching from low volume to mass production. Hence, BIST solutions and in-situ characterization, which use integrated power detectors to provide a low-frequency signal, are the best candidates that can ensure high yield while holding low cost [3]. These solutions reduce the overall test cost since a low-frequency measurement can be made using low-cost instrumentation Manuscript received July 02, 2015; revised September 15, 2015; accepted October 22, 2015. Date of publication November 11, 2015; date of current version December 02, 2015. This work was performed in the RF2THZ SiSoC project of the EUREKA program CATRENE in which the G-INP partner is funded by the DGCIS, France. This paper is an expanded version from the IEEE MTT-S International Microwave Symposium, Phoenix, AZ, USA, May 17–22, 2015. A. Serhan is with the DACLE Department, CEA-LETI, Minatec, 38054 Grenoble, France (e-mail: [email protected]). E. Lauga-Larroze and J.-M. Fournier are with the IMEP-LAHC Laboratory, UMR INPG/UJF/US/CNRS 5130, 38016 Grenoble, France (e-mail: [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2015.2496220

Fig. 1. Power detector sensitivity versus operating frequency in state-of-the-art of CMOS and BiCMOS detectors.

(voltmeter, oscilloscope) instead of high-cost automatic test equipment (ATE) [4], [5]. On the other side, most communication systems require careful management of the signal power to maintain the desired performance and reliability constraints. In such applications, the detector's output is fed back into an analog circuit that controls optimal sensitivity, selectivity, and dynamic range. Figs. 1 and 2 show the trend of the sensitivity and dynamic range of the RF/mmWave power detectors fabricated in CMOS and BiCMOS technologies. We can clearly see the degradation of both the sensitivity and dynamic range of the detectors in the mmWave frequency band. Moreover, detectors that use bipolar transistors have, globally, better performances as compared to their CMOS counterpart. These data [3]–[24] are detailed in Table I. Most of these power detectors are made using one of the following topologies: (i) common-source MOS transistor operating in triode regime benefiting from the non-linear channel resistance [14]; (ii) common-source MOS transistor in strong inversion regime (using the square-law nature of characteristics) [3], [12]; (iii) base-emitter diode non-linear characteristic of a common emitter bipolar transistor [3], [6]; (iv) dynamic translinear circuit with current multiplication principle [23]. Furthermore, bolometer-based power detection is explored in [1]. For this latter, additional technology masks are added to enable the integration of resistors with special temperature characteristics [10]. Particularly, the CMOS detector proposed in

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TABLE I SUMMARY OF THE STATE-OF-THE-ART OF RF/MILLIMETER-WAVE POWER DETECTORS

Fig. 2. Power detector dynamic range versus operating frequency in state-ofthe-art of CMOS and BiCMOS detectors.

[12] has good performances in terms of dynamic range and sensitivity while holding small area and relatively low power consumption. However, its output bandwidth is limited to 100 MHz. On the other side, the BiCMOS detector proposed in [6] has a good dynamic range and sensitivity along with a wide output

bandwidth (around 1 GHz), but it occupies a relatively large silicon area. This paper presents the study and realization of two commonbase/gate power detectors. The CMOS detector with commongate configuration was explored by [4] and used, in its linear detection region, as an envelope detector for BIST applications at 2.4 GHz. In this paper, we demonstrate that this detector can operate either as an envelope detector in linear regime (for high power levels) or in square-law regime (for low power levels). In addition, the BiCMOS version of the detector is developed by replacing the common-gate NMOS transistor with a commonbase bipolar transistor [25]. This paper extends the work published in [25]. The extension includes the comparison between the common-gate and the common-base detectors, a detailed analysis of the transfer characteristics as well as the noise behavior of the detectors, and an explicit explanation of the measurements data. The paper is organized as follows. In Section I, the transistor-level design and the operating principles of the two detectors are described. Analytical equations of the transfer characteristics of the detectors in their different operating regimes are derived. In addition, a noise study is done and used to express the detectors sensitivity in function of the different components parameters. Section III compares the experimental results of the

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Fig. 3. Schematic of the BiCMOS common-base detector including noise sources.

Fig. 4. Schematic of the CMOS common-gate detector including noise sources.

two detectors realized in the same BiCMOS technology. Finally, conclusions are presented in Section IV.

to the square root of the input RF power. This analysis will be demonstrated in the next part using analytical expressions.

II. THEORETICAL STUDY In this section, the operating principles of the two detectors are presented. Next, the theoretical equations describing the mechanism of detection as well as the noise behavior will be derived. Figs. 3 and 4 show the schematics of the proposed detectors including all the noise sources that will be considered during the noise analysis. The input detection stage is composed of a bipolar/NMOS transistor in common-base/gate configuration. The input capacitor allows blocking DC signal. For the BiCMOS detector, transistor is biased via at a low static current density of A m (where is the emitter area of ) that corresponds to the threshold voltage for forward conduction of the emitter-base (EB) diode. Similarly, for the CMOS detector, the static current density (where is the channel width of ) is set to A m so that the transistor is biased in subthreshold region. Hence, its drain current has exponential characteristic similar to that of the transistor in the BiCMOS detector. The size of is chosen small in order to reduce the input capacitance and to maintain the input impedance at a high level. The current in is amplified by the current mirror ( ) and converted into voltage through the resistor . Finally, the low-pass filter ( , ) integrates the output voltage and produces a constant DC signal. The value of contributes to the output bandwidth, the conversion gain and the upper limit of the detection range. The upper limit is mainly limited by the saturation effect of the transistor . Relative to the input RF signal power, each of the detectors can operate either as a square-law detector or as a linear detector. For low input power levels, the square-law approximation of the collector/drain current of leads to a linear relation between the input power and the output DC voltage. For large signal conditions, the transistors operate as rectifiers where are turned off during the positive half-cycle of and are conducting during the negative half cycle of . Hence, the output DC voltage of the detectors is proportional

A. Analytical Study of the Transfer Characteristics To analyze the behavior of the detectors, we assume an input RF signal applied to the base/gate of the transistor : (1) For low input power, the transistor of the CMOS detector works in subthreshold region having an exponential current behavior similar to . Hence, the current in and are formulated as and

(2)

and are the non-ideality factor of and , respectively. is the static DC current (in absence of input power) and is the thermal voltage: at

(3)

Note that the average value of the current depends on the input power level. By expending the exponential part of the current , for low input power levels ( ), using Taylor series, the total current in can be approximated by (4) The first-order term is a high-frequency component, around , and it will be eliminated by the output RC filter. The secondorder term has two main components: a high-frequency component around , which can eliminated by the output RC filter, and a DC component. The final equation of the filtered current is given by (5)

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where represents the wanted incremental component, in the average current, caused by the presence of input power. The transconductance of the transistor is given by (6), and assumed to be constant for low input power levels ( ):

the BiCMOS detector even by considering the increase of the DC current in . For large signal value of , the transistor works as a rectifier. Hence, the resulting DC current in and can be described by (13) where

(6) The incremental current is amplified by the current mirror ( , ) leading to the following final output current equation:

holds for the average transconductance of during the input signal period. Note that (13) is obtained by assuming that the RF current is equal to the current in . Finally, the output incremental voltage for large-signal detection is given by

(7)

(14)

Finally, the incremental component in the output signal voltage ( ) can be described by (8), where is the output impedance of the detector:

For large input signal, the output voltage of the detectors varies proportionally to the square root of the RF input power (i.e., linear region). Finally, the input signal strength level that corresponds to the crossover between the two regions is hard to predict analytically since the DC current in the detection transistors is not constant. However, we can predict that the input power level for which the BiCMOS detector operates in linear region is lower than that of the CMOS one. This is related to the fact that the threshold voltage of the bipolar is higher than that of the MOS leading to an earlier conduction.

(8) To express the voltage in function of the input power , the input voltage is converted into power by referring to the parallel input impedance of the detectors using the following equation: (9) is the inverse of the real part of the input admittance. By replacing in (8) by (9), we obtain (10) This equation describes the principle of small-signal detection for both detectors (i.e., square-law detection). As the input power increases, the DC current in the detection transistors increases as well. Particularly, for the CMOS detection, the increase of the DC current in leads the transistor to operate in its square-law regime instead of subthreshold regime. In this case, the current of the transistor is (11) where , , and are, respectively, the threshold voltage, and the width and the length of the transistor . is the electron mobility in the NMOS channel, is the oxide capacitance, and is the DC voltage applied to the gate of . This leads to the following output voltage for the CMOS detector:

B. Noise Analysis The signal-to-noise ratio (SNR) is the main criteria used to define the sensitivity of analog/RF detection systems (such as in-situ characterization system). In this part, we develop the analytical expressions for detector sensitivity based on the SNR. All expressions are based on the exponential current nature of the detection transistors (2). The validity of this assumption is justified by the fact that the sensitivity corresponds to a low input power level. For the bipolar transistor , the collector shot noise is modeled by a parallel noise current source . Neglecting the effect of flicker noise and the thermal noise of the base resistance, the collector noise current of , for given noise bandwidth , is given by (15) while is a semi-empirical constant that depends on the carrier concentration and the device geometry. For NMOS transistor, since the transistor operates in subthreshold regime, it exhibits shot noise (instead of thermal noise) [26]. However, the flicker noise of MOS transistor cannot be neglected. Hence, the total drain noise of the transistor is given by (16)

(12) is still linearly However, the incremental output voltage related to the RF input power level, but with a different slope. This phenomenon does not happen for the bipolar transistor of

where , , and are, respectively, the oxide capacitance per unit area, and the width and the length of the transistor . is the empirical flicker noise coefficient for NMOS transistors, and is the noise corner frequency. These latter

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two parameters are extracted by simulation. For PMOS transistor, the total output noise is modeled by one equivalent noise current source including the effects of both thermal and flicker noise sources. Hence, the total drain noise of the transistor ( or 2) is given by (17) , , and are, respectively, the width, the where length, and the non-ideality factor of the transistor . is the empirical flicker noise coefficient of PMOS transistors. According to the schematic of the two detectors shown in Figs. 3 and 4, the total output noise current is given by

Fig. 5. Simulated output noise current of the two detectors.

TABLE II dB AND NOISE BEHAVIOR FOR SNR

kHz.

(18) is equal to for BiCMOS detector and equal to for CMOS detector. is the equivalent thermal noise current source of the impedance . The SNR, defined by the ratio between and for both detectors, is expressed by where

(19) Hence, the minimum detectable power , for a given value of SNR, can be estimated by the following equation: (20)

and the One can notice the trade-off between the sensitivity noise bandwidth (i.e., detector output bandwidth). In addition, (20) shows that the higher the is, the better the sensitivity. Moreover, the linear relation between the and the transistor width (in sub-threshold regime) leads to a trade-off between and the maximum detectable power. Indeed, referring to (17), increasing the width of the current mirror ( ), for a constant aspect ratio, will increase the output noise (degrading ) while shifting up the maximum power for which the output voltage will be saturated (as enters into its triode region). C. Noise Simulation Noise behavior of both detectors is verified using AC noise simulation in an ADS simulator (Fig. 5), and compared to the analytical study in Table II. As we can see in Fig. 5, the noise of both detectors is very close while the thermal noise (for kHz) is higher for the BiCMOS version. This is mainly related to the highest transconductance of transistor compared to that of the transistor . The solution of (20) for SNR dB is determined graphically from Fig. 6. In this figure, the total noise current ( ) is integrated over 300 kHz bandwidth (input bandwidth of Keithley 2000 digital voltmeter used for measurements). In addition, the transistor parameters used in (20) were extracted, in function of , and used to calculate the value of in

Fig. 6. Output signal current and output noise current ( for CMOS and BiCMOS detectors as a function of input RF power

kHz) .

Matlab. Despite the close output noise level for the two detectors, the BiCMOS version shows a better sensitivity thanks to its higher conversion gain (i.e., higher ). These results are summarized in Table II. Finally, we mention that the sensitivity of the detectors will be degraded by 10 dB if we increase the output bandwidth from 300 kHz (the noise bandwidth used in our case) to 700 MHz, for the same SNR value. III. MEASUREMENT RESULTS The detectors were fabricated in the 55 nm BiCMOS process from STMicroelectronics and they operate at 1.2 V supply voltage. Fig. 7 shows the measurement setup and the chip photo of the detectors measured on the same die. The active size of each detector is 80 80 m (RF and DC pads excluded). A. Measured Transfer Characteristics The transfer characteristics (TC) of the detectors were measured by extracting the DC output voltage versus the input power ( ) of a 60 GHz continuous-wave (CW) signal. The

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Fig. 8. Transfer characteristics of the CMOS power detector for 60 GHz input signal (simulation and measurement).

Fig. 7. (top) Measurement setup. (bottom) Chip photo of the fabricated detectors.

input signal is generated using Agilent ED257D PSG analog signal generator and the DC output voltage is measured using a Keithley 2000 digital voltmeter. Power source calibration is done using an Agilent V8486 power sensor coupled with E4418B power meter. Figs. 8 and 9 show the measured TC of the CMOS and BiCMOS detector respectively. The output voltage is defined as the voltage difference with and without an input RF power. The maximum detectable power is around 8.5 dBm for both detectors (limited by the saturation of transistor ). Nevertheless, we can notice that the linear detection region for the BiCMOS power detection is about 20 dB against 10 dB for the CMOS detector. For input power lower than 30 dBm, the incremental current (generated by the presence of ) becomes comparable to output offset component (fixed by ) which prevents us from validating the noise behavior. An alternative way to analyze the TC of the detectors, without subtracting the offset voltage, was presented in [25]. The dynamic range of that case is defined based on the conversion gain of the detectors. Early results of the BiCMOS detector have been previously published in [27]. The simulation results in [27] focus on studying the impact of the temperature variations on the performances of the power detector. It has been shown that the increase in temperature reduces the sensitivity of the power detector. Finally, we note that the DC power consumption of both detectors varies from about 40 W for 30 dBm input power and it increases to around 800 W for 8.5 dBm input power. B. Input Impedance These detectors have been mainly developed to be used in an adaptive bias control loop of 60 GHz power amplifiers [28]. For this application, it is important to ensure that the detector input

Fig. 9. Transfer characteristics of the BiCMOS power detector for 60 GHz input signal (simulation and measurement).

impedance is high enough to avoid RF signal path perturbation. For the BiCMOS version, the input impedance equation is given by (21) while for CMOS version:

(22) One can notice that the impedances depend strongly on the transconductance of detection transistors . This means that the input impedance achieved with the CMOS version can be higher than that of the BiCMOS version, since the transconductance of the transistor is lower than that of the transistor for the same average DC current level. The S-parameters measurements were performed using an Anritsu

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Fig. 10. De-embedding of the detector equivalent input impedance.

Fig. 13. Output voltage versus frequency for three different input powers: CMOS detector.

Fig. 11. Measured and simulated input impedance of the BiCMOS detector.

capacitor. In order to validate our analysis, the input impedance is simulated with an ideal coupling capacitor , of the same value. We can notice that, as predicted theoretically, the input impedance of the CMOS detector is higher than that of the BiCMOS detector (Figs. 11 and 12). C. Frequency Response and Output Bandwidth

Fig. 12. Measured and simulated input impedance of the CMOS detector.

ME7808C Broadband VNA. The VNA was calibrated using the line reflect–reflect match (LRRM) calibration method. To extract the impedance at the input of the power detector, the RF pad and access line (used in the layout) were de-embedded from the total measured impedance (Fig. 10). Figs. 11 and 12 show a good agreement between simulations and measurements (after de-embedding). However, both detectors have an input impedance of around 0.25 k around 60 GHz. By analyzing the input impedance network/equations, we concluded that the input impedance is mainly reduced because of the small value and poor quality factor of the metal–oxide–metal (MOM) capacitor used for the decoupling capacitance . Details regarding the model of the MOM capacitor can be found in [29]. Unfortunately, the chosen value was limited by the self-resonance frequency of the MOM

The frequency response of the detectors is evaluated by measuring the DC output voltage while sweeping the frequency of the input signal for constant input power level . Note that the power calibration is performed for each frequency in order to ensure a constant power at the input of the power detector. Fig. 13 shows the output voltage versus frequency of the CMOS detector for three different input powers. The detector shows a quasi-flat response across the frequency from 50 GHz to 66 GHz with less than dBv of error around its average value (obtained at 58 GHz for a given value of ). The fluctuations of the output voltage are related to the stationary nature of the input wave resulting from the mismatch between the 50 source impedance and the input impedance of the detector. Similar results were obtained for the BiCMOS as shown in Fig. 14. Concerning the detectors' response time, it is mainly defined by the output low-pass filter, Figs. 3 and 4, composed of the resistor , the capacitor and the non-linear output resistance ( ) of the transistor . The high-frequency pole introduced by the current mirror was not considered. Hence, the response time from 10% to 90% of the final value of can be expressed as (23) Simulation results show a response time of around 1 ns for both detectors. Nevertheless, time-domain measurements were performed for the common-base detector showing an output bandwidth of about 700 MHz. More details about the experimental procedure can be found in [25]. Back to the data presented in Table I, compared to the existing millimeter-wave detectors, the proposed detectors exhibits the

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Fig. 14. Output voltage versus frequency for three different input powers: BiCMOS detector.

highest measured dynamic range while holding high speed, low power consumption, small footprint, and good sensitivity. IV. CONCLUSION Two common-base/gate millimeter-wave power detectors are presented. Closed-form expressions are derived for the transfer characteristic as well as for the noise behavior of the designed detectors. Two prototypes were fabricated, in a BiCMOS 55 nm process, and used to validate the theoretical analysis. Each of the developed detectors occupies an area of 80 80 m , and exhibits an equivalent input impedance level of around 0.25 k at 60 GHz limited by the quality factor of the input coupling capacitor. The response flatness over 10 GHz bandwidth around 60 GHz is dBv. Measurement results show that the common-base detector has a wider linear detection range than that of the common-gate detector. In addition, the measured 700 MHz output bandwidth proves the ability of these detectors to be used for real-time envelope tracking. Theoretical noise analysis and computer simulations show that, for small output bandwidth (around 300 kHz), the minimum detectable input power is 41 dBm and 50 dBm for the common-gate detector and for the common-base detector, respectively. This demonstrates the capability of these detectors to be used for in-situ measurement as well as for BIST applications. REFERENCES [1] A. Siligaris et al., “A low power 60-GHz 2.2-Gbps UWB transceiver with integrated antennas for short range communications,” in Proc. IEEE Radio Frequency Integrated Circuits Symp., 2013, pp. 297–300. [2] W. Winkler, J. Borngraber, H. Gustat, and F. Korndorfer, “60 GHz transceiver circuits in SiGe: C BiCMOS technology,” in Proc. Eur. Solid-State Circuits Conf., 2004, pp. 83–86. [3] R. Johnson et al., “SiGe wideband power detector and IF-amplifier RFICs for W-band passive imaging systems,” in Proc. IEEE Int. Semiconductor Conf., 2013, vol. 2, pp. 225–228. [4] L. Abdallah, H. G. Stratigopoulos, C. Kelma, and S. Mir, “Sensors for built-in alternate RF test,” in Proc. IEEE Eur. Test Symp., 2010, pp. 49–54.

[5] A. Garcia, R. Venkatasubramanian, J. Silva-Martinez, and E. Sanchez-Sinencio, “A broadband CMOS amplitude detector for on-chip RF measurements,” IEEE Trans. Instrum. Meas., vol. 57, no. 7, pp. 1470–1477, 2008. [6] J. Zhang, V. Fusco, and Y. Zhang, “A compact V-band active SiGe power detector,” in Proc. Eur. Microwave Integrated Circuits Conf., 2012, pp. 528–531. [7] X. Yang, Y. Uchida, L. Qing, and T. Yoshimasu, “Low-power ultrawideband power detector IC in 130 nm CMOS technology,” in Proc. IEEE MTT-S Int. Microwave Workshop, 2012, pp. 1–4. [8] H. Nakamoto, M. Kudo, K. Niratsuka, T. Mori, and S. Yamaura, “A real-time temperature-compensated CMOS RF on-chip power detector with high linearity for wireless applications,” in Proc. Eur. Solid-State Circuits Conf., 2012, pp. 349–352. [9] J. Wu et al., “A linear-in-dB radio-frequency power detector,” in Proc. IEEE Int. Microwave Symp., 2011, pp. 1–4. [10] J. Wursthorn, H. Knapp, K. Aufinger, R. Lachner, J. Al-Eryani, and L. Maurer, “A true-RMS integrated power sensor for on-chip calibration,” in Proc. IEEE BiCMOS Circuits and Technology Meeting, 2014, pp. 13–16. [11] C. Li, F. Gong, and P. Wang, “A low-power ultrawideband CMOS power detector with an embedded amplifier,” IEEE Trans. Instrum. Meas., vol. 59, no. 12, pp. 3270–3278, 2010. [12] J. Gorisse, A. Cathelin, A. Kaiser, and E. Kerherve, “A 60 GHz 65 nm CMOS RMS power detector for antenna impedance mismatch detection,” in Proc. Eur. Solid State Circuits Conf., 2009, pp. 172–175. [13] M.-L. Shieh et al., “Linear radio frequency power detector,” in Proc. Asia Pacific Microwave Conf., 2009, pp. 2316–2319. [14] K. A. Townsend and J. W. Haslett, “A wideband power detection system optimized for the UWB spectrum,” IEEE J. Solid-State Circuits, vol. 44, no. 2, pp. 371–381, Feb. 2009. [15] I. Kim and Y. Kwon, “A broadband logarithmic power detector in 0.13 m CMOS,” IEEE Microw. Wireless Compon. Lett., vol. 23, no. 9, pp. 498–500, 2013. [16] Y. Zhou and M. Y. -W. Chia, “A low-power ultra-wideband CMOS true RMS power detector,” IEEE Trans. Microw. Theory Techn., vol. 56, no. 5, pp. 1052–1058, 2008. [17] U. R. Pfeiffer and D. Goren, “A 20 dBm fully-integrated 60 GHz SiGe power amplifier with automatic level control,” IEEE J. Solid-State Circuits, vol. 42, no. 7, pp. 1455–1463, Jul. 2007. [18] T. Zhang, W. R. Eisenstadt, R. M. Fox, and Q. Yin, “Bipolar MICROWAVE RMS power detectors,” IEEE J. Solid-State Circuits, vol. 41, no. 9, pp. 2188–2192, 2006. [19] Q. Z. Hu, Z. H. Liu, L. Yan, and W. Zhou, “A SiGe power amplifier with power detector and VSWR protection for TD-SCDMA application,” in Proc. Int. Conf. Mixed Design of Integrated Circuits and System, 2006, pp. 214–217. [20] Y. Zhou and M. C. Y. Wah, “A wide band CMOS RF power detector,” in Proc. Int. Symp. Circuits and Systems, 2006, pp. 4228–4231. [21] G. Ferrari, L. Fumagalli, M. Sampietro, E. Prati, and M. Fanciulli, “CMOS fully compatible microwave detector based on MOSFET operating in resistive regime,” IEEE Microw. Wireless Compon. Lett., vol. 15, no. 7, pp. 445–447, 2005. [22] M. Kouwenhoven and A. Van Staveren, “A 2 GHz mean-square power detector with integrated offset chopper,” in IEEE Int. Solid-State Circuits Conf. Dig. Tech. Papers, 2005, vol. 1, pp. 124–588. [23] Q. Yin, W. R. Eisenstadt, R. M. Fox, and T. Zhang, “A translinear RMS detector for embedded test of RF ICs,” IEEE Trans. Instrum. Meas., vol. 54, no. 5, pp. 1708–1714, 2005. [24] T. Zhang, W. R. Eisenstadt, and R. M. Fox, “A novel 5 GHz RF power detector,” in Proc. Int. Symp. Circuits and Systems, 2004, vol. 1, p. 2326. [25] A. Serhan, E. Lauga-Larroze, and J.-M. Fournier, “A 700 MHz output bandwidth, 30 dB dynamic range, common-base mm-wave power detector,” in Proc. Int. Microwave Symp. (IMS MTT-S), 2015, pp. 1–3. [26] J. Fellrath, “Shot noise behavior of subthreshold MOS transistors,” Revue de Physique Appliqué, no. 13, pp. 719–723, 1978. [27] A. Serhan, E. Lauga-Larroze, and J.-M. Fournier, “A V-band BiCMOS power detector for millimeter-wave applications,” in Proc. Int. Conf. Microelectronics (ICM), 2013, pp. 1–4. [28] A. Serhan, E. Lauga-Larroze, and J.-M. Fournier, “Efficiency enhancement using adaptive bias control for 60 GHz power amplifier,” in Proc. IEEE Int. Conf. New Circuits and Systems, 2015, pp. 1–4. [29] T. Quemerais, L. Moquillon, P. Benech, J.-M. Frounier, and S. Pruvost, “CMOS 45 nm 3D metal-oxide-metal capacitors for millimeter wave applications,” Microw. Opt. Technol. Lett., vol. 53, pp. 1476–1478.

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Ayssar Serhan was born in Eain-Kana, Lebanon. He received the M.S. degree in nanoelectronics and nanotechnologies from Joseph Fourier University, Grenoble, France, in 2011, and the Ph.D. degree in nanoelectronics and nanotechnologies from the Grenoble Institute of Technology (INP-G), Grenoble, France, in 2015. From 2012 to 2015, he was a teaching assistant at the School of Engineering and Applied Sciences (Phelma-INPG), Grenoble, France. In October 2015, he joined the CEA-LETI as RF/analog IC design engineer. His research interests include the design of CMOS and BiCMOS RF/mm-wave integrated circuits for wireless applications; design of tunable multi-mode multi-band power amplifiers for 5G applications using LDMOS devices in PD-SOI technologies.

Estelle Lauga-Larroze received the M.Sc. degree in microelectronics from Joseph Fourier University, Grenoble, France, and the Ph.D. degree in micro- and nanoelectronics from the National Polytechnic Institute of Grenoble, Grenoble, in 2003 and 2007, respectively. In 2007, she joined the Swiss Federal Institute of Technology Lausanne where she worked on CMOS single-photon detectors for biological imaging applications. From 2008 to 2010, she was with CEA-LETI, Grenoble, working on CMOS based

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analog circuits for image sensors. Since 2010, she has been an Assistant Professor with the University of Grenoble Alpes. Her research activity with the Institute of Microelectronics Electro-magnetism and Photonic (IMEP-LAHC), Grenoble, focuses on CMOS and BiCMOS analog and RF/mmW integrated circuits and systems for communication and sensors applications.

Jean-Michel Fournier received the electronic engineering degree from the National Engineer School, Toulouse, France, in 1974, and the M.S. and Ph.D. degrees in solid-state physics from the University Claude Bernard, Lyon, France, in 1975 and 1979, respectively. In 1979, he joined the Research and Development Division of the Microelectronic Department, France Telecom, Grenoble, France, where he was involved with analog MOS application-specific integrated circuit development (high-speed video amplifiers, Gm-C filters, device modeling). From 1992 to 1996, he was in charge of the Analog Design Group, during which time he focused his interest on the BiCMOS process for RF applications. Since 1996, he has been a Professor at the School of Electronic and Physics of INPG, Grenoble, and a researcher at the Institute of Microelectronics Electromagnetism and Photonics (IMEP-LAHC). His current research interests include the design of analog RF and millimeter-wave integrated circuits in CMOS technology.

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Modelling and Measurements of the Microwave Dielectric Properties of Microspheres Ali A. Abduljabar, Student Member, IEEE, Xin Yang, David A. Barrow, and Adrian Porch

Abstract—A microwave microstrip sensor incorporating a split ring resonator is presented in this paper for microsphere detection and dielectric characterization within a microfluidic channel. Split ring resonator (SRR) sensor of three different radii, but with approximately equal gap dimensions to change their sensitivity, were designed and fabricated, of resonance frequencies 2.5, 5.0 and 7.5 GHz. To validate the SRR sensors, two sizes of polystyrene micro. Measurements of spheres were tested, of diameters 15 and 25 changes in resonance frequency and insertion loss of the odd SRR mode were related to the dielectric contrast provided by the microspheres and their host solvent, here water. COMSOL Multiphysics was used to model the sensors, and good agreements were found between the simulated and measured results. Index Terms—Cell detection, microspheres, microwave sensor, split ring resonator.

I. INTRODUCTION UCH research has been undertaken in the use of microwave methods for the realization of rapid, reliable, accurate and non-invasive bio-sensors. Recent use of microwave methods for detecting the dielectric properties of human cells has yielded compelling results [1]. The dielectric property of a single cell has also been investigated by using a microwave biosensor [2], incorporating a capacitive sensing zone for trapped cells within microfluidic channel. Microwave dielectric spectroscopy has been identified as a promising method to study the membrane permeabilization of cells induced by chemo-treatment, and its consequences for the cells [3]. An original label free bio-sensing approach for cellular study based on micro-technologies at RF frequencies is also proposed [4]. This bio-detection method presents advantages in that it is label free and of sub-millimetric size, allowing operation at the cell scale and with a limited number of cells. A tuneable, resonant, microwave biosensor that allows measurement of the dielectric permittivity of microscale particles over a range of frequencies is presented in [5]. A cost-effective, scalable microwave system that can be integrated with microfluidic

M

Manuscript received June 05, 2015; revised August 14, 2015 and October 20, 2015; accepted October 20, 2015. Date of publication November 12, 2015; date of current version December 02, 2015. This paper is an expanded version from the IEEE MTT-S International Microwave Symposium, Phoenix, AZ, USA, May 17–22, 2015. A. A. Abduljabar was with the College of Engineering, University of Basrah, Basrah, Iraq. He is now with the School of Engineering, Cardiff University, Cardiff, CF24 3AA, U.K. (e-mail: [email protected]). X. Yang, D. A. Barrow, and A. Porch are with the School of Engineering, Cardiff University, Cardiff, CF24 3AA, U.K. (e-mail: [email protected]; [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2015.2495247

devices enabling remote, simultaneous sensing and heating of individual nanoliter-sized droplets generated in microchannels is proposed in [6]. A new type of biosensor based on a two pole microstrip filter, using the inter-resonator's planar coupling capacitor as an ultrasensitive biosensing element, has been developed to investigate the electrical parameters of human cells [7]. A method to measure the permittivity of single particles and yeast cells at microwave frequencies is presented in [8] and [9], respectively. An electrical approach for single-cell analysis, wherein a 1.6 GHz microwave interferometer detects the capacitance changes produced by single cells flowing past a coplanar interdigitated electrode pair, is demonstrated in [10]. A passive microwave sensor based on microstrip lines for characterizing cell cultivation in aqueous compartments is presented in [11]. The cultivation stadium of a yeast culture was monitored to detect the permittivity changes. In [12] and [13], broadband microwave measurements and sensing of single Jurkat and HEK cells were used to overcome electrode polarization, with ac dielectrophoresis used to precisely place cells between narrowly spaced electrodes, and relatively wide microfluidic channels incorporated to prevent cell clogging. A miniaturized microwave based biosensor was fabricated in [14] for the characterization of living and dead cells via their dielectric properties. Another detection system is based on a microwave coupled transmission line resonator integrated into an interferometer [15], designed for the detection of biomaterials in a variety of suspending fluids. However, most of these works have been dedicated to the dielectric assessment of groups of cells, rather than single cell properties. Increasing evidence in other clinical and pre-clinical studies suggests that the single-cell heterogeneity in the regulation of oncogenic signaling pathways is a general feature of most cancers. In [16] it was shown that the dielectric permittivity, capacitance and conductivity values of cell membranes are higher for normal lymphocytes than for malignant ones. Model-based numerical predictions of the dielectrophoretic behavior of spheroidal biological cells are carried out in [17]. A linear relationship was observed between the DNA content of eukaryotic cells and the change in capacitance in [18] that is evoked by the passage of individual cells across a 1-kHz electric field. Moreover, theoretical analysis and measurement techniques for dielectric spectroscopy of biological cells in the radio frequency range were reviewed in [19]. In this work, we demonstrate a new application for a microwave split ring resonator (SRR) with a narrow, tapered gap section, as a sensor for the dielectric characterization of microparticles. This is shown schematically in Fig. 1, illustrating the gap adaption for single cell investigations in medical and

This work is licensed under a Creative Commons Attribution 3.0 License. For more information, see http://creativecommons.org/licenses/by/3.0/

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Fig. 2. Quasi-TEM modes of the SSR. (a) Odd mode (with large electric field in the gap), and (b) even mode (with small electric field in the gap).

Fig. 1. Schematic of the split-ring microstrip sensor (the ground plane is on the back surface, not shown), connected to a microwave network analyzer and controlled by a LabVIEW program. Microspheres are passed through the gap region via a water filled, glass capillary, after [20].

biological applications. Three sizes of the sensors are presented in this work, model A, B, and C, where the design and measurements of model A was presented in [20]. The added work of this paper is the miniaturization of model A sensor to models B and C to enhance sensor sensitivity. In Section II, the theory and concepts of the polarization of the liquid with and without spheres (“cells”) are presented; also the theoretical enhancements in sensitivity that can be expected by tapering and reducing the gap, and that due to reducing the overall size of the SRR. A description of the sensor design and fabrication (together with simulation results) are presented in Section III. In Section IV, the experimental results are demonstrated and discussed, with final conclusions described in Section V. II. CONCEPTS, THEORY AND SIMULATION A. Odd and Even Resonator Modes The SRR based on the microstrip geometry (i.e., with ground plane) shown in Fig. 1 has odd and even mode resonances. The odd mode has the lower resonance frequency and occurs when the wavelength is equal to the electrical length of the ring plus the gap [21]; the even mode has higher frequency and occurs when the wavelength is equal to the ring length only [22]. The distribution of electric field in the gap cross section for both modes is shown schematically in Fig. 2. In the odd mode configuration the electric field penetrates the gap where the capillary resides, while in even mode the electric field is mostly outside the gap. In our experiments, the odd mode is used to characterize the presence of microspheres whilst the even mode is insensitive to the microspheres but can be used as a useful reference, for example, to account for small changes in temperature. The input and output power couplings of the resonator are mostly inductive owing to their positioning at a magnetic field

Fig. 3. Cross section of the capillary filled by liquid, (a) without a microsphere, and (b) with a microsphere. The dimensions and relative permittivities of all regions are shown.

antinode, with a smaller degree of capacitive coupling arising from the fact that they are extended structures and are made of open-circuit, microstrip sections [23]. B. Electric Dipole Moment Calculations Next we develop a simple, approximate theory to account for the change of electric dipole moment of the capillary within the gap when a microsphere is present. This allows us to calculate the resonator perturbation using first order perturbation theory [24] and [25]. Consider first a liquid of complex relative permittivity completely filling a low loss tube (for example, glass, as in the experiments here). Referring to Fig. 3(a), we define as the (real) permittivity of the tube, and and to be its outer and inner radii, respectively. The complex electric dipole moment induced for a length of a filled tube can be calculated analytically based on the direct solution of Laplace's equation for a quasi-static electric field. The main result is [25]

(1) is the magnitude of the electric field applied perpenwhere dicular to the tube's axis, assumed to be uniform along the length of the tube, and . The perturbations measured experimentally in this paper are due to the presence of polystyrene microspheres within the gap region. Referring to Fig. 3(b), we next analyse quantitatively how the presence of a small spherical particle, assumed to be homogeneous and of relative permittivity , modifies the electric dipole moment of a water filled tube and so leads to perturbations of the resonator parameters. If the sphere occupies a

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volume fraction of the liquid within the tube (with ), the complex permittivity of the liquid in the tube can be consid. This is ered to have changed from to an effective value estimated from simple effective medium theory to be (2) The resulting perturbation in electric dipole moment is then the difference (3) C. Cavity Perturbation Theory First order cavity perturbation theory states that a small due, for example, to a change in electric dipole moment change in will result in changes (i.e., perturbations) in both the resonance frequency and unloaded quality factor , given by the approximate formulae [26]

Fig. 4. The calculated transmission spectrum of the SRR with (dotted) and without (solid) a plastic microsphere in the gap region. Both resonance frequency and microwave loss increase with the presence of the sphere. In this calculation, the SRR is assumed to have a factor of 200 and a resonance frequency of 2.5 GHz when unperturbed by the microsphere. The microsphere is assumed to occupy a volume fraction of 0.1 of the gap volume, and the ratio of tube volume to mode volume is 0.02. The microsphere permittivity is assumed . In this limit when , the to be 2 and the water permittivity gives almost identical results to the more simplified analysis using (7) for rigorous analysis using (1)–(3).

(4) (5) Here the subscripts “1” and “0” denote the perturbed and unperturbed states of the resonator, respectively. The quantity is the time averaged stored energy of the resonator in its unperturbed state, defined by (6) is the unperturbed electric field magnitude at the posiwhere is the mode volume of the resonator. This tion of the tube and latter term quantifies the concentration enhancement of electric energy density at the position of the tube relative to the average electric energy density elsewhere in the resonator. Miniaturizing the resonator by, for example, reducing the gap width or the ring and hence also a deradius, results in a decreased value of creased value of , thus causing larger changes in resonator pa(i.e., enhanced sensitivity rameters for a given perturbation to the cause of the perturbation), which we will return to in more detail below. To gain a better physical understanding of how the presence of a microsphere affects the SRR, for the moment we ignore the presence of the glass tube (assumed to be very thin walled) in the limit when and develop an approximate formula for the permittivity of the host liquid is much greater than that of the microsphere . This will indeed be the case when water at 2.45 GHz) and polystyrene are con( sidered, respectively. Then, (1)–(5) reduce to the very simple results (7) (8) (9)

where is the physical volume of the sample within the gap region. From this we see that on introducing a polystyrene microsphere into the gap region, the resonance frequency increases, but that the factor decreases (i.e., the microwave loss increases). This is illustrated further in Fig. 4, where we consider the effects of the presence of a microsphere on the in the frequency domain, voltage transmission coefficient with perturbation calculated using both (1)–(3) and the simplified formula (7). This can be understood by referring to Fig. 5, where we plot in the space in an around a sphere the electric field intensity placed in a uniform electric field when (a) the sphere's permittivity is much less than that of its host liquid (as is the case here), and (b) when the sphere's permittivity is much greater than that of its host (as would be the case for a metal sphere). In (a), we note that the intensity is enhanced within the host liquid adjacent to the equatorial regions of the sphere, whilst in (b) it is enhanced adjacent to the polar regions. In both cases, this intensity enhancement increases the overall dielectric loss. However, in (b) there is an increase in electrical potential energy owing to the strong polarisation of the sphere, so the resonance frequency would decrease. In (a), since the sphere is of a low permittivity material, its polarisation is small and overall the electric potential energy is reduced, resulting in an increased resonance frequency. D. Sensitivity Enhancement of the SRR It can be seen from the perturbation (4)–(6), and their simplified counterparts (8), (9), that greatest SRR sensitivity to the presence of a single microsphere is attained when its mode is reduced. This is most easily accomplished by volume reducing the ring radius of the SRR. Table I shows the results of a COMSOL Multiphysics 4.4 simulation of the SRR shown in Fig. 1, with varying radii , giving unperturbed resonance frequencies labelled . As expected, to a good approximation since the SRR's lumped inductance is proportional to the ring area , and . The gap region is 70 deep (defined by the thickness of the copper cladding),

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Fig. 5. The calculated electric field intensity around a sphere when (a) its permittivity is much less than that of its host liquid, and (b) much greater than that of its host (the arrows show the direction of the applied field). The enhancein the host in both cases gives rise to increased losses but in (a) the ment of overall electric potential energy is reduced, giving rise to an increased resonance frequency.

TABLE I EFFECT OF VARYING SRR DIMENSIONS (SHOWN IN FIG. 1) ON RESONANCE FREQUENCY, , AND EFFECTIVE VOLUME

Fig. 6. Simulated results of varying the ring radius of the SSR. (a) Resonance frequency for different ring radii. (b) Effective volume for different ring radii (assuming a constant gap geometry).

DIMENSIONS

with in-substrate gap widths of to give a (i.e., total geometrical volume of the gap of ). We also simulate the perturbation on the SRR region imposed by inserting a single, spherical metal particle of radius 7.5 within the gap volume. The sphere volume is 2.1% of the gap volume, thus giving a small perturbation from which the mode for SRRs of varying radii can be computed using (4). volume is also shown The resulting decrease in resonance frequency in Table I. A metal sphere of radius completely depolarises the electric field within it by developing an electric dipole moment , where is the volume of the can be calculated sphere. This means that the mode volume of a metal sphere using from (10) are also shown in Table I. The The resulting values for increases with increasing radius is indicative of fact that the fact that the electrical energy is not solely stored within the gap region, but occupies a much larger volume outside of the gap. This is associated with charge storage on the curved ring surfaces itself, which is more effective the larger the radius . The main results of Table I are plotted in Fig. 6, for the reso(Fig. 6(a)) and also the mode volume nance frequency (Fig. 6(b)) as a function of ring radius . III. DESIGN AND REALIZATION The SRRs were fabricated by initial cutting of the ring shape and the gap structure using laser micromachining followed by

OF

TABLE II THE SPLIT RING RESONATORS SHOWN DIMENSIONS ARE IN MM

IN

FIG. 7, ALL

fine finishing with a milling machine. The gap is defined in this way to a tolerance of 1 to 2 micrometer. A Rogers Corporation RT/duroid 5880 laminate was used with a substrate (dielectric) thickness of 1.57 mm, relative permittivity of 2.20 0.02 and loss tangent 0.0009. The thickness of the copper , which is chosen to be as thick as possible to enis 70 sure a higher quality factor . Polystyrene microspheres (Alfa Aesar, A Johnson Matthey Company) were chosen to validate diameters. These were dispersed in the sensor, of 15 and 25 water and passed through the glass micro-capillary with the aid of a syringe. Three sizes of SRRs were designed to study the effect of the ring radius on the microsphere detection, here denoted models A, B and C; their dimensions are listed in Table II. By changing , which reduces the dimensions we change the mode volume in going from model A to B to C, thus increasing their sensitivity to microsphere detection. In model A the gap was designed to , which is wide enough for two sizes of mibe of width 35 ) to pass through it, while crosphere (diameters 25 and 15 in models B and C the gap and radius were reduced to increase the detection sensitivity of the smaller microspheres (diameter ). 15 The soda glass capillary (SAMCO company) with permittivity of 3.8, inner diameter of 1.3 mm, and outer diameter of

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principle functional operation does demonstrate that further work is justified in order to more effectively integrate the use of microwave interrogation techniques with microfluidic flows. The materials used to form microfluidic circuits depends hugely on the production volumes required, there disposability, solvent resistance, creep specifications, electro-optical transmission characteristics, and range from silicon, glasses, polymers, metals, elastomers, paper, sapphire, and diamond [28]. PTFE based materials, especially Teflon AF, do offer excellent dielectric properties, solvent resistance, and can be light transmissive, but equally are more difficult to bond as integrated capillary structures, and are not so amenable to cost-effective micro-structuring as is silicon and glass. It highly possible that the integrated microwave-microfluidic detectors, such as that demonstrated here, could be fabricated as a separate small-scale plug-in modules, that could be inserted within more complex electrofluidic motherboards, and that possibly the recent advances in additive 3D manufacturing [29] could enable such a hybrid assemblies made from diverse materials sets. COMSOL Multiphysics 4.4 was used to perform 3D simulations of the electromagnetic fields of the sensors with and without polystyrene spheres in water at 25 . The EM waves model was used to simulate the S-parameters of the SRRs. The wave equation in the frequency domain was computed in the EM waves model as described in the software according to (11)

Fig. 7. Photographs of the fabricated sensors A-C, with a magnified view showing the position of the glass capillary within the gap region, model A given in [20].

2 mm was heated and then pulled down to an outer diameter of and inner diameter of 30 in the case of the model A 34 sensor. For the models B and C sensors, the inner and outer cap, respectively. Fig. 7 shows a illary diameters are 28 and 23 photograph of the magnified gap region with the capillary, together with the layout for models A-C. The constructional materials used here for the microwave microfluidic device comprised (i) an RT/duroid 5880 laminate, with (ii) an integrated soda glass capillary. The laminate was chosen because of its favorable dielectric properties due to its PTFE—glass-fiber construction. Whilst, the method used here for integrating the glass capillary and the circuit board, based split ring resonator, do not conform to currently used microfluidic mass-production techniques [27], the proof of

is the permeability, the permittivity and the elecwhere tric conductivity of the material region; is the permittivity of the vacuum, is the wave number in free space, and the angular frequency. The impedance boundary condition is used for the copper surfaces of the resonator and ground in order to incorporate the copper losses. The scattering boundary condition (enwas utilized for the faces of the volume closing the device) to make the boundaries transparent for the scattered waves. Coaxial ports were used to feed the electromagnetic energy to the resonator. The relative permittivity of water was described in the simulation by using Debye Theory [30] as its permittivity is variable with frequency. The properties of the materials that were used in the simulation are shown in Table III. The simulated and measured results of the three models A- C are illustrated in Fig. 8. In Fig. 8 (a), the meaof the model A are shown for sured and simulated results of diameter microsphere, three cases: water only, water and 15 microsphere. The measured and simulated and water and 25 results of models B and C are illustrated in Fig. 8(b) and (c), rediameter microsphere cases. In spectively, for water and 15 all models, the results shown in Fig. 8 demonstrate that there is good agreement between the measured and simulated results. IV. RESULTS AND DISCUSSION A. Measurement Set-Up and Data for Sensor A The bench-top assembly of the split ring resonator with the network analyzer, microscope and computer is shown in Fig. 9. We consider first the results of model A, with a resonance frequency of approximately 2.5 GHz. Fig. 10 shows the broad) of the resonator's first band transmission response (i.e.,

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TABLE III MATERIAL PROPERTIES USED IN THE SIMULATION AT 25

Fig. 9. Photograph of the assembly of the sensor, network analyzer, laptop computer and optical microscope to aid positioning of the polystyrene microspheres in the gap region.

Fig. 10. Measured broadband response of the split ring resonator (model A) given in [20], showing the odd and even mode responses (the even mode has the higher frequency of the two).

Fig. 8. Measured and simulated of the sensors with a single microsphere dispersed in water in the gap region. (a) Model A, after [20]. (b) Model B. (c) Model C.

(odd mode) and second (even mode) resonance frequencies. The odd mode is perturbed by the dielectric properties of the material within the gap as there is a strong electric field there. Conversely, the even mode is almost unperturbed as its electric field is confined mostly between the ring and the ground plane.

The changes in the resonance frequency and the insertion loss of the odd mode with time due to a flow of microspheres along the capillary are shown in Fig. 11(a) and (b), respectively. The results in Fig. 11 were collected by a computer running a LabView program to record instantaneously the change in resonance frequency and insertion loss of both modes owing to the data was fitted to a movement of the microspheres. The Lorentzian curve, from which the resonator parameters were extracted. The network analyzer was an Agilent E5071C, with an IF bandwidth of 10 kHz and 401 sweep points to give a sweep time of approximately 0.07 s. This is fast enough to capture enough data during the short time (around 2 s) when the microsphere occupied the gap region of the SRR. Increases in the odd mode resonance frequencies were measured to be 150 8 kHz and 350 18 kHz due to the presence of the 15 and 25 diameter microspheres, respectively. The increases in insertion loss were measured to be 0.030 0.002 dB and 0.060 0.003 dB, respectively. All errors quoted are random errors estimated from repeating each experiment three times. These dominate over other systematic errors linked to the measurement system.

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Fig. 12. Measured change in the fractional resonance frequency with temperof both odd and even modes given in [20]. ature

would cause the baseline to shift up or down, accordingly. However, this is likely to occur on a timescale which is much longer than the perturbations associated with the presence of the microspheres (typically less than 2 seconds), and these short term changes will be readily separated from the longer term effects of temperature drift. To verify the usefulness of the even mode in correcting for temperature, the sensor was measured in a temperature-controlled oven (Memmert, Model: IPP 400) with a high degree over the range from 20 to of temperature control 32 . The resulting fractional changes in resonance frequencies of both modes with temperature are shown in Fig. 12. The resonance frequencies of both modes increase with temperature as the dielectric thickness expands with increasing temperature. The increase in frequency for the odd mode is some 30% larger than for the even mode due to additional expansion of the gap width, which causes an additional frequency shift. The results of Fig. 12 for the even mode can be used to deduce an accurate value of the temperature, and hence also the additional frequency shift in the odd mode caused by a change in temperature. Fig. 11. Measured variation of the resonator parameters with respect to time diameter microsphere enters the gap region of model A (2.5 when a 15 diameter microsphere, after [20]. (a) The resonance GHz), followed by a 25 frequency of the odd mode, (b) the insertion loss of the odd mode, and (c) the resonance frequency of the even mode.

B. Use of the Even Mode and Effects of Changing Temperature Furthermore, there was no measured perturbation of the even mode with the same microsphere flow, as expected (Fig. 11(c)). Therefore, the even mode has the very useful property that its resonance frequency can be used to monitor (and indeed correct for) minute changes in temperature. This is essential in a practical device owing to the highly temperature-dependent complex permittivity of water. Otherwise, small increases in temperature could be inferred as being due to changes in the dielectric properties of the microspheres. The complex permittivity of the microspheres can be extracted from the resonator measurements using approaches in [23] when the size of the microsphere is known. For example, in model A the extracted relative permittivity of microsphere is 2.1 0.1. Whilst the perturbations on the resonator are small in the case of Fig. 11, they can be unambiguously separated from the effects of small temperature changes. A change in temperature

C. Use of Sensors B and C to Enhance Sensitivity The increase in insertion loss when a microsphere is present is an interesting result that arises since the microsphere enhances the electric field inside the water filled capillary. This subsequently increases the dielectric losses, as has been discussed in detail in Section II-B. To increase the ability of the sensor to discriminate the diameter, or to deal with spheres (such as spheres with 15 biological cells) which may not have such large differences in their permittivity with that of the host liquid, two smaller models B and C have been designed and tested. and In these two models the gap width was reduced to 30 the ring radii were decreased to 3.5 and 2.25 mm for model B and C respectively, as shown in Table II. In model B, the resois shown in Fig. 8(b). nance frequency is set at 5 GHz and its The changes in the resonance frequency and amplitude (losses) are shown in Fig. 13. The shift in resonance frequency is 400 20 kHz and the increase in the insertion loss is 0.012 0.001 diameter microsphere dB, which is more sensitive to the 15 than model A. More sensitive results have been obtained from model C, as shown in Fig. 14. The shift in resonance frequency is now 1.00 0.05 MHz and the increase of the insertion loss is 0.040

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[16] of representative permittivity of 10 and diameter of 12 conductivity of 0.5 at 7.5 GHz [32]. In the small SRR this gives a frequency shift of 0.5 MHz, so we expect our method to be able to quantify both the presence, and measure the complex permittivity, of individual cells. V. CONCLUSION

Fig. 13. Measured variation of the resonator parameters with respect to time diameter microsphere enters the gap region in model B (5 GHz). when a 15 (a) The resonance frequency (b) The insertion loss.

In this work, three models of microwave sensors based on a microstrip split ring resonator were developed and tested for the dielectric measurement, size measurement and counting of microspheres. The high sensitivity of all three resonator models A-C is due to the small size of the gap region, here 35 and 30 . Two sizes of polystyrene microspheres (15 and 25 ) have been used to verify the odd mode's perturbation when a microsphere is present in the gap. Furthermore, it has been demonstrated that the even mode is insensitive to the presence of microspheres and so can be used for temperature compensation. To increase the sensitivity as the real cell permittivity does not have large contrast with liquid permittivity, the gap and ring radii have been reduced in models B and C. Their increased sensitivity is simply due to the associated reduction in mode volume . The observed changes in resonance frequency and insertion loss of the odd mode were due to the dielectric contrast between the microspheres and their host solvent (water). The complex permittivity of the microspheres can be extracted from the resonator measurements either using an optimization routine based on matching the simulated and experimental results or using the theoretical method in [23]. The ability of the split ring resonator sensor to count microspheres, as well as determine their complex permittivity, will next be applied to human cell detection and diagnostics. REFERENCES

Fig. 14. Measured variation of the resonator parameters with respect to time diameter microsphere enters the gap region in model C (7.5 when a 15 GHz). (a) The resonance frequency (b) The insertion loss.

0.002 dB when the 15 diameter sphere passes though the model C's gap. The results have some variation due to small temperature drifts. The change in temperature arises due to the flow of water inside the capillary; the water needs to reach thermal equilibrium to achieve stable, and hence accurate, results. In addition, the variation in results comes from the limitation of the network are very small. analyzer sensitivity as the changes in Finally, since we hope to apply our sensor for the detection of human cells, we have performed a simulation of the SRR with the 15 micron microsphere replaced by a “white blood cell” with

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[9] Y. Yang, H. Zhang, J. Zhu, G. Wang, T.-R. Tzeng, X. Xuan, K. Huang, and P. Wang, “Distinguishing the viability of a single yeast cell with an ultra-sensitive radio frequency sensor,” Lab on a Chip, vol. 10, pp. 553–555, Mar. 2010. [10] G. A. Ferrier, S. F. Romanuik, D. J. Thomson, G. E. Bridges, and M. R. Freeman, “A microwave interferometric system for simultaneous actuation and detection of single biological cells,” Lab on a Chip, vol. 9, pp. 3406–3412, Dec. 2009. [11] J. Wessel, K. Schmalz, J. C. Scheytt, B. Cahill, and G. Gastrock, “Microwave biosensor for characterization of compartments in teflon capillaries,” in Proc. Eur. Microw. Conf. (EuMC), Oct. 29–Nov. 1 2012, pp. 534–537. [12] Y. Ning, C. Multari, X. Luo, C. Palego, X. Cheng, J. C. M. Hwang, A. Denzi, C. Merla, F. Apollonio, and M. Liberti, “Broadband electrical detection of individual biological cells,” IEEE Trans. Microw. Theory Tech., vol. 62, no. 9, pp. 1905–1911, Sep. 2014. [13] A. Denzi, F. Apollonio, M. Liberti, M. Caterina, Y. Ning, C. Multari, C. Palego, X. Cheng, and J. C. M. Hwang, “Cell detection and discrimination by a microfluidic-integrated broadband microchamber,” in Proc. Eur. Microw. Conf. (EuMC), Rome, Oct. 6–9, 2014, pp. 695–698. [14] D. Dubuc, O. Mazouffre, C. Llorens, T. Taris, M. Poupot, J.-J. Fournié, J.-B. Begueret, and K. Grenier, “Microwave-based biosensor for on-chip biological cell analysis,” Analog Integr. Circuits Signal Process, vol. 77, pp. 135–142, Nov. 2013. [15] M. Nikolic-Jaric, S. F. Romanuik, G. A. Ferrier, G. E. Bridges, M. Butler, K. Sunley, D. J. Thomson, and M. R. Freeman, “Microwave frequency sensor for detection of biological cells in microfluidic channels,” Biomicrofluidics, vol. 3, no. 3, p. 034103, Sep. 2009. [16] Y. Polevaya, I. Ermolina, M. Schlesinger, B.-Z. Ginzburg, and Y. Feldman, “Time domain dielectric spectroscopy study of human cells II. Normal and malignant white blood cells,” Biochimica et Biophysica Acta, vol. 1419, pp. 257–271, Jul. 1999. [17] Q. Hu, R. P. Joshi, and A. Beskok, “Model study of electroporation effects on the dielectrophoretic response of spheroidal cells,” J. Appl. Phys., vol. 106, no. 2, p. 024701, Jul. 2009. [18] L. L. Sohn, O. A. Saleh, G. R. Facer, A. J. Beavis, R. S. Allan, and D. A. Notterman, “Capacitance cytometry: Measuring biological cells one by one,” Proc. Nat. Acad. Sci. United States of America (PNAS), vol. 97, no. 20, pp. 10687–10690, Sep. 2000. [19] K. Asami, “Characterization of biological cells by dielectric spectroscopy,” J. Non-Crystalline Solids, vol. 305, no. 1–3, pp. 268–277, Jul. 2002. [20] A. Abduljabar, X. Yang, D. Barrow, and A. Porch, “Microstrip Split Ring Resonator for Microsphere Detection and Characterization,” in Proc/ IEEE MTT-S Int. Microw. Symp. Dig. (IMS), Phoenix, AZ, USA, May 17–22, 2015, pp. 1–4. [21] J. Chen, L. Quyen, and X. Zhu, “Loss compensated high- tunable basspass filter usingmicrostrip ring resonators,” in Proc. Int. Conf. Adv. Technol. Commun., Da Nang, Aug. 2–4, 2011, pp. 191–194. [22] K. Chang and L.-H. Hsieh, Microwave Ring Circuits and Related Structures, 2nd ed. New York, NY, USA: Wiley, 2004. [23] A. A. Abduljabar, D. J. Rowe, A. Porch, and D. A. Barrow, “Novel microwave microfluidic sensor using a microstrip split-ring resonator,” IEEE Trans. Microw. Theory Tech., vol. 62, no. 3, pp. 679–688, Mar. 2014. [24] D. M. Pozar, Microwave Engineering. New York, NY, USA: Wiley, 2005. [25] A. Masood, A. Porch, and D. Barrow, Microwave Resonators for Highly Sensitive Compositional Analysis. Saarbrücken, Germany: LAMBERT, 2010. [26] D. J. Rowe, S. al-Malki, A. A. Abduljabar, A. Porch, D. A. Barrow, and C. J. Allender, “Improved split-ring resonator for microfluidic sensing,” IEEE Trans. Microw. Theory Tech., vol. 62, no. 3, pp. 689–699, Mar. 2014. [27] Y. Temiz, R. D. Lovchik, G. V. Kaigala, and E. Delamarche, “Lab-ona-chip devices: How to close and plug the lab?,” Microelectronic Eng., vol. 132, pp. 156–175, Jan. 2015. [28] K. Ren, J. Zhou, and H. Wu, “Materials for microfluidic chip fabrication,” Acc. Chem. Res., vol. 46, no. 11, pp. 2396–2406, Jun. 2013. [29] S. Gowers, V. F. Curto, C. A. Seneci, C. Wang, S. Anastasova, P. Vadgama, G. Yang, and M. Boutelle, “3D printed microfluidic device with integrated biosensors for online analysis of subcutaneous human microdialysate,” Anal. Chem., vol. 87, no. 15, pp. 7763–7770, Aug. 2015.

[30] H. Frohlich, Theory of Dielectrics. New York, NY, USA: Oxford Univ. Press, 1958. [31] F. Buckley and A. A. Maryott, “Tables of dielectric dispersion data for pure liquids and dilute solutions,” Nat. Bureau Standards Circular, vol. 589, p. 6, Nov. 1958. [32] S. Abdalla, “Complex permittivity of blood cells E.coli suspensions,” J. Molecular Liq., vol. 160, no. 3, pp. 130–135, May 2011. Ali A. Abduljabar (S'14) received the B.Sc. and M.Sc. degrees in electrical engineering from University of Basrah, Basrah, Iraq. He is currently working toward the Ph.D. degree at Cardiff University, Cardiff, U.K. He was a Lecturer in wireless and microwave communications engineering with the University of Basrah, Basrah, Iraq. His research concerns the design of microwave sensors and microwave heating techniques for microfluidic systems and non-invasive applications.

Xin Yang received the B.Sc. degree in biomedical engineering from Beijing Jiaotong University, China, and the M.Sc. degree in medical electronics and physics from Queen Mary, University of London, U.K., and Ph.D. degree in medical engineering from Cardiff University, Cardiff, U.K. He is a Lecturer in medical electronics with the School of Engineering, Cardiff University, who has a background in the medical instrumentation and medical ultrasound. He has been exploring innovative techniques including microwave, electrical and optical methods in cancer detection and diagnosis. Much of his research is multidisciplinary, with collaborations with University Hospital Wales, Cardiff School of Medicine and Dentistry. He has published papers in the field of clinical and preclinical ultrasound, and eight textbooks in electronics.

David A. Barrow received the B.Sc. (hons.) degree in biological sciences and the Ph.D. degree in ecological sciences from the University of Wales, Cardiff, U.K. He is a multidisciplinary Scientist and Professor of microfluidics at Cardiff University School of Engineering, He has researched a diversity microfluidic-based phenomena and devices, including chemical sensors, porous silicon, microacoustics, hybrid integration, micromolding, emulsion and digital microfluidics, chemical separations, plasma etching, CFD, microwave sensors, laser micromachining, and marine microanalysis systems. He was a founder of the metaFAB TSB open-access NanoCentre, MSTB Ltd., researching space microsystems, Protasis Corporation, developing microdevices for chemical separations, and Q-CHIP Ltd., developing injectable microencapsulated pharmaceuticals. He currently researchers the fabrication of nuclear fusion targets, artificial cells and stem cell microcapsules.

Adrian Porch received the M.A. degree in physics and Ph.D. degree in low-temperature physics from Cambridge University, Cambridge, U.K. He is a Professor with the School of Engineering, Cardiff University, Cardiff, U.K., and a member of the Centre for High Frequency Engineering. He is also Deputy Director of School, responsible for Research and Innovation. He has over 25 years of experience in applying microwave methods to measure and understand the fundamental properties of electronic materials. More recently, his techniques have been used to develop new types of electromagnetic sensors, with emphasis on applications across different disciplines.

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Hybrid Nonlinear Modeling Using Adaptive Sampling Paweł Barmuta, Student Member, IEEE, Gustavo Avolio, Member, IEEE, Francesco Ferranti, Member, IEEE, Arkadiusz Lewandowski, Member, IEEE, Luc Knockaert, Senior Member, IEEE, and Dominique M. M.-P. Schreurs, Fellow, IEEE

Abstract—This paper proposes a direct method for the extraction of empirical-behavioral hybrid models using adaptive sampling. The empirical base is responsible for the functionality over a wide range of variables, especially in the extrapolation range. The behavioral part corrects the errors of the empirical part in the region of particular interest, thus, it improves the accuracy in the desired region. Employment of response surface methodology and adaptive sampling allows full automation of the hybrid model extraction and assures its compactness. We used this approach to build a hybrid model composed of a robust empirical model available in CAD tools and a Radial Basis Functions interpolation model with Gaussian basis function. We extracted the hybrid model from measurements of a 0.15 GaAs HEMT and compared it with the pure behavioral and pure empirical models. The hybrid model yields higher accuracy while maintaining extrapolation capabilities. Additionally, the extraction time of the hybrid model is relatively low. We also show that a good accuracy level can be achieved with a small number of measurements. Index Terms—Active device modeling, adaptive sampling, behavioral modeling, experimental design, response surface.

I. INTRODUCTION

T

WO main model types are commonly used for the modeling of microwave transistors: empirical and behavioral models. By accounting for the physical constraints present in the device, empirical models mimic the device behavior over

Manuscript received July 02, 2015; revised September 19, 2015; accepted October 11, 2015. This work was supported in part by the Research Foundation Flanders (FWO-Vlaanderen) and in part by the Hercules Foundation. The work of P. Barmuta was supported in part by the European Union in the framework of European Social Fund through the Warsaw University of Technology Development Programme. The work of A. Lewandowski was supported in part by the Polish National Science Center in the framework of project no. 2011/03/D/ST7/ 01731. This paper is an expanded version from the IEEE MTT-S International Microwave SymposiumPhoenix, AZ, USAMay17–222015. P. Barmuta is with the Department of Electronics and Information Technology, Warsaw University of Technology, 00-661 Warsaw, Poland. He is also with the Department of Electrical Engineering, KU Leuven, 3000 Leuven, Belgium (e-mail: [email protected]; [email protected]. be). G. Avolio and D. M. M.-P. Schreurs are with the Department of Electrical Engineering, KU Leuven, 3000 Leuven, Belgium. F. Ferranti is with the Department of Fundamental Electricity and Instrumentation, Vrije Universiteit Brussel, 1050 Ixelles, Belgium. A. Lewandowski are with the Department of Electronics and Information Technology, Warsaw University of Technology, 00-661 Warsaw, Poland. L. Knockaert is with the Department of Information Technology, Ghent University, 9000 Gent, Belgium. Digital Object Identifier 10.1109/TMTT.2015.2495124

a broad range of various variables, e.g., bias voltages, frequencies, etc. However, user experience and understanding of the physical phenomena are required in order to construct these models. Therefore, empirical models are less general, and their extraction procedures are relatively complex. This leads to multiple model modifications and adjustments preceded by thorough measurement investigations [1], [2]. An opposite scenario is related to behavior models. They are not linked to device physics and are usually straightforward to extract. Their generality allows modeling any kind of devices with great accuracy [3]. However, behavioral models are strictly limited by the regions of input variables, for which the models were extracted. In other words, behavioral models perform very well in interpolation tasks, while their accuracy degrades in extrapolation tasks. Lack of prediction capabilities enforces that the modeling and measurements are performed in the same space of input and output variables, which have to be considered during the transistor measurements [4]. This, in turn, entails the need of collecting a very large number of (typically large-signal) measurements [5], [6], which are used in extraction of very complex models [7], [8]. The last problem can be addressed by employment of the response surface methodology [9], [10]. It is based on adaptive sampling, in which consecutive samples (combinations of input variables' values or Large Signal Operating Points (LSOP)) are determined from the previously acquired data. As a result, the amount of information given by each measurement is maximized, and considerably less samples may be required to build an accurate behavioral model [11]. Many works proposed hybrid models combining the advantages of both approaches while overcoming their drawbacks. Some authors propose to improve the accuracy of the empirical models by expanding the number of model coefficients [12]. More degrees of freedom allow achieving a higher level of generality and accuracy. The other way of constructing a hybrid model is to propagate or add the response of one type of model through the response of a second model. This solution is particularly useful when used to combine a behavioral model for the nonlinear transistor core with an empirical model for the parasitic components [3], [13]–[15]. In the previous work [16], the robust empirical model available in CAD tools [17] has been used as a reference to assess the performance of the behavioral models extracted with adaptive sampling. Even though a response surface methodology is primarily aimed at the modeling of packaged devices or complex systems [11], it is hard to provide a well-established behavioral

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model reference. The idea of adaptive sampling is to consecutively perform the measurements that are expected to provide the most valuable information, e.g., in highly nonlinear areas or undersampled areas. Adaptive sampling allows obtaining behavioral models that outperform the empirical model within already 70 measurement samples [16]. In this paper, which is an extension of [16], the response surface methodology is not only compared with a CAD available empirical model, but it is also proposed as its complementary part. The novelty lies in the proper combination of the advantages provided by empirical and behavioral models, as only a few types of behavioral models are suitable to form a hybrid with good extrapolation capabilities. Due to incorporation of the response surface concepts, a direct and very efficient extraction of the proposed hybrid model is achieved. The paper is organized as follows: In Section II the hybrid model structure is discussed with particular attention paid to the requirements for the behavioral part. Then, in Section III the model extraction procedure is explained in comparison to the classical approach of empirical model extraction using largesignal measurement data. Section IV presents the experimental setup that allows a careful and consistent comparison of the results discussed in Section V. Finally, the conclusions are drawn in Section VI. II. HYBRID MODEL The hybrid model can be formulated as follows:

Furthermore, one can replace the expensive extraction procedures based on the multiobjective optimization of multiple model parameters with usually less accurate but direct extraction procedures. The difference between the measurement value and the empirical model prediction (2) can be approximated by the behavioral model. Of course, the better the fit of the empirical model, the less complex behavioral model is needed. However, the extraction of the behavioral part is relatively cheap in terms of user experience and expertise level, and the whole extraction method of the hybrid model can be easily automated. Even though the proposed formulation (1) is very general, it puts specific demands on the behavioral part of the hybrid model, as described in the following Sections. A. Differentiability The very first requirement is that the behavioral part should be differentiable with respect to the input variables. This is needed by many optimizers and some simulators like harmonic balance analysis. Furthermore, this requirement suits better physical phenomena, in which the speed of processes is limited by the finite amount of power. Most of the behavioral models used in the microwave field meet this requirement. One of the most successful are splines, Artificial Neural Networks (ANN), and Radial Basis Functions (RBF).

(1) where is the value of the modeled quantity calculated for the sample using the empirical and behavioral models. Since the hybrid model should be implementable in CAD environments, should be either a current/voltage or incident/scattered wave pair. The sample can be either LSOP or the time-domain waveform, depending on the simulation set-up and model implementation. Since (1) is very general, it allows a great level of freedom in choosing how each part of the model contributes to the overall accuracy. However, one should have in mind that the behavioral model performs poorly in extrapolation. Therefore, the hybrid model should be based mainly on a robust, well-fitted empirical part to maintain the model functionality in a wide range of input variables. At the same time, the behavioral part can be used to boost the accuracy in the region of interest, as it performs well in the interpolation tasks. The biggest advantage of (1) is that the requirements for the interpolation accuracy of the empirical part are much more relaxed than those for the accuracy of purely empirical models. Therefore, empirical model no longer has to be modified in order to improve the accuracy. As stated before, such modifications require vast user experience and insight into the device behavior. Extraction of the hybrid model allows re-usage of existing tools for the extraction of the empirical part. The additional cost of hybrid model extraction and implementation is relatively small in comparison to the development or modification of the empirical model itself.

B. Convergence in the Extrapolation Region Since the behavioral models are purely data based, they have no or very limited extrapolation capabilities. On the contrary, empirical models usually perform well over a very broad range of different variables. As such, the hybrid model should be based on both models in the interpolation region, and only on the empirical models in the extrapolation region . However, one cannot simply set the response of the behavioral models to zero when entering the extrapolation region, as it will violate the first requirement of differentiability. In theory, splines are possible, but they are not well-suited for scattered data sets generated by the adaptive sampling. Therefore, the behavioral models themselves need to ensure that their response is zero at infinity. For example, the popular ANN with sigmoid activation function cannot be used as the output layer. Instead, some types of RBFs can be employed, e.g., Gaussian and inverse multiquadratic [18]. In this work we consider interpolation Gaussian RBF models (3) is the -th weight, is the -th sample, is the shape where parameter common for all the RBFs and is the number of samples. It is infinitely differentiable, and it has already been shown that it performs well in modeling of nonlinear active devices [11], [16].

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Fig. 1. Flow diagram of the model extraction procedure with optimization of the empirical model against large signal measurements (left branch), and the proposed procedure of hybrid model extraction with response surface methodology (right branch).

III. EXTRACTION PROCEDURE The flow diagram depicting the proposed model extraction procedure is shown in Fig. 1. The first step of the procedure consists of extracting the main parameters of the empirical model directly from measurements, without any optimization steps. Specifically, initial values of the parasitic elements can be extracted from ‘cold’ FET measurements with the channel pinched and the channel open [19]. Next, multibias Y-parameters, derived from multibias S-parameters, can be used to derive initial estimate for the nonlinear capacitances model [20]. Finally, the main parameters of the nonlinear currents can be extracted by few dc measurements in the linear and saturation regions. This paper follows the Angelov model extraction-procedure described in [21]. As regarding the gate Schottky junction, parameters can be extracted by keeping and sweeping to drive the junction in forward conduction. Then, the parameters of the drain current and charge sources are extracted from the sweep, while keeping the device in the saturation region and cold region . For example, the main parameters of the drain current and gate-source charge can be extracted as shown in Fig. 2 and Fig. 3. The other model parameters can be either set to the default values implemented in the CAD or gathered from literature [21]. It has to be noticed that all the parameters of the initial empirical model are determined directly from the data, and there is no need for optimization. Thus, the model extraction is particularly simple in implementation and evaluation [22]. In the classical approach, once initial values of the model parameters are determined, the next step consists of fitting the nonlinear currents and charges against nonlinear measurements [23]. Large signal measurements are typically gathered following the factorial Design of Experiments (DoE) [24]. In this DoE samples are placed equidistantly on the tensor product grid, i.e., samples are uniformly set along each of the input dimensions. The number of samples per dimension is referred to as the factorial DoE level. The process of optimization may be the most troublesome, as it may require user experience and supervision. Since the empirical model consists of multiple

Fig. 2. Measured dc current at the drain port (black dashed line) and (gray solid line) as a function of at . transconductance

Fig. 3. derived from multibias S-parameters at (gray solid line) as a function of line) and its derivative

(black dashed at .

nonlinear functions, the cost function used by the optimizer has very likely multiple local optima. Moreover, the model parameters have to be constrained during optimization to a very particular ranges of values, in order to avoid unphysical or unreasonable results. Another challenge is setting the proper size of the initial DoE in large-signal measurements. A too small size will impede the final model accuracy, while a too large size will unduly prolong the optimization time. Contrary to the classical approach, in the proposed method the large signal measurements are performed sequentially using adaptive sampling algorithms. For each of the LSOP samples, the corresponding response of the initial empirical model is calculated using existing CAD tools, which allows computing the

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difference between the measurement results and empirical model prediction. Since the intermediate models of serve in the adaptive sampling algorithms, the response surface methodology should focus on the regions, where the initial empirical model does not reflect the true behavior of the measured device, i.e., where the prediction error is nonlinear. In this way, the total error of the resulting hybrid model is expected to diminish very quickly with an increasing number of large-signal measurements. The shape parameter of the interpolation RBF models (3) was determined in an evolutionary procedure, which is far computationally-cheaper than nonlinear optimization for . In each modeling iteration, 20 realizations of are generated randomly with normal distribution (trimmed to [0.5, 5] range) around a given starting value . Then, a five-fold cross-validation errormeasure (root relative square error) is calculated and stored for each [9]. If the is set, the model parameters are found by solving a linear system of equations [18]. This can be solved in a single algebraic operation instead of relatively expensive iterative optimization, which is used for example in ANN extraction [25]. In the previous works [11], [16], we have also included a polynomial part in the RBF models to improve their interpolation performance. However, polynomials cannot be used for the hybrid models, as they do not converge to 0 at the infinity, and they will affect the accuracy of the extrapolation. Shape parameters corresponding to the best scores in the whole modeling history are used to calculate the new starting value for the next modeling iteration:

Fig. 4. Picture of the measurement setup and the device-under-test.

TABLE I INITIAL VALUES OF THE EMPIRICAL MODEL PARAMETERS

(4) (5) where is a vector of . The corresponding to the best measure score in the modeling history is used to extract the final model. IV. EXPERIMENTAL SETUP In order to evaluate the proposed method, the measurement system shown in Fig. 4 was set up. It consists of a Source Measure Unit (SMU), which sets the bias voltages and reads the corresponding currents, and a Nonlinear Vector Network Analyzer (NVNA) that is responsible for collecting small signal and large signal data. The Device Under Test (DUT) was a six-finger GaAs pHEMT manufactured by TriQuint with gate dimensions (same technology, but different device than in [16]). Much attention was devoted to the proper calibration, i.e., dc calibration of the lead resistances, TRL calibration with deembedding structures. Inaccurate measurements can perturb the empirical model extraction, and thus bias the comparison results. During the initial stage of the extraction procedure shown in Fig. 1 the dc voltages were swept as follows: gate voltage with 0.1 V step, and drain voltage with 0.2 V step. In order to protect the DUT, the power constraint was set to 0.3 W. For each of the bias points S-parameters were collected over the frequency range with 0.1

GHz step. The initial set of empirical model parameters is shown in Table I. In the second stage of both procedures (standard and proposed), large signal measurements were performed as a function of the following input variables: gate voltage , drain voltage , and input power . The fundamental frequency was . The output variables were the dc currents and scattered traveling voltage waves at the first three harmonics of acquired at gate and drain ports, respectively. As the interpolation RBF models considered in this work support only real output quantities, 14 quantities were modeled in total. For the classical approach, the large signal measurements were acquired according to the factorial DoE, whose level was swept from 2 to 10 (from 8 to 1000 samples). This allowed us investigating how the empirical model optimization process is affected by the amount of training data. The model optimization was performed in Keysight ADS v. 2013 using combination of random and gradient optimizers with 2000 iterations as a stop criterion. All the calculations in this paper were done on the same machine (i7-3610QM @ 2.3 GHz), in order to have a consistent comparison. All the experiments were automated and the controlling software (Matlab) was interfaced with a circuit simulator (Keysight

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ADS v. 2013) enabling harmonic-balance in order to compute the response of the empirical model. Our response surface methodology and adaptive sampling technique are based on a modified version of the SUrrogate MOdeling Toolbox [26]. The adaptive sampling algorithm was a mixture of Voronoi (space exploration), LOLA (nonlinearity exploitation), and model-error minimization methods [11], [27], [28]. In order to combine the adaptive sampling methods, the scores of Voronoi and LOLA rankers were multiplied. As it is impossible to do so with the error-based sampling algorithm, random selection of the sampling method was performed [11]. For each requested sample, the probability of choosing the Voronoi-LOLA mixture was 70%, and the error-based algorithm was 30%. In order to obtain results comparable with the classical approach, the final stop criterion was the evaluation of 512 samples, which corresponds to the factorial DoE level eight. It must be emphasized, though, that the stop criterion in a response surface methodology can usually be set by an error-related threshold value. This prevents oversampling, which might result in model overfitting. Two experiments with hybrid models were conducted. In the first one, the empirical part was the coarse, not-optimized empirical model [17] described by Table I. In the second hybrid model, its empirical part was optimized against 1000 large signal measurements. This allowed assessing the contribution of each of the model parts to the model accuracy. In addition to the large signal measurements collected for both methods, two independent test sets were collected. The first data set consisting of 3000 large signal measurement samples in the same input variables ranges as for the measurements for the model extraction. This dataset was used as a validation set for interpolation capabilities. Since the whole experiment took considerable amount of time (two days), part of this test set ( samples in total) was remeasured between each of the experiment stages ( repetitions in total). This allowed assessing the drifts of the experimental set-up

(6) where is the -th repetition of the measurement for sample . The second test set consisting of 3000 samples was meant for extrapolation assessment. Therefore, the input variables ranges were extended as follows: , , . This test set was constrained by the maximum dissipated power , maximum instantaneous gate voltage , and maximum instantaneous drain voltage . The input space region common with the interpolation test set was excluded. The input variables samples in both validation sets (interpolation and extrapolation) were generated randomly with uniform distribution. The test sets were employed to calculate the error metrics: Mean Absolute Error (MAE), Mean Square Error(MSE), and Mean Relative Error (MRE). The proposed hybrid model is meant for design applications, thus, the Mean Absolute Error is shown in this paper, as it reflects the average performance

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across the whole input variables' space. However, the other metrics are also monitored, as large MSE values indicate the presence of outliers, and large MRE values suggests that the model has problems with prediction of small quantities. V. RESULTS AND DISCUSSION A. Interpolation Fig. 5 shows MAE of the scattered waves as a function of the number of large-signal samples used to train the model. The hybrid models show superior performance over the purely empirical model for all the modeled quantities irrespectively to the error metric (MAE, MSE, MRE). The errors become smaller already within the first 27 samples. In comparison with the purely RBF models, the hybrids also show better performance for all the quantities except for the scattered wave at the gate side at the third harmonic, as shown in Fig. 5(c). This is caused by inaccurate empirical base, which has to replace the polynomial part of a standard RBF model. Coarse empirical model was directly extracted from the S-parameters and dc measurements, and as is does not account for the nonlinearities manifested in large-signal measurements. Moreover, the higher order derivatives, which are used for extracting the nonlinear drain sources, are prone to the measurement noise. Optimized empirical models also fail in accurate prediction of the quantities at higher harmonics since they were optimized to the large-signal data using MSE. Contrary, the purely RBF models are much better in modeling of highly nonlinear quantities at higher harmonics than the relatively linear ones at the fundamental frequency. This is caused by the shape of the basis function. It is particularly pronounced in Fig. 5(a), where an over-fitting occurs for more than 125 samples. More basis functions only causes the response to be more corrugated, while the true device behavior is linear. This is consistent with the results presented in [11], [16]. It can be seen that the accuracy of hybrid models is greater than the sole RBF or empirical models, irrespectively on the empirical base of both hybrids. It only takes less than 27 large signal samples using adaptive sampling to gain smaller MAE than the pure empirical model optimized with 1000 large signal measurements. Furthermore, the error performance is very similar for both hybrids, and the employment of the optimized empirical part improves the results very slightly. Thus, the optimization step of the empirical model can be omitted while building a hybrid model. For the sake of experiment sanity, the modeling errors were compared with the drifts levels gathered in Table II. It can be noticed that the error level is higher than the drift level, even after measurements of more than 12000 large-signal samples including the extrapolation region, and the total time of the experiment exceeding two days. Thus, measurements can be perceived as consistent and the errors originate rather in the models than in the non-stationarity of the measurement system. In order to check if the modeling performance is uniform in the input variables space, the sum of absolute errors for all the modeled quantities was calculated in three bins per input variable. The best models were taken into consideration, i.e.,

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Fig. 6. Absolute error distribution for the considered models in a bin grid. The area of each square is proportional to the total absolute error of the corresponding model. The subsequent squares are placed clockwise starting from top-right around the centers of the bins.

Fig. 7. Samples distribution for models using adaptive sampling in a bin grid. The height of each rectangle is proportional to the number of samples in the corresponding bin.

Fig. 5. Mean absolute error for different models as a function of the number of samples used to train the model. Real parts—black lines, imaginary parts—gray lines. (a)—first harmonic of scattered wave at the HEMT drain port; (b)—third harmonic of scattered wave at the HEMT drain port; (c)—third harmonic of scattered wave at the HEMT gate port.

TABLE II DRIFTS LEVELS

the empirical model optimized with 1000 large signal samples, and RBF-based with 512 samples. The results are reported in Fig. 6. It can be clearly seen that the error relationships between the models, which are depicted in Fig. 5, are maintained in the

whole space of input variables. Thereby, the hybrid models are suitable for describing various phenomena present in the DUT, and not only particular ones. For pure empirical and pure behavioral models the error is highest in the area corresponding to high , , and values, where the values of the modeled quantities are largest. At the same time, for hybrid models the most erroneous area is shifted towards low values, where the DUT shows bigger nonlinearity than in the saturation region. To check how the error is supported by adaptive sampling, the sample distributions were calculated in the same bins as for the error distribution. The results are shown in Fig. 7. It can be noticed that the adaptive sampling places considerably more samples in the highly nonlinear region (LOLA algorithm), while the rest of the input space is sampled evenly (Voronoi algorithm). However, the empirical core of the hybrid model allows focusing more on the more nonlinear regions, e.g., optimized empirical, RBF hybrid vs. pure RBF. Notwithstanding the small differences in distributions, the better error performance of the hybrid models in comparison to pure RBF model is due to employment of the good empirical base for hybrid models.

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Fig. 8. Time-domain waveforms of the scattered waves for the considered models in comparison to the measurement result. The MAE for the considered measurement sample is the closest value to the median absolute error for the hybrid consisting of RBF and initial empirical models. (a)—scattered waves at the HEMT gate port; (b)—scattered waves at the HEMT drain port.

Finally, in order to give a better feeling of the aggregated error measure MAE, the typical performance of the hybrid models was investigated in Fig. 8. The MAE for the considered measurement sample is the closest value to the median error value for the hybrid consisting of RBF and initial empirical models. One can perceive that all the models retain similarity to the measured waveform. The maximum error for the optimized empirical model is equal to 0.0045 V for and 0.091 V for . RBF shows the same error for , but for the maximum error is lower and equal to 0.033 V. However, the hybrid models perform much better irrespectively of the DUT port. For the quantity the error does not exceed 0.0005 V and 0.0003 V for the hybrid model with coarse empirical model and with optimized empirical model, respectively. For the quantity the corresponding error values are 0.002 V and 0.005 V. The results are consistent with Fig. 5. B. Extrapolation After the assessment of the interpolation capabilities of the considered models, their extrapolation performance was evaluated using the extrapolation test set. The total error for all the quantities predicted by different model types was calculated in 1D uniform bins along the input variables. The results are shown

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in Fig. 9. As expected, pure behavioral RBF model has the worst extrapolation performance. At the same time, the hybrid models outperform even the pure empirical ones in all the extrapolation regions. This proves that the assumptions of differentiability and convergence make sense. Since the physical phenomena are differentiable, the resulting characteristics of the DUT are not expected to be very abrupt. As the error of the hybrid models is small in the interpolation region, it should also remain smaller in the close proximity to the interpolation region due to differentiability. In larger distance from the interpolation region, the models profit exponentially from their empirical base, as the behavioral contribution decays with the euclidean norm (3). Therefore, the hybrid model response converges to the response of its empirical part. It is particularly visible in Fig. 9(a), where the extrapolation region is relatively wide in comparison to the interpolation one. Concluding, the extrapolation performance relies mainly on the fitting of the empirical part, as can be seen when comparing the hybrid models with different empirical bases. Example waveforms for a sample located deeply in the extrapolation region ( , , ) are shown in Fig. 10. It can be seen that the error is inversely proportional to the contribution of the empirical model. Pure RBF models show the worst performance with error reaching 0.16 V for and 1.86 V for . The addition of the non-optimized empirical model allows predicting the waveforms significantly better with a maximum error of 0.02 V and 0.35 V for and , respectively. The best extrapolation capabilities were achieved for the optimized empirical model and its hybrid, for which the errors are smaller than 0.005 V for and 0.007 V for . This can be explained by the fact that the response of the hybrid model is almost completely based on its empirical part when it comes to significant extrapolation. The results are consistent with Fig. 9. C. Complexity Last but not least, the computational complexity of the methods was investigated. Thereby, the same MAE figures as in Fig. 5, but as a function of the time needed to reach the corresponding error levels were plotted. The results for are shown in Fig. 11. The benefit of incorporating RBF models with adaptive sampling is now even more pronounced. The initial dc and small-signal measurements and extraction of the initial empirical model took 24 minutes in total. Within this time one can already extract a much more accurate pure RBF model with 141 LSOP samples. However, it takes only additional 8 minutes (27 samples) to extract a hybrid model that is more accurate than the pure empirical model extracted with 1000 LSOP samples. This is true for all the measured quantities. In 5 additional minutes (37 minutes and 52 large signal samples in total), the hybrid model with coarse empirical part becomes more accurate than the pure behavioral model with 203 samples. Similar performance was achieved for all the measured quantities, except the ones for the third harmonic, for which pure RBF models show similar interpolation error with respect to the hybrid models. The measurements and the optimization of the empirical model with 1000 samples took 120 minutes in total. In this time, one can extract a hybrid model with coarse

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Fig. 10. Time-domain waveforms of the scattered waves for the considered models in comparison to the measurement result. The sample was chosen , , to lie deep in the extrapolation region: . (a)—scattered waves at the HEMT gate port; (b)—scattered waves at the HEMT drain port.

Fig. 9. Total mean absolute error of the models in the extrapolation regions per bin along different input variables: (a)—gate voltage , (b)—drain voltage , . The vertical dashed lines delimit the interpolation and (c)—input power extrapolation regions.

empirical part and RBF part based on 370 large signal samples, which has more than one order of magnitude smaller error for . Unless the purpose of the model extraction is providing insight into the device phenomena, the proposed hybrid model is a good candidate for replacement of the lengthy empirical model optimization in design applications. However, it must be emphasized that the computational complexity of the response surface technology is higher than the sole optimization complexity of the empirical model. It can be seen that the optimization with 1000 samples takes less time than achieving 512 samples in response surface technology. This is related to the intermediate modeling steps, as well as the sampling algorithms complexity. Nevertheless, the response surface methodology aims at maximizing the information gain from

Fig. 11. Mean absolute error for different models as a function of measurement and computational time. Real parts—black lines, imaginary parts—gray lines.

the initial samples, where the complexity-related issues are less cumbersome. VI. CONCLUSIONS In this paper, we have discussed a method for the direct extraction of empirical-behavioral hybrid models using adaptive

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sampling. The resulting model is particularly meant for design applications. The hybrid model combines robustness of the empirical part with interpolation accuracy of the behavioral part. Employment of the response surface methodology enabled full automation of the extraction procedure. The adaptive sampling allowed minimizing the number of samples required to achieve an accurate model. The resulting compactness of the hybrid model is an important criterion in the model evaluation and distribution. The model was based on the measurements of a 0.15 GaAs HEMT. The Angelov empirical base of the hybrid model was extracted directly from dc and small-signal measurements. The behavioral part of the hybrid model was based on interpolation Gaussian RBF models, which assures differentiability and convergence of the hybrid to its empirical part in the extrapolation region. The hybrid model allowed achieving a better interpolation performance within the first 27 samples comparing to the empirical model optimized with 1000 samples. In design applications, a short extraction time and straightforward extraction procedure make the hybrid model a good replacement for the time-consuming and experience-demanding optimization procedure of the pure empirical model. At the same time, the hybrid model preserves extrapolation capabilities similar to the optimized empirical model, which is an order of magnitude better than the performance of the pure behavioral model. ACKNOWLEDGMENT P. Barmuta would like to thank Prof. I. Angelov for valuable discussions. REFERENCES [1] S. Albahrani, J. G. Rathmell, and A. E. Parker, “Characterizing drain current dispersion in GaN HEMTs with a new trap model,” in Proc. Eur. Microw. Conf. (EuMC), 2009, pp. 1692–1695, IEEE. [2] P. Cabral, J. Pedro, and N. Carvalho, “Nonlinear device model of microwave power GaN HEMTs for high power-amplifier design,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 11, pp. 2585–2592, Nov. 2004. [3] D. Root, “Future device modeling trends,” IEEE Microw. Mag., vol. 13, no. 7, pp. 45–59, Nov. 2012. [4] P. Roblin, D. Root, J. Verspecht, Y. Ko, and J. Teyssier, “New trends for the nonlinear measurement and modeling of high-power RF transistors and amplifiers with memory effects,” IEEE Trans. Microw. Theory Tech., vol. 60, no. 6, pp. 1964–1978, Jun. 2012. [5] J. Wood, D. Root, and N. B. Tufillaro, “A behavioral modeling approach to nonlinear model-order reduction for RF/microwave ICs and systems,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 9, pp. 2274–2284, Sep. 2004. [6] D. Ribeiro, P. Cruz, and N. Borges Carvalho, “Synchronous oversampled measurements for the extraction of mixed-signal behavioral models in digital to analog integrated transmitters,” IEEE Trans. Microw. Theory Tech., vol. 62, no. 12, pp. 3183–3192, Dec. 2014. [7] P. Cruz and N. Carvalho, “Wideband behavioral model for nonlinear operation of bandpass sampling receivers,” IEEE Trans. Microw. Theory Tech., vol. 59, no. 4, pp. 1006–1015, Apr. 2011. [8] W. Demenitroux, C. Maziere, E. Gatard, S. Dellier, M. Campovecchio, and R. Quere, “Multiharmonic volterra model dedicated to the design of wideband and highly efficient GaN power amplifiers,” IEEE Trans. Microw. Theory Tech., vol. 60, no. 6, pp. 1817–1828, Jun. 2012. [9] A. Forrester, A. Sobester, and A. Keane, Engineering Design via Surrogate Modelling: A Practical Guide. New York, NY, USA: Wiley, 2008.

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[10] D. Motgomery, Design and Analysis of Experiments, 6th Edition. New York, NY, USA: Wiley, 2004. [11] P. Barmuta, F. Ferranti, G. Gibiino, A. Lewandowski, and D. Schreurs, “Compact behavioral models of nonlinear active devices using response surface methodology,” IEEE Trans. Microw. Theory Tech., vol. 63, no. 1, pp. 56–64, Jan. 2015. [12] I. Angelov, N. Rorsman, J. Stenarson, M. Garcia, and H. Zirath, “An empirical table-based fet model,” IEEE Trans. Microw. Theory Tech., vol. 47, no. 12, pp. 2350–2357, Dec. 1999. [13] A. Raffo, G. Bosi, V. Vadala, and G. Vannini, “Behavioral modeling of GaN FETs: A load-line approach,” IEEE Trans. Microw. Theory Tech., vol. 62, no. 1, pp. 73–82, Jan. 2014. [14] A. Santarelli, D. Niessen, R. Cignani, G. Gibiino, P. Traverso, C. Florian, D. Schreurs, and F. Filicori, “GaN FET nonlinear modeling based on double pulse I/V characteristics,” IEEE Trans. Microw. Theory Tech., vol. 62, no. 12, pp. 3262–3273, Dec. 2014. [15] G. Crupi, D. Schreurs, A. Caddemi, I. Angelov, R. Liu, M. Germain, and W. De Raedt, “Combined empirical and look-up table approach for non-quasi-static modelling of GaN HEMTs,” in Proc. 9th Int. Conf. Telecommun. Modern Satellite, Cable, Broadcasting Services, Oct. 2009, pp. 40–43. [16] P. Barmuta, G. Avolio, F. Ferranti, A. Lewandowski, and D. Schreurs, “Large-signal modeling of on-wafer microwave transistors based on response surface methodology,” in Int. Microw. Symp., May 2015, pp. 1–4. [17] I. Angelov, H. Zirath, and N. Rosman, “A new empirical nonlinear model for HEMT and MESFET devices,” IEEE Trans. Microw. Theory Tech., vol. 40, no. 12, pp. 2258–2266, 1992. [18] M. D. Buhmann, “Radial basis functions,” Acta Numerica 2000, vol. 9, pp. 1–38, 2000. [19] G. Crupi, D. Schreurs, and A. Caddemi, “On the small signal modeling of advanced microwave FETs: A comparative study,” Int. J. RF Microw. Comput.-Aided Eng., no. 5, pp. 417–425, May 2008. [20] G. Avolio, A. Raffo, I. Angelov, V. Vadala, G. Crupi, A. Caddemi, G. Vannini, and D. Schreurs, “Millimeter-wave FET nonlinear modelling based on the dynamic-bias measurement technique,” IEEE Trans. Microw. Theory Tech., vol. 62, no. 11, pp. 2526–2537, Nov. 2014. [21] G. Crupi and D. Schreurs, Microwave de-embedding: From Theory to Applications. New York, NY, USA: Academic, 2013. [22] D. Root, J. Xu, F. Sischka, M. Marcu, J. Horn, R. Biernacki, and M. Iwamoto, “Compact and behavioral modeling of transistors from NVNA measurements: New flows and future trends,” in Proc. Custom Integr. Circuits Conf. (CICC), Sep. 2012, pp. 1–6. [23] I. Angelov, M. Thorsell, D. Kuylenstierna, G. Avolio, D. Schreurs, A. Raffo, and G. Vannini, “Hybrid measurement-based extraction of consistent large-signal models for microwave FETs,” in Proc. Eur. Microw. Conf. (EuMC), Oct. 2013, pp. 267–270. [24] T. J. Santner, B. J. Williams, and W. I. Notz, The Design and Analysis of Computer Experiments. New York, NY, USA: Springer, 2003. [25] J. Xu, R. Jones, S. Harris, T. Nielsen, and D. Root, “Dynamic FET model—DynaFET—for GaN transistors from NVNA active source injection measurements,” in Proc. Int. Microw. Symp., Jun. 2014, pp. 1–3. [26] D. Gorissen, K. Crombecq, I. Couckuyt, T. Dhaene, and P. Demeester, “A surrogate modeling and adaptive sampling toolbox for computer based design,” J. Mach. Learning Res., vol. 11, pp. 2051–2055, 2010. [27] K. Crombecq, D. Gorissen, D. Deschrijver, and T. Dhaene, “A novel hybrid sequential design strategy for global surrogate modeling of computer experiments,” SIAM J. Sci. Comput., vol. 33, no. 4, pp. 1948–1974, 2011. [28] K. Crombecq, L. De Tommasi, D. Gorissen, and T. Dhaene, “A novel sequential design strategy for global surrogate modeling,” in Proc. Winter Simulation Conf. (WSC), 2009, pp. 731–742. Paweł Barmuta received the M.Sc. degree in electronic engineering from Warsaw University of Technology, Warsaw, Poland, in 2011. Since 2012 he has been with KU Leuven, Belgium and Warsaw University of Technology, Poland, where he is working towards a dual Ph.D. degree in electrical engineering. His research interests are nonlinear microwave measurements, measurement automation, and calibration techniques.

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Gustavo Avolio was born in Cosenza, Italy, in 1982. He received the the M.Sc. degree in electronic engineering from the University of Calabria, Calabria, Italy, in 2006. In 2012, he received the Ph.D. degree in electronic engineering from KU Leuven, Belgium. He is currently a Postdoctoral Researcher supported by FWO Vlaanderen Belgium. He was a Visiting Scientist with the University of Ferrara, Italy, in 2009, 2011, and 2014. In 2013 and 2014 he was a Visiting Scientist with the National Institute of Standards and Technology (NIST), Boulder, CO, USA. His research work focuses on large-signal measurements and nonlinear modeling of active microwave devices.

Francesco Ferranti (M'10) received the B.S. degree (summa cum laude) in electronic engineering from the Università degli Studi di Palermo, Palermo, Italy, in 2005, the M.S. degree (summa cum laude) (hons.) in electronic engineering from the Università degli Studi dell'Aquila, L'Aquila, Italy, in 2007, and the Ph.D. degree in electrical engineering from Ghent University, Ghent, Belgium, in 2011. He is currently an FWO Post-Doctoral Research Fellow at the Department of Fundamental Electricity and Instrumentation, Vrije Universiteit Brussel, Brussels, Belgium. His research interests include parametric macromodeling, parameterized model order reduction, behavioral modeling, system identification, signal integrity, electromagnetic compatibility and uncertainty quantification.

Arkadiusz Lewandowski (M'09) received the M.Sc. degree and the Ph.D degree (hons.) in electrical engineering from the Warsaw University of Technology, Warsaw, Poland, in 2001 and 2010, respectively. He joined the Institute of Electronics Systems, Warsaw University of Technology, in 2002, where he conducts research in the area of microwave measurements. From 2002 to 2004 he was involved in the development of digital synthesizers of radar signals with the Telecommunications Research Institute, Warsaw, Poland. From 2004 to 2008 he has been a Guest Researcher at the National Institute of Standards and Technology, Boulder, CO, USA, where was engaged in the development of uncertainty analysis and calibration methods for coaxial and on-wafer VNA measurements. His current research interests concern small- and large-signal microwave

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measurements, and modeling of passive and active microwave devices. He has authored and co-authored over 40 scientific papers. Dr. Lewandowski was the recipient of Best Paper Award at the International Microwave Conference MIKON 2008, Poland and the 2005 MTT-S Graduate Fellowship Award.

Luc Knockaert (M'81–SM'00) received the M.Sc. degree in physical engineering, the M.Sc. Degree in telecommunications engineering and the Ph.D. degree in electrical engineering from Ghent University, Ghent, Belgium, in 1974, 1977, and 1987, respectively. From 1979 to 1984 and from 1988 to 1995 he was working in North-South cooperation and development projects at the Universities of the DRC (Democratic Republic of the Congo) and Burundi. He is presently a Professor affiliated with INTEC-IBCN (member of iMinds). As author or co-author he has contributed to more than 150 international peer-reviewed journal papers. His current interests are the application of linear algebra and adaptive methods in signal estimation, model order reduction, machine learning, scientific computing and computational electromagnetics. Dr. Knockaert is a member of MAA and SIAM.

Dominique M. M.-P. Schreurs (S'90–M'97–SM'02–F'12) received the M.Sc. degree in electronic engineering and the Ph.D. degree from the University of Leuven (KU Leuven), Leuven, Belgium. She is currently a Full Professor with KU Leuven, Leuven, Belgium. She has been a Visiting Scientist with Agilent Technologies, Eidgenössische Technische Hochschule Zürich (ETH Zürich), and the National Institute of Standards and Technology (NIST). Her main research interests concern the nonlinear characterization and modeling of active microwave devices and circuits, and system design for wireless power transfer and biomedical applications. Prof. Schreurs is serving on the AdCom of the IEEE Microwave Theory and Techniques Society (MTT-S) and she is editor of the IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES. She also has been MTT-S Distinguished Microwave Lecturer (2012–2014). Moreover she also serves on the Executive Committee of the ARFTG organization and was general chair of the 2007 and 2012 Spring ARFTG Conference. She was also cochair of the European Microwave Conference in 2008.

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A 2.45-GHz Energy-Autonomous Wireless Power Relay Node Massimo Del Prete, Student Member, IEEE, Alessandra Costanzo, Senior Member, IEEE, Apostolos Georgiadis, Senior Member, IEEE, Ana Collado, Senior Member, IEEE, Diego Masotti, Member, IEEE, and Zoya Popović, Fellow, IEEE

Abstract—This paper describes the design and experimental characterization of a battery-less bidirectional 2.45-GHz circuit operating in oscillator mode as a wireless power transmitter or in rectifier mode as an energy harvester, with a measured efficiency greater than 50% in both operating states. The dc voltage harvested in rectifier mode provides the drain bias for the oscillator. The FET-gate self-bias mechanism is exploited in both functionalities, thus eliminating external gate bias. Bi-directionality is based on the time-reversal properties of a transistor oscillator. Energy autonomy is possible at received RF power levels as low as dBm, by means of a bias-assisting feedback loop, consisting of a single matched low-power diode in shunt configuration. A hybrid prototype is demonstrated with the ability to operate as an energy-autonomous power relay node by switching between transmit and receive power modes.

and to enable high-efficiency harvesting capabilities that eliminate the need for battery replacement, thus reducing maintenance cost [3], [4]. In such scenarios, strategically located dedicated RF sources can help increase battery lifetime through wireless power delivery to sensors distributed in the source coverage area. One of the issues in RF energy harvesting (EH) solutions is the unknown and often variable RF link (rectenna location and polarization), which can threaten the effective use of energy-autonomous wireless systems. A useful figure of merit for wireless power transfer (WPT) links is the total RF-to-dc conversion efficiency, from the input of the transmitting antenna to the output of the receiver dc-dc converter [2]:

Index Terms—Autonomous circuit, battery-less, energy harvesting, microwave oscillator, rectifier, wireless power transfer.

I. INTRODUCTION

M

INIATURIZED low-power densely distributed wireless systems are becoming an enabling technology in various applications, such as environmental monitoring, e-health, home and industrial automation [1]. Their main advantages are fast and economical deployment, absence of wiring infrastructure, and seamless dynamic repositioning of devices. Several solutions have been pursued to reduce energy consumption [2],

Manuscript received July 01, 2015; revised September 18, 2015; accepted October 11, 2015. Date of publication November 10, 2015; date of current version December 02, 2015. This work was supported by the EU COST Action IC1301 Wireless Power Transmission for Sustainable Electronics (WIPE). The work of M. Del Prete, A. Costanzo, and D. Masotti was supported in part by the Italian Ministry of the Instruction, University and Research (MIUR), within the framework of the national project GRETA. The work of A. Georgiadis and A. Collado was supported by the Generalitat de Catalunya under Grant 2014 SGR 1551 and by the Spanish Ministry of Economy and Competitiveness and FEDER funds under Project TEC2012-39143. This paper is an expanded paper from the IEEE MTT-S International Microwave Symposium, Phoenix, AZ, USA, May 17–22, 2015. M. Del Prete, A. Costanzo, and D. Masotti are with the Department of Electrical, Electronic and Information Engineering, “Guglielmo Marconi,” University of Bologna, Bologna, Bologna 40126, Italy (e-mail: [email protected]; [email protected]; [email protected]). A. Georgiadis and A. Collado are with Centre Tecnologic de Telecomunicacions de Catalunya (CTTC), Castelldefels, Spain (e-mail: [email protected]; [email protected]). Z. Popovic is with the Department of Electrical, Energy, and Computer Engineering, University of Colorado, Boulder, CO 80309 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2015.2494003

(1) It consists of the product of three power ratios, based on the RF power available at the transmitting antenna input port ( , the RF power received by the rectenna ( , the dc power converted by the rectenna ( , and the dc power ( stored in a dc-dc converter emulating the rectenna optimum load. The transmit-to-receive RF efficiency can be maximized by design of both transmit and receive parts of the WPT system only in the case when dedicated (intentional) RF sources are available. For those devices that are located in areas where these sources would be less efficient, a power relay node can act as an energy repeater. Such a node, capable of bidirectional operation, should be able to harvest sufficient power for its own operation, in addition to providing power to surrounding devices, as illustrated in Fig. 1. Bidirectional systems have been proposed in the literature by exploring the time reversal duality (TRD) [5]. In [6], a 2.4 GHz IMPATT diode based oscillating rectenna demonstrated 85% RF-to-dc efficiency as a rectifier and 1% dc-to-RF efficiency as an oscillator operating at 3 GHz. This publication highlights the challenges in maintaining a high efficiency in both operating modes as well as controlling the oscillation frequency and rectifier bandwidth. In [7], it is demonstrated that class-F RF power amplifiers exhibit comparable efficiencies and power levels when operated as self-synchronous rectifiers. In [8], this concept is extended to a 2.14-GHz 85% efficiency 10-W class-F rectifier and a Fourier expansion-based theory for various classes of harmonically-terminated rectifiers (C, F, ) is developed. In [9] the concept is extended to 10 GHz in a GaN MMIC, and in [10] to a two-stage GaN MMIC. A reconfigurable mW-level class-E oscillator/rectifier in the UHF band is

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Fig. 1. System representation of a bidirectional switchable energy autonomous power relay node: switch in state 1 corresponds to rectifier operating mode; switch in state 2 corresponds to oscillator operating mode.

presented in [11]. Excellent conversion efficiencies (up to 75%) are obtained for both operating modes, but they are strictly dependent on the device bias conditions that need be supplied by external dc batteries. This paper presents a novel circuit solution with bidirectional functionality and without the need for external batteries, by using the energy stored during the rectifier operation mode. The same nonlinear circuit is used to perform the two operations, where two switches are simultaneously driven to position 1 for oscillator operation, and to position 2 for rectifier operation. After initial results reported in [12], the present work develops a systematic description of the system design procedure. The principal nonlinear mechanisms enabling its operational modes are discussed in depth, and the modeling limitations are presented in detail. A new version of the prototype is also presented, and the autonomous operation of the oscillator/rectifier is demonstrated by both simulations and measurements. Finally, the paper presents an experimental proof-of-concept of a wireless power relay node which can switch between the two operations. The remainder of the paper is organized as follows. Section II provides an overview of possible system implementation and addresses the main issues to be solved for successful autonomous power relay node operation. Sections III and IV discuss the nonlinear design of the node: starting from the oscillator design, the rectifier topology is then derived; the two subsystem predicted performances are then experimentally validated. Section V describes the measurement set-up to validate experimentally the ability of the system to behave as an energy-autonomous power relay node. Section VI drives the work conclusions and discusses possible application scenarios where the power relay node can be exploited. II. CIRCUIT LEVEL DESCRIPTION OF THE SYSTEM The main operating principle of the demonstrated power relay node is gate self-biasing of the MESFET [13] for oscillation start-up and rectifier operations with no need for dc biases. For this purpose, a medium power HEMT with weakly negative threshold voltage is chosen, thus enabling to start the device operation from floating gate conditions in both transmit and power-receive modes with the same conversion efficiencies.

In rectification mode, a novel and simple solution based on a single-diode matched network is used as a bias-assisting loop, thus allowing rectification at RF power levels as low as dBm. The network is suitably isolated during oscillator operation by means of a coupler optimized together with the entire nonlinear circuit. Self-sustainability and bidirectionality of the system are then obtained through a sequence of two operations. First, the system is set in rectifying mode to harvest the dc voltage needed to bias the oscillator, and such power can be intentionally provided by RF sources. For this purpose, some recent research has provided the design rules for transmitting ad-hoc RF signals that increase the RF-to-dc conversion efficiency of the receiver [14], [15]. The dc energy can be stored in a super-capacitor or managed for subsequent use. The system can switch into transmitting mode using the harvested dc power to start oscillation. Simultaneous optimization of both operating modes (oscillator and rectifier) is performed with harmonic balance (HB) simulations with optimization goals on the dc-to-RF oscillator efficiency and on RF-to-dc rectifier conversion efficiency. In the present case, an efficiency better than 60% for each optimization is specified as the design goal. The accuracy of the nonlinear simulation is highly dependent on the FET model. For the rectifier and oscillator modelling, a nonlinear model capable of predicting device behaviour in the first and third quadrant of the IV curves is needed, as in [16] and [17]. In particular, the nonlinear models for gate-source, gate-drain, and drain-source capacitances are required to satisfy energy constraints over all drain-source and gate-source voltage variations; the gate-source and gate-drain diodes interchange roles in the two modes of operation. A nonlinear device model from the manufacturer is implemented in KeySight ADS. An acceptable physical consistency with respect to the above mechanisms was tested for the selected device: in Fig. 2 the dc characteristics are plotted, parameterized by for , and by for , showing that the model is able to describe the device symmetry [16]. The dynamic load lines for both the operating modes are given in the same figure: the importance of the third quadrant of the I-V characteristics is evident from the rectifier-mode load line behavior. In order to provide a clear description of the design procedure to be followed, we introduce first the design of the self-biased oscillator, followed by the design of the self-biased rectifier using the TRD principle. Note that the relay node needs to start operating as a rectifier in order to store sufficient energy to become a power transmitter. III. SELF-BIAS OSCILLATOR: DESIGN AND VALIDATION The oscillator circuit topology is shown in Fig. 3, with the switches in State 1. It is designed to obtain a 2.45-GHz Class-F oscillator with a Colpitts-like feedback, embedded in a linear sub-network that is optimized to ensure a class-F second harmonic termination. The higher harmonics are not terminated. To maximize the dc-to-RF efficiency, the drain impedance at each harmonic must satisfy the Class-F harmonic termination condition [18], in addition to the oscillation conditions. For this reason, the HB optimization used in this paper aims to simultaneously meet the Barkhausen conditions and the maximum

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Fig. 2. DC characteristics of the bilateral FET model, parameterized by for , and by for , and dynamic load lines in both operating modes.

Fig. 4. Simulated transient behavior of the oscillator: (a) oscillator output voltage waveform; (b) gate voltage waveforms (gray curve: RF component; black curve: dc component).

Fig. 3. Circuit schematic of the bidirectional energy autonomous power relay node, with 2nd harmonic termination.

dc-to-RF oscillator conversion efficiency, in a suitable range of drain biases. Ideally, the latter condition can be searched during the oscillator design by adding the following constraints to the ratio between the drain voltage and current harmonics to the design goals:

(2) is the drain bias spanning in the interval where oswhere cillation condition is met, and are the drain voltage and current harmonic phasors, and are low and high thresholds, respectively, is the harmonic frequency index of the spectrum. The dc component and 64 harmonics are used, but condition (2) has been applied only for . The active device is a JFET Renesas NE3509M04 with a negative threshold voltage of V. The advantage of a negative threshold is two-fold: 1) the oscillation build-up is possible in the absence of a gate bias, that is, in floating-gate condition and 2) the bias point for optimum conversion efficiency can be reached by gate self-biasing [13]. Note that the same device is used in rectifying mode. In this case, the negative gate threshold

voltage and self-biasing can limit the rectifier sensitivity at low input power levels, but allows bidirectionality without batteries. This can be explained with reference to the nonlinear FET model: as oscillation starts, the gate is floating and the RF signal flows into the gate-source junction through the feed-back draingate capacitance. Due to the Schottky-barrier rectifying property of the gate junction, the RF gate-source voltage generates a dc gate current and the gate capacitance is charged to a negative voltage, thus obtaining a self-biased transistor. In our oscillator topology (Fig. 3), this mechanism is enhanced by the optimized external feed-back network. The transient analysis results of the oscillator start-up are summarized in Fig. 4. Initially, the drain and gate voltages are zero. During oscillation start-up, the self-bias mechanism drives the gate terminal to a negative voltage, the threshold voltage (or lower), thus allowing the oscillator to operate in a high-efficiency region with a reduced conduction angle. This is highlighted in the same figure where the transient behaviour of the dc components of the gate-to-source voltage is superimposed with the time-variable waveform. The shorter the time needed to reach the oscillator class-F steady-state regime, the lower the power dissipated during the oscillator start-up, and the longer the oscillator steady-state operation. This is a critical aspect for energy autonomy of the system, since the energy stored during rectifier operation supports the oscillator steady-state regime. Fig. 5 shows the transient behavior of the drain bias current , representing the transistor transition from a high-loss

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Fig. 5. Simulated transient behavior of the oscillator bias current. Fig. 7. Simulated gate self-bias voltage, and measured and simulated oscillation frequency, with respect to drain bias.

Fig. 6. Measured and simulated oscillator RF-to-dc efficiency and output power with respect to drain bias.

Fig. 8. Measured oscillator output power spectrum.

Class-A to a low-loss Class-F operation. In small-signal condition during start-up, the circuit requires a lot of drain current; after oscillations build-up, the gate terminal is negatively self-biased and the dc drain current is minimized. The dc power consumed to extinguish the oscillator transient is minimized in the present design process and could be further reduced by using a device with shorter channel length. In Fig. 6, the simulated and measured oscillator conversion efficiency and generated output power are plotted versus the drain bias, while Fig. 7 shows the oscillation frequency and gate voltage variations with the drain bias as the tuning variable. To verify by measurements the circuit in oscillator mode, an external bias is used to provide drain polarization (switches of Fig. 3 are in State 1). In Fig. 6, the measured dc-to-RF conversion efficiency and oscillator output power are compared to the simulated ones with varying drain supply voltage. The 15% overestimate in simulations is attributed to the HEMT nonlinear model accuracy. The oscillator efficiency is over 50% for the entire drain supply range starting from 2 V. The oscillator mode has a maximum dc-to-RF conversion efficiency of 52.5% at 4.2 V drain bias voltage and an output power of 14 dBm (Fig. 6). Fig. 8 shows the frequency spectrum of the oscillator, for a drain bias of 4.8 V. As expected, the second harmonic is about 20 dB below the other harmonics.

Fig. 9. Measured phase noise of the oscillator/rectifier circuit in oscillator mode.

The frequency spectrum is measured using an Agilent E4440A PSA spectrum analyzer with a resolution bandwidth of 3 MHz. The oscillator phase noise is shown in Fig. 9. A phase noise of dBc/Hz at 1 MHz from the carrier is measured using the Agilent E4448A PSA vector signal analyzer with span 3 MHz and resolution bandwidth of 1 kHz: the instrument noise floors at frequency offsets of 10 kHz, 100 kHz, and 1 MHz are dBc/Hz, dBc/Hz, and dBc/Hz, respectively. For the phase noise measurements, the circuit was biased with a 4.5-V battery in order to eliminate supply noise.

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IV. SELF-BIAS RECTIFIER: DESIGN AND VALIDATION The goal of this section is to present the design and the simulated performances of the oscillator used as rectifier, without any external bias. By means of the TRD principle [7], rectifiers with high RF-to-dc conversion efficiency can be derived in a straightforward manner from the design of high conversion efficiency amplifier [19] and oscillator [20]. The available solutions usually are not intended for fully autonomous systems and thus make use of external batteries, to adjust the gate bias in rectifier mode, or adopt a different RF gate termination for the rectifier operation. Here, we show a procedure that eliminates the battery and gate termination tuning. Fig. 3 shows the external port arrangement of the system of Fig. 1 for rectifier mode (switches in State 2). The drain is disconnected from the dc bias path and loaded by , which is optimized during the rectifier nonlinear design. The oscillator output port is now fed by the incoming RF signal at 2.45 GHz. Ideally, by means of the TRD principle, according to which the waveforms of a nonlinear device are time reversed versions of their counterparts in the dual device, oscillator, and rectifier drain voltage and current are related by equations (3) thus preserving the intrinsic class-F behavior of the transistor. Consequently, proper device polarization needs be ensured to provide conversion efficiency in rectifier mode, similar to the one obtained in oscillator mode (Fig. 6). However, to pursue the goal of a fully energy-autonomous system, thus getting rid of external batteries, two main issues still need be solved: i) to reach self-synchronized conditions, between the gate and drain voltages, namely waveforms with opposite-phase; ii) to properly select the nonlinear device operating points for several possible RF input power levels, by exploiting the FET self-bias mechanism only. Indeed, synchronous operation has demonstrated to ensure best rectifier conversion efficiency [20]. In this way, a truly seamless switching between the two modes of operation can be performed. To meet the self-synchronization conditions [8], [9] and maximize the efficiency, a nonlinear optimization of the same circuit topology for the concurrent maximization of the oscillator/rectifier performance is carried out. As shown in Section II, a nonlinear device model with accuracy and physical consistencies in the first as well as in the third quadrant of the I-V characteristics (Fig. 2) is mandatory. The load resistance , that plays a crucial role in achieving the best rectifier conversion efficiency, is determined inside the same design procedure, and an optimum value of about 680 is obtained. Figs. 10 and 11 summarize the results of the nonlinear system optimization for the rectifier operation mode. In Fig. 10(a), the simulated RF-to-dc efficiency is plotted. Fig. 10(b) shows the simulated output dc voltage, across the optimum dc load, resulting from the system nonlinear optimization. These plots predict that the circuit is able to operate with efficiency higher than 60% starting from about dBm of input power. This performance is then preserved over a 12-dB RF input power range.

Fig. 10. Measured and simulated RF-to-dc conversion efficiency (a) and output voltage (b) for the oscillator/rectifier circuit operating in rectifier mode, as a function of the input RF power.

Fig. 11. Measured and simulated self-bias gate voltage as a function of the input RF power.

From the same plot, we get the corresponding dc voltage available at the rectifier output. The same figure shows the corresponding measured data: the circuit is able to operate with efficiency higher than 40% starting from input power as low as 4 dBm. This performance is preserved over a 14 dB range in input power.

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Fig. 12. Oscillator/rectifier system schematic with bias assisting loop.

Starting from the floating gate condition , Fig. 11 shows the evolution of the dc gate voltage versus input RF power using the self-bias mechanism. At the lower interval of RF power levels, remains approximately zero; as the power increases, weak rectification is observed up to a selected value at which the dc gate voltage reaches a value lower than the transistor threshold voltage. Increasing further the RF power drives the transistor more deeply in the depletion region, but this does not affect the efficiency performances of the rectifier. Additionally, in Fig. 10, it is shown that the circuit operating in the rectifier mode exhibits hysteretic behavior versus input power. Starting from the minimum RF power levels (solid line), rectification is possible only over 4 dBm. For decreasing input power (dashed line), the measured rectifier operates down to 1.1 dBm. This further limits the input power ranges for which the circuit could rectify, since operating in the hysteresis zone between 1.1 dBm and 4 dBm is undesirable. In the next subsection, we show how we solve this problem by designing a network to act as a bias-assisting loop in rectifier mode without affecting the oscillator mode. A. Bias-Assisting Loop Rectifier As previously mentioned, one drawback of combined oscillator/rectifier circuits based on gate self-bias is that, depending on the transistor threshold voltage, a minimum RF input power is needed to start rectifier operation. To overcome this limitation, a simple network based on a matched low-power diode in shunt configuration, is included to bias the gate when the intrinsic transistor mechanism is not active yet. In this way, the rectifier sensitivity is extended to lower input power levels with an acceptable RF-to-dc conversion efficiency. The bias assisting loop is optimized to operate at low input power levels when the self-bias mechanism is not sufficient. The loop is designed in such a way that it does not affect the oscillator mode of operation, while providing the minimum gate bias to start rectification. Fig. 12 shows the modified architecture of the oscillator/rectifier. The bias-assisting loop is connected to the rectifier input (oscillator output) by means of a microstrip coupler, which drives a sample of the incoming RF signal at 2.45 GHz to the diode through a suitably optimized stepped-impedance open-stub matching network.

Fig. 13. Measured and simulated self-bias gate voltage with bias-assisting loop as a function of the input power.

A Schottky diode (Skyworks SMS7630-079) is chosen and is arranged in shunt configuration providing a negative dc voltage at the transistor gate port. The two quarter-wave lines in the assisting loop play the role of RF blocks, thus ensuring isolation between the Class-F oscillator and the bias-assisting loop. In addition, they provide the dc path for the Schottky diode and the transistor gate. Coupling and isolation coefficients of the coupler are designed to reach the best compromise between high isolation between oscillator and bias assisting loop (demanding high coupler directivity) and minimum power to activate the diode (demanding low coupler directivity). For the present design, a 13-dB coupling coefficient is chosen, resulting in a directivity of 10 dB and an insertion loss of 0.8 dB at 2.45 GHz. A 5% RF-to-dc efficiency degradation has been observed, but the oscillator performance is preserved. Figs. 13 and 14 show the final optimization results for the system of Fig. 12. In Fig. 13, the dc component of the gate voltage is plotted against input RF power: the minimum activation voltage of V is now available at RF input power of dBm. The corresponding simulated RF-to-dc conversion efficiency is shown in Fig. 14: an efficiency better than 60% is ensured for RF power levels ranging from to 10 dBm. Note that for simplicity, the same load is used here for all input power levels. We expect possible improvement in efficiency when a proper dc-to-dc converter is designed to dynamically emulate the optimum load, for any possible RF input [4]. To experimentally characterize the circuit in rectifier mode, the drain bias is disconnected and an input RF signal at 2.45 GHz is fed into the RF port (switches in State 2). The input power levels are varied from dBm up to 18 dBm and the output dc voltage is measured across the output load . Fig. 14 shows the measured output voltage and RF-to-dc conversion efficiency as a function of input power. The same dc load, equal to the one obtained by circuit simulation, was used for these measurements. The measured plot shows that the circuit is able to start operating at dBm, but with an efficiency of about 10%; whereas, for an input power of dBm, the achieved efficiency is better than 40% and this performance is preserved over a 20 dB range in input power. Thus, it can be assumed that the rectifier sensitivity is around dBm. Based on this measured performance,

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Fig. 14. Measured and simulated RF-to-dc conversion efficiency and output voltage with bias-assisting loop as a function of the input power.

Fig. 16. (a) Photo of the fabricated prototype of the bidirectional system with bias-assisting feedback loop; (b) circuit layout with microstrip dimension in mm (width/length).

V. EXPERIMENTAL DEMONSTRATION OF THE ENERGY-AUTONOMOUS POWER RELAY NODE OPERATION Fig. 15. Measured RF-to-dc conversion efficiency and output voltage, with and without bias-assisting loop, as a function of the input power.

the power budget of the link between the RF source and the relay node can be obtained, assuming free-space propagation. For reader and relay node receiving antenna gains of 10 dBi and 7 dBi, respectively, with 1-W transmitted power, the maximum distance needed to guarantee dBm input power to the relay node is about 3.5 m. In comparison with standard reader-tag links, in this case, the knowledge of the position and polarization of the antennas is fully exploited. Note that numerical convergence was difficult to obtain during nonlinear circuit simulation for the results of Figs. 10, 11, 13, 14. Indeed, the circuit simulator was able to handle problems up to about 10 dBm of RF powers, while measurements could be carried out up to 18 dBm. Fig. 15 demonstrates the key role of the bias-assisting loop in enhancing the system performance, by comparing the measured rectifier performance with and without the loop: in the absence of the loop, the rectifier operates over a reduced input power range, approximately from dBm to 18 dBm, with 45–50% of efficiency. With the bias-assisting loop, the minimum voltage required to start gate self-biasing is reached with input power levels as low as dBm, and, by increasing the power, efficiency values similar to the no-loop case are achieved.

The prototype, shown in Fig. 16(a), is realized on an Arlon AN25N substrate ( mm). Two testing ports are placed for measuring the directional coupler insertion loss and the input matching of the bias-assisting loop. Fig. 16(b) shows the circuit layout with details on microstrip dimension (in mm). The adopted SMD components are capacitors from Murata (GRM1885). At the in/out port, an RF switch can be used to connect the node to a directive receiving antenna or to a nondirective transmitting one. To experimentally validate the feasibility of the energy-autonomous power relay node, measurements of the transient waveforms in both rectifying and power transmitting phases were carried out. The block diagram of the measurement set up is shown in Fig. 17; the in/out port of the prototype of Fig. 16(a) are alternatively connected to an RF signal generator (HP B3752A) or to an RF oscilloscope (Tektronix DPO72304DX) through a commercial switch (Skyworks SKY13350-385LF). In the final realization of the system, ad-hoc switch, similar to the one in [22], could be implemented to reduce power consumption and insertion loss. The measurement procedure is carried out in two steps: i) the switch is connected to port 2, i.e., the signal generator and ii) the switch is commuted and is connected through port 3 to the scope. In the first step, the system acts as a rectifier and stores energy into the capacitor . The corresponding charging behavior is plotted in Fig. 18, where the measured time-evolution of is shown. When a stable value of drain voltage is

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Fig. 17. Block diagram of the measurement set-up.

Fig. 18. Measured waveform of the voltage with the system in rectifier mode.

on the storage capacitance

reached, the second step starts and the system oscillation is captured by the scope. For this proof-of-concept demonstration, a storage capacitance of 50 F is used: it can be substituted by a dynamic dc-to-dc converter, able to wake-up the system for low RF input power levels [4], [21]. For the present measurement set-up, we simply make use of a higher input power of 8 dBm, resulting in a rectifier output open circuit voltage of about 2.4 V. This value corresponds to onset of oscillation as shown in the plots of Fig. 6. Fig. 19 reports the measurements of the self-biased oscillator transient, with 2.4 V across the storage capacitor . Specifically, Fig. 19(a) shows the decreasing of with respect to time, corresponding to the discharging behavior of . Fig. 19(b) shows the oscillator RF output voltage evolution along the same time interval: as soon as the system is switched to the oscillator mode, it is loaded by a 50termination with the drain bias of 2.4 V (voltage across ). In such conditions, the oscillation build-up takes place. In Fig. 19(b), it can be observed that, after oscillation build-up, the RF output voltage decreases in the same time as the voltage in the storage capacitor. During this time-interval, the oscillator experiences different nonlinear regimes, as both and change continuously. As a consequence, RF output power, oscillation frequency, and dc-to-RF efficiency change as well. This explains the different slopes observed in Fig. 19(b) during the transient. For the present storage capacitance selection ( F), the rectifier charging and the oscillator transient time intervals are 10-ms and 28-ms, respectively. These different durations are due to the different nonlinear circuits that drive the charging/discharging operations of . It is worth noting that

Fig. 19. Measured waveform of the voltage on the storage capacitance with the system in oscillator mode (a), and transient oscillation waveform (b) of the prototype of Fig. 16(a).

the discharging time (oscillator operation) is three times longer than the charging time, thus allowing a power transmission activity longer than the harvesting one. Of course, both of these transient intervals depend on the value. In this case, the 50 F choice was adopted for measurement purposes to comply with the scope constraint in terms of available memory and sampling rate (12.5 GS/s). For example, for mF and a reduced sampling rate, the measured oscillation is sustained for over half a second, which represents a feasible activation time in real applications [23]. VI. CONCLUSION In this paper, the theoretical and experimental aspects for a true energy autonomous wireless power relay node are presented. The node can operate continuously without a battery, and demonstrates the same efficiency at 2.45 GHz in rectifier power-receive mode and oscillator power-transmit mode. The receiver starts operating at input power levels below 0 dBm and remains in a robust oscillatory regime over a wide range of drain supply voltages. Based on the previously demonstrated time-reversal property, a new oscillator design is developed using the MESFET floating-gate property for self-biasing. An additional feedback network improves the performance of the system. In the rectifier mode of operation, the gate self-bias is enhanced by a single short-circuited diode. An RF switch is included in the prototype to experimentally demonstrate first energy reception and storage, and subsequently autonomous power generation. Measured and simulated results for the 2.45 GHz hybrid prototype

DEL PRETE et al.: 2.45 GHz ENERGY-AUTONOMOUS WIRELESS POWER RELAY NODE

are in good agreement, and the circuit is amenable to monolithic integration. We envision many application scenarios that could take advantage of the presented proof-of-concept: it can be integrated in next-generation sensors, or RFID-enabled sensor tags, for cooperative energy supplying, or it can be configured as a special node/tag, among many standard passive ones, precisely located to fully exploit the point-to-point connection to an RF source. In the first case, randomly placed tags with non-directive antennas will receive or provide energy from/to neighboring nodes depending on their activities. In such situations, the relay capabilities will enable the extension of the nodes energy autonomy. In the second scenario, a highly efficient link can be established between the RF source and the node, while the rest of the (standard) battery-less tags can be randomly and dynamically located in the vicinity of the node, taking advantage of its power generation capabilities. ACKNOWLEDGMENT The authors would like to acknowledge Dr. N. Decarli for his valuable contribution in measurement procedures. REFERENCES [1] S. Kim et al., “Ambient RF energy harvesting technologies for selfsustainable stand-alone wireless sensor platforms,” Proc. IEEE, vol. 102, no. 11, pp. 1649–1666, Nov. 2014. [2] A. Costanzo et al., “Electromagnetic energy harvesting and wireless power transmission: A unified approach,” Proc. IEEE, vol. 102, no. 11, pp. 1692–1711, Nov. 2014. [3] M. Fantuzzi, D. Masotti, and A. Costanzo, “Simultaneous UHf energy harvesting and UWB-RFID communication,” in 2015 IEEE MTT-S Int. Microw. Symp. Dig., May 2015, pp. 1–4. [4] T. Paing, J. Shin, R. Zane, and Z. Popovic, “Resistor emulation approach to low-power RF energy harvesting,” IEEE Trans. Power Electron., vol. 23, no. 3, pp. 1494–1501, May 2008. [5] C. Hamill, “Time reversal duality and the synthesis of a double class E DC-DC converter,” in 21st Power Electron. Specialist Conf. (PESC'90), 1990, pp. 512–521. [6] J. O. McSpadden, R. M. Dickinson, L. Fan, and K. Chang, “A novel oscillating rectenna for wireless microwave power transmission,” in 1998 IEEE MTT-S Int. Microw. Symp. Dig., Jun. 1998, pp. 1161–1164. [7] T. Reveyrand, I. Ramos, and Z. Popović, “Time-reversal duality of high-efficiency RF power amplifiers,” Electron. Lett., vol. 48, no. 25, pp. 1607–1608, Dec. 2012. [8] M. Roberg, T. Reveyrand, I. Ramos, E. Falkenstein, and Z. Popovic, “High-efficiency harmonically terminated diode and transistor rectifiers,” IEEE Trans. Microw. Theory Techn., vol. 60, pp. 4043–4052, Dec. 2012. [9] M. Litchfield, S. Schafer, T. Reveyrand, and Z. Popovic, “High-efficiency X-band MMIC GaN power amplifiers operating as rectifiers,” in 2014 IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2014, pp. 1–4. [10] M. Coffey, S. Schafer, and Z. Popovic, “Two-stage high-efficiency x-band GaN MMIC PA/rectifier,” in 2015 IEEE MTT-S Int. Microw. Symp. Dig., May 2015, pp. 1–4. [11] M. N. Ruiz, A. Gonzalez, R. Marante, and J. A. Garcia, “A reconfigurable class E oscillator/rectifier based on an E-pHEMT,” in 2012 Workshop on Integr. Nonlinear Microw. Millimetre-Wave Circuits (INMMIC), Sept. 2012, pp. 1–3. [12] M. Del Prete, A. Costanzo, A. Georgiadis, A. Collado, D. Masotti, and Z. Popovic, “Energy-autonomous Bi-directional wireless power transmission (WPT) and energy harvesting circuit,” in 2015 IEEE MTT-S Int. Microw. Symp. Dig., May 2015, pp. 1–4. [13] H. Abe, “A GaAs MESFET self-bias mode oscillator (short paper),” IEEE Trans. Microw. Theory Techn., vol. 34, no. 1, pp. 167–172, Jan. 1986. [14] J. A. Hagerty, F. B. Helmbrecht, W. H. McCalpin, R. Zane, and Z. B. Popovic, “Recycling ambient microwave energy with broadband rectenna arrays,” IEEE Trans. Microw. Theory Techn., vol. 52, no. 3, pp. 1014–1024, Mar. 2004.

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[15] A. Boaventura, D. Belo, R. Fernandes, A. Collado, A. Georgiadis, and N. B. Carvalho, “Boosting the efficiency: Unconventional waveform design for efficient wireless power transfer,” IEEE Microw. Mag., vol. 16, no. 3, pp. 87–96, Apr. 2015. [16] V. Rizzoli and A. Costanzo, “An accurate bilateral FET model suitable for general nonlinear and power applications,” Int. J. RF Microw. Comput.-Aided Eng., vol. 10, no. 1, pp. 43–62, 2000. [17] J. Xu, D. Gunyan, M. Iwamoto, J. M. Horn, A. Cognata, and D. E. Root, “Drain-source symmetric artificial neural network-based FET model with robust extrapolation beyond training data,” in 2007 IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2007, pp. 2011–2014. [18] G. Nikandish, E. Babakrpur, and A. Medi, “A harmonic termination technique for single- and multi-band high-efficiency class-F MMIC power amplifiers,” IEEE Trans. Microw. Theory Techn., vol. 62, no. 5, pp. 1212–1220, May 2014. [19] Z. Popovic, T. Reveyrand, S. Schafer, M. Litchfield, I. Ramos, and S. Korhummel, “Efficient transmitters and receivers for high-power wireless powering systems,” in 2014 IEEE Wireless Power Transfer Conf. (WPTC), May 2014, pp. 32–35. [20] M. N. Ruiz, R. Marante, and J. A. Garc´ıa, “A class E synchronous rectifier based on an E-pHEMT device for wireless powering applications,” in 2012 IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2012, pp. 1–3. [21] D. Masotti, A. Costanzo, P. Francia, M. Filippi, and A. Romani, “A load-modulated rectifier for RF micropower harvesting with start-up strategies,” IEEE Trans. Microw. Theory Techn., vol. 62, no. 4, pp. 994–1004, Apr. 2014. [22] A. S. Cardoso, P. Saha, P. S. Chakraborty, D. M. Fleischhauer, and J. D. Cressler, “Low-loss, wideband SPDT switches and switched-line phase shifter in 180-nm RF CMOS on SOI technology,” in 2014 IEEE Radio Wireless Symp. (RWS), Jan. 2014, pp. 199–201. [23] T. Umeda, H. Yoshida, S. Sekine, Y. Fujita, T. Suzuki, and S. Otaka, “A 950-MHz rectifier circuit for sensor network tags with 10-m distance,” IEEE J. Solid-State Circuits, vol. 41, no. 1, pp. 35–41, Jan. 2006.

Massimo Del Prete (S'15) received the B.S. and M.S. degrees in telecommunication engineering from the University of Bologna, Bologna, Italy, in 2007 and 2011, respectively.In 2014, he joined the same Department as a Ph.D. student. His research interests include wearable and multi-band antennas, CAD of microwave integrated circuits, with special emphasis on low-power rectenna, power management for autonomous sensors, and wireless power transmission (WPT). Mr. Del Prete was the 2011 recipient of a research grant issued by the Department of Electrical, Electronic, and information Engineering, University of Bologna, within the ARTEMIS JU SP3 SOFIA European project focused on radio-wave systems design for RFID tags localization in harsh environments.

Alessandra Costanzo (M'99–SM'13) is Associate Professor of electromagnetic fields at the University of Bologna, Italy, and has been since 2001. Her main research interests include multi-domain design (based on nonlinear/electromagnetic co-simulation) of entire wireless links, such as RF-ID, MIMO and UWB, including rigorous modeling of radiating elements and realistic channel models. Recently, she has developed innovative wireless power systems for both far- and near-field solutions. She co-authored more than 150 scientific publications in peer reviewed international journals and conferences and three chapter books; she holds two European and one U.S. patents. She is associate editor of the Cambridge Wireless Power Transfer journal and the International Journal of Microwave and Wireless Technologies. In 2013, she co-funded the EU COST action WiPE “Wireless power transfer for sustainable electronics” where she chairs WG1: “far-field wireless power transfer”. She constantly serves as reviewer of many IEEE TRANSACTIONS. Prof. Costanzo is TPC member of the IEEE MTT-S IMS, EUMW, WPTC, RFID-TA and ICUWB symposia. She has been workshop chair of the EUMW 2014, and is the chair of the IEEE MTT-26 Technical Committee on Wireless Energy Transfer and Conversion, and MTT-S representative of the IEEE Council on RFID.

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Apostolos Georgiadis (S'94–M'02–SM'08) was born in Thessaloniki, Greece. He received the Ph.D. degree in electrical engineering from the University of Massachusetts at Amherst, Amherst, MA, USA, in 2002. In 2007, he joined Centre Tecnologic de Telecomunicacions de Catalunya (CTTC), Barcelona, Spain, as a Senior Researcher, where he is involved in energy harvesting, wireless power transfer and radio-frequency identification (RFID) technology, and active antennas and antenna arrays. Since April 2013, he has been the Group Leader of the Microwave Systems and Nanotechnology Department at CTTC. He was the Chair of EU COST Action IC0803, RF/Microwave communication subsystems for emerging wireless technologies (RFCSET) and presently he is Vice-Chair of EU COST Action IC1301 on Wireless Power Transfer for Sustainable Electronics. Prof. Georgiadis serves as an Associate Editor of the IEEE MICROWAVE WIRELESS COMPONENTS LETTERS, IEEE RFID VIRTUAL JOURNAL, and IET Microwaves Antennas and Propagation journals. He is a Distinguished Lecturer of the IEEE Council on RFID, where he is also recently appointed as VP of Conferences. He is Vice-Chair of URSI Commission D Electronics and Photonics.

Ana Collado (M'08–SM'12) received the M.Sc. and Ph.D. degrees in telecommunications engineering from the University of Cantabria, Santander, Spain, in 2002 and 2007, respectively. She is currently a Senior Research Associate and the Project Management Coordinator at the Technological Telecommunications Center of Catalonia (CTTC), Barcelona, Spain, where she performs her professional activities. Her professional interests include active antennas, substrate integrated waveguide structures, nonlinear circuit design, and energy harvesting and wireless power transmission (WPT) solutions for self-sustainable and energy efficient systems. She has participated in several national and international research projects and has co-authored over 70 papers in journals and conferences. Among her activities, she has collaborated in the organization of several international workshops in different countries of the European Union and also a Training School for Ph.D. students. Dr. Collado was a Marie Curie Fellow of the FP7 project Symbiotic Wireless Autonomous Powered system (SWAP). She serves on the Editorial Board of the Radioengineering Journal and she is currently an Associate Editor of the IEEE Microwave Magazine and a member of the IEEE MTT-26 Wireless Energy Transfer and Conversion and MTT-24 RFID Technologies.

Diego Masotti (M'00) received the Dr. Ing. degree in electronic engineering and Ph.D. degree in electric engineering from the University of Bologna, Bologna, Italy, in 1990 and 1997, respectively. In 1998, he joined the University of Bologna as a Research Associate of electromagnetic fields. His research interests are in the areas of nonlinear microwave circuit simulation and design, with emphasis on nonlinear/electromagnetic co-design of integrated radiating subsystems/systems for wireless power transfer and energy harvesting applications. Dr. Masotti serves on the Editorial Board of the International Journal of Antennas and Propagation, and is a member of the Paper Review Board of the IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, IEEE COMMUNICATION LETTERS, IET-Circuit Devices & Systems, IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, and IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION since 2004, 2010, 2011, 2013, and 2015, respectively.

Zoya Popović (S'86–M'90–SM'99–F'02) received the Dipl.Ing. degree from the University of Belgrade, Serbia, Yugoslavia, in 1985, and the Ph.D. degree from the California Institute of Technology, Pasadena, CA, USA, in 1990. Since 1990, she has been with the University of Colorado at Boulder, Boulder, CO, USA, where she is currently a Distinguished Professor and holds the Hudson Moore Jr. Endowed Chair in the Department of Electrical, Computer and Energy Engineering. She was named the 2015 Distinguished Research Lecturer of the University of Colorado. In 2001–2003 and 2014, she was a Visiting Professor with the Technical University of Munich, Munich, Germany, and ISAE, Toulouse, France, respectively. Since 1991, she has graduated 50 Ph.D. students and currently leads a group of 15 doctoral students and 4 post-doctoral fellows. Her research interests include high-efficiency transmitters for radar and communication, low-noise and broadband microwave and millimeter-wave circuits, antenna arrays, wireless powering for battery less sensors and medical applications of microwaves such as microwave core-body thermometry and travelling-wave MRI. Prof. Popovic was the recipient of the 1993 and 2006 IEEE MTT-S Microwave Prize for the best journal papers. She received the 1996 URSI Issac Koga Gold Medal and was named an NSF White House Presidential Faculty Fellow in 1993. She was the recipient of a 2000 Humboldt Research Award for Senior U.S. Scientists from the German Alexander von Humboldt Stiftung. She was elected a Foreign Member of the Serbian Academy of Sciences and Arts in 2006. She was also the recipient of the 2001 Hewlett-Packard(HP)/American Society for Engineering Education(ASEE) Terman Medal for combined teaching and research excellence. In 2013, she was named a IEEE MTT-S Distinguished Educator.

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3D-Printed Origami Packaging With Inkjet-Printed Antennas for RF Harvesting Sensors John Kimionis, Student Member, IEEE, Michael Isakov, Beom S. Koh, Apostolos Georgiadis, Senior Member, IEEE, and Manos M. Tentzeris, Fellow, IEEE

Abstract—This paper demonstrates the combination of additive manufacturing techniques for realizing complex 3D origami structures for high frequency applications. A 3D-printed compact package for enclosing radio frequency (RF) electronics is built, that features on-package antennas for RF signal reception (for harvesting or communication) at orthogonal orientations. Conventional 3D printing technologies often require significant amounts of time and supporting material to realize certain structures, such as hollow packages. In this work, instead of fabricating the package in its final 3D form, it is 3D-printed as a planar structure with “smart” shape-memory hinges that allow origami folding to a 3D shape after heating. This significantly reduces fabrication time and effectively eliminates the need for supporting material, thus minimizing the overall manufacturing cost. Metallization on the package is performed by directly inkjet printing conductive inks on top of the 3D-printed surface with a modified inkjet-printed process without the need for surface treatment or processing. Inkjet-printed on-package conductive features are successfully fabricated, that are combined with RF energy harvesting electronics to showcase the proof-of-concept of utilizing origami techniques to build fully 3D RF systems. The methodologies presented in this paper will be enabling the manufacturing of numerous real-time shape-changing 3D complex structures for electromagnetic applications. Index Terms—3D printing, additive manufacturing, inkjet printing, origami electronics, RF harvesting.

I. INTRODUCTION

W

HEN designing wireless sensor networks (WSNs), one of the key factors that determines scalability is lowpower connectivity. One of the most prominent challenges in WSN design is power sufficiency, and recent efforts in the area

Manuscript received July 01, 2015; revised September 12, 2015; accepted October 11, 2015. This work was supported by the National Science Foundation-EFRI, the Defense Threat Reduction Agency, and the Spanish Ministry of Economy and Competitiveness and FEDER funds through the project TEC2012-39143. The authors would also like to acknowledge EU COST Action IC1301 Wireless Power Transmission for Sustainable Electronics (WIPE). This paper is an expanded version from the IEEE MTT-S International Microwave Symposium, Phoenix, AZ, USA, May 17-22, 2015. J. Kimionis, B. S. Koh, and M. M. Tentzeris are with the School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0250 USA (e-mail: {ikimionis, bkoh6}@gatech.edu; [email protected]). A. Georgiadis is with the Centre Tecnologic de Telecommunicacions de Catalunya, Castelldefels 08860, Spain (e-mail: [email protected]). M. Isakov is with the School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia, 30332-0250 USA (e-mail: misakov3@gatech. edu). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2015.2494580

of radio frequency (RF) energy harvesting promise to overcome the need for manual battery replacement. This is achieved by either utilizing RF harvesting for autonomous sensor operation, or for automatic battery recharging on-site [1], [2]. There have been numerous efforts related to rectenna design, such as for example ones addressing multiband operation [3], [4], [5]. Also, a large amount of power rectenna arrays have been considered [6], [7], [8] with broadband, dual band, circular or linear polarization characteristics. One of the challenges in designing rectenna arrays has been the trade-off between combining the output of the individual antenna elements in RF forming directive antenna arrays or in dc, forming non-directive rectifier arrays. The combination in RF results in directive systems able to focus towards a specific transmitter. In this work, we mainly consider large-scale systems in outdoor or indoor scenarios for “smart” sensors, energy harvesters, or communicators that require an easy deployment, e.g., spreading sensors with random orientation within a large area, and a compact “rugged” packaging. In such random deployment scenarios, communication or harvesting might be compromised if the node's antenna does not face to the direction of the central station for conveying data or receiving power wirelessly. Typically, WSN nodes employ either wire monopole/dipole antennas, or planar patch antennas, and thus the directivity is limited to one dimension. Employing novel fully 3D structures, such as a cube, allows for the easy placement of (planar) antennas on multiple faces, enabling simultaneous harvesting/communication over different and potentially real-time reconfiguring (e.g., “origami”) orientations (Fig. 1). RF waves from totally orthogonal planes can be exploited for harvesting and backscatter communication, enhancing the total system efficiency when multiple sources/gateways are present. Such a system can also benefit in the case of a single source that lies in an unknown direction: two orthogonal antennas increase the probability of capturing the source-emitted plane waves, compared to a single antenna facing to a single direction that can only capture RF signals from multipath reflections. Hosting the node's antennas directly on the package reduces the total volume that would be required if monopole/dipole wire antennas stemming out of the package were utilized. Mechanical damage (e.g., breaking) of antennas can also be minimized since the antennas are a part of the package in this case. In this paper, a system design is presented that will benefit WSN nodes in terms of harvesting and, possibly, communication: All electronics of the WSN nodes reside inside fully 3D enclosures, in this case a cube, that can be easily deployed on a field. Exposing only the antennas to the outer world and placing

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Fig. 1. 3D cube with orthogonally-positioned on-side planar antennas on the sides and enclosed RF energy harvesting electronics.

necting individual cube sides with adhesives). 3D printing is chosen for creating the plastic outer shell of the system that will a) enclose the electronics and b) host the antennas. Fabricating a cube is a straightforward process with most 3D printers; however, three main challenges appear for a packaging “smart cube” that will be used in this application: 1) The cube must be hollow, to allow for the easy and rugged placement of electronics in its interior. This typically requires the use of a supporting material that has to be removed after fabrication. For a moderately large cube size (in order to fit printed circuit boards, cables, batteries, etc.) the cost of the supporting material often becomes more significant than the cost of the material used for the actual cube. Moreover, the supporting material has to be typically removed with a chemical post-process, thus adding extra steps to the fabrication process and producing waste. 2) The fabrication time for a 3D structure is mainly limited by its exterior volume. For the cube size required for the proof-of-concept structures of this paper ( inch edges), the long fabrication time slows down the prototyping process. 3) The cube must have a way to open/close-preferably in real time-at least one of the sides for placing/replacing electronics in its interior. The aforementioned challenges cannot be directly addressed with typical 3D printing techniques, and demand a non-conventional approach for the fabrication of complex 3D structures, especially with operability up to the RF frequency range. Inspired by the art of Origami folding to build multiple 3D shapes from miniaturized planar (2D) structures, in this paper we introduce novel origami-based concepts as the foundation for the additive manufacturing of real-time shape-changing 3D complex structures targeting high frequency electromagnetic applications. II. ORIGAMI PACKAGING

Fig. 2. Origami folding of planar structure to realize a 3D shape.

all the electronics inside the package makes the node compact, and facilitates deployment. The system design introduced in this paper is expanding the work in [9], where the idea for utilizing on-package antennas on “origami”-foldable 3D packages was first presented, and a proof-of-concept antenna was printed on one of the cube package's sides. In this paper, a detailed design of the package is presented including a study of the materials' mechanical properties, and a methodical fabrication process is developed that combines 3D package printing and inkjet antenna printing. For the fabrication of the package and its antennas, an alladditive manufacturing process is followed to facilitate prototyping and minimize the need for post-processing (e.g., con-

Origami folding is the technique chosen to overcome the long fabrication time and high fabrication cost limitations by “folding” a two-dimensional structure to a three-dimensional one. The original 2D structure can be either a thin easily-foldable substrate, such as paper, a 3D-printed structure made of flexible polymer, or a hard 3D-printed “thick” planar structure with “hinging” features that allow folding [10]. The latter has the advantage of mechanical stability which is important for packaging scenarios, e.g., protecting electronics inside the origami package. The implementation of an origami electromagnetic structure involves two phases. During the first phase, it is designed and simulated in its final 3-dimensional form. The design is optimized to achieve the desired operating performance (e.g., operating frequency), which, apart from the materials and dimensions, also highly depends on the structure geometry. The second phase involves ‘unfolding’ the structure to a 2-dimensional pattern that can be easily fabricated. In the case of a cube, it can be expanded to a cross-shaped planar form, shown in Fig. 2-top. If the cube has dimensions and a thickness of , the fabrication time for a 3D cube is limited by its exterior volume

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Fig. 3. All-additive manufacturing: 3D printing of substrate and inkjet printing of conductive features.

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Fig. 4. Partial views of the package exterior (left) and interior (right).

while for the cross shape it is

which is 1 order of magnitude smaller compared to the cube. Thus, the fabrication time can be significantly reduced, and the need for supporting material can be effectively eliminated. For the metallization of the 3D-printed structure in an additive manufacturing manner, inkjet printing can be utilized. Inkjet printing has proven to be a successful process for realizing low-cost high-frequency structures accurately on a plethora of different substrates, including flexible ones [11]. Printing on 3D-printed surfaces for high frequency sensing and harvesting applications has been demonstrated in [9], showing promising results, even on challenging, rough surfaces. The combination of 3D printing and inkjet printing can greatly facilitate rapid prototyping, as both are fully additive processes. A significant advantage of this combination is that no post-processing is required after the 3D printing phase to start the inkjet-printing phase. In principle, the two processes could be combined in the same piece of equipment capable of performing a sequence of 3D material deposition and jetting of conductive, semiconductive, or dielectric inks (Fig. 3). For proof-of-concept purposes, a cubic-shape packaging structure prototype has been designed in its final 3D form and has been modeled with the ANSYS High Frequency Structure Simulation (HFSS) software to analyze the performance of its electromagnetic features in high frequencies ( band). Since the electronics are contained within the cube, probe-fed patches have been selected as the on-package antennas with coaxial connectors in the interior of the cube. The patches are implemented with microstrip technology, printed on the external sides of the cube, while employing metal ground planes on the respective interior sides. The directivity of patch antennas due to the ground plane limits the electromagnetic coupling between the antennas and the electronics inside the cube. Two patches have been designed on two sides of the cube, so that they face to orthogonal directions (Fig. 4). The cube sides are squares and are 3 mm thick. On two of the cube sides, patch antennas have been designed around the central frequency of 2.3-GHz. The patch width is

Fig. 5. Rendering of the flat configuration of the folding package used for 3D printing.

and its length is . The probe feeding point resides 0.63 cm away from the center of the patch, along the dimension. Apart from the full 3D structure, a single patch on a substrate with the same dimensions as one cube's side has been simulated. The performance of the single patch and the patches on the cube has been similar, i.e., there are no significant coupling effects between the two antennas on the cube's sides that would degrade their performance (tuning/gain). In principle, an antenna could be placed on any side of the cube without a significant effect on the other sides' antennas. It is important to note that since the feeding terminals of the two antennas are separate (no RF combining) and the two antennas show a high isolation, their operation is expected to be orthogonal in terms of radiation pattern directivity. In contrast, if the two antennas utilized a common feeding point or if there was a strong coupling, the result would be a beam steering at the far field which would not be desired for the multi-direction operation of the system in Fig. 1. III. 3D & INKJET ORIGAMI MANUFACTURING A 3D-printed packaging prototype has been fabricated using an Objet Connex 260 3D Polyjet Printer. The structural surfaces of the cube are made of the proprietary material VeroWhite and the hinges are Grey60, both thermoset shape memory polymers (SMP). The cube has been printed in its flat configuration to simplify the manual folding process, minimize material consumption, and reduce turnaround time. The model, which has been designed in SolidWorks and is shown in Fig. 5, has been printed diagonally on the printer bed to accommodate for the

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Fig. 6. Exploitation of the full 3D printer bed for building longer-dimension structures.

Fig. 8. Shape recovery ratio vs. time for Grey60.

Fig. 7. DMA (Dynamic Mechanical Analysis) of Grey60 yielding

of

.

big length across its longest dimension (Fig. 6). The materials for printing were chosen to maximize part strength and minimize the required temperature for folding. A novel hinge design has also been employed to reduce material fracture during the manual folding process after heating it up. Shape memory polymers (SMPs) are polymers that can programmatically change shape “on-demand” [12]. Typically, an SMP is manually folded from an initial primary shape to a secondary shape by applying a mechanical load above the glass transition temperature . The SMP will maintain this deformed shape after subsequently lowering the temperature below and removing the externally-applied mechanical load. Upon reheating above from the secondary shape, the SMP will selffold and recover its primary shape [12]. Shape memory polymers recover at different rates (a measure of the shape recovery ratio with respect to time) and at different temperatures , so material selection is a key design step in achieving desired properties during self-folding. In the case of the folding package designed in this paper, the primary shape is the flat printed configuration and the secondary shape is the manually-folded configuration. For 90 folding, the final shape is a box, while different shapes may result from arbitrary folding angles. The mechanical properties for the hinge material chosen in designing the folding box are shown in Fig. 7. The hinges and structural surfaces of the box have been selected to be as stiff as possible amongst the available Objet materials for part strength.

The structural material has been chosen to have a significantly higher than the hinge material to eliminate undesired deformations during heating. The low of the hinge material has also been chosen to reduce the ambient environmental impact on the assembled device during heating and cooling cycles. The was determined using a Dynamic Mechanical Analyzer (DMA, TA Instruments, Model Q800) and examining the (ratio of loss modulus to storage modulus).1 For Grey60, the is . For VeroWhite, the is and the Young's modulus is 1.2 GPa [10], [13]. The recovery rate is important for the actuating material and is approximately 4.5 seconds for 100% recovery, as it can be seen in Fig. 8. Transitioning from the flat primary shape to the cube shape is generally achieved by heating and subsequently manually deforming the part by hand. This process subjects the hinges of the folding box to irregular and random stress patterns, increasing the likelihood of part failure. To improve the damage tolerance during folding, a periodic step profile was employed along the surface contour of the hinge (Fig. 9). Thinner stepwise sections require lower bending stress and have higher thermal conductivity, making the folding box both easier and faster to fold. Additionally, the periodic profile allows for a wider range of bending motion during folding since the hinge is not subject to restrictive compressive strains. The hinges feature slots to form independent bending sections along themselves and improve their longevity in case of minor fractures (Fig. 9). The hinge radius has been maximized to further simplify the manual folding process. Given the dimensional constraints of the structural faces of the folding box and the build volume of the Objet Connex 3D Inkjet Printer, the highest achievable bend radius of 10.5 mm was chosen. The main challenge for the effective metallization (to realize transmission lines, printed circuits, or antennas) is the direct inkjet printing of conductive features on the 3D-printed surface before folding. This is advantageous for the simplification of the fabrication process: 1Not to be confused with the dielectric loss . Storage modulus: measure of elastic energy of material or energy stored during sinusoidal stretching. Loss modulus: measure of viscous energy of material or energy dissipated as heat during sinusoidal stretching.

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Fig. 10. (a) Silver nanoparticle (SNP) ink layer with partial diamminesilver acetate (DSA) ink layer on top. (b) SNP+DSA patch after heat-drying.

Fig. 9. Rendering of the hinge design in a 90 folded orientation.

1) No post-processing is required, such as surface treatment between the 3D and inkjet printing phases, or use of dielectric layers to smooth the surface before metallization. This is in contrast with inkjet printing on top of silicon integrated circuits (ICs), where the printing of supporting layers is required [14]. 2) Inkjet printing while the structure is still in planar form facilitates and further simplifies printing; the conductive ink drops are deposited vertically in a conventional inkjet printing manner and no high-pressure aerosol jetting techniques are required. Moreover, the thickness of the planar structure (on the order of millimeters) allows for the easy placement of the substrate between the printing bed and printing head; most inkjet printers are limited on the maximum height of the print head since they are mainly designed to accommodate thin substrates and not high 3D structures. It has to be stressed that the 2D inkjet printing process, that has been widely used for the printing of nanoparticle-based (e.g., silver nanoparticle-SNP, dielectrics, and carbon nanotube) inks on photo paper, polyimide films, glass, and other substrates, has to be redefined to address the two main challenges regarding 3D-printed surfaces • 3D-printed surfaces show extensive surface roughness that results in the formation of non-continuous features for a small number of SNP layers. This results in non-conductive or low-conductivity printed features, due to the discrete drop formation. • Typically, SNP inks need to be sintered at temperatures higher than to maximize conductivity [15]. However, high temperature levels cannot be tolerated by commonly utilized 3D-printed plastics or resins, causing deformation of the structure or failure (melting).

The above constraints require a modification of the inkjet printing process, which cannot be based solely on SNP inks for the realization of conductive surfaces. For the metallization on 3D-printed surfaces, a diamminesilver acetate (DSA) ink is used that achieves high conductivity values with moderate temperature curing (ranging from room temperatures up ) [16]. The low temperature range is safe for plastics, and, thus, this is the principal ink used for the fabrication process. Moreover, the DSA ink does not contain any nanoparticles; the particle formation occurs on the substrate after printing. This results in a very low-viscosity ink that spreads easily on the surface and forms continuous conductors. The measured surface tension of the DSA ink is 23 mN/m, which matches the measured surface free energy of the VeroWhite substrate, which is 22 mN/m. To avoid over-spreading of the DSA ink, SNP ink is first printed on the substrate to form the patch area. Two layers of SNP form a mesh of discrete drops that can be seen in Fig. 10(a). This is anticipated, since the measured surface free energy of the VeroWhite is 22 mN/m, while the surface tension of the SNP is between 28 and 31 mN/m [17]. Then, the DSA ink is printed on top of the SNP drops. Due to its low viscosity, it fills the gaps between the SNP drops, forming a continuous conductor. Up to twenty layers of DSA are printed, to achieve high conductivity. After each layer printing, moderate heat drying follows to guarantee DSA curing uniformity. After the process consisting of printing the SNP layers and printing/drying the DSA layers is completed, the result is a uniform conductor on top of the 3D-printed surface, without any ink spreading. It is worth mentioning that no significant effect of poor adhesion between the conductive patch and the polymer substrate was observed, and thus no effects of “flaking” were experienced. A fully-cured silver patch can be seen in Fig. 10(b). In [16], the electrical performance of the DSA is analyzed. Here, a characterization is offered for conductive features formed by inkjet-printing DSA and SNP inks. To characterize the sheet resistance of the DSA ink depending on the number of printed layers, various identical geometry samples have been fabricated with different (5, 10, 15, and 20) layers of DSA, with and without the two SNP layers and the samples' sheet resistance (in per square) is shown in Fig. 11. It can be seen that for both cases, the first 15 layers are critical for reducing the total sheet resistance, while the combination

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Fig. 11. Comparison of sheet resistance between DSA-only and metallization.

Fig. 12. Single patch antenna fabricated on 3D-printed substrate.

always features a lower sheet resistance for the same number of DSA layers, compared to the DSA-only case. Although this might be anticipated due to the extra silver content for the case, it is noted that for the DSA-only structures, more than 5 additional DSA layers are always required to achieve similar sheet resistance levels with the SNP+DSA structure. This is a significant observation, considering that the SNP layers are not fully cured to maximize their conductivity, since heating temperature is kept at levels below . On top of the fact that the SNP layers lower the resistance of the printed features, it has been concluded from multiple printing experiments that the SNP layers have the advantage of preventing ink “bleeding”, and thus the SNP step is always favorable for the fabrication of any structure. A proof-of-concept patch antenna prototype has been fabricated with 2 SNP layers and 20 DSA layers on a 3D-printed slab that has the same dimensions as the designed cube's sides for prototyping. On the top side of the slab, the patch has been printed, which has a thickness around . The bottom side has been covered with adhesive copper tape, to form the ground plane of the antenna for the reason of fabrication simplicity. It is noted that since the ground plane does not require an accuracy of the same level as the patch regarding its dimensions (width, length) or placement (origin point), the copper tape is a convenient way to implement it for proof-of-concept purposes. However, silver ink could be used for the ground plane fabrication as well, since it has been previously demonstrated to perform well for ground plane formation, even with meshed designs [18]. A 36 mil hole has been drilled 0.63 cm away from the center of the patch to accommodate the feeding pin. The hole has been drilled with a conventional drill press, and the exact drilling point has been marked by inkjet-printing a fiducial point with black ink after the metallization process. Such a fiducial point can be seen in Fig. 10(b) as a black cross. An SMA connector has been mounted and its signal pin has been trimmed to match the height of the antenna plane. A conductive silver epoxy has been used to electrically connect the probe pin to the inkjetprinted silver, and at the same time provide mechanical support for the SMA connector at the backside of the plastic slab. The same patch antenna has been printed on two orthogonal sides of the cube, to realize the multi-direction harvesting/communication system, as shown in Fig. 14(a). The two antennas have been printed with the same process, apart from the drying temperature. For the first antenna, a heatgun with a temperature of approximately has been used for 2 minutes, while for the second antenna, the heatgun is set to . The different curing temperature is used to assess the effect of the temperature level on the antennas' performance. After the antennas fabrication, the structure is heated and folded to its 3D form (Fig. 14(b)). IV. ANTENNA MEASUREMENTS

Fig. 13. S-parameters of the patch antennas.

The two antennas have been characterized with a vector network analyzer (VNA) as a full 2-port system, rather than two individual antennas. The measured S-parameters are shown in Fig. 13. Both antennas are tuned around 2.3-GHz and exhibit the same bandwidth of 100 MHz. It is noted that the first

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Fig. 14. (a) Inkjet-printed patch antenna on unfolded 3D-printed cube. (b) “Origami”-folded cube after heating, folding, and cooling down.

antenna shows a return loss (RL) of less than at the resonance frequency, while the second antenna shows a RL of . This is attributed to the different heatgun drying temperatures used for the antennas that affects their conductivity; the higher temperature visibly benefits the RL. However, it is noted that even the lower temperature of is more than sufficient for high conductivity, since 99% of the power exciting the antenna port is delivered to the antenna. For the two antennas, a strong requirement is the isolation between them to guarantee an orthogonal operation across the frequency band. An isolation of more than 40 dB is achieved between the two fabricated patches (Fig. 13), and thus the effect of each antenna to the other is negligible. This is the combined result of both the geometry of the setup (the antennas are placed in perpendicular planes) and the radiation pattern (directive) of the patches. The realized gain of each patch antenna has been characterized using a VNA and standard horn antennas in a lab environment. The measured maximum gain across the frequency band is shown in Fig. 15, where it can be seen that the fabricated patch achieves gain values of up to at the resonance frequency. The cross-polarization isolation (comparison between horizontal polarization field and vertical polarization field) is also measured by rotating the patch by 90 with respect to its center. As it is shown in Fig. 16, an isolation on the order of 25 dB or more is achieved in the antenna operation band.

Fig. 15. Measured and simulated realized gain of a single inkjet-printed patch.

V. RF ENERGY HARVESTER DESIGN As a proof-of-concept demonstration of utilizing additively manufactured origami structures for RF applications, a 2-port multi-direction RF energy harvester is designed, that exploits the independent inputs from the two orthogonal on-package antennas. The constraints for the design of a harvester for such a system are: • The isolation between the two antennas is crucial, or else a far-field beam steering may occur for the total radiation pattern.

Fig. 16. Measured and simulated cross-polarization isolation of a single inkjetprinted patch.

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Fig. 17. Summation of two harvesters' outputs. Top: Single harvester. Bottom: Double harvester.

• The ability for the harvester to operate its two ports independently, without constraining both ports at the same time to a specific input power level, incoming signal frequency, and signal phase coherence. The above constraints are addressed by using a dc-combining topology for the harvesting system, where each port has an individual RF-dc converter (rectifier) and the output voltage of the converters are combined to yield a higher voltage level. A dc combiner, in contrast with an RF-combining topology (e.g., an antenna array with a single RF feeding point), tends to “hide” the characteristics of the incoming RF signal at the dc output of each port's harvester. In that way, different input power/frequency/phase induced RF voltages are converted to dc voltages and combined to a single dc output. To simplify the dc-combining topology, the outputs of the two harvesters are directly connected at the load-driving terminal without any summation network utilizing resistors, diodes, or field effect transistors (FETs). That way, the losses due to resistive elements or parasitics of the summation network are minimized. Considering a single harvester represented as a current source with output impedance driving a load , and two identical harvesters connected in parallel and driving the same load , the voltage gain for the 2-port harvester compared to a 1-port harvester is (1) Asymptotically, the maximum voltage gain that can be achieved for equal power RF inputs is 2, achieving double the voltage for driving the load (Fig. 17). The 3D multi-direction harvester presented in this paper consists of two rectification circuits with their dc outputs combined at a single dc terminal that drives the load. Whether a voltage doubler topology or a single diode harvester topology is preferable has been determined through numerous simulations. One model for each case has been designed, based on full wave circuit board simulation, non-linear diode models, and lumped component models with parasitics. Both designs have been optimized for S-parameters tuning at the same frequency and input power level . However, while sweeping across different frequencies in the band and power

Fig. 18. Schematic of the 2-port harvester with dc combining.

levels from to 0 dBm, it has been noticed that in the case of the voltage doubler the resonance point occurs around 2.3-GHz with little or no shift for any power level. In contrast, for the single diode harvester, the resonance point will be strongly detuned in frequency depending on the power level. Thus, the voltage doubler topology is selected, since it can accommodate for small frequency shifts due to fabrication tolerances. A single-stage voltage doubler is utilized at each antenna port for the RF-dc conversion (Fig. 18). Each voltage doubler uses two Avago HSMS-285 zero-bias Schottky diodes in a standard detector configuration, as described in the manufacturer's datasheet. However, any RF-dc conversion circuit could be used in the place of this voltage doubler, according to the needs of the application (e.g., increased bandwidth, different input power levels, etc). At the output terminal, a large dc capacitor is used for smoothing, along with a high-frequency 6.8 pF capacitor that operates below its self-resonance frequency, and thus is effective for smoothing high frequency signals. A small load of is driven by the harvester output. Load values of this order of magnitude can be found in devices such as low-power microcontrollers that can be used for various WSN node implementations featuring sensors, backscatter communicators, etc. The 2-port harvester has been designed and simulated with the Agilent Advanced Design System (ADS) software, using large signal S-parameters (LSSP) and harmonic balance (HB) simulations. Non-linear models have been utilized for the diodes, and the passive components have been simulated with models that include parasitics. The harvester has been implemented on a thin Rogers RO4003C laminate and can be seen in Fig. 19. The tuning of the ports at 2.3-GHz is performed with single stub matching networks that are implemented on the same board for minimizing losses due to connectors, and to minimize the total electronics' volume. Since the diodes utilized for harvesting typically show a high impedance (and thus mismatch) for low input power levels, the matching network was designed to maximize the power transfer from the antennas to the harvester in low power levels where no power could be compromised. The input power level of has been

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Fig. 19. Fabricated harvester prototype with on-board matching.

Fig. 21. Harvester port matching across frequency band and input power levels. . Resonance around

Fig. 20. Measured harvester ports' return loss and coupling (input power level: ).

Fig. 22. Harvester port isolation across frequency band and input power levels. High isolation (more than 45 dB) for all points.

selected, at which, usable output voltage levels on the order of millivolts are achieved. VI. HARVESTER MEASUREMENTS The 2-port harvester prototype has been fully characterized using a VNA across the band for power levels up to 0 dBm. The matching for both ports is optimal at RF input at each port, with both ports tuned around 2.3-GHz, as it can be seen in Fig. 20. The bandwidth is wider than 120 MHz and the ports show a slight resonant frequency difference between them. The isolation (insertion loss, IL) between the two ports is more than 45 dB over the entire bandwidth; the high RF isolation between the two ports, due to the dc connection point, guarantees the individual operation of the two harvesters regardless of the exact frequency and power level incident at each port. In Fig. 21, the return loss of one of the harvester's ports is shown as a function of both the frequency and the power level of the incident wave on a contour plot. The resonant point at

can be clearly observed. Moreover, the “oval”-shaped contours centered around the resonant point show that for any given power level, the return loss minimum always occurs around 2.3-GHz, as discussed previously for the voltage doubler architecture. In Fig. 22, it can be seen that across the whole frequency band and for any power level, the isolation between the two ports is always higher than 45 dB, with certain points reaching isolation values of 70 dB. The device has been excited in three different scenarios to measure the output voltage: port 1 only, port 2 only, and both ports excitation. In Fig. 23, the simulated output voltage for different input power levels is shown, along with the measured values in these three scenarios. The wired measurements match with the simulation results; as an example, at , a voltage level of 100 mV is achieved for the load when one port is excited. When both ports are excited, the voltage level is boosted to 150 mV. When the ports are excited with high power (0 dBm), the output voltage reaches 1.2 V, even

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Fig. 23. Harvester output voltage versus port input power.

Fig. 24. Origami package with harvester electronics inside.

though the harvester is not optimized for high input power operation. VII. SYSTEM MEASUREMENTS After characterizing the harvester and the packaging individually, everything is connected together for an evaluation of the final system. The electronics are placed inside the cube, connected to the patch antenna ports with short, flexible coaxial cables (Fig. 24). Since the cables are in close proximity inside the package, the coupling between them is measured in extreme scenarios, such as twisting the pair of RF cables together, or running them in parallel. In all cases, the coupling between the cables was lower than , and no specific setup of the cables was required in the package to minimize cross-port interference. A software-defined-radio (SDR) with tunable output power was set up to transmit a 2.3-GHz constant wave (CW) from two ports that were connected to two horn antennas. The horn antennas were chosen for their high directivity, to create plane waves at at specific directions in the far field, i.e., to eliminate any reflections from side- or back-lobes that could potentially excite both patch antennas instead of only the targeted one. The horn antennas were in an orthogonal configuration, to excite one patch each, and at the same distance, to keep path loss at similar levels (Fig. 25). The inkjet-printed patches have been illuminated by the horn antennas at several power levels, while the power induced at each antenna's terminals has been monitored with an RF power meter to precisely monitor the input power to the harvester at each case. After connecting the harvester to the origami antennas, the output voltage has been recorded for each power level. The wireless measurements curve fits with the simulation and the wired measurements one, verifying the system operation with the inkjet-printed antenna on the 3D-printed, “origami”folded cube (Fig. 23). VIII. CONCLUSION-TECHNOLOGY POTENTIAL In this paper, a full system has been presented to showcase the feasibility of utilizing origami-folding principles for high frequency applications. Additive manufacturing technology has

Fig. 25. Wireless measurement setup for the origami RF harvester.

been utilized to build a 3D package for RF electronics of a WSN node. Instead of fabricating the package in its 3D configuration, which would require considerable amounts of time and supporting material cost, a methodology of fabrication processes has been developed that significantly reduces the required fabrication time. Moreover, it effectively eliminates the need for supporting material, thus reducing the overall cost. The process involves the fabrication of a planar structure with 3D printing technology and subsequently utilizing inkjet printing to form conductors directly on its surface. The planar structure can then be folded to a 3D shape in an origami fashion by heat-activating its “smart” shape-memory hinges. As a proof-of-concept a full system has been built that fully utilizes the geometry of the 3D origami package for multi-direction high frequency energy harvesting. Inkjet-printed on-package antennas are effectively utilized to capture RF signals from orthogonal directions, which would not be otherwise possible with directional planar antennas. This work is a successful demonstration of combining 3D-printed origami and inkjet-printed RF structures for demanding high-frequency applications. The potential of utilizing origami techniques for RF applications is not limited to packaging. The ability to change (and retain) the shape of 3D structures opens new paths in electromagnetic applications. Apart from its direct benefits of reducing the

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Fig. 26. Potential for origami technology: shape-changing structures for on-the-fly reconfigurable RF systems and smart wireless sensors.

required fabrication time and material cost by folding 2D shapes to 3D ones, the most significant benefit is the ability for reconfiguration. Shape-memory hinges can be built either to fold or unfold automatically, with heat triggering, and without manual force. This could enable complex structures to be reconfigured on-the-fly based on the ambient temperature conditions. In that case, smart sensors could be built, that signal rapid changes in temperature by changing their RF characteristics. An example could be directional antennas that change their radiation pattern when automatically folded (Fig. 26). In the same manner, reconfigurable antennas, transmission lines, filters, and numerous others RF structures could reconfigure their frequency of operation, gain, bandwidth, or phase. In a different approach, intentional changes of the temperature around the proximity of the system could enable the live, controlled reconfiguration by folding or unfolding the origami structure to tune, for example, a filter. Beam steering for small antenna arrays by physically changing their geometry without the need for servo motors or manual force could be appealing for low-cost applications. This work demonstrated the feasibility of incorporating origami for RF applications and the methodology presented to additively manufacture complex origami structures will be enabling the fabrication of numerous other systems for demanding, non-conventional electromagnetic applications. REFERENCES [1] S. Kim et al., “Ambient RF energy-harvesting technologies for selfsustainable standalone wireless sensor platforms,” Proc. IEEE, vol. 102, no. 11, pp. 1649–1666, Nov. 2014. [2] K. Gudan, S. Chemishkian, J. J. Hull, S. J. Thomas, J. Ensworth, and M. S. Reynolds, “A 2.4 GHz ambient RF energy harvesting system with minimum input power and NiMH battery storage,” in IEEE Int. Conf. on RFID-Technol. and Applicant. (RFID-TA), Tampere, Finland, Sep. 2014, pp. 7–12. [3] Y.-H. Suh and K. Chang, “A high-efficiency dual-frequency rectenna for 2.45-and 5.8-GHz wireless power transmission,” IEEE Trans. Microw. Theory Techn., vol. 50, no. 7, pp. 1784–1789, Jul. 2002. [4] R. Scheeler, S. Korhummel, and Z. Popovic, “A dual-frequency ultralow-power efficient 0.5-g rectenna,” IEEE Microw. Mag., vol. 15, no. 1, pp. 109–114, Jan.-Feb., 2014. [5] D. Masotti, A. Costanzo, M. Del Prete, and V. Rizzoli, “Genetic-based design of a tetra-band high-efficiency radio-frequency energy harvesting system,” IET Microw, Antennas & Propag., vol. 7, no. 15, pp. 1254–1263, 2013. [6] Z. P. N. P. Basta and E. A. Falkenstein, “Bow-tie rectenna arrays,” in Proc. 2015 IEEE MTT-S Wireless Power Transfer Conf. (WPTC), Boulder, CO, USA, May 2015. [7] B. Strassner and K. Chang, “5.8-GHz circularly polarized dualrhombic-loop traveling-wave rectifying antenna for low power-density wireless power transmission applications,” IEEE Trans. Microw. Theory Techn., vol. 51, no. 5, pp. 1548–1553, May 2003.

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[8] N. Shinohara and H. Matsumoto, “Experimental study of large rectenna array for microwave energy transmission,” IEEE Trans. Microw. Theory Techn., vol. 46, no. 3, pp. 261–268, Mar. 1998. [9] J. Kimionis, A. Georgiadis, M. Isakov, H. J. Qi, and M. M. Tentzeris, “3D/inkjet-printed origami antennas for multi-direction RF harvesting,” in IEEE MTT-S Int. Microw. Symp. (IMS), Phoenix, AZ, USA, May 2015, pp. 1–4. [10] Q. Ge, C. K. Dunn, H. J. Qi, and M. L. Dunn, “Active origami by 4D printing,” Smart Materials and Structures, vol. 23, no. 9, p. 094007. [11] J. Hester et al., “Additively manufactured nanotechnology and origami-enabled flexible microwave electronics,” Proc. IEEE, vol. 103, no. 4, pp. 583–606, Apr. 2015. [12] H. J. Qi, T. D. Nguyen, F. Castro, C. M. Yakacki, and R. Shandas, “Finite deformation thermo-mechanical behavior of thermally induced shape memory polymers,” J. Mechanics and Physics of Solids, vol. 56, no. 5, pp. 1730–1751, 2008. [13] Y. Li, N. Kaynia, S. Rudykh, and M. C. Boyce, “Wrinkling of interfacial layers in stratified composites,” Adv. Eng. Mater., vol. 15, no. 10, pp. 921–926, 2013. [14] B. Tehrani, B. S. Cook, and M. M. Tentzeris, “Post-process fabrication of multilayer mm-wave on-package antennas with inkjet printing,” in 2015 IEEE Int. Symp. Antennas and Propag. (APSURSI), Vancouver, BC, Canada, Jul. 2015. [15] B. Cook and A. Shamim, “Inkjet printing of novel wideband and high gain antennas on low-cost paper substrate,” IEEE Trans. Antennas Propag., vol. 60, no. 9, pp. 4148–4156, Sep. 2012. [16] S. B. Walker and J. A. Lewis, “Reactive silver inks for patterning highconductivity features at mild temperatures,” J. Amer. Chemical Soc., vol. 134, no. 3, pp. 1419–1421, 2012. [17] SunTronic Silver Nanoparticle ink Specification Sheet SigmaAldrich. St. Louis , MO, USA, 2014. [18] R. Martinez et al., “Planar monopole antennas on substrates fabricated through an additive manufacturing process,” in 9th Eur. Conf. Antennas and Propag. (EuCAP), Lisbon, Portugal, Apr. 2015.

John Kimionis (S'10) received the Diploma and M.Sc. degrees in electronic and computer engineering from the Technical University of Crete, Chania, Greece, in 2011 and 2013, respectively, where he was with the Telecom Lab. He is currently a Ph.D. candidate at the School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA, USA. He is a Research Assistant with the ATHENA group. His research interests are in the areas of backscatter radio and RFID, software defined radio for backscatter sensor networks, RF front-end design for wireless sensors, and additive manufacturing techniques. He has received fellowship awards for his undergraduate and graduate studies, and he is a Texas Instruments Scholar for his mentoring service for the Opportunity Research Scholars (ORS) program in Georgia Tech. He has received IEEE student travel grants, and was the recipient of the First Best Student Paper Award in the IEEE International Conference on RFID-Technologies and Applications (RFID-TA) 2014, Tampere, Finland, as well as the Second Best Student Paper Award in the IEEE International Conference on RFID-Technologies and Applications (RFID-TA) 2011, Sitges, Barcelona, Spain. Mr. Kimionis has been a Student Member of the IEEE since 2010, a member of the IEEE Microwave Theory and Techniques Society, the IEEE Communications Society, and the IEEE Technical Committee on RFID.

Michael Isakov is a Ph.D. candidate in mechanical engineering at the Georgia Institute of Technology, Atlanta, GA, USA. He received the B.S. degree in mechanical engineering from the Cooper Union in New York, NY, USA. After conducting research at Georgia Tech, Cooper Union, Bell Laboratories' LGS Innovations, and working as a Full Stack Developer at Quantum Networks, he decided to start his own tech company. He is now Founder and CTO of Wooter-the online hub for recreation sports leagues, while still maintaining close ties with his research lab.

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Beom S. Koh was born in Seoul, Korea, in 1990. He is currently pursuing a B.S. degree in the School of Electrical and Computer Engineering at the Georgia Institute of Technology, Atlanta, GA, USA. He has performed undergraduate research and his interests involve inkjet-printed antennas on 3D-printed structures and thick substrates.

Apostolos Georgiadis (S'94–M'02–SM'08) was born in Thessaloniki, Greece. He received the Ph.D. degree in electrical engineering from the University of Massachusetts at Amherst, Amherst, MA, USA, in 2002. In 2007, he joined Centre Tecnologic de Telecomunicacions de Catalunya (CTTC), Barcelona, Spain, as a Senior Researcher, where he is involved in energy harvesting, wireless power transfer and radio-frequency identification (RFID) technology, and active antennas and antenna arrays. Since April 2013, he has been a Group Leader of the Microwave Systems and Nanotechnology Department at CTTC. Dr. Georgiadis was the Chair of EU COST Action IC0803, RF/Microwave communication subsystems for emerging wireless technologies (RFCSET) and presently he is vice-Chair of EU COST Action IC1301 on Wireless Power Transfer for Sustainable Electronics. He serves as an Associate Editor of the IEEE MICROWAVE WIRELESS COMPONENTS LETTERS, IEEE RFID VIRTUAL JOURNAL and IET Microwaves Antennas and Propagation journals. He is a Distinguished Lecturer of the IEEE Council on RFID, where he is also recently appointed as VP of Conferences. He is Vice-Chair of URSI Commission D Electronics and Photonics.

Manos M. Tentzeris (S'89–M'92–SM'03–F'10) received the Diploma degree in electrical and computer engineering from the National Technical University of Athens (“Magna Cum Laude”), Athens, Greece, and the M.S. and Ph.D. degrees in electrical engineering and computer science from the University of Michigan, Ann Arbor, MI, USA. He is currently a Professor with the School of ECE, Georgia Tech, Atlanta, GA, USA. He has published more than 550 papers in refereed Journals and Conference Proceedings, 5 books and 23 book chapters.

Dr. Tentzeris has helped develop academic programs in Highly Integrated/Multilayer Packaging for RF and Wireless Applications using ceramic and organic flexible materials, paper-based RFID's and sensors, biosensors, wearable electronics, 3D/4D/inkjet-printed electronics, “Green” electronics, energy harvesting and wireless power transfer systems, NFC systems, nanotechnology applications in RF, origami-folded Electromagnetics, Microwave MEM's, SOP-integrated (UWB, multiband, mmW, conformal) antennas and heads the ATHENA research group (20 researchers). He has served as the Head of the GT-ECE Electromagnetics Technical Interest Group, the Georgia Electronic Design Center Associate Director for RFID/Sensors research from 2006–2010, and as the Georgia Tech NSF-Packaging Research Center Associate Director for RF Research and the RF Alliance Leader from 2003–2006. He was the recipient/co-recipient of the 2015 IET Microwaves, Antennas and Propagation Premium Award, the 2014 Georgia Tech ECE Distinguished Faculty Achievement Award, the 2014 IEEE RFID-TA Best Student Paper Award, the 2013 IET Microwaves, Antennas and Propagation Premium Award, the 2012 FiDiPro Award in Finland, the iCMG Architecture Award of Excellence, the 2010 IEEE Antennas and Propagation Society Piergiorgio L. E. Uslenghi Letters Prize Paper Award, the 2011 International Workshop on Structural Health Monitoring Best Student Paper Award, the 2010 Georgia Tech Senior Faculty Outstanding Undergraduate Research Mentor Award, the 2009 IEEE Transactions on Components and Packaging Technologies Best Paper Award, the 2009 E.T.S.Walton Award from the Irish Science Foundation, the 2007 IEEE APS Symposium Best Student Paper Award, the 2007 IEEE IMS Third Best Student Paper Award, the 2007 ISAP 2007 Poster Presentation Award, the 2006 IEEE MTT Outstanding Young Engineer Award, the 2006 Asian-Pacific Microwave Conference Award, the 2004 IEEE Transactions on Advanced Packaging Commendable Paper Award, the 2003 NASA Godfrey “Art” Anzic Collaborative Distinguished Publication Award, the 2003 IBC International Educator of the Year Award, the 2003 IEEE CPMT Outstanding Young Engineer Award, the 2002 International Conference on Microwave and Millimeter-Wave Technology Best Paper Award (Beijing, China), the 2002 Georgia Tech-ECE Outstanding Junior Faculty Award, the 2001 ACES Conference Best Paper Award and the 2000 NSF CAREER Award and the 1997 Best Paper Award of the International Hybrid Microelectronics and Packaging Society. He was the TPC Chair for IEEE IMS 2008 Symposium and the Chair of the 2005 IEEE CEM-TD Workshop and he is the Vice-Chair of the RF Technical Committee (TC16) of the IEEE CPMT Society. He is the founder and chair of the RFID Technical Committee (TC24) of the IEEE MTT Society and the Secretary/Treasurer of the IEEE C-RFID. He is the Associate Editor of the IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, IEEE TRANSACTIONS ON ADVANCED PACKAGING and the International Journal on Antennas and Propagation. He was a Visiting Professor with several institutions for the summers of 2002, 2009, and 2010, respectively. He has given more than 100 invited talks to various universities and companies all over the world. He is a Fellow of IEEE, a member of URSI-Commission D, a member of MTT-15 committee, an Associate Member of EuMA, a Fellow of the Electromagnetic Academy and a member of the Technical Chamber of Greece. He served as one of the IEEE MTT-S Distinguished Microwave Lecturers from 2010–2012 and he is currently serving as the IEEE C-RFID Distinguished Lecturer.

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Ambient RF Energy Harvesting From a Two-Way Talk Radio for Flexible Wearable Wireless Sensor Devices Utilizing Inkjet Printing Technologies Jo Bito, Student Member, IEEE, Jimmy G. Hester, Student Member, IEEE, and Manos M. Tentzeris, Fellow, IEEE

Abstract—A complete design and additive fabrication process of flexible wearable radio-frequency (RF) energy harvesters for off-the-shelf 2 W two-way talk radios utilizing inkjet printing technology is discussed in this paper. As a result of numerous output dc power measurements of fabricated proof-of-concept prototypes, a maximum output power of 146.9 mW and 43.2 mW was achieved with an H-field and E-field harvester, respectively. Also, the effect of misalignment between receiver and hand-held radio on harvesting performance is discussed in detail. To verify their potential in real-world wearable autonomous RF modules, the operation of E- and H-field energy harvesters was verified by utilizing an LED and a microcontroller communication module under on-body and on-bottle conditions, and the effect of the energy harvesters on the performance of the harvested communication systems was inspected through received power measurements in an anechoic chamber. Index Terms—Autonomous sensors, energy harvesting, flexible, inkjet printing, on-body, wearable.

I

I. INTRODUCTION

N RECENT years, the desire for a “smart” society, which utilizes technologies such as large scale sensor networks, Internet of Things (IoT) and smart skins is getting increasingly higher. One of the biggest issues to realize the autonomous operation of these sensors and devices is power supply. In order to solve this problem, ambient energy harvesting technology has attracted the interest of the research community in the last couple of decades. There are many different types of potential energy sources for ambient energy harvesting such as solar, heat and vibration. Among them, ambient microwave energy harvesting, because of its inherent applicability even through opaque walls, making it potentially more available than other ambient energy sources. There are many different types of available microwave signals, especially in urban environments, such as VHF/UHF television and WiFi signals [1], [2], although typically their energy density is lower than other sources [3]. As the most fundamental implementation issues associated with the Manuscript received June 30, 2015; revised September 24, 2015; accepted October 17, 2015. Date of publication November 18, 2015; date of current version December 02, 2015. The work of J. Bito, J. G. Hester, and M. M. Tentzeris was supported in part by the National Science Foundation and the Defense Threat Reduction Agency. This paper is an expanded version from the IEEE MTT-S International Microwave Symposium, Phoenix, AZ, USA, May 17–22, 2015. The authors are with the School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA, 30332-250 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2015.2495289

low energy density and the characteristics of Schottky diodes, which are commonly used for RF-dc conversion circuit implementation, it is very difficult to achieve a high enough output voltage that can drive external circuitry. In addition, most integrated circuits (ICs) require more energy than that required for normal operation when they need to activate from “cold start,” which means equivalently that their load resistance becomes very low (typically below 1 ), further complicating the turn-on of the ICs using RF energy harvesters. In order to alleviate this problem, for example, a charged capacitor is utilized to guarantee the start up of ICs [4]. However, there are some “hotspots” where RF energy is fairly high, which can possibly provide enough energy to turn on external circuitry from cold start without using any supplemental energy sources [5]. As an example, the two-way talk radio, which is a commonly used device for short-distance communication, does not use any base station and directly sends the signal to the other mobile devices. Therefore, it generates a relatively high RF power compared to other mobile communication electronics, especially in near field. In general, there is a limited number of technologies that are utilizing the near-field coupling for the purpose of wireless power transfer and the near-field communication, for example the strongly coupled coil configurations and the near-field RFIDs [6]–[8]. In these applications, both Transmitter (Tx) and Receiver (Rx) are arbitrary designed and do not use an ambient energy source. At the same time, most of the ambient energy harvesting circuits do not use the near-field coupling. Nevertheless, as already reported, it is possible to generate substantially high dc power out of the RF signals generated from handheld devices, such as a two-way talk radio [9], [10]. In this paper, a novel near-field RF energy harvesting circuit on a flexible substrate, that can be fabricated with inkjet printing technology, for wearable sensor applications as well as a further characterization of the near-field energy harvester under practical misaligned conditions and an operation test using a microcontroller are discussed in detail as an extension of previously reported results. II. INKJET PRINTING FOR ZERO-POWER FLEXIBLE WEARABLE SENSORS Additive manufacturing such as inkjet printing and 3-D printing is becoming increasingly popular in industry because of its environmentally friendly and low cost fabrication process features. These emerging fabrication techniques can potentially decrease significantly the number of fabrication steps, including the etching processes, and drastically improve the

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Fig. 1. Block diagram of a typical inkjet-printed zero-power wearable sensor device.

fabrication efficiency. Wearable sensor devices are expected to be used extensively in the places where single-time/disposable use is hygienically important, for example in hospitals. From this type of applications, it is desirable to create as many circuit components in the device as possible by utilizing additive manufacturing to reduce the cost of device. Due to recent substantial improvements in fabrication processes and performance, inkjet printing technology has become increasingly attractive for RF and sensor applications. As is depicted in Fig. 1, passive components, such as capacitors and inductors, circuit traces including antennas, battery, and sensors, can be created by utilizing printing technologies [11]–[16]. Inkjet printing technologies with silver nanoparticle-based inks have proven to be a very efficient solution for low-loss RF circuit patterning associated with a high 2-D resolution in the range of 50 to 100 m [17]–[19]. However, it is quite challenging to fabricate durable flexible circuits with printed traces combined with lumped circuit components because of the limited flexibility of the conductive epoxy and the solder, that are commonly utilized as the electrical interconnect between inkjetprinted conductive patterns and circuit components. One of the options to overcome this problem is to create copper traces utilizing inkjet printing-based electroless electroplating, which enables to use conventional soldering to create electrical interconnections on flexible substrates [20]. However, because of the inevitable characteristic as a wearable device, it requires extra durability. In order to guarantee the interconnection under the wearing/flexing conditions, the masking through the use of an inkjet-printed polymer was adopted for the initial prototyping to prove the concept of near-field energy harvesting, and the research was extended to the fabrication of circuit utilizing inkjetprinted conductive traces. The Dimatix-2831 printing platform from Fujifilm was used to print both the masking layer and the conductive traces. A. Inkjet Printing Masking There are four steps in the fabrication of flexible circuit traces utilizing inkjet printing masking as are depicted in Fig. 2. The polymer ink is made of 35 SU-8 polymer from MicroChem, and was used as a mask on a copper-cladded liquid crystalline polymer (LCP) substrate from Rogers Corporation. The thickness and the dielectric constant of the substrate are 100 m and 2.9, respectively. Once the SU-8 ink was printed on the copper cladding layer, the substrate was soft baked at 120 C for 10 min before the masking was exposed to 365 nm ultraviolet (UV) light for cross linking. After the UV light exposure, the substrate was heated at 120 C for additional 5 min, yielding

Fig. 2. Fabrication process of flexible circuit traces utilizing inkjet printing masking.

Fig. 3. Circuit traces for a TDFN8 IC package fabricated with inkjet printing masking.

a 4 to 6 m SU-8 layer thickness [18]. Two layers of SU-8 were printed and then the uncovered copper metallization was etched with ferric chloride (FeCl ) solution. The etching time varied from 30 to 90 min depending on the temperature, size of substrate, thickness of metal layer and freshness of the FeCl solution. After the etching, SU-8 mask is removed by using acetone. Fig. 3 shows the printed conductive traces for a 3 mm 3 mm TDFN8 package that have been fabricated with the above additive fabrication approach. The resolution of the conductive patterning is effectively equal to the resolution of inkjet printing, making it possible to fabricate circuit traces width and spacing of less than 400 m for the prototype in Fig. 3, although narrower spacings below 90 m can be easily realized, which is sufficiently good for many commonly used packaged ICs. B. Inkjet Printed Conductive Traces As an alternative additive manufacturing approach, the conductive traces for the wearable flexible harvesters introduced in this paper were printed by utilizing a silver nanoparticle-based ink, EMD5730 from SunChemical, which contains 40% silver nanoparticles diffused in an ethanediol-based solvent. This ink has a viscosity of 10 to 13 cPs at 25 C and a surface tension of 27 to 31 dynes/cm [21]. Five layers of silver nanoparticle ink were printed on a 125 m Kapton HN substrate from DuPont, which has the dielectric constant of 3.5. After the printing, the circuit was cured on a hotplate at 120 C for 10 min after a

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Fig. 4. Printed harvester circuit traces under bent/flex conditions.

gradual temperature ramp from 30 C with the rate of 360 C per hour to dry the solvent in order to realize uniform printed conductive traces. After the initial curing, the circuit was heated at 150 C for one hour, yielding 12- m-thick layers at the center of a line with a sheet resistance of 0.011 . The curing temperature utilized is the lowest suggested curing temperature in the data sheet of the silver nanoparticle ink. This temperature was chosen in order to prevent the printed conductive traces from the cracks caused by the thermal expansion of the Kapton substrate. The conductivity of the printed traces is sufficiently high even with this relatively low-temperature curing [22]. The printed conductive traces themselves are as flexible as the Kapton substrate as depicted in Fig. 4. The inkjet-printed conductive traces are compatible with both conductive epoxy and low temperature soldering paste, which are typically used materials to make electrical connections to circuit traces and lumped components. The prototypes of the RF-dc conversion circuit using inkjet-printed conductive traces and lumped components which are soldered using the conductive epoxy and the low temperature soldering paste are shown in Fig. 5(a) and (b), respectively. The biggest issue of printed conductive traces for wearable applications in terms of mechanical properties is the stiffness difference between the conductive traces and the interconnection materials. This causes locally high mechanical stress on the edge of interconnections which eventually cracks the conductive traces when the circuit is bent. To alleviate this problem for wearable harvester applications, the RF-dc conversion circuit part in the fabricated prototype was laminated by utilizing a thin epoxy glue layer, which relieves the unequal stress distribution under bent/flexed conditions. III. RF POWER MEASUREMENTS In order to design a flexible wearable energy harvester circuit which can effectively scavenge energy from a hand-held radio, it is necessary to know the EM field distribution around the holding hand and to estimate how much is the input power to the harvesting circuit. A. Near-Field Power Distribution Simulation and Measurement In this paper, a Motorola RDU2020 two-channel two-way talk radio (2 W/1 W) was used as the power source and the radio was held with the right hand. The operation frequencies

Fig. 5. (a) Interconnection using conductive epoxy. (b) Interconnection using low temperature soldering paste.

of this radio are 464.5500 MHz (Channel 1) and 467.9250 MHz (Channel 2), and the radio is utilizing Continuous Tone-Coded Squelch System (CTCSS) which is an analog squelch scheme in the factory setting. It is possible to switch the transmitting power of RDU2020 to 2 W and 1 W. In this research, 2 W mode and Channel 1 were used. The antenna of RDU2020 radio is not detachable, and the actual transmitted power from the radio cannot be directly measured. Therefore, another two-way talk radio, Motorola RDU4100, which can detach the antenna, was programmed to operate at 2 W mode and the output power was directly measured by utilizing a power sensor (NRP-Z211 from Rohde & Schwarz) and a 30 dB attenuator. Eventually, the actual measured transmitted power was 2.2 W. Therefore, in this paper, the transmitted power from RDU2020 radio is assumed to be 2.2 W. Since most people turn on the Walkie-Talkie with their hands, it is assumed that a sufficiently high amount of the output power in the near-field of the radio can be harvested by placing a harvester around the hand. In order to estimate the E- and H-field distribution around the hand holding the radio, various simulations were run on CST. In these simulations, a monopole antenna which has the same operation frequency as RDU2020 was placed near the thumb of the right-hand model which features the human flesh electrical properties. The simulation results of E- and H-field distribution on the back and on the palm sides are shown in Fig. 6. As it can be easily noticed, the E-field intensity is generally much higher than the

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Fig. 6. E-field distribution of (a) Back side. (b) Palm side., and H-field distribution of (c) Back side. (d) Palm side.

H- field intensity, but there are some places where the H-field is locally high. In order to optimize the placement orientation of the wearable energy harvesting circuit, the intensity of electric and magnetic fields around the wrist were measured with an ETS-Lundgren E-field and H-field probe which was connected to a real-time spectrum analyzer, RSA3408A, from Tektronix. The measurement setup and the measured E- and H-field values at 2 to 17 cm away from the radio at various angular positions are shown in Fig. 7(a) and (b), respectively. It can also be concluded from these measurements that the electrical field is stronger than the magnetic field around the wrist. However, due to the typical near-field E-field distribution around a monopole antenna, the optimum E-field receiver needs to be placed parallel to the two-way radio antenna, which is difficult because of typical motions and changes in the relative positions of the radio in common holding arrangements of the radio near the wrist. On the other hand, the power level of the magnetic field at 0 position is relatively higher than any other angle; it is easier to increase the receiving area of the H-field by mounting the harvesting structure on the back of the hand, which is vertically facing the expected H-field, instead of placing the receiver on the wrist. Based on this assumption, receiver circuits for both electrical field and magnetic field were designed for proof-of-concept purposes.

Fig. 7. (a) Near-field probe measurement configuration. (b) Measured E- and H-field power levels at different relative angles and distances.

B. E-Field and H-Field Receiver Design By taking into account the typical size of a hand and a wrist, a width of 5 cm and length of 15 cm were adopted as the size constraints of the E-field receiver, and a width of 5 cm and a length of 8 cm were adopted for the H-field receiver . Based on the near-field power simulations and measurements, and the above wrist-dependent restrictions, receiver circuits for both E- and H-field were designed. A dipole antenna for E-field and an opentype helical coil with four loops for H-field were adopted at the

Fig. 8. Additively manufactured receiver prototypes for (a) E-field, (b) H-field.

wearable harvesting receiver. Both were soldered with the balun (ADT1-1WT) from Coilcraft Ink. The dimensions of the E- and the H-field receiver prototypes are shown in Fig. 8(a) and (b), respectively.

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Fig. 9. System configuration with equivalent -parameters matrix.

C. Input Power Estimation and RF-DC Conversion Circuit Design

Fig. 10. Measured -parameters for E- and H-field receivers.

Since the transmitter and the receiver circuits are placed in the near field, it is very difficult to estimate how much power is actually transferred to the receiver through simulations. The requirement that the proposed receiver had to be wearable, as well as the detrimental proximity effect of the human body, further complicated this estimation. Therefore, in this paper, the power transferred to the receiver port was computed from twoport -parameter measurements with a vector network analyzer (ZVA8 from Rohde & Schwarz). The energy harvesting system can be generally modeled as shown in Fig. 9. In this figure, is the source impedance and is the load impedance. If input and output power at port1 and port2 are defined as , , , and , respectively, the topology of the transmitter antenna and of the harvesting receiver can be expressed as a -parameter matrix. Once the power transferred to the load and the power from the source, defined as and , respectively, the power transfer efficiency from the source to the load can be determined as shown in

a spindle-shape 20-cm-tall water bottle, which has the smallest diameter of 17.5 cm at the middle and the largest diameter of 23 cm at the top and bottom, was used. In order to mimic the two-way talk radio, a stubby UHF antenna, RAN4033 from Motorola, which has similar physical dimension to the one on the two-way talk radio, was placed at the bottom of the water bottle and was used for the -parameter measurements. The E-field receiver was wrapped around the bottle at a distance of 7 cm from the bottom of the bottle in a configuration equivalent to the handheld two-way radio and the “7 cm” position of the harvester in Fig. 7(a). Similarly, the H-field receiver was placed at 2 cm away from the bottom of the water bottle which is equivalent to the “2 cm” position in Fig. 7. The measured -parameters for the transmitting monopole and for the E- and H-field receivers are plotted in Fig. 10 for this specific configuration. Using this data in (1) and (2), the maximum potential power transfer efficiency was determined to be 2.57% and 7.55% for the E-field and the H-field receivers, respectively. For the E-field harvester circuit, the maximum possible transferred power from the 2.2 W transmitter, 56.2 mW, and the load impedance at the maximum power transfer condition, 202 – , were determined from (1) and (2), respectively. From the same equations, the H-field harvester maximum possible transferred power of, 166.0 mW, and the load impedance at the maximum power transfer condition, 10.7 – , were computed. In order to maximize the output voltage with the minimum possible circuit size, a single-stage Dickson voltage doubler with one Schottky diode chip, Avago HSMS282C, was used as the rectifier. Also in order to keep the size of harvester small, an L-shaped LC network was adopted as the matching circuit. The circuit was initially designed with the Advanced Design System (ADS), and the matching circuit was fine-tuned during measurements. The configuration of the E and H-field rectifier prototypes is shown in Fig. 11(a) and (b), respectively.

(1) If the reflection coefficient from the source to port1 ( is substituted with

) in (1) (2)

the efficiency can be expressed only as a function of the reflection coefficient from port2 to the load ( ). Therefore, once the two-port -parameter matrix for the Tx-Rx propagation channel is calculated experimentally, the maximum power transfer efficiency can be analytically computed by sweeping the value of in the range of and to 360 . At the same time, the load impedance value yielding the maximum efficiency can be computed from (2) [9]. In this research, the harvester circuit is expected to be placed on the human body. However, because of regulation issues related to human subject research, a bottle of water was adopted as the substitute material for the human forearm for the preliminary measurements. In reality, the human body has different electrical properties compared to the water. Therefore, in order to imitate the human body effects more accurately, a phantom should be used in future research efforts. However, as a firstorder approximation and as a proof-of-concept of the wearable near-field RF energy harvesting, and without loss of generality,

IV. MEASUREMENT RESULTS A. RF-DC Conversion Efficiency Measurements The output voltage measurements were initially conducted with an RDU2020 handheld radio by arranging the harvester and the radio on the side of the water bottle in a configuration similar to the one on the human arm holding the radio as shown in Figs. 12(a) and 13(a). The output voltage was measured by changing the load resistance of the circuit in the range

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Fig. 13. (a) Open voltage measurement of H-field harvester with an on-bottle setup. (b) Operation verification of the H-field harvester on the hand.

Fig. 11. RF-dc conversion circuit topology for the wearable (a) E-filed energy harvester. (b) H-filed energy harvester.

Fig. 12. (a) Open voltage measurement of E-field harvester with an on-bottle setup. (b) Operation verification of the E-field harvester on the wrist.

of 100 to 6800 , which fully covers the optimal load resistance value range of 1800 to 3000 from ADS simulation. The input power is assumed to be 56.2 mW (17.5 dBm) for the E-field harvester, and 166.0 mW (22.2 dBm) for the H-field

harvester from the input power estimation based on the -parameter measurements. The estimated RF-dc conversion efficiency from both the simulations and the measurements for Eand H-field harvesters as a function of the load resistance are depicted in Figs. 14 and 15, respectively. During the simulation, the matching circuit and the load resistance are optimized to achieve the highest dc output power for the estimated RF input power using ideal circuit components. The RDU two-way talk radios can potentially switch the transmitting power to 1 and 4 W. Therefore, the RF-dc conversion efficiencies when the input power is halved and doubled without changing the matching circuit design are also depicted in Figs. 14 and 15. According to the simulation results, the maximum RF-dc conversion at every input power level observation is almost the same for both E- and H-field harvesters, and the optimal load resistance value shifts slightly lower as the input power increases. These are because the input power is pretty high and the junction capacitance of the diodes, which is input power dependent at low input power levels, is negligibly small, and only the real part of the diode impedance changes as the input power levels are varied. The sharp decrease in the RF-dc conversion efficiency for high load resistance values at high input power levels happens because the output voltage becomes larger than the breakdown voltage of the diode, resulting in limiting effects. As a result of the measurements, the estimated maximum RF-dc conversion efficiency of 76.3% was achieved for the 1772 load resistance for E-field harvester and 88.5% was achieved for the 2996 load resistance for H-field harvester based on the measurements. The reason why the simulation and measurement results for the E- and H-field harvester show minor disagreements in terms of the optimal load resistance is assumed to be the fact that the estimated input power from the -parameters measurement is lower than the actual input power, practically causing some amount of mismatch between the receiver and the RF-dc conversion circuit. Also, the difference between the ideal and the actual lumped components could be the cause of the higher loss in the measurement. As depicted in Figs. 12(b) and 13(b), an operation test using a LED was conducted by replacing the load

BITO et al.: AMBIENT RF ENERGY HARVESTING FROM A TWO-WAY TALK RADIO

Fig. 14. Simulated and estimated RF-dc conversion efficiency values from -parameters measurements and the measured output dc power from E-field harvester prototype with respect to load resistance.

Fig. 15. Simulated and estimated RF-dc conversion efficiency values from -parameters measurements and the measured output dc power from H-field harvester prototype with respect to load resistance.

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Fig. 16. H-field harvester prototype using inkjet-printed conductive traces after lamination with an epoxy glue.

Fig. 17. Output dc power of the conductive inkjet-printed H-field harvester prototype with and without lamination under flat conditions.

resistance with a LED while mounting the prototype of E-field harvester on the wrist, and sticking the H-field harvester prototype on the back of the hand. As a result, the LED was successfully turned on utilizing only the harvested energy from the handheld radio under the typical radio operation conditions for both scenarios [9], [10]. B. Comparison of Inkjet Printing Masking and Inkjet Printed Conductive Traces Based on the assumption that the traces for the RF-dc conversion circuit are electrically small compared to the wavelength at 464 MHz and that the difference in substrate materials do not significantly affect the operation of the circuit, the same circuit design of the inkjet-printed masking prototype was adopted for the conductive inkjet-printed H-field harvester circuit. In order to avoid having the problem of cracking in the printed conductive traces, the conductive epoxy paste used for the electrical connection of lumped components was laminated with a thin epoxy glue layer as depicted in Fig. 16. In order to determine the effect of epoxy lamination on the performance of the harvester circuit, the output dc power from the H-field harvester before and after the lamination were measured on a flat sponge, whose thickness is 35 mm by arranging the hand-held radio on the back side of the sponge. The results are depicted in Fig. 17, verifying that there is no significant difference in performance

Fig. 18. Output dc power from the prototypes of H-field harvester using inkjet printing masking and inkjet-printed conductive traces under “on bottle” bent/flex conditions.

due to the lamination. As a final test, the output power from the conductive inkjet-printed H-field harvester was measured on the water bottle to compare the performance of harvesting with the inkjet printing masking H-field harvester under bent/flex conditions. The output dc power with respect to the load resistance for both inkjet printing masking and inkjet-printed conductive traces are shown in Fig. 18, showing a very good agreement, while the open output voltage of the conductive inkjet-printed H-field harvester is shown in Fig. 19.

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Fig. 19. Open voltage measurement of the conductive inkjet-printed H-field harvester with an on-bottle setup.

Fig. 21. Setup for the operation test of H-field harvester using a microcontroller module.

tations among the transmitter, the harvester and the hand can significantly change the coupling and the matching conditions a lot. In order to overcome this issue, a receiver with misalignment-correction capabilities has to be used. Also, the design of a matching circuit for wide operation power range, for example a real-time active matching circuit, can be introduced to compensate the effect of the misalignment [24]. D. Operation Test Using Microcontroller Module

Fig. 20. Output dc power from E-field and H-field harvester prototypes using LCP substrate on bottle at different misalignment angles.

C. Effect of Misalignment on Harvesting Performance Potential misalignment between the hand-held radio and harvester would possibly degrade the performance of harvesters. It is known that the range of motion of a wrist is about 40 for both flexion and extension, and 40 of combined radial-ulnar deviation [23]. In order to investigate the effect of misalignment for wearable harvesters, output dc power measurements under the condition of aligned positions are conducted. The direction of the misaligning rotation for the E- and the H-field harvester are depicted in Figs. 12(a) and 13(a), respectively. The output dc power with respect to the load resistance at each angle is plotted in Fig. 20. Assuming that the maximum degradation in input power occurs at the highest misalignment angle, the E-field harvester features a maximum of 49.2% output dc power variation compared to the 0 condition. Similarly, the maximum output dc power variation for H-field harvester associated with misalignment is 63.5%. The reason why the dc power of the H-field at is much larger than at 45 can be attributed to the fact that the distance between the antenna and the receiver in the harvester is longer in the case of 45 than in the case of because of the extra transmission line length between the rectangular traces and the balun even if it looks like a symmetric shape. From these results, it can be concluded that alignment is critical to achieve a high RF-dc conversion efficiency with wearable harvester circuit. During the actual on-body operation, it can be assumed that the relative geometrical orien-

One of the fundamental motivations of this research is to overcome the problem of the “cold start” of ICs by introducing a wearable flexible near-field energy harvesting circuit. In order to test the applicability of the proposed harvester to wireless autonomous sensing devices, an operation test using microcontroller modules was conducted. The setup for the operation verification is depicted in Fig. 21. The harvested energy was stored in the energy storage unit, which was composed of a 1000 F Tantulum capacitor and voltage regulators to protect the capacitor and the microcontroller module. The MSP430 base microcontroller unit, eZ430-RF2500 provided by Texas Instruments, was used as the Access Point (AP) and the End Device (ED). The module has the functionality of wireless communication at 2.45 GHz, while functioning as a thermometer utilizing an analog-to-digital converter (ADC). The operation and the duty cycle of the ED, which was powered by an H-field harvester, were optimized to realize a low power consumption. The current flow to the ED when the module was powered by a 3.3 V voltage source was measured by using a digital oscilloscope, Tektronix DPO7354, as is plotted in Fig. 22, which clearly shows an initial operation state and a normal operation state. During the initial operation, the ED is sequentially performing the following four tasks; initializes the microcontroller, establishes communication between the ED and the AP, acquires the temperature data using ADC and sends the data back to the AP by transmitting RF signals. Similarly, the ED acquires the temperature data and sends the data to the AP during the normal operation. In order to start up the operation, it requires about 986 of energy at the supply voltage of 3.3 V. At the normal operation, the module requires about 193 of energy for every measurement. These values are computed by integrating the instant power consumption during the initial and the normal operation states obtained from the previous oscilloscope measurement data. Also,

BITO et al.: AMBIENT RF ENERGY HARVESTING FROM A TWO-WAY TALK RADIO

Fig. 22. Measured microcontroller module (ED) current flow in the initial operation state and in the normal operation state.

the initial operation requires the maximum instantaneous power of 123.75 mW, which is about 1.32 times larger than in the normal operation. Without loss of generality, we assume that the temperature acquisition and data transmission are conducted at an arbitrary interval, which is represented as Td in the Fig. 22. For the operation verification test, the duty cycle was chosen as 5 s for practical proof-of-concept purposes. After each measurement, the ED stays in low power consumption mode until the next measurement, and consumes about 4.3 W of power according to the application note [25]. As a result of the verification test, the ED turns on within 1 s from the “cold start” and starts sending the data once the two-way talk radio was turned on. After 1 s of charging, the ED can repeat the normal operation for three to five times at the duty-cycle of 5 s. The number of operations was confirmed by counting the number of the communication logs shown on the computer. It can be assumed that the variation in the number of operations was caused by the variance in the stored energy in the capacitor after the charging because the dc power from the harvester varies depending on the load resistance and the misalignment. Also, the required energy for the ED to establish the communication with the AP changes depending on how fast they establish the communication link. The number of “autonomous” operations could not exceed 5 times even if the charging time was increased, which is implying that the capacitor in the energy storage unit had been already saturated after 1 s of charging. Therefore, it is assumed that it would be possible to extend the operation time by introducing a high-capacity energy storage device, such as a lithium ion battery. E. Effect of Harvester on the Two-Way Radio Communication Quality Since the energy harvester circuit is utilizing energy which is originally expected to be used for communication signals, it could possibly degrade the quality of communication. In order to specify the effects of the energy harvesting circuit on the handheld radio communication performance, the received power, which represents the quality of communication, was measured in the anechoic chamber for the following three different conditions at 1 and 2 m separation distances between the transmitter and the receiving antenna: i) the harvester prototype

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Fig. 23. Received power measurement in an anechoic chamber.

Fig. 24. Effect of harvester prototype on received communication power.

on the water bottle is placed in the proximity of the radio as is Fig. 12; ii) only the water bottle is placed near the radio; and iii) both the water bottle and the harvester prototype are removed from the vicinity of the radio. The measurement setup is shown in Fig. 23 [9] involving one prototype of the E-field harvester. For the measurement, one prototype of the E-field harvester was used. The receiving antenna was a monopole antenna, ANT-433-CW-QW from Linx Technologies Inc,. The measurement results are depicted in Fig. 24, verifying that the difference in the received power between the case (i) and the case (ii) at two different separation distances in the far field were quite small, meaning that the effects of adding a wearable harvester to a hand holding a radio are almost negligible. On the other hand, the difference between case (ii) and (iii) is quite significant, which implies that the effect of harvesting is small compared to the effect of existence of water bottle, which is probably causing fading. Therefore, it can be concluded that the degradation of the communication performances of the two-way talk radio by the presence of the energy harvesting circuit is much smaller compared to the human body effect. V. CONCLUSIONS In this paper, the design and additive manufacturing fabrication process of flexible near-field ambient energy harvesting circuits for wearable sensor device applications is discussed. Numerous proof-of-concept circuit prototypes were fabricated through the combination of conductive traces realized with

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inkjet printing masking and conductive inkjet printing technologies with lumped circuit components. The input power for the RF-dc conversion circuit was analytically estimated from the measured -parameters, and the maximum output power levels of 146.9 mW and 43.2 mW were achieved with H-field and E-field harvesters, respectively. Numerous operation tests of E- and H-field energy harvesters were conducted by utilizing a LED and a microcontroller communication module under on-body and on-bottle bent/flex conditions, and verified the successful powering of both modules utilizing only the energy from the two-way talk radio. These very promising preliminary results suggest the wide potential applicability of the proposed inkjet-printed flexible energy harvesters to a variety of wearable biomonitoring, WBAN and Internet of Things applications. REFERENCES [1] M. Pinuela, P. D. Mitcheson, and S. Lucyszyn, “Ambient RF energy harvesting in urban and semi-urban environments,” IEEE Trans. Microw. Theory Tech., vol. 61, no. 7, pp. 2715–2726, Jul. 2013. [2] R. J. Vyas, B. B. Cook, Y. Kawahara, and M. M. Tentzeris, “E-WEHP: A batteryless embedded sensor-platform wirelessly powered from ambient digital-TV signals,” IEEE Trans. Microw. Theory Tech., vol. 61, no. 6, pp. 2491–2505, Jun. 2013. [3] J. A. Paradiso and T. Starner, “Energy scavenging for mobile and wireless electronics,” IEEE Pervasive Comput., vol. 4, no. 1, pp. 18–27, Jan. 2005. [4] X. Wang and A. Mortazawi, “Medium wave energy scavenging for wireless structural health monitoring sensors,” IEEE Trans. Microw. Theory Tech., vol. 62, no. 4, pp. 1067–1073, Apr. 2014. [5] S. Kim, R. Vyas, J. Bito, K. Niotaki, A. Collado, A. Georgiadis, and M. Tentzeris, “Ambient RF energy-harvesting technologies for self-sustainable standalone wireless sensor platforms,” Proc. IEEE, vol. 102, no. 11, pp. 1649–1666, Nov. 2014. [6] A. Kurs, A. Karalis, R. Moffatt, J. D. Joannopoulos, P. Fisher, and M. Soljačić, “Wireless power transfer via strongly coupled magnetic resonances,” Science, vol. 317, no. 5834, pp. 83–86, Jul. 2007. [7] R. Want, “An introduction to RFID technology,” IEEE Pervasive Comput., vol. 5, no. 1, pp. 25–33, Jan. 2006. [8] P. V. Nikitin, K. V. S. Rao, and S. Lazar, “An overview of near field UHF RFID,” in Proc. 2007 IEEE Int. Conf. on RFID, Grapevine, TX, USA, Mar. 2007, pp. 167–174. [9] J. Bito, J. G. Hester, and M. M. Tentzeris, “Ambient energy harvesting from a two-way talk radio for flexible wearable devices utilizing inkjet printing masking,” in 2015 IEEE MTT-S Int. Microwave Symp. Dig., Phoenix, AZ, USA, May 2015, pp. 1–4. [10] J. Bito and M. Tentzeris, “A novel flexible wearable magnetic energy harvester utilizing inkjet masking techniques,” in Proc. 2015 IEEE Antennas and Propagation Soc. Int. Symp., Vancouver, BC, Canada, Jul. 2015. [11] L. Yang, A. Rida, R. Vyas, and M. M. Tentzeris, “RFID tag and RF structures on a paper substrate using inkjet-printing technology,” IEEE Trans. Microw. Theory Tech., vol. 55, no. 12, pp. 2894–2901, Dec. 2007. [12] B. S. Cook, J. R. Cooper, and M. M. Tentzeris, “Multi-layer RF capacitors on flexible substrates utilizing inkjet printed dielectric polymers,” IEEE Microw. Wireless Compon. Lett., vol. 23, no. 7, pp. 353–355, Jul. 2013. [13] B. S. Cook, C. Mariotti, J. R. Cooper, D. Revier, B. K. Tehrani, L. A. L. Roselli, and M. M. Tentzeris, “Inkjet-printed, vertically-integrated, high-performance inductors and transformers on flexible LCP substrate,” in 2014 IEEE MTT-S Int. Microwave Symp. Dig., Tampa, FL, USA, Jun. 2014, pp. 1–4. [14] J. G. Hester, Y. Fang, and M. M. Tentzeris, “Inkjet-printed, flexible, high performance, carbon nanomaterial based sensors for ammonia and DMMP gas detection,” in Proc. 45th Eur. Microwave Conf., Paris, France, Sep. 2015. [15] A. C. Arias, J. D. MacKenzie, I. McCulloch, J. Rivnay, and A. Salleo, “Materials and applications for large area electronics: Solution-based approaches,” Chem. Rev., vol. 110, no. 1, pp. 3–24, Jan. 2010. [16] J. G. Hester, S. Kim, J. Bito, T. Le, J. Kimionis, D. Revier, C. Saintsing, S. Wenjing, B. Tehrani, A. Traille, B. S. Cook, and M. M. Tentzeris, “Additively manufactured nanotechnology and origami-enabled flexible microwave electronics,” Proc. IEEE, vol. 103, no. 4, pp. 583–606, Apr. 2015.

[17] Y. Kawahara, S. Hodges, B. S. Cook, C. Zhang, and G. D. Abowd, “Instant inkjet circuits: Lab-based inkjet printing to support rapid prototyping of UbiComp devices,” in Proc. 2013 ACM Int. Joint Conf. on Pervasive and Ubiquitous Computing (UbiComp '13), New York, NY, USA, Sep. 2013, pp. 363–372. [18] B. K. Tehrani, J. Bito, B. S. Cook, and M. M. Tentzeris, “Fully inkjet-printed multilayer microstrip and T-resonator structures for the RF characterization of printable materials and interconnects,” in 2014 IEEE MTT-S Int. Microwave Symp. Dig., Tampa, FL, USA, Jun. 2014, pp. 1–4. [19] J. Bito, B. Tehrani, B. Cook, and M. Tentzeris, “Fully inkjet-printed multilayer microstrip patch antenna for Ku-band applications,” in Proc. 2014 IEEE Antennas and Propagation Soc. Int. Symp., Memphis, TN, USA, Jul. 2014, pp. 854–855. [20] S. Kim, J. Bito, J. Soyeon, A. Georgiadis, and M. M. Tentzeris, “A flexible hybrid printed RF energy harvester utilizing catalyst-based copper printing technologies for far-field RF energy harvesting applications,” in 2015 IEEE MTT-S Int. Microwave Symp. Dig., Phoenix, AZ, USA, May 2015, pp. 1–4. [21] Technical Data Sheet Nanosilver Conductive Ink EMD5730 SunChemical, 2013. [22] B. Cook and A. Shamim, “Inkjet printing of novel wideband and high gain antennas on low-cost paper substrate,” IEEE Trans. Antennas Propag., vol. 60, no. 9, pp. 4148–4156, Sep. 2012. [23] J. Ryu, W. P. Cooney, III, L. J. Askew, K. N. An, and E. Y. S. Chao, “Functional ranges of motion of the wrist joint,” J. Hand Surgery, vol. 16, no. 3, pp. 409–419, May 1991. [24] J. Bito, J. Soyeon, and M. M. Tentzeris, “A real-time electrically controlled active matching circuit utilizing genetic algorithms for biomedical WPT applications,” in Proc. 2015 IEEE Wireless Power Transfer Conf., Boulder, CO, USA, May 2015, pp. 1–4. [25] M. Morales and Z. Shivers, Appl. Note SLAA378D Wireless Sensor Monitor Using the eZ430-RF2500. Dallas, TX, USA: Texas Instruments, 2011.

Jo Bito (S'13) received the B.S. degree in electrical and electronic engineering from Okayama University, Okayama, Japan in 2013. From 2010 to 2011 he was with the International Programs in Engineering (IPENG), and studied at University of Illinois Urbana-Champaign, Champaign, IL, USA. He is currently pursuing the Ph.D. degree in electrical and computer engineering at the Georgia Institute of Technology, Atlanta, GA, USA. He is now a Research Assistant in the ATHENA research group. His research interests include the application of inkjet printing technology for flexible and wearable electronics, RF energy harvesting, and wireless power transfer systems. He is a recipient of the Japan Student Services Organization (JASSO) long-term scholarship from 2013.

Jimmy G. Hester (S'14) spent two intense preparation years studying fundamental chemistry, math, and physics after which he was admitted in INP Toulouse, ENSEEIHT where he received the graduate degree and M.S degree in electrical and signal processing engineering, majoring in radio frequency electronics, in 2012 and 2014, respectively. He received the M.S. degree in electrical and computer engineering from the Georgia Institute of Technology, Atlanta, GA, USA, in 201, where he is now working, as a Research Assistant in the ATHENA group, toward the Ph.D. degree in electrical and computer engineering. His research interests lie at the interface between radio frequency (RF) engineering and material science, in the form of flexible electronics technologies and nanotechnologies. Recently, he has been working toward the use of carbon nanomaterials applied to inkjet-printed RF sensing components for flexible low cost ubiquitous gas sensing applications. His work covers the entire development process, from the development of inkjet inks, improvement of fabrication methods, sensor component design, high-frequency characterization, and environmental testing to the design, simulation, and fabrication of the RF system embedding the sensor.

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Manos M. Tentzeris (S'89–M'92–SM'03–F'10) received the Diploma Degree in electrical and computer engineering from the National Technical University of Athens (“Magna Cum Laude”), Athens, Greece and the M.S. and Ph.D. degrees in electrical engineering and computer science from the University of Michigan, Ann Arbor, MI, USA. He is currently a Professor with School of Electrical and Computer Engineering, Georgia Institute of Technology (Georgia Tech), Atlanta, GA, USA. He has published more than 550 papers in refereed journals and conference proceedings, five books ,and 23 book chapters. He has helped develop academic programs in highly integrated/multilayer packaging for radio frequency (RF) and wireless applications using ceramic and organic flexible materials, paper-based RFIDs and sensors, biosensors, wearable electronics, 3-D/4-D/inkjet-printed electronics, “green” electronics, energy-harvesting and wireless power transfer systems, NFC systems, nanotechnology applications in RF, origami-folded electromagnetics, microwave MEMs, SOP-integrated (UWB, multiband, mmW, conformal) antennas and heads the ATHENA research group (20 researchers). He has served as the Head of the GT-ECE Electromagnetics Technical Interest Group, as the Georgia Electronic Design Center Associate Director for RFID/Sensors research from 2006–2010 and as the Georgia Tech NSF-Packaging Research Center Associate Director for RF Research and the RF Alliance Leader from 2003–2006. He was a Visiting Professor with the Technical University of Munich, Germany for the summer of 2002, a Visiting Professor with GTRI-Ireland in Athlone, Ireland for the summer of 2009, and a Visiting Professor with LAAS-CNRS in Toulouse, France for the summer of 2010. He has given more than 100 invited talks to various universities and companies all over the world. Dr. Tentzeris was the recipient/co-recipient of the 2015 IET Microwaves, Antennas and Propagation Premium Award, the 2014 Georgia Tech ECE Distinguished Faculty Achievement Award, the 2014 IEEE RFID-TA Best Student Paper Award, the 2013 IET Microwaves, Antennas and Propagation Premium

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Award, the 2012 FiDiPro Award in Finland, the iCMG Architecture Award of Excellence, the 2010 IEEE Antennas and Propagation Society Piergiorgio L. E. Uslenghi Letters Prize Paper Award, the 2011 International Workshop on Structural Health Monitoring Best Student Paper Award, the 2010 Georgia Tech Senior Faculty Outstanding Undergraduate Research Mentor Award, the 2009 IEEE Transactions on Components and Packaging Technologies Best Paper Award, the 2009 E.T.S.Walton Award from the Irish Science Foundation, the 2007 IEEE APS Symposium Best Student Paper Award, the 2007 IEEE IMS Third Best Student Paper Award, the 2007 ISAP 2007 Poster Presentation Award, the 2006 IEEE MTT Outstanding Young Engineer Award, the 2006 Asian-Pacific Microwave Conference Award, the 2004 IEEE Transactions on Advanced Packaging Commendable Paper Award, the 2003 NASA Godfrey “Art” Anzic Collaborative Distinguished Publication Award, the 2003 IBC International Educator of the Year Award, the 2003 IEEE CPMT Outstanding Young Engineer Award, the 2002 International Conference on Microwave and Millimeter-Wave Technology Best Paper Award (Beijing, CHINA), the 2002 Georgia Tech-ECE Outstanding Junior Faculty Award, the 2001 ACES Conference Best Paper Award and the 2000 NSF CAREER Award and the 1997 Best Paper Award of the International Hybrid Microelectronics and Packaging Society. He was the TPC Chair for IEEE IMS 2008 Symposium and the Chairof the 2005 IEEE CEM-TD Workshop and he is the Vice-Chair of the RF Technical Committee (TC16) of the IEEE CPMT Society.He is the founder and chair of the RFID Technical Committee (TC24) of the IEEE MTT Society and the Secretary/Treasurer of the IEEE C-RFID. He is an Associate Editor of IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, IEEE TRANSACTIONS ON ADVANCED PACKAGING, and the International Journal on Antennas and Propagation. He is a member of URSI-Commission D, a member of MTT-15 committee, an Associate Member of the European Microwave Association, a Fellow of the Electromagnetic Academy, and a member of the Technical Chamber of Greece. He served as one of the IEEE Microwave Theory and Techniques Society Distinguished Microwave Lecturers from 2010–2012, and he is currently serving as the IEEE C-RFID Distinguished Lecturer.

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Breaking the Efficiency Barrier for Ambient Microwave Power Harvesting With Heterojunction Backward Tunnel Diodes Carlos Henrique Petzl Lorenz, Student Member, IEEE, Simon Hemour, Member, IEEE, Wenjun Li, Yi Xie, Jules Gauthier, Patrick Fay, Senior Member, IEEE, and Ke Wu, Fellow, IEEE

Abstract—Harvesting low-density ambient microwave power as an alternative power source for small ubiquitous wireless nodes has been proposed in recent papers discussing emerging technologies like the Internet of Things and Smart Cities. However, a literature review of the state-of-the-art Schottky diode based microwave rectifiers shows that a maximum efficiency has been reached for such devices operating in the low-power regime, as is the case for ambient microwave power-harvesters. This work examines the underlying physical mechanisms responsible for this RF-to-dc power conversion efficiency limitation, and explores a high I-V curvature backward tunnel diode to overcome this efficiency limitation. Measurements of the 2.4 GHz RF-to-dc power conversion efficiency at 40 dBm input power demonstrates that the backward tunnel diode outperforms the HSMS-285B Schottky diode by a factor of 10.5 and the Skyworks SMS7630 by a factor of 5.5 in a lossless matching network scenario. A prototype built using a new GSG probe embedded with a matching circuit showed a total power conversion efficiency of 3.8% for 40 dBm input power and 18.2% for 30 dBm input power at 2.35 GHz. Index Terms—Backward tunnel diode, microwave power harvesting, microwave power rectification, rectenna, Schottky diode.

I. INTRODUCTION

T

HE way the internet is perceived by its users is going through a significant transformation. Today, nearly two billion people have access to the internet [1], using it to browse websites, play games, work, send and receive e-mails and messages, among many other on-line applications. Most of these applications, however, share a common characteristic: an end-user terminal. Nonetheless an important revolution is in progress, in which ubiquitous objects will be more and more connected to the internet or other local networks, leading to the Internet of Things (IoT) [1], [2]. Some emerging applications of this new

Manuscript received July 01, 2015; revised September 30, 2015; accepted October 13, 2015. Date of publication November 18, 2015; date of current version December 02, 2015. This work was supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC) and CREATE PERSWADE Training Program. This paper is an expanded version from the IEEE MTT-S International Microwave Symposium, Phoenix, AZ, USA, May 17–22, 2015. C. H. P. Lorenz, S. Hemour, J. Gauthier, and K. Wu are with the Poly-Grames Research Center, École Polytechnique de Montréal, Montreal, QC H3T 1J4, Canada (e-mail: [email protected]). W. Li, Y. Xie, and P. Fay are with the Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN 46556 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2015.2495356

paradigm in networking include monitoring the structural health of buildings and monuments, smart roads to help detect heavy traffic so that efficient itineraries can be suggested and traffic light timings can be optimized, remote health monitoring of patients, to cite just a few [3]. Emerging hardware technologies are being studied to enable these Smart Cities, Smart Building Automation and Monitoring, as well as Wearable Devices applications. These usually require wireless connections and small form-factor energy sources to remotely power the ubiquitous sensing and controlling devices, without the burden of a heavy and bulky battery that may be difficult to replace—as in the case of body implants and sensors embedded into building structural parts. Resonant power transfer technology has shown to be a good alternative when a charger may be placed in close proximity to the wireless device of interest, as is the case for parked electric vehicles and even body implants that may be charged at periodic intervals [4]. However, very short operational distances between the charger and device becomes a fundamental obstacle when omnipresent, distributed sensor networks are deployed. Microwave Power Harvesting (MPH) has been proposed as an alternative wireless power source for such low power consumption and low duty cycle ubiquitous devices [5]–[7]. However, an overview of the state of the art in the field of microwave power harvesting suggests that a limitation in the efficiency of Schottky diode-based converters at low incident power levels has been reached [5], [8], [9]. In practice, microwave power rectifiers capable of operating below 30 dBm are needed for ambient microwave power harvesting (AMPH) as indicated in recent ambient microwave power density assessments [5], [10]. However, to date RF-to-dc conversion efficiency has not yet reached even 10% at frequencies above 1 GHz at such low-density power levels. Overcoming this performance barrier is essential for AMPH systems to become a practical reality. Schottky diodes rely on the thermionic emission, which limits the zero-bias current responsivity to 19.34 A/W at 300 K [8]. As shown in [8], [9], the rectification efficiency of microwave rectifiers operating in the diode's square-law region is directly proportional to the square of . Backward tunnel diodes, which make use of quantum mechanical tunneling rather than thermionic emission, have been reported that overcome the Schottky diodes' inherent , reaching values near 24 A/W for devices optimized for millimeter-wave operation [8], [11] or

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even as high as 35 A/W for lower-frequency devices [12]. This paper presents a deeper evaluation of the application of such diodes to overcome the low-power RF-to-dc conversion efficiency limitation observed with Schottky diode microwave rectifiers, an idea which was first introduced in [13] and is extended in this paper. A comparison between a backward diode and an HSMS-285B Schottky diode is presented, demonstrating an increase in RF-to-dc conversion efficiency at extremely low incident power levels, as required when harvesting ambient power below 30 dBm. II. MICROWAVE POWER HARVESTING In order to explore possible ways of increasing the power conversion efficiency PCE (1) of ambient microwave power harvesters, it is, first of all, necessary to understand the mechanisms that play a role in the energy rectification process at very low input powers levels, as found in ambient microwave power harvesting scenarios. In such applications, the expected operation power range has maximum peaks reaching 15 dBm in very high power density areas, with a typical average power of 30 dBm and below [5], [10]. At such power levels, the square-law microwave power rectification model presented in [9] can be used as a good approximation. In this rectification model, the power conversion mechanism is sub-divided into different steps, each one with an intrinsic efficiency. These efficiencies combine to produce the total rectifier's PCE, as summarized below: is the matching network efficiency;

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Fig. 1. Shockley diode model with package/pads parasitic components.

the diode zero-bias current responsivity. The parasitic efficiency can then be calculated by using [9]: (3) where is the angular frequency of operation. The matching network efficiency largely depends on the matching topology and circuit/component technology used to implement the matching network. However, (4) and (5) [14] can be used to estimate the relative increase or decrease of achieved with different candidate diodes, provided that the quality factor of the matching network can be maintained at the same level. Such an assumption of constant is true if the source and load mismatch does not change substantially (i.e., the diode impedances under consideration are not dramatically different). Under these assumptions, (4)

is the parasitic efficiency; is the non-linear junction RF-to-dc power conversion efficiency;

(5)

is the dc power transfer efficiency, which gives the percentage of the total rectified dc power that is actually delivered to the load. The total power conversion efficiency PCE can thus be calculated using (1): (1) is the dc power delivered to the load and is where the input RF power. The non-linear device characteristics influence in different ways each of these efficiencies. In the case of diodes, which are the subject of the study presented in this work, the Shockley diode model with package parasitic components is used, as shown in Fig. 1. In this figure, represents the diode's non-linear junction resistance, the junction capacitance, the package parasitic capacitance, , the package inductance, and the series resistance. Using this model, the total efficiency when the load connected to the diode is equal to is given by [9]: (2) where is the microwave power delivered to the junction resistance, is the junction resistance at zero-bias, and is

where is the required quality factor, which depends on the mismatch between the highest and lowest impedances ( and , respectively) that are to be matched. In the case of diode-based matching for AMPH, this is typically the source impedance and the diode's . Using (1)through (5), one can understand the diode parameters that need to be optimized in order to maximize the power conversion efficiency. As expected, equation (3) suggests that lowering the parasitic resistance and junction capacitance improves the parasitic efficiency. The importance of choosing devices with low parasitic capacitance is already well-known in the microwave community and will not be further discussed here. The junction resistance has a more complex influence on AMPH performance. A higher increases the efficiency, assuming that the load magnitude can be adjusted to match that of the junction resistance. However, exhibits the opposite trend, and decreases when is increased. Similarly, also degrades as increases since the losses in the matching network rise with an increased mismatch between source and diode junction resistance. The maximum PCE limitation that is reflected in the current-state-of-the-art AMPH designs [8], [9] resides in the fact that an optimum has been established, and for which reaches its maximum for Schottky diodes.

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Consequently, to improve power conversion efficiency at low incident power levels, the only remaining parameter to consider is the diode's zero-bias current responsivity . However, as presented in the next section, Schottky diodes' is limited by thermionic emission over a potential barrier. This work explores and harnesses the use of another class of diodes, backward tunnel diodes, which are not governed by thermionic emission, for their use in AMPH applications. III. DIODES FOR ENERGY HARVESTING Energy harvesting based on detection of low-level ac waveforms fundamentally relies on achieving a large second-order nonlinearity in order to maximize the RF-to-dc conversion. While large-signal rectification (i.e., switching) simply requires a strongly asymmetric I-V relationship to maximize the impedance difference between on- and off-states, harvesting energy from low-level sources that are insufficient to induce switching is more challenging. In this low-level signal regime, conversion efficiency is directly related to the square of the current responsivity as shown in (2), which equals half the curvature, , of the detection device at the zero-bias condition [8]. This metric can be directly assessed from the I-V characteristics of the device, and thus provides a convenient means for comparison among technologies. For thermionic devices such as Schottky and PN junctions for which the I-V relationship is of the form , one can see that at room temperature, independent of technology or the details of device design. This imposes fundamental physical limits on the ultimately achievable performance of thermionic detectors for energy harvesting applications. To circumvent this limitation, devices based on alternative physical operation principles for which is not limited to are potentially attractive. One promising physical mechanism that can be leveraged to obtain a higher curvature is interband tunneling. In contrast to Schottky diodes, PN junctions, and transistor-based passive detectors (e.g. diode-connected FETs, Schottky diodes using HEMT gates) in which carriers in a single band interact with a voltage-controlled potential barrier as the basis for detection and rectification, interband tunnel diodes are governed by the combination of the density of states and occupancy probabilities on both sides of the tunnel junction as well as the tunneling probability. In this way, the density of states in both the conduction and valence bands, as well as the details of the tunnel barrier, can be used to engineer devices with increased second-order nonlinearity and thus offer the potential for improved detection and conversion efficiency. An analytical treatment of homojunction interband tunnel diodes can be found in [15]; within the simplified model used, an arbitrarily large curvature can be achieved by a proper selection of the Fermi levels within the device [15]. Fundamentally, these devices can offer larger curvatures than thermionic-emission based devices because the overlap between the occupied electron and hole densities of states is “filtered” by the bandgaps at the heterojunction, leading to a truncation of the Fermi-Dirac distribution for the carriers. Devices of this type have been demonstrated experimentally as millimeter-wave detectors [16], and curvatures as high as 70 have been reported

experimentally [12], broadly consistent with the expectations with theory. It should be noted that in order to achieve these high curvatures, a “backward” tunnel diode structure is needed, in contrast to an Esaki diode [17], [18]. In the case of an Esaki diode, extremely high doping is used on both sides of the junction, leading to low junction resistance and the onset of negative differential resistance in the forward characteristic. For detector and harvester applications, however, the negative differential resistance is not desirable (the curvature changes sign at the onset of negative differential resistance, leading to a partial cancellation of the detected signal with an increasing input power) and the second-order curvature near zero bias is smaller than with the more modestly-doped backward diode structures [15]. However, homojunction tunnel diodes such as those described above also pose some challenges in energy harvesting applications. Of particular concern for RF and microwave applications, homojunction tunnel diodes have a large capacitance per unit area (as a direct consequence of the use of heavy doping to achieve the thin depletion region and band degeneracy required to enable tunneling). This limits the frequency range of application, due to increased parasitic losses, as well as the bandwidth achievable with reactive matching networks. It has also been reported that Ge-based tunnel junctions can pose reliability and manufacturability challenges [19]. As an alternative, heterostructure backward tunnel diodes are an attractive approach. These devices maintain the fundamental operational principles of homojunction tunnel diodes (interband tunneling) and thus the possibility for high curvature, while at the same time introducing significant additional degrees of freedom in the device design to allow optimization of the device performance for specific applications. For example, devices of this type have previously been demonstrated to provide high-sensitivity, low-noise microwave and millimeter-wave detection [11], [20], [21], [22] for applications such as passive millimeter-wave imaging, with an extremely low noise equivalent power (NEP) of 0.18 [11]. This record-low NEP is made possible by a combination of both extremely low device noise, in conjunction with higher curvature arising from the operational physics. To maximize performance for detection, the devices are designed to maximize the second order nonlinearity at zero bias, thereby allowing the detectors to be used without externally applied bias. This dramatically reduces 1/f noise (resulting in nearly thermal-noise-limited performance) [21], [23], and it has been shown that zero-bias second-order nonlinearity in excess of what is possible with Schottky diodes can be achieved [11]. This degree of control of the device characteristics is made possible by the substantial design flexibility in heterostructure devices. Low-level RF energy harvesters have similar requirements, i.e., strong nonlinearity near zero bias is needed for efficient RF-to-dc conversion, and thus these devices are also attractive for this application. Fig. 2(a) shows a schematic cross-sectional diagram of the nominal heterostructure backward diode used in this work; the corresponding measured Current Density-Voltage characteristics are shown in Fig. 2(b). As can be seen, a rectifying characteristic is obtained, with an extremely asymmetric I-V characteristic and “knee” at very low voltage, indicative of a strong cur-

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Fig. 2. (a) Schematic cross-section diagram for the heterostructure backward diode used in this work. The energy filtering enforced by the small tunneling window results in strongly nonlinear current-voltage characteristics and high sensitivity. (b) Current Density-Voltage characteristic for the heterostructure backward diodes used for the power harvesting prototypes presented in this work. (c) Calculated energy band diagram. (d) Scanning electron micrograph of fabricated backward tunnel diode with ground-signal-ground probe pads.

vature. In addition, the turn-on is in the ‘reverse’ direction (i.e., in the opposite sense from a conventional PN junction diode), as expected for a backward diode. As discussed previously, the efficiency of a power harvester is directly related to the junction resistance and curvature. Due to the interband tunneling mechanism in heterostructure backward diodes, can be much larger than what is possible with conventional Schottky or other thermionic emission-based devices; optimizing a heterostructure backward tunnel diode for energy harvesting applications requires maximizing the curvature while keeping the junction resistance at an acceptably low level. The key parameters that enable control over the device performance are the anode and cathode doping concentrations (and doping profiles), the tunnel barrier thickness, and the energy band offset between the valence band in the anode and the conduction band in the cathode. As one example, Fig. 2(c) shows the computed energy band diagram for the backward diode structure shown in Fig. 2(a). The choice of an aluminum composition of 12% in the anode layer leads to a small overlap between the conduction and valence bands, and thus as shown Fig. 2(c), only carriers occupying a narrow range of energies can participate in tunneling through the AlSb tunnel barrier. Carriers with higher energies in either the anode or cathode are blocked by the bandgaps (i.e., are filtered) and cannot contribute to the current [15], [24]. The choice of the AlSb tunnel barrier thickness allows independent control of the junction resistance (since to first order tunneling prob-

ability is exponential in barrier thickness) without altering the densities of states in the cathode and anode appreciably. The doping profiles in the anode and cathode are selected to enhance transmission through the structure, with a -doping plane incorporated into the cathode in this structure to provide a nearly flat band profile. The device heterostructure was grown by molecular beam epitaxy on a semi-insulating GaAs substrate. Device fabrication included evaporated Ti/Au anode and cathode contacts, mesa isolation using selective wet chemical etchants [25], and passivation with benzocyclobutene. The devices had an area of approximately 0.5 ; electron beam lithography was used to accurately define the device active area. Optical lithography was used to define the pads, mesas, contacts, and passivation layers. For the power harvesting experiments performed here, devices with the nominal heterostructure shown in Fig. 2(a) were used; this results in a measured zero-bias curvature , and as will be shown, this improved curvature and low turn-on voltage result in high power harvester efficiency even at low incident RF levels. To further increase the harvester efficiency, increased curvature is desirable. Fundamentally, increases in curvature are correlated with improved energy filtering at the tunnel junction; one promising approach for narrowing the energy window over which tunneling can occur is by modifying the composition of the AlGaSb anode (i.e., increasing the Al composition results in a smaller tunneling window). Physics-

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Fig. 4. Measured and modeled backward tunnel diode I-V curve. Fig. 3. Projected curvature and junction resistance as a function of anode composition as obtained from physics-based simulations. Discrete points have been computed using the simulations; the curves are exponential fits to the simulated data. Increased curvature as well as junction resistance result from narrowing of the tunneling window with increasing Al composition in the anode.

based simulations of heterostructures with the same basic form as shown in Fig. 2(c), except with varying compositions, have been performed, and the junction resistance and curvature expected from these models is shown in Fig. 3. Details of the modeling framework have been reported previously [26]. As can be seen in Fig. 3, increasing the Al composition in the anode results in a significant increase in curvature, with curvatures approaching 90 possible for compositions of approximately 25%. This increased curvature arises from the more narrowly-filtered carrier energy, but as expected this narrower energy range for tunneling is also accompanied by an increase in junction resistance. Our models project a harvester efficiency of 63% for such a diode at 40 dBm input power, indicating that despite the promising results obtained to date and reported here, considerable additional improvements are possible. While further increases in curvature can be obtained, they come at the expense of a significant increase in junction resistance that may limit overall conversion efficiency. The junction resistance increase can be counterbalanced to some extent by increasing the diode's junction area, however at the cost of an increased junction capacitance. As a result, the optimum anode composition and junction area is also a function of the intended frequency of operation. Detailed study of these tradeoffs is the subject of ongoing work. IV. BACKWARD TUNNEL DIODE CHARACTERIZATION Backward tunnel diodes with 12% anode Al composition have been characterized using a 100 pitch GSG (Ground-Signal-Ground) probe on a Cascade Summit probe station. A Keysight PNA network analyzer was used to measure the parameters and also as a calibrated microwave power source. The PNA network analyzer output power was calibrated at the probe K-connector interface using a power meter, and the probe insertion loss was loaded into the network analyzer to compensate for power losses inherent from the probe. In this way, the power delivered to the diode could be precisely controlled. The diode sensitivity and I-V characteristics were measured using a 6–1/2 digit HP 34401A precision multimeter,

connected to the network analyzer's internal bias-T. The dc current-voltage characteristic, as well as the diode's sensitivity and reflection coefficient from 500 MHz to 40 GHz were measured for an input power ranging from 30 dBm to 5 dBm, in 5 dB steps. The diode model parameters given in Fig. 1 were then extracted from the measurements. The nonlinear junction currentvoltage equation was modeled using a 7th order polynomial, given in (6); the coefficients were obtained through least-squares curve fitting to the measured I-V characteristics. A comparison between the modeling results and measurements is shown in Fig. 4. The dc non-linear model has been verified between 100 mV and 200 mV; this voltage range is sufficient to cover the voltages experienced by the device in ambient energy harvesting applications.

(6) polynomial given in (6), the diode's juncUsing the tion resistance , and current responsivity were calculated and are shown in Fig. 5 [27]. Having the non-linear junction behavior already defined, the measured sensitivity and reflection coefficient were used to extract the linear parasitic model parameters; these were found to be , and . Although may in general be bias-dependent, for the model developed here was approximated by a linear (constant) capacitance of 4.5 fF. Modeling results and measurements are compared in Fig. 6. Although the measurements were limited to 40 GHz, the simulation results have been projected up to 100 GHz to show the expected diode behavior. The modeled diode resistance and responsivity near zero-bias are shown in Fig. 5, over the expected operating region for the AMPH application presented here. From this figure, a of 21.65 A/W and of 12.5 are obtained for the particular backward tunnel diode used for this work. Assuming that the parasitic efficiency is comparable for Schottky and tunnel diodes, the increase in the diode's from 19.34 A/W in the ideal Schottky diode case to the measured tunnel diode responsivity of 21.65 A/W indicates that the efficiency at square-law power levels is expected to increase by a factor of 1.25 according to (2).

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TABLE I RECTIFIER EFFICIENCIES AT 40 DBM @ 2.4 GHz

Fig. 5. Calculated backward diode and fitted to the measured I-V relationship.

, using the 7th order polynomial

Fig. 7. Simplified schematic of the setup used for the microwave rectifier PCE measurements.

Fig. 8. Picture of part of the setup used to compare the PCE of the HSMS-2850 and backward tunnel diode. The picture shows the probe station and the Focus Microwaves Tuner, used as matching network.

Fig. 6. Comparison between measured and modeled backward diode RF char, real and imaginary compoacteristics at 30 dBm. (a) Input impedance, nents. (b) Voltage sensitivity; the simulation has been projected to 100 GHz.

V. COMPARISON OF BACKWARD TUNNEL DIODE SCHOTTKY DIODE MICROWAVE RECTIFIERS

AND

Neglecting the matching losses and considering that parasitic losses are negligible at 2.45 GHz due to very low , the studied backward diode has a calculated RF-to-dc power conversion efficiency equal to 14.7% at 40 dBm input power. Two commonly used Schottky diodes in AMPH applications were also evaluated and compared to the proposed backward diode, these

are the Avago HSMS-2850 and the Skyworks SMS7630 diodes. Table I compares the expected power conversion efficiencies at 40 dBm input power, 2.4 GHz center frequency, and resistive load matched to each diode's . The efficiencies were calculated using the backward diode model parameters presented previously, and Schottky diodes parameters from the manufacturer datasheets. This comparison highlights two important advantages that arise from the use of the backward tunnel diode in AMPH applications. The first is the discussed increase in the efficiency product due to the increased . However, another advantage that should be noted is the very high parasitic efficiency due to the low junction capacitance that results from the backward tunnel diode structure used here. From Table I, it can be seen that a large advantage is expected when using backward tunnel diode in AMPH applications; the expected PCE for the tunnel diode case is nearly 7 times the PCE of the SMS7630 diode at microwave input power levels typical of ambient harvesting applications.

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Fig. 9. Measured, simulated, and calculated efficiencies of the backward tunnel diode and HSMS-285B diode microwave rectifiers at 2.4 GHz. Matching network losses have been de-embedded.

In order to verify the increase in PCE predicted by the theory, both HSMS-285B and the backward diode rectification efficiencies were measured. The choice of the Schottky diode was based on the value of , which should be near to that presented by the backward diode to ensure a valid comparison. The microwave power rectification setup in our experiments consisted of a Keysight PNA Network Analyzer with an integrated bias-T, a Focus microwave tuner system used as matching network, and a 6–1/2 digit HP 34401A multimeter connected to a variable resistor, used as the dc load. The output power of the PNA was calibrated at the tuner input plane (source side) so that it could be used as the microwave power source. At the same time, the PNA was used to measure the reflection coefficient and ensure that a good matching was obtained at 2.4 GHz. A schematic diagram of the setup is shown in Fig. 7 and a picture in Fig. 8. To evaluate the power incident on the diodes, the open-circuit detector voltage was measured, using the diodes as microwave power detectors. This information together with the diode's sensitivity measured during the characterization step was then used to extract the insertion losses of the matching circuit. In this way, the rectifier's RF-to-dc conversion efficiency and parasitic efficiency were evaluated for both diode types, independently of any losses that originated from the matching circuit implementation. For the efficiency measurement, the variable load was adjusted to its optimum value; 13 was used for the backward diode, and 9 for the HSMS-285B diode. The measured, calculated, and simulated results are given in Fig. 9 together with an indication of the maximum efficiency that an ideal Schottky diode with no parasitic losses and the same as the studied backward diode could attain. The simulation tool used was the Keysight ADS harmonic balance simulator. The results given in Fig. 9 show the two predicted advantages of the evaluated backward diode for AMPH applications. The first is the improvement in power conversion efficiency due to the higher current responsivity. Even when compared to the ideal Schottky diode theoretical limit, the backward diode has a 25.3% higher efficiency at extremely low input power, showing a very good agreement with the previously calculated factor of 1.25. The second advantage comes from the low junction capacitance resulting from the backward diode construc-

Fig. 10. An adapter characterization is done to extract the S parameters of the probe, along with the substrate it is soldered on and the SMA connector.

tion. The resulting parasitic loss is extremely low at 2.4 GHz, leading to a 10.5 times higher efficiency when compared to the HSMS-285B diode at 40 dBm input power. This result too is in very good accordance with the previously calculated results given in Table I. VI. BACKWARD TUNNEL DIODE RECTIFIER PROTOTYPE In order to demonstrate a microwave power rectifier working at AMPH input power levels, a prototype with a narrow-band matching network has been fabricated to demonstrate operation in a more realistic context, including matching network losses. An in-house GSG probe was developed so multiple backward diodes could be tested using the same matching network board so the repeatability of the predicted result could be verified. A. GSG Probe Fabrication The GSG probes have been developed with the goal of being embeddable to any PCB circuit. For convenience, all test and qualification measurements have been done on the same 30 mil Rogers RT/Duroid 6002 substrate. A 50 Ohm tapered coplanar line is used as a transition from the connector to the GSG probe, as seen in Fig. 10. The GSG probe tips are realized on a thin 8 mil sheet of brass which is first welded to the PCB. The brass is then micromachined with a laser (indicated in Fig. 10 by the dotted lines) along the shape of the required tip. Alignment references are

LORENZ et al.: BREAKING THE EFFICIENCY BARRIER FOR AMBIENT MICROWAVE POWER HARVESTING

Fig. 11. Reflection and transmission parameter of the probe extracted through an adapter characterization procedure.

Fig. 12. Simulated PCE for different matching networks impedances. 30 load. The arrow indicates an increasing PCE. dBm input power, 2.4 GHz, 13

set from the sides of the transmission line to ensure the cutting contour fits the line and PCB gap. The dimensions of the probe tip (starting pitch as well as the pitch of the tip) are determined on one side by our PCB fabrication process, which allows a minimum 5 mil gap between the ground plane and the 42 mil center conductor, and the on-wafer diode pads which have a 100 pitch for the diodes reported here. A photograph of the micromachined probe tips can be seen in Fig. 13. To allow micro-positioning using standardized probe stations, a customized probe holder has been fabricated. The scattering matrix has been extracted and validated using an adapter characterization procedure [28], [29], [30], which uses two calibration planes. The first reference plane is set with APC 3.5 mm calibration standards (before the connector) and the second reference plane is set at the end of the tips, with an on-wafer SOL calibration (using Picoprobe CS-5 standards). and are shown in Fig. 11. B. Rectifier Prototype Measurements The substrate used for the matching network construction is 30 mil Rogers RT/Duroid 6002. This design was based on the ideal matching network impedance given in Fig. 12, and includes a matching network with an adjustable length short cir-

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Fig. 13. Photograph of the rectifier circuit using a backward diode. The matching network was built and integrated with an in-house GSG probe used to , , , interface with the diode pads (inset). , , , . Width of the line in , width of the line in (6 mil separation between line and ground).

Fig. 14. Measured efficiencies for different diode samples at optimum load, the simulated result has been added for comparison.

cuit stub, which was used to fine-tune the narrow band matching network. A picture of the circuit is shown in Fig. 13. Fig. 12 shows the PCE as a function of the matching network output impedance. The simulation was done using the backward diode model presented previously with an L-section matching network composed of a 50 series transmission line and 50 short-circuited stub which is used as the dc rectified current return path. The line and stub lengths were swept from 0.05 mm up to . The very high initial mismatch between the 50 source and the 12.5 diode introduces almost 3 dB matching network insertion loss, resulting in a reduced peak PCE of approximately 20% at 30 dBm input power, while the lossless case presented in Fig. 9 had a PCE near 37% at the same frequency and input power. An important remark that can be made based on the results from Fig. 12 is that the impedance to be matched is nearly real, with very low imaginary part. This means that the proposed backward tunnel diodes may be matched to a large bandwidth using more complex matching network structures according to the Bode-Fano criterion [31]. Due to the 3 dB matching network insertion losses resulting from the high mismatch between the source and the diode junction resistance [32], an overall rectifier efficiency at 100 nW of 3.8% has been measured. Although well below the 11.6%

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Fig. 15. Backward tunnel diode AMPH measured result compared to the state of the art microwave power harvesters and transmitters. Historical references have been added for reference. The symbol form has been maintained between rectifiers using the same diode.

TABLE II REFERENCES FROM CURVES GIVEN IN FIG. 15

Fig. 16. Expected power conversion efficiency improvement for different backward tunnel diode anode Al compositions, the diode junction area was junction resistance. calculated to mantain a 12.5

PCE expected from the measurements in Fig. 9, the device technology has proved to be promising based on this first demonstration. Fig. 14 shows the measured PCE for four different samples of the backward tunnel diode, showing the repeatability of the results across several tunnel diodes. The dc loads connected to the circuit were adjusted for each diode, in order to reach the maximum PCE. Measurements and Harmonic Balance (HB) simulation using the proposed backward tunnel diode model agree very well, indicating that the parameters extracted are in accordance with the actual diodes evaluated. The matching network was simulated using the Keysight Momentum electromagnetic fields simulator. VII. CONCLUSION This paper has reported and demonstrated for the first time the possibility of overcoming the microwave power harvesting

rectification efficiency limit of Schottky diode rectifiers, at low power levels typical of AMPH applications, through the use of backward tunnel diodes. A 25.3% increase in efficiency was observed when the backward diode rectifier model was compared to a theoretically ideal Schottky diode with the same , while a 10.5 times higher efficiency was obtained when compared to a real HSMS-285B Schottky diode, due to lower diode parasitic losses and improved intrinsic current responsivity . The rectifier's measured efficiency for three different backward diodes agreed with the simulation results and showed a good repeatability between different backward diode devices. The best measured result from Fig. 14 is compared to other state-of-the-art published results in Fig. 15 and Table II; only diode based rectifiers operating between 1.5 GHz and 3 GHz were included in this comparison. The efficiency limitation of Schottky diode based AMPH is evident from this figure, even though different diodes, matching technologies and loads are

LORENZ et al.: BREAKING THE EFFICIENCY BARRIER FOR AMBIENT MICROWAVE POWER HARVESTING

used in the reports cited here, all of the Schottky-based rectifiers show an abrupt drop in the efficiency below approximately 10 input power. The presented rectifier, based on a backward tunnel diode, on the other hand demonstrates good conversion efficiency for input powers in the 1 range due to its low parasitic junction capacitance and increased current responsivity. The input power range for this figure has been extended to higher power levels to give the reader a good understanding of the power range where the backward tunnel diode can be used to increase microwave power transmission (MPT) and AMPH efficiency. The backward diode rectifier efficiency roll off seen at higher powers likely originates from a larger voltage swing increasing the forward (thermionic) current, thereby limiting the efficiency. This could be addressed by using maximum power point tracking (MPPT) [33], rectification bridges using more diodes, or structural modifications to the diode design if input power is expected to reach higher values. The results presented in this work were obtained using backward tunnel diodes optimized for low-level power detection and imaging applications. As shown in Fig. 3, the junction composition could be further optimized to increase the diode curvature , and consequently its current responsivity , increasing the power conversion efficiency even more at lower input powers. The diode junction area, on the other hand, could be increased to optimize , which could be used to minimize matching losses, although this would also increase the junction capacitance . The authors believe this increase in would not be large enough to impact significantly performance in AMPH applications, since the frequencies of signals where higher power density appear are usually below 3 GHz [5], [10]. The expected improvements in AMPH for a varying backward tunnel diode anode Al composition are shown in Fig. 16; this efficiency improvement was calculated using the simulation results given in Fig. 3 adjusting the junction area so that a 12.5 was maintained. The intrinsic capacitance value remains negligible at 2.45 GHz even with an increasing anode Al composition. As a result, the power conversion efficiency is improving in the same exponential fashion as the curvature . This low power analysis forecasts a significant improvement of at least one order of magnitude on the efficiency for narrower tunneling window. Determining and verifying the optimum characteristics of a backward tunnel diode for AMPH remains the subject of future work. ACKNOWLEDGMENT The authors would like to thank Rogers Corporation for providing the laminates used in this project. The authors would also like to thank the support provided by the Poly-GRAMES Research Center technical support team, who are: Traian Antonescu, Steve Dubé, Maxime Thibault, and Jean-Sébastien Décarie. REFERENCES [1] D. Miorandi, S. Sicari, F. De Pellegrini, and I. Chlamtac, “Internet of things: Vision, applications and research challenges,” Ad Hoc Netw., vol. 10, pp. 1497–1516, 2012. [2] J. Gubbi, R. Buyya, S. Marusic, and M. Palaniswami, “Internet of Things (IoT): A vision, architectural elements, future directions,” Future Generation Comput. Syst., vol. 29, pp. 1645–1660, 2013.

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[3] Libelium, (2015, 15/06/2015), 50 Sensor Applications for a Smarter World [Online]. Available: http://www.libelium.com/ top_50_iot_sensor_applications_ranking/ [4] W. Wang, S. Hemour, and K. Wu, “Coupled resonance energy transfer over gigahertz frequency range using ceramic filled cavity for medical implanted sensors,” IEEE Trans. Microw. Theory Techn., vol. 62, no. 4, pp. 956–964, Apr. 2014. [5] K. Sangkil et al., “Ambient RF energy-harvesting technologies for selfsustainable standalone wireless sensor platforms,” Proc. IEEE, vol. 102, no. 11, pp. 1649–1666, Nov. 2014. [6] Z. Popovic, “Cut the cord: Low-power far-field wireless powering,” IEEE Microw. Mag., vol. 14, no. 2, pp. 55–62, Mar.-Apr. 2013. [7] D. Masotti, A. Costanzo, P. Francia, M. Filippi, and A. Romani, “A load-modulated rectifier for RF micropower harvesting with start-up strategies,” IEEE Trans. Microw. Theory Techn., vol. 62, no. 4, pp. 994–1004, Apr. 2014. [8] S. Hemour and K. Wu, “Radio-frequency rectifier for electromagnetic energy harvesting: Development path and future outlook,” Proc. IEEE, vol. 102, no. 11, pp. 1667–1691, Nov. 2014. [9] S. Hemour et al., “Towards low-power high-efficiency RF and microwave energy harvesting,” IEEE Trans. Microw. Theory Techn., vol. 62, no. 4, pp. 965–976, Apr. 2014. [10] F. Giuppi, K. Niotaki, A. Collado, and A. Georgiadis, “Challenges in energy harvesting techniques for autonomous self-powered wireless sensors,” in , 2013 Eur. Microw. Conf. (EuMC), 2013, pp. 854–857. [11] Z. Zhang, R. Rajavel, P. Deelman, and P. Fay, “Sub-micron area heterojunction backward diode millimeter-wave detectors with 0.18 noise equivalent power,” IEEE Microw. Compon. Lett., vol. 21, no. 5, pp. 267–269, May 2011. [12] J. Karlovský, “The curvature coefficient of germanium tunnel and backward diodes,” Solid-State Electron., vol. 10, pp. 1109–1111, 1967. [13] C. H. P. Lorenz et al., “Overcoming the efficiency limitation of low microwave power harvesting with backward tunnel diodes,” in 2015 IEEE MTT-S Int. Microw. Symp. Dig.,, May 2015, pp. 1–4. [14] A. M. Niknejad, Electromagnetics for High-Speed Analog and Digital Communication Circuits. Cambridge, U.K.: Cambridge Univ. Press, 2007. [15] S. M. Sze and K. K. Ng, Physics of Semiconductor Devices. Hoboken, NJ, USA: Wiley, 2006. [16] C. Burrus, “Backward diodes for low-level millimeter-wave detection,” IEEE Trans. Microw. Theory Techn., vol. 11, no. 5, pp. 357–362, Sep. 1963. [17] L. Esaki, “New phenomenon in narrow germanium p-n junctions,” Phys. Rev., vol. 109, p. 603, 1958. [18] L. Esaki, “Discovery of the tunnel diode,” IEEE Trans. Electron. Devices, vol. 23, no. 7, pp. 644–647, Jul. 1976. [19] R. Meyers, P. Fay, J. Schulman, S. Thomas, III, D. Chow, and J. Zinck et al., “Bias and temperature dependence of Sb-based heterostructure millimeter-wave detectors with improved sensitivity,” IEEE Electron. Device Lett., vol. 25, no. 1, pp. 4–6, Jan. 2004. [20] J. Schulman et al., “Quantum tunneling Sb-heterostructure millimeterwave diodes,” in IEDM Tech Dig., 2001, pp. 35.1. 1–35.1. 3. [21] H. Moyer et al., “W-band Sb-diode detector MMICs for passive millimeter wave imaging,” IEEE Microw. Compon. Lett., vol. 18, no. 10, pp. 686–688, Oct. 2008. [22] N. Su, R. Rajavel, P. Deelman, J. N. Schulman, and P. Fay, “Sb-heterostructure millimeter-wave detectors with reduced capacitance and noise equivalent power,” IEEE Electron. Device Lett., vol. 29, no. 6, pp. 536–539, June 2008. [23] J. J. Lynch et al., “Passive millimeter-wave imaging module with preamplified zero-bias detection,” IEEE Trans. Microw. Theory Techn., vol. 56, no. 7, pp. 1592–1600, Jul. 2008. [24] J. Schulman and D. Chow, “Sb-heterostructure interband backward diodes,” IEEE Electron. Device Lett., vol. 21, no. 7, pp. 353–355, Jul. 2000. [25] N. Su, Y. Tang, Z. Zhang, T. Kuech, and P. Fay, “Observation and control of electrochemical etching effects in the fabrication of InAs/ AlSb/GaSb heterostructure devices,” J. Vacuum Science & Technol. B, vol. 26, pp. 1025–1029, 2008. [26] M. Shams, I. Bin, Y. Xie, Y. Lu, and P. Fay, “An accurate interband tunneling model for InAs/GaSb heterostructure devices,” Physica Status Solidi (c), vol. 10, pp. 740–743, 2013. [27] H. C. Torrey, C. A. Whitmer, and S. A. Goudsmit, Crystal Rectifiers, 1st ed. New York, NY, USA: McGraw-Hill Book Co., 1948. [28] Keysight, (2002, 29/06/2015), [VBA Sample Program] Adapter Characterization. User Manual No. 16000-95024 [Online]. Available: http://www.keysight.com/main/editorial.jspx?cc=VN&lc=vie&ckey=85082&nid=-11143.0.00&id=85082

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[29] Agilent, (29/06/2015), Measuring Noninsertable Devices. Product Note No. 8510-13 [Online]. Available: http://cp.literature.agilent.com/litweb/pdf/5956-4373E.pdf [30] J. Randa, W. Wiatr, and R. L. Billinger, “Comparison of adapter characterization methods,” IEEE Trans. Microw. Theory Techn., vol. 47, no. 12, pp. 2613–2620, Dec. 1999. [31] R. M. Fano, “Theoretical limitations on the broadband matching of arbitrary impedances,” J. Franklin Inst., vol. 249, pp. 57–83, 1950. [32] C. H. P. Lorenz, S. Hemour, and K. Wu, “Modeling and influence of matching network insertion losses on ambient microwave power harvester,” presented at the Conf. Numerical Electromagnetic and Multiphysics Modeling and Optimization (NEMO), 2015 IEEE MTT-S Int., Ottawa, ON, Canada, 2015, unpublished. [33] A. Dolgov, R. Zane, and Z. Popovic, “Power management system for online low power RF energy harvesting optimization,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 57, no. 7, pp. 1802–1811, Jul. 2010. [34] Y.-H. Suh and K. Chang, “A high-efficiency dual-frequency rectenna for 2.45- and 5.8-GHz wireless power transmission,” IEEE Trans. Microw. Theory Techn., vol. 50, no. 7, pp. 1784–1789, Jul. 2002. [35] C. M. Ghiglino, “Ultra-Wideband (UWB) Rectenna Design for Electromagnetic Energy Harvesting,” M.S. thesis, Dept. Teoria del Senyal i Comun., Escola Técnica Superior d'Enginyeria de Telecomun, de Barcelona, Catalunya, Spain, 2010. [36] E. Falkenstein, M. Roberg, and Z. Popović, “Low-power wireless power delivery,” IEEE Trans. Microw. Theory Techn., vol. 60, no. 7, pp. 2277–2286, Jul. 2012. [37] G. Andia Vera, A. Georgiadis, A. Collado, and S. Via, “Design of a 2.45 GHz rectenna for electromagnetic (EM) energy scavenging,” in 2010 IEEE Radio and Wireless Symp. (RWS), 2010, pp. 61–64. [38] K. Lui, A. Vilches, and C. Toumazou, “Ultra-efficient microwave harvesting system for battery-less micropower microcontroller platform,” IET Microw., Antennas & Propag., vol. 5, pp. 811–817, 2011. [39] W. Haboubi et al., “An efficient dual-circularly polarized rectenna for RF energy harvesting in the 2.45 GHz Ism band,” Progress in Electromagn. Res., vol. 148, pp. 31–39, 2014. [40] V. Marian, B. Allard, C. Vollaire, and J. Verdier, “Strategy for microwave energy harvesting from ambient field or a feeding source,” IEEE Trans. Power Electron., vol. 27, no. 11, pp. 4481–4491, Nov. 2012. [41] Z. Liu, Z. Zhong, and Y.-X. Guo, “High-efficiency triple-band ambient RF energy harvesting for wireless body sensor network,” in RF and Wireless Technologies for Biomedical and Healthcare Applications (IMWS-Bio), 2014 IEEE MTT-S Int. Microw. Workshop Series, 2014, pp. 1–3. [42] B. R. Franciscatto, V. Freitas, J.-M. Duchamp, C. Defay, and T. P. Vuong, “High-efficiency rectifier circuit at 2.45 GHz for low-inputpower RF energy harvesting,” in 2013 Eur. Microw. Conf. (EuMC), 2013, pp. 507–510. [43] S. Riviere, F. Alicalapa, A. Douyere, and J.-D. Lan Sun Luk, “A compact rectenna device at low power level,” Progress in Electromagn. Res. C, vol. 16, pp. 137–146, 2010. [44] H. Takhedmit et al., “A 2.45-GHz dual-diode RF-to-dc rectifier for rectenna applications,” in 2010 Eur. Microw. Conf. (EuMC), 2010, pp. 37–40. [45] R. M. Dickinson, “Performance of a high-power, 2.388-GHz receiving array in wireless power transmission over 1.54 km,” in 1976 IEEE MTT-S Int. Microw. Symp., New York, NY, USA, 14–16, Jun. 1976, pp. 139–141. [46] M. Roberg, T. Reveyrand, I. Ramos, E. A. Falkenstein, and Z. Popovic, “High-efficiency harmonically terminated diode and transistor rectifiers,” IEEE Trans. Microw. Theory Techn., vol. 60, no. 12, pp. 4043–4052, Dec. 2012.

Simon Hemour (S'08–M'11) received the B.S. degree in electrical engineering from the University of Grenoble, Grenoble, France, in 2004 and the M.S. and Ph.D. degrees in optics, optoelectronics, and microwave engineering from the Grenoble Institute of Technology, Grenoble, France, in 2006 and 2010, respectively. In 2003, he was with the European Organization for Nuclear Research (CERN), Geneva, Switzerland, as a part of the Instrumentation Department, where he was involved with the ATLAS experiment on the Large Hadron Collided (LHC). From 2006 to 2007, he was a Research Assistant with the Pidstryhach Institute of Applied Problems of Mechanics and Mathematics (IAPMM), National Academy of Science of Ukraine (NASU), Lviv, Ukraine. In 2007, he joined the IMEP—LAHC MINATEC Laboratory, Grenoble, France. From 2011 to 2015, he was with the Poly-Grames Research Center, Ecole Polytechnique de Montréal, Montréal, QC, Canada, leading the wireless power transmission and harvesting research group Since 2015, he has been with the University of Bordeaux, France, as an Assistant Professor of Electrical Engineering. His research interest include wireless power transfer and energy harvesting, ferrite-based RF circuits, nonlinear devices, innovative RF measurements, RF interferometry, low-power microwave, and millimeter-wave conversion circuits, and RF biomedical applications. Dr. Hemour is a member of the IEEE MTT-26 “Wireless Energy Transfer and Conversion” Technical Committee.

Carlos Henrique Petzl Lorenz (S'14) received the Dipl. Ing degree in electrical engineering from the Federal Technological University of Parana, Parana, Brazil, in 2007, and is concluding his Master studies at École Polytechnique de Montréal, Montreal, QC, Canada. From 2007 to 2013, he was a Research and Development Engineer with Landis+Gyr Brazil, where he was responsible for the development of wireless communication interfaces. In 2013, he joined the Poly-Grames Research Center, École Polytechnique de Montréal. His research interests include microwave energy harvesting and power conversion and generation for low-power systems.

Patrick Fay (S'89–M'91–SM'02) received a Ph.D. degree in electrical engineering from the University of Illinois at Urbana-Champaign, Urbana, IL, USA, in 1996. He is a Professor in the Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN, USA. His research interests include the design, fabrication, and characterization of microwave and millimeter-wave electronic devices and circuits, as well as high-speed optoelectronic devices and optoelectronic integrated circuits. His research also includes the development and use of micromachining techniques for the fabrication of microwave components and packaging.

Wenjun Li received the B.S. degree in optoelectronics from Huazhong University of Science and Technology, Wuhan, China, in 2011. She is currently pursuing the Ph.D. degree in the Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN, USA. Her research interests include design, fabrication, and characterization of III-Nitride electronic devices, millimeter-wave detectors, III-V optoelectronics, and low power applications.

Yi Xi received the M.S. degree in electrical engineering from the University of Notre Dame, Notre Dame, IN, USA, in 2014. In 2011, she joined Dr. Fay's group as a graduate student and her research was in the area of Sb-based millimeter-wave detectors. She is currently a Control Engineer with Cummins Inc., Columbus, IN, USA.

Jules Gauthier, photograph and biography not available at the time of publication.

LORENZ et al.: BREAKING THE EFFICIENCY BARRIER FOR AMBIENT MICROWAVE POWER HARVESTING

Ke Wu (M'87–SM'92–F'01) received B.Sc. degree (with distinction) in radio engineering from Nanjing Institute of Technology (now Southeast University), China, in 1982 and D.E.A. and Ph.D. degrees in optics, optoelectronics, and microwave engineering (with distinction) from the Institut National Polytechnique de Grenoble (INPG), Grenoble, France, and the University of Grenoble, Grenoble, France, in 1984 and 1987, respectively. He is Professor of electrical engineering, and Tier-I Canada Research Chair in RF and millimeter-wave engineering at the Ecole Polytechnique (University of Montreal). He is the Director of the Poly-Grames Research Center. He was the founding Director of the Center for Radiofrequency Electronics Research of Quebec (Regroupement stratégique of FRQNT). He has also held guest, visiting and honorary professorship at many universities around the world. He has authored or co-authored over 1000 referred papers, and a number of books/book chapters and filed more than 30 patents. His current research interests involve substrate integrated circuits (SICs), antenna arrays, advanced CAD and modeling techniques, wireless power transmission and harvesting, and development of low-cost RF and millimeter-wave transceivers and sensors for wireless systems and biomedical applications. He is also interested in the modeling and design of microwave and terahertz photonic circuits and systems. Dr. Wu is a member of Electromagnetics Academy, Sigma Xi Honorary Society, and URSI. He has held key positions in and has served on various panels

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and international committees including the chair of technical program committees, international steering committees and international conferences/symposia. In particular, he was the general chair of the 2012 IEEE MTT-S International Microwave Symposium. He has served on the editorial/review boards of many technical journals, transactions, proceedings and letters as well as scientific encyclopedia including editors and guest editors. He is currently the chair of the joint IEEE chapters of MTTS/APS/LEOS in Montreal. He is an elected IEEE MTT-S AdCom member for 2006–2015 and served as Chair of the IEEE MTT-S Transnational Committee, Member and Geographic Activities (MGA) Committee and Technical Coordinating Committee (TCC) among many other AdCom functions. He is the 2016 IEEE MTT-S President. He is the inaugural three-year representative of North America as Member of the European Microwave Association (EuMA) General Assembly. He was the recipient of many awards and prizes including the first IEEE MTT-S Outstanding Young Engineer Award, the 2004 Fessenden Medal of the IEEE Canada and the 2009 Thomas W. Eadie Medal of the Royal Society of Canada, the Queen Elizabeth II Diamond Jubilee Medal in 2013, the 2013 FCCP Education Foundation Award of Merit, the 2014 IEEE MTT-S Microwave Application Award, the 2014 Marie-Victorin Prize (Prix du Quebec-the highest distinction of Québec in the natural sciences and engineering), the 2015 Prix d'Excellence en Recherche et Innovation of Polytechnique Montréal, and the 2015 IEEE Montreal Section Medal of Achievement. He is a Fellow of the Canadian Academy of Engineering (CAE) and a Fellow of the Royal Society of Canada (The Canadian Academy of the Sciences and Humanities). He was an IEEE MTT-S Distinguished Microwave Lecturer from Jan. 2009 to Dec. 2011.

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Cooperative Integration of Harvesting RF Sections for Passive RFID Communication Gianfranco Andia Vera, Dahmane Allane, Apostolos Georgiadis, Senior Member, IEEE, Ana Collado, Senior Member, IEEE, Yvan Duroc, and Smail Tedjini, Senior Member, IEEE

Abstract—This paper proposes a novel cooperative composite energy harvesting system that consists in the association of a traditional passive UHF Radio Frequency Identification (RFID) chip with an Electromagnetic Energy Harvesting Circuit (EEH-C). The objective is to exploit the i-v nonlinearity of the rectifier by applying a signal with time-varying envelope in order to improve the RF-to-dc conversion efficiency. Thanks to a multisource configuration, i.e., an RFID reader at 0.868 GHz and an external source at 2.45 GHz, the EEH-C is able to rectify the harmonic product of the RFID chip, in addition to the 2.45 GHz signal, without compromising the RFID communication. Additionally, digitally modulated signals are used at 2.45 GHz to further enhance the harvesting efficiency of the EEH-C. From theory, simulations and measurement it is demonstrated that the exploitation of the three nonlinear effects of rectifying circuits, i.e., (i) impedance power dependency, (ii) harmonic signals production, and (iii) waveform dependency can greatly improve the conversion efficiency of the EEH-C. Index Terms—Energy harvesting, harmonic balance, non-linearity, RFID, UHF passive tags, wireless power transmission.

I. INTRODUCTION

R

ADIO Frequency Identification (RFID) is a wireless datacollection technology very popular in different applications and services such as logistics, manufacturing, access con-

Manuscript received July 02, 2015; revised October 03, 2015; accepted October 22, 2015. This work was supported in part by the EU COST Action IC1301 “Wireless Power Transmission for Sustainable Electronics” (WIPE) and in part by EU COST Action IC1301, OSEO France, and ARC6 program of Région Rhône-Alpes (France). The work of A. Georgiadis and A. Collado was supported in part by the Spanish MEC and FEDER funds through project TEC201239143 and the Generalitat de Catalunya under grant 2014 SGR 1551. The work of D. Allane was supported in part by the grant PROFAS B+ initiative. The work of A. Georgiadis and A. Collado was supported in part by the Generalitat de Catalunya under grant 2014 SGR 1551 and by the Spanish Ministry of Economy and Competitiveness and FEDER funds through the project TEC2012-39143. This paper is an expanded version from the IEEE MTT-S International Microwave Symposium, Phoenix, AZ, USA, May 17–22, 2015. G. Andia Vera and S. Tedjini are with the Laboratoire de Conception et d'Intégration des Systèmes (LCIS), Grenoble Institute of Technology (Grenoble INP), 26902 Valence, France (e-mail: [email protected]; [email protected]). D. Allane is with the Université des Sciences et de la Technologie Houari Boumediene (USTHB), Bab Ezzouar 16111, Algeria (e-mail: [email protected]) Y. Duroc is with the Ampere Lab, Lyon University, 69622 Villeurbanne, France (e-mail: [email protected]). A. Georgiadis and A. Collado are with the Centre Tecnologic de Telecomunicacions de Catalunya (CTTC), 08860 Castelldefels, Spain (e-mail: [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2015.2495351

trol and security. Sixty years after the publication of its principle of operation [1], the RFID technology continues being part of the «« top ten »» technologies worldwide. The scope of the RFID technology is nowadays not only limited to the identification and tracking of inventory, but it is capable to collect and compile massive amounts of detailed real-time data in different types of environments around us. Therefore the evolution of RFID opens the way for a plethora of new applications in the area of Internet of Things (with 50 billion connected objects expected for 2020), Smart Skins, Man-to-Machine and Cognitive Intelligence [2]. This growing interest is primarily related to the significant benefits of passive Ultra High Frequency (UHF) RFID, in particular, its passive and wireless features that provide decisive practical advantages. For passive UHF RFID tags the reader transfers energy wirelessly to the tag by sending Radio Frequency (RF) power (at 868 MHz in Europe and in 902-926 MHz band in US) that the tag must collect and transform into dc power to operate and respond using the backscattering modulation technique [3]. Consequently the passive RFID technology naturally embeds the principle of Wireless Power Transmission (WPT) using an intentional Electromagnetic (EM) source. However the requirement of additional functions for smart tags has strongly raised the need of additional sources of energy [4]. The idea of the tag-sensor approach is to associate new sensing capabilities to the tag while it is still enjoying the identification functionality and all this in a wireless environment. Many studies have demonstrated the possibilities of this concept in different contexts, e.g., for industrial or urban areas, agricultural zones, or Body Area Networks (BAN). A wide variety of sensor capabilities have been also shown: temperature, pressure, humidity, deformation, crack width, accelerometer, chemical sensors, etc. Two types of implementations are used where either the tag integrates the sensor or the sensor function is integrated in the tag [5]. In the first case, the difficulties reside in the supply autonomously the sensor via the rectifier circuit of the tag itself (very constraint solution) or via another energy recovery circuit. Among the possible energy sources, the natural or ecologic sources such as solar, thermal, kinetic are of first interest. However and always with an ecofriendly regard, the presented work only focuses on the EM sources and proposes a new and original cooperative powering system that exploits wasted EM energies. The approach consists in the association of a traditional passive UHF RFID tag with an Electromagnetic Energy Harvesting Circuit (EEH-C) that efficiently performs RF-to-dc conversion from an RF source at 2.45 GHz combined with the harmonic product generated by the chip (so-called ).

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Contrary to some works in the literature that present a cooperative harvesting operation by adding the dc outputs of different harvesters, i.e., at dc level [6], [7], It is worth noting that the cooperation proposed in this approach is done at RF level, i.e., it is based on the co-existence and mutual cooperation of two RF systems (EEH-C and RFID chip) without compromising the communication function. The proposed study covers all the aspects from theory, simulation and experimental results in order to highlight the three nonlinear effects of rectifying circuits exploited with mutual benefits: (i) impedance power dependency [8], (ii) harmonic signals production [9], and (iii) waveform dependency [10]. The paper is organized as follows. In Section II, the stateof-art and underpinning theory about the exploitation of the nonlinear i-v characteristic of rectifier circuits used in this composite system are exposed. Section III introduces the original composite harvesting system proposed in this work and explains the design methodology of the system. Section IV presents the results of an in-depth simulation study based on the multisource operation and the rectification. In Section V, the approach is validated by means of experimental tests using conducted measurements. Finally Section VI draws the final conclusions and associated perspectives. II. REVIEW AND THEORY The proposed work builds on the possibility of enhancing the RF-to-dc conversion efficiency of rectifier circuits by applying a multi-frequency excitation signal. The nonlinear i-v characteristic of rectifier circuits can potentially lead to an enhanced RF-to-dc conversion efficiency when they are excited simultaneously by more than one signal relative to a single Continuous Wave (CW) signal of the same average power, such as the signal provided by the standard RFID reader. This effect was verified experimentally in [11], where the performance of a wideband rectifier was tested using pairs of CW tone signals with different frequencies and power levels. In [12], an improvement in the read range of passive RFID tags of up to 24% was obtained by interrogating them using multi-tone signals with up to 8 subcarriers which were named power-optimized waveforms. A composite signal of a number of tones, or alternatively a finite bandwidth signal with arbitrary modulation can be expressed mathematically in a general form as a (multi-harmonic) signal with a time-varying envelope. A time-varying envelope results in the presence of instantaneous power peaks in the signal and a certain Peak-to-Average-Power-Ratio (PAPR). An improvement in the rectifier RF-to-dc conversion efficiency using Quadrature Phase-Shift Keying (QPSK) modulated input signals was reported in [13]. Interest in the potential efficiency improvement by tailoring the transmitted signal envelope properties has spurred a number of subsequent publications studying the effect of efficiency and the PAPR of multi-sine signals [14]–[16], or modulated signals [10], [17] and even white noise and chaotic waveforms [10], [18]. In [19] an efficiency improvement compared to CW signal was demonstrated using a composite 2-tone signal which included two approximately harmonically related tones at 0.810 GHz and 1.580 GHz. In the work presented here, a composite energy harvesting system is considered which includes two rectifier circuits, one operating

at the fundamental UHF RFID frequency of 0.868 GHz and a second one operating near its harmonic. The reason behind the choice of the second operating frequency band is two-fold, first in order to potentially recover energy from generated harmonic products from the first rectifier circuit, i.e., the RFID chip, and second to harvest energy from digitally modulated signals corresponding to existing ambient transmissions at the 2.4 GHz Industrial Scientific and Medical (ISM) band such as nearby Wi-Fi routers. It should be emphasized that the efficiency improvement is dependent on the average power of the input signal [10], [11], [15], since the increased instantaneous peak power may drive the nonlinear rectifying element (e.g., Schottky diode) in its breakdown region which results in increased dissipation losses, or lead to impedance mismatch at the input of the rectifier which results in reflection losses and subsequently a reduction in the obtained efficiency. In summary, the actual improvement in efficiency is a function of the signal properties such as its average power and envelope characteristics like its PAPR, the nonlinear rectifying device i-v characteristic, as well as the input matching network of the rectifier and rectifier load. III. COMPOSITE ENERGY HARVESTING SYSTEM With the intention to profit from the nonlinear i-v characteristic of rectifier circuits in presence of time-varying envelope signals, a composite signal generated by a composite energy harvesting system (multisource) and will be build. This section describes the composite system. The approach of using a finite bandwidth signal with arbitrary modulation will be later exploited (see Section V) using the same composite energy harvesting system. A. Frequency Considerations and Power Management In this work, the RFID communication is set to operate with a fixed carrier at 0.868 GHz as per the regulation in Europe, in where the frequency hopping mode is not implemented [20]. A wider bandwidth centered at 2.45 GHz ISM band is also considered. Indeed frequencies from 802.11 b/g/n Wi-Fi standards with communications channels located between 2.44 GHz and 2.46 GHz are exploited [21]. It is worth noting that the scope of this work does not consider the harvesting power management but only proposes an innovative cooperative harvesting method. However, some complements on the power management trends in harvesting applications are discussed in the following paragraph. One point to be considered is that most of the ambient RF power densities to be harvested are very low and the produced energy usually is not enough for most continuous electronic functions. However if this energy is efficiently stored over time, realistic functions can be performed in discrete time intervals. Some groups are currently dedicating efforts to study and develop efficient techniques of harvested power-management [22], [23]. The techniques are based in the co-design of harvester and power-management blocks in order to transfer the energy with minimal loss to the energy storage element and to monitor the energy storage and provide charge control and protection for the energy storage used. The deployment of autonomous nodes including operation functions (e.g.,

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Fig. 1. Schematic of the model used to evaluate the benefits of the nonlinear operation of rectifier devices operating at different frequencies and cohabiting in a single system, i.e., the augmented tag. The RFID reader generates ASK signals and the WPT-S generates CW and signals with different modulations. In a real scenario, the channel losses represent the link budget of an RF communication considering antennas and propagation losses. The model used considers the , , ; TPMN , , , following component values: RFID chip model , ; EEH section , , , SMS7630, .

identification, moisture or temperature sensing, etc. [24], [25]) is possible thanks to the managing and monitoring of the harvested power. The harvesting approach proposed in this paper may be a candidate to integrate such a managing system. B. System Considerations The proposed system, so-called augmented tag integrates two sections: (i) the RFID section composed by a passive RFID chip and an RFID reader both operating at 0.868 GHz, and (ii), the Electromagnetic Energy Harvesting (EEH) section composed by an EEH-C and a Wireless Power Transmitter Source (WPT-S) both operating at 2.45 GHz. The schematic of the augmented tag is presented in Fig. 1 and explained below. • The RFID chip is modeled by a 4 diode-based voltage doubler stages constituting a rectifier circuit with a configuration similar to one used in the Dickson charge pump [26]. • A dual-frequency Three-Port Matching Network (TPMN) is included to interconnect both the different sections in a common system. The TPMN matches the capacitive impedance of the chip in port 2 to the input corresponding to an antenna (at 868 MHz) and to the of the coupler that goes through the EEH-C (at 2.604 GHz). In the dual-frequency multiport operation context, a design trade-off is done in order to achieve the dual band operation of port 2. • A directional coupler with 10 dB Coupling Factor (CF) is used to combine the with the WPT-S signal at the input of the EEH-C. It is worth noting that hereinafter all WPT-S power configurations refer to the power injected by the source before the coupler. • The EEH-C is composed by a single stage of a voltage doubler and a matching network centered in 2.45 GHz. A first value of is as the load that allows achieving the higher RF-to-dc conversion. The value is driven by the load input value of the dc input of a RFID EM432 chip

where the dc energy could be consumed in an application example [27]. The EEH-C design is similar to the one proposed in [13]. • The RFID reader and the WPT-S are modeled by two RF sources. Simulations consider for both, the RFID reader and the WPT-S, CW signals. Contrary the experimental part considers ASK RFID signals for the reader and different modulations for the WPT-S. • The propagation losses in a real scenario, in where transmitting and receiving antennas are used are considered by the parameter channel losses in Fig. 1. C. System Design Methodology Advanced Design Software (ADS) simulation tools from Keysight are used for the design of each section and its integration to constitute a single system. Three main steps define the design methodology: • The step is the modeling of the RFID chip. Using the Large-Signal S-Parameters (LSSP) and Harmonic Balance (HB) tools, the RFID chip model is optimized at 0.868 GHz and for input power, considered to be its activation threshold (EM 43235 RFID chip is used). Three main directives leaded the model design: (i) nonlinearity, i.e., harmonic generation and impedance-power dependency should be reproduced; (ii) the model should present a capacitive input impedance comparable to the ones reported in commercial RFID chips [9]; (iii) under power regulations, the model should produce at least 1V of dc required to activate the logic part of the chip [24]. A first value for that allows complying with the directives is here selected. The dc management and voltage regulator for high dc levels are out of the scope of this work. Fig. 2 depicts the input impedance of the RFID chip model at its activation threshold; at 0.868 GHz the model presents as impedance.

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Fig. 2. Input impedance of the RF model for a passive RFID chip. At 0.868 . GHz the model has an impedance of

• The step is the TPMN design using the S-parameters tool and considering in first approach the other devices as linear in order to define its topology. The dual-frequency functionality of the TPMN with addition to three impedance matching functions represents the major difficulty for its design. Being the redirection of towards the EEH-C the key of the proposed approach, the TPMN design is foremost driven by this priority. • The step is the system integration performing the TPMN optimization. This step uses LSSP and HB tools and considers the nonlinearity of the RFID chip and EEH-C. The optimization goal is to satisfy the 1 V requirement at the RFID chip dc output and to maximize the level at the EEH-C input. Two limit configurations of the power injected into node 1 of Fig. 1 are defined: represents the power that allows activating the augmented tag, and represents the power when the reader transmits the maximum allowed by regulations [28]. Fig. 3 shows the dc output of the RFID in function of the power delivered by the WPT-S and for the two reader power configurations injected into node 1. The 1 V dc voltage need is satisfied and its output does not depends on the WPT-S power, then validating the correct operation of the TPMN. From the presented methodology, the last optimization step leads to the optimal component values of the system detailed in Fig. 1. Table I presents the reflection coefficient and quality factor of the optimized TPMN. The dual band matching trade-off at port 2 presents a slightly diminished reflection coefficient at 868 MHz, i.e., , prioritizing the one at 2.604 GHz, i.e., . The diminished matching at 0.868 GHz is enough to activate the chip satisfying the three modeling directives above exposed. From the presented model, the proposed full system in terms of the nonlinear exploitation is in-depth studied in the next section. IV. SIMULATION STUDY The aim of this section is to highlight and quantify the nonlinear contribution of the cooperative system above modeled. The power matching, multisource operation, rectification and its effects on the RF-to-dc conversion efficiency of the EEH-C are notably studied.

Fig. 3. DC voltage produced by the rectifier part of the RFID chip versus WPT-S power. The values are modeled at two limit powers injected into node 1. In both cases, the requirement of 1 V to feed the logic part of the chip is satisfied.

TABLE I PERFORMANCE OF THE TPMN

A. Contribution of the RFID Chip Nonlinearity In order to quantify the nonlinearity introduced by the RFID level, a linear model of the RFID chip is chip, i.e., the used as a comparative reference. The linear model, which does not produce any harmonic nor changes its impedance respect to the power, consists of the impedance file of the nonlinear RFID chip model calculated at its activation threshold. Let assume an RFID reader that communicates with the augmented tag (considering 0 dB tag antenna gain) for 1 m distance between each other (i.e., 31.21 dB of propagation losses at 0.868 GHz). If the augmented tag sensitivity is , the power injected into node 1 of Fig. 1, so-called , should be equal to . The maximum power injected into the same node, considering the propagation losses in agreement with the regulations [28] and so-called , would be approximately 5 dBm. Additionally, three WPT-S power configuration cases are defined: • (case 1) which corresponds to the injected power into the augmented tag by a Wi-Fi router transmitting at its maximum allowed Equivalent Isotropic Radiated Power (EIRP), i.e., 36 dBm at 1 m distance [21]; • (case 2) which corresponds to the injected power into the augmented tag by the same Wi-Fi router distanced 3 meters; • WPT-S is off (case 3). Hereinafter the values of , and the three WPT-S power configurations are kept constant for all the simulation tests. In order to quantify in function of the reader power, the Power Spectral Density (PSD) calculated at the EEH-C input

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Fig. 4. Power spectrum with linear RFID chip model. The PSD is taken at the input of the EEH section in Fig. 1. There is not generation of harmonics due to the chip but a weak harmonic coming from the reader.

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Fig. 6. versus the power received in node 1 from the reader. Continuous lines harmonic and dash lines reprepresent with the chip model generating a . resent with a linear chip model. (a) and (b) Case 1, WPT-S equal to . (e) and (f) Case 3, WPT-S off. (c) and (d) Case 2, WPT-S equal to

the power at 2.45 GHz coming from the WPT-S , and the power at 2.604 GHz due to the contribution . The intermodulation products observed in the PSD are very weak and therefore noncontributory to . With these considerations, of the EEH-C is defined in (1) (1)

Fig. 5. Power spectrum with nonlinear RFID chip model. The PSD is taken at harmonic signal. the input of the EEH section in Fig. 1. The chip generates a The reader power slightly affects the signal level at 2.45 GHz.

is analyzed at . Figs. 4 and 5 show the PSD for a linear chip model and for the chip producing harmonics, respectively. Thanks to the HB tool, the analysis of the linear chip allows determining the weak presence of the harmonic of the RFID reader signal produced by the EEH-C (indeed, the linear chip does not produce harmonics but the EEH-C is always nonlinear). The weak leakage of is only distinguishable for . The analysis of the nonlinear chip model shows a greatly distinguishable level: reaches with and more than with . The rectification of this is the aim of the intended multisource operation. Finally, small variations on the 2.45 GHz signal strength due to the reader power injected into node 1 can be also observed. This phenomenon is studied in detail in subsequent paragraphs. B. System Performance The key parameter to evaluate the EEH-C performance is the RF-to-dc conversion efficiency defined as the ratio of the dc output power by the RF input power into the EEH-C . Given the multisource operation and the exploitation approach, a fair evaluation of the EEH-C needs an accurate definition of . From the PSD analysis shown in Fig. 5, the RF signals that significantly contribute to are: the power at 0.868 GHz leaked from the reader ,

1) Effects of the Reader Power in the System: In order to quantify the effect of the reader power and the contribution of in the EEH-C performance, Fig. 6 shows versus the reader power injected into node 1 and for the different WPT-S configurations. Continuous lines represent with the chip model generating a harmonic and dash lines represent with a linear chip model. The benefit, introduced only by the multisource operation, can be studied with the linear chip model when is not present. Looking at Fig. 6 in curves (b) and (d) in where the multisource is set and a linear chip model is considered (i.e., does not exist), the EEH-C conversion efficiency is higher respect to curve (f) in where only the reader is active. The benefit introduced only by the rectification can be studied comparing the linear and nonlinear chip models when the WPT-S is off. Looking at Fig. 6 in curve (e) in where only the reader transmits and a nonlinear chip model is considered (i.e., exists), the EEH-C conversion efficiency is higher respect to curve (f), in where the chip has a linear model. Indeed the can be increased, so also , by increasing the reader power. However at higher levels, due to the saturation behavior of the diode at large signals, is limited and all curves converge. 2) Effects of the WPT-S Power in the System: Besides the contribution of , the effect of the WPT-S power in the EHH-C conversion performance is studied. Fig. 7 shows versus the WPT-S power for three power cases: , and reader off, and for the two chip models (i.e., linear and nonlinear). At low WPT-S power, the multisource operation cases (red and blue curves) allows achieving an enhancement of compared to the single WPT-S case (black curve), especially as high reader power. At high WPT-S power, the greater contributor to is the WPT-S, due to the optimized design of the EHH-C

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Fig. 7. versus WPT-S power. Continuous lines represent with the chip harmonic and dash lines represent with a linear chip model generating a model.

at 2.45 GHz. Combining both sources, in the best of the cases (blue curve with in respect to black curve), an RF-to-dc conversion efficiency 55% greater than the case using only the WPT-S is achieved. As a result, the approach of improving by means of a multisource operation and rectification is demonstrated by simulations. V. EXPERIMENTAL EVALUATION The aim of this section is to experimentally verify and quantify the nonlinear contribution of the proposed cooperative system considering a commercial RFID passive chip and also more complex WPT-S signals. As discussed in Section II, alternatively a finite bandwidth signal with arbitrary modulation can be expressed mathematically in a general form as a (multi-harmonic) signal with a time-varying envelope. Based on the described concept an emulated prototype is designed, and two kinds of experiments are performed in order to evaluate the RF-to-dc conversion efficiency of the EEH section in function of: (i) the composite signal (Section V-A); (ii) the WPT-S waveform, i.e., a finite bandwidth signal with arbitrary modulation, (Section V-B). The complete setup is shown in Fig. 8. Specific details are below described. • The RFID section is composed by two parts: (i) the antenna emulator composed by two impedance tuners Microlab SF-30F connected in series to offer a power matching between reader, chip and EHH section; (ii) the RFID chip EM4325 shown in Fig. 8(a) is fixed in a SMA connector [9]; when the matching is achieved, the chip response is detected by the reader. • The TPMN shown in Fig. 8(b) is emulated by the combination of the impedance tuners with a first directional coupler with Coupling Factor . A trade-off power matching is done by activating the chip while maximizing the level at the input of the EEH section. • A second directional coupler is used to couple the with the WPT-S signal and feed the EEH section. • The EEH section shown in Fig. 8(c) is the same to the one designed in the simulation study. It is composed by a matching network in series with a single stage of a voltage

Fig. 8. Measurement setup and emulated prototype. Schematic diagram at the top and implemented setup at the bottom. (a) RFID chip. (b) Three port matching network. (c) EEH section.

doubler consisting of two Skyworks SMS7630 Schottkty diodes as in [13]. The dc section at the output consists of a low-pass filter capacitor and a resistor in where the dc level is measured. • The Speedway Revolution RFID reader and an external source at 2.45 GHz (Agilent N5182A Vector Signal Generator (VSG)) represents the reader and the WPT-S respectively as above described. • For power tests, a digital Oscilloscope (Agilent 91204 DSO) is connected instead of the EEH section in order to measure the PSD of the input. Once all sections are integrated, a power matching trade-off is done with the impedance tuners. The principle is to activate the RFID chip (looking for the minimum chip activation threshold in the RFID reader) while maximizing the level at the input of the EEH section. The visualization of the PSD in the DSO allows performing this analysis. Four main differences valorize this experimental evaluation from the reported one in [29]: (i) the reader, that activates the RFID chip, is always present, and it varies its power; (ii) the losses in the system are reduced due to the use of two directional couplers instead of three; (iii) the dc output of the EHH-C is not connected to the dc input of the chip because of the intention to quantify its value; (iv) a new definition of presented in Section IV-B, allows evaluating the EEH-C more accurately.

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Fig. 9. Harvested dc output in function of the input power at 2.45 GHz. The experiment is performed for the two reader power configurations. Greater values . are obtained when the reader transmits its maximum allowed, i.e.,

Following the power limits defined in Section IV-A, and considering the described setup, the conducted power of the Speedway Revolution reader that activates the augmented tag is 17.5 dBm, and the maximum one is 31.5 dBm. After calibration, these values represent and (subtracting 26.5 dB of losses in the coupled path of Fig. 8 due to the CF and connectivity). Hereinafter the values of and are kept constant for all experimental tests. These power settings allow calculating the scaled read range of the augmented tag. Always considering a tag antenna of 0 dB gain and sensitivity, a read range of 4.8 m is estimated in over-the-air configuration complying with the regulations [28], [30]. It is worth noting that the chip sensitivity of the chosen sample, i.e., , is not affected by the system integration, therefore the standard reading range for tags using this kind of chip is respected. A. Multisource Power Dependency This first analysis evaluates under a multisource operation scenario, i.e., in terms of the power simultaneously emitted by the RFID reader and the WPT-S. Fig. 9 depicts the measured dc output versus the WPT-S power for the two reader power configurations and without reader. Results for and reader off are quite close each other due to the losses introduced by the emulated TPMN; however the improvement of combining sources is still notable. Moreover, higher dc values are obtained for . In order to accurately calculate as in (1), an experimental PSD analysis at the input of the EEH section is necessary. The analysis is possible thanks to the use of the DSO. Fig. 10, comparable with Fig. 5, shows the normalized measured PSD of a multisource configuration (reader and WPT-S) firstly reported in [29]. When both sources are active, the PSD shows measurable values of (RFID communication signal), (signal to be harvested), and ( to be harvested). Performing the analysis with the setup above described, the experimental calculation of is possible. Fig. 11 shows versus the WPT-S power for both reader configurations and without reader, and compares the results to

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Fig. 10. Normalized power spectral density visualized on the DSO when the sections are interconnected in the setup reported in [19]. When both sources are active, a richest spectrum favors the conversion efficiency of the harvester circuit.

Fig. 11. RF-to-dc conversion efficiency of the EEH-C in function of the input power at 2.45 GHz. In dashed line the simulated values.

the ones obtained by simulation at the lowest power. An improvement of 8% in can be noted for at low WPT-S power (blue curve from to ) compared to the single WPT-S operation (black curve). As a result, the behavior predicted by simulations in Section IV-B is verified by measurement, i.e., the combined with the WPT-S signal triggers in an enhanced . Even if the magnitudes are less than the simulated ones (comparing simulated and measured cases); the experimental results validate the approach. Magnitude differences from the simulation results have two expected reasons: (i) losses in the emulated prototype (especially the use of a coupler in the TPMN and chip fixture); and (ii), differences in the commercial performance compared to the simulated model. B. WPT-S Waveforms Dependency The previous tests have considered the WPT-S transmitting a CW tone. In this part, a time-varying envelope signal generated at the input of the EHH section by the composite signal composed by the tone triggered by the multisource operation of the system and the harmonic RFID product. Hereinafter, and

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Fig. 12. Normalized power spectral density visualized on the DSO at the EEH input when the sections are interconnected. The average power is the same for all signals. 14 MHz are taking into account for the waveform analysis. Fig. 13. Measured CCDF of the envelope of the test signals.

in addition to the composite tone signal approach, the WPT-S signal waveform is configured with the intention to study its effect on EEH section conversion efficiency. It is worth noting that during all tests the RFID reader and chip are communicating. 1) Studied Waveforms and Their Characteristics: At the input of the EHH section, four kinds of composite waveforms are studied by combining a modulated signal from the WPT-S with the leaked signal at 0.868 GHz and the redirected . It is worth noting that the 0.868 GHz and signals are from the RFID communication using ASK modulation [28]. In the WPT-S, three modulations commonly used in wireless systems are set, in addition to the CW tone: Orthogonal Frequency-Division Multiplexing (OFDM), Gaussian Minimum-Shift Keying (GMSK), and Amplitude-Shift Keying (ASK). Fig. 12 shows the normalized PSD of the three modulated and the CW tone above considered. All signals are set with the same average power and centered at 2.45 GHz. Using a Tektronix RSA5000 Spectrum Analyzer in the position of the DSO in Fig. 8, the Complementary Cumulative Distribution Function (CCDF) of the envelope of the composite waveforms (WPT-S signal plus leaked 0.868 GHz signal and the redirected ) in function of the distance to its average power in dB is measured and results are shown in Fig. 13. This plot gives information about the instantaneous power of the composite time signal. Actually, the value in where the CCDF curve intersects the x-axis indicates the maximum PAPR of the signal envelope; and therefore, the maximum PAPR of the signal can be estimated adding 3 dB to the PAPR of the signal envelope [10]. According to Fig. 13, composite signals using OFDM in the WPT-S have the highest PAPR, followed by the ones using ASK and finally, very close to each other, are the one using GMSK and the CW tone, with PAPR values very close to zero due to the almost null variation of the envelope. 2) Effect of the Waveform in the Conversion Efficiency: In order to evaluate when different waveforms are used to operate the EEH section, the signal power is evaluated as the total average power in 14 MHz bandwidth around the carrier (see in Fig. 12). An accurate evaluation of should also consider the effect of the reader (the signal level entering to the EEH section

Fig. 14. Figure of gain in the conversion efficiency defined as in (2).

at 2.45 GHz is slightly affected by the reader power as seen in Fig. 5), in this context a figure of gain is defined in (2) Efficiency gain

(2)

and are the conversion efficiency of the where EEH-C calculated for and , respectively. Measured values of the conversion efficiency and the power harvested in the EEH-C load are unfolded in Table II for the limit power configuration cases, and Fig. 14 depicts the figure of gain for each kind of waveforms. At low WPT-S (“a” columns in Table II), higher gain is obtained combining an optimum waveform with a high reader signal power, i.e., . At high WPT-S power, i.e., above in Fig. 14. (“b” column in Table II), a negative figure of gain is obtained. This means that in a relative comparison, a higher is obtained when the WPT-S signals are combined with low power from the reader, i.e., as depicted in Table II. The same effect is explained in Section IV-B2 (see Fig. 7) for the case of CW tone. Reported results show that the waveform can enhance the RF-to-dc conversion efficiency of the EEH-C. Considering the CCDF analysis, OFDM and ASK signals produce higher

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TABLE II CONVERSION EFFICIENCY AND HARVESTED POWER IN THE EEH-C LOAD FOR DIFFERENT WAVEFORMS

conversion efficiency because of their higher PAPR compared to GSM and CW signals [10]. The findings of using waveforms with high PAPR in order to increase the conversion efficiency agree with results postulated in the literature [10],[12], [14]–[19]. VI. CONCLUSION AND DISCUSSION Nowadays RFID is a well-established technology for identification purposes. Moreover, due to its huge practical advantages such as passive and wireless features, it is more and more considered in order to enable many other applications under the paradigm of Internet of Things. This mainly consists to integrate more of functionalities to the RFID tags such as sensing and localization capabilities. Such an evolution of RFID tag structures requires new additional source of energy and also its optimized management. This paper proposes and demonstrates the cooperative exploitation of two effects in order to improve the power budget available for augmented passive RFID tags. The first effect is related to the non-linearity of RFID chip that generates wasted power at the harmonic of fundamental frequency, i.e., 868 MHz in Europe. The second effect lies in the enhancing of the RF-dc conversion efficiency of rectifier circuits by applying multi-frequency excitation signal. Combining the exploitation of these two effects, a unique design is simulated and experimentally emulated. The developed prototype consists of an emulated RFID tag operating at 868 MHz and an Electromagnetic Energy Harvesting circuit operating at the 2.45 GHz ISM band corresponding to existing ambient transmissions, both integrated to operate with a mutual enhanced performance. Moreover, since the composite energy harvesting system exploits the nonlinear i-v characteristic of rectifier circuits using time-varying envelope signals, experiments using different waveforms, i.e., different digitally modulated signals in the 2.45 GHz source are performed. It is worth noting that the emulated prototype has not as objective to reproduce the simulated performances but to validate the exposed concepts using a commercial RFID chip. Three significant results are highlighted: 1) Simulation results based on a simplified chip model show enhancement in the RF-to-dc conversion efficiency when the cooperative operation, considering the RFID chip

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non-linearity is established. The conversion efficiency rises from 1% when the 2.45 GHz source transmits at and the RFID reader is off to 56% when the power injected into the augmented tag at 2.45 GHz (external source) is and the power injected at 0.868 GHz (RFID reader) is 5 dBm. 2) Experimental results also demonstrate an improvement in the RF-to-dc conversion efficiency when the cooperative operation, considering a commercial RFID chip and an emulated prototype, is established. An 8% enhancement in the conversion efficiency is achieved when the power injected into the tag at 2.45 GHz (using a CW tone) is and the power injected at 0.868 GHz is 5 dBm. 3) Experimental results show an RF-to-dc conversion efficiency enhancement using composite signals with high PAPR. The conversion efficiency rises from 14.41% when the composite system uses a CW signal at 2.45 GHz to 23.16% when it uses an OFDM signal. In this case the power injected into the tag at 2.45 GHz is and the power injected at 0.868 GHz is equal to the tag sensitivity i.e., and represents 4.8 m of estimated tag read range. Finally in terms of perspectives, further efforts can be devoted to the use of the cooperative integration milestones exposed in this paper in order to design a single and miniaturized device. Regarding the tag size, a final prototype of the augmented tag may be comparable with current passive RFID tags, e.g., a credit card size using a double face structure integrating an antenna and reducing costs seems feasible [24]. Otherwise, the additional power produced by the cooperative RF harvesting could be profited by low-consumption electronics, e.g., humidity, temperature [24], [25], or air pollution sensors like the CleanSpace-Tag from Drayson-Technologies. Such an enhancement can be also potentially empowered in indoor scenarios where Wi-Fi sources can be seen as hot spots of the application. Furthermore, the read range enhancement can be an option when considerable power is harvested from the additional source (e.g., 2.45 GHz) compensating the propagation losses at 868 MHz. REFERENCES [1] H. Stockman, “Communication by means of reflected power,” Proc. IRE, pp. 1196–1204, Oct. 1948. [2] A. Rida, L. Yang, and M. Tentzeris, RFID-Enabled Sensor Design and Applications. Norwood, MA, USA: Artech House, 2010. [3] D. Paret, RFID at Ultra and Super High Frequencies: Theory and Application. New York, NY, USA: Wiley, 2010. [4] L. Yan, Y. Zhang, L. Yang, and H. Ning, The Internet of Things: From RFID to the Next-Generation Pervasive Networked Systems, ser. Wireless Networks and Mobile Communications. Boca Raton, FL, USA: CRC Press, 2008. [5] C. Occhiuzzi and G. Marrocco, “Constrained-design of passive UHF RFID sensor antennas,” IEEE Trans. Antennas Propag., vol. 61, no. 6, pp. 2972–2980, Jun. 2013. [6] K. Niotaki, F. Giuppi, A. Georgiadis, and A. Collado, “Solar/EM energy harvester for autonomous operation of a monitoring sensor platform,” Wireless Power Transfer, vol. 1, no. 01, pp. 44–50, 2014. [7] C. H. P. Lorenz, S. Hemour, W. Liu, A. Badel, F. Formosa, and K. Wu, “Hybrid power harvesting for increased power conversion efficiency,” IEEE Microw. Compon. Lett., vol. 25, no. 10, pp. 687–689, Oct., 2015. [8] A. Georgiadis, G. Andia Vera, and A. Collado, “Rectenna design and optimization using reciprocity theory and harmonic balance analysis for electromagnetic (EM) energy harvesting,” IEEE Antennas Wireless Propag. Lett., vol. 9, pp. 444–446, 2010.

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[9] G. Andia Vera, Y. Duroc, and S. Tedjini, “RFID test platform: Nonlinear characterization,” IEEE Trans. Instrum. Meas., vol. 63, no. 9, pp. 2299–2305, Sep. 2014. [10] A. Collado and A. Georgiadis, “Optimal waveforms for efficient wireless power transmission,” IEEE Microw. Compon. Lett., vol. 24, no. 5, pp. 354–356, May 2014. [11] J. A. Hagerty, F. B. Helmbrecht, W. H. McCalpin, R. Zane, and Z. B. Popovic, “Recycling ambient microwave energy with broad-band rectenna arrays,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 3, pp. 1014–1024, Mar. 2004. [12] M. S. Trotter, J. D. Griffin, and G. D. Durgin, “Power-optimized waveforms for improving the range and reliability of RFID systems,” in Proc. IEEE Int. Conf. RFID, Apr. 27-28, 2009, pp. 80–87. [13] G. Andia Vera, A. Georgiadis, A. Collado, and S. Via, “Design of a 2.45 GHz rectenna for electromagnetic (EM) energy scavenging,” in Proc. IEEE Radio Wireless Symp., Jan. 10–14, 2010, pp. 61–64. [14] A. S. Boaventura and N. B. Carvalho, “Maximizing DC power in energy harvesting circuits using multi-sine excitation,” in Proc. IEEE Int. Microw. Symp., Jun. 5–10, 2011. [15] A. Boaventura, A. C. Collado, N. B. Carvalho, and A. Georgiadis, “Optimum behavior: Wireless power transmission system design through behavioral models and efficient synthesis techniques,” IEEE Microwave, vol. 14, no. 2, pp. 26–35, Mar.-Apr. 2013. [16] C. R. Valenta and G. D. Durgin, “Rectenna performance under poweroptimized waveform excitation,” in Proc. IEEE Int. Conf. RFID, Apr. 30, 2013, pp. 237–244. [17] G. Fukuda, S. Yoshida, Y. Kai, N. Hasegawa, and S. Kawasaki, “Evaluation on use of modulated signal for microwave power transmission,” in Proc. 44th Eur. Microw. Conf., Oct. 6–9, 2014, pp. 425–428. [18] A. Collado and A. Georgiadis, “Improving wireless power transmission efficiency using chaotic waveforms,” in Proc. IEEE Int. Microw. Symp., Jun. 17–22, 2012, pp. 1–3. [19] D. Belo and N. B. Carvalho, “Behavior of multi-band RF-DC converters in presence of modulated signals for space based wireless sensors,” in Proc. Asia-Pacific Microw. Conf., Nov. 4–7, 2014, pp. 170–172. [20] Electromagnetic Compatibility and Radio Spectrum Matters (erm); Radio Frequency Identification Equipment Operating in the Band 865 MHz to 868 MHz With Power Levels up to 2 W; Part 1: Technical Requirements and Methods of Measurement EN 302 208-1 V1.2.1 2008, ETSI. [21] IEEE Std 802.11 Standard for Information Technology—Telecommunications and Information Exchange Between Systems Local and Metropolitan Area Networks—Specific Requirements Part 11: Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications, IEEE Standards Association [Online]. Available: http://standards.ieee.org/getieee802/download/802.11-2012.pdf [22] Z. Popovic, S. Korhummel, S. Dunbar, R. Scheeler, A. Dolgov, R. Zane, E. Falkenstein, and J. Hagerty, “Scalable RF energy harvesting,” IEEE Trans. Microw. Theory Tech., vol. 62, no. 4, pp. 1046–1056, Apr. 2014. [23] A. Dolgov, R. Zane, and Z. Popovic, “Power management system for online low power RF energy harvesting optimization,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 57, no. 7, pp. 1802–1811, Jul. 2010. [24] V. Palazzi, F. Alimenti, C. Mariotti, M. Virili, G. Orecchini, L. Roselli, and P. Mezzanotte, “Demonstration of a high dynamic range chipless RFID sensor in paper substrate based on the harmonic radar concept,” in Proc. IEEE Int. Microw. Symp., May 17-22, 2015, pp. 1–4. [25] M. Buettner, R. Prasad, A. Sample, D. Yeager, B. Greenstein, J. Smith, and D. Wetherall, “RFID sensor networks with the Intel WISP,” in Proc. 6th ACM Conf. Embedded Network Sensor Syst., Nov. 2008, pp. 393–394. [26] G. De Vita and G. Iannaccone, “Design criteria for the RF section of UHF and microwave passive RFID transponders,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 9, pp. 2978–2990, Sep. 2005. [27] G. Andia Vera, S. Nawale, Y. Duroc, and S. Tedjini, “Optimum integration of passive UHF RFID tag-rectenna in a single feed dual band antenna,” in Proc. General Assembly Scientific Symp., Aug. 2014, pp. 1–4. [28] UHF Gen2 Air Interface Protocol, EPC Standard 2.0.1, 2015. [29] G. Andia Vera, Y. Duroc, and S. Tedjini, “Cooperative integration of harvesting sections for passive RFID communication,” in Proc. IEEE Int. Microwave Symp., May 17-22, 2015, pp. 1–3. [30] K. V. S. Rao, P. Nikitin, and S. Lam, “Antenna design for UHF RFID tags: A review and a practical application,” IEEE IEEE Trans. Antennas Propag., vol. 53, no. 12, pp. 3870–3876, Dec. 2005.

Gianfranco Andia Vera (M’13) was born in Puno, Peru, in 1986. He received the dual M.Sc. degree in telecommunications engineering from the Universitat Politecnica de Catalunya (UPC), Barcelona, Spain, and the Pontificia Universidad Catolica del Peru (PUCP), Lima, Peru, in 2009, the Postgraduate degree in development and management of networks on information technology from UPC, in 2010, and the Ph.D. degree in optics and radiofrequency from the Grenoble Institute of Technology (Grenoble INP), Valence, France, in 2014. He was a Communication Engineer involved in RF planning and network deployment for a telecom carrier from 2009 to 2011. Since 2011, he has been with the Laboratoire de Conception et d'Integration des Systemes. His current research interests include RFID, antennas, energy harvesting, wireless networks, and microwave devices. He serves as expert-reviewer for international scientific committees including IEEE (MTT, MWCL, Sensors), IET (AP), Cambridge (WPT, IJMWT).

Dahmane Allane was born in Ain Taya, Algeria, in 1990. He received the Master’s degree in telecommunication systems from Université des Sciences et de la Technologie Houari Boumediene (USTHB), Algeria, in 2012. Currently, he is working toward the Ph.D degree at Electronic Departement of Instrumentation (LINS/FEI), with the team Systèmes Radio Fréquences et Microondes (SRFM). Since Febrary 2015 he is a Visiting Doctoral Researcher at the Laboratoire de Conception et d'Integration des Systèmes (LCIS) of University GrenobleAlpes, Valence, France. His research interests are in power harvesting systems for UHF RFID Tags, and RFID Sensor Tags.

Apostolos Georgiadis was born in Thessaloniki, Greece. He received the Ph.D. degree in electrical engineering from the University of Massachusetts, Amherst, MA, in 2002. In 2007, he joined Centre Tecnologic de Telecomunicacions de Catalunya (CTTC), Barcelona, Spain, as a Senior Researcher, where he is involved in energy harvesting, wireless power transfer and radiofrequency identification (RFID) technology and active antennas and antenna arrays. Since April 2013 he is Group Leader of the Microwave Systems and Nanotechnology Department at CTTC. He was the Chair of EU COST Action IC0803, RF/Microwave communication subsystems for emerging wireless technologies (RFCSET) and presently he is vice-Chair of EU COST Action IC1301 on Wireless Power Transfer for Sustainable Electronics. Dr. Georgiadis serves as an Associate Editor of the IEEE MICROWAVE WIRELESS COMPONENTS LETTERS, IEEE RFID Virtual Journal and IET Microwaves Antennas and Propagation journals. He is a Distinguished Lecturer of IEEE Council on RFID, where he is also recently appointed as VP of Conferences. He is Vice-Chair of URSI Commission D Electronics and Photonics.

Ana Collado (M'07) was born in Santander, Spain. She received the B.S. degree in telecommunications engineering and Ph.D. degree from the University of Cantabria, Santander, Spain, in 2002 and 2007, respectively. In 2002, she was with the University of the Basque Country, Bilbao, Spain, where she was involved in the study of the uncertainty in noise-figure measurements in monolithic-microwave integrated-circuit low-noise amplifiers. Since July 2007, she has been a Research Associate with the Centre Tecnològic de Telecomunicacions de Catalunya, Castelldefels, Spain, where she is involved in the area of communication subsystems. Her areas of interest include the development of techniques for practical bifurcation control and stability analysis of power amplifiers and coupled oscillator systems, RFID technology, energy harvesting, and wireless power transmission solutions.

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. ANDIA VERA et al.: COOPERATIVE INTEGRATION OF HARVESTING RF SECTIONS FOR PASSIVE RFID COMMUNICATION

Dr. Collado was a 2011 Marie Curie Fellow Researcher for Project EU FP7–251557 Symbiotic Wireless Autonomous Powered system (SWAP), and Management Committee Member and Grant Holder Representative of EU COST Action IC0803, RF/microwave communication subsystems for emerging wireless technologies (RFCSET).

Yvan Duroc received the Teaching degree Agregation (French national degree) in applied physics in 1995 from Ministry of National Education, Higher Education, and Research, France, the Ph.D. degree in electrical engineering from the Grenoble Institute of Technology, Grenoble, France, in 2007 and the Habilitation Diriger des Recherches degree (HDR) from Grenoble University, Grenoble, France, in 2012. He was a Teaching Associate at Esisar Engineering School from 1997 to 2009, where he was an Associate Professor from 2009 to 2013. He is currently a Professor at the University Claude Bernard Lyon 1, France. He is in charge of lectures in signal and image processing, RF and microwave, electronics and embedded systems for the engineer and M.Sc. levels. His current research interests include microwave and applied signal processing with special attention to ultra-wideband and radio frequency identification technologies, backscattered modulations, energy harvesting, sensors and antennas. Prof. Duroc is a member of several TPC and serves as expert-reviewer for national and international scientific committees and conferences including IEEE, IET, Cambridge, PIER, Hindawi, Eurasip, URSI, EUCAP, ATC, ANR, ARC6. He is the vice-chair of the URSI Commission C, France.

Smail Tedjini (SM’92) received the Ph.D. degree in physics from Grenoble University, Grenoble, France, in 1985. He was an Assistant Professor at the Electronics Department of Grenoble Institute of Technology (Grenoble-inp), Grenoble, France, from 1981 to 1986, and Senior Researcher for the CNRS (Research French National Center) from 1986 to 1993. He became University Full Professor in 1993 and since 1996 he is Professor at the esisar, Embedded Systems Department of Grenoble-inp. His main teaching topics concern applied electromagnetism, radio frequency, wireless

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systems and optoelectronics. He has more than 30 years experience in academic education, research and management of university affairs. He served as coordinator and staff member in numerous academic programs both for education and research. He was coordinator for Ph.D. program, Master’s and Bachelor’s Programs for the Universities at Grenoble, some of these programs are under collaboration with international universities from Europe, Canada, Brazil, Vietnam, Egypt, and Maghreb. He served as the Director of esisar, Grenoble-inp. His main topics in research are applied electromagnetism, modeling of devices and circuits at both RF and optoelectronic domains. His current research concerns wireless systems with specific attention to RFID technology and its applications. He is the Founder and past Director of the LCIS Lab. He is the founder of ORSYS group and he leaded this group 2008–2014. He supervised more than 35 PhD and he has more than 250 publications. He serves as Examiner-reviewer for tens of Ph.D. degrees for universities in many countries (France, Germany, Finland, Spain, Ireland, Italy, Sweden, Vietnam, Australia, Singapore, India, Brazil, Egypt, Maghreb). Dr. Tedjini is a ember of several TPC and serves as expert reviewer for national and international scientific committees and conferences including journals such Piers, IEEE (MTT, AP, Sensors, MWCL), URSI, ISO, ANR, OSEO, FNQRT. He organized several conferences-workshops and was TPC chair-cochair in numerous conferences. Recently he was the General Chair of IEEE RFID-TA 2012. Senior Member IEEE, President and founder of the EEE-CPMT French Chapter, Vice-President of IEEE Section France and elected as the ViceChair of URSI Commission D Electronics and Photonics in 2008. He was reelected as vice-chair of IEEE-France-section and he is serving as the Chair of URSI Commission D for the triennium 2011–2014. In particular the preparation on the General Assembly and Scientific Symposium which was held in Beijing August 2014. Recently he was elected as the President of URSI-France 2015–2018. Now, Smail Tedjini is leading several research contracts. He is supervising several Ph.D. students and post-doc. He is involved in many national and international scientific committees and organization or program such as URSI, IEEE, European COST, European RISE.

IEEE Xplore® Document Notice

As originally published there is an error in reference [25] of “A Distributed Positioning System Based on a Predictive Fingerprinting Method Enabling Sub-Metric Precision in IEEE 802.11 Networks” The corrected reference should read as follows: [25] M. Di Filippo, L. Lucci, D. Marabissi, and S. Selleri, "Design of a smart antenna for mobile ad hoc network applications," Int. J. Antennas Propag., vol. 2015, 2015, Article ID 273047, 7 pp.

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A Distributed Positioning System Based on a Predictive Fingerprinting Method Enabling Sub-Metric Precision in IEEE 802.11 Networks Stefano Maddio, Member, IEEE, Marco Passafiume, Alessandro Cidronali, Senior Member, IEEE, and Gianfranco Manes, Senior Member, IEEE

Abstract—In this paper, we present a distributed positioning system for indoor environment based on a mesh of compact independent anchor nodes. Each node is built of low-cost off-the-shelf components and operates as specialized access points capable of standard connectivity at 2.45 GHz. The key technology for the localization strategy is the switched beam antenna (SBA), which enables a space division multiple access (SDMA) paradigm. The coordinated operation of SBA-equipped anchor nodes constitutes a legacy unmodified IEEE 802.11 network which can exploit the multiplexing mechanism. The latter is the driving force of the estimation strategy, with the positional information obtained as the result of a maximum likelihood algorithm driven by the comparison of a real-time received signal strength indicator (RSSI) with the predicted signal level distribution, which can be estimated and stored without the need of lengthy offline measurement. The signal level prediction is based on a simple propagation model which is effective because benefits of both the elementary antenna radiation beams directivity and the circular polarization operation, two strong aids for the mitigation of the multipath impairment. In turn, these feature make the estimation procedure tolerant to noisy power measurements, hence particularly suitable for cost-effective solutions based on RSSI. Experimental validations demonstrate the performance of a network composed of four anchors arranged in a 2.6 3.8 m mesh in a 6 7 m office room, and dealing with a single target node. The mean error inside the mesh area is 63 cm while the mean error in the entire room is 1.1 m. Focusing on the cumulative distribution of the error, the 90th percentile value is 1 m considering only the mesh and 1.9 m for the entire room. Index Terms—Indoor positioning system, space division multiple access (SDMA), switched beam antenna (SBA).

I. INTRODUCTION

T

HE subject of positioning systems in GPS-denied scenarios has witnessed a constantly growing interest in the last decade, [1]. The position awareness resulting from localization has fostered a wide spectrum of unattended and non-invasive applications, for instance, cultural heritage monitoring, [2], [3], agricultural monitoring [4], [5], environment monitoring [6], [7], disaster management [8], [9], and asset tracking [10].

Manuscript received July 01, 2015; revised September 09, 2015; accepted October 22, 2015. Date of publication November 18, 2015; date of current version December 02, 2015. This paper is an expanded version from the IEEE MTT-S International Microwave Symposium, Phoenix, AZ, USA, May 17-22, 2015. The authors are with the Department of Information Engineering, University of Florence, I-50139 Florence, Italy (e-mail: Stefano.Maddio@unifi.it). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2015.2496196

Such new and emerging scenarios have inspired different localization techniques and related technologies. These are enabled by several approaches available in the literature, which can be classified according to the specific signal features involved in the position estimation, [11]–[13], such as time of arrival, [14], [15], direction of arrival, [16], [17], network connectivity, and received signal strength indicator (RSSI), [18]–[20]. The technique based on the latter has several advantages because of its inherent simplicity and the low cost of its integration in legacy transceivers. They adopt a range estimation technique based on the inversion of the path loss estimation and positioning by the subsequent trilateration (or multilateration) approach, [13]. On the other hand, due to the complexity of any radio channel, the extraction of range information is affected by a great inaccuracy, furthermore, the RSSI reading embedded in commercial transceivers is typically available with 1 dB resolution, thus leading to an additional source of range estimation inaccuracy, [21]. A different strategy based on the RSSI, known as radio fingerprinting, estimates the position of the target node by matching the measured RSSI at the node with a map composed of the RSSI measured in the calibration phase at any possible target node position, [22]. A minimization technique is generally adopted to estimate the target node position. The main drawback of this approach consists in its lengthy training phase. The RSSI measurements can also be employed in combination with the space division multiple access (SDMA) paradigm: This is a channel access method based on the signal reception using directive antennas, which was originally introduced to increase the spectral efficiency through spatial multiplexing. One effective way to implement SDMA is by the use of switched beam antennas (SBAs), i.e., an active antenna capable of selectively enabling the signal reception to be only from a specific angular region, [23]. This approach was conveniently employed to track target nodes in 2D scenarios, exploiting cylindrical antenna arrays [24], [25]. In [21], [26]–[28], the authors exploited a special sectorized SBA capable of SDMA for direction of arrival (DoA) estimation based on RSSI. Similar solutions were successfully adopted for absolute position estimation purposes [29]–[31]. In this paper, we extend the already proposed technique, [32], by considering a mesh of anchor nodes operating as a coordinated network of identical SBA-based anchors and capable of establishing an unmodified IEEE 802.11x communication with the target node. The absolute position of the mobile user can

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be identified by translating the DoA, determined by each anchor, into Cartesian information assuming an almost constant height for the mobile node, which is a not-unrealistic hypothesis for handheld mobile devices [27], [28]. The fusion of the anchor-detected observations allows a robust signal-level partition of the positioning domain. Therefore, the positional information is directly estimated by a likelihood criterion applied to the measured multilevel signal partition and the expected one, which is a prediction of the normalized fingerprinting associated with each element of any SBA. The latter claim is justified considering the angular selection feature of the SBA beam-set, which permits the adoption of a simple propagation model neglecting scattering and reflections. To further enhance the angular filtering mechanism, the antennas operate in circular polarization (CP), which makes the radio link more robust against multipath [33], [34]. With respect to the present state of the art, the proposed method enables position estimation within indoor environments, with the following features. First, it is based on relative signal magnitude measurements, involving neither absolute magnitude nor phase measurements; second, it augments legacy standard protocols; third, it does not need a preliminary characterization of the specific electromagnetic scenario; lastly, its implementation requires only planar printed antennas and single-pole multiple-through switches connected to the wireless transceiver and controlled by the microcontroller unit. The indoor positioning technique description and the experimental validation are provided in this paper, which is organized as follows: Section II describes the system technology, and Section III presents its characterization. In Section IV we introduce the approach in exam for the localization based on the SDMA approach, and in Section V we report the actual measured performance obtained in a realistic indoor experiment. II. ARCHITECTURE OF THE POSITIONING SYSTEM A. Anchor Node Architecture The anchor node is based on a commercial transceiver integrated with a microcontroller, which is connected to the SBA by a single-pole 8-through switch in the present implementation; see Fig. 1. The sensitivity of the transceiver is normally enough (typical values are in the range of to dBm) to establish a link of sufficient quality in the indoor environment for the purpose of the localization procedure. For this purpose, the embedded 8-bit core is compatible with the high-performance and efficient 8051 industrial controller, with an embedded in-system programmable flash memory up to 128 Kbyte and 16 Kbyte RAM, as well as other sensors and peripherals, such as an analog–digital converter (ADC), timers, an AES 128 coprocessor, a watchdog timer, a 32 kHz crystal oscillator with sleep mode timer, and 21 digital pins, which can be accessed by peripherals to manage the I/O operations. The embedded built-in RSSI along with the link quality indicator are always available to the micro and to the end user via the I/O ports. The RSSI module operates on the received signal, averaging the energy over 8-symbol periods (128 s), in accordance with the IEEE protocol. This 8-bit data is related to the effective incoming power in dBm through a linear regression provided by

Fig. 1. Simplified block diagram of the anchor node architecture.

the manufacturer: typically 1 dB of accuracy is provided. The message exchange is through the unsynchronized and sequential activation of the SBA beams, driven by the microcontroller input–output pins. For commercially available SoC, 1 ms is required to collect an RSSI observation including the settling of the switch, which is adequate for an indoor channel coherence time at 2.45 GHz. Finally, the data that are presented hereinafter assumes a target node equipped with the same SoC. B. Switched Beam Antenna The SBA is an electronically controlled antenna array capable of selecting the pointing direction of its directive antenna elements. In this proposal, the SBA is composed of eight differently oriented antennas, arranged in a regular form, fed by a single-pole 8-through switch. For this purpose, a GaAs SP8T non-reflective switch minimizes the interaction between the antennas, a suitable condition for obtaining beam independence. Each antenna element consists of a patch antenna operating in circular polarization (CP), which enable robustness against multipath impairment and in turn increase the precision of RSSI data [35]. Furthermore, CP makes it possible to communicate regardless of the relative orientation, an ideal condition for the localization task. Each SBA antenna element consists of a canonical circular radiator in which its fundamental mode is degenerated to obtain a directive CP radiator [36]–[38]. The use of this antenna for localization purposes has been reported in [39], [27], and [28]. Alongside the antenna element in Fig. 2(a), source of a directive beam, a different type of element is implemented within the SBA, which is depicted in Fig. 2(b). This is built by assembling a patch similar to the former with another one operating in the next higher order mode, the mode, and it is a two-beam antenna in itself. The external patch is in fact characterized by a conical beam pattern, similar to the torus-like pattern of a monopole antenna (deep nulls in the upper and lower boresight directions) with a maximum in the region around 35 –70 [40, pp. 346–349], [41, pp. 135–149]. The measured principal cuts of the antennas in Fig. 2 are presented in Fig. 3. C. Switched Beam Antenna Arrangement To meet the requirements of uniformity, the best solid arrangement for the SBA is the polyhedron depicted in Fig. 4(a), arranged on a light shell of aluminum. This shape, while not Platonic, is the best tradeoff between the desired performance

MADDIO et al.: A DISTRIBUTED POSITIONING SYSTEM BASED ON A PREDICTIVE FINGERPRINTING METHOD ENABLING SUB-METRIC PRECISION

Fig. 2. Geometry of the two types of antennas employed for the anchor node. (a) Type I antenna. (b) Type II antenna.

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Fig. 4. Switched beam antenna arrangement. (a) Top view of the SBA. (b) Definition of the anchor polar reference.

the 3D cardioid model [39], approximates with sufficient accuracy the radiation solid for the purpose of positioning. III. INDOOR LOCALIZATION TECHNIQUE In this section, the rationale for the indoor localization approach is explained with explicit reference to the single-anchor scenario. In the next section, the technique will be extended to a cluster of cooperative anchors. Fig. 3. Measured principal cuts of the antennas fabricated according to the design in Fig. 2. Both patterns present body-of-revolution symmetry. (a) Type I antenna. (b) Type II antenna.

and the physical constraints [42]. With reference to Fig. 4(b), the antenna elements labeled from #2 to #7 are of type I. They are arranged hexagonally, with the dihedral angle between them around 120 . The dihedral angle between #2–#7 and the top #1 face is around 115 . The complementary behavior of the type II antenna, in terms of the coordinate, makes it a perfect candidate for the top element of the SBA, namely beams #1 and #8. This arrangement and the choice of different types of antenna elements are designed to maximize the angular diversity, which is the key feature for the localization algorithm, while keeping the structure as simple as possible. In fact, while the diversity in the direction is granted by the presence of six antennas arranged as an uniform circular array, in the direction only three beams cover the entire elevation angle, e.g., only face #2, face #1+8 and face #5 cover the arc in Fig. 4(b). The type II antenna provides two complementary beams, listed as #1 and #8, which increases the angular diversity in the elevation sense [43], [28]. The anchor node performance was experimentally characterized with a vector network analyzer (VNA) in an anechoic set-up, with a probe antenna matched to the type I faces of the device. The data were collected at the central frequency of 2.45 GHz, according to the SBA reference depicted in Fig. 4. On the basis of the data collected in the principal cuts, the 3D pattern of the beam-set has been interpolated using the dedicated approximation technique [44], [45]; the resultant reconstruction is depicted in Fig. 5. The observed regularity of the gain pattern suggests that an analytical pattern model, for instance such as

A. Predictive Signal Level Distribution Exploiting the SBA features introduced in Section II-C, the positioning algorithm derives the positional information by a likelihood criterion driven by the comparison between the expected angular response, characterized in Fig. 5, and the actual RSSI measurements. A more discriminating beam-set implies more accurate position estimation toward the random RSSI variations, the latter being due to measurement noise and deterministic but untraceable scattering mechanisms. In this regard, the complementarity of the patterns in Fig. 5(a) and (h)—beams #1 and #8—discriminates the direction. Despite that both are solid of revolution, beam #1 is characterized by a mild plateau in , while #8 exhibits a deep zero. This characteristic can be used by itself for localization purposes [43]. With reference to Fig. 6, the anchor position acts as the center of a spherical reference at the coordinates and the target node is located at with respect to the same Cartesian system. The target is assumed to be free to move everywhere in the 2D space, but constrained to the plane . The , that is the RSSI through the th beam, is estimated by the observation model for this scenario in its logarithmic form by (1) From (1), the received signal level corresponds to the summation of the th gain pattern through the nominal direction of the target, , the power of the wavefront impinging at the anchor section, and the noise. The incident power can be assumed to be (2)

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Fig. 5. 3D measured pattern for the eight beams. The angular variables are matched with the one indicated in Fig. 4(b). (a) Measured pattern #1. (b) Measured pattern #2. (c) Measured pattern #3. (d) Measured pattern #4. (e) Measured pattern #5. (f) Measured pattern #6. (g) Measured pattern #7. (h) Measured pattern #8.

where the additive term is the power transmitted by the target node, is the pathloss exponent, and is the gain of the target antenna. As a side note, is taken to be constant on the patch antennas due to the far-field (array) hypothesis. It is also assumed that the target antenna is circularly polarized with the same sense of rotation of the SBA; this permits to consider the same power budget link regardless of the relative axial rotation between target and anchor. The 3D pattern of the beam-set can be either interpolated on the basis of the data collected in Fig. 5 using a dedicated approximation technique [44], [45], or based on an analytical model for the sake of generality. For the type I antennas, a simple but not-unrealistic model for the cardioid pattern pointing toward a generic direction is [39, eq. (3)] (3) where, according to the spherical law of cosines,

Fig. 6. Local reference system of an anchor node and definition of the involved metric quantities.

where the parameters and are adjusted to fit the actual maximum position and slope [43, eq. (10)]. Having defined the auxiliary quantity , the following simplified Cartesian-to-spherical coordinate transformations hold:

(4) where the exponent is inversely proportional to the half-power angle. The pointing angle and exponent can be determined by observing the measurement set in Fig. 5. A similar expression can be written also for the conic beam of type II antenna in Fig. 5(h):

(5)

(6)

Therefore, the observation model in (1) can be recast as

(7)

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Fig. 7. Projection of the beam in Fig. 5 according to the transformation in (6). The areas of influence of each antenna is the key of the likelihood mechanism driving the localization algorithm. (a) Projected pattern #1. (b) Projected pattern #2. (c) Projected pattern #3. (d) Projected pattern #4. (e) Projected pattern #5. (f) Projected pattern #6. (g) Projected pattern #7. (h) Projected pattern #8.

where (8) is the predicted received power map of the SBA th beam. Considering the available set of 8 beams, (8) is a bijective function associating the position to the power level (in dBm) which the anchor expects to receive by its th beam while communicating with the target. From the statistical point of view, the model in (7) can be considered a normal probability distribution characterized by the expected value in vector form (8) and the measurement variance : (9) It is worth noting that when the patterns of the SBAs are either numerically available or analytically estimated as closed formulas, the global map in (9) is uniquely determined once the anchor position is established, by the projection of the beams through the mechanism of free space propagation. In other words, the approach in view can be defined as a predictive fingerprinting mechanism, and the quantity can be adopted as the fingerprint database [46, eq. 1]. Therefore, the map is analytically computed instead of estimated with a lengthy offline phase, which at last is the canonical solution for fingerprinting methods.

The effectiveness of the use of the predictive model, instead of a measurement database, is corroborated by the angular filtering nature of the directive beams of the considered SBA, and by the CP feature, which increases the reliability of simple channel models. B. Positioning Performance Within the Elementary Cell To clarify the mechanism of the localization approach and to provide a preliminary validation, the basic cell of the distributed system is analyzed in this section. This cell is identified as a square region within the operating range of a single anchor and centered on the same anchor. With reference to Fig. 6, choosing m and m, the power distribution in Fig. 7 is obtained using the model expressed in (8), assuming dBm, and dB in (2) (i. e. isotropic antenna), to emphasize the properties of the anchor by itself. In the figure, the seven areas determined by the elements from #1 to #7 are well determined, indicating a good azimuthal behavior of the proposed device. The projection of antenna #8, in Fig. 7(h), is lower than of any other antenna, as can be recognized in Fig. 5, by comparing Fig. 5(h) to the other plots. Fig. 8 depicts the cumulative projection of the beams in Fig. 7 in operative conditions, when the term due to the target is also considered with a more realistic model. It is assumed that the target antenna gain is equal to , since it exploits a type I antenna facing the ceiling. The anchor node has been experimentally characterized in a controlled setup to validate the observation model, employing the measurement set-up

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Fig. 8. Simulated signal coverage due to the anchor node beam set. The contribution of the target is considered in the link budget.

Fig. 10. Cumulative measured signal level through the whole beam set of the anchor node.

Information Matrix (FIM) for the model in view, expressed by (8), is

.. .

.. .

(10)

which, considering (8), can be recast in compact form as [39]

(11) Fig. 9. Semi-anechoic setup for characterization of the anchor (on the left side). The target node, down-facing, is on the right side.

depicted in Fig. 9. For practical reasons, the anchor node was placed in a fixed position at a height of 80 cm, with the spherical reference facing upward. The target node, was hung on a moving tripod, at the height of 2 m, with the antenna pointing toward the floor. This arrangement allows the same relative positioning of anchor and target as the one in the actual operating setup, where the anchor is fixed on the ceiling facing down to the ground. Rotating the anchor over the entire domain, and moving the target radially from 0 to 4 m, an area equivalent to the one in the simulation can be replicated. The resulting coverage, obtained as the average of 100 samples for each position, is presented in Fig. 10. The matching of the two sets of plots evidences the accuracy of the predictive model for the considered SBA. Furthermore, the comparison of the measurement in Fig. 10 and the model in Fig. 8 is useful for the fine tuning of the various system parameters, such as the pathloss exponent in (2). From the same observation model, it is also possible to derive useful information on the statistical behavior of the localization performance, with an approach similar to the one presented in [42] and [47]. In particular, following the results of the Fisher information theory [48], it is possible to derive an a priori lower limit for the uncertainty of the localization approach based on the specific observation model used. In particular, the Fisher

where is the normalized , i.e., is equal to except for the unit . The Cramer–Rao Bound (CRB), which is the limit of the variance of any unbiased estimator, is formally defined as the inverse of the FIM matrix. In particular, the limit variance for the - and -directional errors are [27, eq. 9, 10]

(12a)

(12b) These quantities give an interesting insight into the limit of the localization performance of any unbiased estimator, and it is useful for drawing conclusions about the performance of the anchor regardless of the measurement noise or the actual algorithm involved in the position estimation. The expression in (12) is composed of two factors. The first is the variance , which accounts for the noise measurement but also for the deterministic but virtually untraceable scattering mechanisms. The second factor depends only on the anchor characteristics, and represents the possible dilution of precision (DoP) as a function of the position. The value of can be determined by comparative experiments as follows. In Fig. 11, two RSSI statistics are presented,

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Fig. 12. Cramer–Rao Bound for the observation model represented by the predicted power map depicted in Fig. 7.

C. Experimental Validation Within the Elementary Cell

Fig. 11. Experimental RSSI variance for indoor experiments with different polarization: linear (LP) and circular (CP). Experimental data: target at 2 m height, 3 m radial dist. (3.6 m link distance D), 25e3 packets exchanged. (a) Link between beam #1 and target. (b) Link between beam #4 and target.

corresponding to two communication links deployed in the same multipath time-varying environment and using the same anchor and target hardware. The two experiments consider the target as static and are equipped with two different antennas: one circularly polarized and matched with the one at the anchor, and the other one linearly polarized. Two anchor beams are considered: beam #1 in Fig. 11(a) and beam #4 in Fig. 11(b). In principle, in both cases communication between the anchor and the target is possible regardless of the relative orientation. However, the cases CP–CP outperform CP–LP, as can be seen in estimating the signal standard deviation taken with a great number of messages (25,000). In the experimental case, it can be concluded that the CP–CP links bring a CRB reduction due to about 2 to 3.5 times of the ratio between and . Observing the statistics, the conservative value of dB was picked for the system under investigation. Fig. 12 depicts the Euclidean CRB, defined after (12) as

(13) for the single-anchor cell. It can be observed that the minimum value of the CRB, i.e., the region where the best localization results are expected, is underneath the anchor, with the iso-clines almost circular. This is a consequence of the diversity highlighted in Fig. 7 as well as the omni-directional coverage in the cumulative sense predicted in Fig. 8 and confirmed in Fig. 10. The radial discrimination is granted by the complementarity of the beams #1 and #8, as anticipated in Fig. 7.

The collected data summarized in Fig. 10 in cumulative form are used to estimate the absolute position of the target node. In doing so, the vector at any coordinate of the position domain is compared with the expected power distribution predicted by (8) and cumulatively illustrated in Fig. 8. Various localization strategies belonging to the class of maximum likelihood criteria can be effectively applied. Here, the least squares estimator (LSE) is used. Defining the LSE cost function as (14) with , the number of beams, the estimated position is formally found as (15) i.e., the one which fits best, in the LSE mean, the actual online measurement. This method is applied to the experimental data, obtaining the experimental error depicted in Fig. 13. The matching between the localization error in Fig. 13 and the CRB in Fig. 12 reveals significant matching between the predicted and actual position accuracy; both the error distributions resemble a bi-dimensional parabola with a minimum lying underneath the anchor. By comparing the two contours, it can be observed that the CRB and the measurements are very well matched, meaning that the estimate dB after the statistics in Fig. 11 is adequate. This small value follows from the antenna's operating in CP, which offers more robustness to multipath, interference, which is one of the principal causes of level dispersion. This assessment is verified by the following experimental results. As a final note, it is worth remarking that the collection of RSSI vectors is an automatic operation during the normal exchange of messages between the anchor and the target node. Considering also the low complexity of the operation described in (14), the positional information can be estimated in real time, with a refresh time dictated only by the switching time of the

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four anchors. As a result, the global observation model can be recast as

(16)

Fig. 13. Experimental localization error for the single anchor case, based on the RSSI measurements cumulatively summarized in Fig. 10.

Fig. 14. Predicted power coverage of the mesh composed of four anchors.

SBA. In normal conditions and with sufficient transceiver sensitivity, the switching between the several beams does not produce a loss of communication. IV. DISTRIBUTED LOCALIZATION STRATEGY In this section, the results of the single anchor approach are generalized to a cluster of anchors, which are coordinated by a remote unit and operate as a structured IEEE 802.11 network. We focus on a scenario characterized by a moderately dense anchor distribution, when a mobile target node is within the range of a subset of three to four anchors on the basis of the connectivity and RSSI level. With reference to Fig. 14, an elementary network composed of four anchor nodes is considered as the optimum subset mesh of a possible larger network; a subset composed of only three anchors is considered as the absolute minimum subset mesh dimension [32]. The figure depicts the predicted power distribution in a 10 10 m area with the same meaning of the experiment already discussed in Section III-A, where the anchor was arranged in a slightly smaller square domain. The observation model is derived by following the formalism in (8), but in this case applied to the composite beam-set of the

assumes the same meaning of power level map where as in the fingerprinting approaches, such as [46, eq. 1]. The maps corresponding to the incident power at the th anchor are computed following the projection model in (6), considering the specific coordinate of each anchor. It is worthwhile to note that, the target being equipped with a type I antenna operating in CP, its projected maps are indifferent to the target rotation around its axis (at least with the same statistics as in Fig. 11). Therefore, the proposed system has the same degree of freedom of a vertical monopole, as in canonical FPs. Furthermore, the target pattern being hemidirectional, similar to the pattern in Fig. 3(a), it is also robust to variations of the reference plane, as long as the pointing angle is within 60 around the vertical position. In this range the gain variation is comparable to the statistics variation in Fig. 11. In the analysis under consideration, the target node operates in broadcast, while the anchors are in receiving mode scheduling their eight channels. Therefore, the maps exploited by the algorithm are reception maps, different from canonical power maps of common fingerprinting methods which are transmission maps. As for the single anchor case, the predicted power distribution depicted in Fig. 14 in the cumulative sense can be used to estimate the limit error by the CRB. The same formulation in (12) is applied to the -dimensional map in (8) describing the space observed by the 4 anchor mesh. Comparing Fig. 12 with Fig. 15, the effect of each anchor is quite evident near each corner, where a well-defined area of local minimum is observed under each anchor of the mesh. In addition, the constructive effect of the collaboration between the anchors is revealed as a merging mechanism between the CRB regions, which follows almost the same shape as the cumulative power of Fig. 14, thus confirming the concept of robustness due to redundancy. The region delimited by the four anchors has an almost constant CRB, therefore this area corresponds to the most measurement error-tolerant region for the positioning. Nevertheless, in the center of the observed area, the power distribution has a minimum for this SBA configuration. This is reflected in Fig. 15, where a small area at the center of the mesh has a slightly higher value than the region of better reliability inside the mesh. Much synthetic information can be derived from the CRB contour, such as the mean error, maximum error, or the cumulative density function. This synthetic data can be used to drive the design phase of the mesh. To gain a deeper insight into the problem, the mesh dimension, and hence the anchor position, is varied inside the same 10 m 10 m space, which is used as a global space reference. Denoting the side of the square mesh by , the CRB for the cases ranging from m to m are sequentially evaluated. The synthetic information obtained by this analysis is presented in Fig. 16, where the various cases are ordered with the increasing mesh surface . To better analyze the scenario, for each case, two error metrics are evalu-

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Fig. 17. Photograph of the laboratory where the network of anchors was deployed.

Fig. 15. Cramer–Rao Bound of the mesh of four anchors.

As a final remark, the characteristics of the anchor, in particular antenna directivity and arrangement, have a tremendous impact on the CRB of the single node, hence on the CRB of the system [42], [47]. Different scenarios (room size and height, hallway shape, furniture-induced canyoning, etc.) could be better covered with different anchor architecture. V. EXPERIMENTAL VALIDATION

Fig. 16. Mean and max error for various sizes of the mesh.

ated, focusing on the predicted localization error inside the mesh area — solid lines in the figure — or in the entire region corresponding to the 10 m square edge, i.e., the global scenario — dotted lines in the figure. The error is considered both in the mean and max sense, obtained by evaluating the CRB function. Some interesting conclusions can be drawn by inspecting the figure. Inside the mesh, both the mean and max error grow almost linearly with the area. This is expected, considering the combination mechanism of the influence area of each anchor, which is less effective as the distance increases. While the mean error is almost linear with from the beginning, the max error has a residual component even for small areas, meaning that an error is always present, despite the dimension of the observed mesh. In contrast to the previous analysis, it can be observed that both the mean and the max error have a convex shape if the entire 10 m 10 m area is considered. In particular, the mean error is minimized with a m, while the max error is minimized for m. This analysis is useful for predicting the behavior of the tiled repetition of the same -based mesh. Since it is to be expected that the extremal anchors almost do not collaborate, as can be inferred also from Fig. 15, the behavior of the area inside the mesh can be repeated for each 4-anchor cell. At least the presence of more anchors can be marginally constructive, but never disruptive. The behavior at the periphery of a tiled mesh is expected to be the same as that for the 4-anchor mesh, for the same reason. Therefore, the design principle summarized in Fig. 16 can be easily extended to a tiled distribution.

This section presents the system's experimental validation. An intensive measurement campaign was conducted in an indoor office room: a wide-open space measuring 7 6 m completed with desks and furniture. Fig. 17 shows a photo of the area employed. The positioning measure reference is centered in the upper left corner of the area, while the positions of the four anchors are identified by increasing numbers. The anchors were installed on the ceiling, at a height of 2.7 m, pointing toward the floor, while the mobile nodes were fixed to a mobile support, at a height of 1.2 m, meaning that the minimum distance from the anchor to the target was 1.5 m, compatible with the model developed in the previous sections. In the following sections it is assumed that, on the basis of a simple scheduling protocol, the mobile target node is asked to broadcast a standard IEEE 802.11 “hello” message and each anchor acquires the 8-dimensional RSSI data. The complete acquisition of the -dimensional RSSI vector, which can be collected in approximately 1 ms, is the trigger for the estimation algorithm, which is executed without any form of time averaging, to emphasize the real-time operation of the proposed approach. A. Global Performance Fig. 18 depicts the schematic layout of the test area, which was monitored within a grid of 36 cm corresponding to (wavelength) at the center frequency of 2.45 GHz, enough for the application in view. For the experiment, the tag node was fixed to a moving tripod which was exactly positioned on the grid points. A synthetic view of the experimental results is depicted in Fig. 19, showing the error distribution map for each sample point averaging 100 instantaneous localization estimates. The performance of the system was evaluated both with reference to the 4-anchor mesh and with reference to the global observation area, i.e., the area corresponding to the available positions in the room. While the analysis inside the mesh is meaningful

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Fig. 18. Top view of the test room for the localization experiment. The four anchors composing the mesh are indicated by four numbers in sequence.

for the exhaustive tiling of a larger area, the performance outside the mesh is useful to quantify the robustness of the system. The minimum error measured in the middle of the test area was 0 cm, while the mean error for the area delimited by the four anchors was 63 cm. Considering the entire room, the mean error was 1.1 m. This increase in error is principally caused by isolated singular points, like the one placed at m, m. It can be seen that the error distribution confirms the qualitative behavior predicted by the CRB in Fig. 15, with a relative constant minimum at the center of the mesh and a parabolic growth when departing from this point. The cumulative distribution function of the errors, shown in Fig. 20, confirms the previous analysis for both the inside and for the general case. Inside the mesh, the error has a maximum of 1.6 m and a median of 74 cm, below the mean error. Focusing on the entire observation area, the distribution has a median error of 1.1 m with a fast rising front and a long tail of errors. The latter error distribution and the direct inspection of Fig. 19 suggest that the system performs well even outside the nominal four-anchor tile, except for limited critical areas, such as the one near a complex metal which scatters the field distribution beyond the possibility of modeling. Comparing the analysis of Fig. 19 with the model in Fig. 18 and the photograph of the room in Fig. 17, it can be seen that the error is concentrated near the walls, in particular near the south and east walls, where, due to the intense multipath effect caused by large metallic furniture, even CP antennas cannot avoid diffusive effects. This effect means that the CRB function in Fig. 15 has to be multiplied by a very high RSSI variance to actually take the complexity into account. To better appreciate the effectiveness of the proposed method and mesh arrangement, Fig. 21 depicts the mean error along with the first three quartiles for increasing test areas inside the observed area. The analysis has to be interpreted in the following manner. Starting from an area of 1 square meter at the center of the mesh, where the error is minimal in both the mean and the maximum sense, the observed area is progressively increased, and for each sub-region, the mean and the three quartiles, (25%), (50%) and (75%), are computed and presented in the plot. The final configuration corresponds to the entire observation area. This analysis is apparently similar to the one in Fig. 16, but with the important difference that in this case the mesh is

Fig. 19. Global error distribution for the experiment covering the entire test room.

Fig. 20. Cumulative distribution function of the error in Fig. 19.

Fig. 21. Error analysis for variable observation areas.

fixed and it is the test area which is varied. An interesting conclusion can be drawn. As the area increases, the mean error tends to stabilize around 1 m, with a mild increasing behavior. A significant slope on the error growth is observed only when the entire area is monitored, i.e., when the regions near the walls are considered, where the multipath impairment is unavoidable. The same mildly increasing behavior is observed for the third quartile, with the second one, coincident with the median, almost identical to the mean value. Therefore, it can be concluded that with a 4-anchor mesh, larger indoor areas characterized by a similar complexity could be covered with a similar error level, meaning that an even better

MADDIO et al.: A DISTRIBUTED POSITIONING SYSTEM BASED ON A PREDICTIVE FINGERPRINTING METHOD ENABLING SUB-METRIC PRECISION

Fig. 22. Tracking experiment: Horizontal path. The position of the four anchors is indicated with a colored dot.

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Fig. 23. Tracking experiment: Vertical path.

total area/mean error ratio is possible. To fix ideas, an area of 27 m , which is about three times the area delimited by the mesh of the four anchors, is covered with a mean error of 88 cm, just 30% more than the error inside the mesh. This is an important figure of merit to be considered in the planning stage of the anchor distribution. In the case of a wide area tiled with a regular mesh like the one in Fig. 15, each internal anchor would benefit of the presence of four first neighbors, with the consequent mitigation of the error. The shape of the CRB would be periodic with the tile, with the beneficial effect on the DOP, reduced by the redundancy. B. Tracking Experiment In this section, the localization performance of the proposed system was further validated with a real-time tracking experiment. The target device was held by an user who followed some simple trajectory. The tracking path represents the sequence of the localization estimation as the RSSI is updated in real time. The only additional manipulation is that the progressive position estimation is based on a reduced domain centered on the last estimated position. The area can be adjusted on the basis of the speed of the user. A more refined approach, like the Kalman filter, is not considered in this paper, so as to emphasize the effectiveness of the system even in its most basic application. Fig. 22 depicts the result of the first tracking experiment. Trying to maintain a straight direction, a user moved from left to right in a region about the center of the mesh. Due to the nature of the experiment, the declared reference path is only nominal, it being impossible for a human being to follow exactly a straight line or a right-angle bend. It is therefore difficult to exactly quantify the tracking error. It can be observed that the experimental path is clearly a west–east line followed by a reverse line just 50 cm under the first, as the reference path. While difficult to quantify, the approximate errors do not exceed 50 cm, confirming the global error estimation in Fig. 19. A similar analysis is depicted in Fig. 23, but this time the chosen path is from the south wall to the north wall and back. In this case the path is less ideal, especially in the south area. From the photograph in Fig. 17, it can be seen that in this area a complex metallic structure is present. Due to its complexity, the projection model

Fig. 24. Tracking experiment: Roundtrip below the anchors.

TABLE I SIMILAR POSITION SYSTEMS COMPARISON.

may be too coarse, leading to an inaccurate prediction. However the north–south direction of the path is clearly recognized, and the mean error is comparable to the previous case. Finally, Fig. 24 depicts the result of a closed path underneath the four anchors. As expected from the error analysis in Fig. 15, the positioning on this path is better than those of the previous ones, especially in the north–south segment. An accuracy problem can be observed in the south wall region, the same area where the path in Fig. 23 had some issues. Despite this fact, the two cycles on the reference square are almost identical, meaning that the system has a high precision.

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VI. CONCLUSIONS A positioning system based on a network of distributed anchor nodes was presented, designed, and analyzed. The basic element of the system is an anchor node built as an augmented IEEE 802.11 access point, equipped with a specialized switched beam antenna. The multiplexing mechanism is the key to the localization system, which is based on a simple likelihood criterion comparing the expected signal distribution driven by the switched beam mechanism to the RSSI measurements. The mesh is suited for tiling, and thus scaling the positioning capability within a larger area. A mesh of the presented nodes can be configured as a system enabling a space division multiple access paradigm at the network level, while being compatible with the selected communication protocol. The paper has proved that a mesh of 9.8 m with anchors at each of its corners, and installed on the ceiling of an indoor office room, is capable of estimating the position within the mesh area with a mean accuracy of 63 cm, while the max error is less than 1.5 m. Indeed, 90% of the mesh area is covered with sub-metric accuracy. Considering that the entire room area monitored by the network is 42 m , hence more than four times larger than the mesh area, the mean error is 1.1 m, with 90% of the area below 1.9 m. In literature, the class of canonical fingerprinting systems operates on the basis of lengthy offline training phase, necessary to collect and store the radio maps. The on-line phase consists of the search of the best match of the actual RSSI measurement within the RSSI database. In addition to the need of the training phase, the consistency of the radio maps is affected by the strong time-variation of the radio signals as well as the issue of deterministic while untraceable multipath. The proposed approach, while similar in the sense of comparing actual RSSI to stored maps, is therefore different by nature. The training problem and the consistency issues are solved with the optimal anchor technology, implementing a space division multiple access (SDMA) boosted by operation in circular polarization (CP), predicting the signal power distribution. In Table I a summary of recent localization results is reported, where only approaches with similar arrangement and topology of the monitored area are considered. To the best of the authors’ knowledge, the reported results are comparable to those available in literature for the class of low-cost maximum-likelihood indoor positioning systems, despite the fact that the herein-discussed technique does not rely on calibration or training phase.

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[4] L. Bencini, S. Maddio, G. Collodi, D. Di Palma, G. Manes, and A. Manes, “Development of wireless sensor networks for agricultural monitoring,” in Smart Sensing Technology for Agriculture and Environmental Monitoring. Berlin, Germany: Springer-Verlag, 2012, pp. 157–186. [5] S. Mukhopadhyay, Smart Sensing Technology for Agriculture and Environmental Monitoring. Berlin, Germany: Springer-Verlag, 2012. [6] G. Werner-Allen, K. Lorincz, M. Ruiz, O. Marcillo, J. Johnson, J. Lees, and M. Welsh, “Deploying a wireless sensor network on an active volcano,” IEEE Internet Comput., vol. 10, no. 2, pp. 18–25, Mar. 2006. [7] N. Malhotra, M. Krasniewski, C. Yang, S. Bagchi, and W. Chappell, “Location estimation in ad hoc networks with directional antennas,” in Proc. 25th Int. Conf. Distributed Computing Systems, 2005, pp. 633–642. [8] M. Harris, “The way through the flames,” IEEE Spectrum, vol. 50, no. 9, pp. 30–35, Sep. 2013. [9] U. Rüppel, K. M. Stübbe, and U. Zwinger, “Indoor navigation integration platform for firefighting purposes,” in Proc. 1st Int. Conf. Indoor Positioning and Indoor Navigation (IPIN), 2010, pp. 1–6. [10] N. Li, S. Li, G. Calis, and B. Becerik-Gerber, “Improving in-building asset localization by offset vector and convergence calibration methods,” J. Comput. Civil Eng., vol. 27, no. 4, pp. 337–344, 2012. [11] J. Hightower and G. Borriello, “Location systems for ubiquitous computing,” IEEE Computer, no. 8, pp. 57–66, Aug. 2001. [12] A. H. Sayed, A. Tarighat, and N. Khajehnouri, “Network-based wireless location: Challenges faced in developing techniques for accurate wireless location information,” IEEE Signal Process. Mag., vol. 22, no. 4, pp. 24–40, Jul. 2005. [13] R. Zekavat and R. Buehrer, Handbook of Position Location: Theory, Practice and Advances. New York, NY, USA: Wiley-IEEE Press, 2011. [14] S. Gezici, Z. Tian, G. B. Giannakis, H. Kobayashi, A. F. Molisch, H. V. Poor, and Z. Sahinoglu, “Localization via ultra-wideband radios: A look at positioning aspects for future sensor networks,” IEEE Signal Process. Mag., vol. 22, no. 4, pp. 70–84, Jul. 2005. [15] N. Patwari, A. O. Hero, III, M. Perkins, N. S. Correal, and R. J. O'dea, “Relative location estimation in wireless sensor networks,” IEEE Trans. Signal Process., vol. 51, no. 8, pp. 2137–2148, Aug. 2003. [16] B. N. Hood and P. Barooah, “Estimating DoA from radio-frequency RSSI measurements using an actuated reflector,” IEEE Sensors J., vol. 11, no. 2, pp. 413–417, Feb. 2011. [17] L. Kumar, A. Tripathy, and R. M. Hegde, “Robust multi-source localization over planar arrays using music-group delay spectrum,” IEEE Trans. Signal Process., vol. 62, no. 17, pp. 4627–4636, Sep. 2014. [18] S.-H. Fang and T.-N. Lin, “A dynamic system approach for radio location fingerprinting in wireless local area networks,” IEEE Trans. Commun., vol. 58, no. 4, pp. 1020–1025, Apr. 2010. [19] X. Shen, Z. Wang, P. Jiang, R. Lin, and Y. Sun, “Connectivity and RSSI based localization scheme for wireless sensor networks,” in Advances in Intelligent Computing. Berlin, Germany: Springer-Verlag, 2005, pp. 578–587. [20] S.-H. Fang and T.-N. Lin, “Indoor location system based on discriminant-adaptive neural network in IEEE 802.11 environments,” IEEE Trans. Neural Netw., vol. 19, no. 11, pp. 1973–1978, Nov. 2008. [21] M. Passafiume, S. Maddio, A. Cidronali, and G. Manes, “MuSiC algorithm for RSSI-based DoA estimation on standard IEEE 802.11/802. 15.X systems,” WSEAS Trans. Signal Process., vol. 11, pp. 58–68, 2015. [22] Y. Kim, Y. Chon, and H. Cha, “Smartphone-based collaborative and autonomous radio fingerprinting,” IEEE Trans. Syst., Man, Cybern., Syst., vol. 42, no. 1, pp. 112–122, Jan. 2012. [23] A. Kalis and T. Antonakopoulos, “Direction finding in IEEE 802.11 wireless networks,” IEEE Trans. Instrum. Meas., vol. 51, no. 5, pp. 940–948, Oct. 2002. [24] D. Mastela, L. Reindl, L. Wiebking, and L. Zander, “Development of a cylindrical microstrip phased array antenna for a radio tracking system,” in Int. Workshop on Antenna Technology Small Antennas and Novel Metamaterials, 2006, pp. 381–383. [25] M. D. Filippo, L. Lucci, D. Marabissi, and S. Selleri, “Design of a smart antenna for mobile ad hoc network applications,” Int. J. Antennas Propag., vol. 2015, 2015, Article ID 273047, 7 pp.

MADDIO et al.: A DISTRIBUTED POSITIONING SYSTEM BASED ON A PREDICTIVE FINGERPRINTING METHOD ENABLING SUB-METRIC PRECISION

[26] S. Maddio, A. Cidronali, G. Giorgetti, and G. Manes, “Analysis of the indoor positioning performance of a switched six-beams dodecahedral antenna,” in Proc. Radio and Wireless Symp. (RWS), 2010, pp. 156–159. [27] A. Cidronali, S. Maddio, G. Giorgetti, and G. Manes, “Analysis and performance of a smart antenna for 2.45-GHz single-anchor indoor positioning,” IEEE Trans. Microw. Theory Techn., vol. 58, no. 1, pp. 21–31, Jan. 2010. [28] S. Maddio, M. Passafiume, A. Cidronali, and G. Manes, “A scalable distributed positioning system augmenting WiFi technology,” in Proc. 4th Int. Conf. Indoor Positioning and Indoor Navigation (IPIN), 2013, pp. 1–10. [29] L. Brás, M. Oliveira, L. Guenda, N. B. Carvalho, and P. Pinho, “Localization system improvement using a special designed sectorised antenna,” in Proc. Int. Symp. Antennas and Propagation (APSURSI), 2011, pp. 1375–1378. [30] L. Brás, N. B. Carvalho, and P. Pinho, “Pentagonal patch-excited sectorized antenna for localization systems,” IEEE Trans. Antennas Propag., vol. 60, no. 3, pp. 1634–1638, Mar. 2012. [31] L. Brás, N. B. Carvalho, P. Pinho, L. Kulas, and K. Nyka, “A review of antennas for indoor positioning systems,” Int. J. Antennas Propag., vol. 2012, 2012, Article ID 953269, 14 pp. [32] S. Maddio, M. Passafiumem, A. Cidronali, and G. Manes, “A distributed positioning system based on real-time RSSI enabling decimetric precision in unmodified IEEE 802.11 networks,” in Proc. 2015 Conf. Int. Microwave Symp. (IMS), 2015, pp. 1–4. [33] R. Szumny, K. Kurek, and J. Modelski, “Attenuation of multipath components using directional antennas and circular polarization for indoor wireless positioning systems,” in Proc. 2007 Conf. European Radar Conf. (EuRAD), 2007, pp. 401–404. [34] L. Kanaris, A. Kokkinis, M. Raspopoulos, A. Liotta, and S. Stavrou, “Improving RSS fingerprint-based localization using directional antennas,” in Proc. 8th Eur. Conf. Antennas and Propagation (EuCAP), 2014, pp. 1593–1597. [35] Z. Szalay and L. Nagy, “Utilization of linearly and circularly polarized antennas for indoor positioning,” in Proc. 17th Int. Conf. Transparent Optical Networks (ICTON), 2015, pp. 1–4. [36] S. Maddio, A. Cidronali, and G. Manes, “A new design method for single-feed circular polarization microstrip antenna with an arbitrary impedance matching condition,” IEEE Trans. Antennas Propag., vol. 59, no. 2, pp. 379–389, Feb. 2011. [37] S. Maddio, A. Cidronali, I. Magrini, and G. Manes, “A design method for single-feed wideband microstrip patch antenna for switchable circular polarization,” in Proc. Conf. Eur. Microwave Conf., 2007, pp. 262–265. [38] S. Maddio, “A compact wideband circularly polarized antenna array for C-band applications,” IEEE Antennas Wireless Propag. Lett., vol. 14, no. 9, pp. 1081–1084, Dec. 2015. [39] S. Maddio, A. Cidronali, and G. Manes, “Smart antennas for direction-of-arrival indoor positioning applications,” in Handbook of Position Location: Theory, Practice, and Advances. New York, NY, USA: Wiley Online Library, 2011, pp. 319–355. [40] R. Garg, Microstrip Antenna Design Handbook. Boston, MA, USA: Artech House, 2001. [41] J. James, C. Wood, and P. Hall, Microstrip Antenna Theory and Design. London, U.K.: IET, 1986. [42] S. Maddio, M. Passafiume, A. Cidronali, and G. Manes, “Impact of the dihedral angle of switched beam antennas in indoor positioning based on RSSI,” in Proc. Conf. 11th Eur. Radar Conf. (EuRAD), 2014, pp. 317–320. [43] S. Maddio, A. Cidronali, and G. Manes, “An azimuth of arrival detector based on a compact complementary antenna system,” in Proc. Conf. Eur. Wireless Technology (EuWIT), 2010, pp. 249–252. [44] T. G. Vasiliadis, A. G. Dimitriou, and G. D. Sergiadis, “A novel technique for the approximation of 3-D antenna radiation patterns,” IEEE Trans. Antennas Propag., vol. 53, no. 7, pp. 2212–2219, Jul. 2005. [45] F. Gil, A. R. Claro, J. M. Ferreira, C. Pardelinha, and L. M. Correia, “A 3D interpolation method for base-station-antenna radiation patterns,” IEEE Antennas Propag. Mag., vol. 43, no. 2, pp. 132–137, Apr. 2001. [46] V. Honkavirta, T. Perala, S. Ali-Loytty, and R. Piché, “A comparative survey of WLAN location fingerprinting methods,” in Proc. 6th Workshop on Positioning, Navigation and Communication, WPNC 2009, 2009, pp. 243–251.

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[47] G. Giorgetti, S. Maddio, A. Cidronali, S. Gupta, and G. Manes, “Switched beam antenna design principles for angle of arrival estimation,” in Proc. Conf. Eur. Wireless Technology (EuWIT), 2009, pp. 5–8. [48] H. V. Poor, An Introduction to Signal Detection and Estimation. Berlin, Germany: Springer-Verlag, 1994. [49] X. Luo, W. J. O'Brien, and C. L. Julien, “Comparative evaluation of received signal-strength index (RSSI) based indoor localization techniques for construction jobsites,” Advanced Engineering Informatics, vol. 25, no. 2, pp. 355–363, Apr. 2011. [50] R. Zhang, W. Xia, Z. Jia, and L. Shen, “The indoor localization method based on the integration of RSSI and inertial sensor,” in Proc. Global Conf. Consumer Electronics (GCCE), 2014, pp. 332–336.

Stefano Maddio (M'12) was born in Florence, Italy, on September 3, 1978. He received the Laurea and Ph.D. degrees in electronics engineering from the University of Florence, Florence, Italy, in 2005 and 2009, respectively. He joined the Department of Information Engineering of the University of Florence as a Research Associate. His research activities cover both the electromagnetic and electronic topics of the microwave engineering, such as the analysis and design of radiative systems for microelectronics in the field of smart antenna technology for wireless applications, with particular emphasis on the issues of wireless localization and special-purpose antenna systems for dedicated short range communications. His scientific interests also cover the area of signal elaboration and manipulation at front-end level, with particular emphasis on active and passive filtering and noise mitigation as well as numerical techniques for free and guided electromagnetic propagation.

Marco Passafiume was born in Florence, Italy, on February 6, 1987. He received the Laurea degree in electronic engineering (cum laude) from the University of Florence, Italy, in 2012. Currently he is pursuing the Ph.D. degree in the Department of Information Engineering, and working in the Microelectronics and HF research group. His research activities covers developing of digital systems for communication (also working with private institutes, such as Autostrade Tech., on development of new infomobility systems), highly integrated SoC/SiP and human interface devices. He is studying new development technologies based on FPGA and various aspects of computer science evolution and digital communications/software-defined radios. His scientific interests also cover the area of data elaboration methodologies, with particular attention to algorithmic development.

Alessandro Cidronali (M'89–SM'11) received the Laurea and Ph.D. degrees in electronics engineering from the University of Florence, Florence, Italy, in 1992 and 1997, respectively. From 1999 to 2011, he was an Assistant Professor in the Department of Electronics and Telecommunications of the University of Florence. From 1999 to 2003, he was a Visiting Researcher with the Motorola Physics Science Research Laboratory. From 2002 to 2005, he was a Guest Researcher with the Non-Linear Device Characterization Group, Electromagnetic Division, National Institute of Standards and Technology (NIST), Gaithersburg, MD, USA. Under the frame of the IST-EU FP6 Network TARGET (IST-1–507893-NOE), he served as Workpackage Leader for the

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transmitters modeling/architectures for wireless broadband access' work packages. Currently, he is an Associate Professor in the Department of Information Engineering of the University of Florence, where he teaches courses on electron devices and integrated microwave circuits. His research activities concern the study of analysis and synthesis methods for nonlinear microwave circuits, the design of broadband microwave integrated circuits and the development of computer-aided design (CAD) modeling for microwave devices and circuits. Prof. Cidronali was the recipient of the Best Paper Award presented at the 61st ARFTG Conference. From 2004 to 2006, he was an Associate Editor for the IEEE TRANSACTION ON MICROWAVE THEORY AND TECHNIQUES. Currently, he is a member of the IEEE MTT-S TC-20 “Wireless Communications” and TC-27 “Vehicular Technologies and Communications”.

Gianfranco Manes (M'01–SM'02) is currently a Full Professor in the Electronics and Telecommunication Department, University of Florence, Florence, Italy. He is active in the field of microwave engineering and wireless technology, including wireless sensor networks. He is the founder and Head of the MIDRA Consortium, a joint venture between the University of Florence Autostrade Tech SpA and Motorola SpA and the Head of the Research Centre for ICT for Environment Quality and Safety, taking scientific responsibility for leading both national and international research projects. He has authored or coauthored over 150 paper published in books, society journals, and referenced international conferences. Prof. Manes was a Technical Program Committee (TPC) member and session chairman since 2002 to 2005 for the IEEE Microwave Theory and Techniques Society (IEEE MTT-S) International Microwave Symposium (IMS).

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Real-World Implementation Challenges of a Novel Dual-Polarized Compact Printable Chipless RFID Tag Md Aminul Islam, Student Member, IEEE, and Nemai Chandra Karmakar, Senior Member, IEEE

Abstract—A novel compact printable dual-polarized (DP) chipless radio-frequency identification (RFID) tag is presented along with its real-world implementation challenges. First, the DP tag with simulation and measurement results is presented, where ‘U’ shaped slot resonators are re-used in both vertical (V) and horizontal (H) polarizations to double the encoding capacity within a fixed bandwidth. Next, slot-length variation encoding technique is added to reduce the tag size by 50%. After that, a 16-bit proof data of concept DP tag is developed that achieved 16.6 density, which is the highest among the reported works. Next, a step-by-step guideline is presented to overcome the real-world challenges for implementing printable chipless RFID tags, which starts with a detail study on the effect of ink conductivity, and permittivity and loss tangent of the substrate on the tag performance. Then, a quick approximate substrate characterization technique is presented, which is verified by measurement of thermal printed patch tags. Finally, tag printing procedure on paper using a thermal printer is briefed, which is followed by a discussion on some printing inaccuracies and their plausible solutions. All these analysis will build a firm understanding and practical insight on implementing the proposed promising conductive ink printed chipless RFID tag for identification, authentication and sensing. Index Terms—Conductivity, frequency-selective surfaces (FSSs), permittivity, radio-frequency identification, RFID tags.

I. INTRODUCTION

R

FID is an old technology, which has been matured enough in recent years and successfully used in numerous applications. For a different scenario, application specific tags and readers are used. Some of them use tags with long reading range, powered by a battery inside it, and some other systems use tags with shorter reading range without a battery. Hence, the cost of different systems varies significantly and it plays an important role for deploying this technology in any sector. RFID tags have the potential to replace barcodes for long reading range, non-line-of-sight reading, and automated identiManuscript received July 01, 2015; revised September 12, 2015 and October 20, 2015; accepted October 22, 2015. Date of publication November 18, 2015; date of current version December 02, 2015. This work was supported in part by the Australian Research Council Linkage Project grant ( LP0991435: Back-scatter based RFID system capable of reading multiple chipless tags for libraries). This paper is an expanded version from the IEEE MTT-S International Microwave Symposium, Phoenix, AZ, USA, May 17–22, 2015. The authors are with the Department of Electrical and Computer Systems Engineering, Monash University, Victoria 3800, Australia (e-mail: aminul.mithu. [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2015.2495285

fication and tracking. However, due to their high cost compared to that of barcodes, the current chipped RFID technology has not yet gained wide acceptance, especially in the field of item-level tagging of cheap items, such as for anti-counterfeiting in banknotes, stamps, secured papers, and for identification in lowcost products. It is already predicted by researchers that, trillions of tags will be required for these low cost items, if the cost of a tag can be lowered to less than a cent [1]. Currently, multi-bit passive chipped RFID tags are used for tagging only costly items, where the cost of the tag depends mainly on the used silicon chip [2]. Moreover, brittleness of the chip bound the chipped tags' application areas by one more degree. Therefore, research has focused on developing chipless RFID tags that can be printed directly on products and packaging like barcodes using conductive ink. Although, a number of printable chipless RFID tags have been proposed in the research literature using time, frequency, phase, and image-based encoding techniques, none of the techniques shows the ability to encode a sufficient number of bits within a small area, e.g., the area of a credit card. In Table I, a detailed comparison of data density, printability, 64-bit tag size, and increment in size with the number of bits are presented for some potential tags from the literature. It is noticed that, among printable tags, frequency domainbased tags have higher data density compared to time domainand phase domain-based tags. However, most of the tag designs in the frequency domain are in need of an extra resonator to encode an extra bit that makes the size of the tag bigger than the size of a credit card, which is not commercially viable. Besides, only 35-bit data capacity [6] has been reported to date within the license-free ultra-wide band (UWB) from 3.1–10.6 GHz. As each resonator usually has an average bandwidth of 200 MHz, therefore it is not enough for encoding 64 bit data within this 7.5 GHz UWB frequency band. Moreover, incorporation of the sensing materials [18] with the printable chipless RFID tags have opened a totally new dimension in the field of its applications. Besides, for reading these frequency domain based chipless RFID tags, few readers [19], [20] have been developed also. In addition, researchers are now focusing on signal processing, tag localization, and other reading techniques for chipless RFID tags as well [21]. In contrast, most of the proposed tags encoding concepts are verified by measurements of fabricated tags on different low loss RF substrates only, which cannot be used commercially as the

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TABLE I COMPARISON OF DIFFERENT CHIPLESS RFID TAGS [3]

Fig. 1. Content flow diagram of the paper.

,

(2 sided)

tags are needed to be printed directly on the paper or plastic packaging using conductive ink. Recently, few printed tags are presented in [22], but no general guideline is available on how to address the issues related to substrate characterization, designing, and printing tags on new papers and plastics with different specifications. Electromagnetic (EM) properties of different paper and plastic materials differ from each other; hence, the performances of the optimized tags on them will differ as well. Therefore, a thorough study is required for determining the EM properties of new substrates, on different tag printing procedures using conductive inks and the effects of different parameters on the tags' responses. To overcome these challenges on implementing the compact printable chipless RFID system in the real-world, first, a novel frequency domain based DP tag is presented in [13] as a representative of a new generation of chipless RFID. Initially, DP is applied here to overcome the data capacity limitation by doubling the number of bits. Then, slot-length variation technique is applied to overcome the limitation of data density. In continuation to this research on implementing the printable chipless RFID system in the real-world, a detail investigation is presented in this paper addressing the effects of different substrate and ink parameters on the tag responses, characterizing the substrates (determining permittivity and loss tangent), exploring printer facilities, printing procedures, errors in printing different shapes, and edges with their probable solutions. This investigation will provide a step-by-step guideline for implementing any frequency domain based chipless RFID tags in reality. Following this guideline, the proposed single sided compact DP tag can be printed directly over different items using conductive ink. They can be used for authentication in the secured items like banknotes, postage stamps, important documents and for identification in ID or credit cards, and also can be used for item-level tagging. The rest of the paper is organized as Fig. 1.

Fig. 2. Slot-length modified LP tags (a) reference, (b) right shift—length decreases by 0.4 mm, (c) left shift—length increases by 0.4 mm, and (d) slot remagnitudes of the moved, (e) simulated RCS magnitudes, and (f) measured fabricated tags using the measurement setup of Fig. 3.

II. 8-BIT LINEARLY-POLARIZED (LP) TAG USING 4- ‘U’ SLOTS ‘U’ shaped slot resonators are used for the LP tag to create frequency signatures in the backscattered signal, where slotlength of each ‘U’ slot is varied four times to encode two bits of data [13]. Data encoding technique using slot-length variation in 8-bit LP tags loaded with four ‘U’ slots is explained with the simulation and measurement results of the tags in Fig. 2. Here, the length of the second slot is modified four times to represent two bits by that single slot. To facilitate laboratory measurement, the slot lengths are optimized to make them resonant within 7–12 GHz frequency band. Available two LP horn antennas with the frequency bandwidth from 7–13 GHz and 12 dBi gain are used for the fabricated tag measurement, which is shown in Fig. 3. From Agilent PNA-8361A vector network analyzer (VNA), 0 dBm power is transmitted through port 1 and the transmission coefficients between the two antennas are measured. Simulated RCS magnitudes and measured magnitudes of the four tags are shown in Fig. 2(e) and (f), respectively. Here, the optimized tag dimensions are: , , , and , width and length of the longest and 5.3 mm, permittivity of the used Taconic TLX-0 and . The original slot length is used as a reference and denoted by bits ‘10’ in Fig. 2(a), and the simulated and measured results are shown in Fig. 2(e) and (f), respectively, with solid red lines. The length of the second slot is then decreased by 0.4 mm as shown in Fig. 2(b), which shifts the notch position toward the right side of the reference notch as shown in Fig. 2(e) and (f) with blue dotted lines and is denoted by bits ‘11’. An increase in the length of the second slot by 0.4 mm decreases the resonant frequency toward the left of the reference, which is denoted by bits ‘01’ in

ISLAM AND KARMAKAR: REAL-WORLD IMPLEMENTATION CHALLENGES OF A NOVEL DUAL-POLARIZED COMPACT PRINTABLE CHIPLESS RFID TAG

Fig. 3. Tag measurement setup using two LP horn antennas.

Fig. 2(c) and its simulated and measured magnitude responses are shown in Fig. 2(e) and (f), respectively, with black dashed lines. The resonant notch due to the second slot is removed by shorting the corners of the slot as shown in Fig. 2(d), which is denoted by bits ‘00’ and its simulated and measured magnitude responses are shown in Fig. 2(e) and (f) in green dot-dashed lines, where no magnitude jumps are created within the used bandwidth for encoding (7–12 GHz). However, the third notch position in the measured result curve for this corner shorted tag (green dot-dashed line) in Fig. 2(f) is shifted left a bit, which might be due to the etching inaccuracy of that slot during the in-house fabrication process of these tags. Thus, a single slot can be used to encode two bits of data instead of one and this will reduce the number of required slots to encode a certain number of bits and in turn this will reduce the total tag size. In addition, a correlation between the magnitude and phase signature is also found for the ‘U’ slots [23]. Therefore, phase signature detection can also be added to improve its reading reliability. III. 16-BIT DUAL-POLARIZED (DP) TAG USING 8-‘U’ SLOTS The polarization property of ‘U’ slot resonators [13] is applied here to double the encoding capacity within a fixed bandwidth. The reading process is shown in Fig. 4, where the DP tag is excited by a DP transmitter antenna (Tx) and the frequency encoded backscattered signal from the DP tag is received by another DP receiver antenna (Rx). The V-polarized receiver (Vr) will receive the frequency encoded signal from the V-slots of the tag, since they show frequency response only to the V-polarized transmitted signal (Vt). Similarly, the H-polarized receiver (Hr) will receive the frequency encoded signal from the H-slots, which respond only to the H-polarized signal (Ht). These responses from V-and H-slots are independent of each other and can be changed without affecting the same frequency of the other [13]. A. Simulation of 16-Bit DP Tag Using Slot-length Variation Slot-length variation encoding technique in DP tags is also similar to the LP tags, which is described in the previous section. DP plane wave and DP RCS probes are used for the DP tags for their CST simulation. Here, slot lengths in both polarizations are varied for encoding data, which is explained with four different DP tags as shown in Fig. 5. The tag of Fig. 5(a) is the reference tag with all its X (H) and Y (V)-polarized slots

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Fig. 4. Tag reading procedure for the proposed DP tag.

Fig. 5. DP tags with different IDs using slot-length variation encoding: (a) ‘ ’, (b) ‘ ’, and (d) ‘ (c) ‘ ’.

’,

are in their unchanged positions. Its simulated RCS responses are shown in Fig. 6(a), where the four notches in both X and Y-probe results are seen at the same positions and identified as a tag with ID ‘ ’. The tag in Fig. 5(b) is identified as ‘ ’, where all four X-polarized slot lengths are reduced by 0.4 mm, which shift the X-probe notches toward the right of the Y-probe notches as shown in Fig. 6(b). In Fig. 5(c), all of the four slots in X-polarity are shorted to remove the notches in the X-probe result, which are shown in Fig. 6(c) and the tag is identified as ‘ ’. The tag in Fig. 5(d) is identified as ‘ ’, where all four Y-polarized and the third X-polarized slot lengths are increased by 0.4 mm to shift their notch positions toward the left and the first two X-slots are decreased by 0.4 mm to right shift their notch positions, whereas the fourth X-slot is shorted at the corners to remove its notch in the X-probe result and these occurrences are shown in the simulation results in Fig. 6(d). Here, the minimum frequency shift is determined by the frequency resolution of the reader and the maximum shift is determined by the closest position of the adjacent notches. B. Measurement of 16-Bit DP Tags for Proving the Concept The four tags of Fig. 5 are fabricated and measurements are done in both X and Y-polarity using the setup shown in Fig. 3. Measured results are shown in Fig. 7, which matches with the predicted results from the simulation as shown in Fig. 6. Though DP tag measurements using LP horn antennas are only

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Fig. 6. Simulation results (a) , (c)

, (b) , and (d) .

and can encode 16-bit in DP, instead of 8 bit in V/H polarization. Hence, the density of data bits per square cm converts to 16.6 , which is higher than any other reported tags in the literature to date [3]. Moreover, lengths of the ‘U’ slot resonators can be adjusted to obtain more frequency signatures within the UWB band (5.3–10.6 GHz) and finer tag dimensions can also be used in a better tag printer to accommodate more number of slots inside a similar sized patch. Hence, from only the tag design view point, the maximum encoding capacity will be limited by the bandwidth of the ‘U’ slots. Simulated and measured results indicate that the average bandwidth of the ‘U’ slots is around 0.15–0.8 GHz, which depends on the resonant frequency, ink conductivity, permittivity, and loss tangent of the substrate and a few more parameters. Hence, if the full 5.3 GHz of the UWB band is used for encoding data following the proposed techniques, then in the LP tag, 6 to 35 bits ( to ) could be encoded and it would be doubled to 12 to 70 bits in the DP tag. These might facilitate to achieve a 64-bit RFID tag in the chipless domain, which is compact and easily printable. D. On Reading Range and Noise Immunity in DP Tag Reader The isolation between the two feed lines of the reader DP antennas and the isolation between the reader Tx/Rx antennas determine the reader's dynamic range, accuracy, reading range, and reliability. The maximum theoretical reading range can be calculated from (1) [24]

(1)

Fig. 7. Measurement results (a) , (c)

, (b) , and (d) .

presented here due to the inaccessibility to DP horns, the absence of notches from the orthogonal ‘U’ slots in the LP measurement proved the DP encoding concept. Therefore, from the simulation and measurement results, it can be inferred that, any bit combinations in both polarization can be achieved using the slot-length variation encoding technique. C. Data bit Encoding Density and Capacity Calculation Data bit encoding density and capacity are enhanced here for the proposed tag by using two hypotheses. First, the DP encoding technique in compact ‘U’ shaped slot resonators is used for doubling the data bits within a fixed bandwidth, where ‘U’ slots are re-used in both V- and H-polarizations. Next, slotlength variation encoding technique is added, where two bits are encoded by using only one ‘U’ slot, which reduced the tag size to 50%. For example, due to the slot-length variation encoding, the developed 16-bit DP prototype tag captures only 0.96 of area instead of 1.92 ,

is the transmitting power, is the gain of the transwhere mitting antenna, is the gain of the receiving antenna, is the lowest wavelength that corresponds to the highest frequency used in the reader, is the receiver sensitivity, and is the minimum RCS level that is expected to be detected in the reader. Here, the sensitivity of the receiver will be defined by the noise level of the reader and this can be minimized to achieve a sensitivity of in the indoor environment. Moreover, the gain and isolation between the two ports of the DP antennas are needed to be improved to achieve a higher reading range. Besides, use of slots on a metal surface for the proposed DP tags increase their RCS values, which also increase their reading range. From the measured results, it is observed that the average notch depth is more than 8 dB, and based on the sensitivity values of the reported readers, around 3 dB differences can be detected. The reader's sensitivity value also affected by the antenna temperature and its impulse response, the noise figure, gain and linearity of the receiver's low noise amplifiers (LNA), the delay spread of passive components such as power dividers and filters, the noise due to inappropriate shielding and grounding, and the noise introduced by the tag due to printing errors and variations in substrate materials and design inaccuracies [25]. Therefore, the proposed tag has around 5 dB of margin to encounter the effects of these noises. Moreover,

ISLAM AND KARMAKAR: REAL-WORLD IMPLEMENTATION CHALLENGES OF A NOVEL DUAL-POLARIZED COMPACT PRINTABLE CHIPLESS RFID TAG

phase jump information can be added with the magnitude notch position, as the phase information is more resilient to noise and can be read from a greater distance when compared to the amplitude information [25]. The noise immunity can be improved further by using different signal processing techniques, such as moving average filtering, tag localization, signal space representation of frequency signatures, and many others [21]. In addition, calibration process for data decoding using the ‘no tag’ data as the reference will also reduce the impact of environmental interference and system noise [21]. E. Effect of Tag Orientation

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Fig. 8. Effect of the change in orientation angle on (a) co-polar and cross-polar notch depths at resonance, and (b) resonant frequencies.

Mismatch on Tag Response

If the ‘U’ slotted DP tag is rotated by an angle with the E-field polarization of the reader antenna, then the incident V-polarized RF signal will serve a small component to the H-slots to respond. As a result, the H-slots (cross-polar) will also respond back partly in V-polarity and the V-probe receiver will receive the combined response from both V-slots (co-polar) and H-slots (cross-polar) and vice versa. If this rotation angle is small, then the cross-polar responses from orthogonal slots will be small too, and these effects will not be able to alter the encoded bit patters in the co-polar slots. But if the rotation angle keeps on increasing, then the co-polar response will start diminishing, whereas the cross-polar response will start dominating and beyond a certain angle of rotation, the cross-polar effect will be significant enough to alter the encoded co-polar bits. The effects of changes in the orientation angle on co-polar and cross-polar notch depth at resonance and on resonant frequency are shown in Fig. 8 for a clear view. From Fig. 8(a), it is seen that the co-polar notch depth value at resonance decreases from 50 dBsm to 0 dBsm (dashed line) with the increase in the orientation mismatch from 0 to 90 and more than 40 dBsm notch depth is obtained at resonance for up to 30 of orientation mismatch. In contrast, the contribution from the cross-polar slot increases from 0 to 50 dBsm (solid line), when the mismatch angle increases from 0 to 90 . However, up to 30 of orientation mismatch, the cross-polar response rises to only 2.1 dBsm. Moreover, only a small shift is observed in the resonant frequency notch position for 30 of mismatch (Fig. 8(b)). Furthermore, this small contribution from cross-polar slots ( 2.1 dBsm) can be overcome by adding some threshold conditions in the reader detection algorithm, such as greater than 3 dBsm difference is needed to change the logic level of a bit from ‘1’ to ‘0’ and vice versa. In this way, the proposed dual-polarized tag can be used up to a certain degree (e.g., ) of orientation independency. However, if the DP tag is rotated by an angle of 90 , then the encoded bits in the H- and V-polarity inside the tag will be read as V- and H-polar data in the reader, respectively. This 90 mismatch can be overcome by using slightly different frequency resonators in the V- and H-polarity within the DP bandwidth for differentiating them in the reader. IV. DIFFERENT PARAMETERS' EFFECT ON CHIPLESS TAGS Frequency response of printed tags over different materials will differ due to their different electromagnetic properties. In addition, conductivity of the inks also affects the selectivity of notches at resonance. Furthermore, if the tag is placed inside two

Fig. 9. Effect of the change in ink conductivity on the (a) resonant bandwidth and frequencies, and (b) notch depth at resonance.

layers, then permittivity of both the superstrate and the substrate are needed to be considered for calculating the resonant frequencies. Thorough discussions about these parameter effects on the tag response are made in this section. A. Effect of Ink Conductivity

on Tag Response

Conductive inks are usually formed from three major constituents (i) silver/metal 45 65%, (ii) polymer 6 4%, and (iii) solvent 49 31%. The amount of silver/metal significantly improves the ink conductivity; however, it will increase the cost of the conductive ink significantly. Investigations are going on different types of techniques for printing with conductive ink, such as, Gravure, Screen, Flexo, etc., to reduce the printing cost, as well as having good ink conductivity. Although, for proving the design concept, researchers usually use annealed copper with conductivity, during their tag simulation and fabrication process, the conductivities of the available conductive inks in the market are much lower than this. To check the effect of conductive ink on the tag response, it is simulated using different conductivity values, varied from a perfect electric conductor (PEC) to a metal with very low . The effect of the metallic ink conductivity on the resonant bandwidth (BW), frequency and notch depth at resonance are shown in Fig. 9. From the solid line in Fig. 9(a), it is seen that the bandwidth at resonance affects significantly by the ink conductivity. From PEC to a lower value up to , the bandwidth remains less than 0.75 GHz and for further dropping in the conductivity, it increases sharply to 1.75 GHz. The resonant frequency is not affected much for the ink conductivity value up to , which is shown with the dotted line in Fig. 9(a). Effect of the ink conductivity on notch depth at resonance is shown in Fig. 9(b), which is similar to its effect on bandwidth. Maximum 40 dBsm notch depth is observed for PEC and it reduces to 10 dBsm for the conductivity, and after that it reduces further, which will be

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Fig. 10. (a) Non-etched tag, (b) etched tag, and (c) comparison between them.

Fig. 11. Effect of the change in the substrate relative permittivity on (a) resonant bandwidth and frequencies, and (b) notch depth at resonance.

harder to detect using chipless RFID tag readers. Hence, it can be inferred that, though the depth of the frequency notch reduces and its BW also increases with the decrease in the conductivity value, it is still acceptable to have an ink with a conductivity value as low as for printing frequency domain based chipless tags. The total amount of ink required for printing a bulk amount of tags is also a concern for commercialization. Therefore, an investigation is made in this research to reduce the requirement of ink in the proposed ‘U’ slotted tag design. From the surface current densities around the slots at their resonances, it has been noted that the solid metal part in the middle of the ‘U’ slots marked in Fig. 10(a), is not required for providing the current path at resonance for the ‘U’ slots and hence, it should not affect the ‘U’ slot's performance at resonance. Therefore, the metal part in the middle is etched as shown in Fig. 10(b) and the simulation results for this etched tag is compared with the non-etched tag, which is shown in Fig. 10(c). From the simulation results, it is proved that these two tags perform equally, which is also supported later by their measurement results. In addition, the etched tag reduces the ink requirement to 70% of its previous requirement without deteriorating the performance. Similar metal etching technique can also be used in the middle part of the ‘O’ [12] and the ‘I’ slotted [11] tags to reduce their ink consumption, as well as their printing costs. B. Effect of Permittivity

Fig. 12. (a) Card layers and (b) simulation results for different combinations.

The notch depth at resonance decreases with the increase in the permittivity value, which is shown in Fig. 11(b). Moreover, when chipped tags are buried inside papers or plastics, the layers over (superstrate) and under (substrate) the tags do not alter the encoded bits inside them, as the data are encoded inside the chips. On the other hand, frequency domain based chipless RFID tags perform based on the resonances of the used resonators, which vary with the permittivity values of the substrates. Hence, to be used in these types of applications, the designed tag dimensions are just needed to be re-adjusted based on the permittivity values of the used layers. This scenario is explained for a typical ID card with few layers as shown in Fig. 12(a) [3], where the tag is simulated for three different conditions. It is seen that in all cases, the ID card configuration creates significant notches; however, the dimensions of the slots are needed to be re-adjusted prior to printing to fix the shifts in the resonances. In case of a superstrate, the formula for determining the half wave ‘U’ slot length for a particular resonant frequency is needed to be modified as (2) [26], where the relative permittivity of the superstrate is also considered. In addition, if the tag is printed on a separate material (substrate 1) as shown in Fig. 12(a) and two layers are added, one in-front (superstrate) and the other behind (substrate 2) the tag, then the equivalent permittivity of the substrate, can be calculated by (3) [26]. Here, and are the thickness of substrate 1 and substrate 2, respectively. Tag design can be modified after determining of the substrate for a particular item type to obtain resonance at particular frequencies. (2)

(3)

of Substrates on Tag Response

The effect of the relative permittivity on the tag response is shown in Fig. 11. The ‘ ’ of the tag substrate is varied from 2 to 4 in the simulation, as the common plastic and paper items have relative permittivity values within this range and its effects on an unchanged ‘U’ slot resonant notch bandwidth and resonant frequency are shown in Fig. 11(a) with a solid and a dashed line, respectively. It is seen that, both the resonant bandwidth and frequency decrease gradually with the increase in the permittivity value.

C. Effect of Loss Tangent

on Tag Response

value of a substrate is another imporLoss tangent tant parameter that substantially affects the performance of the tag. Researchers usually use substrates with very low loss tangent values for their proof of concept tag development, such as, Taconic TLX with loss tangent value, is used in this paper as the substrate during the tag design and fabrication process. However, in real field, paper and plastic materials will be used as the substrate and usually they have higher

ISLAM AND KARMAKAR: REAL-WORLD IMPLEMENTATION CHALLENGES OF A NOVEL DUAL-POLARIZED COMPACT PRINTABLE CHIPLESS RFID TAG

Fig. 13. Effect of change in substrate loss tangent on (a) resonant bandwidth and frequencies, and (b) notch depth at resonance.

wise readers, for example, same tags printed on banknotes will be read by a banknote reader and printed on postage stamps will be read by a different postage stamp reader worldwide. Some of the required RF parameters, such as, ink conductivity, thickness, surface roughness, resistance, printing resolution, etc., are usually provided by the manufacturers. However, RF properties of the substrates are needed to be characterized, which include determining the relative permittivity and loss tangent of the substrate, as they are not usually provided by the manufacturer at the required frequency. In this section, a quick guideline is provided for approximate determination of and of the substrates, which will be used first to adjust the tag dimension. Then, after measuring the printed tags, tag dimensions can be readjusted and finalized in their next iterations. A. Determination of Permittivity

Fig. 14. Effect of change in substrate thickness on (a) resonant bandwidth and frequencies, and (b) notch depth at resonance.

losses than the low loss Taconic substrate. To check the effect of the loss tangent on the tag response, it is simulated for different values, varied from 0.002 to 0.2. The effect of on the resonant notch bandwidth, notch depth at resonance, and frequency at resonance are shown in Fig. 13. The solid line in Fig. 13(a) shows that, the bandwidth at resonance increases from 0.45 GHz to 1 GHz, when the value of the increases from 0.002 to 0.2. The resonant frequency is not affected much due to the change in the value, which is shown by the dashed line in Fig. 13(a). The most significant effect of is seen on the notch depth values at resonance, which is shown in Fig. 13(b). Maximum 35 dBsm notch depth is observed for and it reduces to 10 dBsm for and after that it reduces further, which will be harder to detect using tag readers. Therefore, a lower value is desirable to achieve a higher notch depth with lower bandwidth and it is still acceptable to have a dielectric substrate material with the value as high as 0.1 to get a chipless RFID tag with detectable notches. D. Effect of Substrate Thickness

on Tag Response

Thickness of paper and plastic packets of different items takes a wide range of values based on their application areas. Effect of different substrate thickness on the bandwidth and frequency at resonance, and notch depth at resonance are shown in Fig. 14(a) and (b), respectively. It is seen that, the resonant bandwidth and notch depth reduce very slowly with the increase in the thickness. The resonant frequency changes in a very small scale due to the increase in the thickness. V. CHARACTERIZATION PROCESS OF TAG SUBSTRATES Tag dimensions are needed to be readjusted to make all of them resonant at their predetermined frequencies to facilitate reading by a single tag reader worldwide. In contrast, the same design can be printed on different items and can be read by item-

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of Paper Substrate

The relative permittivity of the substrate is planned to be determined by printing and measuring different simple resonant structure using conductive ink and matching them with the simulation results. However, notch depth at the resonant frequency of few common resonators traditionally used for characterization, such as, line resonator and ring resonator are very sensitive to printing inaccuracy. Hence, simple patch antenna is chosen for characterization, as its resonant notch depth is more reluctant to printing inaccuracy. Resonant frequency of a rectangular patch antenna as shown in Fig. 15(a) can be determined from (4) [27].

(4) where and are the length and width of the patch, and are the resonant mode number, and is the effective dielectric constant, which is related to the relative dielectric constant as (5) [27], where is the substrate thickness.

(5) ; Eqn. (5) can be approximated as (6), where here, is the extended incremental length, which can be neglected for thin substrates [27]. (6) Eqn. (6) can be expressed as (7) to calculate the value of effective dielectric constant

(7) From the measured resonant frequencies of the printed patches, can be calculated using effective dielectric constant (7). From the values of , relative permittivity of the substrate can be determined using (5). The determined

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Fig. 15. (a) General layout of a patch antenna with parameters, (b) assembled printed patch antenna, and (c) simulation and measured results comparison.

TABLE II AND CORRESPONDING PRINTED PATCH ANTENNA DIMENSIONS, MEASURED VALUES FROM (7) AND CST SIMULATION

Fig. 16. Simulated and measured refection coefficients matching by values for (a) Patch P6 and (b) Patch P7. varying loss tangent

considers the losses inside the substrates. The dielectric quality factor of a substrate can be represented as (8)

(8)

permittivity values can be compared with CST Microwave Studio (MWS) simulation results for further reliability. Patches with different dimensions and resonant frequencies are designed in CST MWS and they are next printed on paper substrate using a thermal printer manufactured by SATO (detail on the printing process is provided in Section VI). Printed patches on paper are then connected with SMA connectors using epoxy and their refection coefficients are measured in the VNA. One of the assembled printed antennas is shown in Fig. 15(b) and its measured result is shown in Fig. 15(c) with a red dotted line. The same antenna is simulated again in CST with variable values to find out the matched value with the measured result for that patch, which is shown in Fig. 15(c) with a black solid line. In this way, values for 10 different patches are determined. Eqn. (7) is also used for determining the values for comparison. The dimensions of the 10 patches, their measured resonant frequencies and corresponding approximate values of calculated from (7) and CST matched values are listed in Table II. From these values, the average relative permittivity value for the used paper substrate is found equal to 2.74 from CST (Table II). Here, the standard deviation of the measured permittivity values with the average value is found only 0.064, which confirms an acceptable accuracy and precision in the measured data during of the experiment. This average permittivity value (2.74) is used in the next section for calculating the loss tangent value. B. Determination of Loss Tangent

of Paper Substrate

Due to the difference in losses inside substrates, the amount of current over the metallic surface differs, which affects the radiation from the patch and loss tangent is a parameter that

where, is the angular resonant frequency, is the total energy stored in the patch at resonance, is the dielectric loss, and is the loss tangent of the dielectric. It is noticed from (8) that, the dielectric quality factor is inversely related to the loss tangent value of the substrate. Hence, a substrate with lower value is desirable from the tag design viewpoint, as it will help to achieve a tag with sharper notches and more number of bits within a fixed bandwidth. The printed patch antennas are simulated in CST MWS using the permittivity value found in the previous section. During the simulation, the value is varied to match the bandwidth and depth of the simulation results with the measurement results and two of the matched results are shown in Fig. 16(a) and (b). From the matching, it is found that, for value of 0.02, similar results as measurement can be replicated in simulation for most of the patches. C. Proximity Reading Performance of Printed Patch Tags The values achieved after characterization of the paper substrate (permittivity, , loss tangent, , and paper thickness provided by the manufacturer, ) are used to design co-planar patch tags as shown in Fig. 17(a). Three patch tags with different dimensions are printed on the paper using the same SATO thermal printer used during the characterization process. The printed patch tags are then measured as a 1-bit chipless tag in the near field as shown in Fig. 17(b), which is similar to the proximity measurement setup used in [3] for the ‘U’ slot loaded tag measurement. The measured results are then compared with the simulated results and one comparison graphs for patch tag P6 is shown in Fig. 17(c), which shows a decent agreement between simulation and measurement results. In the other two cases for patch tag P3 and patch tag P9, acceptable differences are seen between the simulated and measured results, values of which are listed in Table III. These differences might be overcome through perfect transfer of the conductive ribbon in thermal printing to the paper, which could be investigated further in a better printer with higher resolution and consistency.

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Fig. 17. (a) General layout of a patch tag with parameters, (b) near-field waveguide measurement setup of a SATO thermal printed patch tag, and (c) plot for simulated and measured results comparison.

TABLE III PRINTED PATCH TAG DIMENSIONS, MEASURED ‘ ’ , AND CORRESPONDING SIMULATED ‘ ’ Values

Fig. 18. (a) Thermal printer developed by SATO and (b) tag printing process.

VI. PRINTING PROCESS, ERRORS, AND THEIR SOLUTIONS Error in determining the of the substrate results in a left or right shift in the resonant frequencies of the tag resonators, which can be easily adjusted by slight decrement or increment in the resonators' lengths before finalizing the tag designs. On the other hand, of a particular paper affects the quality factor of each resonator on it, which will limit the maximum number of bits that can be encoded on that paper. However, if the error happens inconsistently in the printing process, then it cannot be overcome. Therefore, investigations are carried out in this section on the tag printing process, different types of errors in printing, effect of ageing on tag substrates and conductive inks, and their probable solutions. A. Chipless RFID Tag Printing Process in Thermal Printer For large scale commercial tag manufacturing, Gravure, Screen, and Flexo printing techniques can be used. Their printing resolution and ink conductivity are improving day by day with a decrease in their costs. However, a small thermal printer as shown in Fig. 18(a) is used for printing different shapes in this research and a small printer like this can be used in retail shops for printing their tags. Here, direct thermal transfer is done from a conductive silver ribbon to a paper substrate. The used thermal ribbon is resin based and has a conductivity value of and a thickness of 4.5 micrometer. Tag printing procedure using this thermal printer is shown in the flowchart of Fig. 18(b). First, tag designs are needed to be optimized in any full-wave EM solver according to the requirement and substrate specifications. Then, it is needed to be exported as a bitmap ( .bmp) file with 609 DPI resolution, as 609 DPI is the used thermal printer's maximum resolution. Then, after setting up a proper connection with the printer, a selected tag can be printed in the SATO thermal printer. From a prototype tag design, all bit combinations can be generated automatically and stored inside a SATO thermal printer using available software, which can be printed instantly from the printer like barcode printing.

Fig. 19. Error comparison between rectangular and circular shapes (a) normal view and (b) expanded view, which shows higher deviation in circular shapes.

B. Error in Printing Different Shapes It is found that, rectangular shapes are printed more accurately in the thermal printer than circular shapes. In Fig. 19(a), rectangular ‘U’ slotted tag [3] and circular ‘O’ slot loaded tag [12] are compared and their zoomed versions which are shown in Fig. 19(b). It is clearly visible that, rectangular slots are perfect, whereas circular slots are pixelated and when tag printing will be required in sub-millimeter level of accuracy, circular shapes would be more prone to this printing error. Therefore, the ‘U’ slotted DP-OI tags presented in this paper are more reluctant to the printing errors and can be printed more accurately than other shapes in the thermal printer. C. Error in Printing Vertical and Horizontal Edges The thermal printer also shows some inconsistency in printing vertical, horizontal, and square edges of a rectangular shape, which are depicted for a square patch with vertical (V) and horizontal (H) insets as shown in Fig. 20. Here, the edges of the horizontal insets seem near perfect, whereas the vertical edges are found a bit zigzag when observed carefully under microscope in 200 times magnified view. Moreover, rectangular edges are also printed a bit roundish by the thermal printer. These inconsistencies are needed to be included during the tag simulation to avoid any unidentifiable effect afterwards. D. Error in Printing Vertical and Horizontal Lengths The last inconsistency in printing to be addressed is the difference in vertical and horizontal lengths of the printed output from the input values. For example, the input file to the thermal

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VII. CONCLUSION

Fig. 20. Printing inconsistency in horizontal, vertical , and square edges.

Fig. 21. Size comparison between (a) input file and (b) printed output image.

printer is a square patch with length and width ‘ ’. But the printed output patch dimension is horizontal length ‘ ’ and the vertical length ‘ ’, which are portrayed in Fig. 21(a) and (b). Usually, this happens to a particular direction (vertical or horizontal); therefore, it can be compensated by adjusting the dimension of the affected side in the input file. E. Effect of Ageing on Tag Substrates and Conductive Inks Though the plastic substrates are very reluctant to the ageing effect, paper substrates might be affected significantly due to the ageing and adverse environment. As the resonant frequencies depend on the tag substrate thickness, therefore, change in the substrate thickness will affect the tag's resonant frequencies. Moreover, the amount of moisture in the paper will also affect its permittivity and loss tangent values, and these will change the resonant frequency notch positions and notch depths as well. In addition, the conductivity of the ink will also be affected significantly with ageing, if no protection layer is placed over them. Due to these ageing effects on the tag substrates and inks, the original encoded data in paper printed tags might move and after a certain degree of change in the initial values, tags will not be giving the original encoded data. Therefore, to avoid the long term ageing and environmental effects on the chipless RFID tags, a protection layer should be added in addition of their proper monitoring. Besides, this study on ageing and moisture like environmental effects might open a new research field in chipless RFID. In summary, from these studies, insights can be achieved on the thermal printer tag printing process, errors in printing circular shapes, in vertical, horizontal, and square edges, in V-H dimensions, and effect of ageing on tag substrates and conductive inks with solutions, which can be utilized to realize the printable chipless RFID tags in real-field.

A novel compact printable dual-polarized chipless RFID tag is presented in this paper with its practical implementation challenges. The proposed tag encoding concept is based on (a) obtaining double number of bits within a fixed frequency band using dual-polarization and (b) reducing the tag size by incorporating slot-length variation encoding technique. These concepts have been proved by the simulation and measurement of a 16-bit DP tag prototype. Then, detail parametric studies on the effect of different substrate and ink properties are described. First, the effect of ink conductivity on the tag response is described, which is followed by the discussion on the effect of substrate permittivity on the tag response. Next, the effects of loss tangent on the tag response are discussed. Then, a quick approximate paper characterization technique is described, where patches are printed on the paper, measured, simulated, and compared to determine the paper permittivity and loss tangent values. These values are next used to design single patch tags to check the accuracy of the determined values, which showed a good match. After that, tag's printing related issues are discussed in detail, which includes: detail tag printing procedure using a thermal printer, inaccuracies in printing circular shapes, vertical, horizontal and square edges, vertical and horizontal lengths, effect of ageing on tag substrates and conductive inks, and their probable solutions. This single sided compact tag has a great potential to be printed directly on many items like barcode, such as for anti-counterfeiting in banknotes, stamps, secured papers, and for identification in low-cost products. In future research, further investigations will be carried out on more printing technologies, their improvement in printing accuracy, printing resolution, and consistency in repeated printing with an improved ink and at a reduced printing cost. REFERENCES [1] P. Harrop and R. Das, “Printed and chipless RFID forecasts, technologies & players 2011–2021,” in IDTechEx Ltd., Cambridge, UK, 2011. [2] U. Kaiser and W. Steinhagen, “A low-power transponder IC for highperformance identification systems,” IEEE J. Solid-State Circuits, vol. 30, no. 3, pp. 306–310, Mar. 1995. [3] M. A. Islam and N. C. Karmakar, “A novel compact printable dualpolarized chipless RFID system,” IEEE Trans. Microw. Theory Techn., vol. 60, no. 7, pp. 2142–2151, Jul. 2012. [4] C. S. Hartmann, “A global SAW ID tag with large data capacity,” in Proc. IEEE Ultrasonics Symp., 2002, pp. 65–69. [5] S. Botao, C. Qiang, Y. Amin, D. S. Mendoza, L. Ran, and Z. Li-Rong, “An ultra-low-cost RFID tag with 1.67 Gbps data rate by ink-jet printing on paper substrate,” in Proc. IEEE Asian Solid-State Circuits Conf., 2010, pp. 1–4. [6] S. Preradovic and N. C. Karmakar, “Design of fully printable planar chipless RFID transponder with 35-bit data capacity,” in Proc. Eur. Microw. Conf. (EuMC), 2009, pp. 13–16. [7] J. Hyeong-Seok, L. Won-Gyu, O. Kyoung-Sub, M. Seong-Mo, and Y. Jong-Won, “Design of low-cost chipless system using printable chipless tag with electromagnetic code,” IEEE Microw. Wireless Compon. Lett., vol. 20, no. 11, pp. 640–642, Nov. 2010. [8] A. Vena, E. Perret, and S. Tedjini, “Design of compact and auto-compensated single-layer chipless RFID tag,” IEEE Trans. Microw. Theory Techn., vol. 60, no. 9, pp. 2913–2924, Sep. 2012. [9] M. Hamdi, F. Garet, L. Duvillaret, P. Martinez, and G. Eymin-PetotTourtollet, “New approach for chipless and low cost identification tag in the THz frequency domain,” in Proc. IEEE Int. Conf. RFID-Technol. Appl.(RFID-TA), 2012, pp. 24–28.

ISLAM AND KARMAKAR: REAL-WORLD IMPLEMENTATION CHALLENGES OF A NOVEL DUAL-POLARIZED COMPACT PRINTABLE CHIPLESS RFID TAG

[10] M. A. Islam and N. C. Karmakar, “Design of a 16-bit ultra-low cost fully printable slot-loaded dual-polarized chipless RFID tag,” in Proc. Asia-Pac. Microw. Conf. (APMC), 2011, pp. 1482–1485. [11] M. A. Islam and N. C. Karmakar, “Compact printable chipless RFID tags using polarization diversity,” in Proc. Eur. Microw. Conf. (EuMC), 2012, pp. 912–915. [12] M. A. Islam, Y. Yap, N. C. Karmakar, and A. K. M. Azad, “Orientation independent compact chipless RFID tag,” in Proc. IEEE Int. Conf. RFID-Technol. Appl. (RFID-TA), 2012, pp. 137–141. [13] M. A. Islam and N. C. Karmakar, “On a compact printable dual-polarized chipless RFID tag using slot length variation encoding technique for barcode replacement,” in IEEE MTT-S Int. Microw. Symp. Dig., May 2015, pp. 1–4. [14] G. Karimi and S. Majidifar, “A novel chipless RFID tag using spiral resonator to achieve the pentamerous data encoding form,” J. Electromagn. Waves and Appl., vol. 28, no. 1, pp. 13–27, 2014. [15] A. Vena, E. Perret, and S. Tedjini, “Chipless RFID tag using hybrid coding technique,” IEEE Trans. Microw. Theory Techn., vol. 59, no. 12, pp. 3356–3364, Dec. 2011. [16] SAR Code Identification Viewed on 03/06/2011 [Online]. Available: http://www.inksure.com/images/stories/presentations/SARCodeIntroduction%202 09.pdf, Inksure, 2009 [17] R. M. Mays and A. M. Grishin, “Microwave Readable Dielectric Barcode,” US Patent 20060125491, June 15, 2006. [18] N. C. Karmakar, E. M. Amin, and J. K. Saha, Chipless RFID Sensors. Hoboken, NJ, USA: Wiley, 2015. [19] N. C. Karmakar, R. Kosowatta, P. Kalansurya, and R. E. Azim, Chipless RFID Reader Architecture. Norwood, MA, USA: Artech House, 2013. [20] M. A. Islam, A. K. M. Azad, and N. C. Karmakar, “A novel reader architecture for chipless RFID tags,” in Proc. Asia-Pac. Int. Symp. Exhib. EMC (APEMC), 2013, pp. 193–196. [21] N. C. Karmakar, P. Kalansurya, R. E. Azim, and R. Kosowatta, Chipless RFID Reader Signal Processing. Hoboken, NJ, USA: Wiley, 2015. [22] A. Vena, E. Perret, S. Tedjini, G. Eymin-Petot-Tourtollet, A. Delattre, F. Garet, and Y. Boutant, “Design of chipless RFID tags printed on paper by flexography,” IEEE Trans. Antennas Propag., vol. 61, no. 12, pp. 5868– 5877, Dec. 2013. [23] M. A. Islam, “Compact Printable Chipless RFID Systems” Ph.D. dissertation, Dept. ECSE, Monash Univ., Clayton, Vic., Australia, 2014 [Online]. Available: http://arrow.monash.edu.au/hdl/ 1959.1/1049047, pp. 212 [24] A. Vena et al., “Design and realization of stretchable sewn chipless RFID tags and sensors for wearable applications,” in IEEE Int. Conf. RFID (RFID), 2013, pp. 176–183.

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[25] R. V. Koswatta, “Readers for Frequency Signature-Based Chipless RFID Tags,” Ph.D. dissertation, Dept. ECSE, Monash Univ., Clayton, Vic., Australia, 2013. [26] N. C. Karmakar, “Investigations into a cavity-backed circular-patch antenna,” IEEE Trans. Antennas Propag., vol. 50, no. 12, pp. 1706–1715, Dec. 2002. [27] C. A. Balanis, Antenna Theory, Analysis and Design, Second ed. Hoboken, NJ, USA: Wiley, 1982.

Md Aminul Islam (S'11) received the B.Sc. degree in electrical and electronic engineering from Bangladesh University of Engineering and Technology, Dhaka, Bangladesh, in October 2009, and the Ph.D. degree from Monash University, Clayton, Victoria, Australia, in October 2014. He worked as a Research Support Officer at Monash Microwave, Antennas, RFID, and Sensor (MMARS) laboratory in 2014–2015. Currently, he is working as an Assistant Professor at the Military Institute of Science and Technology (MIST), Bangladesh. His research interest is in chipless RFID tag, reader, and antenna designing.

Nemai Chandra Karmakar (S'91–M'91–SM'99) received the M.Sc. degree in electrical engineering from the University of Saskatchewan, SK, Canada, in 1991, and the Ph.D. degree from the University of Queensland, Brisbane, Queensland, Australia, in 1999. He is an Associate Professor with the Department of Electrical and Computer Systems Engineering, Monash University, Clayton, Victoria, Australia. He possesses approximately 20 years of teaching, design, and development experience in antennas, microwave active and passive circuits, and RFIDs in Canada, Australia, and Singapore. He has authored or coauthored over 300 referred journal and conference papers, 40 book chapters, and 8 books. He has 8 international patent applications on chipless RFID and sensors.

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Gesture Sensing Using Retransmitted Wireless Communication Signals Based on Doppler Radar Technology Fu-Kang Wang, Member, IEEE, Mu-Cyun Tang, Yen-Chen Chiu, and Tzyy-Sheng Horng, Senior Member, IEEE

Abstract—This paper presents a Doppler radar based on an injection-locked quadrature receiver (ILQR) architecture that can use the wireless communication signals from an input cable or an antenna to perform gesture sensing at a short distance. Since the proposed radar does not require an illumination source, radio interference does not occur. To study parametrically the effect of the signal parameters on radar detection performance, a simulation was carried out by modeling the radar system in the discrete-time domain, and the results were verified experimentally using an actuator. In demonstrated applications, the radar uses an input 20 MHz Long-Term Evolution (LTE) signal or captures an ambient Wi-Fi signal to detect several gestures quite successfully. Index Terms—Doppler radar, gesture sensor, injection locking, injection-locked quadrature receiver, injection pulling, radio interference, Wi-Fi radar, wireless communication signal.

I. INTRODUCTION

W

IRELESS control using gestures in mobile devices, game stations and smart homes is gaining popularity, and therefore has attracted great attention from the worldwide information and communications technology industry. Most gesture sensors are of the contact type, such as inertia sensors in the Wii system [1], bend sensors in the CyberGlove system [2], and electromyographic sensors in the Myo system [3]. However, non-contact gesture sensors are more favored because they allow for more freedom in the making of the gestures. The most well-known example is Xbox Kinect, which is a device that tracks a user's gestures based on a three-dimensional video analysis [4]. However, the device consumes considerable power and is affected by ambient light conditions. Moreover, the device cannot detect through obstacles. Other infrared-based [5] and electric-near-field-based [6] gesture sensors may solve the problems of power consumption and background light, but

Manuscript received July 01, 2015; revised September 18, 2015; accepted October 20, 2015. Date of publication November 13, 2015; date of current version December 02, 2015. This work was supported in part by the Ministry of Science and Technology, Taiwan, under Grant MOST 103-2221-E-110-013-MY3 and Grant MOST 103-2221-E-110-016-MY2. This paper is an expanded version from the IEEE MTT-S International Microwave Symposium, Phoenix, AZ, USA, May 17–22, 2015. The authors are with the Department of Electrical Engineering, National Sun Yat-Sen University, Kaohsiung 804, Taiwan, R.O.C. (e-mail: [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2015.2495298

they do so at the expense of reduced sensing range and they still cannot detect through obstacles. Ultrasonic [7]–[9] and microwave [10]–[12] Doppler radars consume much less power and react much faster in gesture detection than do the aforementioned non-Doppler-based sensors. Furthermore, these radars can sense gestures when they are concealed in the clothes or bags and even behind walls. Nonetheless, interference between these radars, which all use similar frequencies, is a problem as it degrades the quality of the captured Doppler signal. Ambient noise and interferers also degrade the quality of the Doppler signal. This problem is particularly evident for microwave Doppler radars which may be overwhelmed by wireless communication devices that are present in the environment. Unfortunately, microwave Doppler radars have not been regulated by standards that seek to resolve radio interference with wireless communication devices. Passive radar is a receive-only radar that exploits radio energy from the environment as the transmission source. Over the past decade or more, there have been many communication signals utilized as “illuminators of opportunity” for this radar, such as television, direct-broadcast satellite, FM radio, global system for mobile communication (GSM), worldwide inter-operability for microwave access (WiMAX), digital audio/video broadcast (DAB/DVB), and Wi-Fi signals [13]–[20]. The conventional passive radar consists of two separate receivers with their own antennas to receive the direct path reference signal from the opportunity transmitter and the echo signal reflected from the target. Then, the Doppler information can be processed by correlating/mixing these two received signals. However, such a signal-reception mechanism is difficult to implement in indoor environments because of multipath reflections. Recently, based on the concept of passive radar, gesture sensors that use wireless communication signals have been extensively reported upon. Pu et al. presented a WiSee system to sense and recognize human gestures and motion by leveraging Wi-Fi signals in an indoor environment [21]. However, this system requires a data-equalizing re-encoder to transform each received orthogonal frequency-division multiplexing (OFDM) symbol through a Wi-Fi connection into the same symbol for creating narrowband signals with a clear Doppler shift, greatly increasing the complexity of baseband processing. Kellogg et al. proposed an Allsee system that extracts Doppler information from the amplitude of wireless communications signals, such as TV and RFID transmissions, for use in sensors with low complexity and power consumption, to enable always-on

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TABLE I LIST OF COMPONENTS USED IN THE RADAR SYSTEM

various received signal conditions was unclear. This paper includes a parametric investigation of the influence of the key received signal parameters on the detection performance of the radar. Quantitative simulations and experiments are conducted to confirm the findings of this parametric study. The rest of the paper is organized as follows: Section II discusses the architecture and operating principle of the proposed radar system. In Section III, the system simulation model and results are presented. Meanwhile, the experiments are conducted to verify the simulation results. Section IV demonstrates the application of the system to the detection of hand gestures. Finally, Section V provides the conclusion. II. SYSTEM ARCHITECTURE AND PRINCIPLE OF DETECTION

Fig. 1. Proposed Doppler radar for gesture sensing applications. (a) Block diagram. (b) Hardware implementation.

gesture recognition for smartphones and tablets [22]. Nevertheless, owing to the limited sensitivity of the amplitude detection circuit, the Allsee system needs to receive a sufficiently strong signal to recognize human gestures accurately. The authors' recent work [23] demonstrated a novel Doppler radar to perform gesture sensing with ambient wireless communication signals. This radar uses a similar concept to the passive radar that detects moving objects by processing echoes from opportunity transmitters. However, it differs from the passive radar by adding a retransmitting and coupling mechanism to separate the received echo signal from the received opportunity signal. The function of this radar was experimentally validated in an indoor Wi-Fi environment using an injection-locked quadrature receiver (ILQR) to provide sufficient sensitivity for reliable gesture detection. Nevertheless, the performance of the radar under

As shown in Fig. 1(a), the proposed Doppler radar comprises an ILQR, a branch-line coupler, two bandpass filters (BPFs), one transmit (TX) antenna, and one receive cable that is connected to an input signal source or a receive (RX) antenna. The ILQR consists of two cascaded low-noise amplifiers (LNAs), an injection-locked oscillator (ILO), a quadrature mixer, and two lowpass filters (LPFs). The output baseband in-phase (I) and quadrature (Q) signals of the receiver are sampled by a digital storage oscilloscope (DSO) and then processed by computer calculations to obtain Doppler information. Fig. 1(b) displays a prototype of the radar that operates in the 2.4–2.5 GHz frequency range to cover the 2.4 GHz Wi-Fi band and Long-Term Evolution (LTE) band 40. The ILO [24] and branch-line coupler [25] are PCB circuits that were made by the authors. The rest of the components are commercially available off-the-shelf items. The key specifications of these components are listed in Table I. The system receives a wireless communication signal from either the input signal source or the RX antenna and then passes this signal through the bandpass filters and branch-line coupler to the TX antenna. Then, the TX antenna radiates the received wireless communication signal as a radar source signal. Notably, the polarizations of the TX/RX antennas are orthogonal to each other to enhance their mutual isolation. The branch-line coupler provides, in addition to the TX and RX ports, another two ports for delivering the radar echo and reference signals

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with good isolation to the ILQR. The radar echo signal is the signal that is reflected from the hand as a gesture is made, while the radar reference signal is part of the received wireless communication signal. Both signals are coupled from the TX/RX ports to the ILQR with the help of the branch-line coupler. It is worth mentioning that the RF components in the proposed radar are similar to those in a conventional CW radar [11], except that a branch-line coupler is used to connect between the TX/RX antennas and the active RF circuits and an ILO, rather than a voltage-controlled oscillator (VCO), is used as a local oscillator. Since the proposed radar and the conventional CW radar have similar RF circuit complexity, their power consumption in the RF part should be similar to each other. Theoretically, the received wireless communication signal at the RX port is described by (1) and are the amplitude and phase modulawhere tions of the carrier wave at frequency . For simplicity, power dissipation and group delay in the antennas, bandpass filters, and branch-line coupler are not considered in this analysis. The signal that is transmitted by the TX antenna is expressed as (2) where is the through coefficient of the branch-line coupler. This transmitted signal is reflected from the hand and then received by the TX antenna as an echo signal when a gesture is made. This echo signal is coupled to the RF port of the branch-line coupler, as specified by (3).

where

is the amplitude of oscillation and (6)

is the locking range of the ILO with a tank quality factor . The subscript denotes the root mean square value. Equation (5) indicates that when the reference signal is injected into the ILO, the output signal of the ILO preserves the low-frequency phase modulation of the reference signal within the locking range of the ILO. In (5), represents the injection-pulled part of the phase modulation that happens when the offset frequency exceeds the locking range, i.e., , or approaches zero near the zero crossings. Moreover, is the delay of injection locking, which depends on the difference between the free-running oscillator frequency and the received signal carrier frequency , as given by [26] (7) where . The ILO output signal given by (5) is further split into two quadrature signals of equal amplitude as the local oscillator (LO) signals of the quadrature mixer. Lowpass filtering with a cutoff frequency set below yields the baseband I and Q signals of the ILQR as

(8)

(9) (3) where is the coupling coefficient of the branch-line coupler; is the instantaneous round-trip time between the hand and the TX antenna; is the echo coefficient of the moving hand, which depends on the distance or round-trip time between the hand and the TX antenna, and is the Doppler phase shift that is caused by the hand motion associated with the gesture. A part of the received wireless signal is coupled to the REF port of the branch-line coupler as a radar reference signal, as represented by (4).

where is the combined gain of the LNA and quadrature mixer; is the relative delay of the RF path to the LO path, and and represent the residual phase modulations resulting from the injection locking and injection pulling of the ILO, respectively. Generally, depends on the ILO output signal level in the locking range and is negligible compared to or for gesture detection at short range. Finally, the magnitude and phase of the IQ signal vector are obtained as

(4) In the ILQR, the radar echo signal given by (3) is amplified using two cascaded LNAs and then split into two in-phase signals of equal amplitude to provide the RF signals of the quadrature mixer. The radar reference signal is fed to an ILO which functions as a high gain and high selectivity bandpass amplifier when the offset frequency from the carrier is less than the locking range of the ILO, , resulting in an ILO output signal that is given by

(5)

(10)

(11) where MOD stands for a remainder function. The first term and the combination of the second and third terms on the right hand side of (11) are regarded as the dc offset and modulation noise, respectively, that are added to the Doppler phase shift .

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Fig. 2. Simulation platform for the radar system.

Notably, the first two of these terms can be minimized by satisfying the delay matching condition , while the third one can be suppressed by reducing the modulation or zero-crossing rates of the received wireless communication signal. Equation (11) reveals that under the delay matching condition, the phase modulation of the baseband signal is cancelled out within the locking range of the ILO and then the low-frequency phase of the baseband signal is mainly the Doppler phase shift . To evaluate more rigorously the Doppler signal quality in terms of the received signal parameters such as modulation type, symbol rate, received power, and RF path delay, a system simulation platform that is based on a discrete-time model of the ILO is established and discussed in the following section.

Fig. 3. Experimental setup for detecting a periodic back-and-forth motion of a metal plate. (a) Sketch and (b) photo.

A. Discrete-Time ILO Model

III. PERFORMANCE SIMULATION AND VERIFICATION Fig. 2 shows the system simulation platform, which is established in the Keysight Advanced Design System Ptolemy environment. This platform is composed of a wireless communication signal generator, a two-way power splitter, a Doppler phase modulator, a variable time-delay unit, a discrete-time ILO model, and a quadrature demodulator. In the signal processing simulation, the generator output signal is split along two paths. The signal along one path imitates the received RF signal that has been phase-modulated by a Doppler signal and then delayed for a variable time . The other path provides a reference signal that is injected into the ILO to generate a LO signal for use in the quadrature demodulator. The output baseband I and Q signals from the quadrature demodulator are used to recover the Doppler signal for comparison with the actual one. It is noted that a Chebyshev digital finite impulse response (FIR) lowpass filter with a cut-off frequency of 50 Hz is applied to these baseband signals. In this system simulation, the Doppler signal is given as a periodic triangular function to modulate the phase of the signal that is input to the phase modulator. Mathematically, this modulated phase is written as

Based on Adler's theory [27] and the authors' previous work [28], the ILO that receives by injection the reference modulation signal expressed in (4) has an instantaneous frequency:

(13) where (14) . In (13) and (14), Recall from (7) that represents the instantaneous phase difference between the freerunning oscillator signal and the injected reference modulation signal. Substituting (14) into (13) gives (15) where is the instantaneous phase of the ILO output signal. To solve the phase differential equation in (15), a discrete-time recursive approach is used, starting with the following finitedifference approximations:

(12) (16) where is a phase modulation index and is the speed of light. The ILO model used herein is based on an algorithm in the discrete-time domain that was derived by the authors as shown below.

(17) (18)

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where is an index of discrete time steps and is the time step of discretization. Then, discretizing (14) using approximations (16) and (17) yields a recursive equation for :

(19) The recursively calculated values of are substituted into another recursive equation that is derived from (15) and (18) to find the instantaneous phase variation of the ILO under the injection of modulation signal, which is given by

(20) Ultimately, the ILO output signal is reconstructed as (21) where (22) is the impulse response of the reconstruction filter. It is noted that (5) represents the output signal of an oscillator that is injected by a constant envelope modulated signal. To fit into this equation, the applied non-constant envelope modulated signal is approximated beforehand and expressed as a modulated signal with an average root-mean-square envelope. In contrast, (21) provides a much more comprehensive basis for analyzing the behavior of an oscillator with a non-constant envelope modulated injection signal than (5). B. Experimental Setup for Validation of Simulation Results Fig. 3 presents the experimental setup of the prototype radar shown in Fig. 1(b) to measure the motion of a metal plate that is about the size of a palm. This plate was controlled by an actuator to move in a periodic back-and-forth motion with a frequency of 0.1 Hz and a peak-to-peak displacement of 5 cm. The minimum distance between this plate and the TX antenna of the radar was 40 cm. A Keysight E4433B digital RF signal generator was used to generate continuous-wave (CW) and various wireless communication signals. Fig. 4(a) shows, as an example, the simulated spectrum of a generated 2.4 GHz LTE Time Domain Duplex (TDD) signal that uses OFDM 64-quadrature amplitude modulation (64-QAM) with a symbol rate of 20 Msps and an output power of 20 dBm. After being injected with this signal that has been passed through the BPF and branch-line coupler, the ILO yields an output spectrum that is also displayed in Fig. 4(a), which is determined by a combination of the injection-locking and pulling effects, as described by (5). These simulated spectra in Fig. 4(a) are in good agreement with the corresponding measured spectra that are shown in Fig. 4(b). In this case, the locking range of the ILO is estimated to be 2.65 MHz according to the simulation results.

Fig. 4. Received LTE TDD signal spectrum at a power level of 20 dBm and resultant ILO output signal spectrum at a power level of 7 dBm. (a) Simulation and (b) measurement.

Equalizing the frequencies of the free-running oscillator signal and the received reference modulation signal, , yields a delay of approximately 60 ns for the locking of the ILO by the injected modulation signal, as obtained using (7). Therefore, for delay matching, the RF path delay is set to the same value in both the simulation and experiment. The actual Doppler phase shift that is caused by the moving metal plate with a 5 cm periodic back-and-forth motion has a phase modulation index of and a peak-to-peak phase change of 288 according to (12). The simulation with the aforementioned settings yields the Doppler I and Q signals shown in Fig. 5(a). Since the applied Doppler phase-modulation frequency is only 0.1 Hz, which is much smaller than the locking range of the ILO, the dc offset and modulation noise that are added to the Doppler phase shift, as given by the first two terms on the right hand side of (11), are eliminated if the delay matching condition is satisfied, as it is in this case. Fig. 5(b) plots the magnitude and phase of the IQ signal vector, showing a rms magnitude of 13 mV and a rms phase error percentage (i.e., the rms difference between the actual and detected phases divided by the actual peak-to-peak phase change) of 3.3%. The glitches in the quadrature Doppler demodulation results seen in Figs. 5(a) and 5(b) arise mainly from the effect of injection pulling on the ILO output signal, particularly during the time periods near the zero crossings of the injected modulation signal. The experiment of detecting the motion of the actuator-controlled metal plate with the prototype radar yields the baseband I and Q signals. Further processing of these signals to obtain the desired Doppler signals requires an arctangent demodulation procedure that involves the processes of dc calibration and phase unwrapping [29], [30]. The details of the comparison between the simulated and experimental results are discussed in the following subsection. C. Effects of Various Signal Parameters and Conditions Figs. 6(a) and 6(b) respectively compare the simulated and experimental rms magnitudes and phase error percentages of the IQ signal vectors when the radar receives the 2.4 GHz OFDM 64-QAM signals with the same settings as before, except for the change in symbol rate. The comparisons show close agreement. These figures reveal that, as the symbol rate increases, the magnitude of the IQ signal vector declines while the phase error percentage thereof increases, so the quality of the Doppler

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Fig. 7. Effects of the delay mismatch of received LTE TDD signal on quadrature Doppler demodulation. (a) IQ magnitude. (b) IQ phase error percentage.

Fig. 5. Demodulated quadrature Doppler signals. (a) I and Q signals. (b) IQ magnitude and phase.

Fig. 8. Effects of the power of received LTE TDD signal on quadrature Doppler demodulation. (a) IQ magnitude. (b) IQ phase error percentage.

Fig. 6. Effects of the symbol rate of received LTE TDD signal on quadrature Doppler demodulation. (a) IQ magnitude. (b) IQ phase error percentage.

signal is degraded. This effect arises because a larger proportion of the signal bandwidth falls outside of the locking range of the ILO when a modulation signal with a higher symbol rate is injected. This phenomenon generally weakens injection-locking but strengthens injection-pulling. Unfortunately, for the radar system, the former effect contributes mostly to the signal while the latter contributes mostly to the noise in the Doppler band. Figs. 7(a) and 7(b) compare the results of the demodulated quadrature Doppler signals when the radar receives the same modulation signal as displayed in Fig. 4 with different delays. These different delays are realized by inserting one to several coaxial cables, each with a 14 ns delay, into the RF path whose original delay matches that of the LO path. The comparisons indicate similar trends between simulated and experimental results. Fig. 7(a) reveals that the delay mismatch has no detectable effect on the magnitude of the IQ signal vector because changing the RF path delay does not affect the locking range of the ILO. However, Fig. 7(b) indicates that the associated phase error percentage increases with the delay mismatch, primarily because

Fig. 9. Effects of the modulation type of received signal on quadrature Doppler demodulation. (a) IQ magnitude. (b) IQ phase error percentage.

the modulation noise term in (11) becomes more important. Figs. 8(a) and 8(b) present the demodulated results for the radar operating with the same modulation signal as displayed in Fig. 4 but with changes in received power. The simulated magnitude and phase error percentage of the IQ signal vector are highly consistent with the experimental data. In this radar, the amplitude of the RF and reference modulation signals increases in square root of the received signal power. This relationship not only enlarges the magnitude of the output IQ signal vector according to (10), but also improves the locking range of the ILO according to (6) and thereby lowers the associated phase error percentage. Figs. 9(a) and 9(b) compare the results of the demodulated quadrature Doppler signals that were obtained when the radar receives variously modulated 2.4 GHz signals. The symbol

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Fig. 10. Spectrum of the received LTE TDD signal of by the ILO leakage.

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50 dBm that is distorted

rate, delay mismatch, and received power of these signals are set to 20 Msps, 0 ns, and 20 dBm, respectively. The comparisons again reveal a close agreement between simulated and experimental data. Since the ILO produces an output signal completely synchronized with the received unmodulated continuous-wave (CW) signal, feeding the radar with this signal leads to the largest magnitude and lowest phase error percentage of the output IQ signal vector, and hence achieves the best Doppler signal quality among all of the received signals. Moreover, the Gaussian minimum shift keying (GMSK) signal concentrates more power density around the carrier frequency than does the quadrature phase shift keying (QPSK) or OFDM 64-QAM signal. The ILO output signal can therefore capture more phase information from the former signal within the locking range, causing the radar to achieve a better Doppler signal quality than the latter two modulation signals. The QPSK and 64-QAM OFDM signals are time-varying envelope modulation signals. The radar yields similar Doppler signal magnitudes in demodulating these two signals. However, the QPSK signal appears to have a higher zero-crossing rate than the OFDM 64-QAM signal [31], resulting in the highest Doppler signal phase error among all of the signals that were received by the radar. D. Limitations in System Sensitivity The limitation of the proposed radar is to require that the locking range of the ILO is much larger than the maximum Doppler frequency shift caused by the motion to be measured. This limitation restricts the minimum received signal power, but can be much improved by adding a LNA in front of the ILO. Nonetheless, one may be interested in this minimum received signal power that is known as the system sensitivity for the prototype radar to function properly. In this study, the lowest received signal power was set to 40 dBm because of the limitation of ILO leakage. As illustrated in Fig. 10, when the radar receives the OFDM 64-QAM signal with a power of 50 dBm, the signal spectrum measured in the air near the TX antenna is obviously distorted by the ILO leakage signal. It is therefore deduced that the ILO leakage signal becomes an important part of the radar source signal if the radar receives weak communication signals with power below 40 dBm. Operating under this situation, the radar may no longer be claimed not requiring an illumination source.

Fig. 11. Field test environment of the prototype radar used for detecting gestures.

IV. GESTURE SENSING APPLICATIONS Fig. 11 shows the field test environment. The radar, placed in an instrument room, performs gesture sensing with two experimental setups. In the first setup, the radar uses the RX antenna that is connected to the input terminal of the branch-line coupler to capture the through-wall Wi-Fi signals generated by an IEEE 802.11 b/g/n access point (AP) in an adjacent office room. The AP runs in mixed b/g/n mode with a maximum bandwidth of 20 MHz. The received Wi-Fi signal at the RX antenna of the radar has a center frequency of 2.412 GHz and a power of about 40 dBm. Figs. 12(a) and 12(b) shows the measured spectra of the received Wi-Fi signal and the resultant ILO output signal, respectively. Fig. 12(b) reveals that the weak Wi-Fi injection signal causes the ILO to reduce the locking range significantly compared to the previous case shown in Fig. 4(b). In the second setup, the radar uses a signal generator instead in connection to the input terminal of the branch-line coupler to input a 2.412 GHz LTE TDD signal with a power of 20 dBm and a symbol rate of 20 Msps. The operating frequency of the ILO in these two setups is set to 2.412 GHz to make in (7) zero for a minimum delay during injection locking. When a gesture is made, the closet distance of the hand to the TX antenna of the radar is at least 40 cm. Fig. 13(a) presents the detection of a “push” gesture by the radar that uses the captured Wi-Fi signals from the AP. The subject moves his palm toward the TX antenna with a displacement of about 20 cm. Fig. 13(b) plots the output Doppler I and Q signals from the radar. The I signal leads the Q signal. In Fig. 13(c), the magnitude of the IQ signal vector, represented by the green line, rises from 0.3 to 4.7 mV across the period of the gesture. This rise in magnitude is attributed to an increase of the echo signal power as the palm moves closer to the TX

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Fig. 12. Measured signal spectra for the prototype radar using the ambient Wi-Fi AP signals to detect gestures. (a) Received Wi-Fi signal spectrum at a power level of about 40 dBm. (b) Resultant ILO output signal spectrum at a power level of 7 dBm.

Fig. 14. Field test results of the prototype radar in detecting a “push” gesture with the input LTE TDD signal. (a) Output I and Q signals. (b) Magnitude and phase of the IQ signal vector.

Fig. 13. Field test results of the prototype radar in detecting a “push” gesture with the ambient Wi-Fi AP signals. (a) Continuous shooting of the gesture. (b). Output I and Q signals. (c) Magnitude and phase of the IQ signal vector.

antenna. Nevertheless, due to multipath reflection interference, the plot of magnitude exhibits irregular fluctuations in the period between 0.8 and 1.1 s. By contrast, the unwrapped phase of the IQ signal vector, represented by the blue line, provides more useful information on the gesture. In this example, it changes smoothly from to during the period of the gesture. A phase difference of is obtained and divided by the factor to yield an estimated displacement of 20.3 cm in moving the palm toward the TX antenna. This estimated displacement is close to the actual one as mentioned above. Figs. 14(a) and 14(b) show the results of the demodulated quadrature Doppler signals when the radar detects the “push” gesture using the LTE TDD signal from the signal generator. Clearly, the noise on the data curves is obviously smaller than those in Figs. 13(b) and 13(c) because the received signal power

in this case is significantly larger. This gesture motion causes the magnitude and unwrapped phase to vary from 2.9 to 18.9 mV and from to , respectively, as shown in Fig. 14(b). The latter result can provide an estimate of the displacement of the gesture, which is 20.2 cm. Fig. 15(a) presents the detection of a “pull” gesture by the radar using the ambient Wi-Fi AP signals. The displacement of the gesture remains about 20 cm. The detection results of this gesture, as shown in Figs. 15(b) and 15(c), follows an opposite trend compared to those of a “push” gesture. In Fig. 15(b), the Q signal leads the I signal. In Fig. 14(c), the magnitude data decreases from 4.88 to 3.68 mV and the unwrapped phase data increases from to across the period of the gesture. The former information indicates that the echo signal becomes weaker as the palm moves away from the TX antenna. Moreover, the irregular magnitude fluctuations can be found in most of the period of the gesture motion. The latter information yields an estimated displacement of 20.3 cm, which agrees closely with the actual displacement, in moving the palm away from the TX antenna. Figs. 16(a) and 16(b) show the detection results of the “pull’ gesture from the radar using the LTE-TDD signal. The magnitude and unwrapped phase of the IQ signal vector in Fig. 16(b) change from 19.852 to 3.058 mV and from to , respectively, because of this gesture, where the latter result yields an estimated displacement of 20.1 cm for the gesture motion. Fig. 17(a) presents the last gesture “push-pull” with an about 20 cm peak-to-peak displacement. Figs. 17(b) and 17(c) show the detection outputs of the radar that uses the ambient Wi-Fi AP signals. The Doppler characteristics of a “push-pull” gesture can be approximately viewed as those of a “push” gesture followed by a “pull” gesture. In Fig. 17(b), the I signal leads the Q signal in 0–0.9 s while the Q signal leads the I signal in 1.1–2

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Fig. 15. Field test results of the prototype radar in detecting a “pull” gesture with the ambient Wi-Fi AP signals. (a) Continuous shooting of the gesture. (b). Output I and Q signals. (c) Magnitude and phase of the IQ signal vector.

Fig. 16. Field test results of the prototype radar in detecting a “pull” gesture with the input LTE TDD signal. (a) Output I and Q signals. (b) Magnitude and phase of the IQ signal vector.

s, exhibiting a phase reversal period between 0.9 and 1.1 s. In Fig. 17(c), the magnitude of the IQ signal vector has an obvious drop in the middle of the phase reversal period, which can be attributed to multipath fading. The unwrapped phase of the IQ signal vector, with a maximum value of 38.3 and a minimum

Fig. 17. Field test results of the prototype radar in detecting a “push-pull” gesture with the ambient Wi-Fi AP signals. (a) Continuous shooting of the gesture. (b). Output I and Q signals. (c) Magnitude and phase of the IQ signal vector.

value of , reveals an estimated peak-to-peak displacement of 20.6 cm. The “push-pull” gesture detection is repeated by using the LTE TDD signal, yielding the results shown in Figs. 18(a) and 18(b). In Fig. 18(a), a phase reversal period is identified from 0.9 to 1.2 s. The curve of the unwrapped phase in Fig. 18(b) shows a maximum value of 7.8 and a minimum value of . The peak-to-peak displacement is therefore calculated to be 20.3 cm. Based on Figs. 13 to 18, the radar uses ambient Wi-Fi AP or input LTE TDD signals to detect three gestures—“push”, “pull”, and “push-pull”. Regardless of which received signal is used, the locking ranges of the ILO in the prototype radar are much larger than the frequency range of the Doppler signals caused by the gestures, so the additive modulation noise resulting from the wireless communication signals can be effectively canceled and thereby the Doppler signals can be correctly detected. Therefore, the actual and detected displacements of the gestures agree very closely. The worst detected displacement error in the gesture sensing experiments is estimated below 1 cm. Undoubtedly, the detected phase information is much more useful than the detected magnitude information for determining the displacement of the gesture. Finally, a couple of comments should be made on the practical use of this work. One comment concerns the influence of possible surrounding clutters on the performance of the radar system. Generally speaking, the surrounding clutters, if

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REFERENCES

Fig. 18. Field test results of the prototype radar in detecting a “push-pull” gesture with the input LTE TDD signal. (a) Output I and Q signals. (b) Magnitude and phase of the IQ signal vector.

stationary, cause a dc offset in the output I and Q signals. If they are moving clutters, i.e., the reflections of the retransmitted signal from other moving targets, the resultant effects will impact the detection of gestures. However, since the gestures are made within a short distance from the radar, the illumination of other objects in the environment using the retransmitted signal is mostly blocked by the hand during the gesture period. Therefore, the overall effect of the surrounding clutters is not significant in the gesture period. The other comment is on the gesture recognition. By referring to [21] and [32], the gestures can be recognized using their Doppler signatures. The method first constructs a data set for the features of gestures that are extracted from the Doppler spectrogram. Then, the machine learning technique is used to train a classification algorithm to distinguish the gestures.

V. CONCLUSION This paper presents a Doppler radar that can retransmit a mobile device signal or a received ambient wireless signal for the purpose of sensing human gestures. Experiments that were conducted with various received signal parameters, including modulation type, symbol rate, RF path delay, and received power, confirm the operating effectiveness of the presented system architecture. Measurements agree closely with the results of discrete-time simulations. Finally, for gesture sensing applications, a prototype radar was demonstrated to accurately detect various gestures using the Wi-Fi signals produced by a far AP or an LTE TDD signal generated by an instrument. In the future, we will endeavor to deploy multiple radars to recognize three-dimensional gestures through their connections to all kinds of wireless communication devices.

[1] T. Schlömer, B. Poppinga, N. Henze, and S. Boll, “Gesture recognition with a wii controller,” in Proc. Int. Conf. Tangible Embedded Interaction, 2008, pp. 11–14. [2] L. Dipietro, A. Sabatini, and P. Dario, “A survey of glove-based systems and their applications,” IEEE Trans. Syst., Man, Cybern. C, Appl. Rev., vol. 38, no. 4, pp. 461–482, Jul. 2008. [3] A. Attenberger and K. Buchenrieder, “RemoteHand: A wireless myoelectric interface,” in Proc. Human-Computer Interaction Int. Conf., Part II, 2014, pp. 3–11. [4] Z. Zhang, “Microsoft kinect sensor and its effect,” IEEE Multimedia, vol. 19, no. 2, pp. 4–10, Feb. 2012. [5] Y. S. Kim and K.-H. Baek, “A motion gesture sensor using photodiodes with limited field-of-view,” Optics Express, vol. 21, no. 8, pp. 9206–9214, Apr. 2013. [6] M. Valtonen, L. Kaila, J. Mäentausta, and J. Vanhala, “Unobtrusive human height and posture recognition with a capacitive sensor,” J. Ambient Intell. Smart Environ., vol. 3, no. 4, pp. 305–332, Oct. 2011. [7] B. Raj, K. Kalgaonkar, C. Harrison, and P. Dietz, “Ultrasonic Doppler sensing in HCI,” IEEE Pervasive Comput., vol. 11, no. 2, pp. 24–29, Feb. 2012. [8] S. Gupta, D. Morris, S. Patel, and D. Tan, “Soundwave: Using the Doppler effect to sense gestures,” in Proc. SIGCHI Conf. Human Factors Comput. Syst., 2012, pp. 1911–1914. [9] R. J. Przybyla, H. Tang, S. E. Shelton, D. A. Horsley, and B. E. Boser, “3D ultrasonic gesture recognition,” in Int. Solid-State Circuits Conf. Dig. Tech., 2014, pp. 210–211. [10] F. Adib, Z. Kabelac, D. Katabi, and R. C. Miller, “3D tracking via body radio reflections,” in Proc. USENIX Conf. Netw. Syst. Design Implementation, 2014, pp. 1–13. [11] Q. Wan, Y. Li, C. Li, and R. Pal, “Gesture recognition for smart home applications using portable radar sensors,” in Proc. Int. Conf. IEEE Eng. Med. Biol. Soc., 2014, pp. 6414–6417. [12] P. Molchanov, S. Gupta, K. Kim, and K. Pulli, “Short-range FMCW monopulse radar for hand-gesture sensing,” in Proc. IEEE Radar Conf., 2015, pp. 1491–1496. [13] P. E. Howland, “Target tracking using television-based bistatic radar,” IEE Proc. Radar Sonar Navig., vol. 146, no. 3, pp. 166–174, Jun. 1999. [14] H. D. Griffiths, C. J. Baker, J. Baubert, N. Kitchen, and M. Treagust, “Bistatic radar using satellite-borne illuminators,” in Proc. IEE Radar Conf., 2002, pp. 1–5. [15] P. E. Howland, D. Maksimiuk, and G. Reitsma, “FM radio based bistatic radar,” IEE Proc. Radar Sonar Navig., vol. 152, no. 3, pp. 107–115, Jun. 2005. [16] D. K. P. Tan, H. Sun, Y. Lu, M. Lesturgie, and H. L. Chan, “Passive radar using global system for mobile communication signal: Theory, implementation and measurements,” IEE Proc. Radar Sonar Navig., vol. 152, no. 3, pp. 116–123, Jun. 2005. [17] Q. Wang, C. Hou, and Y. Lu, “An experimental study of WiMAXbased passive radar,” IEEE Trans. Microw. Theory Techn., vol. 58, no. 12, pp. 3502–3510, Dec. 2010. [18] C. R. Berger, B. Demissie, J. Heckenbach, P. Willett, and S. Zhou, “Signal processing for passive radar using OFDM waveforms,” IEEE J. Sel. Topics Signal Process., vol. 4, no. 1, pp. 226–238, Feb. 2010. [19] F. Colone, K. Woodbridge, H. Guo, D. Mason, and C. J. Baker, “Ambiguity function analysis of wireless LAN transmissions for passive radar,” IEEE Trans. Aerosp. Electron. Syst., vol. 47, no. 1, pp. 240–264, Jan. 2011. [20] J. E. Palmer, H. A. Harms, S. J. Searle, and L. M. Davis, “DVB-T passive radar signal processing,” IEEE Trans. Signal Process., vol. 61, no. 8, pp. 2116–2126, Apr. 2013. [21] Q. Pu, S. Gupta, S. Gollakota, and S. Patel, “Whole-home gesture recognition using wireless signals,” in Proc. Int. Conf. Mobile Comput. Netw., 2013, pp. 27–38. [22] B. Kellogg, V. Talla, and S. Gollakota, “Bringing gesture recognition to all devices,” in Proc. USENIX Conf. Netw. Syst. Design Implementation, 2014, pp. 1–14. [23] M.-C. Tang, F.-K. Wang, and T.-S. Horng, “Human gesture sensor using ambient wireless signals based on passive radar technology,” in IEEE MTT-S Int. Microw. Symp. Dig., 2015, pp. 1–4. [24] C.-T. Chen, T.-S. Horng, K.-C. Peng, and C.-J. Li, “High-gain and high-efficiency EER/polar transmitters using injection-locked oscillators,” IEEE Trans. Microw. Theory Techn., vol. 60, no. 12, pp. 4117–4128, Dec. 2012. [25] D. M. Pozar, Microwave Engineering, 4th ed. New York, NY, USA: Wiley, 2011, pp. 343–346.

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[26] C.-T. Chen, C.-H. Hsiao, T.-S. Horng, K.-C. Peng, and C.-J. Li, “Cognitive polar receiver using two injection-locked oscillator stages,” IEEE Trans. Microw. Theory Techn., vol. 59, no. 12, pp. 3484–3493, Dec. 2011. [27] R. Adler, “A study of locking phenomena in oscillators,” Proc. IRE, vol. 34, no. 6, pp. 351–357, Jun. 1946. [28] C.-J. Li, F.-K. Wang, T.-S. Horng, and K.-C. Peng, “A novel RF sensing circuit using injection locking and frequency demodulation for cognitive radio applications,” IEEE Trans. Microw. Theory Techn., vol. 57, no. 12, pp. 3143–3152, Nov. 2009. [29] B.-K. Park, O. Boric-Lubecke, and V. M. Lubecke, “Arctangent demodulation with DC offset compensation in quadrature doppler radar receiver systems,” IEEE Trans. Microw. Theory Techn., vol. 55, no. 5, pp. 1073–1079, May 2007. [30] Q. Lv et al., “High dynamic-range motion imaging based on linearizer Doppler radar sensor,” IEEE Trans. Microw. Theory Techn., vol. 62, no. 9, pp. 1837–1846, Sep. 2014. [31] X. Zhang, L. E. Larson, and P. M. Asbeck, “Linearity performance of outphasing power amplifier systems,” in Design of Linear RF Outphasing Power Amplifiers. Norwood, MA, USA: Artech House, 2003, pp. 35–85. [32] Y. Kim and H. Ling, “Human activity classification based on micro-Doppler signatures using a support vector machine,” IEEE Trans. Geosci. Remote Sens., vol. 47, no. 5, pp. 1328–1337, May 2009. Fu-Kang Wang (S'10–M'13) was born in Kaohsiung, Taiwan, on May 15, 1985. He received the B.S.E.E., M.S.E.E., and Ph. D. degrees from National Sun Yat-Sen University, Kaohsiung, Taiwan, in 2007, 2009, and 2013, respectively. After the compulsory military service in Taiwan, he joined the Department of Electrical Engineering, National Sun Yat-Sen University, Kaohsiung, Taiwan, as a Postdoctoral Research Fellow. He holds five U.S. Patents about radar systems. His research interest is focused on RF sensing techniques. Dr. Wang was awarded a grant by the Ministry of Science and Technology, Taiwan, to perform his postdoctoral research at Wearable Health Monitoring Laboratory, Interuniversity Micro-Electronics Center (IMEC), Leuven, Belgium, in 2015. He was the recipient of the Outstanding Doctoral Dissertation Award presented by National Sun Yat-Sen University in 2013. He was also the recipient of the Postdoctoral Research Abroad Program Fellowship granted by the Ministry of Science and Technology, Taiwan, in 2014.

Mu-Cyun Tang was born November 13, 1989, in Kaohsiung, Taiwan. He received the B.S.E.E. degree from National Sun Yat-Sen University, Kaohsiung, Taiwan, in 2014. He is currently working toward the Ph.D. degree in electrical engineering at National Sun Yat-Sen University, Kaohsiung, Taiwan. His research interests include wireless sensing technologies and their biomedical applications.

Yen-Chen Chiu was born October 30, 1989, in Taoyuan, Taiwan. He received the B.S.E.E. and M.S.E.E. degrees from National Sun Yat-Sen University, Kaohsiung, Taiwan, in 2012 and 2014, respectively. His M.S. thesis work is dedicated to detecting hand gestures and vital signs using a Doppler radar.

Tzyy-Sheng Horng (S'88–M'92–SM'05) was born in Taichung, Taiwan, on December 7, 1963. He received the B.S.E.E. degree from National Taiwan University, Taipei, Taiwan, in 1985, and the M.S.E.E. and Ph.D. degrees from the University of California at Los Angeles (UCLA), in 1990 and 1992, respectively. Since August 1992, he has been with the Department of Electrical Engineering, National Sun Yat-Sen University, Kaohsiung, Taiwan, where he was the Director of the Telecommunication Research and Development Center (2003–2008) and Director of the Institute of Communications Engineering (2004–2007), and where he is currently a Professor. He has authored or coauthored over 230 technical publications published in refereed journals and conferences proceedings, mostly in IEEE publications. He holds over 10 U.S. patents. His research interests include RF and microwave ICs and components, RF signal integrity for wireless system-in-package, digitally assisted RF technologies, and green radios for cognitive sensors and Doppler radars. Dr. Horng has served on several Technical Program Committees of international conferences including the International Association of Science and Technology for Development (IASTED) International Conference on Wireless and Optical Communications, the IEEE Region 10 International Technical Conference, the IEEE International Workshop on Electrical Design of Advanced Packaging and Systems (EDAPS), the Asia-Pacific Microwave Conference (APMC), the IEEE Radio and Wireless Symposium (RWS), and the Electronic Components and Technology Conference (ECTC). He has also served on the Project Review Board in the Programs of Communications Engineering and Microelectronics Engineering at the Ministry of Science and Technology, Taiwan. He was the recipient of the 1996 Young Scientist Award presented by the International Union of Radio Science, the 1998 Industry-Education Cooperation Award presented by the Ministry of Education, Taiwan, and the 2010 Distinguished Electrical Engineer Award presented by the Chinese Institute of Electrical Engineering, Kaohsiung Branch, Taiwan. Recently, he was awarded with the 2011 Advanced Semiconductor Engineering (ASE) Inc. Chair Professorship and the 2012 Outstanding Research Award at the National Sun Yat-Sen University. Dr. Horng is the Founder Chair of the IEEE MTT-S Tainan Chapter, and currently an Associate Editor of the IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, and a member of the IEEE MTT-S Technical Committee MTT-10 and MTT-20.

Digital Object Identifier 10.1109/TMTT.2015.2503950

Digital Object Identifier 10.1109/TMTT.2015.2503951

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2015 Index IEEE Transactions on Microwave Theory and Techniques Vol. 63 This index covers all technical items — papers, correspondence, reviews, etc. — that appeared in this periodical during 2015, and items from previous years that were commented upon or corrected in 2015. Departments and other items may also be covered if they have been judged to have archival value. The Author Index contains the primary entry for each item, listed under the first author's name. The primary entry includes the coauthors’ names, the title of the paper or other item, and its location, specified by the publication abbreviation, year, month, and inclusive pagination. The Subject Index contains entries describing the item under all appropriate subject headings, plus the first author’s name, the publication abbreviation, month, and year, and inclusive pages. Note that the item title is found only under the primary entry in the Author Index. AUTHOR INDEX A Abbak, M., see Akinci, M. N., TMTT Sep. 2015 2730-2740 Abbasi, M., see Carpenter, S., TMTT May 2015 1666-1675 Abdelaziz, M., see Kiayani, A., TMTT Nov. 2015 3608-3623 Abdin, M. M., see Ketterl, T. P., TMTT Dec. 2015 4382-4394 Abduljabar, A. A., Yang, X., Barrow, D. A., and Porch, A., Modelling and Measurements of the Microwave Dielectric Properties of Microspheres; TMTT Dec. 2015 4492-4500 Abduljabar, A. A., Choi, H., Barrow, D. A., and Porch, A., Adaptive Coupling of Resonators for Efficient Microwave Heating of Microfluidic Systems; TMTT Nov. 2015 3681-3690 Abouzied, M. A., and Sanchez-Sinencio, E., Low-Input Power-Level CMOS RF Energy-Harvesting Front End; TMTT Nov. 2015 3794-3805 Acar, O., Johansen, T. K., and Zhurbenko, V., A High-Power Low-Loss Continuously Tunable Bandpass Filter With Transversely Biased Ferrite-Loaded Coaxial Resonators; TMTT Oct. 2015 3425-3432 Accatino, L., Bertin, G., and Mongiardo, M., Modal Loss Analysis of - and -Plane Filtering Structures; TMTT Jan. 2015 40-47 Addamo, G., see Tibaldi, A., TMTT Jan. 2015 11-19 Addamo, G., see Tibaldi, A., TMTT Jan. 2015 115-124 Addamo, G., see Peverini, O. A., TMTT Oct. 2015 3361-3373 Addamo, G., Orta, R., Virone, G., Peverini, O. A., and Tascone, R., Radial Transmission-Line Approach for the Analysis of Ring Loaded Slots in Circular Waveguide; TMTT May 2015 1468-1474 Adnan, M., and Afshari, E., Efficient Microwave and Millimeter-Wave Frequency Multipliers Using Nonlinear Transmission Lines in CMOS Technology; TMTT Sep. 2015 2889-2896 Afshari, E., see Adnan, M., TMTT Sep. 2015 2889-2896 Agarwala, V., see Panwar, R., TMTT Aug. 2015 2438-2448 Agneessens, S., see Moro, R., TMTT Feb. 2015 422-432 Aguila, P., see Zuffanelli, S., TMTT Jul. 2015 2133-2141 Ahmadi, B., and Banai, A., Direct Coupled Resonator Filters Realized by Gap Waveguide Technology; TMTT Oct. 2015 3445-3452 Ahmadzay, H., see Akinci, M. N., TMTT Sep. 2015 2730-2740 Ahmed, S., see Alam, A. U., TMTT Dec. 2015 3874-3887 Ahn, S., see Kim, M., TMTT Nov. 2015 3806-3813 AHN, S., see KIM, J., TMTT Mar. 2015 778-779 Ahn, S., see Lee, S. B., TMTT Mar. 2015 813-820 Aikio, J. P., Rahkonen, T., and Pedro, J. C., Extraction of a Multi-Dimensional Polynomial Device Model for an Improved Distortion Contribution Analysis Technique; TMTT Jan. 2015 155-164 Akbarpour, M., Helaoui, M., and Ghannouchi, F. M., Analytical Design Methodology for Generic Doherty Amplifier Architectures Using Three-Port Input/Output Networks; TMTT Oct. 2015 3242-3253 Akduman, I., see Akinci, M. N., TMTT Sep. 2015 2730-2740 Akhtar, M. J., see Jha, A. K., TMTT Aug. 2015 2418-2426 Akinci, M. N., Caglayan, T., Ozgur, S., Alkasi, U., Ahmadzay, H., Abbak, M., Cayoren, M., and Akduman, I., Qualitative Microwave Imaging With Scattering Parameters Measurements; TMTT Sep. 2015 2730-2740

Akram, H., see Riehl, P. S., TMTT Mar. 2015 780-790 Alaaeddine, H., see Laur, V., TMTT Dec. 2015 4376-4381 Alam, A. U., Holland, K. D., Wong, M., Ahmed, S., Kienle, D., and Vaidyanathan, M., RF Linearity Performance Potential of Short-Channel Graphene Field-Effect Transistors; TMTT Dec. 2015 3874-3887 Alaverdyan, S. A., Kabanov, I. N., Komarov, V. V., and Meschanov, V. P., Development and Computer-Aided Design of Metal Gratings for Microwave Mesh Polarizers; TMTT Aug. 2015 2509-2514 Alkasi, U., see Akinci, M. N., TMTT Sep. 2015 2730-2740 Allane, D., see Andia Vera, G., TMTT Dec. 2015 4556-4566 Allegue-Martinez, M., see Reina-Tosina, J., TMTT Feb. 2015 745-753 Allilomes, P. C., see Zekios, C. L., TMTT Jul. 2015 2082-2093 Alomainy, A., and Grenier, K., Guest Editorial; TMTT Oct. 2015 3005-3006 Alt, A. R., and Bolognesi, C. R., (InP) HEMT Small-Signal Equivalent-Circuit Extraction as a Function of Temperature; TMTT Sep. 2015 2751-2755 Alu, A., see Soric, J. C., TMTT Nov. 2015 3558-3567 Alvarez, J., see Angulo, L. D., TMTT Oct. 2015 3081-3093 Alvarez Melcon, A., see Quesada Pereira, F. D., TMTT Dec. 2015 3862-3873 Alvarez-Botero, G., Torres-Torres, R., and Murphy-Arteaga, R. S., Consistent Modeling and Power Gain Analysis of Microwave SiGe HBTs in CE and CB Configurations; TMTT Dec. 2015 3888-3895 Amari, S., see Rosenberg, U., TMTT Jul. 2015 2390 Ambacher, O., see Seelmann-Eggebert, M., TMTT Jul. 2015 2335-2342 Ambrosio, E. P., see Peverini, O. A., TMTT Oct. 2015 3361-3373 Amiri, M. V., Bassam, S. A., Helaoui, M., and Ghannouchi, F. M., Partitioned Distortion Mitigation in LTE Radio Uplink to Enhance Transmitter Efficiency; TMTT Aug. 2015 2661-2671 An, J., see He, Z., TMTT May 2015 1683-1692 Anakabe, A., see Pelaz, J., TMTT Jun. 2015 1923-1936 Andersson, C. M., see Sanchez-Perez, C., TMTT Aug. 2015 2579-2588 Andia Vera, G., Allane, D., Georgiadis, A., Collado, A., Duroc, Y., and Tedjini, S., Cooperative Integration of Harvesting RF Sections for Passive RFID Communication; TMTT Dec. 2015 4556-4566 Andiia Vera, G., Duroc, Y., and Tedjini, S., Third Harmonic Exploitation in Passive UHF RFID; TMTT Sep. 2015 2991-3004 Andres, F. L. H., see Vazquez Antuna, C., TMTT Apr. 2015 1361-1369 Angulo, L. D., Alvarez, J., Teixeira, F. L., Pantoja, M. F., and Garcia, S. G., A Nodal Continuous-Discontinuous Galerkin Time-Domain Method for Maxwell's Equations; TMTT Oct. 2015 3081-3093 Antes, J., and Kallfass, I., Performance Estimation for Broadband Multi-Gigabit Millimeter- and Sub-Millimeter-Wave Wireless Communication Links; TMTT Oct. 2015 3288-3299 Antoniadis, D., see Choi, P., TMTT Apr. 2015 1163-1173 Anttila, L., see Kiayani, A., TMTT Nov. 2015 3608-3623 Anttila, L., see Singh, S., TMTT May 2015 1721-1734 Arcuti, P., see Monti, G., TMTT Nov. 2015 3814-3822 Arnal, N. C., see Ketterl, T. P., TMTT Dec. 2015 4382-4394 Arnaud-Cormos, D., see Kohler, S., TMTT Jun. 2015 2032-2040 Arora, R. K., see Hooker, J. W., TMTT Jul. 2015 2107-2114 Arpesi, P. G., see Ayllon, N., TMTT Dec. 2015 4429-4436 Asbeck, P., see Hanafi, B., TMTT Jun. 2015 1937-1950 Asbeck, P. M., see Farsi, S., TMTT Apr. 2015 1250-1262 Asbeck, P. M., see Liu, Y., TMTT May 2015 1556-1568 Asbeck, P. M., see Dabag, H.-T., TMTT Jul. 2015 2364-2374 Avolio, G., see Barmuta, P., TMTT Dec. 2015 4501-4510 Avolio, G., Raffo, A., Jargon, J., Hale, P. D., Schreurs, D. M. M.-P., and Williams, D. F., Evaluation of Uncertainty in Temporal Waveforms of Microwave Transistors; TMTT Jul. 2015 2353-2363 Avramidis, K. A., see Chelis, I. G., TMTT Jun. 2015 1781-1790 Avramidis, K. A., see Wu, C., TMTT Aug. 2015 2459-2467 Ayllon, N., and Arpesi, P. G., Highly Efficient and Multipaction-Free P-Band GaN High-Power Amplifiers for Space Applications; TMTT Dec. 2015 4429-4436 Azadet, K., see Hwang, T., TMTT Jul. 2015 2185-2198

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B Babakhani, A., see Yang, X., TMTT Nov. 2015 3727-3735 Badolato, A., see Grajal, J., TMTT Mar. 2015 1097-1107 Bae, B., see Kong, S., TMTT Mar. 2015 833-846 Bae, J., and Yoo, H.-J., The Effects of Electrode Configuration on Body Channel Communication Based on Analysis of Vertical and Horizontal Electric Dipoles; TMTT Apr. 2015 1409-1420 Baek, D., see Park, J., TMTT Apr. 2015 1399-1408 Bagheri, M., Bagheri, R., Buckwalter, J. F., and Larson, L. E., Tuning-Range Enhancement Through Deterministic Mode Selection in RF Quadrature Oscillators; TMTT Nov. 2015 3713-3726 Bagheri, R., see Bagheri, M., TMTT Nov. 2015 3713-3726 Bahramzy, P., Olesen, P., Madsen, P., Bojer, J., Barrio, S., Tatomirescu, A., Bundgaard, P., Morris III, A. S., and Pedersen, G. F., A Tunable RF Front-End With Narrowband Antennas for Mobile Devices; TMTT Oct. 2015 3300-3310 Bajestan, M. M., Rezaei, V. D., and Entesari, K., A Low Phase-Noise Wide Tuning-Range Quadrature Oscillator Using a Transformer-Based Dual-Resonance LC Ring; TMTT Apr. 2015 1142-1153 Bakri-Kassem, M., and Mansour, R. R., High Power Latching RF MEMS Switches; TMTT Jan. 2015 222-232 Baltus, P. G. M., see Ma, Q., TMTT Sep. 2015 2942-2952 Ban, Y., see Gao, Z., TMTT Oct. 2015 3109-3121 Banai, A., see Ahmadi, B., TMTT Oct. 2015 3445-3452 Banai, A., see Zargar, H., TMTT Feb. 2015 766-774 Bandler, J. W., see Koziel, S., TMTT Jan. 2015 107-114 Bandler, J. W., see Koziel, S., TMTT Dec. 2015 4247-4254 Bandler, J. W., see Zhang, C., TMTT Jul. 2015 2154-2165 Banys, J., see Bellucci, S., TMTT Jun. 2015 2024-2031 Bao, L., see He, Z., TMTT May 2015 1683-1692 Bao, M., see Yan, Y., TMTT Sep. 2015 2897-2904 Barabino, N., and Silveira, F., Digitally Assisted CMOS RF Detectors With Self-Calibration for Variability Compensation; TMTT May 2015 1676-1682 Barakat, A., see Thian, M., TMTT Feb. 2015 659-671 Barannik, A. A., see Bunyaev, S. A., TMTT Sep. 2015 2776-2781 Barannik, A. A., see Gubin, A. I., TMTT Jun. 2015 2003-2009 Barmatz, M. B., Jackson, H. W., Javeed, A. S., Jamieson, C. S., and Steinfeld, D. E., An Accurate Radially Stratified Approach for Determining the Complex Permittivity of Liquids in a Cylindrical Microwave Cavity; TMTT Feb. 2015 504-508 Barmuta, P., Ferranti, F., Gibiino, G. P., Lewandowski, A., and Schreurs, D. M. M.-P., Compact Behavioral Models of Nonlinear Active Devices Using Response Surface Methodology; TMTT Jan. 2015 56-64 Barmuta, P., Avolio, G., Ferranti, F., Lewandowski, A., Knockaert, L., and Schreurs, D. M. M.-P., Hybrid Nonlinear Modeling Using Adaptive Sampling; TMTT Dec. 2015 4501-4510 Barrio, S., see Bahramzy, P., TMTT Oct. 2015 3300-3310 Barroso, J. J., see Hasar, U. C., TMTT Jul. 2015 2313-2321 Barrow, D. A., see Abduljabar, A. A., TMTT Dec. 2015 4492-4500 Barrow, D. A., see Abduljabar, A. A., TMTT Nov. 2015 3681-3690 Barthwal, A., Rawat, K., and Koul, S., Bandwidth Enhancement of ThreeStage Doherty Power Amplifier Using Symmetric Devices; TMTT Aug. 2015 2399-2410 Barton, T. W., and Perreault, D. J., Theory and Implementation of RF-Input Outphasing Power Amplification; TMTT Dec. 2015 4273-4283 Bassam, S. A., see Amiri, M. V., TMTT Aug. 2015 2661-2671 Bastioli, S., see Snyder, R. V., TMTT Oct. 2015 3324-3360 Bastioli, S., see Tomassoni, C., TMTT Dec. 2015 4366-4375 Batra, J. S., see Pourghorban Saghati, A., TMTT Aug. 2015 2515-2525 Bautista, A., Franc, A.-F., and Ferrari, P., Accurate Parametric Electrical Model for Slow-Wave CPW and Application to Circuits Design; TMTT Dec. 2015 4225-4235 Bekasiewicz, A., see Koziel, S., TMTT Dec. 2015 4019-4026 Belenguer, A., Borja, A. L., Esteban, H., and Boria, V. E., High-Performance Coplanar Waveguide to Empty Substrate Integrated Coaxial Line Transition; TMTT Dec. 2015 4027-4034 Bellucci, S., Bistarelli, S., Cataldo, A., Micciulla, F., Kranauskaite, I., Macutkevic, J., Banys, J., Volynets, N., Paddubskaya, A., Bychanok, D., Kuzhir, P., Maksimenko, S., Fierro, V., and Celzard, A., Broadband Dielectric Spectroscopy of Composites Filled With Various Carbon Materials; TMTT Jun. 2015 2024-2031 Bellucci, S., see Pierantoni, L., TMTT Aug. 2015 2491-2497 + Check author entry for coauthors

Benech, P., see Lim, T., TMTT Nov. 2015 3747-3759 Benner, P., see Hess, M. W., TMTT Nov. 2015 3549-3557 Benton, D. M., see Gamlath, C. D., TMTT Feb. 2015 374-383 Bernstein, G. H., see Russer, J. A., TMTT Dec. 2015 4236-4246 Berroth, M., see Huang, H., TMTT Apr. 2015 1211-1218 Bertin, G., see Accatino, L., TMTT Jan. 2015 40-47 Beutler, J., see Choi, H., TMTT Oct. 2015 3016-3025 Beyers, R. D., and de Villiers, D. I. L., Corrections to “Compact ConicalLine Power Combiner Design Using Circuit Models” [Nov 14 2650-2658]; TMTT Jul. 2015 2391 Bhat, R., Chakrabarti, A., and Krishnaswamy, H., Large-Scale Power Combining and Mixed-Signal Linearizing Architectures for Watt-Class mmWave CMOS Power Amplifiers; TMTT Feb. 2015 703-718 Bhattacharya, A., Mandal, D., and Bhattacharyya, T. K., A 1.3–2.4-GHz 3.1-mW VCO Using Electro-Thermo- Mechanically Tunable Self-Assembled MEMS Inductor on HR Substrate; TMTT Feb. 2015 459-469 Bhattacharyya, T. K., see Bhattacharya, A., TMTT Feb. 2015 459-469 Bia, P., see Mescia, L., TMTT Dec. 2015 4191-4193 Biedrzycki, R., see Lewandowski, A., TMTT Mar. 2015 1076-1089 Bieler, M., Fuser, H., and Pierz, K., Time-Domain Optoelectronic Vector Network Analysis on Coplanar Waveguides; TMTT Nov. 2015 3775-3784 Bien, F., see Na, K., TMTT Jan. 2015 295-304 Birchall, J., see Choi, H., TMTT Oct. 2015 3016-3025 Bistarelli, S., see Bellucci, S., TMTT Jun. 2015 2024-2031 Bito, J., Hester, J. G., and Tentzeris, M. M., Ambient RF Energy Harvesting From a Two-Way Talk Radio for Flexible Wearable Wireless Sensor Devices Utilizing Inkjet Printing Technologies; TMTT Dec. 2015 4533-4543 Bluestone, A., Spencer, D. T., Srinivasan, S., Guerra, D., Bowers, J. E., and Theogarajan, L., An Ultra-Low Phase-Noise 20-GHz PLL Utilizing an Optoelectronic Voltage-Controlled Oscillator; TMTT Mar. 2015 1046-1052 Bogoni, A., see Scotti, F., TMTT Feb. 2015 546-552 Boix, R. R., see Fernandez-Prieto, A., TMTT Jun. 2015 1843-1853 Bojer, J., see Bahramzy, P., TMTT Oct. 2015 3300-3310 Bolognesi, C. R., see Alt, A. R., TMTT Sep. 2015 2751-2755 Bonache, J., see Velez, P., TMTT Apr. 2015 1272-1280 Bonache, J., see Sans, M., TMTT Dec. 2015 3896-3908 Bonache, J., see Zuffanelli, S., TMTT Jul. 2015 2133-2141 Boon, C.-C., see Choi, P., TMTT Apr. 2015 1163-1173 Borges Carvalho, N., see Dias Fernandes, R., TMTT Sep. 2015 2983-2990 Boria, V., see Carceller, C., TMTT Oct. 2015 3398-3407 Boria, V. E., Macchiarella, G., and Yu, M., Guest Editorial; TMTT Oct. 2015 3321-3323 Boria, V. E., see Sirci, S., TMTT Dec. 2015 4341-4354 Boria, V. E., see Belenguer, A., TMTT Dec. 2015 4027-4034 Boria, V. E., see Sans, M., TMTT Dec. 2015 3896-3908 Boria, V. E., see Cogollos, S., TMTT Aug. 2015 2540-2549 Boric-Lubecke, O., see Yavari, E., TMTT Nov. 2015 3834-3842 Boriskin, A. V., see Diedhiou, D. L., TMTT Jul. 2015 2245-2252 Borja, A. L., see Belenguer, A., TMTT Dec. 2015 4027-4034 Borjesson, P. O., see Lindqvist, F., TMTT Nov. 2015 3568-3578 Bornemann, J., see Rosenberg, U., TMTT Jul. 2015 2390 Bosch, W., see Sirci, S., TMTT Dec. 2015 4341-4354 Boubekeur, N., see El Matbouly, H., TMTT Dec. 2015 4150-4156 Boumaiza, S., see Huang, H., TMTT Dec. 2015 4297-4305 Boumaiza, S., see Jundi, A., TMTT Nov. 2015 3691-3700 Bourgeat, J., see Lim, T., TMTT Nov. 2015 3747-3759 Bowers, J. E., see Bluestone, A., TMTT Mar. 2015 1046-1052 Bowers, S. M., Safaripour, A., and Hajimiri, A., An Integrated Slot-Ring Traveling-Wave Radiator; TMTT Apr. 2015 1154-1162 Boyd, T. A., see Morgan, M. A., TMTT Apr. 2015 1263-1271 Bozzi, M., and Perregrini, L., Guest Editorial [Mini-Special Issue on 2014 IEEE International Conference on Numerical Electromagnetic Modeling and Optimization for RF, Microwave, and Terahertz Applications (NEMO2014; TMTT Jan. 2015 1-2 Bozzi, M., see Moscato, S., TMTT Oct. 2015 3175-3182 Bozzi, M., see Moro, R., TMTT Feb. 2015 422-432 Bozzi, M., see Pierantoni, L., TMTT Aug. 2015 2491-2497 Braithwaite, R. N., Closed-Loop Digital Predistortion (DPD) Using an Observation Path With Limited Bandwidth; TMTT Feb. 2015 726-736 Bratman, V. L., see Zhang, L., TMTT Mar. 2015 1090-1096 Brazalez, A. A., Rajo-Iglesias, E., Vazquez-Roy, J.-L., Vosoogh, A., and Kildal, P.-S., Design and Validation of Microstrip Gap Waveguides and Their Transitions to Rectangular Waveguide, for Millimeter-Wave Applications; TMTT Dec. 2015 4035-4050

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 63, NO. 12, DECEMBER 2015

Brazil, T. J., see Chen, P., TMTT Dec. 2015 4263-4272 Brazil, T. J., see Cai, J., TMTT May 2015 1518-1529 Brey, W. W., see Hooker, J. W., TMTT Jul. 2015 2107-2114 Brumos, M., see Cogollos, S., TMTT Aug. 2015 2540-2549 Bruns, H.-D., see Hardock, A., TMTT Mar. 2015 976-985 Buckwalter, J. F., see Li, J., TMTT Jan. 2015 266-278 Buckwalter, J. F., see Luo, C., TMTT Oct. 2015 3514-3524 Buckwalter, J. F., see Bagheri, M., TMTT Nov. 2015 3713-3726 Buckwalter, J. F., see Hanafi, B., TMTT Jun. 2015 1937-1950 Buckwalter, J. F., see Dabag, H.-T., TMTT Jul. 2015 2364-2374 Buckwalter, J. F., see Mehrjoo, M. S., TMTT Jul. 2015 2289-2300 Bundgaard, P., see Bahramzy, P., TMTT Oct. 2015 3300-3310 Bunyaev, S. A., Barannik, A. A., and Cherpak, N. T., Microstrip WhisperingGallery-Mode Resonator; TMTT Sep. 2015 2776-2781 Burdin, F., Iskandar, Z., Podevin, F., and Ferrari, P., Design of Compact Reflection-Type Phase Shifters With High Figure-of-Merit; TMTT Jun. 2015 1883-1893 Bychanok, D., see Bellucci, S., TMTT Jun. 2015 2024-2031 Byun, W.-J., see Kim, S.-M., TMTT Mar. 2015 847-856 C Cabral, P. M., see Pedro, J. C., TMTT Apr. 2015 1239-1249 Cacciamani, F., see Pelliccia, L., TMTT Oct. 2015 3381-3390 Caddemi, A., see Nalli, A., TMTT Aug. 2015 2498-2508 Caglayan, T., see Akinci, M. N., TMTT Sep. 2015 2730-2740 Cai, G., see Liu, N., TMTT Oct. 2015 3094-3102 Cai, J., King, J. B., Zhu, A., Pedro, J. C., and Brazil, T. J., Nonlinear Behavioral Modeling Dependent on Load Reflection Coefficient Magnitude; TMTT May 2015 1518-1529 Calignano, F., see Peverini, O. A., TMTT Oct. 2015 3361-3373 Caloz, C., see Zhang, Q., TMTT Sep. 2015 2782-2792 Caloz, C., see Gupta, S., TMTT Mar. 2015 1007-1018 Camacho-Penalosa, C., see Esteban, J., TMTT Oct. 2015 3208-3217 Camarchia, V., Pirola, M., Quaglia, R., Jee, S., Cho, Y., and Kim, B., The Doherty Power Amplifier: Review of Recent Solutions and Trends; TMTT Feb. 2015 559-571 Campanella, H., Narducci, M., Wang, N., and Soon, J. B. W., RF-Designed High-Power Lamb-Wave Aluminum–Nitride Resonators; TMTT Feb. 2015 331-339 Canavero, F. G., see Manfredi, P., TMTT May 2015 1502-1511 Canos, A. J., see Catala-Civera, J. M., TMTT Sep. 2015 2905-2914 Cao, B., see Lu, X., TMTT Apr. 2015 1281-1293 Cao, W., see Yu, C., TMTT Dec. 2015 4306-4318 Cao, W. P., see Yu, X. H., TMTT Dec. 2015 3845-3850 Cao, W.-P., see Yu, X., TMTT Feb. 2015 326-330 Cappello, T., see Florian, C., TMTT Aug. 2015 2589-2602 Caratelli, D., see Mescia, L., TMTT Dec. 2015 4191-4193 Carceller, C., Soto, P., Boria, V., Guglielmi, M., and Gil, J., Design of Compact Wideband Manifold-Coupled Multiplexers; TMTT Oct. 2015 3398-3407 Carignan, L.-P., see Helszajn, J., TMTT May 2015 1603-1608 Carpenter, S., Abbasi, M., and Zirath, H., Fully Integrated D-Band Direct Carrier Quadrature (I/Q) Modulator and Demodulator Circuits in InP DHBT Technology; TMTT May 2015 1666-1675 Carroll, J., see Chen, W.-T. S., TMTT Dec. 2015 4157-4168 Carta, C., see Fritsche, D., TMTT Jun. 2015 1910-1922 Carvalho, N. B., see Ribeiro, D. C., TMTT Oct. 2015 3277-3287 Casula, G. A., see Valente, G., TMTT Oct. 2015 3218-3227 Catala-Civera, J. M., Canos, A. J., Plaza-Gonzalez, P., Gutierrez, J. D., GarciaBanos, B., and Penaranda-Foix, F. L., Dynamic Measurement of Dielectric Properties of Materials at High Temperature During Microwave Heating in a Dual Mode Cylindrical Cavity; TMTT Sep. 2015 2905-2914 Cataldo, A., see Bellucci, S., TMTT Jun. 2015 2024-2031 Cataldo, A., see Pierantoni, L., TMTT Aug. 2015 2491-2497 Cayoren, M., see Akinci, M. N., TMTT Sep. 2015 2730-2740 Cecchini, P., see Peverini, O. A., TMTT Oct. 2015 3361-3373 Ceccuzzi, S., Ponti, C., Ravera, G. L., and Schettini, G., Mode Filters for Oversized Rectangular Waveguides: A Modal Approach; TMTT Aug. 2015 2468-2481 Celzard, A., see Bellucci, S., TMTT Jun. 2015 2024-2031 Cervera, F., and Hong, J., High Rejection, Self-Packaged Low-Pass Filter Using Multilayer Liquid Crystal Polymer Technology; TMTT Dec. 2015 3920-3928 + Check author entry for coauthors

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Chae, J., see Schwerdt, H. N., TMTT Sep. 2015 2965-2970 Chae, J., see Lee, C. W. L., TMTT Jun. 2015 2060-2068 Chakrabarti, A., see Bhat, R., TMTT Feb. 2015 703-718 Chalkiadaki, M.-A., and Enz, C. C., RF Small-Signal and Noise Modeling Including Parameter Extraction of Nanoscale MOSFET From Weak to Strong Inversion; TMTT Jul. 2015 2173-2184 Chan, K.K.M., Tan, A. E.-C., Li, L., and Rambabu, K., Material Characterization of Arbitrarily Shaped Dielectrics Based on Reflected Pulse Characteristics; TMTT May 2015 1700-1709 Chan, L. H. K., Yeo, K. S., Chew, K. W. J., and Ong, S. N., High-Frequency Noise Modeling of MOSFETs for Ultra Low-Voltage RF Applications; TMTT Jan. 2015 141-154 Chang, C., Guo, L., Tantawi, S. G., Liu, Y., Li, J., Chen, C., and Huang, W., A New Compact High-Power Microwave Phase Shifter; TMTT Jun. 2015 1875-1882 Chang, C.-W., see Yang, H.-S., TMTT Dec. 2015 4437-4443 Chang, C.-W., see Liang, K.-F., TMTT Aug. 2015 2603-2608 Chang, C.-Y., see Chou, P.-J., TMTT Dec. 2015 3971-3980 Chang, D.-C., see Li, C.-H., TMTT Feb. 2015 470-480 Chang, H.-Y., see Liu, Y.-C., TMTT Sep. 2015 2841-2853 Chang, J.-F., Kao, J.-C., Lin, Y.-H., and Wang, H., Design and Analysis of 24-GHz Active Isolator and Quasi-Circulator; TMTT Aug. 2015 2638-2649 Chang, M.-C. F., see Wu, H., TMTT Mar. 2015 1053-1062 Chao, T.-Y., see Li, C.-H., TMTT Feb. 2015 470-480 Chao, Y., Luong, H. C., and Hong, Z., Analysis and Design of a 14.1-mW 50/100-GHz Transformer-Based PLL With Embedded Phase Shifter in 65-nm CMOS; TMTT Apr. 2015 1193-1201 Che, W., see Feng, W., TMTT Dec. 2015 4013-4018 Cheang, C.-F., see Un, K.-F., TMTT Oct. 2015 3228-3241 Chelis, I. G., Avramidis, K. A., and Vomvoridis, J. L., Resonant Modes of DiskLoaded Cylindrical Structures With Open Boundaries; TMTT Jun. 2015 1781-1790 Chen, C., see Chang, C., TMTT Jun. 2015 1875-1882 Chen, F.-C., see Wong, S.-W., TMTT Dec. 2015 3947-3953 Chen, F.-J., Wu, L.-S., Qiu, L.-F., and Mao, J.-F., A Four-Way Microstrip Filtering Power Divider With Frequency-Dependent Couplings; TMTT Oct. 2015 3494-3504 Chen, H., see Yu, F., TMTT Feb. 2015 403-413 Chen, J., see Feng, S., TMTT Jan. 2015 305-313 Chen, J., see He, Z., TMTT May 2015 1683-1692 Chen, J.-H., see Yang, H.-S., TMTT Dec. 2015 4437-4443 Chen, J.-H., see Yang, H.-S., TMTT Nov. 2015 3671-3680 Chen, J.-H., see Liang, K.-F., TMTT Aug. 2015 2603-2608 Chen, J.-X., see Zhu, X.-C., TMTT Feb. 2015 494-503 Chen, J.-X., see Xu, K., TMTT Aug. 2015 2561-2569 Chen, J.-Y., see Chien, K.-H., TMTT Sep. 2015 2877-2888 Chen, K., see Liu, Y.-C., TMTT Sep. 2015 2841-2853 Chen, P., Merrick, B. M., and Brazil, T. J., Bayesian Optimization for Broadband High-Efficiency Power Amplifier Designs; TMTT Dec. 2015 42634272 Chen, P., see Dai, Z., TMTT Feb. 2015 449-458 Chen, S. T. W., see Xu, Z., TMTT Apr. 2015 1219-1227 Chen, T.-C., Wang, L., Goodyear, G., Yializis, A., and Xin, H., Broadband Microwave Characterization of Nanostructured Thin Film With Giant Dielectric Response; TMTT Nov. 2015 3768-3774 Chen, W.-C., see Li, C.-H., TMTT Feb. 2015 470-480 Chen, W.-T. S., Stewart, K. M. E., Yang, C. K., Mansour, R. R., Carroll, J., and Penlidis, A., Wearable RF Sensor Array Implementing Coupling-Matrix Readout Extraction Technique; TMTT Dec. 2015 4157-4168 Chen, X., Li, W., and Yao, J., Dynamic-Range Enhancement for a Microwave Photonic Link Based on a Polarization Modulator; TMTT Jul. 2015 23842389 Chen, Y.-J. E., see Yang, H.-S., TMTT Nov. 2015 3671-3680 Chen, Z., see Gui, X., TMTT Jan. 2015 233-243 Chen, Z., see Gui, X., TMTT Mar. 2015 945-953 Chen, Z. N., see Kianinejad, A., TMTT Jun. 2015 1817-1825 Cheng, C.-H., see Hsiao, C.-Y., TMTT Jun. 2015 1894-1901 Cheng, H.-H., see Ho, C.-Y., TMTT Sep. 2015 2923-2930 Cheng, K.-K. M., and Chik, M.-C. J., A Varactor-Based Variable Attenuator Design With Enhanced Linearity Performance; TMTT Oct. 2015 3191-3198 Cheng, K.-K. M., see Fang, X.-H., TMTT Sep. 2015 2811-2820 Cheng, Q.-F., Zhu, S.-K., and Fu, H.-P., Comments on “High-Efficiency Class E/F Lumped and Transmission-Line Power Amplifiers”; TMTT Aug. 2015 2703-2704

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Cheng, Y. T., see Li, C.-H., TMTT Feb. 2015 470-480 Cheong, P., Wu, K., and Tam, K.-W., Nonlinear Communication System With Harmonic Diversity; TMTT Dec. 2015 4130-4149 Cherpak, N. T., see Bunyaev, S. A., TMTT Sep. 2015 2776-2781 Cherpak, N. T., see Gubin, A. I., TMTT Jun. 2015 2003-2009 Chew, K. W. J., see Chan, L. H. K., TMTT Jan. 2015 141-154 Chi, B., see Jia, H., TMTT May 2015 1645-1657 Chi, B., see Jia, H., TMTT Feb. 2015 719-725 Chi, B., see Yin, Y., TMTT Feb. 2015 672-682 Chi, N., see Yu, J., TMTT Jun. 2015 1836-1842 Chien, J.-C., see Kuo, N.-C., TMTT Apr. 2015 1130-1141 Chien, K.-H., Chen, J.-Y., and Chiou, H.-K., Designs of K-Band Divide-by-2 and Divide-by-3 Injection-Locked Frequency Divider With Darlington Topology; TMTT Sep. 2015 2877-2888 Chik, M.-C. J., see Cheng, K.-K. M., TMTT Oct. 2015 3191-3198 Chiou, H.-K., see Chien, K.-H., TMTT Sep. 2015 2877-2888 Chiu, Y.-C., see Wang, F.-K., TMTT Dec. 2015 4592-4602 Cho, I.-K., see Kim, S.-M., TMTT Mar. 2015 847-856 Cho, Y., see Moon, K., TMTT Apr. 2015 1324-1333 Cho, Y., see Camarchia, V., TMTT Feb. 2015 559-571 Cho, Y., see Kim, J., TMTT Dec. 2015 4072-4082 Cho, Y.-H., and Rebeiz, G. M., Tunable 4-Pole Dual-Notch Filters for Cognitive Radios and Carrier Aggregation Systems; TMTT Apr. 2015 1308-1314 Cho, Y.-H., and Rebeiz, G. M., Tunable 4-Pole Noncontiguous 0.7–2.1-GHz Bandpass Filters Based on Dual Zero-Value Couplings; TMTT May 2015 1579-1586 Choi, H., see Abduljabar, A. A., TMTT Nov. 2015 3681-3690 Choi, H., see Imtiaz, A., TMTT Oct. 2015 3007-3015 Choi, H., Naylon, J., Luzio, S., Beutler, J., Birchall, J., Martin, C., and Porch, A., Design and In Vitro Interference Test of Microwave Noninvasive Blood Glucose Monitoring Sensor; TMTT Oct. 2015 3016-3025 Choi, H.-C., see Kim, S.-M., TMTT Mar. 2015 847-856 Choi, J., see Lee, I.-Y., TMTT Apr. 2015 1202-1210 Choi, J., see Kim, J., TMTT Mar. 2015 791-800 Choi, J.-Y., see Merkle, T., TMTT Feb. 2015 481-493 Choi, K., see Lee, S., TMTT Dec. 2015 4406-4414 Choi, P., Goswami, S., Radhakrishna, U., Khanna, D., Boon, C.-C., Lee, H.-S., Antoniadis, D., and Peh, L.-S., A 5.9-GHz Fully Integrated GaN Frontend Design With Physics-Based RF Compact Model; TMTT Apr. 2015 11631173 Choi, W.-W., see Yang, L., TMTT Jul. 2015 2225-2232 Choi, Y.-C., Seong, Y.-J., Yoo, Y.-J., Lee, S.-K., Velazquez Lopez, M., and Yoo, H.-J., Multi-Standard Hybrid PLL With Low Phase-Noise Characteristics for GSM/EDGE and LTE Applications; TMTT Oct. 2015 3254-3264 Chong, W. K., Ramiah, H., and Vitee, N., A 0.12-mm 2.4-GHz CMOS Inductorless High Isolation Subharmonic Mixer With Effective Current-Reuse Transconductance; TMTT Aug. 2015 2427-2437 Chou, P.-J., Lin, Y.-W., and Chang, C.-Y., Exact Synthesis of Full- and Half-Symmetric Rat-Race Ring Hybrids With or Without Impedance Transforming Characteristics; TMTT Dec. 2015 3971-3980 Chu, Q.-X., see Wong, S.-W., TMTT Oct. 2015 3416-3424 Chu, Q.-X., and Qiu, L.-L., Wideband Balanced Filters With High Selectivity and Common-Mode Suppression; TMTT Oct. 2015 3462-3468 Chu, Q.-X., see Wong, S.-W., TMTT Dec. 2015 3947-3953 Chu, Q.-X., Mo, D.-Y., and Wu, Q.-S., An Isolated Radial Power Divider via -Mode Transducer; TMTT Dec. 2015 3988-3996 Circular Waveguide Chu, T.-H., see Lin, Y.-C., TMTT Jul. 2015 2343-2352 Chu, T.-S., see Tan, K.-W., TMTT Apr. 2015 1380-1387 Chung, S., Ma, R., Shinjo, S., Nakamizo, H., Parsons, K., and Teo, K. H., Concurrent Multiband Digital Outphasing Transmitter Architecture Using Multidimensional Power Coding; TMTT Feb. 2015 598-613 Church, K. H., see Ketterl, T. P., TMTT Dec. 2015 4382-4394 Cidronali, A., see Maddio, S., TMTT Dec. 2015 4567-4580 Cidronali, A., see Maddio, S., TMTT Feb. 2015 509-519 Cinar, G., see Nordebo, S., TMTT Jun. 2015 1791-1799 Cnaan-On, I., Thomas, S. J., Krolik, J. L., and Reynolds, M. S., Multichannel Backscatter Communication and Ranging for Distributed Sensing With an FMCW Radar; TMTT Jul. 2015 2375-2383 Coccetti, F., see De Paolis, R., TMTT Aug. 2015 2570-2578 Coffey, M., see Zai, A., TMTT Sep. 2015 2953-2964 Cogollos, S., Soto, P., Boria, V. E., Guglielmi, M., Brumos, M., Gimeno, B., and Raboso, D., Efficient Design of Waveguide Manifold Multiplexers Based on Low-Order EM Distributed Models; TMTT Aug. 2015 2540-2549 Collado, A., see Andia Vera, G., TMTT Dec. 2015 4556-4566 + Check author entry for coauthors

Collado, A., see Del Prete, M., TMTT Dec. 2015 4511-4520 Collado, C., see Mira, F., TMTT Dec. 2015 3939-3946 Collantes, J.-M., see Suarez, A., TMTT Jan. 2015 165-180 Collantes, J.-M., see Pelaz, J., TMTT Jun. 2015 1923-1936 Collins, G., see Pelaz, J., TMTT Jun. 2015 1923-1936 Conway, G. D., see Koenen, C., TMTT Dec. 2015 3954-3961 Cordoba-Erazo, M. F., see Ketterl, T. P., TMTT Dec. 2015 4382-4394 Cormier, G., see Ross, T. N., TMTT Jan. 2015 244-255 Costanzo, A., see Del Prete, M., TMTT Dec. 2015 4511-4520 Crespo-Cadenas, C., see Reina-Tosina, J., TMTT Feb. 2015 745-753 Cross, A. W., see Zhang, L., TMTT Oct. 2015 3183-3190 Cross, A. W., see Zhang, L., TMTT Mar. 2015 1090-1096 Cruces, S., see Reina-Tosina, J., TMTT Feb. 2015 745-753 Crupi, G., see Nalli, A., TMTT Aug. 2015 2498-2508 Cruz, P. M., see Ribeiro, D. C., TMTT Oct. 2015 3277-3287 Cryan, M. J., see Gamlath, C. D., TMTT Feb. 2015 374-383 Cuenca, J. A., Thomas, E., Mandal, S., Williams, O., and Porch, A., Investigating the Broadband Microwave Absorption of Nanodiamond Impurities; TMTT Dec. 2015 4110-4118 Cui, C., Kim, S.-K., Song, R., Song, J.-H., Nam, S., and Kim, B.-S., A 77-GHz FMCW Radar System Using On-Chip Waveguide Feeders in 65-nm CMOS; TMTT Nov. 2015 3736-3746 Cui, J., see Sun, Y., TMTT Oct. 2015 3131-3141 Cui, W., see Zhao, J., TMTT May 2015 1633-1644 Cumby, B. L., Mast, D. B., Tabor, C. E., Dickey, M. D., and Heikenfeld, J., Robust Pressure-Actuated Liquid Metal Devices Showing Reconfigurable Electromagnetic Effects at GHz Frequencies; TMTT Oct. 2015 3122-3130 D D'Angelo, S., see Nalli, A., TMTT Aug. 2015 2498-2508 Dabag, H., see Hanafi, B., TMTT Jun. 2015 1937-1950 Dabag, H.-T., see Farsi, S., TMTT Apr. 2015 1250-1262 Dabag, H.-T., Hanafi, B., Gurbuz, O. D., Rebeiz, G. M., Buckwalter, J. F., and Asbeck, P. M., Transmission of Signals With Complex Constellations Using Millimeter-Wave Spatially Power-Combined CMOS Power Amplifiers and Digital Predistortion; TMTT Jul. 2015 2364-2374 Dai, Z., He, S., You, F., Peng, J., Chen, P., and Dong, L., A New Distributed Parameter Broadband Matching Method for Power Amplifier via Real Frequency Technique; TMTT Feb. 2015 449-458 Dai, Z., see Pang, J., TMTT Dec. 2015 4061-4071 Daneshmand, M., see Vahabisani, N., TMTT Feb. 2015 340-351 Darraji, R., Kwan, A. K., Ghannouchi, F. M. G., and Helaoui, M., Digitally Equalized Doherty RF Front-End Architecture for Broadband and Multistandard Wireless Transmitters; TMTT Jun. 2015 1978-1988 Darwazeh, I., see Eriksson, K., TMTT Apr. 2015 1334-1341 Darwish, A. M., Ibrahim, A. A., Qiu, J. X., Viveiros, E., and Hung, H. A., A Broadband 1-to- Power Divider/Combiner With Isolation and Reflection Cancellation; TMTT Jul. 2015 2253-2263 Dasgupta, K., Sengupta, K., Pai, A., and Hajimiri, A., A mm-Wave Segmented Power Mixer; TMTT Apr. 2015 1118-1129 Day, S. E., see Deo, P., TMTT Apr. 2015 1388-1398 De, S., see Zhang, Y.-J., TMTT Mar. 2015 883-890 de Cos, J., and Suarez, A., Efficient Simulation of Solution Curves and Bifurcation Loci in Injection-Locked Oscillators; TMTT Jan. 2015 181-197 de Cos, J., Suarez, A., and Garcia, J. A., Hysteresis and Oscillation in HighEfficiency Power Amplifiers; TMTT Dec. 2015 4284-4296 De Flaviis, F., see Papio Toda, A., TMTT Mar. 2015 1063-1075 De Paolis, F., see Vanin, F. M., TMTT Feb. 2015 397-402 De Paolis, R., Payan, S., Maglione, M., Guegan, G., and Coccetti, F., HighTunability and High- -Factor Integrated Ferroelectric Circuits up to Millimeter Waves; TMTT Aug. 2015 2570-2578 de Rooij, M. A., see Twieg, M., TMTT Dec. 2015 4169-4177 de Villiers, D. I. L., see Beyers, R. D., TMTT Jul. 2015 2391 Deffenbaugh, P. I., see Ketterl, T. P., TMTT Dec. 2015 4382-4394 Del Prete, M., Costanzo, A., Georgiadis, A., Collado, A., Masotti, D., and Popovic, Z., A 2.45-GHz Energy-Autonomous Wireless Power Relay Node; TMTT Dec. 2015 4511-4520 Deltimple, N., see Kerherve, E., TMTT May 2015 1621-1632 Demirel, N., see Kerherve, E., TMTT May 2015 1621-1632 Deng, J., see Yu, X., TMTT Feb. 2015 326-330 Deng, J. L., see Yu, X. H., TMTT Dec. 2015 3845-3850 Denisov, G. G., see Zhang, L., TMTT Mar. 2015 1090-1096

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 63, NO. 12, DECEMBER 2015

Deo, P., Mirshekar-Syahkal, D., Seddon, L., Day, S. E., and Fernandez, F. A., Microstrip Device for Broadband (15–65 GHz) Measurement of Dielectric Properties of Nematic Liquid Crystals; TMTT Apr. 2015 1388-1398 Dey, S., and Koul, S. K., Reliability Analysis of Ku-Band 5-bit Phase Shifters Using MEMS SP4T and SPDT Switches; TMTT Dec. 2015 3997-4012 Dias Fernandes, R., Matos, J. N., and Borges Carvalho, N., Resonant Electrical Coupling: Circuit Model and First Experimental Results; TMTT Sep. 2015 2983-2990 Diaz, R. C., see Vazquez Antuna, C., TMTT Apr. 2015 1361-1369 Dickey, M. D., see Cumby, B. L., TMTT Oct. 2015 3122-3130 Diebold, S., Wagner, S., Massler, H., Pahl, P., Leuther, A., Tessmann, A., Zwick, T., and Kallfass, I., A Novel 1 4 Coupler for Compact and High-Gain Power Amplifier MMICs Around 250 GHz; TMTT Mar. 2015 999-1006 Diedhiou, D. L., Sauleau, R., and Boriskin, A. V., Microfluidically Tunable Microstrip Filters; TMTT Jul. 2015 2245-2252 Dierck, A., see Moro, R., TMTT Feb. 2015 422-432 Dietrich, J. L., Corrections to “Unified Theory of Linear Noisy Two-Ports” [Nov 13 3986-3997]; TMTT Feb. 2015 554 Ding, W., Ji, Z., Ye, F., Lou, C., and Xing, D., Near-Field Microwave Distribution Measurement With a Point Detector Base on Thermoacoustic Effect; TMTT Oct. 2015 3272-3276 Ding, W.-Q., see Hao, Z.-C., TMTT Nov. 2015 3651-3662 Ding, X., see Yu, F., TMTT Feb. 2015 403-413 Dionigi, M., Mongiardo, M., and Perfetti, R., Rigorous Network and Full-Wave Electromagnetic Modeling of Wireless Power Transfer Links; TMTT Jan. 2015 65-75 Djerafi, T., see Doghri, A., TMTT Jan. 2015 209-221 Doghri, A., Djerafi, T., Ghiotto, A., and Wu, K., Substrate Integrated Waveguide Directional Couplers for Compact Three-Dimensional Integrated Circuits; TMTT Jan. 2015 209-221 Domingue, F., see El Matbouly, H., TMTT Dec. 2015 4150-4156 Donaldson, C. R., see Zhang, L., TMTT Oct. 2015 3183-3190 Dong, L., see Dai, Z., TMTT Feb. 2015 449-458 Draxler, P., Guest Editorial; TMTT Feb. 2015 557-558 Du, Y., see Wu, H., TMTT Mar. 2015 1053-1062 Duchamp, J.-M., see Parment, F., TMTT Apr. 2015 1228-1238 Dudorov, S., see Topfer, F., TMTT Jun. 2015 2050-2059 Durgin, G. D., see Valenta, C. R., TMTT May 2015 1758-1767 Duroc, Y., see Andia Vera, G., TMTT Dec. 2015 4556-4566 Duroc, Y., see Andiia Vera, G., TMTT Sep. 2015 2991-3004

E

Edison, A. S., see Hooker, J. W., TMTT Jul. 2015 2107-2114 Eibert, T. F., see Koenen, C., TMTT Dec. 2015 3954-3961 Eisenstadt, W. R., see Hur, B., TMTT Aug. 2015 2650-2660 El Matbouly, H., Boubekeur, N., and Domingue, F., Passive Microwave Substrate Integrated Cavity Resonator for Humidity Sensing; TMTT Dec. 2015 4150-4156 Eleftheriades, G. V., see Wong, J. P. S., TMTT Mar. 2015 913-924 Elkhouly, E., Fathy, A. E., and Mahfouz, M. R., Signal Detection and Noise Modeling of a 1-D Pulse-Based Ultra-Wideband Ranging System and Its Accuracy Assessment; TMTT May 2015 1746-1757 Ellinger, F., see Fritsche, D., TMTT Jun. 2015 1910-1922 Elnaggar, S. Y., Tervo, R. J., and Mattar, S. M., Energy Coupled Mode Theory for Electromagnetic Resonators; TMTT Jul. 2015 2115-2123 Elnaggar, S. Y., Tervo, R. J., and Mattar, S. M., Coupled Mode Theory Applied to Resonators in the Presence of Conductors; TMTT Jul. 2015 2124-2132 Emanuelsson, T., see Horberg, M., TMTT Aug. 2015 2619-2629 Endo, Y., Saito, K., and Ito, K., The Development of Forceps-Type Microwave Tissue Coagulator for Surgical Operation; TMTT Jun. 2015 2041-2049 Englund, M., see Ostman, K. B., TMTT Apr. 2015 1370-1379 Entesari, K., see Pourghorban Saghati, A., TMTT Dec. 2015 4329-4340 Entesari, K., see Bajestan, M. M., TMTT Apr. 2015 1142-1153 Entesari, K., see Sepidband, P., TMTT Dec. 2015 4098-4109 Entesari, K., see Pourghorban Saghati, A., TMTT Aug. 2015 2515-2525 Enz, C., see Thirunarayanan, R., TMTT Apr. 2015 1110-1117 Enz, C. C., see Chalkiadaki, M.-A., TMTT Jul. 2015 2173-2184 Epp, M., see Singh, S., TMTT May 2015 1721-1734 Eriksson, K., Sobis, P. J., Gunnarsson, S. E., Hanning, J., and Zirath, H., InP DHBT Amplifier Modules Operating Between 150–300 GHz Using Membrane Technology; TMTT Feb. 2015 433-440 + Check author entry for coauthors

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Eriksson, K., Darwazeh, I., and Zirath, H., InP DHBT Distributed Amplifiers With Up to 235-GHz Bandwidth; TMTT Apr. 2015 1334-1341 Ertugrul, M., see Hasar, U. C., TMTT Jul. 2015 2313-2321 Esteban, H., see Belenguer, A., TMTT Dec. 2015 4027-4034 Esteban, J., and Camacho-Penalosa, C., Compact Orthomode Transducer Polarizer Based on a Tilted-Waveguide T-Junction; TMTT Oct. 2015 32083217

F Fager, C., see Sanchez-Perez, C., TMTT Aug. 2015 2579-2588 Fan, H., Geng, J., Liang, X., Jin, R., and Zhou, X., A Three-Way Reconfigurable Power Divider/Combiner; TMTT Mar. 2015 986-998 Fan, J., see Zhang, Y.-J., TMTT Mar. 2015 883-890 Fang, X.-H., and Cheng, K.-K. M., Improving Power Utilization Factor of Broadband Doherty Amplifier by Using Bandpass Auxiliary Transformer; TMTT Sep. 2015 2811-2820 Farhat, L. A., see Laur, V., TMTT Dec. 2015 4376-4381 Farinelli, P., see Pelliccia, L., TMTT Oct. 2015 3381-3390 Farsi, S., Gheidi, H., Dabag, H.-T., Gudem, P. S., Schreurs, D., and Asbeck, P. M., Modeling of Deterministic Output Emissions of Power Amplifiers Into Adjacent Receive Bands; TMTT Apr. 2015 1250-1262 Fathy, A. E., see Elkhouly, E., TMTT May 2015 1746-1757 Fay, P., see Lorenz, C. H. P., TMTT Dec. 2015 4544-4555 Feng, F., see Zhang, C., TMTT Jul. 2015 2154-2165 Feng, N., Yue, Y., and Liu, Q. H., Direct -Transform Implementation of the CFS-PML Based on Memory-Minimized Method; TMTT Mar. 2015 877-882 Feng, S., Qiang, R., Kainz, W., and Chen, J., A Technique to Evaluate MRIInduced Electric Fields at the Ends of Practical Implanted Lead; TMTT Jan. 2015 305-313 Feng, S.-F., see Wong, S.-W., TMTT Oct. 2015 3416-3424 Feng, S.-F., see Wong, S.-W., TMTT Dec. 2015 3947-3953 Feng, W., see Qian, H., TMTT Oct. 2015 3153-3163 Feng, W., Zhao, C., Che, W., and Xue, Q., Wideband Balanced Network with High Isolation Using Double-Sided Parallel-Strip Line; TMTT Dec. 2015 4013-4018 Fernandez, F. A., see Deo, P., TMTT Apr. 2015 1388-1398 Fernandez-Prieto, A., see Velez, P., TMTT Apr. 2015 1272-1280 Fernandez-Prieto, A., Lujambio, A., Martel, J., Medina, F., Mesa, F., and Boix, R. R., Simple and Compact Balanced Bandpass Filters Based on Magnetically Coupled Resonators; TMTT Jun. 2015 1843-1853 Ferranti, F., see Barmuta, P., TMTT Jan. 2015 56-64 Ferranti, F., see Barmuta, P., TMTT Dec. 2015 4501-4510 Ferrari, P., see Bautista, A., TMTT Dec. 2015 4225-4235 Ferrari, P., see Burdin, F., TMTT Jun. 2015 1883-1893 Fertner, A., see Lindqvist, F., TMTT Nov. 2015 3568-3578 Fierro, V., see Bellucci, S., TMTT Jun. 2015 2024-2031 Filicori, F., see Traverso, P. A., TMTT Feb. 2015 352-366 Filicori, F., see Florian, C., TMTT Aug. 2015 2589-2602 Fino, P., see Peverini, O. A., TMTT Oct. 2015 3361-3373 Florian, C., see Traverso, P. A., TMTT Feb. 2015 352-366 Florian, C., Cappello, T., Paganelli, R. P., Niessen, D., and Filicori, F., Envelope Tracking of an RF High Power Amplifier With an 8-Level Digitally Controlled GaN-on-Si Supply Modulator; TMTT Aug. 2015 2589-2602 Fornieles, J., see Salinas, A., TMTT Aug. 2015 2449-2458 Fournier, J.-M., see Serhan, A., TMTT Dec. 2015 4483-4491 Fournier, J.-M., see Lim, T., TMTT Nov. 2015 3747-3759 Franc, A.-F., see Bautista, A., TMTT Dec. 2015 4225-4235 Francois, B., and Reynaert, P., Highly Linear Fully Integrated Wideband RF PA for LTE-Advanced in 180-nm SOI; TMTT Feb. 2015 649-658 Fritsche, D., Tretter, G., Carta, C., and Ellinger, F., Millimeter-Wave LowNoise Amplifier Design in 28-nm Low-Power Digital CMOS; TMTT Jun. 2015 1910-1922 Fu, H.-P., see Cheng, Q.-F., TMTT Aug. 2015 2703-2704 Fu, J., see Sun, Y., TMTT Oct. 2015 3131-3141 Fu, J., see Gou, Y., TMTT Oct. 2015 3142-3152 Fu, M., Zhang, T., Ma, C., and Zhu, X., Efficiency and Optimal Loads Analysis for Multiple-Receiver Wireless Power Transfer Systems; TMTT Mar. 2015 801-812 Fuge, G., see Meyne nee Haase, N., TMTT Oct. 2015 3026-3033 Furlan, V., Glinsek, S., Kmet, B., Pecnik, T., Malic, B., and Vidmar, M., Influence of Numerical Method and Geometry Used by Maxwell's Equation

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Solvers on Simulations of Ferroelectric Thin-Film Capacitors; TMTT Mar. 2015 891-896 Fusco, V., see Thian, M., TMTT Feb. 2015 659-671 Fuser, H., see Bieler, M., TMTT Nov. 2015 3775-3784

G Gaffar, Md., and Jiao, D., Alternative Method for Making Explicit FDTD Unconditionally Stable; TMTT Dec. 2015 4215-4224 Galy, P., see Lim, T., TMTT Nov. 2015 3747-3759 Gamlath, C. D., Benton, D. M., and Cryan, M. J., Microwave Properties of an Inhomogeneous Optically Illuminated Plasma in a Microstrip Gap; TMTT Feb. 2015 374-383 Ganne, J. P., see Laur, V., TMTT Dec. 2015 4376-4381 Gao, F., Zhang, F., Wakatsuchi, H., and Sievenpiper, D. F., Synthesis and Design of Programmable Subwavelength Coil Array for Near-Field Manipulation; TMTT Sep. 2015 2971-2982 Gao, L., Zhang, X. Y., and Xue, Q., Compact Tunable Filtering Power Divider With Constant Absolute Bandwidth; TMTT Oct. 2015 3505-3513 Gao, P., see Gui, X., TMTT Jan. 2015 233-243 Gao, X., see Yu, X., TMTT Feb. 2015 326-330 Gao, X., see Yu, X. H., TMTT Dec. 2015 3845-3850 Gao, Z., Kang, K., Zhao, C., Wu, Y., Ban, Y., Sun, L., Hong, W., and Xue, Q., A Broadband and Equivalent-Circuit Model for Millimeter-Wave On-Chip M:N Six-Port Transformers and Baluns; TMTT Oct. 2015 3109-3121 Garcia, J. A., see Ramos, I., TMTT Dec. 2015 4473-4482 Garcia, J. A., see de Cos, J., TMTT Dec. 2015 4284-4296 Garcia, M. F., see Vazquez Antuna, C., TMTT Apr. 2015 1361-1369 Garcia, S. G., see Angulo, L. D., TMTT Oct. 2015 3081-3093 Garcia-Banos, B., see Catala-Civera, J. M., TMTT Sep. 2015 2905-2914 Garcia-Fernandez, M. A., see Kohler, S., TMTT Jun. 2015 2032-2040 Garcia-Pino, A., see Grajal, J., TMTT Mar. 2015 1097-1107 Garner, J. R., see Zhang, L., TMTT Oct. 2015 3183-3190 Garrec, P., see Kerherve, E., TMTT May 2015 1621-1632 Gauthier, J., see Lorenz, C. H. P., TMTT Dec. 2015 4544-4555 Ge, C., Zhu, X.-W., Jiang, X., and Xu, X.-J., Analysis of Weakly Nonlinear Effect for Varactor-Tuned Bandpass Filter; TMTT Nov. 2015 3641-3650 Geng, J., see Fan, H., TMTT Mar. 2015 986-998 Gentili, F., see Sirci, S., TMTT Dec. 2015 4341-4354 Georgiadis, A., see Andia Vera, G., TMTT Dec. 2015 4556-4566 Georgiadis, A., see Del Prete, M., TMTT Dec. 2015 4511-4520 Georgiadis, A., see Kimionis, J., TMTT Dec. 2015 4521-4532 Ghafouri Fard, M. R., see Maunder, A., TMTT Jul. 2015 2322-2334 Ghannouchi, F. M., see Akbarpour, M., TMTT Oct. 2015 3242-3253 Ghannouchi, F. M., see Amiri, M. V., TMTT Aug. 2015 2661-2671 Ghannouchi, F. M. G., see Darraji, R., TMTT Jun. 2015 1978-1988 Gharib, A., Weigel, R., and Kissinger, D., Broadband Circuit Techniques for Multi-Terahertz Gain-Bandwidth-Product Low-Power Applications; TMTT Nov. 2015 3701-3712 Gharpurey, R., Guest Editorial; TMTT Apr. 2015 1109 Gheidi, H., see Farsi, S., TMTT Apr. 2015 1250-1262 Gheitanchi, S., see Naraharisetti, N., TMTT Jul. 2015 2199-2210 Ghelfi, P., see Scotti, F., TMTT Feb. 2015 546-552 Ghiotto, A., see Doghri, A., TMTT Jan. 2015 209-221 Ghiotto, A., see Parment, F., TMTT Apr. 2015 1228-1238 Ghiotto, A., see Kerherve, E., TMTT May 2015 1621-1632 Ghorbani, K., and Vinoy, K. J., Guest Editorial; TMTT Aug. 2015 2397-2398 Gibiino, G. P., see Barmuta, P., TMTT Jan. 2015 56-64 Gil, J., see Carceller, C., TMTT Oct. 2015 3398-3407 Gilabert, P. L., and Montoro, G., 3-D Distributed Memory Polynomial Behavioral Model for Concurrent Dual-Band Envelope Tracking Power Amplifier Linearization; TMTT Feb. 2015 638-648 Gimeno, B., see Cogollos, S., TMTT Aug. 2015 2540-2549 Glinsek, S., see Furlan, V., TMTT Mar. 2015 891-896 Glock, S., Rascher, J., Sogl, B., Ussmueller, T., Mueller, J.-E., and Weigel, R., A Memoryless Semi-Physical Power Amplifier Behavioral Model Based on the Correlation Between AM–AM and AM–PM Distortions; TMTT Jun. 2015 1826-1835 Gomez-Garcia, R., see Psychogiou, D., TMTT Dec. 2015 4319-4328 Gomez-Garcia, R., and Guyette, A. C., Reconfigurable Multi-Band Microwave Filters; TMTT Apr. 2015 1294-1307 Gomez-Garcia, R., see Psychogiou, D., TMTT Jul. 2015 2233-2244 + Check author entry for coauthors

Gomez-Tornero, J. L., Martinez-Ros, A. J., Mercader-Pellicer, S., and Goussetis, G., Simple Broadband Quasi-Optical Spatial Multiplexer in Substrate Integrated Technology; TMTT May 2015 1609-1620 Gong, H., see Wei, W., TMTT May 2015 1445-1456 Gong, K., see Zhu, X.-C., TMTT Feb. 2015 494-503 Gong, Y., see Wei, W., TMTT May 2015 1445-1456 Gongal-Reddy, V.-M.-R., see Zhang, C., TMTT Jul. 2015 2154-2165 Gonzalez-Valdes, B., see Grajal, J., TMTT Mar. 2015 1097-1107 Goodyear, G., see Chen, T.-C., TMTT Nov. 2015 3768-3774 Goswami, S., see Choi, P., TMTT Apr. 2015 1163-1173 Gotzen, R., see Merkle, T., TMTT Feb. 2015 481-493 Gou, Y., Lin, M., Wu, Q., and Fu, J., Analytical Reflection Coefficient Expressions Utilizing Load-Dependent -Parameters; TMTT Oct. 2015 31423152 Goussetis, G., see Gomez-Tornero, J. L., TMTT May 2015 1609-1620 Grajal, J., Badolato, A., Rubio-Cidre, G., Ubeda-Medina, L., Mencia-Oliva, B., Garcia-Pino, A., Gonzalez-Valdes, B., and Rubinos, O., 3-D High-Resolution Imaging Radar at 300 GHz With Enhanced FoV; TMTT Mar. 2015 1097-1107 Grebennikov, A., Author's Reply; TMTT Aug. 2015 2705 Green, M. M., see Gui, X., TMTT Mar. 2015 945-953 Grenier, K., see Alomainy, A., TMTT Oct. 2015 3005-3006 Griswold, M. A., see Twieg, M., TMTT Dec. 2015 4169-4177 Grozing, M., see Huang, H., TMTT Apr. 2015 1211-1218 Grundel, S., see Hess, M. W., TMTT Nov. 2015 3549-3557 Gruszczynski, S., see Sorocki, J., TMTT Feb. 2015 384-396 Grzyb, J., see Statnikov, K., TMTT Feb. 2015 520-532 Gu, D., and Walker, D. K., Application of Coherence Theory to Modeling of Blackbody Radiation at Close Range; TMTT May 2015 1475-1488 Gu, Q. J., see Xu, Z., TMTT Apr. 2015 1219-1227 Gu, X., see Zhang, Y.-J., TMTT Mar. 2015 883-890 Guan, J., see Nghiem, X. A., TMTT Sep. 2015 2821-2832 Gubin, A. I., Barannik, A. A., Cherpak, N. T., Protsenko, I. A., Pud, S., Offenhausser, A., and Vitusevich, S. A., Whispering-Gallery-Mode Resonator Technique With Microfluidic Channel for Permittivity Measurement of Liquids; TMTT Jun. 2015 2003-2009 Gudem, P. S., see Luo, C., TMTT Oct. 2015 3514-3524 Gudem, P. S., see Farsi, S., TMTT Apr. 2015 1250-1262 Guegan, G., see De Paolis, R., TMTT Aug. 2015 2570-2578 Guerra, D., see Bluestone, A., TMTT Mar. 2015 1046-1052 Guglielmi, M., see Carceller, C., TMTT Oct. 2015 3398-3407 Guglielmi, M., see Cogollos, S., TMTT Aug. 2015 2540-2549 Gui, X., Gao, P., and Chen, Z., A CML Ring Oscillator-Based Supply-Insensitive PLL With On-Chip Calibrations; TMTT Jan. 2015 233-243 Gui, X., Chen, Z., and Green, M. M., Analysis of Nonlinearities in InjectionLocked Frequency Dividers; TMTT Mar. 2015 945-953 Gunel, S., and Zoral, E. Y., Parametric History Analysis for Material Properties Using Finite Elements and Adaptive Perturbations; TMTT Jan. 2015 90-98 Gunnarsson, S. E., see Eriksson, K., TMTT Feb. 2015 433-440 Gunnarsson, S. E., see Yan, Y., TMTT Sep. 2015 2897-2904 Guo, D., see Yu, F., TMTT Feb. 2015 403-413 Guo, L., see Chang, C., TMTT Jun. 2015 1875-1882 Guo, T., see Zhang, Q., TMTT Sep. 2015 2782-2792 Guo, X., see Lu, X., TMTT Apr. 2015 1281-1293 Guo, X., Zhu, L., Tam, K.-W., and Wu, W., Wideband Differential Bandpass Filters on Multimode Slotline Resonator With Intrinsic Common-Mode Rejection; TMTT May 2015 1587-1594 Guo, X., Zhu, L., Wang, J., and Wu, W., Wideband Microstrip-to-Microstrip Vertical Transitions Via Multiresonant Modes in a Slotline Resonator; TMTT Jun. 2015 1902-1909 Guo, Y., see Yu, C., TMTT Dec. 2015 4306-4318 Guo, Y., Yu, C., and Zhu, A., Power Adaptive Digital Predistortion for Wideband RF Power Amplifiers With Dynamic Power Transmission; TMTT Nov. 2015 3595-3607 Gupta, S., Zhang, Q., Zou, L., Jiang, L. J., and Caloz, C., Generalized CoupledLine All-Pass Phasers; TMTT Mar. 2015 1007-1018 Gurbuz, O., see Hanafi, B., TMTT Jun. 2015 1937-1950 Gurbuz, O. D., and Rebeiz, G. M., A 1.6–2.3-GHz RF MEMS Reconfigurable Quadrature Coupler and Its Application to a 360 Reflective-Type Phase Shifter; TMTT Feb. 2015 414-421 Gurbuz, O. D., see Dabag, H.-T., TMTT Jul. 2015 2364-2374 Gustafsson, M., see Vakili, I., TMTT Sep. 2015 2915-2922 Gustafsson, S., see Nordebo, S., TMTT Jun. 2015 1791-1799 Gutierrez, J. D., see Catala-Civera, J. M., TMTT Sep. 2015 2905-2914

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Guyette, A. C., see Naglich, E. J., TMTT Oct. 2015 3479-3486 Guyette, A. C., see Gomez-Garcia, R., TMTT Apr. 2015 1294-1307

H Ha, K.-W., see Park, J., TMTT Apr. 2015 1399-1408 Hadarig, A. I., see Vazquez Antuna, C., TMTT Apr. 2015 1361-1369 Hajimiri, A., see Bowers, S. M., TMTT Apr. 2015 1154-1162 Hajimiri, A., see Dasgupta, K., TMTT Apr. 2015 1118-1129 Hajimiri, A., see Sengupta, K., TMTT Sep. 2015 2867-2876 Hale, P. D., see Remley, K. A., TMTT May 2015 1710-1720 Hale, P. D., see Avolio, G., TMTT Jul. 2015 2353-2363 9.06 dBm IIP3 Han, H. G., Jung, D. H., and Kim, T. W., A 2.88 mW Common-Gate LNA With Dual Cross-Coupled Capacitive Feedback; TMTT Mar. 2015 1019-1025 Hanafi, B., Gurbuz, O., Dabag, H., Buckwalter, J. F., Rebeiz, G., and Asbeck, P., -Band Spatially Combined Power Amplifier Arrays in 45-nm CMOS SOI; TMTT Jun. 2015 1937-1950 Hanafi, B., see Dabag, H.-T., TMTT Jul. 2015 2364-2374 Handel, P., see Zenteno, E., TMTT Feb. 2015 754-765 Hanning, J., see Eriksson, K., TMTT Feb. 2015 433-440 Hao, Z.-C., Huo, X.-P., Ding, W.-Q., and Hong, W., Efficient Design of Compact Contiguous-Channel SIW Multiplexers Using the Space-Mapping Method; TMTT Nov. 2015 3651-3662 Hao, Z.-C., see Zhu, X.-C., TMTT Feb. 2015 494-503 Hardock, A., see Preibisch, J. B., TMTT Jun. 2015 1809-1816 Hardock, A., Bruns, H.-D., and Schuster, C., Chebyshev Filter Design Using Vias as Quasi-Transmission Lines in Printed Circuit Boards; TMTT Mar. 2015 976-985 Hart, A. J., see Li, S., TMTT Nov. 2015 3588-3594 Hasar, U. C., Kaya, Y., Barroso, J. J., and Ertugrul, M., Determination of Reference-Plane Invariant, Thickness-Independent, and Broadband Constitutive Parameters of Thin Materials; TMTT Jul. 2015 2313-2321 Hashemi, H., see Imani, A., TMTT May 2015 1658-1665 He, S., see Dai, Z., TMTT Feb. 2015 449-458 He, S., see Pang, J., TMTT Dec. 2015 4061-4071 He, W., see Zhang, L., TMTT Oct. 2015 3183-3190 He, W., see Zhang, L., TMTT Mar. 2015 1090-1096 He, Z., Chen, J., Svensson, C., Bao, L., Rhodin, A., Li, Y., An, J., and Zirath, H., A Hardware Efficient Implementation of a Digital Baseband Receiver for High-Capacity Millimeter-Wave Radios; TMTT May 2015 1683-1692 He, Z., Nopchinda, D., Swahsn, T., and Zirath, H., A 15-Gb/s 8-PSK Demodulator With Comparator-Based Carrier Synchronization; TMTT Aug. 2015 2630-2637 Heikenfeld, J., see Cumby, B. L., TMTT Oct. 2015 3122-3130 Heilmeyer, J., see Huang, H., TMTT Apr. 2015 1211-1218 Heinemann, B., see Statnikov, K., TMTT Feb. 2015 520-532 Heitz, B., see Lim, T., TMTT Nov. 2015 3747-3759 Helaoui, M., see Akbarpour, M., TMTT Oct. 2015 3242-3253 Helaoui, M., see Darraji, R., TMTT Jun. 2015 1978-1988 Helaoui, M., see Amiri, M. V., TMTT Aug. 2015 2661-2671 Helsing, J., and Karlsson, A., Determination of Normalized Magnetic Eigenfields in Microwave Cavities; TMTT May 2015 1457-1467 Helszajn, J., and Carignan, L.-P., Quality Factor of the Waveguide Re-Entrant Turnstile Junction Circulator; TMTT May 2015 1603-1608 Hemour, S., see Lorenz, C. H. P., TMTT Dec. 2015 4544-4555 Hess, M. W., Grundel, S., and Benner, P., Estimating the Inf-Sup Constant in Reduced Basis Methods for Time-Harmonic Maxwell’s Equations; TMTT Nov. 2015 3549-3557 Hester, J. G., see Bito, J., TMTT Dec. 2015 4533-4543 Hettak, K., see Ross, T. N., TMTT Jan. 2015 244-255 Hitko, D. A., see Xu, Z., TMTT Apr. 2015 1219-1227 Ho, C.-Y., Cheng, H.-H., Pan, P.-C., Wang, C.-C., and Hung, C.-P., Dielectric Characterization of Ultra-Thin Low-Loss Build-Up Substrate for Systemin-Package (SiP) Modules; TMTT Sep. 2015 2923-2930 Ho, M.-C., see Kohler, S., TMTT Jun. 2015 2032-2040 Hoefer, W. J. R., Computational Time Reversal—A Frontier in Electromagnetic Structure Synthesis and Design; TMTT Jan. 2015 3-10 Hoeye, S. V., see Vazquez Antuna, C., TMTT Apr. 2015 1361-1369 Holland, K. D., see Alam, A. U., TMTT Dec. 2015 3874-3887 Hong, J., see Cervera, F., TMTT Dec. 2015 3920-3928 Hong, S., see Lee, S., TMTT May 2015 1735-1745 Hong, S., see Oh, J., TMTT Aug. 2015 2609-2618 + Check author entry for coauthors

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Hong, S., see Koo, H., TMTT Mar. 2015 1036-1045 Hong, W., see Hao, Z.-C., TMTT Nov. 2015 3651-3662 Hong, W., see Gao, Z., TMTT Oct. 2015 3109-3121 Hong, W., see Zhu, X.-C., TMTT Feb. 2015 494-503 Hong, Z., see Chao, Y., TMTT Apr. 2015 1193-1201 Honjo, K., see Watanabe, S., TMTT Feb. 2015 572-579 Hooker, J. W., Ramaswamy, V., Arora, R. K., Edison, A. S., Withers, R. S., Nast, R. E., and Brey, W. W., An Empirical Expression to Predict the Resonant Frequencies of Archimedean Spirals; TMTT Jul. 2015 2107-2114 Horberg, M., Emanuelsson, T., Lai, S., Thanh, T. N. D., Zirath, H., and Kuylenstierna, D., Phase-Noise Analysis of an X-Band Ultra-Low Phase-Noise GaN HEMT Based Cavity Oscillator; TMTT Aug. 2015 2619-2629 Horng, T.-S., see Wang, F.-K., TMTT Dec. 2015 4592-4602 Hotopan, G. R., see Vazquez Antuna, C., TMTT Apr. 2015 1361-1369 Hou, L., see Huang, S. Y., TMTT Aug. 2015 2482-2490 Hrobak, M., Sterns, M., Schramm, M., Stein, W., and Schmidt, L.-P., Corrections to “Design and Fabrication of Broadband Hybrid GaAs Schottky Diode Frequency Multipliers” [Dec 13 4442-4460]; TMTT Feb. 2015 553 Hsiao, C.-Y., Huang, Y.-C., and Wu, T.-L., An Ultra-Compact Common-Mode Bandstop Filter With Modified-T Circuits in Integrated Passive Device (IPD) Process; TMTT Nov. 2015 3624-3631 Hsiao, C.-Y., Cheng, C.-H., and Wu, T.-L., A New Broadband Common-Mode Noise Absorption Circuit for High-Speed Differential Digital Systems; TMTT Jun. 2015 1894-1901 Hsu, H.-L., see Lee, M.-L., TMTT Feb. 2015 614-624 Hsu, S. S. H., see Tan, K.-W., TMTT Apr. 2015 1380-1387 Hu, S., Kousai, S., and Wang, H., Antenna Impedance Variation Compensation by Exploiting a Digital Doherty Power Amplifier Architecture; TMTT Feb. 2015 580-597 Hua, W., see Li, S., TMTT Nov. 2015 3588-3594 Huang, C., see Pang, J., TMTT Dec. 2015 4061-4071 Huang, F., Suppression of Harmonics in Microstrip Filters Using a Combination of Techniques; TMTT Oct. 2015 3453-3461 Huang, H., Xia, J., Islam, A., Ng, E., Levine, P. M., and Boumaiza, S., Digitally Assisted Analog/RF Predistorter With a Small-Signal-Assisted Parameter Identification Algorithm; TMTT Dec. 2015 4297-4305 Huang, H., see Qian, H., TMTT Oct. 2015 3153-3163 Huang, H., Heilmeyer, J., Grozing, M., Berroth, M., Leibrich, J., and Rosenkranz, W., An 8-bit 100-GS/s Distributed DAC in 28-nm CMOS for Optical Communications; TMTT Apr. 2015 1211-1218 Huang, K., and Liao, Y., Transient Power Loss Density of Electromagnetic Pulse in Debye Media; TMTT Jan. 2015 135-140 Huang, S. Y., Hou, L., and Wu, J., MRI-Based Electrical Property Retrieval by Applying the Finite-Element Method (FEM); TMTT Aug. 2015 2482-2490 Huang, S.-Y., see Liu, Y.-C., TMTT Sep. 2015 2841-2853 Huang, W., see Chang, C., TMTT Jun. 2015 1875-1882 Huang, Y.-C., see Hsiao, C.-Y., TMTT Nov. 2015 3624-3631 Huang, Z., see Yu, F., TMTT Feb. 2015 403-413 Hung, C.-P., see Ho, C.-Y., TMTT Sep. 2015 2923-2930 Hung, H. A., see Darwish, A. M., TMTT Jul. 2015 2253-2263 Hunter, I., see Snyder, R. V., TMTT Oct. 2015 3324-3360 Hunter, I. C., see Musonda, E., TMTT Dec. 2015 4355-4365 Hunter, I. C., see Musonda, E., TMTT Mar. 2015 954-964 Huo, X.-P., see Hao, Z.-C., TMTT Nov. 2015 3651-3662 Hur, B., and Eisenstadt, W. R., CMOS Broadband Programmable Gain Active Balun With 0.5-dB Gain Steps; TMTT Aug. 2015 2650-2660 Hwang, T., Azadet, K., Wilson, R. S., and Lin, J., Linearization and Imbalance Correction Techniques for Broadband Outphasing Power Amplifiers; TMTT Jul. 2015 2185-2198

I Ibrahim, A. A., see Darwish, A. M., TMTT Jul. 2015 2253-2263 Im, D., Kim, B.-K., Im, D.-K., and Lee, K., A Stacked-FET Linear SOI CMOS Cellular Antenna Switch With an Extremely Low-Power Biasing Strategy; TMTT Jun. 2015 1964-1977 Im, D.-K., see Im, D., TMTT Jun. 2015 1964-1977 Imani, A., and Hashemi, H., An FBAR/CMOS Frequency/Phase Discriminator and Phase Noise Reduction System; TMTT May 2015 1658-1665 Imtiaz, A., Lees, J., Choi, H., and Joshi, L. T., An Integrated Continuous ClassMode Power Amplifier Design Approach for Microwave Enhanced Portable Diagnostic Applications; TMTT Oct. 2015 3007-3015 Ioannidis, Z. C., see Savaidis, S. P., TMTT Jan. 2015 125-134

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Isakov, M., see Kimionis, J., TMTT Dec. 2015 4521-4532 Isaksson, M., see Zenteno, E., TMTT Feb. 2015 754-765 Ishikawa, R., see Watanabe, S., TMTT Feb. 2015 572-579 Ishikuro, H., see Nakamura, T., TMTT Dec. 2015 4090-4097 Iskandar, Z., see Burdin, F., TMTT Jun. 2015 1883-1893 Islam, A., see Huang, H., TMTT Dec. 2015 4297-4305 Islam, M. A., and Karmakar, N. C., Real-World Implementation Challenges of a Novel Dual-Polarized Compact Printable Chipless RFID Tag; TMTT Dec. 2015 4581-4591 Islam, M. A., and Karmakar, N. C., Compact Printable Chipless RFID Systems; TMTT Nov. 2015 3785-3793 Islam, Md. M., Rasilainen, K., and Viikari, V., Implementation of Sensor RFID: Carrying Sensor Information in the Modulation Frequency; TMTT Aug. 2015 2672-2681 Ito, K., see Endo, Y., TMTT Jun. 2015 2041-2049

J Jackson, H. W., see Barmatz, M. B., TMTT Feb. 2015 504-508 Jacob, A. F., see Meyne nee Haase, N., TMTT Oct. 2015 3026-3033 Jameson, S., and Socher, E., A Wide-Band CMOS to Waveguide Transition at mm-Wave Frequencies With Wire-Bonds; TMTT Sep. 2015 2741-2750 Jamieson, C. S., see Barmatz, M. B., TMTT Feb. 2015 504-508 Jang, G., see Wang, X., TMTT Mar. 2015 965-975 Jang, H., see Na, K., TMTT Jan. 2015 295-304 Jang, H., see Lin, Y., TMTT Sep. 2015 2764-2775 Jang, I. G., see Lee, S. B., TMTT Mar. 2015 813-820 Jang, J., see Oh, J., TMTT Aug. 2015 2609-2618 Jantunen, H., see Rashidian, A., TMTT Sep. 2015 2720-2729 Jargon, J., see Remley, K. A., TMTT May 2015 1710-1720 Jargon, J., see Avolio, G., TMTT Jul. 2015 2353-2363 Javeed, A. S., see Barmatz, M. B., TMTT Feb. 2015 504-508 Jawad, G. N., Sloan, R., and Missous, M., On the Design of Gyroelectric Resonators and Circulators Using a Magnetically Biased 2-D Electron Gas (2-DEG); TMTT May 2015 1512-1517 Jee, S., Lee, J., Son, J., Kim, S., Kim, C. H., Moon, J., and Kim, B., Asymmetric Broadband Doherty Power Amplifier Using GaN MMIC for Femto-Cell Base-Station; TMTT Sep. 2015 2802-2810 Jee, S., see Camarchia, V., TMTT Feb. 2015 559-571 Jelonnek, J., see Wu, C., TMTT Aug. 2015 2459-2467 Jeon, J., see Ji, D., TMTT May 2015 1530-1543 Jeon, M.-S., Woo, J.-L., Park, S., and Kwon, Y., A Pulsed Dynamic Load Modulation Technique for High-Efficiency Linear Transmitters; TMTT Sep. 2015 2854-2866 Jeon, S., see Kim, Y., TMTT Jan. 2015 256-265 Jeong, Y., see Kim, M., TMTT Nov. 2015 3806-3813 Jha, A. K., and Akhtar, M. J., Design of Multilayered Epsilon-Near-Zero Microwave Planar Sensor for Testing of Dispersive Materials; TMTT Aug. 2015 2418-2426 Ji, D., Jeon, J., and Kim, J., A Novel Load Mismatch Detection and Correction Technique for 3G/4G Load Insensitive Power Amplifier Application; TMTT May 2015 1530-1543 Ji, Z., see Ding, W., TMTT Oct. 2015 3272-3276 Jia, H., Chi, B., Kuang, L., and Wang, Z., A 47.6–71.0-GHz 65-nm CMOS VCO Based on Magnetically Coupled -Type LC Network; TMTT May 2015 1645-1657 Jia, H., Chi, B., Kuang, L., and Wang, Z., A W-Band Power Amplifier Utilizing a Miniaturized Marchand Balun Combiner; TMTT Feb. 2015 719-725 Jiang, L. J., see Gupta, S., TMTT Mar. 2015 1007-1018 Jiang, X., see Ge, C., TMTT Nov. 2015 3641-3650 Jiang, Y., see Jin, J. Y., TMTT Oct. 2015 3374-3380 Jiang, Y., see Yu, X., TMTT Feb. 2015 326-330 Jiang, Y. N., see Yu, X. H., TMTT Dec. 2015 3845-3850 Jiao, D., see Gaffar, Md., TMTT Dec. 2015 4215-4224 Jiao, D., see Yan, J., TMTT Dec. 2015 4201-4214 Jiao, D., see Zhou, B., TMTT Oct. 2015 3066-3080 Jiao, D., see Omar, S., TMTT Mar. 2015 897-912 Jimenez, J., see Lim, T., TMTT Nov. 2015 3747-3759 Jin, J. Y., Lin, X. Q., Jiang, Y., and Xue, Q., A Novel Compact -Plane Waveguide Filter With Multiple Transmission Zeroes; TMTT Oct. 2015 3374-3380 Jin, R., see Fan, H., TMTT Mar. 2015 986-998 Jin, S., see Moon, K., TMTT Apr. 2015 1324-1333 + Check author entry for coauthors

Jirauschek, C., see Russer, J. A., TMTT Dec. 2015 4236-4246 Johansen, T. K., see Acar, O., TMTT Oct. 2015 3425-3432 Joshi, L. T., see Imtiaz, A., TMTT Oct. 2015 3007-3015 Joshi, M. S., see Kulkarni, S., TMTT Aug. 2015 2411-2417 Joubert, J., see Kloke, K. H., TMTT Oct. 2015 3103-3108 Juan, B., see Riehl, P. S., TMTT Mar. 2015 780-790 Jundi, A., Sarbishaei, H., and Boumaiza, S., An 85-W Multi-Octave Push–Pull GaN HEMT Power Amplifier for High-Efficiency Communication Applications at Microwave Frequencies; TMTT Nov. 2015 3691-3700 Jung, D. H., see Kong, S., TMTT Mar. 2015 833-846 Jung, D. H., see Han, H. G., TMTT Mar. 2015 1019-1025 Juuti, J., see Rashidian, A., TMTT Sep. 2015 2720-2729

K

Kabanov, I. N., see Alaverdyan, S. A., TMTT Aug. 2015 2509-2514 Kainz, W., see Feng, S., TMTT Jan. 2015 305-313 Kallfass, I., see Antes, J., TMTT Oct. 2015 3288-3299 Kallfass, I., see Diebold, S., TMTT Mar. 2015 999-1006 Kameda, S., see Ta, T. T., TMTT Aug. 2015 2682-2691 Kameoka, J., see Pourghorban Saghati, A., TMTT Aug. 2015 2515-2525 Kang, D., see Kim, J., TMTT Dec. 2015 4072-4082 Kang, K., see Gao, Z., TMTT Oct. 2015 3109-3121 Kao, J.-C., see Chang, J.-F., TMTT Aug. 2015 2638-2649 Karami, H., see Maftooli, H., TMTT Jan. 2015 99-106 Karlsson, A., see Helsing, J., TMTT May 2015 1457-1467 Karmakar, N. C., see Islam, M. A., TMTT Dec. 2015 4581-4591 Karmakar, N. C., see Islam, M. A., TMTT Nov. 2015 3785-3793 Kasparek, W., see Wu, Z., TMTT Oct. 2015 3537-3546 Kaya, Y., see Hasar, U. C., TMTT Jul. 2015 2313-2321 Kaymaksut, E., Zhao, D., and Reynaert, P., Transformer-Based Doherty Power Amplifiers for mm-Wave Applications in 40-nm CMOS; TMTT Apr. 2015 1186-1192 Kerherve, E., Demirel, N., Ghiotto, A., Larie, A., Deltimple, N., Pham, J.-M., Mancuso, Y., and Garrec, P., A Broadband 4.5–15.5-GHz SiGe Power Amplifier With 25.5-dBm Peak Saturated Output Power and 28.7% Maximum PAE; TMTT May 2015 1621-1632 Ketterl, T. P., Vega, Y., Arnal, N. C., Stratton, J. W. I., Rojas-Nastrucci, E. A., Cordoba-Erazo, M. F., Abdin, M. M., Perkowski, C. W., Deffenbaugh, P. I., Church, K. H., and Weller, T. M., A 2.45 GHz Phased Array Antenna Unit Cell Fabricated Using 3-D Multi-Layer Direct Digital Manufacturing; TMTT Dec. 2015 4382-4394 Khalaf, K., see Mangraviti, G., TMTT Jul. 2015 2301-2312 Khamaisi, B., and Socher, E., 130-320-GHz CMOS Harmonic Down-Converters Around and Above the Cutoff Frequency; TMTT Jul. 2015 22752288 Khan, B. A., see Zhang, Q., TMTT Sep. 2015 2782-2792 Khanna, D., see Choi, P., TMTT Apr. 2015 1163-1173 Kiang, J.-F., see Lo, Y.-T., TMTT Apr. 2015 1353-1360 Kianinejad, A., Chen, Z. N., and Qiu, C.-W., Design and Modeling of Spoof Surface Plasmon Modes-Based Microwave Slow-Wave Transmission Line; TMTT Jun. 2015 1817-1825 Kiayani, A., Abdelaziz, M., Anttila, L., Lehtinen, V., and Valkama, M., Digital Mitigation of Transmitter-Induced Receiver Desensitization in Carrier Aggregation FDD Transceivers; TMTT Nov. 2015 3608-3623 Kienle, D., see Alam, A. U., TMTT Dec. 2015 3874-3887 Kildal, P.-S., see Brazalez, A. A., TMTT Dec. 2015 4035-4050 Kim, B., see Moon, K., TMTT Apr. 2015 1324-1333 Kim, B., see Jee, S., TMTT Sep. 2015 2802-2810 Kim, B., see Camarchia, V., TMTT Feb. 2015 559-571 Kim, B., see Kim, J., TMTT Dec. 2015 4072-4082 Kim, B.-K., see Im, D., TMTT Jun. 2015 1964-1977 Kim, B.-S., see Cui, C., TMTT Nov. 2015 3736-3746 Kim, C. H., see Jee, S., TMTT Sep. 2015 2802-2810 Kim, C.-Y., see Lee, S., TMTT May 2015 1735-1745 Kim, C.-Y., see Oh, J., TMTT Aug. 2015 2609-2618 Kim, C.-Y., see Koo, H., TMTT Mar. 2015 1036-1045 Kim, D., see Kim, M., TMTT Nov. 2015 3806-3813 Kim, D., see Moon, K., TMTT Apr. 2015 1324-1333 Kim, D., see Kim, J., TMTT Dec. 2015 4072-4082 Kim, D.-H., see Kim, J., TMTT Mar. 2015 791-800 Kim, H., see Kim, M., TMTT Nov. 2015 3806-3813

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 63, NO. 12, DECEMBER 2015

Kim, H.-J., Rashidinejad, A., and Weiner, A. M., Low-Loss Ultrawideband Programmable RF Photonic Phase Filter for Spread Spectrum Pulse Compression; TMTT Dec. 2015 4178-4187 Kim, J., see Moon, K., TMTT Apr. 2015 1324-1333 Kim, J., see Ji, D., TMTT May 2015 1530-1543 Kim, J., Kim, D., Cho, Y., Kang, D., Park, B., Moon, K., and Kim, B., Analysis of Far-Out Spurious Noise and its Reduction in Envelope-Tracking Power Amplifier; TMTT Dec. 2015 4072-4082 Kim, J., see Kong, S., TMTT Mar. 2015 833-846 Kim, J., see Kong, S., TMTT Mar. 2015 833-846 Kim, J., see Shin, H., TMTT Mar. 2015 1026-1035 KIM, J., and AHN, S., Guest Editorial; TMTT Mar. 2015 778-779 Kim, J., Kim, D.-H., Choi, J., Kim, K.-H., and Park, Y.-J., Free-Positioning Wireless Charging System for Small Electronic Devices Using a BowlShaped Transmitting Coil; TMTT Mar. 2015 791-800 Kim, J. J., see Kong, S., TMTT Mar. 2015 833-846 Kim, J.-G., see Park, J., TMTT Apr. 2015 1399-1408 Kim, K.-H., see Kim, J., TMTT Mar. 2015 791-800 Kim, M., Kim, H., Kim, D., Jeong, Y., Park, H.-H., and Ahn, S., A ThreePhase Wireless-Power-Transfer System for Online Electric Vehicles With Reduction of Leakage Magnetic Fields; TMTT Nov. 2015 3806-3813 Kim, N., see Shin, H., TMTT Mar. 2015 1026-1035 Kim, S., see Kim, Y., TMTT Jan. 2015 256-265 Kim, S., see Lee, I.-Y., TMTT Apr. 2015 1202-1210 Kim, S., see Xu, Z., TMTT Apr. 2015 1219-1227 Kim, S., see Jee, S., TMTT Sep. 2015 2802-2810 Kim, S., see Kong, S., TMTT Mar. 2015 833-846 Kim, S.-K., see Cui, C., TMTT Nov. 2015 3736-3746 Kim, S.-M., Moon, J.-I., Cho, I.-K., Yoon, J.-H., Byun, W.-J., and Choi, H.-C., Advanced Power Control Scheme in Wireless Power Transmission for Human Protection From EM Field; TMTT Mar. 2015 847-856 Kim, T. W., see Han, H. G., TMTT Mar. 2015 1019-1025 Kim, U., see Park, S., TMTT Apr. 2015 1174-1185 Kim, Y., Kim, S., Lee, I., Urteaga, M., and Jeon, S., A 220–320-GHz Vector-Sum Phase Shifter Using Single Gilbert-Cell Structure With Lossy Output Matching; TMTT Jan. 2015 256-265 Kim, Y., and Kwon, Y., Analysis and Design of Millimeter-Wave Power Amplifier Using Stacked-FET Structure; TMTT Feb. 2015 691-702 Kimionis, J., Isakov, M., Koh, B. S., Georgiadis, A., and Tentzeris, M. M., 3D-Printed Origami Packaging With Inkjet-Printed Antennas for RF Harvesting Sensors; TMTT Dec. 2015 4521-4532 King, J. B., see Cai, J., TMTT May 2015 1518-1529 Kiourti, A., see Lee, C. W. L., TMTT Jun. 2015 2060-2068 Kissinger, D., see Gharib, A., TMTT Nov. 2015 3701-3712 Kitazawa, N., see Nakamura, T., TMTT Dec. 2015 4090-4097 Kloke, K. H., Joubert, J., and Odendaal, J. W., Coaxial End-Launched and Microstrip to Partial -Plane Waveguide Transitions; TMTT Oct. 2015 3103-3108 Kmet, B., see Furlan, V., TMTT Mar. 2015 891-896 Knockaert, L., see Barmuta, P., TMTT Dec. 2015 4501-4510 Ko, C. H., and Rebeiz, G. M., A 1.4–2.3-GHz Tunable Diplexer Based on Reconfigurable Matching Networks; TMTT May 2015 1595-1602 Ko, C.-H., Tran, A., and Rebeiz, G. M., Tunable 500–1200-MHz Dual-Band and Wide Bandwidth Notch Filters Using RF Transformers; TMTT Jun. 2015 1854-1862 Ko, C.-L., see Li, C.-H., TMTT Feb. 2015 470-480 Ko, J., see Lee, I.-Y., TMTT Apr. 2015 1202-1210 Koch, S., see Merkle, T., TMTT Feb. 2015 481-493 Kodera, T., see Zhang, Q., TMTT Sep. 2015 2782-2792 Koenen, C., Siart, U., Eibert, T. F., Conway, G. D., and Stroth, U., A Configurable Coupling Structure for Broadband Millimeter-Wave Split-Block Networks; TMTT Dec. 2015 3954-3961 Kogami, Y., see Shimizu, T., TMTT Jan. 2015 279-286 Koh, B., see Lee, B., TMTT Nov. 2015 3632-3640 Koh, B. S., see Kimionis, J., TMTT Dec. 2015 4521-4532 Kohira, K., see Nakamura, T., TMTT Dec. 2015 4090-4097 Kohler, S., Levine, Z. A., Garcia-Fernandez, M. A., Ho, M.-C., Vernier, P. T., Leveque, P., and Arnaud-Cormos, D., Electrical Analysis of Cell Membrane Poration by an Intense Nanosecond Pulsed Electric Field Using an Atomistic-to-Continuum Method; TMTT Jun. 2015 2032-2040 Kojima, S., see Shimizu, T., TMTT Jan. 2015 279-286 Kokkorakis, G. C., see Zouros, G. P., TMTT Oct. 2015 3054-3065 Kolezas, G. D., see Zouros, G. P., TMTT Oct. 2015 3042-3053 Koli, K., see Ostman, K. B., TMTT Apr. 2015 1370-1379 + Check author entry for coauthors

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Komarov, V. V., see Alaverdyan, S. A., TMTT Aug. 2015 2509-2514 Kong, S., see Lee, S., TMTT May 2015 1735-1745 Kong, S., Bae, B., Jung, D. H., Kim, J. J., Kim, S., Song, C., Kim, J., and Kim, J., An Investigation of Electromagnetic Radiated Emission and Interference From Multi-Coil Wireless Power Transfer Systems Using Resonant Magnetic Field Coupling; TMTT Mar. 2015 833-846 Koo, H., Kim, C.-Y., and Hong, S., A G-Band Standing-Wave Push–Push VCO Using a Transmission-Line Resonator; TMTT Mar. 2015 1036-1045 Kotsis, A. D., see Zouros, G. P., TMTT Mar. 2015 864-876 Koufogiannis, I. D., Mattes, M., and Mosig, J. R., On the Development and Evaluation of Spatial-Domain Green’s Functions for Multilayered Structures With Conductive Sheets; TMTT Jan. 2015 20-29 Koul, S., see Barthwal, A., TMTT Aug. 2015 2399-2410 Koul, S. K., see Dey, S., TMTT Dec. 2015 3997-4012 Kousai, S., see Hu, S., TMTT Feb. 2015 580-597 Koziel, S., and Bandler, J. W., Rapid Yield Estimation and Optimization of Microwave Structures Exploiting Feature-Based Statistical Analysis; TMTT Jan. 2015 107-114 Koziel, S., and Bandler, J. W., Reliable Microwave Modeling by Means of Variable-Fidelity Response Features; TMTT Dec. 2015 4247-4254 Koziel, S., and Bekasiewicz, A., Expedited Geometry Scaling of Compact Microwave Passives by Means of Inverse Surrogate Modeling; TMTT Dec. 2015 4019-4026 Kranauskaite, I., see Bellucci, S., TMTT Jun. 2015 2024-2031 Krishnaswamy, H., see Bhat, R., TMTT Feb. 2015 703-718 Krolik, J. L., see Cnaan-On, I., TMTT Jul. 2015 2375-2383 Kuang, L., see Jia, H., TMTT May 2015 1645-1657 Kuang, L., see Jia, H., TMTT Feb. 2015 719-725 Kuhn, V., Lahuec, C., Seguin, F., and Person, C., A Multi-Band Stacked RF Energy Harvester With RF-to-DC Efficiency Up to 84%; TMTT May 2015 1768-1778 Kulkarni, S., and Joshi, M. S., Design and Analysis of Shielded Vertically Stacked Ring Resonator as Complex Permittivity Sensor for Petroleum Oils; TMTT Aug. 2015 2411-2417 Kumar, T. B., see Ma, K., TMTT Dec. 2015 4395-4405 Kung, M.-L., and Lin, K.-H., Enhanced Analysis and Design Method of DualBand Coil Module for Near-Field Wireless Power Transfer Systems; TMTT Mar. 2015 821-832 Kuo, C.-N., see Li, C.-H., TMTT Feb. 2015 470-480 Kuo, M.-C., see Li, C.-H., TMTT Feb. 2015 470-480 Kuo, N.-C., Chien, J.-C., and Niknejad, A. M. N., Design and Analysis on Bidirectionally and Passively Coupled QVCO With Nonlinear Coupler; TMTT Apr. 2015 1130-1141 Kusiek, A., Lech, R., Marynowski, W., and Mazur, J., An Analysis of Multistrip Line Configuration on Elliptical Cylinder; TMTT Jun. 2015 1800-1808 Kuylenstierna, D., see Sanchez-Perez, C., TMTT Aug. 2015 2579-2588 Kuylenstierna, D., see Horberg, M., TMTT Aug. 2015 2619-2629 Kuzhir, P., see Bellucci, S., TMTT Jun. 2015 2024-2031 Kwak, C., see Lee, B., TMTT Nov. 2015 3632-3640 Kwan, A. K., see Darraji, R., TMTT Jun. 2015 1978-1988 Kwark, Y. H., see Zhang, Y.-J., TMTT Mar. 2015 883-890 Kwon, Y., see Lee, S., TMTT Dec. 2015 4406-4414 Kwon, Y., see Park, S., TMTT Apr. 2015 1174-1185 Kwon, Y., see Jeon, M.-S., TMTT Sep. 2015 2854-2866 Kwon, Y., see Kim, Y., TMTT Feb. 2015 691-702 Kyriacou, G. A., see Zekios, C. L., TMTT Jul. 2015 2082-2093

L Ladan, S., and Wu, K., Nonlinear Modeling and Harmonic Recycling of Millimeter-Wave Rectifier Circuit; TMTT Mar. 2015 937-944 Laghezza, F., see Scotti, F., TMTT Feb. 2015 546-552 Lahuec, C., see Kuhn, V., TMTT May 2015 1768-1778 Lai, C.-W., see Li, C.-H., TMTT Feb. 2015 470-480 Lai, S., see Horberg, M., TMTT Aug. 2015 2619-2629 Lancaster, M. J., see Tornielli di Crestvolant, V., TMTT Oct. 2015 3433-3444 Larie, A., see Kerherve, E., TMTT May 2015 1621-1632 Laroche, E., see Laur, V., TMTT Dec. 2015 4376-4381 Larson, L. E., see Thomas, C. M., TMTT Oct. 2015 3525-3536 Larson, L. E., see Bagheri, M., TMTT Nov. 2015 3713-3726 Lau, M., see Xu, Z., TMTT Apr. 2015 1219-1227 Lauga-Larroze, E., see Serhan, A., TMTT Dec. 2015 4483-4491

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Laur, V., Verissimo, G., Queffelec, P., Farhat, L. A., Alaaeddine, H., Laroche, E., Martin, G., Lebourgeois, R., and Ganne, J. P., Self-Biased Y-Junction Circulators Using Lanthanum- and Cobalt-Substituted Strontium Hexaferrites; TMTT Dec. 2015 4376-4381 Lebourgeois, R., see Laur, V., TMTT Dec. 2015 4376-4381 Lech, R., see Kusiek, A., TMTT Jun. 2015 1800-1808 Lee, B., Nam, S., Koh, B., Kwak, C., and Lee, J., K-Band Frequency Tunable Substrate-Integrated- Waveguide Resonator Filter With Enhanced Stopband Attenuation; TMTT Nov. 2015 3632-3640 Lee, B., see Wang, X., TMTT Mar. 2015 965-975 Lee, C. W. L., Kiourti, A., Chae, J., and Volakis, J. L., A High-Sensitivity Fully Passive Neurosensing System for Wireless Brain Signal Monitoring; TMTT Jun. 2015 2060-2068 Lee, C.-I., Lin, W.-C., Lin, Y.-T., and Yang, B.-S., Investigation of RF Avalanche Inductive Effect on Reduction of Intermodulation Distortion of MOSFETs Using Volterra Series Analysis; TMTT Feb. 2015 367-373 Lee, C.-I., Lin, Y.-T., and Lin, W.-C., An Improved VBIC Large-Signal Equivalent-Circuit Model for SiGe HBT With an Inductive Breakdown Network by -Parameters; TMTT Sep. 2015 2756-2763 Lee, C.-M., see Riehl, P. S., TMTT Mar. 2015 780-790 Lee, C.-S., and Yang, C.-L., Single-Compound Complementary Split-Ring Resonator for Simultaneously Measuring the Permittivity and Thickness of Dual-Layer Dielectric Materials; TMTT Jun. 2015 2010-2023 Lee, H.-S., see Choi, P., TMTT Apr. 2015 1163-1173 Lee, I., see Kim, Y., TMTT Jan. 2015 256-265 Lee, I.-Y., Kim, S., Lee, S.-S., Choi, J., Ko, J., and Lee, S.-G., Spur Reduction Techniques With a Switched-Capacitor Feedback Differential PLL and a DLL-Based SSCG in UHF RFID Transmitter; TMTT Apr. 2015 1202-1210 Lee, J., see Lee, B., TMTT Nov. 2015 3632-3640 Lee, J., see Jee, S., TMTT Sep. 2015 2802-2810 Lee, J., see Saeedi, S., TMTT Dec. 2015 3929-3938 Lee, J., see Lee, T.-C., TMTT Aug. 2015 2526-2539 Lee, K., see Im, D., TMTT Jun. 2015 1964-1977 Lee, M.-L., Liou, C.-Y., Tsai, W.-T., Lou, C.-Y., Hsu, H.-L., and Mao, S.-G., Fully Monolithic BiCMOS Reconfigurable Power Amplifier for Multi-Mode and Multi-Band Applications; TMTT Feb. 2015 614-624 Lee, S., Park, H., Choi, K., and Kwon, Y., A Broadband GaN pHEMT Power Amplifier Using Non-Foster Matching; TMTT Dec. 2015 4406-4414 Lee, S., Kong, S., Kim, C.-Y., and Hong, S., A K-Band CMOS UWB FourChannel Radar Front-End With Coherent Pulsed Oscillator Array; TMTT May 2015 1735-1745 Lee, S. B., Ahn, S., and Jang, I. G., Development of the Optimization Framework for Low-Power Wireless Power Transfer Systems; TMTT Mar. 2015 813-820 Lee, S.-G., see Lee, I.-Y., TMTT Apr. 2015 1202-1210 Lee, S.-K., see Choi, Y.-C., TMTT Oct. 2015 3254-3264 Lee, S.-S., see Lee, I.-Y., TMTT Apr. 2015 1202-1210 Lee, T.-C., Lee, J., and Peroulis, D., Dynamic Bandpass Filter Shape and Interference Cancellation Control Utilizing Bandpass–Bandstop Filter Cascade; TMTT Aug. 2015 2526-2539 Leenaerts, D. M. W., see Ma, Q., TMTT Sep. 2015 2942-2952 Lees, J., see Imtiaz, A., TMTT Oct. 2015 3007-3015 Lehtinen, V., see Kiayani, A., TMTT Nov. 2015 3608-3623 Leibrich, J., see Huang, H., TMTT Apr. 2015 1211-1218 Leuther, A., see Seelmann-Eggebert, M., TMTT Jul. 2015 2335-2342 Leuther, A., see Diebold, S., TMTT Mar. 2015 999-1006 Leveque, P., see Kohler, S., TMTT Jun. 2015 2032-2040 Levine, P. M., see Huang, H., TMTT Dec. 2015 4297-4305 Levine, Z. A., see Kohler, S., TMTT Jun. 2015 2032-2040 Lewandowski, A., see Barmuta, P., TMTT Jan. 2015 56-64 Lewandowski, A., see Barmuta, P., TMTT Dec. 2015 4501-4510 Lewandowski, A., Wiatr, W., Opalski, L. J., and Biedrzycki, R., Accuracy and Bandwidth Optimization of the Over-Determined Offset-Short Reflectometer Calibration; TMTT Mar. 2015 1076-1089 Li, B., see Wang, H., TMTT Jul. 2015 2094-2106 Li, C., see Zhao, J., TMTT May 2015 1633-1644 Li, C., see Li, H., TMTT Mar. 2015 925-936 Li, C.-H., Chao, T.-Y., Lai, C.-W., Chen, W.-C., Ko, C.-L., Kuo, C.-N., Cheng, Y. T., Kuo, M.-C., and Chang, D.-C., A 37.5-mW 8-dBm-EIRP 15.5 -HPBW 338-GHz Terahertz Transmitter Using SoP Heterogeneous System Integration; TMTT Feb. 2015 470-480 Li, H., Ye, D., Shen, F., Zhang, B., Sun, Y., Zhu, W., Li, C., and Ran, L., Reconfigurable Diffractive Antenna Based on Switchable Electrically Induced Transparency; TMTT Mar. 2015 925-936 + Check author entry for coauthors

Li, J., Parlak, M., Mukai, H., Matsuo, M., and Buckwalter, J. F., A Reconfigurable 50-Mb/s-1 Gb/s Pulse Compression Radar Signal Processor With Offset Calibration in 90-nm CMOS; TMTT Jan. 2015 266-278 Li, J., see Chang, C., TMTT Jun. 2015 1875-1882 Li, J. C., see Xu, Z., TMTT Apr. 2015 1219-1227 Li, J.-Q., see Wang, H., TMTT Jul. 2015 2094-2106 Li, L., see Chan, K.K.M., TMTT May 2015 1700-1709 Li, S., Hua, W., Liang, M., Tuo, M., Tawfick, S., Hart, A. J., Zhu, Q., and Xin, H., Anisotropic Microwave Conductivity Dispersion of Horizontally Aligned Multi-Walled Carbon- Nanotube Thin Film on Flexible Substrate; TMTT Nov. 2015 3588-3594 Li, S., see Yu, X., TMTT Feb. 2015 326-330 Li, S. M., see Yu, X. H., TMTT Dec. 2015 3845-3850 Li, W., see Lorenz, C. H. P., TMTT Dec. 2015 4544-4555 Li, W., see Zou, X., TMTT Apr. 2015 1421-1430 Li, W., see Chen, X., TMTT Jul. 2015 2384-2389 Li, X., see Yu, J., TMTT Jun. 2015 1836-1842 Li, X., Tzuang, C.-K. C., and Wu, H.-S., Anomalous Dispersion Characteristics of Periodic Substrate Integrated Waveguides From Microwave to Terahertz; TMTT Jul. 2015 2142-2153 Li, Y., see He, Z., TMTT May 2015 1683-1692 Liang, K.-F., Yang, H.-S., Chang, C.-W., and Chen, J.-H., A Wideband PulseModulated Polar Transmitter Using Envelope Correction for LTE Applications; TMTT Aug. 2015 2603-2608 Liang, M., see Li, S., TMTT Nov. 2015 3588-3594 Liang, X., see Fan, H., TMTT Mar. 2015 986-998 Liao, Y., see Huang, K., TMTT Jan. 2015 135-140 Lim, T., Benech, P., Jimenez, J., Fournier, J.-M., Heitz, B., Bourgeat, J., and Galy, P., Generic Electrostatic Discharges Protection Solutions for RF and Millimeter-Wave Applications; TMTT Nov. 2015 3747-3759 Lin, F.-C., see Riehl, P. S., TMTT Mar. 2015 780-790 Lin, J., see Schreurs, D., TMTT Sep. 2015 2709 Lin, J., see Nieh, C.-M., TMTT Jun. 2015 2069-2078 Lin, J., see Hwang, T., TMTT Jul. 2015 2185-2198 Lin, J., see Schreurs, D., TMTT Jul. 2015 2081 Lin, J., see Schreurs, D., TMTT Mar. 2015 777 Lin, K.-H., see Kung, M.-L., TMTT Mar. 2015 821-832 Lin, L., Zhou, L., Wang, R., Tong, L., and Yin, W.-Y., Electrothermal Effects on Performance of GaAs HBT Power Amplifier During Power Versus Time (PVT) Variation at GSM/DCS Bands; TMTT Jun. 2015 1951-1963 Lin, L., see Xu, K., TMTT Aug. 2015 2561-2569 Lin, M., see Gou, Y., TMTT Oct. 2015 3142-3152 Lin, W.-C., see Lee, C.-I., TMTT Feb. 2015 367-373 Lin, W.-C., see Lee, C.-I., TMTT Sep. 2015 2756-2763 Lin, X. Q., see Jin, J. Y., TMTT Oct. 2015 3374-3380 Lin, Y., Quindroit, C., Jang, H., and Roblin, P., 3-D Fourier Series Based Digital Predistortion Technique for Concurrent Dual-Band Envelope Tracking With Reduced Envelope Bandwidth; TMTT Sep. 2015 2764-2775 Lin, Y.-C., and Chu, T.-H., Multiport Scattering Matrix Determination From One-Port Measurements; TMTT Jul. 2015 2343-2352 Lin, Y.-H., see Chang, J.-F., TMTT Aug. 2015 2638-2649 Lin, Y.-S., see Shao, J.-Y., TMTT Oct. 2015 3469-3478 Lin, Y.-T., see Lee, C.-I., TMTT Feb. 2015 367-373 Lin, Y.-T., see Lee, C.-I., TMTT Sep. 2015 2756-2763 Lin, Y.-W., see Chou, P.-J., TMTT Dec. 2015 3971-3980 Lindqvist, F., Magesacher, T., Fertner, A., Odling, P., and Borjesson, P. O., Estimation of Nonhomogeneous and Multi-Section Twisted-Pair Transmission-Line Parameters; TMTT Nov. 2015 3568-3578 Liou, C.-Y., see Lee, M.-L., TMTT Feb. 2015 614-624 Lioubtchenko, D. V., see Nefedova, I. I., TMTT Oct. 2015 3265-3271 Litchfield, M., Reveyrand, T., and Popovic, Z., Load Modulation Measurements of X-Band Outphasing Power Amplifiers; TMTT Dec. 2015 41194129 Liu, D., see Zhang, Y.-J., TMTT Mar. 2015 883-890 Liu, J., see Wu, P., TMTT Jun. 2015 1863-1874 Liu, N., Cai, G., Zhu, C., Tang, Y., and Liu, Q. H., The Mixed Spectral-Element Method for Anisotropic, Lossy, and Open Waveguides; TMTT Oct. 2015 3094-3102 Liu, N., Tobon, L. E., Zhao, Y., Tang, Y., and Liu, Q. H., Mixed SpectralElement Method for 3-D Maxwell's Eigenvalue Problem; TMTT Feb. 2015 317-325 Liu, Q. H., see Liu, N., TMTT Oct. 2015 3094-3102 Liu, Q. H., see Liu, N., TMTT Feb. 2015 317-325 Liu, Q. H., see Feng, N., TMTT Mar. 2015 877-882

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 63, NO. 12, DECEMBER 2015

Liu, T., see Zhu, R., TMTT Aug. 2015 2692-2702 Liu, Y., Yan, J. J., and Asbeck, P. M., Concurrent Dual-Band Digital Predistortion With a Single Feedback Loop; TMTT May 2015 1556-1568 Liu, Y., Pan, W., Shao, S., and Tang, Y., A General Digital Predistortion Architecture Using Constrained Feedback Bandwidth for Wideband Power Amplifiers; TMTT May 2015 1544-1555 Liu, Y., see Chang, C., TMTT Jun. 2015 1875-1882 Liu, Y.-C., Chang, H.-Y., Huang, S.-Y., and Chen, K., Design and Analysis of CMOS High-Speed High Dynamic-Range Track-and-Hold Amplifiers; TMTT Sep. 2015 2841-2853 Liu, Z., see Sun, Y., TMTT Oct. 2015 3131-3141 Lo, A.-H., see Tan, K.-W., TMTT Apr. 2015 1380-1387 Lo, Y.-T., and Kiang, J.-F., Comparison of Injection-Locked and Coupled Oscillator Arrays for Beamforming; TMTT Apr. 2015 1353-1360 Loeches-Sanchez, R., see Psychogiou, D., TMTT Jul. 2015 2233-2244 Loo-Yau, J. R., see Pulido-Gaytan, M. A., TMTT May 2015 1693-1699 Lorenz, C. H. P., Hemour, S., Li, W., Xie, Y., Gauthier, J., Fay, P., and Wu, K., Breaking the Efficiency Barrier for Ambient Microwave Power Harvesting With Heterojunction Backward Tunnel Diodes; TMTT Dec. 2015 4544-4555 Lou, C., see Ding, W., TMTT Oct. 2015 3272-3276 Lou, C.-Y., see Lee, M.-L., TMTT Feb. 2015 614-624 Lu, B., see Zou, X., TMTT Apr. 2015 1421-1430 Lu, H., see Zhao, J., TMTT Feb. 2015 533-545 Lu, X., Wei, B., Xu, Z., Cao, B., Guo, X., Zhang, X., Wang, R., and Song, F., Superconducting Ultra-Wideband (UWB) Bandpass Filter Design Based on Quintuple/Quadruple/ Triple-Mode Resonator; TMTT Apr. 2015 12811293 Lubecke, O.-B., see Rahman, A., TMTT Oct. 2015 3034-3041 Lubecke, V. M., see Rahman, A., TMTT Oct. 2015 3034-3041 Lucyszyn, S., see Sanchez-Martinez, J. J., TMTT Jan. 2015 198-208 Lugli, P., see Russer, J. A., TMTT Dec. 2015 4236-4246 Lujambio, A., see Fernandez-Prieto, A., TMTT Jun. 2015 1843-1853 Luo, C., Gudem, P. S., and Buckwalter, J. F., A 0.2–3.6-GHz 10-dBm B1dB 29-dBm IIP3 Tunable Filter for Transmit Leakage Suppression in SAWLess 3G/4G FDD Receivers; TMTT Oct. 2015 3514-3524 Luong, H. C., see Chao, Y., TMTT Apr. 2015 1193-1201 Luzio, S., see Choi, H., TMTT Oct. 2015 3016-3025 Lynch, J. J., see Rengarajan, S. R., TMTT Dec. 2015 3981-3987 M Ma, C., see Fu, M., TMTT Mar. 2015 801-812 Ma, H., see Na, K., TMTT Jan. 2015 295-304 Ma, K., Kumar, T. B., and Yeo, K. S., A Reconfigurable K-/Ka-Band Power Amplifier With High PAE in 0.18- m SiGe BiCMOS for Multi-Band Applications; TMTT Dec. 2015 4395-4405 Ma, Q., Leenaerts, D. M. W., and Baltus, P. G. M., Silicon-Based True-TimeDelay Phased-Array Front-Ends at Ka-Band; TMTT Sep. 2015 2942-2952 Ma, R., see Chung, S., TMTT Feb. 2015 598-613 Ma, Y., and Yamao, Y., Spectra-Folding Feedback Architecture for Concurrent Dual-Band Power Amplifier Predistortion; TMTT Oct. 2015 3164-3174 Macchiarella, G., see Tamiazzo, S., TMTT Oct. 2015 3408-3415 Macchiarella, G., see Snyder, R. V., TMTT Oct. 2015 3324-3360 Macchiarella, G., see Boria, V. E., TMTT Oct. 2015 3321-3323 Macutkevic, J., see Bellucci, S., TMTT Jun. 2015 2024-2031 Maddio, S., Passafiume, M., Cidronali, A., and Manes, G., A Distributed Positioning System Based on a Predictive Fingerprinting Method Enabling Sub-Metric Precision in IEEE 802.11 Networks; TMTT Dec. 2015 45674580 Maddio, S., Cidronali, A., and Manes, G., Real-Time Adaptive Transmitter Leakage Cancelling in 5.8-GHz Full-Duplex Transceivers; TMTT Feb. 2015 509-519 Madsen, P., see Bahramzy, P., TMTT Oct. 2015 3300-3310 Maftooli, H., Sadeghi, S. H. H., Moini, R., and Karami, H., Time-Domain Electromagnetic Analysis of Multilayer Structures Using the Surface Equivalent Principle and Mixed-Potential Integral Equations; TMTT Jan. 2015 99-106 Magesacher, T., see Lindqvist, F., TMTT Nov. 2015 3568-3578 Maglione, M., see De Paolis, R., TMTT Aug. 2015 2570-2578 Mahfouz, M. R., see Elkhouly, E., TMTT May 2015 1746-1757 Mak, P.-I., see Un, K.-F., TMTT Oct. 2015 3228-3241 Maksimenko, S., see Bellucci, S., TMTT Jun. 2015 2024-2031 + Check author entry for coauthors

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Maksimovic, D., see Ramos, I., TMTT Dec. 2015 4473-4482 Malic, B., see Furlan, V., TMTT Mar. 2015 891-896 Mancuso, Y., see Kerherve, E., TMTT May 2015 1621-1632 Mandal, D., see Bhattacharya, A., TMTT Feb. 2015 459-469 Mandal, S., see Cuenca, J. A., TMTT Dec. 2015 4110-4118 Manes, G., see Maddio, S., TMTT Dec. 2015 4567-4580 Manes, G., see Maddio, S., TMTT Feb. 2015 509-519 Manfredi, D., see Peverini, O. A., TMTT Oct. 2015 3361-3373 Manfredi, P., and Canavero, F. G., Efficient Statistical Simulation of Microwave Devices Via Stochastic Testing-Based Circuit Equivalents of Nonlinear Components; TMTT May 2015 1502-1511 Mangraviti, G., Khalaf, K., Parvais, B., Vaesen, K., Szortyka, V., Vandersteen, G., and Wambacq, P., Design and Tuning of Coupled-LC mm-Wave Subharmonically Injection-Locked Oscillators; TMTT Jul. 2015 2301-2312 Mansour, R. R., see Bakri-Kassem, M., TMTT Jan. 2015 222-232 Mansour, R. R., see Chen, W.-T. S., TMTT Dec. 2015 4157-4168 Mao, J.-F., see Chen, F.-J., TMTT Oct. 2015 3494-3504 Mao, S.-G., see Lee, M.-L., TMTT Feb. 2015 614-624 Marongiu, P., see Valente, G., TMTT Oct. 2015 3218-3227 Marquez-Segura, E., see Sanchez-Martinez, J. J., TMTT Jan. 2015 198-208 Martel, J., see Velez, P., TMTT Apr. 2015 1272-1280 Martel, J., see Fernandez-Prieto, A., TMTT Jun. 2015 1843-1853 Martianez, J. D., see Sirci, S., TMTT Dec. 2015 4341-4354 Martin, C., see Choi, H., TMTT Oct. 2015 3016-3025 Martin, F., see Velez, P., TMTT Apr. 2015 1272-1280 Martin, F., see Sans, M., TMTT Dec. 2015 3896-3908 Martin, F., see Zuffanelli, S., TMTT Jul. 2015 2133-2141 Martin, G., see Laur, V., TMTT Dec. 2015 4376-4381 Martin Iglesias, P., see Tornielli di Crestvolant, V., TMTT Oct. 2015 34333444 Martinez-Ros, A. J., see Gomez-Tornero, J. L., TMTT May 2015 1609-1620 Martins, R. P., see Un, K.-F., TMTT Oct. 2015 3228-3241 Marynowski, W., see Kusiek, A., TMTT Jun. 2015 1800-1808 Masotti, D., see Del Prete, M., TMTT Dec. 2015 4511-4520 Massler, H., see Seelmann-Eggebert, M., TMTT Jul. 2015 2335-2342 Massler, H., see Diebold, S., TMTT Mar. 2015 999-1006 Mast, D. B., see Cumby, B. L., TMTT Oct. 2015 3122-3130 Mata-Contreras, J., see Velez, P., TMTT Apr. 2015 1272-1280 Mateu, J., see Mira, F., TMTT Dec. 2015 3939-3946 Matos, J. N., see Dias Fernandes, R., TMTT Sep. 2015 2983-2990 Matsuo, M., see Li, J., TMTT Jan. 2015 266-278 Mattar, S. M., see Elnaggar, S. Y., TMTT Jul. 2015 2115-2123 Mattar, S. M., see Elnaggar, S. Y., TMTT Jul. 2015 2124-2132 Mattes, M., see Koufogiannis, I. D., TMTT Jan. 2015 20-29 Maunder, A., Taheri, O., Ghafouri Fard, M. R., and Mousavi, P., Calibrated Layer-Stripping Technique for Level and Permittivity Measurement With UWB Radar in Metallic Tanks; TMTT Jul. 2015 2322-2334 Maya-Sanchez, M. C., see Pulido-Gaytan, M. A., TMTT May 2015 1693-1699 Mazur, J., see Kusiek, A., TMTT Jun. 2015 1800-1808 McElhinney, P., see Zhang, L., TMTT Oct. 2015 3183-3190 McStravick, M., see Zhang, L., TMTT Mar. 2015 1090-1096 Medi, A., see Nikandish, G., TMTT Feb. 2015 441-448 Medina, F., see Velez, P., TMTT Apr. 2015 1272-1280 Medina, F., see Fernandez-Prieto, A., TMTT Jun. 2015 1843-1853 Mehrjoo, M. S., Zihir, S., Rebeiz, G. M., and Buckwalter, J. F., A 1.1-Gbit/s 10-GHz Outphasing Modulator With 23-dBm Output Power and 60-dB Dynamic Range in 45-nm CMOS SOI; TMTT Jul. 2015 2289-2300 Mencarelli, D., see Pierantoni, L., TMTT Aug. 2015 2491-2497 Mencia-Oliva, B., see Grajal, J., TMTT Mar. 2015 1097-1107 Meng, F., see Sun, Y., TMTT Dec. 2015 4051-4060 Mercader-Pellicer, S., see Gomez-Tornero, J. L., TMTT May 2015 1609-1620 Merkle, T., Gotzen, R., Choi, J.-Y., and Koch, S., Polymer Multichip Module Process Using 3-D Printing Technologies for D-Band Applications; TMTT Feb. 2015 481-493 Merrick, B. M., see Chen, P., TMTT Dec. 2015 4263-4272 Mesa, F., see Fernandez-Prieto, A., TMTT Jun. 2015 1843-1853 Meschanov, V. P., see Alaverdyan, S. A., TMTT Aug. 2015 2509-2514 Mescia, L., Bia, P., and Caratelli, D., Authors’ Reply; TMTT Dec. 2015 41914193 Meyne nee Haase, N., Fuge, G., Trieu, H. K., Zeng, A.-P., and Jacob, A. F., Miniaturized Transmission-Line Sensor for Broadband Dielectric Characterization of Biological Liquids and Cell Suspensions; TMTT Oct. 2015 3026-3033 Micciulla, F., see Bellucci, S., TMTT Jun. 2015 2024-2031

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Micciulla, F., see Pierantoni, L., TMTT Aug. 2015 2491-2497 Mira, F., Mateu, J., and Collado, C., Mechanical Tuning of Substrate Integrated Waveguide Filters; TMTT Dec. 2015 3939-3946 Miranda, F. A., see Schwerdt, H. N., TMTT Sep. 2015 2965-2970 Mirshekar-Syahkal, D., see Deo, P., TMTT Apr. 2015 1388-1398 Mishakin, S. V., see Zhang, L., TMTT Mar. 2015 1090-1096 Missous, M., see Jawad, G. N., TMTT May 2015 1512-1517 Mitilineos, S. A., see Savaidis, S. P., TMTT Jan. 2015 125-134 Mizzoni, R., see Peverini, O. A., TMTT Oct. 2015 3361-3373 Mo, D.-Y., see Chu, Q.-X., TMTT Dec. 2015 3988-3996 Moini, R., see Maftooli, H., TMTT Jan. 2015 99-106 Mongiardo, M., see Dionigi, M., TMTT Jan. 2015 65-75 Mongiardo, M., see Accatino, L., TMTT Jan. 2015 40-47 Monti, G., Arcuti, P., and Tarricone, L., Resonant Inductive Link for Remote Powering of Pacemakers; TMTT Nov. 2015 3814-3822 Montisci, G., see Valente, G., TMTT Oct. 2015 3218-3227 Montoro, G., see Gilabert, P. L., TMTT Feb. 2015 638-648 Moon, J., see Jee, S., TMTT Sep. 2015 2802-2810 Moon, J.-I., see Kim, S.-M., TMTT Mar. 2015 847-856 Moon, K., Cho, Y., Kim, J., Jin, S., Park, B., Kim, D., and Kim, B., Investigation of Intermodulation Distortion of Envelope Tracking Power Amplifier for Linearity Improvement; TMTT Apr. 2015 1324-1333 Moon, K., see Kim, J., TMTT Dec. 2015 4072-4082 Morente-Molinera, J. A., see Salinas, A., TMTT Aug. 2015 2449-2458 Morgan, M. A., and Boyd, T. A., Reflectionless Filter Structures; TMTT Apr. 2015 1263-1271 Moro, R., see Moscato, S., TMTT Oct. 2015 3175-3182 Moro, R., Agneessens, S., Rogier, H., Dierck, A., and Bozzi, M., Textile Microwave Components in Substrate Integrated Waveguide Technology; TMTT Feb. 2015 422-432 Moro, R., see Pierantoni, L., TMTT Aug. 2015 2491-2497 Morris, K. A., see Zhou, J., TMTT Sep. 2015 2793-2801 Morris III, A. S., see Bahramzy, P., TMTT Oct. 2015 3300-3310 Mortazawi, A., see Snyder, R. V., TMTT Oct. 2015 3324-3360 Morys, M. M., see Valenta, C. R., TMTT May 2015 1758-1767 Moscato, S., Moro, R., Pasian, M., Bozzi, M., and Perregrini, L., Two-Material Ridge Substrate Integrated Waveguide for Ultra-Wideband Applications; TMTT Oct. 2015 3175-3182 Moscato, S., see Pierantoni, L., TMTT Aug. 2015 2491-2497 Mosig, J. R., see Koufogiannis, I. D., TMTT Jan. 2015 20-29 Mousavi, P., see Maunder, A., TMTT Jul. 2015 2322-2334 Mueller, J.-E., see Glock, S., TMTT Jun. 2015 1826-1835 Mukai, H., see Li, J., TMTT Jan. 2015 266-278 Muratov, V., see Riehl, P. S., TMTT Mar. 2015 780-790 Murphy-Arteaga, R. S., see Zarate-Rincon, F., TMTT Dec. 2015 4255-4262 Murphy-Arteaga, R. S., see Alvarez-Botero, G., TMTT Dec. 2015 3888-3895 Musonda, E., and Hunter, I. C., Exact Design of a New Class of Generalized Chebyshev Low-Pass Filters Using Coupled Line/Stub Sections; TMTT Dec. 2015 4355-4365 Musonda, E., and Hunter, I. C., Microwave Bandpass Filters Using Re-Entrant Resonators; TMTT Mar. 2015 954-964

N Na, K., Jang, H., Ma, H., and Bien, F., Tracking Optimal Efficiency of Magnetic Resonance Wireless Power Transfer System for Biomedical Capsule Endoscopy; TMTT Jan. 2015 295-304 Nafe, A., and Shamim, A., An Integrable SIW Phase Shifter in a Partially Magnetized Ferrite LTCC Package; TMTT Jul. 2015 2264-2274 Nagayama, T., and Sanada, A., Planar Distributed Full-Tensor Anisotropic Metamaterials for Transformation Electromagnetics; TMTT Dec. 2015 3851-3861 Naglich, E. J., and Guyette, A. C., Reflection-Mode Bandstop Filters With Minimum Through-Line Length; TMTT Oct. 2015 3479-3486 Nakamizo, H., see Chung, S., TMTT Feb. 2015 598-613 Nakamura, T., Kitazawa, N., Kohira, K., and Ishikuro, H., A Prototype SAWLess LTE Transmitter With a High-Linearity Modulator Using BPF-Based I/Q Summing and a Triple-Layer Marchand Balun; TMTT Dec. 2015 40904097 Nalli, A., Raffo, A., Crupi, G., D'Angelo, S., Resca, D., Scappaviva, F., Salvo, G., Caddemi, A., and Vannini, G., GaN HEMT Noise Model Based on Electromagnetic Simulations; TMTT Aug. 2015 2498-2508 Nam, S., see Lee, B., TMTT Nov. 2015 3632-3640 + Check author entry for coauthors

Nam, S., see Cui, C., TMTT Nov. 2015 3736-3746 Naqui, J., see Velez, P., TMTT Apr. 2015 1272-1280 Naraharisetti, N., Roblin, P., Quindroit, C., and Gheitanchi, S., Efficient LeastSquares 2-D-Cubic Spline for Concurrent Dual-Band Systems; TMTT Jul. 2015 2199-2210 Narducci, M., see Campanella, H., TMTT Feb. 2015 331-339 Nassar, I. T., and Weller, T. M., A Compact Dual-Channel Transceiver for Long-Range Passive Embedded Monitoring; TMTT Jan. 2015 287-294 Nast, R. E., see Hooker, J. W., TMTT Jul. 2015 2107-2114 Natarajan, A., Valdes-Garcia, A., Sadhu, B., Reynolds, S. K., and Parker, B. D., -Band Dual-Polarization Phased-Array Transceiver Front-End in SiGe BiCMOS; TMTT Jun. 2015 1989-2002 Navarrini, A., see Valente, G., TMTT Oct. 2015 3218-3227 Navarro, E. A., see Salinas, A., TMTT Aug. 2015 2449-2458 Naylon, J., see Choi, H., TMTT Oct. 2015 3016-3025 Nefedov, I. S., see Nefedova, I. I., TMTT Oct. 2015 3265-3271 Nefedova, I. I., Lioubtchenko, D. V., Nefedov, I. S., and Raisanen, A. V., Dielectric Constant Estimation of a Carbon Nanotube Layer on the Dielectric Rod Waveguide at Millimeter Wavelengths; TMTT Oct. 2015 3265-3271 Negra, R., see Nghiem, X. A., TMTT Sep. 2015 2821-2832 Neihart, N. M., see Sessou, K. K., TMTT Apr. 2015 1315-1323 Ng, E., see Huang, H., TMTT Dec. 2015 4297-4305 Nghiem, X. A., Guan, J., and Negra, R., Broadband Sequential Power Amplifier With Doherty-Type Active Load Modulation; TMTT Sep. 2015 2821-2832 Nieh, C.-M., Wei, C., and Lin, J., Concurrent Detection of Vibration and Distance Using Unmodulated CW Doppler Vibration Radar With An Adaptive Beam-Steering Antenna; TMTT Jun. 2015 2069-2078 Niessen, D., see Florian, C., TMTT Aug. 2015 2589-2602 Nikandish, G., and Medi, A., Transformer-Feedback Interstage Bandwidth Enhancement for MMIC Multistage Amplifiers; TMTT Feb. 2015 441-448 Niknejad, A. M. N., see Kuo, N.-C., TMTT Apr. 2015 1130-1141 Nilsson, B., see Nordebo, S., TMTT Jun. 2015 1791-1799 Nopchinda, D., see He, Z., TMTT Aug. 2015 2630-2637 Nordebo, S., Cinar, G., Gustafsson, S., and Nilsson, B., Dispersion Modeling and Analysis for Multilayered Open Coaxial Waveguides; TMTT Jun. 2015 1791-1799 Nunes, L. C., see Pedro, J. C., TMTT Apr. 2015 1239-1249 O Oberhammer, J., see Topfer, F., TMTT Jun. 2015 2050-2059 Odendaal, J. W., see Kloke, K. H., TMTT Oct. 2015 3103-3108 Odling, P., see Lindqvist, F., TMTT Nov. 2015 3568-3578 Offenhausser, A., see Gubin, A. I., TMTT Jun. 2015 2003-2009 Oh, J., Jang, J., Kim, C.-Y., and Hong, S., A W-Band 4-GHz Bandwidth PhaseModulated Pulse Compression Radar Transmitter in 65-nm CMOS; TMTT Aug. 2015 2609-2618 Oh, T. C., see Xu, Z., TMTT Apr. 2015 1219-1227 Ohlrogge, M., see Seelmann-Eggebert, M., TMTT Jul. 2015 2335-2342 Ohlsson, L., see Vakili, I., TMTT Sep. 2015 2915-2922 Olesen, P., see Bahramzy, P., TMTT Oct. 2015 3300-3310 Omar, S., and Jiao, D., A Linear Complexity Direct Volume Integral Equation Solver for Full-Wave 3-D Circuit Extraction in Inhomogeneous Materials; TMTT Mar. 2015 897-912 Ong, S. N., see Chan, L. H. K., TMTT Jan. 2015 141-154 Opalski, L. J., see Lewandowski, A., TMTT Mar. 2015 1076-1089 Orlov, A. O., see Russer, J. A., TMTT Dec. 2015 4236-4246 Orta, R., see Tibaldi, A., TMTT Jan. 2015 11-19 Orta, R., see Tibaldi, A., TMTT Jan. 2015 115-124 Orta, R., see Addamo, G., TMTT May 2015 1468-1474 Ostman, K. B., Englund, M., Viitala, O., Stadius, K., Koli, K., and Ryynanen, J., RF Input Matching Design for Closed-Loop Direct Delta–Sigma Receivers; TMTT Apr. 2015 1370-1379 Otegi, N., see Pelaz, J., TMTT Jun. 2015 1923-1936 Ozen, M., see Sanchez-Perez, C., TMTT Aug. 2015 2579-2588 Ozgur, S., see Akinci, M. N., TMTT Sep. 2015 2730-2740 P Paddubskaya, A., see Bellucci, S., TMTT Jun. 2015 2024-2031 Paganelli, R. P., see Florian, C., TMTT Aug. 2015 2589-2602 Pahl, P., see Diebold, S., TMTT Mar. 2015 999-1006 Pai, A., see Dasgupta, K., TMTT Apr. 2015 1118-1129

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Pan, P.-C., see Ho, C.-Y., TMTT Sep. 2015 2923-2930 Pan, W., see Zou, X., TMTT Apr. 2015 1421-1430 Pan, W., see Liu, Y., TMTT May 2015 1544-1555 Pang, J., He, S., Huang, C., Dai, Z., Peng, J., and You, F., A Post-Matching Doherty Power Amplifier Employing Low-Order Impedance Inverters for Broadband Applications; TMTT Dec. 2015 4061-4071 Pantoja, M. F., see Angulo, L. D., TMTT Oct. 2015 3081-3093 Panwar, R., Puthucheri, S., Agarwala, V., and Singh, D., Fractal Frequency-Selective Surface Embedded Thin Broadband Microwave Absorber Coatings Using Heterogeneous Composites; TMTT Aug. 2015 2438-2448 Papio Toda, A., and De Flaviis, F., 60-GHz Substrate Materials Characterization Using the Covered Transmission-Line Method; TMTT Mar. 2015 1063-1075 Paredes, F., see Zuffanelli, S., TMTT Jul. 2015 2133-2141 Park, B., see Moon, K., TMTT Apr. 2015 1324-1333 Park, B., see Kim, J., TMTT Dec. 2015 4072-4082 Park, H., see Lee, S., TMTT Dec. 2015 4406-4414 Park, H.-H., see Kim, M., TMTT Nov. 2015 3806-3813 Park, J., Ryu, H., Ha, K.-W., Kim, J.-G., and Baek, D., 76–81-GHz CMOS Transmitter With a Phase-Locked-Loop-Based Multichirp Modulator for Automotive Radar; TMTT Apr. 2015 1399-1408 Park, J. S., and Wang, H., A Transformer-Based Poly-Phase Network for UltraBroadband Quadrature Signal Generation; TMTT Dec. 2015 4444-4457 Park, N., see Wang, X., TMTT Mar. 2015 965-975 Park, S., Woo, J.-L., Kim, U., and Kwon, Y., Broadband CMOS Stacked RF Power Amplifier Using Reconfigurable Interstage Network for Wideband Envelope Tracking; TMTT Apr. 2015 1174-1185 Park, S., see Jeon, M.-S., TMTT Sep. 2015 2854-2866 Park, Y., see Remley, K. A., TMTT May 2015 1710-1720 Park, Y.-J., see Kim, J., TMTT Mar. 2015 791-800 Parker, B. D., see Natarajan, A., TMTT Jun. 2015 1989-2002 Parlak, M., see Li, J., TMTT Jan. 2015 266-278 Parment, F., Ghiotto, A., Vuong, T.-P., Duchamp, J.-M., and Wu, K., Air-Filled Substrate Integrated Waveguide for Low-Loss and High Power-Handling Millimeter-Wave Substrate Integrated Circuits; TMTT Apr. 2015 1228-1238 Parsons, K., see Chung, S., TMTT Feb. 2015 598-613 Parvais, B., see Mangraviti, G., TMTT Jul. 2015 2301-2312 Pasian, M., see Moscato, S., TMTT Oct. 2015 3175-3182 Passafiume, M., see Maddio, S., TMTT Dec. 2015 4567-4580 Payan, S., see De Paolis, R., TMTT Aug. 2015 2570-2578 Pecnik, T., see Furlan, V., TMTT Mar. 2015 891-896 Pedersen, G. F., see Bahramzy, P., TMTT Oct. 2015 3300-3310 Pedro, J. C., see Aikio, J. P., TMTT Jan. 2015 155-164 Pedro, J. C., Nunes, L. C., and Cabral, P. M., A Simple Method to Estimate the Output Power and Efficiency Load–Pull Contours of Class-B Power Amplifiers; TMTT Apr. 2015 1239-1249 Pedro, J. C., see Cai, J., TMTT May 2015 1518-1529 Pedro, J. C., see Zargar, H., TMTT Feb. 2015 766-774 Peh, L.-S., see Choi, P., TMTT Apr. 2015 1163-1173 Pelaz, J., Collantes, J.-M., Otegi, N., Anakabe, A., and Collins, G., Experimental Control and Design of Low-Frequency Bias Networks for Dynamically Biased Amplifiers; TMTT Jun. 2015 1923-1936 Pelliccia, L., Cacciamani, F., Farinelli, P., and Sorrentino, R., High- Tunable Waveguide Filters Using Ohmic RF MEMS Switches; TMTT Oct. 2015 3381-3390 Penaranda-Foix, F. L., see Catala-Civera, J. M., TMTT Sep. 2015 2905-2914 Peng, J., see Dai, Z., TMTT Feb. 2015 449-458 Peng, J., see Pang, J., TMTT Dec. 2015 4061-4071 Penlidis, A., see Chen, W.-T. S., TMTT Dec. 2015 4157-4168 Perantie, J., see Rashidian, A., TMTT Sep. 2015 2720-2729 Perfetti, R., see Dionigi, M., TMTT Jan. 2015 65-75 Perkowski, C. W., see Ketterl, T. P., TMTT Dec. 2015 4382-4394 Peroulis, D., see Psychogiou, D., TMTT Dec. 2015 4319-4328 Peroulis, D., see Lee, T.-C., TMTT Aug. 2015 2526-2539 Peroulis, D., see Psychogiou, D., TMTT Jul. 2015 2233-2244 Perreault, D. J., see Barton, T. W., TMTT Dec. 2015 4273-4283 Perregrini, L., see Bozzi, M., TMTT Jan. 2015 1-2 Perregrini, L., see Moscato, S., TMTT Oct. 2015 3175-3182 Perregrini, L., see Pierantoni, L., TMTT Aug. 2015 2491-2497 Person, C., see Kuhn, V., TMTT May 2015 1768-1778 Peschel, D., see Seelmann-Eggebert, M., TMTT Jul. 2015 2335-2342 Peverini, O. A., see Tibaldi, A., TMTT Jan. 2015 11-19 Peverini, O. A., see Tibaldi, A., TMTT Jan. 2015 115-124 + Check author entry for coauthors

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Peverini, O. A., Addamo, G., Tascone, R., Virone, G., Cecchini, P., Mizzoni, R., Calignano, F., Ambrosio, E. P., Manfredi, D., and Fino, P., Enhanced Topology of -Plane Resonators for High-Power Satellite Applications; TMTT Oct. 2015 3361-3373 Peverini, O. A., see Addamo, G., TMTT May 2015 1468-1474 Pfeiffer, U. R., see Statnikov, K., TMTT Feb. 2015 520-532 Pham, J.-M., see Kerherve, E., TMTT May 2015 1621-1632 Phelps, A. D. R., see Zhang, L., TMTT Mar. 2015 1090-1096 Piekarz, I., see Sorocki, J., TMTT Feb. 2015 384-396 Pierantoni, L., Mencarelli, D., Bozzi, M., Moro, R., Moscato, S., Perregrini, L., Micciulla, F., Cataldo, A., and Bellucci, S., Broadband Microwave Attenuator Based on Few Layer Graphene Flakes; TMTT Aug. 2015 2491-2497 Pierz, K., see Bieler, M., TMTT Nov. 2015 3775-3784 Pinto, M., see Zai, A., TMTT Sep. 2015 2953-2964 Pirola, M., see Camarchia, V., TMTT Feb. 2015 559-571 Pisanu, T., see Valente, G., TMTT Oct. 2015 3218-3227 Plaum, B., see Wu, Z., TMTT Oct. 2015 3537-3546 Plaza-Gonzalez, P., see Catala-Civera, J. M., TMTT Sep. 2015 2905-2914 Plumb, W., see Riehl, P. S., TMTT Mar. 2015 780-790 Podevin, F., see Burdin, F., TMTT Jun. 2015 1883-1893 Ponti, C., and Vellucci, S., Scattering by Conducting Cylinders Below a Dielectric Layer With a Fast Noniterative Approach; TMTT Jan. 2015 30-39 Ponti, C., see Ceccuzzi, S., TMTT Aug. 2015 2468-2481 Ponton, M., and Suarez, A., Optimized Design of Frequency Dividers Based on Varactor-Inductor Cells; TMTT Dec. 2015 4458-4472 Popovic, Z., see Ramos, I., TMTT Dec. 2015 4473-4482 Popovic, Z., see Del Prete, M., TMTT Dec. 2015 4511-4520 Popovic, Z., see Zai, A., TMTT Sep. 2015 2953-2964 Popovic, Z., see Schafer, S., TMTT Sep. 2015 2931-2941 Popovic, Z., see Litchfield, M., TMTT Dec. 2015 4119-4129 Porch, A., see Abduljabar, A. A., TMTT Dec. 2015 4492-4500 Porch, A., see Abduljabar, A. A., TMTT Nov. 2015 3681-3690 Porch, A., see Choi, H., TMTT Oct. 2015 3016-3025 Porch, A., see Cuenca, J. A., TMTT Dec. 2015 4110-4118 Porod, W., see Russer, J. A., TMTT Dec. 2015 4236-4246 Porti, J., see Salinas, A., TMTT Aug. 2015 2449-2458 Pourghorban Saghati, A., and Entesari, K., Ultra-Miniature SIW Cavity Resonators and Filters; TMTT Dec. 2015 4329-4340 Pourghorban Saghati, A., see Pourghorban Saghati, A., TMTT Dec. 2015 4329-4340 Pourghorban Saghati, A., Batra, J. S., Kameoka, J., and Entesari, K., A Miniaturized Microfluidically Reconfigurable Coplanar Waveguide Bandpass Filter With Maximum Power Handling of 10 Watts; TMTT Aug. 2015 2515-2525 Prata, A., see Ribeiro, D. C., TMTT Oct. 2015 3277-3287 Preibisch, J. B., Hardock, A., and Schuster, C., Physics-Based Via and Waveguide Models for Efficient SIW Simulations in Multilayer Substrates; TMTT Jun. 2015 1809-1816 Protsenko, I. A., see Gubin, A. I., TMTT Jun. 2015 2003-2009 Psychogiou, D., Gomez-Garcia, R., and Peroulis, D., Coupling-Matrix-Based Design of High- Bandpass Filters Using Acoustic-Wave Lumped-Element Resonator (AWLR) Modules; TMTT Dec. 2015 4319-4328 Psychogiou, D., Gomez-Garcia, R., Loeches-Sanchez, R., and Peroulis, D., Hybrid Acoustic-Wave-Lumped-Element Resonators (AWLRs) for HighBandpass Filters With Quasi-Elliptic Frequency Response; TMTT Jul. 2015 2233-2244 Pud, S., see Gubin, A. I., TMTT Jun. 2015 2003-2009 Pulido-Gaytan, M. A., Reynoso-Hernandez, J. A., Loo-Yau, J. R., Zarate-de Landa, A., and Maya-Sanchez, M. C., Generalized Theory of the ThruReflect-Match Calibration Technique; TMTT May 2015 1693-1699 Puthucheri, S., see Panwar, R., TMTT Aug. 2015 2438-2448 Q Qi, G., see Un, K.-F., TMTT Oct. 2015 3228-3241 Qian, H., Yao, S., Huang, H., Yang, X., and Feng, W., Low Complexity Coefficient Estimation for Concurrent Dual-Band Digital Predistortion; TMTT Oct. 2015 3153-3163 Qian, K., Zhao, L., and Wu, K.-L., An LTCC Coupled Resonator Decoupling Network for Two Antennas; TMTT Oct. 2015 3199-3207 Qiang, R., see Feng, S., TMTT Jan. 2015 305-313 Qin, T., see Wang, X., TMTT May 2015 1489-1501 Qiu, C.-W., see Kianinejad, A., TMTT Jun. 2015 1817-1825

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Qiu, J. X., see Darwish, A. M., TMTT Jul. 2015 2253-2263 Qiu, L.-F., see Chen, F.-J., TMTT Oct. 2015 3494-3504 Qiu, L.-L., see Chu, Q.-X., TMTT Oct. 2015 3462-3468 Quaglia, R., see Camarchia, V., TMTT Feb. 2015 559-571 Queffelec, P., see Laur, V., TMTT Dec. 2015 4376-4381 Quesada Pereira, F. D., Romera Perez, A., Vera Castejon, P., and Alvarez Melcon, A., Integral-Equation Formulation for the Analysis of Capacitive Waveguide Filters Containing Dielectric and Metallic Arbitrarily Shaped Objects and Novel Applications; TMTT Dec. 2015 3862-3873 Quindroit, C., see Lin, Y., TMTT Sep. 2015 2764-2775 Quindroit, C., see Rawat, M., TMTT Feb. 2015 625-637 Quindroit, C., see Naraharisetti, N., TMTT Jul. 2015 2199-2210

R Raboso, D., see Cogollos, S., TMTT Aug. 2015 2540-2549 Radhakrishna, U., see Choi, P., TMTT Apr. 2015 1163-1173 Raffo, A., see Nalli, A., TMTT Aug. 2015 2498-2508 Raffo, A., see Avolio, G., TMTT Jul. 2015 2353-2363 Rahkonen, T., see Aikio, J. P., TMTT Jan. 2015 155-164 Rahman, A., Yavari, E., Singh, A., Lubecke, V. M., and Lubecke, O.-B., A Low-IF Tag-Based Motion Compensation Technique for Mobile Doppler Radar Life Signs Monitoring; TMTT Oct. 2015 3034-3041 Raisanen, A. V., see Nefedova, I. I., TMTT Oct. 2015 3265-3271 Rajo-Iglesias, E., see Brazalez, A. A., TMTT Dec. 2015 4035-4050 Ramaswamy, V., see Hooker, J. W., TMTT Jul. 2015 2107-2114 Rambabu, K., see Chan, K.K.M., TMTT May 2015 1700-1709 Ramiah, H., see Chong, W. K., TMTT Aug. 2015 2427-2437 Ramirez, F., see Suarez, A., TMTT Jan. 2015 165-180 Ramirez, F., see Suarez, A., TMTT Dec. 2015 4415-4428 Ramos, I., Ruiz Lavin, M. N., Garcia, J. A., Maksimovic, D., and Popovic, Z., GaN Microwave DC–DC Converters; TMTT Dec. 2015 4473-4482 Ran, L., see Zhao, J., TMTT May 2015 1633-1644 Ran, L., see Li, H., TMTT Mar. 2015 925-936 Rascher, J., see Glock, S., TMTT Jun. 2015 1826-1835 Rashidian, A., Shafai, L., Sobocinski, M., Perantie, J., Juuti, J., and Jantunen, H., Printable Planar Dielectric Waveguides Based on High-Permittivity Films; TMTT Sep. 2015 2720-2729 Rashidinejad, A., see Kim, H.-J., TMTT Dec. 2015 4178-4187 Rasilainen, K., see Islam, Md. M., TMTT Aug. 2015 2672-2681 Ravera, G. L., see Ceccuzzi, S., TMTT Aug. 2015 2468-2481 Rawat, K., see Barthwal, A., TMTT Aug. 2015 2399-2410 Rawat, M., Roblin, P., Quindroit, C., Salam, K., and Xie, C., Concurrent DualBand Modeling and Digital Predistortion in the Presence of Unfilterable Harmonic Signal Interference; TMTT Feb. 2015 625-637 Rebeiz, G., see Hanafi, B., TMTT Jun. 2015 1937-1950 Rebeiz, G. M., see Yang, H.-H., TMTT Nov. 2015 3760-3767 Rebeiz, G. M., see Gurbuz, O. D., TMTT Feb. 2015 414-421 Rebeiz, G. M., see Cho, Y.-H., TMTT Apr. 2015 1308-1314 Rebeiz, G. M., see Ko, C. H., TMTT May 2015 1595-1602 Rebeiz, G. M., see Cho, Y.-H., TMTT May 2015 1579-1586 Rebeiz, G. M., see Yang, T., TMTT May 2015 1569-1578 Rebeiz, G. M., see Ko, C.-H., TMTT Jun. 2015 1854-1862 Rebeiz, G. M., see Dabag, H.-T., TMTT Jul. 2015 2364-2374 Rebeiz, G. M., see Mehrjoo, M. S., TMTT Jul. 2015 2289-2300 Redoute, J.-M., see Thotahewa, K. M. S., TMTT Nov. 2015 3823-3833 Reina-Tosina, J., Allegue-Martinez, M., Crespo-Cadenas, C., Yu, C., and Cruces, S., Behavioral Modeling and Predistortion of Power Amplifiers Under Sparsity Hypothesis; TMTT Feb. 2015 745-753 Rekanos, I. T., Comments on “Fractional Derivative Based FDTD Modeling of Transient Wave Propagation in Havriliak–Negami Media”; TMTT Dec. 2015 4188-4190 Remley, K. A., Williams, D. F., Hale, P. D., Wang, C.-M., Jargon, J., and Park, Y., Millimeter-Wave Modulated-Signal and Error-Vector-Magnitude Measurement With Uncertainty; TMTT May 2015 1710-1720 Ren, L., see Zhang, Y.-J., TMTT Mar. 2015 883-890 Rengarajan, S. R., and Lynch, J. J., Design of a Traveling-Wave Slot Array Power Divider Using the Method of Moments and a Genetic Algorithm; TMTT Dec. 2015 3981-3987 Resca, D., see Nalli, A., TMTT Aug. 2015 2498-2508 Reveyrand, T., see Litchfield, M., TMTT Dec. 2015 4119-4129 Reynaert, P., see Kaymaksut, E., TMTT Apr. 2015 1186-1192 Reynaert, P., see Francois, B., TMTT Feb. 2015 649-658 + Check author entry for coauthors

Reynaert, P., see Zhao, D., TMTT Feb. 2015 683-690 Reynaert, P., see Zhao, D., TMTT Dec. 2015 4083-4089 Reynolds, M. S., see Cnaan-On, I., TMTT Jul. 2015 2375-2383 Reynolds, S. K., see Natarajan, A., TMTT Jun. 2015 1989-2002 Reynoso-Hernandez, J. A., see Pulido-Gaytan, M. A., TMTT May 2015 16931699 Rezaei, V. D., see Bajestan, M. M., TMTT Apr. 2015 1142-1153 Rhodin, A., see He, Z., TMTT May 2015 1683-1692 Ribeiro, D. C., Prata, A., Cruz, P. M., and Carvalho, N. B., -Parameters: A Novel Framework for Characterization and Behavioral Modeling of MixedSignal Systems; TMTT Oct. 2015 3277-3287 Riehl, P. S., Satyamoorthy, A., Akram, H., Yen, Y.-C., Yang, J.-C., Juan, B., Lee, C.-M., Lin, F.-C., Muratov, V., Plumb, W., and Tustin, P. F., Wireless Power Systems for Mobile Devices Supporting Inductive and Resonant Operating Modes; TMTT Mar. 2015 780-790 Riessle, M., see Seelmann-Eggebert, M., TMTT Jul. 2015 2335-2342 Robertson, C. W., see Zhang, L., TMTT Mar. 2015 1090-1096 Roblin, P., see Lin, Y., TMTT Sep. 2015 2764-2775 Roblin, P., see Rawat, M., TMTT Feb. 2015 625-637 Roblin, P., see Naraharisetti, N., TMTT Jul. 2015 2199-2210 Rodenbeck, C. T., Guest Editorial; TMTT Dec. 2015 4199-4200 Rodriguez, A., see Sans, M., TMTT Dec. 2015 3896-3908 Rogier, H., see Moro, R., TMTT Feb. 2015 422-432 Rojas-Nastrucci, E. A., see Ketterl, T. P., TMTT Dec. 2015 4382-4394 Romera Perez, A., see Quesada Pereira, F. D., TMTT Dec. 2015 3862-3873 Ronald, K., see Zhang, L., TMTT Mar. 2015 1090-1096 Rorsman, N., see Sanchez-Perez, C., TMTT Aug. 2015 2579-2588 Rosenberg, U., Salehi, M., Amari, S., and Bornemann, J., Corrections to “Compact Multi-Port Power Combination/Distribution With Inherent Bandpass Filter Characteristics” [Nov 14 2659-2672]; TMTT Jul. 2015 2390 Rosenkranz, W., see Huang, H., TMTT Apr. 2015 1211-1218 Ross, T. N., Hettak, K., Cormier, G., and Wight, J. S., Design of X-Band GaN Phase Shifters; TMTT Jan. 2015 244-255 Roumeliotis, J. A., see Zouros, G. P., TMTT Oct. 2015 3042-3053 Roumeliotis, J. A., see Zouros, G. P., TMTT Mar. 2015 864-876 Royter, Y., see Xu, Z., TMTT Apr. 2015 1219-1227 Rubinos, O., see Grajal, J., TMTT Mar. 2015 1097-1107 Rubio-Cidre, G., see Grajal, J., TMTT Mar. 2015 1097-1107 Ruffieux, D., see Thirunarayanan, R., TMTT Apr. 2015 1110-1117 Ruiz Lavin, M. N., see Ramos, I., TMTT Dec. 2015 4473-4482 Russer, J. A., and Russer, P., Modeling of Noisy EM Field Propagation Using Correlation Information; TMTT Jan. 2015 76-89 Russer, J. A., Jirauschek, C., Szakmany, G. P., Schmidt, M., Orlov, A. O., Bernstein, G. H., Porod, W., Lugli, P., and Russer, P., High-Speed Antenna-Coupled Terahertz Thermocouple Detectors and Mixers; TMTT Dec. 2015 4236-4246 Russer, P., see Russer, J. A., TMTT Jan. 2015 76-89 Russer, P., see Russer, J. A., TMTT Dec. 2015 4236-4246 Ryu, H., see Park, J., TMTT Apr. 2015 1399-1408 Ryynanen, J., see Ostman, K. B., TMTT Apr. 2015 1370-1379

S Sadeghi, S. H. H., see Maftooli, H., TMTT Jan. 2015 99-106 Sadhu, B., see Natarajan, A., TMTT Jun. 2015 1989-2002 Saeedi, S., Lee, J., and Sigmarsson, H. H., Novel Coupling Matrix Synthesis for Single-Layer Substrate-Integrated Evanescent-Mode Cavity Tunable Bandstop Filter Design; TMTT Dec. 2015 3929-3938 Safaripour, A., see Bowers, S. M., TMTT Apr. 2015 1154-1162 Saito, K., see Endo, Y., TMTT Jun. 2015 2041-2049 Salam, K., see Rawat, M., TMTT Feb. 2015 625-637 Salehi, M., see Rosenberg, U., TMTT Jul. 2015 2390 Salinas, A., Porti, J., Fornieles, J., Toledo-Redondo, S., Navarro, E. A., and Morente-Molinera, J. A., TLM Nodes: A New Look at an Old Problem; TMTT Aug. 2015 2449-2458 Salmon, N. A., 3-D Radiometric Aperture Synthesis Imaging; TMTT Nov. 2015 3579-3587 Salvo, G., see Nalli, A., TMTT Aug. 2015 2498-2508 Samsonov, S. V., see Zhang, L., TMTT Mar. 2015 1090-1096 Sanada, A., see Nagayama, T., TMTT Dec. 2015 3851-3861 Sanchez-Martinez, J. J., Marquez-Segura, E., and Lucyszyn, S., Synthesis and Design of High-Selectivity Wideband Quasi-Elliptic Bandpass Filters Using Multiconductor Transmission Lines; TMTT Jan. 2015 198-208

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Sanchez-Perez, C., Ozen, M., Andersson, C. M., Kuylenstierna, D., Rorsman, N., and Fager, C., Optimized Design of a Dual-Band Power Amplifier With SiC Varactor-Based Dynamic Load Modulation; TMTT Aug. 2015 25792588 Sanchez-Sinencio, E., see Abouzied, M. A., TMTT Nov. 2015 3794-3805 Sanchez-Soriano, M. A., see Sirci, S., TMTT Dec. 2015 4341-4354 Sancho, S., see Suarez, A., TMTT Jan. 2015 165-180 Sancho, S., see Suarez, A., TMTT Dec. 2015 4415-4428 Sans, M., Selga, J., Velez, P., Rodriguez, A., Bonache, J., Boria, V. E., and Martin, F., Automated Design of Common-Mode Suppressed Balanced Wideband Bandpass Filters by Means of Aggressive Space Mapping; TMTT Dec. 2015 3896-3908 Sarbishaei, H., see Jundi, A., TMTT Nov. 2015 3691-3700 Sasaki, K., see Shiina, T., TMTT Oct. 2015 3311-3318 Satyamoorthy, A., see Riehl, P. S., TMTT Mar. 2015 780-790 Sauleau, R., see Diedhiou, D. L., TMTT Jul. 2015 2245-2252 Savaidis, S. P., Ioannidis, Z. C., Mitilineos, S. A., and Stathopoulos, N. A., Design of Waveguide Microwave Pulse Compressors Using Equivalent Circuits; TMTT Jan. 2015 125-134 Scappaviva, F., see Nalli, A., TMTT Aug. 2015 2498-2508 Schafer, S., and Popovic, Z., Multi-Frequency Measurements for Supply Modulated Transmitters; TMTT Sep. 2015 2931-2941 Schellenberg, J. M., A 2-W W-Band GaN Traveling-Wave Amplifier With 25-GHz Bandwidth; TMTT Sep. 2015 2833-2840 Schettini, G., see Ceccuzzi, S., TMTT Aug. 2015 2468-2481 Schlechtweg, M., see Seelmann-Eggebert, M., TMTT Jul. 2015 2335-2342 Schlecker, W., see Singh, S., TMTT May 2015 1721-1734 Schmidt, L.-P., see Hrobak, M., TMTT Feb. 2015 553 Schmidt, M., see Russer, J. A., TMTT Dec. 2015 4236-4246 Schmitt, D., see Vanin, F. M., TMTT Feb. 2015 397-402 Schramm, M., see Hrobak, M., TMTT Feb. 2015 553 Schreurs, D., see Farsi, S., TMTT Apr. 2015 1250-1262 Schreurs, D., and Lin, J., Editorial; TMTT Sep. 2015 2709 Schreurs, D., and Lin, J., Editorial; TMTT Jul. 2015 2081 Schreurs, D., and Lin, J., Editorial; TMTT Mar. 2015 777 Schreurs, D. M. M.-P., see Barmuta, P., TMTT Jan. 2015 56-64 Schreurs, D. M. M.-P., see Barmuta, P., TMTT Dec. 2015 4501-4510 Schreurs, D. M. M.-P., see Avolio, G., TMTT Jul. 2015 2353-2363 Schuster, C., see Preibisch, J. B., TMTT Jun. 2015 1809-1816 Schuster, C., see Hardock, A., TMTT Mar. 2015 976-985 Schuster, C., see Zhang, Y.-J., TMTT Mar. 2015 883-890 Schwerdt, H. N., Miranda, F. A., and Chae, J., Wireless Fully Passive Multichannel Recording of Neuropotentials Using Photo-Activated RF Backscattering Methods; TMTT Sep. 2015 2965-2970 Scotti, F., Laghezza, F., Ghelfi, P., and Bogoni, A., Multi-Band Software-Defined Coherent Radar Based on a Single Photonic Transceiver; TMTT Feb. 2015 546-552 Seddon, L., see Deo, P., TMTT Apr. 2015 1388-1398 Seelmann-Eggebert, M., Ohlrogge, M., Weber, R., Peschel, D., Massler, H., Riessle, M., Tessmann, A., Leuther, A., Schlechtweg, M., and Ambacher, O., On the Accurate Measurement and Calibration of S-Parameters for Millimeter Wavelengths and Beyond; TMTT Jul. 2015 2335-2342 Seguin, F., see Kuhn, V., TMTT May 2015 1768-1778 Selga, J., see Sans, M., TMTT Dec. 2015 3896-3908 Selvanayagam, M., see Wong, J. P. S., TMTT Mar. 2015 913-924 Sengupta, K., see Dasgupta, K., TMTT Apr. 2015 1118-1129 Sengupta, K., and Hajimiri, A., Mutual Synchronization for Power Generation and Beam-Steering in CMOS With On-Chip Sense Antennas Near 200 GHz; TMTT Sep. 2015 2867-2876 Seong, Y.-J., see Choi, Y.-C., TMTT Oct. 2015 3254-3264 Sepidband, P., and Entesari, K., A CMOS Spectrum Sensor Based on QuasiCyclostationary Feature Detection for Cognitive Radios; TMTT Dec. 2015 4098-4109 Serhan, A., Lauga-Larroze, E., and Fournier, J.-M., Common-Base/CommonGate Millimeter-Wave Power Detectors; TMTT Dec. 2015 4483-4491 Sessou, K. K., and Neihart, N. M., An Integrated 700–1200-MHz Class-F PA With Tunable Harmonic Terminations in 0.13- m CMOS; TMTT Apr. 2015 1315-1323 Shafai, L., see Rashidian, A., TMTT Sep. 2015 2720-2729 Shamim, A., see Nafe, A., TMTT Jul. 2015 2264-2274 Shang, Y., see Yu, F., TMTT Feb. 2015 403-413 Shao, J.-Y., and Lin, Y.-S., Narrowband Coupled-Line Bandstop Filter With Absorptive Stopband; TMTT Oct. 2015 3469-3478 Shao, L., see Zou, X., TMTT Apr. 2015 1421-1430 + Check author entry for coauthors

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Shao, S., see Liu, Y., TMTT May 2015 1544-1555 Shen, D., see Zhu, R., TMTT Aug. 2015 2692-2702 Shen, F., see Li, H., TMTT Mar. 2015 925-936 Shi, J., see Xu, K., TMTT Aug. 2015 2561-2569 Shi, Y., see Yu, J., TMTT Jun. 2015 1836-1842 Shiina, T., Suzuki, Y., Sasaki, K., Watanabe, S., and Taki, M., High-Efficiency Applicator Based on Printed Circuit Board in Millimeter-Wave Region; TMTT Oct. 2015 3311-3318 Shimizu, T., Kojima, S., and Kogami, Y., Accurate Evaluation Technique of Complex Permittivity for Low-Permittivity Dielectric Films Using a Cavity Resonator Method in 60-GHz Band; TMTT Jan. 2015 279-286 Shin, H., Kim, J., and Kim, N., Source Degenerated Derivative Superposition Method for Linearizing RF FET Differential Amplifiers; TMTT Mar. 2015 1026-1035 Shinjo, S., see Chung, S., TMTT Feb. 2015 598-613 Siart, U., see Koenen, C., TMTT Dec. 2015 3954-3961 Siden, J., see Wang, L., TMTT Dec. 2015 3962-3970 Sievenpiper, D. F., see Gao, F., TMTT Sep. 2015 2971-2982 Sigmarsson, H. H., see Saeedi, S., TMTT Dec. 2015 3929-3938 Silveira, F., see Barabino, N., TMTT May 2015 1676-1682 Singh, A., see Rahman, A., TMTT Oct. 2015 3034-3041 Singh, D., see Panwar, R., TMTT Aug. 2015 2438-2448 Singh, S., Anttila, L., Epp, M., Schlecker, W., and Valkama, M., Analysis, Blind Identification, and Correction of Frequency Response Mismatch in TwoChannel Time-Interleaved ADCs; TMTT May 2015 1721-1734 Sirci, S., Sanchez-Soriano, M. A., Martianez, J. D., Boria, V. E., Gentili, F., Bosch, W., and Sorrentino, R., Design and Multiphysics Analysis of Direct and Cross-Coupled SIW Combline Filters Using Electric and Magnetic Couplings; TMTT Dec. 2015 4341-4354 Sloan, R., see Jawad, G. N., TMTT May 2015 1512-1517 Snyder, R. V., Mortazawi, A., Hunter, I., Bastioli, S., Macchiarella, G., and Wu, K., Present and Future Trends in Filters and Multiplexers; TMTT Oct. 2015 3324-3360 Snyder, R. V., see Tomassoni, C., TMTT Dec. 2015 4366-4375 Sobis, P. J., see Eriksson, K., TMTT Feb. 2015 433-440 Sobocinski, M., see Rashidian, A., TMTT Sep. 2015 2720-2729 Socher, E., see Yanay, N., TMTT Apr. 2015 1342-1352 Socher, E., see Jameson, S., TMTT Sep. 2015 2741-2750 Socher, E., see Khamaisi, B., TMTT Jul. 2015 2275-2288 Sogl, B., see Glock, S., TMTT Jun. 2015 1826-1835 Son, J., see Jee, S., TMTT Sep. 2015 2802-2810 Song, C., see Kong, S., TMTT Mar. 2015 833-846 Song, F., see Lu, X., TMTT Apr. 2015 1281-1293 Song, J.-H., see Cui, C., TMTT Nov. 2015 3736-3746 Song, R., see Cui, C., TMTT Nov. 2015 3736-3746 Soon, J. B. W., see Campanella, H., TMTT Feb. 2015 331-339 Soric, J. C., and Alu, A., Longitudinally Independent Matching and Arbitrary Wave Patterning Using -Near-Zero Channels; TMTT Nov. 2015 35583567 Sorocki, J., Piekarz, I., Wincza, K., and Gruszczynski, S., Right/Left-Handed Transmission Lines Based on Coupled Transmission Line Sections and Their Application Towards Bandpass Filters; TMTT Feb. 2015 384-396 Sorrentino, R., see Pelliccia, L., TMTT Oct. 2015 3381-3390 Sorrentino, R., see Sirci, S., TMTT Dec. 2015 4341-4354 Soto, P., see Carceller, C., TMTT Oct. 2015 3398-3407 Soto, P., see Cogollos, S., TMTT Aug. 2015 2540-2549 Spencer, D. T., see Bluestone, A., TMTT Mar. 2015 1046-1052 Spranger, C., see Strauss, G., TMTT Nov. 2015 3663-3670 Srinivasan, S., see Bluestone, A., TMTT Mar. 2015 1046-1052 Stadius, K., see Ostman, K. B., TMTT Apr. 2015 1370-1379 Stathopoulos, N. A., see Savaidis, S. P., TMTT Jan. 2015 125-134 Statnikov, K., Grzyb, J., Heinemann, B., and Pfeiffer, U. R., 160-GHz to 1-THz Multi-Color Active Imaging With a Lens-Coupled SiGe HBT Chip-Set; TMTT Feb. 2015 520-532 Stein, W., see Hrobak, M., TMTT Feb. 2015 553 Steinfeld, D. E., see Barmatz, M. B., TMTT Feb. 2015 504-508 Sterns, M., see Hrobak, M., TMTT Feb. 2015 553 Stevens, N., see Thoen, B., TMTT Mar. 2015 857-863 Stewart, K. M. E., see Chen, W.-T. S., TMTT Dec. 2015 4157-4168 Stratton, J. W. I., see Ketterl, T. P., TMTT Dec. 2015 4382-4394 Strauss, G., and Spranger, C., Modeling of Inline Transitions Between Different Waveguides as Impedance Inverters for the Use in Novel Filter Designs; TMTT Nov. 2015 3663-3670 Stroth, U., see Koenen, C., TMTT Dec. 2015 3954-3961

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Suarez, A., Ramirez, F., Sancho, S., and Collantes, J.-M., Global Stability Analysis of Coupled-Oscillator Systems; TMTT Jan. 2015 165-180 Suarez, A., see de Cos, J., TMTT Jan. 2015 181-197 Suarez, A., see Ponton, M., TMTT Dec. 2015 4458-4472 Suarez, A., see de Cos, J., TMTT Dec. 2015 4284-4296 Suarez, A., Ramirez, F., and Sancho, S., Generalized Stability Criteria for Power Amplifiers Under Mismatch Effects; TMTT Dec. 2015 4415-4428 Suematsu, N., see Ta, T. T., TMTT Aug. 2015 2682-2691 Sun, L., see Gao, Z., TMTT Oct. 2015 3109-3121 Sun, Y., Fu, J., Yang, J., Xu, J., Wang, Y., Cui, J., Zhou, W., Wei, Z., and Liu, Z., An Improved Small-Signal Model for SiGe HBT Under OFF-State, Derived From Distributed Network and Corresponding Model Parameter Extraction; TMTT Oct. 2015 3131-3141 Sun, Y., Zhu, X.-W., Zhai, J., Zhang, L., and Meng, F., Highly Efficient Concurrent Power Amplifier With Controllable Modes; TMTT Dec. 2015 40514060 Sun, Y., see Li, H., TMTT Mar. 2015 925-936 Suzuki, Y., see Shiina, T., TMTT Oct. 2015 3311-3318 Svensson, C., see He, Z., TMTT May 2015 1683-1692 Swahsn, T., see He, Z., TMTT Aug. 2015 2630-2637 Szakmany, G. P., see Russer, J. A., TMTT Dec. 2015 4236-4246 Szortyka, V., see Mangraviti, G., TMTT Jul. 2015 2301-2312

T Ta, T. T., Tanifuji, S., Taira, A., Kameda, S., Suematsu, N., Takagi, T., and Tsubouchi, K., A Millimeter-Wave WPAN Adaptive Phased Array Control Method Using Low-Frequency Part of Signal for Self-Directed System; TMTT Aug. 2015 2682-2691 Tabor, C. E., see Cumby, B. L., TMTT Oct. 2015 3122-3130 Taheri, O., see Maunder, A., TMTT Jul. 2015 2322-2334 Taira, A., see Ta, T. T., TMTT Aug. 2015 2682-2691 Takagi, T., see Ta, T. T., TMTT Aug. 2015 2682-2691 Takayama, Y., see Watanabe, S., TMTT Feb. 2015 572-579 Taki, M., see Shiina, T., TMTT Oct. 2015 3311-3318 Tam, K.-W., see Guo, X., TMTT May 2015 1587-1594 Tam, K.-W., see Cheong, P., TMTT Dec. 2015 4130-4149 Tam, K.-W., see Yang, L., TMTT Jul. 2015 2225-2232 Tamiazzo, S., and Macchiarella, G., Synthesis of Cross-Coupled Prototype Filters Including Resonant and Non-Resonant Nodes; TMTT Oct. 2015 34083415 Tan, A. E.-C., see Chan, K.K.M., TMTT May 2015 1700-1709 Tan, K.-W., Lo, A.-H., Chu, T.-S., and Hsu, S. S. H., A K-Band Reconfigurable Pulse-Compression Automotive Radar Transmitter in 90-nm CMOS; TMTT Apr. 2015 1380-1387 Tan, T., Non-Reflecting SFBF Termination Inverting From TFSF Discontinuity Decomposition; TMTT Sep. 2015 2710-2719 Tang, H.-J., see Zhu, X.-C., TMTT Feb. 2015 494-503 Tang, M.-C., see Wang, F.-K., TMTT Dec. 2015 4592-4602 Tang, X., see Yu, J., TMTT Jun. 2015 1836-1842 Tang, Y., see Liu, N., TMTT Oct. 2015 3094-3102 Tang, Y., see Liu, N., TMTT Feb. 2015 317-325 Tang, Y., see Liu, Y., TMTT May 2015 1544-1555 Tanifuji, S., see Ta, T. T., TMTT Aug. 2015 2682-2691 Tantawi, S. G., see Chang, C., TMTT Jun. 2015 1875-1882 Tarricone, L., see Monti, G., TMTT Nov. 2015 3814-3822 Tascone, R., see Tibaldi, A., TMTT Jan. 2015 11-19 Tascone, R., see Tibaldi, A., TMTT Jan. 2015 115-124 Tascone, R., see Peverini, O. A., TMTT Oct. 2015 3361-3373 Tascone, R., see Addamo, G., TMTT May 2015 1468-1474 Tatomirescu, A., see Bahramzy, P., TMTT Oct. 2015 3300-3310 Tawfick, S., see Li, S., TMTT Nov. 2015 3588-3594 Tedjini, S., see Andia Vera, G., TMTT Dec. 2015 4556-4566 Tedjini, S., see Andiia Vera, G., TMTT Sep. 2015 2991-3004 Teixeira, F. L., see Angulo, L. D., TMTT Oct. 2015 3081-3093 Tentzeris, M. M., see Bito, J., TMTT Dec. 2015 4533-4543 Tentzeris, M. M., see Kimionis, J., TMTT Dec. 2015 4521-4532 Teo, K. H., see Chung, S., TMTT Feb. 2015 598-613 Tervo, R. J., see Elnaggar, S. Y., TMTT Jul. 2015 2115-2123 Tervo, R. J., see Elnaggar, S. Y., TMTT Jul. 2015 2124-2132 Tessmann, A., see Seelmann-Eggebert, M., TMTT Jul. 2015 2335-2342 Tessmann, A., see Diebold, S., TMTT Mar. 2015 999-1006 Thanh, T. N. D., see Horberg, M., TMTT Aug. 2015 2619-2629 + Check author entry for coauthors

Theogarajan, L., see Bluestone, A., TMTT Mar. 2015 1046-1052 Thian, M., Barakat, A., and Fusco, V., High-Efficiency Harmonic-Peaking Class-EF Power Amplifiers With Enhanced Maximum Operating Frequency; TMTT Feb. 2015 659-671 Thirunarayanan, R., Ruffieux, D., and Enz, C., Reducing Energy Dissipation in ULP Systems: PLL-Free FBAR-Based Fast Startup Transmitters; TMTT Apr. 2015 1110-1117 Thoen, B., and Stevens, N., Development of a Communication Scheme for Wireless Power Applications With Moving Receivers; TMTT Mar. 2015 857-863 Thomas, C. M., and Larson, L. E., Broadband Synthetic Transmission-Line N-Path Filter Design; TMTT Oct. 2015 3525-3536 Thomas, E., see Cuenca, J. A., TMTT Dec. 2015 4110-4118 Thomas, S. J., see Cnaan-On, I., TMTT Jul. 2015 2375-2383 Thotahewa, K. M. S., Redoute, J.-M., and Yuce, M. R., Propagation, Power Absorption, and Temperature Analysis of UWB Wireless Capsule Endoscopy Devices Operating in the Human Body; TMTT Nov. 2015 3823-3833 Thumm, M., see Wu, C., TMTT Aug. 2015 2459-2467 Tibaldi, A., Orta, R., Peverini, O. A., Addamo, G., Virone, G., and Tascone, R., Skew Incidence Plane-Wave Scattering From 2-D Dielectric Periodic Structures: Analysis by the Mortar-Element Method; TMTT Jan. 2015 11-19 Tibaldi, A., Addamo, G., Peverini, O. A., Orta, R., Virone, G., and Tascone, R., Analysis of Axisymmetric Waveguide Components by a Multi-Domain Spectral Method; TMTT Jan. 2015 115-124 Tobon, L. E., see Liu, N., TMTT Feb. 2015 317-325 Toledo-Redondo, S., see Salinas, A., TMTT Aug. 2015 2449-2458 Tomassoni, C., Bastioli, S., and Snyder, R. V., Propagating Waveguide Filters Using Dielectric Resonators; TMTT Dec. 2015 4366-4375 Tong, L., see Lin, L., TMTT Jun. 2015 1951-1963 Topfer, F., Dudorov, S., and Oberhammer, J., Millimeter-Wave Near-Field Probe Designed for High-Resolution Skin Cancer Diagnosis; TMTT Jun. 2015 2050-2059 Tornielli di Crestvolant, V., Martin Iglesias, P., and Lancaster, M. J., Advanced Butler Matrices With Integrated Bandpass Filter Functions; TMTT Oct. 2015 3433-3444 Torres-Torres, R., see Zarate-Rincon, F., TMTT Dec. 2015 4255-4262 Torres-Torres, R., see Alvarez-Botero, G., TMTT Dec. 2015 3888-3895 Tran, A., see Ko, C.-H., TMTT Jun. 2015 1854-1862 Traverso, P. A., Florian, C., and Filicori, F., A Fully Nonlinear Compact Modeling Approach for High-Frequency Noise in Large-Signal Operated Microwave Electron Devices; TMTT Feb. 2015 352-366 Tretter, G., see Fritsche, D., TMTT Jun. 2015 1910-1922 Trieu, H. K., see Meyne nee Haase, N., TMTT Oct. 2015 3026-3033 Tsai, W.-T., see Lee, M.-L., TMTT Feb. 2015 614-624 Tsubouchi, K., see Ta, T. T., TMTT Aug. 2015 2682-2691 Tuo, M., see Li, S., TMTT Nov. 2015 3588-3594 Tustin, P. F., see Riehl, P. S., TMTT Mar. 2015 780-790 Twieg, M., de Rooij, M. A., and Griswold, M. A., Active Detuning of MRI Receive Coils with GaN FETs; TMTT Dec. 2015 4169-4177 Tzuang, C.-K. C., see Li, X., TMTT Jul. 2015 2142-2153 U Ubeda-Medina, L., see Grajal, J., TMTT Mar. 2015 1097-1107 Un, K.-F., Yu, W.-H., Cheang, C.-F., Qi, G., Mak, P.-I., and Martins, R. P., A Sub-GHz Wireless Transmitter Utilizing a Multi-Class-Linearized PA and Time-Domain Wideband-Auto I/Q-LOFT Calibration for IEEE 802.11af WLAN; TMTT Oct. 2015 3228-3241 Urteaga, M., see Kim, Y., TMTT Jan. 2015 256-265 Ussmueller, T., see Glock, S., TMTT Jun. 2015 1826-1835 V Vaesen, K., see Mangraviti, G., TMTT Jul. 2015 2301-2312 Vahabisani, N., and Daneshmand, M., Monolithic Millimeter-Wave MEMS Waveguide Switch; TMTT Feb. 2015 340-351 Vaidyanathan, M., see Alam, A. U., TMTT Dec. 2015 3874-3887 Vakili, I., Ohlsson, L., Wernersson, L.-E., and Gustafsson, M., Time-Domain System for Millimeter-Wave Material Characterization; TMTT Sep. 2015 2915-2922 Valdes-Garcia, A., see Natarajan, A., TMTT Jun. 2015 1989-2002

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Valenta, C. R., Morys, M. M., and Durgin, G. D., Theoretical Energy-Conversion Efficiency for Energy-Harvesting Circuits Under Power-Optimized Waveform Excitation; TMTT May 2015 1758-1767 Valente, G., Montisci, G., Pisanu, T., Navarrini, A., Marongiu, P., and Casula, G. A., A Compact L-Band Orthomode Transducer for Radio Astronomical Receivers at Cryogenic Temperature; TMTT Oct. 2015 3218-3227 Valkama, M., see Kiayani, A., TMTT Nov. 2015 3608-3623 Valkama, M., see Singh, S., TMTT May 2015 1721-1734 Valles, I., see Xu, Z., TMTT Apr. 2015 1219-1227 Vandersteen, G., see Mangraviti, G., TMTT Jul. 2015 2301-2312 Vanin, F. M., De Paolis, F., and Schmitt, D., Resonator Voltage Prediction in Microwave Bandpass Filters; TMTT Feb. 2015 397-402 Vannini, G., see Nalli, A., TMTT Aug. 2015 2498-2508 Vassilev, V., see Yan, Y., TMTT Sep. 2015 2897-2904 Vazquez Antuna, C., Hadarig, A. I., Hoeye, S. V., Garcia, M. F., Diaz, R. C., Hotopan, G. R., and Andres, F. L. H., High-Order Subharmonic MillimeterWave Mixer Based on Few-Layer Graphene; TMTT Apr. 2015 1361-1369 Vazquez-Roy, J.-L., see Brazalez, A. A., TMTT Dec. 2015 4035-4050 Vega, Y., see Ketterl, T. P., TMTT Dec. 2015 4382-4394 Velazquez Lopez, M., see Choi, Y.-C., TMTT Oct. 2015 3254-3264 Velez, P., Naqui, J., Fernandez-Prieto, A., Bonache, J., Mata-Contreras, J., Martel, J., Medina, F., and Martin, F., Ultra-Compact (80 mm ) Differential-Mode Ultra-Wideband (UWB) Bandpass Filters With Common-Mode Noise Suppression; TMTT Apr. 2015 1272-1280 Velez, P., see Sans, M., TMTT Dec. 2015 3896-3908 Vellucci, S., see Ponti, C., TMTT Jan. 2015 30-39 Vera Castejon, P., see Quesada Pereira, F. D., TMTT Dec. 2015 3862-3873 Verissimo, G., see Laur, V., TMTT Dec. 2015 4376-4381 Vernier, P. T., see Kohler, S., TMTT Jun. 2015 2032-2040 Vidmar, M., see Furlan, V., TMTT Mar. 2015 891-896 Viikari, V., see Islam, Md. M., TMTT Aug. 2015 2672-2681 Viitala, O., see Ostman, K. B., TMTT Apr. 2015 1370-1379 Vinoy, K. J., see Ghorbani, K., TMTT Aug. 2015 2397-2398 Virone, G., see Tibaldi, A., TMTT Jan. 2015 11-19 Virone, G., see Tibaldi, A., TMTT Jan. 2015 115-124 Virone, G., see Peverini, O. A., TMTT Oct. 2015 3361-3373 Virone, G., see Addamo, G., TMTT May 2015 1468-1474 Vitee, N., see Chong, W. K., TMTT Aug. 2015 2427-2437 Vitusevich, S. A., see Gubin, A. I., TMTT Jun. 2015 2003-2009 Viveiros, E., see Darwish, A. M., TMTT Jul. 2015 2253-2263 Volakis, J. L., see Lee, C. W. L., TMTT Jun. 2015 2060-2068 Volynets, N., see Bellucci, S., TMTT Jun. 2015 2024-2031 Vomvoridis, J. L., see Chelis, I. G., TMTT Jun. 2015 1781-1790 Vosoogh, A., see Brazalez, A. A., TMTT Dec. 2015 4035-4050 Vuong, T.-P., see Parment, F., TMTT Apr. 2015 1228-1238 W Wagner, S., see Diebold, S., TMTT Mar. 2015 999-1006 Wakatsuchi, H., see Gao, F., TMTT Sep. 2015 2971-2982 Walker, D. K., see Gu, D., TMTT May 2015 1475-1488 Wambacq, P., see Mangraviti, G., TMTT Jul. 2015 2301-2312 Wang, C.-C., see Ho, C.-Y., TMTT Sep. 2015 2923-2930 Wang, C.-M., see Remley, K. A., TMTT May 2015 1710-1720 Wang, F.-K., Tang, M.-C., Chiu, Y.-C., and Horng, T.-S., Gesture Sensing Using Retransmitted Wireless Communication Signals Based on Doppler Radar Technology; TMTT Dec. 2015 4592-4602 Wang, G., see Wang, L., TMTT Dec. 2015 3962-3970 Wang, H., see Park, J. S., TMTT Dec. 2015 4444-4457 Wang, H., see Hu, S., TMTT Feb. 2015 580-597 Wang, H., see Chang, J.-F., TMTT Aug. 2015 2638-2649 Wang, H., Xu, L., Li, J.-Q., and Li, B., An Inverse-Based Multifrontal Block Incomplete LU Preconditioner for the 3-D Finite-Element Eigenvalue Analysis of Lossy Slow-Wave Structures; TMTT Jul. 2015 2094-2106 Wang, J., see Guo, X., TMTT Jun. 2015 1902-1909 Wang, K.-X., Zhang, X. Y., Zheng, S. Y., and Xue, Q., Compact Filtering RatRace Hybrid With Wide Stopband; TMTT Aug. 2015 2550-2560 Wang, L., see Chen, T.-C., TMTT Nov. 2015 3768-3774 Wang, L., see Yu, F., TMTT Feb. 2015 403-413 Wang, L., Wang, G., and Siden, J., Design of High-Directivity Wideband Microstrip Directional Coupler With Fragment-Type Structure; TMTT Dec. 2015 3962-3970 Wang, N., see Campanella, H., TMTT Feb. 2015 331-339 + Check author entry for coauthors

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Wang, N.-Y., see Wu, H., TMTT Mar. 2015 1053-1062 Wang, R., see Lu, X., TMTT Apr. 2015 1281-1293 Wang, R., see Lin, L., TMTT Jun. 2015 1951-1963 Wang, W., see Wei, W., TMTT May 2015 1445-1456 Wang, X., Qin, T., Witte, R. S., and Xin, H., Computational Feasibility Study of Contrast-Enhanced Thermoacoustic Imaging for Breast Cancer Detection Using Realistic Numerical Breast Phantoms; TMTT May 2015 1489-1501 Wang, X., Jang, G., Lee, B., and Park, N., Compact Quad-Mode Bandpass Filter Using Modified Coaxial Cavity Resonator With Improved -Factor; TMTT Mar. 2015 965-975 Wang, Y., see Sun, Y., TMTT Oct. 2015 3131-3141 Wang, Y., see Yu, F., TMTT Feb. 2015 403-413 Wang, Z., see Yu, F., TMTT Feb. 2015 403-413 Wang, Z., see Jia, H., TMTT May 2015 1645-1657 Wang, Z., see Jia, H., TMTT Feb. 2015 719-725 Wang, Z., see Yin, Y., TMTT Feb. 2015 672-682 Watanabe, S., see Shiina, T., TMTT Oct. 2015 3311-3318 Watanabe, S., Takayama, Y., Ishikawa, R., and Honjo, K., A Miniature Broadband Doherty Power Amplifier With a Series-Connected Load; TMTT Feb. 2015 572-579 Watkins, G. T., see Zhou, J., TMTT Sep. 2015 2793-2801 Weber, R., see Seelmann-Eggebert, M., TMTT Jul. 2015 2335-2342 Weerasekera, R., see Zhang, S., TMTT Oct. 2015 3487-3493 Wei, B., see Lu, X., TMTT Apr. 2015 1281-1293 Wei, C., see Nieh, C.-M., TMTT Jun. 2015 2069-2078 Wei, G., see Xu, J., TMTT Dec. 2015 3909-3919 Wei, W., Wei, Y., Wang, W., Zhang, M., Gong, H., and Gong, Y., Dispersion Equations of a Rectangular Tape Helix Slow-Wave Structure; TMTT May 2015 1445-1456 Wei, Y., see Wei, W., TMTT May 2015 1445-1456 Wei, Z., see Sun, Y., TMTT Oct. 2015 3131-3141 Weigel, R., see Gharib, A., TMTT Nov. 2015 3701-3712 Weigel, R., see Glock, S., TMTT Jun. 2015 1826-1835 Weiner, A. M., see Kim, H.-J., TMTT Dec. 2015 4178-4187 Weller, T. M., see Nassar, I. T., TMTT Jan. 2015 287-294 Weller, T. M., see Ketterl, T. P., TMTT Dec. 2015 4382-4394 Wernersson, L.-E., see Vakili, I., TMTT Sep. 2015 2915-2922 Whyte, C. G., see Zhang, L., TMTT Mar. 2015 1090-1096 Wiatr, W., see Lewandowski, A., TMTT Mar. 2015 1076-1089 Wight, J. S., see Ross, T. N., TMTT Jan. 2015 244-255 Williams, D. F., see Remley, K. A., TMTT May 2015 1710-1720 Williams, D. F., see Avolio, G., TMTT Jul. 2015 2353-2363 Williams, O., see Cuenca, J. A., TMTT Dec. 2015 4110-4118 Wilson, R. S., see Hwang, T., TMTT Jul. 2015 2185-2198 Wincza, K., see Sorocki, J., TMTT Feb. 2015 384-396 Winklea, D., see Xu, Z., TMTT Apr. 2015 1219-1227 Withers, R. S., see Hooker, J. W., TMTT Jul. 2015 2107-2114 Witte, R. S., see Wang, X., TMTT May 2015 1489-1501 Wong, J. P. S., Selvanayagam, M., and Eleftheriades, G. V., Polarization Considerations for Scalar Huygens Metasurfaces and Characterization for 2-D Refraction; TMTT Mar. 2015 913-924 Wong, M., see Alam, A. U., TMTT Dec. 2015 3874-3887 Wong, S.-W., Feng, S.-F., Zhu, L., and Chu, Q.-X., Triple- and QuadrupleMode Wideband Bandpass Filter Using Simple Perturbation in Single Metal Cavity; TMTT Oct. 2015 3416-3424 Wong, S.-W., Zhang, Z.-C., Feng, S.-F., Chen, F.-C., Zhu, L., and Chu, Q.-X., Triple-Mode Dielectric Resonator Diplexer for Base-Station Applications; TMTT Dec. 2015 3947-3953 Woo, J.-L., see Park, S., TMTT Apr. 2015 1174-1185 Woo, J.-L., see Jeon, M.-S., TMTT Sep. 2015 2854-2866 Wu, C., Avramidis, K. A., Thumm, M., and Jelonnek, J., An Improved Broadband Boundary Condition for the RF Field in Gyrotron Interaction Modeling; TMTT Aug. 2015 2459-2467 Wu, H., Wang, N.-Y., Du, Y., and Chang, M.-C. F., A Blocker-Tolerant Current Mode 60-GHz Receiver With 7.5-GHz Bandwidth and 3.8-dB Minimum NF in 65-nm CMOS; TMTT Mar. 2015 1053-1062 Wu, H.-S., see Li, X., TMTT Jul. 2015 2142-2153 Wu, J., see Huang, S. Y., TMTT Aug. 2015 2482-2490 Wu, K., see Doghri, A., TMTT Jan. 2015 209-221 Wu, K., see Snyder, R. V., TMTT Oct. 2015 3324-3360 Wu, K., see Lorenz, C. H. P., TMTT Dec. 2015 4544-4555 Wu, K., see Zhu, X.-C., TMTT Feb. 2015 494-503 Wu, K., see Parment, F., TMTT Apr. 2015 1228-1238 Wu, K., see Cheong, P., TMTT Dec. 2015 4130-4149

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Wu, K., see Ladan, S., TMTT Mar. 2015 937-944 Wu, K.-L., see Qian, K., TMTT Oct. 2015 3199-3207 Wu, L.-S., see Chen, F.-J., TMTT Oct. 2015 3494-3504 Mode Wu, P., Liu, J., and Xue, Q., Wideband Excitation Technology of Substrate Integrated Waveguide (SIW) and Its Applications; TMTT Jun. 2015 1863-1874 Wu, Q., see Gou, Y., TMTT Oct. 2015 3142-3152 Wu, Q.-S., see Chu, Q.-X., TMTT Dec. 2015 3988-3996 Wu, T.-L., see Hsiao, C.-Y., TMTT Nov. 2015 3624-3631 Wu, T.-L., see Hsiao, C.-Y., TMTT Jun. 2015 1894-1901 Wu, W., see Guo, X., TMTT May 2015 1587-1594 Wu, W., see Xu, J., TMTT Dec. 2015 3909-3919 Wu, W., see Guo, X., TMTT Jun. 2015 1902-1909 Wu, Y., see Gao, Z., TMTT Oct. 2015 3109-3121 Wu, Z., Kasparek, W., and Plaum, B., Design and Characterization of a 170-GHz Resonant Diplexer for High-Power ECRH Systems; TMTT Oct. 2015 3537-3546 X Xia, J., see Huang, H., TMTT Dec. 2015 4297-4305 Xia, J., see Yu, C., TMTT Jul. 2015 2211-2224 Xie, C., see Rawat, M., TMTT Feb. 2015 625-637 Xie, Y., see Lorenz, C. H. P., TMTT Dec. 2015 4544-4555 Xin, H., see Chen, T.-C., TMTT Nov. 2015 3768-3774 Xin, H., see Li, S., TMTT Nov. 2015 3588-3594 Xin, H., see Wang, X., TMTT May 2015 1489-1501 Xing, D., see Ding, W., TMTT Oct. 2015 3272-3276 Xu, J., see Sun, Y., TMTT Oct. 2015 3131-3141 Xu, J., Wu, W., and Wei, G., Compact Multi-Band Bandpass Filters With Mixed Electric and Magnetic Coupling Using Multiple-Mode Resonator; TMTT Dec. 2015 3909-3919 Xu, K., see Zhao, J., TMTT May 2015 1633-1644 Xu, K., Shi, J., Lin, L., and Chen, J.-X., A Balanced-to-Unbalanced Microstrip Power Divider With Filtering Function; TMTT Aug. 2015 2561-2569 Xu, L., see Wang, H., TMTT Jul. 2015 2094-2106 Xu, X., see Yu, F., TMTT Feb. 2015 403-413 Xu, X.-J., see Ge, C., TMTT Nov. 2015 3641-3650 Xu, Z., Winklea, D., Oh, T. C., Kim, S., Chen, S. T. W., Royter, Y., Lau, M., Valles, I., Hitko, D. A., Li, J. C., and Gu, Q. J., 0.8/2.2-GHz Programmable Active Bandpass Filters in InP/Si BiCMOS Technology; TMTT Apr. 2015 1219-1227 Xu, Z., see Lu, X., TMTT Apr. 2015 1281-1293 Xue, Q., see Jin, J. Y., TMTT Oct. 2015 3374-3380 Xue, Q., see Gao, L., TMTT Oct. 2015 3505-3513 Xue, Q., see Gao, Z., TMTT Oct. 2015 3109-3121 Xue, Q., see Feng, W., TMTT Dec. 2015 4013-4018 Xue, Q., see Wu, P., TMTT Jun. 2015 1863-1874 Xue, Q., see Wang, K.-X., TMTT Aug. 2015 2550-2560 Y Yamaguchi, K., see Zhou, J., TMTT Sep. 2015 2793-2801 Yamao, Y., see Ma, Y., TMTT Oct. 2015 3164-3174 Yan, J., and Jiao, D., Accurate and Stable Matrix-Free Time-Domain Method in 3-D Unstructured Meshes for General Electromagnetic Analysis; TMTT Dec. 2015 4201-4214 Yan, J. J., see Liu, Y., TMTT May 2015 1556-1568 Yan, L., see Zou, X., TMTT Apr. 2015 1421-1430 Yan, Y., Bao, M., Gunnarsson, S. E., Vassilev, V., and Zirath, H., A 110–170-GHz Multi-Mode Transconductance Mixer in 250-nm InP DHBT Technology; TMTT Sep. 2015 2897-2904 Yanay, N., and Socher, E., Wide Tuning-Range mm-Wave Voltage-Controlled Oscillator Employing an Artificial Magnetic Transmission Line; TMTT Apr. 2015 1342-1352 Yang, B.-S., see Lee, C.-I., TMTT Feb. 2015 367-373 Yang, C. K., see Chen, W.-T. S., TMTT Dec. 2015 4157-4168 Yang, C.-L., see Lee, C.-S., TMTT Jun. 2015 2010-2023 Yang, H.-H., and Rebeiz, G. M., Micromachined Room-Temperature Air-Suspended Ni/Cr Nanobolometer; TMTT Nov. 2015 3760-3767

+ Check author entry for coauthors

Yang, H.-S., Chang, C.-W., and Chen, J.-H., A Highly Efficient LTE PulseModulated Polar Transmitter Using Wideband Power Recycling; TMTT Dec. 2015 4437-4443 Yang, H.-S., Chen, J.-H., and Chen, Y.-J. E., A Wideband and Highly Symmetric Multi-Port Parallel Combining Transformer Technology; TMTT Nov. 2015 3671-3680 Yang, H.-S., see Liang, K.-F., TMTT Aug. 2015 2603-2608 Yang, J., see Sun, Y., TMTT Oct. 2015 3131-3141 Yang, J.-C., see Riehl, P. S., TMTT Mar. 2015 780-790 Yang, L., Choi, W.-W., Tam, K.-W., and Zhu, L., Balanced Dual-Band Bandpass Filter With Multiple Transmission Zeros Using Doubly Short-Ended Resonator Coupled Line; TMTT Jul. 2015 2225-2232 Yang, T., and Rebeiz, G. M., Tunable 1.25–2.1-GHz 4-Pole Bandpass Filter With Intrinsic Transmission Zero Tuning; TMTT May 2015 1569-1578 Yang, X., see Abduljabar, A. A., TMTT Dec. 2015 4492-4500 Yang, X., and Babakhani, A., A Single-Chip Electron Paramagnetic Resonance Transceiver in 0.13- m SiGe BiCMOS; TMTT Nov. 2015 3727-3735 Yang, X., see Qian, H., TMTT Oct. 2015 3153-3163 Yao, J., see Zhang, J., TMTT Jul. 2015 2166-2172 Yao, J., see Chen, X., TMTT Jul. 2015 2384-2389 Yao, S., see Qian, H., TMTT Oct. 2015 3153-3163 Yassini, B., and Yu, M., Ka-Band Dual-Mode Super Filters and Multiplexers; TMTT Oct. 2015 3391-3397 Yavari, E., and Boric-Lubecke, O., Channel Imbalance Effects and Compensation for Doppler Radar Physiological Measurements; TMTT Nov. 2015 3834-3842 Yavari, E., see Rahman, A., TMTT Oct. 2015 3034-3041 Ye, D., see Zhao, J., TMTT May 2015 1633-1644 Ye, D., see Li, H., TMTT Mar. 2015 925-936 Ye, F., see Ding, W., TMTT Oct. 2015 3272-3276 Yen, Y.-C., see Riehl, P. S., TMTT Mar. 2015 780-790 Yeo, K. S., see Chan, L. H. K., TMTT Jan. 2015 141-154 Yeo, K. S., see Ma, K., TMTT Dec. 2015 4395-4405 Yializis, A., see Chen, T.-C., TMTT Nov. 2015 3768-3774 Yin, W.-Y., see Lin, L., TMTT Jun. 2015 1951-1963 Yin, Y., Yu, X., Wang, Z., and Chi, B., An Efficiency-Enhanced Stacked 2.4-GHz CMOS Power Amplifier With Mode Switching Scheme for WLAN Applications; TMTT Feb. 2015 672-682 Yoo, H.-J., see Choi, Y.-C., TMTT Oct. 2015 3254-3264 Yoo, H.-J., see Bae, J., TMTT Apr. 2015 1409-1420 Yoo, Y.-J., see Choi, Y.-C., TMTT Oct. 2015 3254-3264 Yoon, J.-H., see Kim, S.-M., TMTT Mar. 2015 847-856 You, F., see Dai, Z., TMTT Feb. 2015 449-458 You, F., see Pang, J., TMTT Dec. 2015 4061-4071 Young, A. R., see Zhang, L., TMTT Mar. 2015 1090-1096 Yu, C., Cao, W., Guo, Y., and Zhu, A., Digital Compensation for Transmitter Leakage in Non-Contiguous Carrier Aggregation Applications With FPGA Implementation; TMTT Dec. 2015 4306-4318 Yu, C., see Guo, Y., TMTT Nov. 2015 3595-3607 Yu, C., see Reina-Tosina, J., TMTT Feb. 2015 745-753 Yu, C., Xia, J., Zhu, X.-W., and Zhu, A., Single-Model Single-Feedback Digital Predistortion for Concurrent Multi-Band Wireless Transmitters; TMTT Jul. 2015 2211-2224 Yu, F., Wang, Y., Wang, Z., Zheng, Q., Zhou, M., Guo, D., Ding, X., Xu, X., Wang, L., Chen, H., Shang, Y., and Huang, Z., Temporal Coupled-Mode Theory and the Combined Effect of Dual Orthogonal Resonant Modes in Microstrip Bandpass Filters; TMTT Feb. 2015 403-413 Yu, J., Li, X., Tang, X., Zhang, H., Chi, N., and Shi, Y., High-Speed Signal Transmission at W-Band Over Dielectric-Coated Metallic Hollow Fiber; TMTT Jun. 2015 1836-1842 Yu, M., see Yassini, B., TMTT Oct. 2015 3391-3397 Yu, M., see Boria, V. E., TMTT Oct. 2015 3321-3323 Yu, W.-H., see Un, K.-F., TMTT Oct. 2015 3228-3241 Yu, X., Deng, J., Cao, W.-P., Li, S., Gao, X., and Jiang, Y., Method for Synthesis of Mode Converter for Gyrotron by the NURBS Technique; TMTT Feb. 2015 326-330 Yu, X., see Yin, Y., TMTT Feb. 2015 672-682 Yu, X. H., Deng, J. L., Li, S. M., Cao, W. P., Gao, X., and Jiang, Y. N., A -toCircular Mode Converter Design; Universal Solution to TMTT Dec. 2015 3845-3850 Yuce, M. R., see Thotahewa, K. M. S., TMTT Nov. 2015 3823-3833 Yue, Y., see Feng, N., TMTT Mar. 2015 877-882

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Zai, A., Pinto, M., Coffey, M., and Popovic, Z., Supply-Modulated Radar Transmitters With Amplitude-Modulated Pulses; TMTT Sep. 2015 2953-2964 Zamora, G., see Zuffanelli, S., TMTT Jul. 2015 2133-2141 Zappelli, L., Simple, Fast, and Effective Identification of an Equivalent Circuit of a Waveguide Junction With Ports; TMTT Jan. 2015 48-55 Zappelli, L., Corrections to “Simple, Fast, and Effective Identification of an Equivalent Circuit of a Waveguide Junction With Ports” [Jan 15 48-55]; TMTT Mar. 2015 1108 Zarate-de Landa, A., see Pulido-Gaytan, M. A., TMTT May 2015 1693-1699 Zarate-Rincon, F., Torres-Torres, R., and Murphy-Arteaga, R. S., Consistent DC and RF MOSFET Modeling Using an -Parameter Measurement-Based Parameter Extraction Method in the Linear Region; TMTT Dec. 2015 4255-4262 Zargar, H., Banai, A., and Pedro, J. C., A New Double Input-Double Output Complex Envelope Amplifier Behavioral Model Taking Into Account Source and Load Mismatch Effects; TMTT Feb. 2015 766-774 Zekios, C. L., Allilomes, P. C., and Kyriacou, G. A., DC and Imaginary Spurious Modes Suppression for Both Unbounded and Lossy Structures; TMTT Jul. 2015 2082-2093 Zeng, A.-P., see Meyne nee Haase, N., TMTT Oct. 2015 3026-3033 Zenteno, E., Isaksson, M., and Handel, P., Output Impedance Mismatch Effects on the Linearity Performance of Digitally Predistorted Power Amplifiers; TMTT Feb. 2015 754-765 Zhai, J., see Sun, Y., TMTT Dec. 2015 4051-4060 Zhang, B., see Zhao, J., TMTT May 2015 1633-1644 Zhang, B., see Li, H., TMTT Mar. 2015 925-936 Zhang, C., Feng, F., Gongal-Reddy, V.-M.-R., Zhang, Q. J., and Bandler, J. W., Cognition-Driven Formulation of Space Mapping for Equal-Ripple Optimization of Microwave Filters; TMTT Jul. 2015 2154-2165 Zhang, F., see Gao, F., TMTT Sep. 2015 2971-2982 Zhang, H., see Yu, J., TMTT Jun. 2015 1836-1842 Zhang, J., and Yao, J., Broadband and Precise Microwave Time Reversal Using a Single Linearly Chirped Fiber Bragg Grating; TMTT Jul. 2015 2166-2172 Zhang, L., He, W., Donaldson, C. R., Garner, J. R., McElhinney, P., and Cross, A. W., Design and Measurement of a Broadband Sidewall Coupler for a W-Band Gyro-TWA; TMTT Oct. 2015 3183-3190 Zhang, L., see Sun, Y., TMTT Dec. 2015 4051-4060 Zhang, L., Mishakin, S. V., He, W., Samsonov, S. V., McStravick, M., Denisov, G. G., Cross, A. W., Bratman, V. L., Whyte, C. G., Robertson, C. W., Young, A. R., Ronald, K., and Phelps, A. D. R., Experimental Study of Microwave Pulse Compression Using a Five-Fold Helically Corrugated Waveguide; TMTT Mar. 2015 1090-1096 Zhang, M., see Wei, W., TMTT May 2015 1445-1456 Zhang, P.-P., see Zhu, X.-C., TMTT Feb. 2015 494-503 Zhang, Q., Guo, T., Khan, B. A., Kodera, T., and Caloz, C., Coupling Matrix Synthesis of Nonreciprocal Lossless Two-Port Networks Using Gyrators and Inverters; TMTT Sep. 2015 2782-2792 Zhang, Q., see Gupta, S., TMTT Mar. 2015 1007-1018 Zhang, Q. J., see Zhang, C., TMTT Jul. 2015 2154-2165 Zhang, S., Zhu, L., and Weerasekera, R., Synthesis of Inline Mixed Coupled Resonators; TMTT Oct. 2015 Quasi-Elliptic Bandpass Filters Based on 3487-3493 Zhang, T., see Fu, M., TMTT Mar. 2015 801-812 Zhang, X., see Lu, X., TMTT Apr. 2015 1281-1293 Zhang, X., see Zhu, R., TMTT Aug. 2015 2692-2702 Zhang, X. Y., see Gao, L., TMTT Oct. 2015 3505-3513 Zhang, X. Y., see Wang, K.-X., TMTT Aug. 2015 2550-2560 Zhang, Y.-J., Ren, L., Liu, D., De, S., Gu, X., Kwark, Y. H., Schuster, C., and Fan, J., An Efficient Hybrid Finite-Element Analysis of Multiple Vias Sharing the Same Anti-Pad in an Arbitrarily Shaped Parallel-Plate Pair; TMTT Mar. 2015 883-890 Zhang, Z.-C., see Wong, S.-W., TMTT Dec. 2015 3947-3953 Zhao, C., see Gao, Z., TMTT Oct. 2015 3109-3121 Zhao, C., see Feng, W., TMTT Dec. 2015 4013-4018 Zhao, D., see Kaymaksut, E., TMTT Apr. 2015 1186-1192 Zhao, D., and Reynaert, P., An E-Band Power Amplifier With Broadband Parallel-Series Power Combiner in 40-nm CMOS; TMTT Feb. 2015 683-690 Zhao, D., and Reynaert, P., A 40-nm CMOS E-Band 4-Way Power Amplifier With Neutralized Bootstrapped Cascode Amplifier and Optimum Passive Circuits; TMTT Dec. 2015 4083-4089 + Check author entry for coauthors

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Zhao, J., and Lu, H., Reduction of Exposure Inhomogeneity for MillimeterWave Experiments on Cells In Vitro; TMTT Feb. 2015 533-545 Zhao, J., Zhu, Z., Cui, W., Xu, K., Zhang, B., Ye, D., Li, C., and Ran, L., Power Synthesis at 110-GHz Frequency Based on Discrete Sources; TMTT May 2015 1633-1644 Zhao, L., see Qian, K., TMTT Oct. 2015 3199-3207 Zhao, Y., see Liu, N., TMTT Feb. 2015 317-325 Zheng, Q., see Yu, F., TMTT Feb. 2015 403-413 Zheng, S. Y., see Wang, K.-X., TMTT Aug. 2015 2550-2560 Zhou, B., and Jiao, D., Direct Finite-Element Solver of Linear Complexity for Large-Scale 3-D Electromagnetic Analysis and Circuit Extraction; TMTT Oct. 2015 3066-3080 Zhou, J., Morris, K. A., Watkins, G. T., and Yamaguchi, K., Improved Reactance-Compensation Technique for the Design of Wideband Suboptimum Class-E Power Amplifiers; TMTT Sep. 2015 2793-2801 Zhou, L., see Lin, L., TMTT Jun. 2015 1951-1963 Zhou, M., see Yu, F., TMTT Feb. 2015 403-413 Zhou, W., see Sun, Y., TMTT Oct. 2015 3131-3141 Zhou, X., see Fan, H., TMTT Mar. 2015 986-998 Zhu, A., see Yu, C., TMTT Dec. 2015 4306-4318 Zhu, A., see Guo, Y., TMTT Nov. 2015 3595-3607 Zhu, A., see Cai, J., TMTT May 2015 1518-1529 Zhu, A., Decomposed Vector Rotation-Based Behavioral Modeling for Digital Predistortion of RF Power Amplifiers; TMTT Feb. 2015 737-744 Zhu, A., see Yu, C., TMTT Jul. 2015 2211-2224 Zhu, C., see Liu, N., TMTT Oct. 2015 3094-3102 Zhu, L., see Zhang, S., TMTT Oct. 2015 3487-3493 Zhu, L., see Wong, S.-W., TMTT Oct. 2015 3416-3424 Zhu, L., see Guo, X., TMTT May 2015 1587-1594 Zhu, L., see Wong, S.-W., TMTT Dec. 2015 3947-3953 Zhu, L., see Guo, X., TMTT Jun. 2015 1902-1909 Zhu, L., see Yang, L., TMTT Jul. 2015 2225-2232 Zhu, Q., see Li, S., TMTT Nov. 2015 3588-3594 Zhu, R., Shen, D., Zhang, X., and Liu, T., Analysis of Dual Wavelength Linearization Technique for Radio-Over-Fiber Systems With Electro-Absorption Modulator; TMTT Aug. 2015 2692-2702 Zhu, S.-K., see Cheng, Q.-F., TMTT Aug. 2015 2703-2704 Zhu, W., see Li, H., TMTT Mar. 2015 925-936 Zhu, X., see Fu, M., TMTT Mar. 2015 801-812 Zhu, X.-C., Hong, W., Zhang, P.-P., Hao, Z.-C., Tang, H.-J., Gong, K., Chen, J.-X., and Wu, K., Extraction of Dielectric and Rough Conductor Loss of Printed Circuit Board Using Differential Method at Microwave Frequencies; TMTT Feb. 2015 494-503 Zhu, X.-W., see Ge, C., TMTT Nov. 2015 3641-3650 Zhu, X.-W., see Sun, Y., TMTT Dec. 2015 4051-4060 Zhu, X.-W., see Yu, C., TMTT Jul. 2015 2211-2224 Zhu, Z., see Zhao, J., TMTT May 2015 1633-1644 Zhurbenko, V., see Acar, O., TMTT Oct. 2015 3425-3432 Zihir, S., see Mehrjoo, M. S., TMTT Jul. 2015 2289-2300 Zirath, H., see Eriksson, K., TMTT Feb. 2015 433-440 Zirath, H., see Eriksson, K., TMTT Apr. 2015 1334-1341 Zirath, H., see Yan, Y., TMTT Sep. 2015 2897-2904 Zirath, H., see He, Z., TMTT May 2015 1683-1692 Zirath, H., see Carpenter, S., TMTT May 2015 1666-1675 Zirath, H., see He, Z., TMTT Aug. 2015 2630-2637 Zirath, H., see Horberg, M., TMTT Aug. 2015 2619-2629 Zoral, E. Y., see Gunel, S., TMTT Jan. 2015 90-98 Zou, L., see Gupta, S., TMTT Mar. 2015 1007-1018 Zou, X., Li, W., Lu, B., Pan, W., Yan, L., and Shao, L., Photonic Approach to Wide-Frequency-Range High-Resolution Microwave/Millimeter-Wave Doppler Frequency Shift Estimation; TMTT Apr. 2015 1421-1430 Zouros, G. P., Kolezas, G. D., and Roumeliotis, J. A., Fast Solution of the Electromagnetic Scattering by Composite Spheroidal–Spherical and Spherical–Spheroidal Configurations; TMTT Oct. 2015 3042-3053 Zouros, G. P., and Kokkorakis, G. C., Electromagnetic Scattering by a General Rotationally Symmetric Inhomogeneous Anisotropic Sphere; TMTT Oct. 2015 3054-3065 Zouros, G. P., Kotsis, A. D., and Roumeliotis, J. A., Efficient Calculation of the Electromagnetic Scattering by Lossless or Lossy, Prolate or Oblate Dielectric Spheroids; TMTT Mar. 2015 864-876 Zuffanelli, S., Zamora, G., Aguila, P., Paredes, F., Martin, F., and Bonache, J., On the Radiation Properties of Split-Ring Resonators (SRRs) at the Second Resonance; TMTT Jul. 2015 2133-2141 Zwick, T., see Diebold, S., TMTT Mar. 2015 999-1006

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SUBJECT INDEX

Numeric

3G mobile communication A 0.2–3.6-GHz 10-dBm B1dB 29-dBm IIP3 Tunable Filter for Transmit Leakage Suppression in SAW-Less 3G/4G FDD Receivers. Luo, C., +, TMTT Oct. 2015 3514-3524 A Multi-Band Stacked RF Energy Harvester With RF-to-DC Efficiency Up to 84%. Kuhn, V., +, TMTT May 2015 1768-1778 4G mobile communication A 0.2–3.6-GHz 10-dBm B1dB 29-dBm IIP3 Tunable Filter for Transmit Leakage Suppression in SAW-Less 3G/4G FDD Receivers. Luo, C., +, TMTT Oct. 2015 3514-3524 III-V semiconductor materials Corrections to “Design and Fabrication of Broadband Hybrid GaAs Schottky Diode Frequency Multipliers” [Dec 13 4442-4460]. Hrobak, M., +, TMTT Feb. 2015 553 III-V semiconductors (InP) HEMT Small-Signal Equivalent-Circuit Extraction as a Function of Temperature. Alt, A. R., +, TMTT Sep. 2015 2751-2755 0.8/2.2-GHz Programmable Active Bandpass Filters in InP/Si BiCMOS Technology. Xu, Z., +, TMTT Apr. 2015 1219-1227 A 110–170-GHz Multi-Mode Transconductance Mixer in 250-nm InP DHBT Technology. Yan, Y., +, TMTT Sep. 2015 2897-2904 A 2-W W-Band GaN Traveling-Wave Amplifier With 25-GHz Bandwidth. Schellenberg, J. M., TMTT Sep. 2015 2833-2840 A 5.9-GHz Fully Integrated GaN Frontend Design With Physics-Based RF Compact Model. Choi, P., +, TMTT Apr. 2015 1163-1173 A Broadband GaN pHEMT Power Amplifier Using Non-Foster Matching. Lee, S., +, TMTT Dec. 2015 4406-4414 A Memoryless Semi-Physical Power Amplifier Behavioral Model Based on the Correlation Between AM–AM and AM–PM Distortions. Glock, S., +, TMTT Jun. 2015 1826-1835 A Miniature Broadband Doherty Power Amplifier With a Series-Connected Load. Watanabe, S., +, TMTT Feb. 2015 572-579 A New Double Input-Double Output Complex Envelope Amplifier Behavioral Model Taking Into Account Source and Load Mismatch Effects. Zargar, H., +, TMTT Feb. 2015 766-774 A Post-Matching Doherty Power Amplifier Employing Low-Order Impedance Inverters for Broadband Applications. Pang, J., +, TMTT Dec. 2015 4061-4071 Active Detuning of MRI Receive Coils with GaN FETs. Twieg, M., +, TMTT Dec. 2015 4169-4177 An 85-W Multi-Octave Push–Pull GaN HEMT Power Amplifier for HighEfficiency Communication Applications at Microwave Frequencies. Jundi, A., +, TMTT Nov. 2015 3691-3700 Mode Power Amplifier Design ApAn Integrated Continuous Classproach for Microwave Enhanced Portable Diagnostic Applications. Imtiaz, A., +, TMTT Oct. 2015 3007-3015 Bandwidth Enhancement of Three-Stage Doherty Power Amplifier Using Symmetric Devices. Barthwal, A., +, TMTT Aug. 2015 2399-2410 Compact Behavioral Models of Nonlinear Active Devices Using Response Surface Methodology. Barmuta, P., +, TMTT Jan. 2015 56-64 Concurrent Dual-Band Digital Predistortion With a Single Feedback Loop. Liu, Y., +, TMTT May 2015 1556-1568 Design of X-Band GaN Phase Shifters. Ross, T. N., +, TMTT Jan. 2015 244-255 Digitally Assisted Analog/RF Predistorter With a Small-Signal-Assisted Parameter Identification Algorithm. Huang, H., +, TMTT Dec. 2015 42974305 Electrothermal Effects on Performance of GaAs HBT Power Amplifier During Power Versus Time (PVT) Variation at GSM/DCS Bands. Lin, L., +, TMTT Jun. 2015 1951-1963 Envelope Tracking of an RF High Power Amplifier With an 8-Level Digitally Controlled GaN-on-Si Supply Modulator. Florian, C., +, TMTT Aug. 2015 2589-2602 Fully Integrated D-Band Direct Carrier Quadrature (I/Q) Modulator and Demodulator Circuits in InP DHBT Technology. Carpenter, S., +, TMTT May 2015 1666-1675 GaN HEMT Noise Model Based on Electromagnetic Simulations. Nalli, A., +, TMTT Aug. 2015 2498-2508 + Check author entry for coauthors

GaN Microwave DC–DC Converters. Ramos, I., +, TMTT Dec. 2015 44734482 High-Efficiency Harmonic-Peaking Class-EF Power Amplifiers With Enhanced Maximum Operating Frequency. Thian, M., +, TMTT Feb. 2015 659-671 Highly Efficient and Multipaction-Free P-Band GaN High-Power Amplifiers for Space Applications. Ayllon, N., +, TMTT Dec. 2015 4429-4436 Hybrid Nonlinear Modeling Using Adaptive Sampling. Barmuta, P., +, TMTT Dec. 2015 4501-4510 Hysteresis and Oscillation in High-Efficiency Power Amplifiers. de Cos, J., +, TMTT Dec. 2015 4284-4296 InP DHBT Distributed Amplifiers With Up to 235-GHz Bandwidth. Eriksson, K., +, TMTT Apr. 2015 1334-1341 Investigation of Intermodulation Distortion of Envelope Tracking Power Amplifier for Linearity Improvement. Moon, K., +, TMTT Apr. 2015 13241333 Load Modulation Measurements of X-Band Outphasing Power Amplifiers. Litchfield, M., +, TMTT Dec. 2015 4119-4129 Supply-Modulated Radar Transmitters With Amplitude-Modulated Pulses. Zai, A., +, TMTT Sep. 2015 2953-2964 Transformer-Feedback Interstage Bandwidth Enhancement for MMIC Multistage Amplifiers. Nikandish, G., +, TMTT Feb. 2015 441-448

A Absorption coefficients Near-Field Microwave Distribution Measurement With a Point Detector Base on Thermoacoustic Effect. Ding, W., +, TMTT Oct. 2015 3272-3276 Acoustic resonator filters An FBAR/CMOS Frequency/Phase Discriminator and Phase Noise Reduction System. Imani, A., +, TMTT May 2015 1658-1665 Bandpass Filters Using Coupling-Matrix-Based Design of HighAcoustic-Wave Lumped-Element Resonator (AWLR) Modules. Psychogiou, D., +, TMTT Dec. 2015 4319-4328 Present and Future Trends in Filters and Multiplexers. Snyder, R. V., +, TMTT Oct. 2015 3324-3360 Acoustic resonators Reducing Energy Dissipation in ULP Systems: PLL-Free FBAR-Based Fast Startup Transmitters. Thirunarayanan, R., +, TMTT Apr. 2015 1110-1117 Active networks Active Detuning of MRI Receive Coils with GaN FETs. Twieg, M., +, TMTT Dec. 2015 4169-4177 Compact Behavioral Models of Nonlinear Active Devices Using Response Surface Methodology. Barmuta, P., +, TMTT Jan. 2015 56-64 Actuators High Power Latching RF MEMS Switches. Bakri-Kassem, M., +, TMTT Jan. 2015 222-232 Adaptive antenna arrays Concurrent Detection of Vibration and Distance Using Unmodulated CW Doppler Vibration Radar With An Adaptive Beam-Steering Antenna. Nieh, C.-M., +, TMTT Jun. 2015 2069-2078 Adaptive equalizers Digitally Equalized Doherty RF Front-End Architecture for Broadband and Multistandard Wireless Transmitters. Darraji, R., +, TMTT Jun. 2015 19781988 Adaptive filters A Low-IF Tag-Based Motion Compensation Technique for Mobile Doppler Radar Life Signs Monitoring. Rahman, A., +, TMTT Oct. 2015 3034-3041 Adjacent channel interference Concurrent Dual-Band Modeling and Digital Predistortion in the Presence of Unfilterable Harmonic Signal Interference. Rawat, M., +, TMTT Feb. 2015 625-637 Partitioned Distortion Mitigation in LTE Radio Uplink to Enhance Transmitter Efficiency. Amiri, M. V., +, TMTT Aug. 2015 2661-2671 Air gaps Broadband Microwave Attenuator Based on Few Layer Graphene Flakes. Pierantoni, L., +, TMTT Aug. 2015 2491-2497 Alumina Reliability Analysis of Ku-Band 5-bit Phase Shifters Using MEMS SP4T and SPDT Switches. Dey, S., +, TMTT Dec. 2015 3997-4012 Aluminum A Wide-Band CMOS to Waveguide Transition at mm-Wave Frequencies With Wire-Bonds. Jameson, S., +, TMTT Sep. 2015 2741-2750

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 63, NO. 12, DECEMBER 2015

Enhanced Topology of -Plane Resonators for High-Power Satellite Applications. Peverini, O. A., +, TMTT Oct. 2015 3361-3373 Aluminum alloys Triple- and Quadruple-Mode Wideband Bandpass Filter Using Simple Perturbation in Single Metal Cavity. Wong, S.-W., +, TMTT Oct. 2015 34163424 Aluminum compounds RF-Designed High-Power Lamb-Wave Aluminum–Nitride Resonators. Campanella, H., +, TMTT Feb. 2015 331-339 Amplification Broadband Sequential Power Amplifier With Doherty-Type Active Load Modulation. Nghiem, X. A., +, TMTT Sep. 2015 2821-2832 Amplifiers A Reconfigurable 50-Mb/s-1 Gb/s Pulse Compression Radar Signal Processor With Offset Calibration in 90-nm CMOS. Li, J., +, TMTT Jan. 2015 266-278 Compact Behavioral Models of Nonlinear Active Devices Using Response Surface Methodology. Barmuta, P., +, TMTT Jan. 2015 56-64 GaN HEMT Noise Model Based on Electromagnetic Simulations. Nalli, A., +, TMTT Aug. 2015 2498-2508 Amplitude estimation Low Complexity Coefficient Estimation for Concurrent Dual-Band Digital Predistortion. Qian, H., +, TMTT Oct. 2015 3153-3163 Amplitude modulation A Memoryless Semi-Physical Power Amplifier Behavioral Model Based on the Correlation Between AM–AM and AM–PM Distortions. Glock, S., +, TMTT Jun. 2015 1826-1835 Theory and Implementation of RF-Input Outphasing Power Amplification. Barton, T. W., +, TMTT Dec. 2015 4273-4283 Analog processing circuits Simple Broadband Quasi-Optical Spatial Multiplexer in Substrate Integrated Technology. Gomez-Tornero, J. L., +, TMTT May 2015 1609-1620 Analog-digital conversion A Hardware Efficient Implementation of a Digital Baseband Receiver for High-Capacity Millimeter-Wave Radios. He, Z., +, TMTT May 2015 16831692 A Reconfigurable 50-Mb/s-1 Gb/s Pulse Compression Radar Signal Processor With Offset Calibration in 90-nm CMOS. Li, J., +, TMTT Jan. 2015 266-278 An Investigation of Electromagnetic Radiated Emission and Interference From Multi-Coil Wireless Power Transfer Systems Using Resonant Magnetic Field Coupling. Kong, S., +, TMTT Mar. 2015 833-846 Analysis, Blind Identification, and Correction of Frequency Response Mismatch in Two-Channel Time-Interleaved ADCs. Singh, S., +, TMTT May 2015 1721-1734 Design and Analysis of CMOS High-Speed High Dynamic-Range Trackand-Hold Amplifiers. Liu, Y.-C., +, TMTT Sep. 2015 2841-2853 Spectra-Folding Feedback Architecture for Concurrent Dual-Band Power Amplifier Predistortion. Ma, Y., +, TMTT Oct. 2015 3164-3174 Anisotropic media Electromagnetic Scattering by a General Rotationally Symmetric Inhomogeneous Anisotropic Sphere. Zouros, G. P., +, TMTT Oct. 2015 3054-3065 Antenna arrays An LTCC Coupled Resonator Decoupling Network for Two Antennas. Qian, K., +, TMTT Oct. 2015 3199-3207 Calibrated Layer-Stripping Technique for Level and Permittivity Measurement With UWB Radar in Metallic Tanks. Maunder, A., +, TMTT Jul. 2015 2322-2334 Antenna feeds -Band Spatially Combined Power Amplifier Arrays in 45-nm CMOS SOI. Hanafi, B., +, TMTT Jun. 2015 1937-1950 A Configurable Coupling Structure for Broadband Millimeter-Wave SplitBlock Networks. Koenen, C., +, TMTT Dec. 2015 3954-3961 Antenna phased arrays A 2.45 GHz Phased Array Antenna Unit Cell Fabricated Using 3-D MultiLayer Direct Digital Manufacturing. Ketterl, T. P., +, TMTT Dec. 2015 4382-4394 An Integrable SIW Phase Shifter in a Partially Magnetized Ferrite LTCC Package. Nafe, A., +, TMTT Jul. 2015 2264-2274 Concurrent Detection of Vibration and Distance Using Unmodulated CW Doppler Vibration Radar With An Adaptive Beam-Steering Antenna. Nieh, C.-M., +, TMTT Jun. 2015 2069-2078

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Antenna radiation patterns A 37.5-mW 8-dBm-EIRP 15.5 -HPBW 338-GHz Terahertz Transmitter Using SoP Heterogeneous System Integration. Li, C.-H., +, TMTT Feb. 2015 470-480 An Integrated Slot-Ring Traveling-Wave Radiator. Bowers, S. M., +, TMTT Apr. 2015 1154-1162 Compact Printable Chipless RFID Systems. Islam, M. A., +, TMTT Nov. 2015 3785-3793 Modeling of Noisy EM Field Propagation Using Correlation Information. Russer, J. A., +, TMTT Jan. 2015 76-89 On the Development and Evaluation of Spatial-Domain Green’s Functions for Multilayered Structures With Conductive Sheets. Koufogiannis, I. D., +, TMTT Jan. 2015 20-29 On the Radiation Properties of Split-Ring Resonators (SRRs) at the Second Resonance. Zuffanelli, S., +, TMTT Jul. 2015 2133-2141 Qualitative Microwave Imaging With Scattering Parameters Measurements. Akinci, M. N., +, TMTT Sep. 2015 2730-2740 Antennas A Stacked-FET Linear SOI CMOS Cellular Antenna Switch With an Extremely Low-Power Biasing Strategy. Im, D., +, TMTT Jun. 2015 19641977 Antenna Impedance Variation Compensation by Exploiting a Digital Doherty Power Amplifier Architecture. Hu, S., +, TMTT Feb. 2015 580-597 Reduction of Exposure Inhomogeneity for Millimeter-Wave Experiments on Cells In Vitro. Zhao, J., +, TMTT Feb. 2015 533-545 Aperture antennas Reconfigurable Diffractive Antenna Based on Switchable Electrically Induced Transparency. Li, H., +, TMTT Mar. 2015 925-936 Aperture-coupled antennas Compact Printable Chipless RFID Systems. Islam, M. A., +, TMTT Nov. 2015 3785-3793 Approximation methods Authors’ Reply. Mescia, L., +, TMTT Dec. 2015 4191-4193 Approximation theory Comments on “Fractional Derivative Based FDTD Modeling of Transient Wave Propagation in Havriliak–Negami Media”. Rekanos, I. T., TMTT Dec. 2015 4188-4190 Energy Coupled Mode Theory for Electromagnetic Resonators. Elnaggar, S. Y., +, TMTT Jul. 2015 2115-2123 Estimating the Inf-Sup Constant in Reduced Basis Methods for Time-Harmonic Maxwell’s Equations. Hess, M. W., +, TMTT Nov. 2015 3549-3557 Non-Reflecting SFBF Termination Inverting From TFSF Discontinuity Decomposition. Tan, T., TMTT Sep. 2015 2710-2719 Nonlinear Behavioral Modeling Dependent on Load Reflection Coefficient Magnitude. Cai, J., +, TMTT May 2015 1518-1529 Printable Planar Dielectric Waveguides Based on High-Permittivity Films. Rashidian, A., +, TMTT Sep. 2015 2720-2729 RF Linearity Performance Potential of Short-Channel Graphene Field-Effect Transistors. Alam, A. U., +, TMTT Dec. 2015 3874-3887 Array signal processing A Millimeter-Wave WPAN Adaptive Phased Array Control Method Using Low-Frequency Part of Signal for Self-Directed System. Ta, T. T., +, TMTT Aug. 2015 2682-2691 Comparison of Injection-Locked and Coupled Oscillator Arrays for Beamforming. Lo, Y.-T., +, TMTT Apr. 2015 1353-1360 Mutual Synchronization for Power Generation and Beam-Steering in CMOS With On-Chip Sense Antennas Near 200 GHz. Sengupta, K., +, TMTT Sep. 2015 2867-2876 Assembling 160-GHz to 1-THz Multi-Color Active Imaging With a Lens-Coupled SiGe HBT Chip-Set. Statnikov, K., +, TMTT Feb. 2015 520-532 Atmospheric measuring apparatus Passive Microwave Substrate Integrated Cavity Resonator for Humidity Sensing. El Matbouly, H., +, TMTT Dec. 2015 4150-4156 Attenuators A Varactor-Based Variable Attenuator Design With Enhanced Linearity Performance. Cheng, K.-K. M., +, TMTT Oct. 2015 3191-3198 Broadband Microwave Attenuator Based on Few Layer Graphene Flakes. Pierantoni, L., +, TMTT Aug. 2015 2491-2497 Automotive engineering Guest Editorial. KIM, J., +, TMTT Mar. 2015 778-779

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Avalanche breakdown Investigation of RF Avalanche Inductive Effect on Reduction of Intermodulation Distortion of MOSFETs Using Volterra Series Analysis. Lee, C.-I., +, TMTT Feb. 2015 367-373 B Backscatter Compact Printable Chipless RFID Systems. Islam, M. A., +, TMTT Nov. 2015 3785-3793 Multichannel Backscatter Communication and Ranging for Distributed Sensing With an FMCW Radar. Cnaan-On, I., +, TMTT Jul. 2015 2375-2383 Wireless Fully Passive Multichannel Recording of Neuropotentials Using Photo-Activated RF Backscattering Methods. Schwerdt, H. N., +, TMTT Sep. 2015 2965-2970 Ballistic transport RF Linearity Performance Potential of Short-Channel Graphene Field-Effect Transistors. Alam, A. U., +, TMTT Dec. 2015 3874-3887 Baluns A 0.12-mm 2.4-GHz CMOS Inductorless High Isolation Subharmonic Mixer With Effective Current-Reuse Transconductance. Chong, W. K., +, TMTT Aug. 2015 2427-2437 A Broadband and Equivalent-Circuit Model for Millimeter-Wave On-Chip M:N Six-Port Transformers and Baluns. Gao, Z., +, TMTT Oct. 2015 31093121 A Prototype SAW-Less LTE Transmitter With a High-Linearity Modulator Using BPF-Based I/Q Summing and a Triple-Layer Marchand Balun. Nakamura, T., +, TMTT Dec. 2015 4090-4097 A W-Band Power Amplifier Utilizing a Miniaturized Marchand Balun Combiner. Jia, H., +, TMTT Feb. 2015 719-725 An 85-W Multi-Octave Push–Pull GaN HEMT Power Amplifier for HighEfficiency Communication Applications at Microwave Frequencies. Jundi, A., +, TMTT Nov. 2015 3691-3700 Broadband Circuit Techniques for Multi-Terahertz Gain-BandwidthProduct Low-Power Applications. Gharib, A., +, TMTT Nov. 2015 3701-3712 CMOS Broadband Programmable Gain Active Balun With 0.5-dB Gain Steps. Hur, B., +, TMTT Aug. 2015 2650-2660 Optimized Design of Frequency Dividers Based on Varactor-Inductor Cells. Ponton, M., +, TMTT Dec. 2015 4458-4472 The Effects of Electrode Configuration on Body Channel Communication Based on Analysis of Vertical and Horizontal Electric Dipoles. Bae, J., +, TMTT Apr. 2015 1409-1420 Mode Substrate Integrated Wideband Excitation Technology of Waveguide (SIW) and Its Applications. Wu, P., +, TMTT Jun. 2015 1863-1874 Band-pass filters 0.8/2.2-GHz Programmable Active Bandpass Filters in InP/Si BiCMOS Technology. Xu, Z., +, TMTT Apr. 2015 1219-1227 A 1.4–2.3-GHz Tunable Diplexer Based on Reconfigurable Matching Networks. Ko, C. H., +, TMTT May 2015 1595-1602 A Four-Way Microstrip Filtering Power Divider With Frequency-Dependent Couplings. Chen, F.-J., +, TMTT Oct. 2015 3494-3504 A High-Power Low-Loss Continuously Tunable Bandpass Filter With Transversely Biased Ferrite-Loaded Coaxial Resonators. Acar, O., +, TMTT Oct. 2015 3425-3432 A Miniaturized Microfluidically Reconfigurable Coplanar Waveguide Bandpass Filter With Maximum Power Handling of 10 Watts. Pourghorban Saghati, A., +, TMTT Aug. 2015 2515-2525 A Prototype SAW-Less LTE Transmitter With a High-Linearity Modulator Using BPF-Based I/Q Summing and a Triple-Layer Marchand Balun. Nakamura, T., +, TMTT Dec. 2015 4090-4097 Advanced Butler Matrices With Integrated Bandpass Filter Functions. Tornielli di Crestvolant, V., +, TMTT Oct. 2015 3433-3444 Analysis of Weakly Nonlinear Effect for Varactor-Tuned Bandpass Filter. Ge, C., +, TMTT Nov. 2015 3641-3650 Automated Design of Common-Mode Suppressed Balanced Wideband Bandpass Filters by Means of Aggressive Space Mapping. Sans, M., +, TMTT Dec. 2015 3896-3908 Balanced Dual-Band Bandpass Filter With Multiple Transmission Zeros Using Doubly Short-Ended Resonator Coupled Line. Yang, L., +, TMTT Jul. 2015 2225-2232

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Broadband Synthetic Transmission-Line N-Path Filter Design. Thomas, C. M., +, TMTT Oct. 2015 3525-3536 Compact Filtering Rat-Race Hybrid With Wide Stopband. Wang, K.-X., +, TMTT Aug. 2015 2550-2560 Compact Multi-Band Bandpass Filters With Mixed Electric and Magnetic Coupling Using Multiple-Mode Resonator. Xu, J., +, TMTT Dec. 2015 3909-3919 Compact Quad-Mode Bandpass Filter Using Modified Coaxial Cavity Resonator With Improved -Factor. Wang, X., +, TMTT Mar. 2015 965-975 Corrections to “Compact Multi-Port Power Combination/Distribution With Inherent Bandpass Filter Characteristics” [Nov 14 2659-2672]. Rosenberg, U., +, TMTT Jul. 2015 2390 Corrections to “Design and Fabrication of Broadband Hybrid GaAs Schottky Diode Frequency Multipliers” [Dec 13 4442-4460]. Hrobak, M., +, TMTT Feb. 2015 553 Bandpass Filters Using Coupling-Matrix-Based Design of HighAcoustic-Wave Lumped-Element Resonator (AWLR) Modules. Psychogiou, D., +, TMTT Dec. 2015 4319-4328 Dynamic Bandpass Filter Shape and Interference Cancellation Control Utilizing Bandpass–Bandstop Filter Cascade. Lee, T.-C., +, TMTT Aug. 2015 2526-2539 Guest Editorial. Boria, V. E., +, TMTT Oct. 2015 3321-3323 Hybrid Acoustic-Wave-Lumped-Element Resonators (AWLRs) for HighBandpass Filters With Quasi-Elliptic Frequency Response. Psychogiou, D., +, TMTT Jul. 2015 2233-2244 K-Band Frequency Tunable Substrate-Integrated- Waveguide Resonator Filter With Enhanced Stopband Attenuation. Lee, B., +, TMTT Nov. 2015 3632-3640 Microfluidically Tunable Microstrip Filters. Diedhiou, D. L., +, TMTT Jul. 2015 2245-2252 Microwave Bandpass Filters Using Re-Entrant Resonators. Musonda, E., +, TMTT Mar. 2015 954-964 Modeling of Inline Transitions Between Different Waveguides as Impedance Inverters for the Use in Novel Filter Designs. Strauss, G., +, TMTT Nov. 2015 3663-3670 Reconfigurable Multi-Band Microwave Filters. Gomez-Garcia, R., +, TMTT Apr. 2015 1294-1307 Resonator Voltage Prediction in Microwave Bandpass Filters. Vanin, F. M., +, TMTT Feb. 2015 397-402 Simple and Compact Balanced Bandpass Filters Based on Magnetically Coupled Resonators. Fernandez-Prieto, A., +, TMTT Jun. 2015 1843-1853 Superconducting Ultra-Wideband (UWB) Bandpass Filter Design Based on Quintuple/Quadruple/ Triple-Mode Resonator. Lu, X., +, TMTT Apr. 2015 1281-1293 Synthesis and Design of High-Selectivity Wideband Quasi-Elliptic Bandpass Filters Using Multiconductor Transmission Lines. Sanchez-Martinez, J. J., +, TMTT Jan. 2015 198-208 Synthesis of Inline Mixed Coupled Quasi-Elliptic Bandpass Filters Based Resonators. Zhang, S., +, TMTT Oct. 2015 3487-3493 on Temporal Coupled-Mode Theory and the Combined Effect of Dual Orthogonal Resonant Modes in Microstrip Bandpass Filters. Yu, F., +, TMTT Feb. 2015 403-413 Triple- and Quadruple-Mode Wideband Bandpass Filter Using Simple Perturbation in Single Metal Cavity. Wong, S.-W., +, TMTT Oct. 2015 34163424 Tunable 1.25–2.1-GHz 4-Pole Bandpass Filter With Intrinsic Transmission Zero Tuning. Yang, T., +, TMTT May 2015 1569-1578 Tunable 4-Pole Noncontiguous 0.7–2.1-GHz Bandpass Filters Based on Dual Zero-Value Couplings. Cho, Y.-H., +, TMTT May 2015 1579-1586 Ultra-Compact (80 mm ) Differential-Mode Ultra-Wideband (UWB) Bandpass Filters With Common-Mode Noise Suppression. Velez, P., +, TMTT Apr. 2015 1272-1280 Wideband Balanced Filters With High Selectivity and Common-Mode Suppression. Chu, Q.-X., +, TMTT Oct. 2015 3462-3468 Wideband Differential Bandpass Filters on Multimode Slotline Resonator With Intrinsic Common-Mode Rejection. Guo, X., +, TMTT May 2015 1587-1594 Band-stop filters A Novel Compact -Plane Waveguide Filter With Multiple Transmission Zeroes. Jin, J. Y., +, TMTT Oct. 2015 3374-3380 An Ultra-Compact Common-Mode Bandstop Filter With Modified-T Circuits in Integrated Passive Device (IPD) Process. Hsiao, C.-Y., +, TMTT Nov. 2015 3624-3631

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 63, NO. 12, DECEMBER 2015

Dynamic Bandpass Filter Shape and Interference Cancellation Control Utilizing Bandpass–Bandstop Filter Cascade. Lee, T.-C., +, TMTT Aug. 2015 2526-2539 Exact Design of a New Class of Generalized Chebyshev Low-Pass Filters Using Coupled Line/Stub Sections. Musonda, E., +, TMTT Dec. 2015 43554365 K-Band Frequency Tunable Substrate-Integrated- Waveguide Resonator Filter With Enhanced Stopband Attenuation. Lee, B., +, TMTT Nov. 2015 3632-3640 Narrowband Coupled-Line Bandstop Filter With Absorptive Stopband. Shao, J.-Y., +, TMTT Oct. 2015 3469-3478 Novel Coupling Matrix Synthesis for Single-Layer Substrate-Integrated Evanescent-Mode Cavity Tunable Bandstop Filter Design. Saeedi, S., +, TMTT Dec. 2015 3929-3938 Present and Future Trends in Filters and Multiplexers. Snyder, R. V., +, TMTT Oct. 2015 3324-3360 Reflection-Mode Bandstop Filters With Minimum Through-Line Length. Naglich, E. J., +, TMTT Oct. 2015 3479-3486 Textile Microwave Components in Substrate Integrated Waveguide Technology. Moro, R., +, TMTT Feb. 2015 422-432 Wideband Balanced Filters With High Selectivity and Common-Mode Suppression. Chu, Q.-X., +, TMTT Oct. 2015 3462-3468 Bandwidth A Transformer-Based Poly-Phase Network for Ultra-Broadband Quadrature Signal Generation. Park, J. S., +, TMTT Dec. 2015 4444-4457 Bandwidth compression Design of X-Band GaN Phase Shifters. Ross, T. N., +, TMTT Jan. 2015 244-255 Barium Printable Planar Dielectric Waveguides Based on High-Permittivity Films. Rashidian, A., +, TMTT Sep. 2015 2720-2729 Barium compounds Influence of Numerical Method and Geometry Used by Maxwell's Equation Solvers on Simulations of Ferroelectric Thin-Film Capacitors. Furlan, V., +, TMTT Mar. 2015 891-896 Present and Future Trends in Filters and Multiplexers. Snyder, R. V., +, TMTT Oct. 2015 3324-3360 Battery chargers Development of the Optimization Framework for Low-Power Wireless Power Transfer Systems. Lee, S. B., +, TMTT Mar. 2015 813-820 Battery powered vehicles A Three-Phase Wireless-Power-Transfer System for Online Electric Vehicles With Reduction of Leakage Magnetic Fields. Kim, M., +, TMTT Nov. 2015 3806-3813 Bayes methods Bayesian Optimization for Broadband High-Efficiency Power Amplifier Designs. Chen, P., +, TMTT Dec. 2015 4263-4272 Beam steering Concurrent Detection of Vibration and Distance Using Unmodulated CW Doppler Vibration Radar With An Adaptive Beam-Steering Antenna. Nieh, C.-M., +, TMTT Jun. 2015 2069-2078 Mutual Synchronization for Power Generation and Beam-Steering in CMOS With On-Chip Sense Antennas Near 200 GHz. Sengupta, K., +, TMTT Sep. 2015 2867-2876 Reconfigurable Diffractive Antenna Based on Switchable Electrically Induced Transparency. Li, H., +, TMTT Mar. 2015 925-936 Bicmos analog integrated circuits A Broadband 4.5–15.5-GHz SiGe Power Amplifier With 25.5-dBm Peak Saturated Output Power and 28.7% Maximum PAE. Kerherve, E., +, TMTT May 2015 1621-1632 A Reconfigurable K-/Ka-Band Power Amplifier With High PAE in 0.18- m SiGe BiCMOS for Multi-Band Applications. Ma, K., +, TMTT Dec. 2015 4395-4405 Fully Monolithic BiCMOS Reconfigurable Power Amplifier for Multi-Mode and Multi-Band Applications. Lee, M.-L., +, TMTT Feb. 2015 614-624 BiCMOS integrated circuits 0.8/2.2-GHz Programmable Active Bandpass Filters in InP/Si BiCMOS Technology. Xu, Z., +, TMTT Apr. 2015 1219-1227 160-GHz to 1-THz Multi-Color Active Imaging With a Lens-Coupled SiGe HBT Chip-Set. Statnikov, K., +, TMTT Feb. 2015 520-532 -Band Dual-Polarization Phased-Array Transceiver Front-End in SiGe BiCMOS. Natarajan, A., +, TMTT Jun. 2015 1989-2002 A Single-Chip Electron Paramagnetic Resonance Transceiver in 0.13- m SiGe BiCMOS. Yang, X., +, TMTT Nov. 2015 3727-3735 + Check author entry for coauthors

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Common-Base/Common-Gate Millimeter-Wave Power Detectors. Serhan, A., +, TMTT Dec. 2015 4483-4491 Silicon-Based True-Time-Delay Phased-Array Front-Ends at Ka-Band. Ma, Q., +, TMTT Sep. 2015 2942-2952 Bifurcation Efficient Simulation of Solution Curves and Bifurcation Loci in InjectionLocked Oscillators. de Cos, J., +, TMTT Jan. 2015 181-197 Global Stability Analysis of Coupled-Oscillator Systems. Suarez, A., +, TMTT Jan. 2015 165-180 Hysteresis and Oscillation in High-Efficiency Power Amplifiers. de Cos, J., +, TMTT Dec. 2015 4284-4296 Binary codes Envelope Tracking of an RF High Power Amplifier With an 8-Level Digitally Controlled GaN-on-Si Supply Modulator. Florian, C., +, TMTT Aug. 2015 2589-2602 Bioacoustics Computational Feasibility Study of Contrast-Enhanced Thermoacoustic Imaging for Breast Cancer Detection Using Realistic Numerical Breast Phantoms. Wang, X., +, TMTT May 2015 1489-1501 Biochemistry Design and In Vitro Interference Test of Microwave Noninvasive Blood Glucose Monitoring Sensor. Choi, H., +, TMTT Oct. 2015 3016-3025 Electrical Analysis of Cell Membrane Poration by an Intense Nanosecond Pulsed Electric Field Using an Atomistic-to-Continuum Method. Kohler, S., +, TMTT Jun. 2015 2032-2040 Whispering-Gallery-Mode Resonator Technique With Microfluidic Channel for Permittivity Measurement of Liquids. Gubin, A. I., +, TMTT Jun. 2015 2003-2009 Bioelectric phenomena A Technique to Evaluate MRI-Induced Electric Fields at the Ends of Practical Implanted Lead. Feng, S., +, TMTT Jan. 2015 305-313 Computational Feasibility Study of Contrast-Enhanced Thermoacoustic Imaging for Breast Cancer Detection Using Realistic Numerical Breast Phantoms. Wang, X., +, TMTT May 2015 1489-1501 MRI-Based Electrical Property Retrieval by Applying the Finite-Element Method (FEM). Huang, S. Y., +, TMTT Aug. 2015 2482-2490 Bioelectric potentials Electrical Analysis of Cell Membrane Poration by an Intense Nanosecond Pulsed Electric Field Using an Atomistic-to-Continuum Method. Kohler, S., +, TMTT Jun. 2015 2032-2040 Wireless Fully Passive Multichannel Recording of Neuropotentials Using Photo-Activated RF Backscattering Methods. Schwerdt, H. N., +, TMTT Sep. 2015 2965-2970 Biological effects of fields Advanced Power Control Scheme in Wireless Power Transmission for Human Protection From EM Field. Kim, S.-M., +, TMTT Mar. 2015 847-856 Electrical Analysis of Cell Membrane Poration by an Intense Nanosecond Pulsed Electric Field Using an Atomistic-to-Continuum Method. Kohler, S., +, TMTT Jun. 2015 2032-2040 Biological organs Propagation, Power Absorption, and Temperature Analysis of UWB Wireless Capsule Endoscopy Devices Operating in the Human Body. Thotahewa, K. M. S., +, TMTT Nov. 2015 3823-3833 Tracking Optimal Efficiency of Magnetic Resonance Wireless Power Transfer System for Biomedical Capsule Endoscopy. Na, K., +, TMTT Jan. 2015 295-304 Biological tissues Propagation, Power Absorption, and Temperature Analysis of UWB Wireless Capsule Endoscopy Devices Operating in the Human Body. Thotahewa, K. M. S., +, TMTT Nov. 2015 3823-3833 Tracking Optimal Efficiency of Magnetic Resonance Wireless Power Transfer System for Biomedical Capsule Endoscopy. Na, K., +, TMTT Jan. 2015 295-304 Biomedical communication The Effects of Electrode Configuration on Body Channel Communication Based on Analysis of Vertical and Horizontal Electric Dipoles. Bae, J., +, TMTT Apr. 2015 1409-1420 Biomedical electrodes The Effects of Electrode Configuration on Body Channel Communication Based on Analysis of Vertical and Horizontal Electric Dipoles. Bae, J., +, TMTT Apr. 2015 1409-1420 Wireless Fully Passive Multichannel Recording of Neuropotentials Using Photo-Activated RF Backscattering Methods. Schwerdt, H. N., +, TMTT Sep. 2015 2965-2970

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Biomedical electronics Guest Editorial. Alomainy, A., +, TMTT Oct. 2015 3005-3006 Synthesis and Design of Programmable Subwavelength Coil Array for NearField Manipulation. Gao, F., +, TMTT Sep. 2015 2971-2982 Tracking Optimal Efficiency of Magnetic Resonance Wireless Power Transfer System for Biomedical Capsule Endoscopy. Na, K., +, TMTT Jan. 2015 295-304 Biomedical equipment Design and In Vitro Interference Test of Microwave Noninvasive Blood Glucose Monitoring Sensor. Choi, H., +, TMTT Oct. 2015 3016-3025 Miniaturized Transmission-Line Sensor for Broadband Dielectric Characterization of Biological Liquids and Cell Suspensions. Meyne nee Haase, N., +, TMTT Oct. 2015 3026-3033 Biomedical materials A Technique to Evaluate MRI-Induced Electric Fields at the Ends of Practical Implanted Lead. Feng, S., +, TMTT Jan. 2015 305-313 Biomedical measurement Channel Imbalance Effects and Compensation for Doppler Radar Physiological Measurements. Yavari, E., +, TMTT Nov. 2015 3834-3842 Miniaturized Transmission-Line Sensor for Broadband Dielectric Characterization of Biological Liquids and Cell Suspensions. Meyne nee Haase, N., +, TMTT Oct. 2015 3026-3033 Biomedical MRI A Technique to Evaluate MRI-Induced Electric Fields at the Ends of Practical Implanted Lead. Feng, S., +, TMTT Jan. 2015 305-313 MRI-Based Electrical Property Retrieval by Applying the Finite-Element Method (FEM). Huang, S. Y., +, TMTT Aug. 2015 2482-2490 Synthesis and Design of Programmable Subwavelength Coil Array for NearField Manipulation. Gao, F., +, TMTT Sep. 2015 2971-2982 Tracking Optimal Efficiency of Magnetic Resonance Wireless Power Transfer System for Biomedical Capsule Endoscopy. Na, K., +, TMTT Jan. 2015 295-304 Biomedical telemetry A High-Sensitivity Fully Passive Neurosensing System for Wireless Brain Signal Monitoring. Lee, C. W. L., +, TMTT Jun. 2015 2060-2068 Biomembranes Electrical Analysis of Cell Membrane Poration by an Intense Nanosecond Pulsed Electric Field Using an Atomistic-to-Continuum Method. Kohler, S., +, TMTT Jun. 2015 2032-2040 BioMEMS Miniaturized Transmission-Line Sensor for Broadband Dielectric Characterization of Biological Liquids and Cell Suspensions. Meyne nee Haase, N., +, TMTT Oct. 2015 3026-3033 Biomolecular effects of radiation Electrical Analysis of Cell Membrane Poration by an Intense Nanosecond Pulsed Electric Field Using an Atomistic-to-Continuum Method. Kohler, S., +, TMTT Jun. 2015 2032-2040 Biothermics Computational Feasibility Study of Contrast-Enhanced Thermoacoustic Imaging for Breast Cancer Detection Using Realistic Numerical Breast Phantoms. Wang, X., +, TMTT May 2015 1489-1501 The Development of Forceps-Type Microwave Tissue Coagulator for Surgical Operation. Endo, Y., +, TMTT Jun. 2015 2041-2049 Bipolar MIMIC A Reconfigurable K-/Ka-Band Power Amplifier With High PAE in 0.18- m SiGe BiCMOS for Multi-Band Applications. Ma, K., +, TMTT Dec. 2015 4395-4405 Bipolar MMIC A Reconfigurable K-/Ka-Band Power Amplifier With High PAE in 0.18- m SiGe BiCMOS for Multi-Band Applications. Ma, K., +, TMTT Dec. 2015 4395-4405 Bipolar transistor circuits Fully Integrated D-Band Direct Carrier Quadrature (I/Q) Modulator and Demodulator Circuits in InP DHBT Technology. Carpenter, S., +, TMTT May 2015 1666-1675 Blackbody radiation Application of Coherence Theory to Modeling of Blackbody Radiation at Close Range. Gu, D., +, TMTT May 2015 1475-1488 Blind equalizers Analysis, Blind Identification, and Correction of Frequency Response Mismatch in Two-Channel Time-Interleaved ADCs. Singh, S., +, TMTT May 2015 1721-1734 Blood Design and In Vitro Interference Test of Microwave Noninvasive Blood Glucose Monitoring Sensor. Choi, H., +, TMTT Oct. 2015 3016-3025 + Check author entry for coauthors

Blood vessels The Development of Forceps-Type Microwave Tissue Coagulator for Surgical Operation. Endo, Y., +, TMTT Jun. 2015 2041-2049 Bolometers Micromachined Room-Temperature Air-Suspended Ni/Cr Nanobolometer. Yang, H.-H., +, TMTT Nov. 2015 3760-3767 Boundary-value problems Analysis of Axisymmetric Waveguide Components by a Multi-Domain Spectral Method. Tibaldi, A., +, TMTT Jan. 2015 115-124 Skew Incidence Plane-Wave Scattering From 2-D Dielectric Periodic Structures: Analysis by the Mortar-Element Method. Tibaldi, A., +, TMTT Jan. 2015 11-19 Bragg gratings Broadband and Precise Microwave Time Reversal Using a Single Linearly Chirped Fiber Bragg Grating. Zhang, J., +, TMTT Jul. 2015 2166-2172 Brain modeling A High-Sensitivity Fully Passive Neurosensing System for Wireless Brain Signal Monitoring. Lee, C. W. L., +, TMTT Jun. 2015 2060-2068 Broadband antennas A 37.5-mW 8-dBm-EIRP 15.5 -HPBW 338-GHz Terahertz Transmitter Using SoP Heterogeneous System Integration. Li, C.-H., +, TMTT Feb. 2015 470-480 Compact Printable Chipless RFID Systems. Islam, M. A., +, TMTT Nov. 2015 3785-3793 Broadband communication Corrections to “Design and Fabrication of Broadband Hybrid GaAs Schottky Diode Frequency Multipliers” [Dec 13 4442-4460]. Hrobak, M., +, TMTT Feb. 2015 553 Broadband networks A Highly Efficient LTE Pulse-Modulated Polar Transmitter Using Wideband Power Recycling. Yang, H.-S., +, TMTT Dec. 2015 4437-4443 Broadband CMOS Stacked RF Power Amplifier Using Reconfigurable Interstage Network for Wideband Envelope Tracking. Park, S., +, TMTT Apr. 2015 1174-1185 Performance Estimation for Broadband Multi-Gigabit Millimeter- and SubMillimeter-Wave Wireless Communication Links. Antes, J., +, TMTT Oct. 2015 3288-3299 Buffer circuits A 1.1-Gbit/s 10-GHz Outphasing Modulator With 23-dBm Output Power and 60-dB Dynamic Range in 45-nm CMOS SOI. Mehrjoo, M. S., +, TMTT Jul. 2015 2289-2300 Built-in self test Digitally Assisted CMOS RF Detectors With Self-Calibration for Variability Compensation. Barabino, N., +, TMTT May 2015 1676-1682 Butterworth filters Hybrid Acoustic-Wave-Lumped-Element Resonators (AWLRs) for HighBandpass Filters With Quasi-Elliptic Frequency Response. Psychogiou, D., +, TMTT Jul. 2015 2233-2244 Synthesis and Design of High-Selectivity Wideband Quasi-Elliptic Bandpass Filters Using Multiconductor Transmission Lines. Sanchez-Martinez, J. J., +, TMTT Jan. 2015 198-208 C Calibration A CML Ring Oscillator-Based Supply-Insensitive PLL With On-Chip Calibrations. Gui, X., +, TMTT Jan. 2015 233-243 A Compact Dual-Channel Transceiver for Long-Range Passive Embedded Monitoring. Nassar, I. T., +, TMTT Jan. 2015 287-294 Accuracy and Bandwidth Optimization of the Over-Determined Offset-Short Reflectometer Calibration. Lewandowski, A., +, TMTT Mar. 2015 1076-1089 Design and In Vitro Interference Test of Microwave Noninvasive Blood Glucose Monitoring Sensor. Choi, H., +, TMTT Oct. 2015 3016-3025 Evaluation of Uncertainty in Temporal Waveforms of Microwave Transistors. Avolio, G., +, TMTT Jul. 2015 2353-2363 Generalized Theory of the Thru-Reflect-Match Calibration Technique. Pulido-Gaytan, M. A., +, TMTT May 2015 1693-1699 Cancer Computational Feasibility Study of Contrast-Enhanced Thermoacoustic Imaging for Breast Cancer Detection Using Realistic Numerical Breast Phantoms. Wang, X., +, TMTT May 2015 1489-1501 Millimeter-Wave Near-Field Probe Designed for High-Resolution Skin Cancer Diagnosis. Topfer, F., +, TMTT Jun. 2015 2050-2059

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 63, NO. 12, DECEMBER 2015

MRI-Based Electrical Property Retrieval by Applying the Finite-Element Method (FEM). Huang, S. Y., +, TMTT Aug. 2015 2482-2490 Cantilevers Monolithic Millimeter-Wave MEMS Waveguide Switch. Vahabisani, N., +, TMTT Feb. 2015 340-351 Capacitance Ultra-Miniature SIW Cavity Resonators and Filters. Pourghorban Saghati, A., +, TMTT Dec. 2015 4329-4340 Capacitors A Broadband GaN pHEMT Power Amplifier Using Non-Foster Matching. Lee, S., +, TMTT Dec. 2015 4406-4414 Experimental Control and Design of Low-Frequency Bias Networks for Dynamically Biased Amplifiers. Pelaz, J., +, TMTT Jun. 2015 1923-1936 Low-Input Power-Level CMOS RF Energy-Harvesting Front End. Abouzied, M. A., +, TMTT Nov. 2015 3794-3805 Suppression of Harmonics in Microstrip Filters Using a Combination of Techniques. Huang, F., TMTT Oct. 2015 3453-3461 Ultra-Compact (80 mm ) Differential-Mode Ultra-Wideband (UWB) Bandpass Filters With Common-Mode Noise Suppression. Velez, P., +, TMTT Apr. 2015 1272-1280 Carbon Broadband Dielectric Spectroscopy of Composites Filled With Various Carbon Materials. Bellucci, S., +, TMTT Jun. 2015 2024-2031 Carbon nanotubes Dielectric Constant Estimation of a Carbon Nanotube Layer on the Dielectric Rod Waveguide at Millimeter Wavelengths. Nefedova, I. I., +, TMTT Oct. 2015 3265-3271 Cardiology Channel Imbalance Effects and Compensation for Doppler Radar Physiological Measurements. Yavari, E., +, TMTT Nov. 2015 3834-3842 Carrier density Microwave Properties of an Inhomogeneous Optically Illuminated Plasma in a Microstrip Gap. Gamlath, C. D., +, TMTT Feb. 2015 374-383 Carrier lifetime Microwave Properties of an Inhomogeneous Optically Illuminated Plasma in a Microstrip Gap. Gamlath, C. D., +, TMTT Feb. 2015 374-383 Cavity resonator filters Compact Quad-Mode Bandpass Filter Using Modified Coaxial Cavity Resonator With Improved -Factor. Wang, X., +, TMTT Mar. 2015 965-975 Mechanical Tuning of Substrate Integrated Waveguide Filters. Mira, F., +, TMTT Dec. 2015 3939-3946 Propagating Waveguide Filters Using Dielectric Resonators. Tomassoni, C., +, TMTT Dec. 2015 4366-4375 Cavity resonators Accurate Evaluation Technique of Complex Permittivity for Low-Permittivity Dielectric Films Using a Cavity Resonator Method in 60-GHz Band. Shimizu, T., +, TMTT Jan. 2015 279-286 An Accurate Radially Stratified Approach for Determining the Complex Permittivity of Liquids in a Cylindrical Microwave Cavity. Barmatz, M. B., +, TMTT Feb. 2015 504-508 An Improved Broadband Boundary Condition for the RF Field in Gyrotron Interaction Modeling. Wu, C., +, TMTT Aug. 2015 2459-2467 Mode Power Amplifier Design ApAn Integrated Continuous Classproach for Microwave Enhanced Portable Diagnostic Applications. Imtiaz, A., +, TMTT Oct. 2015 3007-3015 Coupled Mode Theory Applied to Resonators in the Presence of Conductors. Elnaggar, S. Y., +, TMTT Jul. 2015 2124-2132 Extraction of Dielectric and Rough Conductor Loss of Printed Circuit Board Using Differential Method at Microwave Frequencies. Zhu, X.-C., +, TMTT Feb. 2015 494-503 Passive Microwave Substrate Integrated Cavity Resonator for Humidity Sensing. El Matbouly, H., +, TMTT Dec. 2015 4150-4156 Phase-Noise Analysis of an X-Band Ultra-Low Phase-Noise GaN HEMT Based Cavity Oscillator. Horberg, M., +, TMTT Aug. 2015 2619-2629 Triple-Mode Dielectric Resonator Diplexer for Base-Station Applications. Wong, S.-W., +, TMTT Dec. 2015 3947-3953 Ultra-Miniature SIW Cavity Resonators and Filters. Pourghorban Saghati, A., +, TMTT Dec. 2015 4329-4340 Cellular biophysics Miniaturized Transmission-Line Sensor for Broadband Dielectric Characterization of Biological Liquids and Cell Suspensions. Meyne nee Haase, N., +, TMTT Oct. 2015 3026-3033

+ Check author entry for coauthors

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Cellular effects of radiation Electrical Analysis of Cell Membrane Poration by an Intense Nanosecond Pulsed Electric Field Using an Atomistic-to-Continuum Method. Kohler, S., +, TMTT Jun. 2015 2032-2040 Reduction of Exposure Inhomogeneity for Millimeter-Wave Experiments on Cells In Vitro. Zhao, J., +, TMTT Feb. 2015 533-545 Cellular radio A Multi-Band Stacked RF Energy Harvester With RF-to-DC Efficiency Up to 84%. Kuhn, V., +, TMTT May 2015 1768-1778 Multi-Standard Hybrid PLL With Low Phase-Noise Characteristics for GSM/EDGE and LTE Applications. Choi, Y.-C., +, TMTT Oct. 2015 3254-3264 Ceramic packaging An Integrable SIW Phase Shifter in a Partially Magnetized Ferrite LTCC Package. Nafe, A., +, TMTT Jul. 2015 2264-2274 An LTCC Coupled Resonator Decoupling Network for Two Antennas. Qian, K., +, TMTT Oct. 2015 3199-3207 Ceramics Dynamic Measurement of Dielectric Properties of Materials at High Temperature During Microwave Heating in a Dual Mode Cylindrical Cavity. Catala-Civera, J. M., +, TMTT Sep. 2015 2905-2914 Channel bank filters A Tunable RF Front-End With Narrowband Antennas for Mobile Devices. Bahramzy, P., +, TMTT Oct. 2015 3300-3310 Channel capacity Nonlinear Communication System With Harmonic Diversity. Cheong, P., +, TMTT Dec. 2015 4130-4149 Chaos Efficient Statistical Simulation of Microwave Devices Via Stochastic Testing-Based Circuit Equivalents of Nonlinear Components. Manfredi, P., +, TMTT May 2015 1502-1511 Characteristics measurement Dispersion Equations of a Rectangular Tape Helix Slow-Wave Structure. Wei, W., +, TMTT May 2015 1445-1456 Chebyshev approximation Corrections to “Compact Multi-Port Power Combination/Distribution With Inherent Bandpass Filter Characteristics” [Nov 14 2659-2672]. Rosenberg, U., +, TMTT Jul. 2015 2390 Chebyshev filters A Four-Way Microstrip Filtering Power Divider With Frequency-Dependent Couplings. Chen, F.-J., +, TMTT Oct. 2015 3494-3504 Advanced Butler Matrices With Integrated Bandpass Filter Functions. Tornielli di Crestvolant, V., +, TMTT Oct. 2015 3433-3444 Chebyshev Filter Design Using Vias as Quasi-Transmission Lines in Printed Circuit Boards. Hardock, A., +, TMTT Mar. 2015 976-985 Exact Design of a New Class of Generalized Chebyshev Low-Pass Filters Using Coupled Line/Stub Sections. Musonda, E., +, TMTT Dec. 2015 43554365 Synthesis and Design of High-Selectivity Wideband Quasi-Elliptic Bandpass Filters Using Multiconductor Transmission Lines. Sanchez-Martinez, J. J., +, TMTT Jan. 2015 198-208 Chirp modulation Low-Loss Ultrawideband Programmable RF Photonic Phase Filter for Spread Spectrum Pulse Compression. Kim, H.-J., +, TMTT Dec. 2015 4178-4187 Chromium A 1.3–2.4-GHz 3.1-mW VCO Using Electro-Thermo- Mechanically Tunable Self-Assembled MEMS Inductor on HR Substrate. Bhattacharya, A., +, TMTT Feb. 2015 459-469 Micromachined Room-Temperature Air-Suspended Ni/Cr Nanobolometer. Yang, H.-H., +, TMTT Nov. 2015 3760-3767 Circuit analysis Corrections to “Simple, Fast, and Effective Identification of an Equivalent Ports” [Jan 15 48-55]. Zappelli, Circuit of a Waveguide Junction With L., TMTT Mar. 2015 1108 Circuit complexity A Linear Complexity Direct Volume Integral Equation Solver for Full-Wave 3-D Circuit Extraction in Inhomogeneous Materials. Omar, S., +, TMTT Mar. 2015 897-912 Power Adaptive Digital Predistortion for Wideband RF Power Amplifiers With Dynamic Power Transmission. Guo, Y., +, TMTT Nov. 2015 35953607

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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 63, NO. 12, DECEMBER 2015

Circuit feedback An FBAR/CMOS Frequency/Phase Discriminator and Phase Noise Reduction System. Imani, A., +, TMTT May 2015 1658-1665 Broadband Circuit Techniques for Multi-Terahertz Gain-BandwidthProduct Low-Power Applications. Gharib, A., +, TMTT Nov. 2015 3701-3712 RF Input Matching Design for Closed-Loop Direct Delta–Sigma Receivers. Ostman, K. B., +, TMTT Apr. 2015 1370-1379 Circuit noise A New Broadband Common-Mode Noise Absorption Circuit for High-Speed Differential Digital Systems. Hsiao, C.-Y., +, TMTT Jun. 2015 1894-1901 Corrections to “Unified Theory of Linear Noisy Two-Ports” [Nov 13 39863997]. Dietrich, J. L., TMTT Feb. 2015 554 Circuit optimization Automated Design of Common-Mode Suppressed Balanced Wideband Bandpass Filters by Means of Aggressive Space Mapping. Sans, M., +, TMTT Dec. 2015 3896-3908 Optimized Design of Frequency Dividers Based on Varactor-Inductor Cells. Ponton, M., +, TMTT Dec. 2015 4458-4472 Circuit oscillations Generalized Stability Criteria for Power Amplifiers Under Mismatch Effects. Suarez, A., +, TMTT Dec. 2015 4415-4428 Circuit reliability Reliability Analysis of Ku-Band 5-bit Phase Shifters Using MEMS SP4T and SPDT Switches. Dey, S., +, TMTT Dec. 2015 3997-4012 Circuit simulation Active Detuning of MRI Receive Coils with GaN FETs. Twieg, M., +, TMTT Dec. 2015 4169-4177 Reliable Microwave Modeling by Means of Variable-Fidelity Response Features. Koziel, S., +, TMTT Dec. 2015 4247-4254 Circuit stability A 40-nm CMOS E-Band 4-Way Power Amplifier With Neutralized Bootstrapped Cascode Amplifier and Optimum Passive Circuits. Zhao, D., +, TMTT Dec. 2015 4083-4089 Experimental Control and Design of Low-Frequency Bias Networks for Dynamically Biased Amplifiers. Pelaz, J., +, TMTT Jun. 2015 1923-1936 Hysteresis and Oscillation in High-Efficiency Power Amplifiers. de Cos, J., +, TMTT Dec. 2015 4284-4296 Circuit theory Resonant Electrical Coupling: Circuit Model and First Experimental Results. Dias Fernandes, R., +, TMTT Sep. 2015 2983-2990 Circuit tuning A 1.3–2.4-GHz 3.1-mW VCO Using Electro-Thermo- Mechanically Tunable Self-Assembled MEMS Inductor on HR Substrate. Bhattacharya, A., +, TMTT Feb. 2015 459-469 A 1.4–2.3-GHz Tunable Diplexer Based on Reconfigurable Matching Networks. Ko, C. H., +, TMTT May 2015 1595-1602 A Varactor-Based Variable Attenuator Design With Enhanced Linearity Performance. Cheng, K.-K. M., +, TMTT Oct. 2015 3191-3198 Active Detuning of MRI Receive Coils with GaN FETs. Twieg, M., +, TMTT Dec. 2015 4169-4177 Analysis of Weakly Nonlinear Effect for Varactor-Tuned Bandpass Filter. Ge, C., +, TMTT Nov. 2015 3641-3650 Mechanical Tuning of Substrate Integrated Waveguide Filters. Mira, F., +, TMTT Dec. 2015 3939-3946 Reconfigurable Multi-Band Microwave Filters. Gomez-Garcia, R., +, TMTT Apr. 2015 1294-1307 Transformer-Based Doherty Power Amplifiers for mm-Wave Applications in 40-nm CMOS. Kaymaksut, E., +, TMTT Apr. 2015 1186-1192 Tuning-Range Enhancement Through Deterministic Mode Selection in RF Quadrature Oscillators. Bagheri, M., +, TMTT Nov. 2015 3713-3726 Circular waveguides -toCircular Mode Converter Design. A Universal Solution to Yu, X. H., +, TMTT Dec. 2015 3845-3850 -Mode An Isolated Radial Power Divider via Circular Waveguide Transducer. Chu, Q.-X., +, TMTT Dec. 2015 3988-3996 Efficient Design of Waveguide Manifold Multiplexers Based on Low-Order EM Distributed Models. Cogollos, S., +, TMTT Aug. 2015 2540-2549 Radial Transmission-Line Approach for the Analysis of Ring Loaded Slots in Circular Waveguide. Addamo, G., +, TMTT May 2015 1468-1474 Closed loop systems RF Input Matching Design for Closed-Loop Direct Delta–Sigma Receivers. Ostman, K. B., +, TMTT Apr. 2015 1370-1379 + Check author entry for coauthors

Cmos analog integrated circuits -Band Spatially Combined Power Amplifier Arrays in 45-nm CMOS SOI. Hanafi, B., +, TMTT Jun. 2015 1937-1950 A 1.1-Gbit/s 10-GHz Outphasing Modulator With 23-dBm Output Power and 60-dB Dynamic Range in 45-nm CMOS SOI. Mehrjoo, M. S., +, TMTT Jul. 2015 2289-2300 A 2.88 mW 9.06 dBm IIP3 Common-Gate LNA With Dual Cross-Coupled Capacitive Feedback. Han, H. G., +, TMTT Mar. 2015 1019-1025 A 40-nm CMOS E-Band 4-Way Power Amplifier With Neutralized Bootstrapped Cascode Amplifier and Optimum Passive Circuits. Zhao, D., +, TMTT Dec. 2015 4083-4089 A Low Phase-Noise Wide Tuning-Range Quadrature Oscillator Using a Transformer-Based Dual-Resonance LC Ring. Bajestan, M. M., +, TMTT Apr. 2015 1142-1153 A Reconfigurable 50-Mb/s-1 Gb/s Pulse Compression Radar Signal Processor With Offset Calibration in 90-nm CMOS. Li, J., +, TMTT Jan. 2015 266-278 A W-Band Power Amplifier Utilizing a Miniaturized Marchand Balun Combiner. Jia, H., +, TMTT Feb. 2015 719-725 An E-Band Power Amplifier With Broadband Parallel-Series Power Combiner in 40-nm CMOS. Zhao, D., +, TMTT Feb. 2015 683-690 Analysis of Far-Out Spurious Noise and its Reduction in Envelope-Tracking Power Amplifier. Kim, J., +, TMTT Dec. 2015 4072-4082 Antenna Impedance Variation Compensation by Exploiting a Digital Doherty Power Amplifier Architecture. Hu, S., +, TMTT Feb. 2015 580-597 Broadband CMOS Stacked RF Power Amplifier Using Reconfigurable Interstage Network for Wideband Envelope Tracking. Park, S., +, TMTT Apr. 2015 1174-1185 Large-Scale Power Combining and Mixed-Signal Linearizing Architectures for Watt-Class mmWave CMOS Power Amplifiers. Bhat, R., +, TMTT Feb. 2015 703-718 Millimeter-Wave Low-Noise Amplifier Design in 28-nm Low-Power Digital CMOS. Fritsche, D., +, TMTT Jun. 2015 1910-1922 Transmission of Signals With Complex Constellations Using Millimeter-Wave Spatially Power-Combined CMOS Power Amplifiers and Digital Predistortion. Dabag, H.-T., +, TMTT Jul. 2015 2364-2374 Wide Tuning-Range mm-Wave Voltage-Controlled Oscillator Employing an Artificial Magnetic Transmission Line. Yanay, N., +, TMTT Apr. 2015 13421352 CMOS digital integrated circuits A Reconfigurable 50-Mb/s-1 Gb/s Pulse Compression Radar Signal Processor With Offset Calibration in 90-nm CMOS. Li, J., +, TMTT Jan. 2015 266-278 Antenna Impedance Variation Compensation by Exploiting a Digital Doherty Power Amplifier Architecture. Hu, S., +, TMTT Feb. 2015 580-597 Millimeter-Wave Low-Noise Amplifier Design in 28-nm Low-Power Digital CMOS. Fritsche, D., +, TMTT Jun. 2015 1910-1922 CMOS integrated circuits 130-320-GHz CMOS Harmonic Down-Converters Around and Above the Cutoff Frequency. Khamaisi, B., +, TMTT Jul. 2015 2275-2288 60-GHz Substrate Materials Characterization Using the Covered Transmission-Line Method. Papio Toda, A., +, TMTT Mar. 2015 1063-1075 76–81-GHz CMOS Transmitter With a Phase-Locked-Loop-Based Multichirp Modulator for Automotive Radar. Park, J., +, TMTT Apr. 2015 13991408 A 0.12-mm 2.4-GHz CMOS Inductorless High Isolation Subharmonic Mixer With Effective Current-Reuse Transconductance. Chong, W. K., +, TMTT Aug. 2015 2427-2437 A 0.2–3.6-GHz 10-dBm B1dB 29-dBm IIP3 Tunable Filter for Transmit Leakage Suppression in SAW-Less 3G/4G FDD Receivers. Luo, C., +, TMTT Oct. 2015 3514-3524 A 1.3–2.4-GHz 3.1-mW VCO Using Electro-Thermo- Mechanically Tunable Self-Assembled MEMS Inductor on HR Substrate. Bhattacharya, A., +, TMTT Feb. 2015 459-469 A 37.5-mW 8-dBm-EIRP 15.5 -HPBW 338-GHz Terahertz Transmitter Using SoP Heterogeneous System Integration. Li, C.-H., +, TMTT Feb. 2015 470-480 A 47.6–71.0-GHz 65-nm CMOS VCO Based on Magnetically Coupled -Type LC Network. Jia, H., +, TMTT May 2015 1645-1657 A Blocker-Tolerant Current Mode 60-GHz Receiver With 7.5-GHz Bandwidth and 3.8-dB Minimum NF in 65-nm CMOS. Wu, H., +, TMTT Mar. 2015 1053-1062 A CML Ring Oscillator-Based Supply-Insensitive PLL With On-Chip Calibrations. Gui, X., +, TMTT Jan. 2015 233-243

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A CMOS Spectrum Sensor Based on Quasi-Cyclostationary Feature Detection for Cognitive Radios. Sepidband, P., +, TMTT Dec. 2015 4098-4109 A K-Band Reconfigurable Pulse-Compression Automotive Radar Transmitter in 90-nm CMOS. Tan, K.-W., +, TMTT Apr. 2015 1380-1387 A Memoryless Semi-Physical Power Amplifier Behavioral Model Based on the Correlation Between AM–AM and AM–PM Distortions. Glock, S., +, TMTT Jun. 2015 1826-1835 A mm-Wave Segmented Power Mixer. Dasgupta, K., +, TMTT Apr. 2015 1118-1129 A Prototype SAW-Less LTE Transmitter With a High-Linearity Modulator Using BPF-Based I/Q Summing and a Triple-Layer Marchand Balun. Nakamura, T., +, TMTT Dec. 2015 4090-4097 A Pulsed Dynamic Load Modulation Technique for High-Efficiency Linear Transmitters. Jeon, M.-S., +, TMTT Sep. 2015 2854-2866 A Stacked-FET Linear SOI CMOS Cellular Antenna Switch With an Extremely Low-Power Biasing Strategy. Im, D., +, TMTT Jun. 2015 19641977 A Sub-GHz Wireless Transmitter Utilizing a Multi-Class-Linearized PA and Time-Domain Wideband-Auto I/Q-LOFT Calibration for IEEE 802.11af WLAN. Un, K.-F., +, TMTT Oct. 2015 3228-3241 A W-Band 4-GHz Bandwidth Phase-Modulated Pulse Compression Radar Transmitter in 65-nm CMOS. Oh, J., +, TMTT Aug. 2015 2609-2618 A Wide-Band CMOS to Waveguide Transition at mm-Wave Frequencies With Wire-Bonds. Jameson, S., +, TMTT Sep. 2015 2741-2750 An 8-bit 100-GS/s Distributed DAC in 28-nm CMOS for Optical Communications. Huang, H., +, TMTT Apr. 2015 1211-1218 An Efficiency-Enhanced Stacked 2.4-GHz CMOS Power Amplifier With Mode Switching Scheme for WLAN Applications. Yin, Y., +, TMTT Feb. 2015 672-682 An FBAR/CMOS Frequency/Phase Discriminator and Phase Noise Reduction System. Imani, A., +, TMTT May 2015 1658-1665 An Integrated 700–1200-MHz Class-F PA With Tunable Harmonic Terminations in 0.13- m CMOS. Sessou, K. K., +, TMTT Apr. 2015 1315-1323 Analysis and Design of a 14.1-mW 50/100-GHz Transformer-Based PLL With Embedded Phase Shifter in 65-nm CMOS. Chao, Y., +, TMTT Apr. 2015 1193-1201 Analysis and Design of Millimeter-Wave Power Amplifier Using Stacked-FET Structure. Kim, Y., +, TMTT Feb. 2015 691-702 Analysis of Nonlinearities in Injection-Locked Frequency Dividers. Gui, X., +, TMTT Mar. 2015 945-953 Anomalous Dispersion Characteristics of Periodic Substrate Integrated Waveguides From Microwave to Terahertz. Li, X., +, TMTT Jul. 2015 2142-2153 Broadband Synthetic Transmission-Line N-Path Filter Design. Thomas, C. M., +, TMTT Oct. 2015 3525-3536 CMOS Broadband Programmable Gain Active Balun With 0.5-dB Gain Steps. Hur, B., +, TMTT Aug. 2015 2650-2660 Comparison of Injection-Locked and Coupled Oscillator Arrays for Beamforming. Lo, Y.-T., +, TMTT Apr. 2015 1353-1360 Design and Analysis of 24-GHz Active Isolator and Quasi-Circulator. Chang, J.-F., +, TMTT Aug. 2015 2638-2649 Design and Analysis of CMOS High-Speed High Dynamic-Range Trackand-Hold Amplifiers. Liu, Y.-C., +, TMTT Sep. 2015 2841-2853 Design and Analysis on Bidirectionally and Passively Coupled QVCO With Nonlinear Coupler. Kuo, N.-C., +, TMTT Apr. 2015 1130-1141 Design and Tuning of Coupled-LC mm-Wave Subharmonically InjectionLocked Oscillators. Mangraviti, G., +, TMTT Jul. 2015 2301-2312 Designs of K-Band Divide-by-2 and Divide-by-3 Injection-Locked Frequency Divider With Darlington Topology. Chien, K.-H., +, TMTT Sep. 2015 2877-2888 Digitally Assisted CMOS RF Detectors With Self-Calibration for Variability Compensation. Barabino, N., +, TMTT May 2015 1676-1682 Efficient Microwave and Millimeter-Wave Frequency Multipliers Using Nonlinear Transmission Lines in CMOS Technology. Adnan, M., +, TMTT Sep. 2015 2889-2896 Generic Electrostatic Discharges Protection Solutions for RF and Millimeter-Wave Applications. Lim, T., +, TMTT Nov. 2015 3747-3759 Investigation of Intermodulation Distortion of Envelope Tracking Power Amplifier for Linearity Improvement. Moon, K., +, TMTT Apr. 2015 13241333 Low-Input Power-Level CMOS RF Energy-Harvesting Front End. Abouzied, M. A., +, TMTT Nov. 2015 3794-3805

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Multi-Standard Hybrid PLL With Low Phase-Noise Characteristics for GSM/EDGE and LTE Applications. Choi, Y.-C., +, TMTT Oct. 2015 3254-3264 Mutual Synchronization for Power Generation and Beam-Steering in CMOS With On-Chip Sense Antennas Near 200 GHz. Sengupta, K., +, TMTT Sep. 2015 2867-2876 RF Input Matching Design for Closed-Loop Direct Delta–Sigma Receivers. Ostman, K. B., +, TMTT Apr. 2015 1370-1379 RF Small-Signal and Noise Modeling Including Parameter Extraction of Nanoscale MOSFET From Weak to Strong Inversion. Chalkiadaki, M.-A., +, TMTT Jul. 2015 2173-2184 Source Degenerated Derivative Superposition Method for Linearizing RF FET Differential Amplifiers. Shin, H., +, TMTT Mar. 2015 1026-1035 Transformer-Based Doherty Power Amplifiers for mm-Wave Applications in 40-nm CMOS. Kaymaksut, E., +, TMTT Apr. 2015 1186-1192 Tuning-Range Enhancement Through Deterministic Mode Selection in RF Quadrature Oscillators. Bagheri, M., +, TMTT Nov. 2015 3713-3726 Coaxial cables Dispersion Modeling and Analysis for Multilayered Open Coaxial Waveguides. Nordebo, S., +, TMTT Jun. 2015 1791-1799 High-Performance Coplanar Waveguide to Empty Substrate Integrated Coaxial Line Transition. Belenguer, A., +, TMTT Dec. 2015 4027-4034 Coaxial waveguides Coaxial End-Launched and Microstrip to Partial -Plane Waveguide Transitions. Kloke, K. H., +, TMTT Oct. 2015 3103-3108 Dispersion Modeling and Analysis for Multilayered Open Coaxial Waveguides. Nordebo, S., +, TMTT Jun. 2015 1791-1799 High-Performance Coplanar Waveguide to Empty Substrate Integrated Coaxial Line Transition. Belenguer, A., +, TMTT Dec. 2015 4027-4034 Longitudinally Independent Matching and Arbitrary Wave Patterning Using -Near-Zero Channels. Soric, J. C., +, TMTT Nov. 2015 3558-3567 Cobalt compounds Self-Biased Y-Junction Circulators Using Lanthanum- and Cobalt-Substituted Strontium Hexaferrites. Laur, V., +, TMTT Dec. 2015 4376-4381 Code division multiple access A Novel Load Mismatch Detection and Correction Technique for 3G/4G Load Insensitive Power Amplifier Application. Ji, D., +, TMTT May 2015 1530-1543 Bandwidth Enhancement of Three-Stage Doherty Power Amplifier Using Symmetric Devices. Barthwal, A., +, TMTT Aug. 2015 2399-2410 Behavioral Modeling and Predistortion of Power Amplifiers Under Sparsity Hypothesis. Reina-Tosina, J., +, TMTT Feb. 2015 745-753 Efficient Least-Squares 2-D-Cubic Spline for Concurrent Dual-Band Systems. Naraharisetti, N., +, TMTT Jul. 2015 2199-2210 Fully Monolithic BiCMOS Reconfigurable Power Amplifier for Multi-Mode and Multi-Band Applications. Lee, M.-L., +, TMTT Feb. 2015 614-624 Improving Power Utilization Factor of Broadband Doherty Amplifier by Using Bandpass Auxiliary Transformer. Fang, X.-H., +, TMTT Sep. 2015 2811-2820 Optimized Design of a Dual-Band Power Amplifier With SiC VaractorBased Dynamic Load Modulation. Sanchez-Perez, C., +, TMTT Aug. 2015 2579-2588 Cognitive radio A CMOS Spectrum Sensor Based on Quasi-Cyclostationary Feature Detection for Cognitive Radios. Sepidband, P., +, TMTT Dec. 2015 4098-4109 Tunable 4-Pole Dual-Notch Filters for Cognitive Radios and Carrier Aggregation Systems. Cho, Y.-H., +, TMTT Apr. 2015 1308-1314 Coils Active Detuning of MRI Receive Coils with GaN FETs. Twieg, M., +, TMTT Dec. 2015 4169-4177 Synthesis and Design of Programmable Subwavelength Coil Array for NearField Manipulation. Gao, F., +, TMTT Sep. 2015 2971-2982 Tunable 500–1200-MHz Dual-Band and Wide Bandwidth Notch Filters Using RF Transformers. Ko, C.-H., +, TMTT Jun. 2015 1854-1862 Wireless Power Systems for Mobile Devices Supporting Inductive and Resonant Operating Modes. Riehl, P. S., +, TMTT Mar. 2015 780-790 Comb filters Design and Multiphysics Analysis of Direct and Cross-Coupled SIW Combline Filters Using Electric and Magnetic Couplings. Sirci, S., +, TMTT Dec. 2015 4341-4354

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Compensation Digital Compensation for Transmitter Leakage in Non-Contiguous Carrier Aggregation Applications With FPGA Implementation. Yu, C., +, TMTT Dec. 2015 4306-4318 Improved Reactance-Compensation Technique for the Design of Wideband Suboptimum Class-E Power Amplifiers. Zhou, J., +, TMTT Sep. 2015 27932801 Partitioned Distortion Mitigation in LTE Radio Uplink to Enhance Transmitter Efficiency. Amiri, M. V., +, TMTT Aug. 2015 2661-2671 Composite materials Broadband Dielectric Spectroscopy of Composites Filled With Various Carbon Materials. Bellucci, S., +, TMTT Jun. 2015 2024-2031 Computational complexity 3-D Distributed Memory Polynomial Behavioral Model for Concurrent Dual-Band Envelope Tracking Power Amplifier Linearization. Gilabert, P. L., +, TMTT Feb. 2015 638-648 Low Complexity Coefficient Estimation for Concurrent Dual-Band Digital Predistortion. Qian, H., +, TMTT Oct. 2015 3153-3163 Computational electromagnetics Direct -Transform Implementation of the CFS-PML Based on MemoryMinimized Method. Feng, N., +, TMTT Mar. 2015 877-882 Direct Finite-Element Solver of Linear Complexity for Large-Scale 3-D Electromagnetic Analysis and Circuit Extraction. Zhou, B., +, TMTT Oct. 2015 3066-3080 Efficient Calculation of the Electromagnetic Scattering by Lossless or Lossy, Prolate or Oblate Dielectric Spheroids. Zouros, G. P., +, TMTT Mar. 2015 864-876 Guest Editorial [Mini-Special Issue on 2014 IEEE International Conference on Numerical Electromagnetic Modeling and Optimization for RF, Microwave, and Terahertz Applications (NEMO2014. Bozzi, M., +, TMTT Jan. 2015 1-2 Mixed Spectral-Element Method for 3-D Maxwell's Eigenvalue Problem. Liu, N., +, TMTT Feb. 2015 317-325 Conducting materials Coupled Mode Theory Applied to Resonators in the Presence of Conductors. Elnaggar, S. Y., +, TMTT Jul. 2015 2124-2132 Scattering by Conducting Cylinders Below a Dielectric Layer With a Fast Noniterative Approach. Ponti, C., +, TMTT Jan. 2015 30-39 Conductors (electric) A 2.45 GHz Phased Array Antenna Unit Cell Fabricated Using 3-D MultiLayer Direct Digital Manufacturing. Ketterl, T. P., +, TMTT Dec. 2015 4382-4394 Broadband Microwave Attenuator Based on Few Layer Graphene Flakes. Pierantoni, L., +, TMTT Aug. 2015 2491-2497 Dielectric Constant Estimation of a Carbon Nanotube Layer on the Dielectric Rod Waveguide at Millimeter Wavelengths. Nefedova, I. I., +, TMTT Oct. 2015 3265-3271 Conformal mapping Broadband Microwave Characterization of Nanostructured Thin Film With Giant Dielectric Response. Chen, T.-C., +, TMTT Nov. 2015 3768-3774 Consumer electronics Efficiency and Optimal Loads Analysis for Multiple-Receiver Wireless Power Transfer Systems. Fu, M., +, TMTT Mar. 2015 801-812 Guest Editorial. KIM, J., +, TMTT Mar. 2015 778-779 Convergence Compact Behavioral Models of Nonlinear Active Devices Using Response Surface Methodology. Barmuta, P., +, TMTT Jan. 2015 56-64 Converters Design and Modeling of Spoof Surface Plasmon Modes-Based Microwave Slow-Wave Transmission Line. Kianinejad, A., +, TMTT Jun. 2015 18171825 Method for Synthesis of Mode Converter for Gyrotron by the NURBS Technique. Yu, X., +, TMTT Feb. 2015 326-330 Radial Transmission-Line Approach for the Analysis of Ring Loaded Slots in Circular Waveguide. Addamo, G., +, TMTT May 2015 1468-1474 Cooperative communication Cooperative Integration of Harvesting RF Sections for Passive RFID Communication. Andia Vera, G., +, TMTT Dec. 2015 4556-4566 Coplanar transmission lines Wide Tuning-Range mm-Wave Voltage-Controlled Oscillator Employing an Artificial Magnetic Transmission Line. Yanay, N., +, TMTT Apr. 2015 13421352

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Coplanar waveguides A Miniaturized Microfluidically Reconfigurable Coplanar Waveguide Bandpass Filter With Maximum Power Handling of 10 Watts. Pourghorban Saghati, A., +, TMTT Aug. 2015 2515-2525 A Novel 1 4 Coupler for Compact and High-Gain Power Amplifier MMICs Around 250 GHz. Diebold, S., +, TMTT Mar. 2015 999-1006 A Wide-Band CMOS to Waveguide Transition at mm-Wave Frequencies With Wire-Bonds. Jameson, S., +, TMTT Sep. 2015 2741-2750 Accurate Parametric Electrical Model for Slow-Wave CPW and Application to Circuits Design. Bautista, A., +, TMTT Dec. 2015 4225-4235 Broadband Microwave Characterization of Nanostructured Thin Film With Giant Dielectric Response. Chen, T.-C., +, TMTT Nov. 2015 3768-3774 High-Performance Coplanar Waveguide to Empty Substrate Integrated Coaxial Line Transition. Belenguer, A., +, TMTT Dec. 2015 4027-4034 Monolithic Millimeter-Wave MEMS Waveguide Switch. Vahabisani, N., +, TMTT Feb. 2015 340-351 Reliability Analysis of Ku-Band 5-bit Phase Shifters Using MEMS SP4T and SPDT Switches. Dey, S., +, TMTT Dec. 2015 3997-4012 Time-Domain Optoelectronic Vector Network Analysis on Coplanar Waveguides. Bieler, M., +, TMTT Nov. 2015 3775-3784 Copper Microstrip Whispering-Gallery-Mode Resonator. Bunyaev, S. A., +, TMTT Sep. 2015 2776-2781 Coupled circuits A 1.6–2.3-GHz RF MEMS Reconfigurable Quadrature Coupler and Its Application to a 360 Reflective-Type Phase Shifter. Gurbuz, O. D., +, TMTT Feb. 2015 414-421 A 47.6–71.0-GHz 65-nm CMOS VCO Based on Magnetically Coupled -Type LC Network. Jia, H., +, TMTT May 2015 1645-1657 A Highly Efficient LTE Pulse-Modulated Polar Transmitter Using Wideband Power Recycling. Yang, H.-S., +, TMTT Dec. 2015 4437-4443 An LTCC Coupled Resonator Decoupling Network for Two Antennas. Qian, K., +, TMTT Oct. 2015 3199-3207 Compact Filtering Rat-Race Hybrid With Wide Stopband. Wang, K.-X., +, TMTT Aug. 2015 2550-2560 Compact Multi-Band Bandpass Filters With Mixed Electric and Magnetic Coupling Using Multiple-Mode Resonator. Xu, J., +, TMTT Dec. 2015 3909-3919 Compact Tunable Filtering Power Divider With Constant Absolute Bandwidth. Gao, L., +, TMTT Oct. 2015 3505-3513 Comparison of Injection-Locked and Coupled Oscillator Arrays for Beamforming. Lo, Y.-T., +, TMTT Apr. 2015 1353-1360 Design and Multiphysics Analysis of Direct and Cross-Coupled SIW Combline Filters Using Electric and Magnetic Couplings. Sirci, S., +, TMTT Dec. 2015 4341-4354 Efficient Design of Waveguide Manifold Multiplexers Based on Low-Order EM Distributed Models. Cogollos, S., +, TMTT Aug. 2015 2540-2549 Exact Design of a New Class of Generalized Chebyshev Low-Pass Filters Using Coupled Line/Stub Sections. Musonda, E., +, TMTT Dec. 2015 43554365 Global Stability Analysis of Coupled-Oscillator Systems. Suarez, A., +, TMTT Jan. 2015 165-180 Resonant Electrical Coupling: Circuit Model and First Experimental Results. Dias Fernandes, R., +, TMTT Sep. 2015 2983-2990 Resonator Voltage Prediction in Microwave Bandpass Filters. Vanin, F. M., +, TMTT Feb. 2015 397-402 Synthesis of Inline Mixed Coupled Quasi-Elliptic Bandpass Filters Based on Resonators. Zhang, S., +, TMTT Oct. 2015 3487-3493 Temporal Coupled-Mode Theory and the Combined Effect of Dual Orthogonal Resonant Modes in Microstrip Bandpass Filters. Yu, F., +, TMTT Feb. 2015 403-413 Tuning-Range Enhancement Through Deterministic Mode Selection in RF Quadrature Oscillators. Bagheri, M., +, TMTT Nov. 2015 3713-3726 Wideband Balanced Filters With High Selectivity and Common-Mode Suppression. Chu, Q.-X., +, TMTT Oct. 2015 3462-3468 Mode Substrate Integrated Wideband Excitation Technology of Waveguide (SIW) and Its Applications. Wu, P., +, TMTT Jun. 2015 1863-1874 Coupled mode analysis Coupled Mode Theory Applied to Resonators in the Presence of Conductors. Elnaggar, S. Y., +, TMTT Jul. 2015 2124-2132 Energy Coupled Mode Theory for Electromagnetic Resonators. Elnaggar, S. Y., +, TMTT Jul. 2015 2115-2123

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 63, NO. 12, DECEMBER 2015

Coupled transmission lines Balanced Dual-Band Bandpass Filter With Multiple Transmission Zeros Using Doubly Short-Ended Resonator Coupled Line. Yang, L., +, TMTT Jul. 2015 2225-2232 Generalized Coupled-Line All-Pass Phasers. Gupta, S., +, TMTT Mar. 2015 1007-1018 Couplings A Transformer-Based Poly-Phase Network for Ultra-Broadband Quadrature Signal Generation. Park, J. S., +, TMTT Dec. 2015 4444-4457 Cryogenics A Compact L-Band Orthomode Transducer for Radio Astronomical Receivers at Cryogenic Temperature. Valente, G., +, TMTT Oct. 2015 32183227 Current density Time-Domain Electromagnetic Analysis of Multilayer Structures Using the Surface Equivalent Principle and Mixed-Potential Integral Equations. Maftooli, H., +, TMTT Jan. 2015 99-106 Current-mode circuits A Blocker-Tolerant Current Mode 60-GHz Receiver With 7.5-GHz Bandwidth and 3.8-dB Minimum NF in 65-nm CMOS. Wu, H., +, TMTT Mar. 2015 1053-1062 Current-mode logic A CML Ring Oscillator-Based Supply-Insensitive PLL With On-Chip Calibrations. Gui, X., +, TMTT Jan. 2015 233-243 CW radar A 77-GHz FMCW Radar System Using On-Chip Waveguide Feeders in 65-nm CMOS. Cui, C., +, TMTT Nov. 2015 3736-3746 Concurrent Detection of Vibration and Distance Using Unmodulated CW Doppler Vibration Radar With An Adaptive Beam-Steering Antenna. Nieh, C.-M., +, TMTT Jun. 2015 2069-2078 Multichannel Backscatter Communication and Ranging for Distributed Sensing With an FMCW Radar. Cnaan-On, I., +, TMTT Jul. 2015 2375-2383 D Data communication A Hardware Efficient Implementation of a Digital Baseband Receiver for High-Capacity Millimeter-Wave Radios. He, Z., +, TMTT May 2015 16831692 Data visualization Computational Feasibility Study of Contrast-Enhanced Thermoacoustic Imaging for Breast Cancer Detection Using Realistic Numerical Breast Phantoms. Wang, X., +, TMTT May 2015 1489-1501 DC-DC power converters GaN Microwave DC–DC Converters. Ramos, I., +, TMTT Dec. 2015 44734482 Decomposition Theory and Implementation of RF-Input Outphasing Power Amplification. Barton, T. W., +, TMTT Dec. 2015 4273-4283 Delay lock loops A Reconfigurable 50-Mb/s-1 Gb/s Pulse Compression Radar Signal Processor With Offset Calibration in 90-nm CMOS. Li, J., +, TMTT Jan. 2015 266-278 Spur Reduction Techniques With a Switched-Capacitor Feedback Differential PLL and a DLL-Based SSCG in UHF RFID Transmitter. Lee, I.-Y., +, TMTT Apr. 2015 1202-1210 Delta-sigma modulation RF Input Matching Design for Closed-Loop Direct Delta–Sigma Receivers. Ostman, K. B., +, TMTT Apr. 2015 1370-1379 Demodulation Multichannel Backscatter Communication and Ranging for Distributed Sensing With an FMCW Radar. Cnaan-On, I., +, TMTT Jul. 2015 2375-2383 Demodulators A 15-Gb/s 8-PSK Demodulator With Comparator-Based Carrier Synchronization. He, Z., +, TMTT Aug. 2015 2630-2637 Fully Integrated D-Band Direct Carrier Quadrature (I/Q) Modulator and Demodulator Circuits in InP DHBT Technology. Carpenter, S., +, TMTT May 2015 1666-1675

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4633

Detector circuits A Novel Load Mismatch Detection and Correction Technique for 3G/4G Load Insensitive Power Amplifier Application. Ji, D., +, TMTT May 2015 1530-1543 Determinants Analytical Reflection Coefficient Expressions Utilizing Load-Dependent -Parameters. Gou, Y., +, TMTT Oct. 2015 3142-3152 Diamond Investigating the Broadband Microwave Absorption of Nanodiamond Impurities. Cuenca, J. A., +, TMTT Dec. 2015 4110-4118 Dielectric liquids Microstrip Device for Broadband (15–65 GHz) Measurement of Dielectric Properties of Nematic Liquid Crystals. Deo, P., +, TMTT Apr. 2015 13881398 Dielectric loss measurement Microstrip Device for Broadband (15–65 GHz) Measurement of Dielectric Properties of Nematic Liquid Crystals. Deo, P., +, TMTT Apr. 2015 13881398 Dielectric losses 60-GHz Substrate Materials Characterization Using the Covered Transmission-Line Method. Papio Toda, A., +, TMTT Mar. 2015 1063-1075 Investigating the Broadband Microwave Absorption of Nanodiamond Impurities. Cuenca, J. A., +, TMTT Dec. 2015 4110-4118 Printable Planar Dielectric Waveguides Based on High-Permittivity Films. Rashidian, A., +, TMTT Sep. 2015 2720-2729 Real-World Implementation Challenges of a Novel Dual-Polarized Compact Printable Chipless RFID Tag. Islam, M. A., +, TMTT Dec. 2015 4581-4591 Resonant Modes of Disk-Loaded Cylindrical Structures With Open Boundaries. Chelis, I. G., +, TMTT Jun. 2015 1781-1790 Dielectric materials A Linear Complexity Direct Volume Integral Equation Solver for Full-Wave 3-D Circuit Extraction in Inhomogeneous Materials. Omar, S., +, TMTT Mar. 2015 897-912 An Analysis of Multistrip Line Configuration on Elliptical Cylinder. Kusiek, A., +, TMTT Jun. 2015 1800-1808 Dynamic Measurement of Dielectric Properties of Materials at High Temperature During Microwave Heating in a Dual Mode Cylindrical Cavity. Catala-Civera, J. M., +, TMTT Sep. 2015 2905-2914 Integral-Equation Formulation for the Analysis of Capacitive Waveguide Filters Containing Dielectric and Metallic Arbitrarily Shaped Objects and Novel Applications. Quesada Pereira, F. D., +, TMTT Dec. 2015 38623873 Material Characterization of Arbitrarily Shaped Dielectrics Based on Reflected Pulse Characteristics. Chan, K.K.M., +, TMTT May 2015 1700-1709 Scattering by Conducting Cylinders Below a Dielectric Layer With a Fast Noniterative Approach. Ponti, C., +, TMTT Jan. 2015 30-39 Single-Compound Complementary Split-Ring Resonator for Simultaneously Measuring the Permittivity and Thickness of Dual-Layer Dielectric Materials. Lee, C.-S., +, TMTT Jun. 2015 2010-2023 Two-Material Ridge Substrate Integrated Waveguide for Ultra-Wideband Applications. Moscato, S., +, TMTT Oct. 2015 3175-3182 Dielectric measurement Time-Domain System for Millimeter-Wave Material Characterization. Vakili, I., +, TMTT Sep. 2015 2915-2922 Dielectric properties An Empirical Expression to Predict the Resonant Frequencies of Archimedean Spirals. Hooker, J. W., +, TMTT Jul. 2015 2107-2114 Broadband Microwave Characterization of Nanostructured Thin Film With Giant Dielectric Response. Chen, T.-C., +, TMTT Nov. 2015 3768-3774 Computational Feasibility Study of Contrast-Enhanced Thermoacoustic Imaging for Breast Cancer Detection Using Realistic Numerical Breast Phantoms. Wang, X., +, TMTT May 2015 1489-1501 Dielectric resonator filters Propagating Waveguide Filters Using Dielectric Resonators. Tomassoni, C., +, TMTT Dec. 2015 4366-4375 Dielectric resonators Coupled Mode Theory Applied to Resonators in the Presence of Conductors. Elnaggar, S. Y., +, TMTT Jul. 2015 2124-2132 Microstrip Whispering-Gallery-Mode Resonator. Bunyaev, S. A., +, TMTT Sep. 2015 2776-2781 Resonant Modes of Disk-Loaded Cylindrical Structures With Open Boundaries. Chelis, I. G., +, TMTT Jun. 2015 1781-1790

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Single-Compound Complementary Split-Ring Resonator for Simultaneously Measuring the Permittivity and Thickness of Dual-Layer Dielectric Materials. Lee, C.-S., +, TMTT Jun. 2015 2010-2023 Triple-Mode Dielectric Resonator Diplexer for Base-Station Applications. Wong, S.-W., +, TMTT Dec. 2015 3947-3953 Dielectric thin films Accurate Evaluation Technique of Complex Permittivity for Low-Permittivity Dielectric Films Using a Cavity Resonator Method in 60-GHz Band. Shimizu, T., +, TMTT Jan. 2015 279-286 Broadband Microwave Characterization of Nanostructured Thin Film With Giant Dielectric Response. Chen, T.-C., +, TMTT Nov. 2015 3768-3774 Dielectric waveguides Dielectric Constant Estimation of a Carbon Nanotube Layer on the Dielectric Rod Waveguide at Millimeter Wavelengths. Nefedova, I. I., +, TMTT Oct. 2015 3265-3271 Millimeter-Wave Near-Field Probe Designed for High-Resolution Skin Cancer Diagnosis. Topfer, F., +, TMTT Jun. 2015 2050-2059 Printable Planar Dielectric Waveguides Based on High-Permittivity Films. Rashidian, A., +, TMTT Sep. 2015 2720-2729 Dielectrics Authors’ Reply. Mescia, L., +, TMTT Dec. 2015 4191-4193 Differential amplifiers A 40-nm CMOS E-Band 4-Way Power Amplifier With Neutralized Bootstrapped Cascode Amplifier and Optimum Passive Circuits. Zhao, D., +, TMTT Dec. 2015 4083-4089 A Highly Efficient LTE Pulse-Modulated Polar Transmitter Using Wideband Power Recycling. Yang, H.-S., +, TMTT Dec. 2015 4437-4443 An 85-W Multi-Octave Push–Pull GaN HEMT Power Amplifier for HighEfficiency Communication Applications at Microwave Frequencies. Jundi, A., +, TMTT Nov. 2015 3691-3700 Broadband Circuit Techniques for Multi-Terahertz Gain-BandwidthProduct Low-Power Applications. Gharib, A., +, TMTT Nov. 2015 3701-3712 Source Degenerated Derivative Superposition Method for Linearizing RF FET Differential Amplifiers. Shin, H., +, TMTT Mar. 2015 1026-1035 Differential equations Non-Reflecting SFBF Termination Inverting From TFSF Discontinuity Decomposition. Tan, T., TMTT Sep. 2015 2710-2719 Diffraction gratings Design and Characterization of a 170-GHz Resonant Diplexer for HighPower ECRH Systems. Wu, Z., +, TMTT Oct. 2015 3537-3546 Development and Computer-Aided Design of Metal Gratings for Microwave Mesh Polarizers. Alaverdyan, S. A., +, TMTT Aug. 2015 2509-2514 Reconfigurable Diffractive Antenna Based on Switchable Electrically Induced Transparency. Li, H., +, TMTT Mar. 2015 925-936 Robust Pressure-Actuated Liquid Metal Devices Showing Reconfigurable Electromagnetic Effects at GHz Frequencies. Cumby, B. L., +, TMTT Oct. 2015 3122-3130 Skew Incidence Plane-Wave Scattering From 2-D Dielectric Periodic Structures: Analysis by the Mortar-Element Method. Tibaldi, A., +, TMTT Jan. 2015 11-19 Digital filters A New Broadband Common-Mode Noise Absorption Circuit for High-Speed Differential Digital Systems. Hsiao, C.-Y., +, TMTT Jun. 2015 1894-1901 Digital radio A Hardware Efficient Implementation of a Digital Baseband Receiver for High-Capacity Millimeter-Wave Radios. He, Z., +, TMTT May 2015 16831692 Digital signal processing Guest Editorial. Draxler, P., TMTT Feb. 2015 557-558 Digital subscriber lines Estimation of Nonhomogeneous and Multi-Section Twisted-Pair Transmission-Line Parameters. Lindqvist, F., +, TMTT Nov. 2015 3568-3578 Digital video broadcasting A CMOS Spectrum Sensor Based on Quasi-Cyclostationary Feature Detection for Cognitive Radios. Sepidband, P., +, TMTT Dec. 2015 4098-4109 Behavioral Modeling and Predistortion of Power Amplifiers Under Sparsity Hypothesis. Reina-Tosina, J., +, TMTT Feb. 2015 745-753 Digital-analog conversion A 1.1-Gbit/s 10-GHz Outphasing Modulator With 23-dBm Output Power and 60-dB Dynamic Range in 45-nm CMOS SOI. Mehrjoo, M. S., +, TMTT Jul. 2015 2289-2300 + Check author entry for coauthors

A Reconfigurable 50-Mb/s-1 Gb/s Pulse Compression Radar Signal Processor With Offset Calibration in 90-nm CMOS. Li, J., +, TMTT Jan. 2015 266-278 An 8-bit 100-GS/s Distributed DAC in 28-nm CMOS for Optical Communications. Huang, H., +, TMTT Apr. 2015 1211-1218 Envelope Tracking of an RF High Power Amplifier With an 8-Level Digitally Controlled GaN-on-Si Supply Modulator. Florian, C., +, TMTT Aug. 2015 2589-2602 Dipole antenna arrays A 2.45 GHz Phased Array Antenna Unit Cell Fabricated Using 3-D MultiLayer Direct Digital Manufacturing. Ketterl, T. P., +, TMTT Dec. 2015 4382-4394 Modeling of Noisy EM Field Propagation Using Correlation Information. Russer, J. A., +, TMTT Jan. 2015 76-89 Dipole antennas On the Radiation Properties of Split-Ring Resonators (SRRs) at the Second Resonance. Zuffanelli, S., +, TMTT Jul. 2015 2133-2141 Robust Pressure-Actuated Liquid Metal Devices Showing Reconfigurable Electromagnetic Effects at GHz Frequencies. Cumby, B. L., +, TMTT Oct. 2015 3122-3130 Direction-of-arrival estimation Signal Detection and Noise Modeling of a 1-D Pulse-Based Ultra-Wideband Ranging System and Its Accuracy Assessment. Elkhouly, E., +, TMTT May 2015 1746-1757 Directional couplers Corrections to “Simple, Fast, and Effective Identification of an Equivalent Ports” [Jan 15 48-55]. Zappelli, Circuit of a Waveguide Junction With L., TMTT Mar. 2015 1108 Design and Analysis of 24-GHz Active Isolator and Quasi-Circulator. Chang, J.-F., +, TMTT Aug. 2015 2638-2649 Design of High-Directivity Wideband Microstrip Directional Coupler With Fragment-Type Structure. Wang, L., +, TMTT Dec. 2015 39623970 Modeling of Inline Transitions Between Different Waveguides as Impedance Inverters for the Use in Novel Filter Designs. Strauss, G., +, TMTT Nov. 2015 3663-3670 Simple, Fast, and Effective Identification of an Equivalent Circuit of a Waveguide Junction With Ports. Zappelli, L., TMTT Jan. 2015 48-55 Directive antennas A 37.5-mW 8-dBm-EIRP 15.5 -HPBW 338-GHz Terahertz Transmitter Using SoP Heterogeneous System Integration. Li, C.-H., +, TMTT Feb. 2015 470-480 Discriminators An FBAR/CMOS Frequency/Phase Discriminator and Phase Noise Reduction System. Imani, A., +, TMTT May 2015 1658-1665 Discs (structures) Microstrip Whispering-Gallery-Mode Resonator. Bunyaev, S. A., +, TMTT Sep. 2015 2776-2781 Dispersion (wave) Anomalous Dispersion Characteristics of Periodic Substrate Integrated Waveguides From Microwave to Terahertz. Li, X., +, TMTT Jul. 2015 2142-2153 Dispersion Equations of a Rectangular Tape Helix Slow-Wave Structure. Wei, W., +, TMTT May 2015 1445-1456 Dispersion relations Dispersion Equations of a Rectangular Tape Helix Slow-Wave Structure. Wei, W., +, TMTT May 2015 1445-1456 Dispersive media Comments on “Fractional Derivative Based FDTD Modeling of Transient Wave Propagation in Havriliak–Negami Media”. Rekanos, I. T., TMTT Dec. 2015 4188-4190 Distortion Closed-Loop Digital Predistortion (DPD) Using an Observation Path With Limited Bandwidth. Braithwaite, R. N., TMTT Feb. 2015 726-736 Concurrent Dual-Band Digital Predistortion With a Single Feedback Loop. Liu, Y., +, TMTT May 2015 1556-1568 Digital Compensation for Transmitter Leakage in Non-Contiguous Carrier Aggregation Applications With FPGA Implementation. Yu, C., +, TMTT Dec. 2015 4306-4318 Linearization and Imbalance Correction Techniques for Broadband Outphasing Power Amplifiers. Hwang, T., +, TMTT Jul. 2015 2185-2198 Distributed amplifiers InP DHBT Distributed Amplifiers With Up to 235-GHz Bandwidth. Eriksson, K., +, TMTT Apr. 2015 1334-1341

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Diversity reception Nonlinear Communication System With Harmonic Diversity. Cheong, P., +, TMTT Dec. 2015 4130-4149 Doppler radar A Low-IF Tag-Based Motion Compensation Technique for Mobile Doppler Radar Life Signs Monitoring. Rahman, A., +, TMTT Oct. 2015 3034-3041 Channel Imbalance Effects and Compensation for Doppler Radar Physiological Measurements. Yavari, E., +, TMTT Nov. 2015 3834-3842 Concurrent Detection of Vibration and Distance Using Unmodulated CW Doppler Vibration Radar With An Adaptive Beam-Steering Antenna. Nieh, C.-M., +, TMTT Jun. 2015 2069-2078 Gesture Sensing Using Retransmitted Wireless Communication Signals Based on Doppler Radar Technology. Wang, F.-K., +, TMTT Dec. 2015 4592-4602 Doppler shift Photonic Approach to Wide-Frequency-Range High-Resolution Microwave/Millimeter-Wave Doppler Frequency Shift Estimation. Zou, X., +, TMTT Apr. 2015 1421-1430 Driver circuits A Stacked-FET Linear SOI CMOS Cellular Antenna Switch With an Extremely Low-Power Biasing Strategy. Im, D., +, TMTT Jun. 2015 19641977 An Integrated Slot-Ring Traveling-Wave Radiator. Bowers, S. M., +, TMTT Apr. 2015 1154-1162 Source Degenerated Derivative Superposition Method for Linearizing RF FET Differential Amplifiers. Shin, H., +, TMTT Mar. 2015 1026-1035 E Eigenvalues and eigenfunctions A New Compact High-Power Microwave Phase Shifter. Chang, C., +, TMTT Jun. 2015 1875-1882 Accurate and Stable Matrix-Free Time-Domain Method in 3-D Unstructured Meshes for General Electromagnetic Analysis. Yan, J., +, TMTT Dec. 2015 4201-4214 An Inverse-Based Multifrontal Block Incomplete LU Preconditioner for the 3-D Finite-Element Eigenvalue Analysis of Lossy Slow-Wave Structures. Wang, H., +, TMTT Jul. 2015 2094-2106 DC and Imaginary Spurious Modes Suppression for Both Unbounded and Lossy Structures. Zekios, C. L., +, TMTT Jul. 2015 2082-2093 Determination of Normalized Magnetic Eigenfields in Microwave Cavities. Helsing, J., +, TMTT May 2015 1457-1467 Efficient Calculation of the Electromagnetic Scattering by Lossless or Lossy, Prolate or Oblate Dielectric Spheroids. Zouros, G. P., +, TMTT Mar. 2015 864-876 Energy Coupled Mode Theory for Electromagnetic Resonators. Elnaggar, S. Y., +, TMTT Jul. 2015 2115-2123 Mixed Spectral-Element Method for 3-D Maxwell's Eigenvalue Problem. Liu, N., +, TMTT Feb. 2015 317-325 Parametric History Analysis for Material Properties Using Finite Elements and Adaptive Perturbations. Gunel, S., +, TMTT Jan. 2015 90-98 The Mixed Spectral-Element Method for Anisotropic, Lossy, and Open Waveguides. Liu, N., +, TMTT Oct. 2015 3094-3102 Electric connectors Robust Pressure-Actuated Liquid Metal Devices Showing Reconfigurable Electromagnetic Effects at GHz Frequencies. Cumby, B. L., +, TMTT Oct. 2015 3122-3130 Electric fields Development of the Optimization Framework for Low-Power Wireless Power Transfer Systems. Lee, S. B., +, TMTT Mar. 2015 813-820 Synthesis and Design of Programmable Subwavelength Coil Array for NearField Manipulation. Gao, F., +, TMTT Sep. 2015 2971-2982 Time-Domain Electromagnetic Analysis of Multilayer Structures Using the Surface Equivalent Principle and Mixed-Potential Integral Equations. Maftooli, H., +, TMTT Jan. 2015 99-106 Electric impedance measurement Design and Analysis of Shielded Vertically Stacked Ring Resonator as Complex Permittivity Sensor for Petroleum Oils. Kulkarni, S., +, TMTT Aug. 2015 2411-2417 Electric potential A Three-Phase Wireless-Power-Transfer System for Online Electric Vehicles With Reduction of Leakage Magnetic Fields. Kim, M., +, TMTT Nov. 2015 3806-3813 + Check author entry for coauthors

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Electric sensing devices Design and Analysis of Shielded Vertically Stacked Ring Resonator as Complex Permittivity Sensor for Petroleum Oils. Kulkarni, S., +, TMTT Aug. 2015 2411-2417 Electrical conductivity MRI-Based Electrical Property Retrieval by Applying the Finite-Element Method (FEM). Huang, S. Y., +, TMTT Aug. 2015 2482-2490 Electrical contacts Reliability Analysis of Ku-Band 5-bit Phase Shifters Using MEMS SP4T and SPDT Switches. Dey, S., +, TMTT Dec. 2015 3997-4012 Electrical resistivity Broadband Microwave Attenuator Based on Few Layer Graphene Flakes. Pierantoni, L., +, TMTT Aug. 2015 2491-2497 Electro-optical modulation Analysis of Dual Wavelength Linearization Technique for Radio-Over-Fiber Systems With Electro-Absorption Modulator. Zhu, R., +, TMTT Aug. 2015 2692-2702 Electroabsorption Analysis of Dual Wavelength Linearization Technique for Radio-Over-Fiber Systems With Electro-Absorption Modulator. Zhu, R., +, TMTT Aug. 2015 2692-2702 Electrodynamics Transient Power Loss Density of Electromagnetic Pulse in Debye Media. Huang, K., +, TMTT Jan. 2015 135-140 Electroencephalography Synthesis and Design of Programmable Subwavelength Coil Array for NearField Manipulation. Gao, F., +, TMTT Sep. 2015 2971-2982 Electromagnetic compatibility An Investigation of Electromagnetic Radiated Emission and Interference From Multi-Coil Wireless Power Transfer Systems Using Resonant Magnetic Field Coupling. Kong, S., +, TMTT Mar. 2015 833-846 Electromagnetic devices Rapid Yield Estimation and Optimization of Microwave Structures Exploiting Feature-Based Statistical Analysis. Koziel, S., +, TMTT Jan. 2015 107-114 Resonator Voltage Prediction in Microwave Bandpass Filters. Vanin, F. M., +, TMTT Feb. 2015 397-402 Electromagnetic field theory Alternative Method for Making Explicit FDTD Unconditionally Stable. Gaffar, Md., +, TMTT Dec. 2015 4215-4224 Electromagnetic fields Advanced Power Control Scheme in Wireless Power Transmission for Human Protection From EM Field. Kim, S.-M., +, TMTT Mar. 2015 847-856 Development of the Optimization Framework for Low-Power Wireless Power Transfer Systems. Lee, S. B., +, TMTT Mar. 2015 813-820 Dispersion Equations of a Rectangular Tape Helix Slow-Wave Structure. Wei, W., +, TMTT May 2015 1445-1456 Enhanced Analysis and Design Method of Dual-Band Coil Module for NearField Wireless Power Transfer Systems. Kung, M.-L., +, TMTT Mar. 2015 821-832 Modeling of Noisy EM Field Propagation Using Correlation Information. Russer, J. A., +, TMTT Jan. 2015 76-89 Electromagnetic interference An Investigation of Electromagnetic Radiated Emission and Interference From Multi-Coil Wireless Power Transfer Systems Using Resonant Magnetic Field Coupling. Kong, S., +, TMTT Mar. 2015 833-846 Broadband Dielectric Spectroscopy of Composites Filled With Various Carbon Materials. Bellucci, S., +, TMTT Jun. 2015 2024-2031 Modeling of Noisy EM Field Propagation Using Correlation Information. Russer, J. A., +, TMTT Jan. 2015 76-89 Spur Reduction Techniques With a Switched-Capacitor Feedback Differential PLL and a DLL-Based SSCG in UHF RFID Transmitter. Lee, I.-Y., +, TMTT Apr. 2015 1202-1210 Electromagnetic metamaterials Planar Distributed Full-Tensor Anisotropic Metamaterials for Transformation Electromagnetics. Nagayama, T., +, TMTT Dec. 2015 3851-3861 Electromagnetic modeling Corrections to “Simple, Fast, and Effective Identification of an Equivalent Ports” [Jan 15 48-55]. Zappelli, Circuit of a Waveguide Junction With L., TMTT Mar. 2015 1108 Guest Editorial [Mini-Special Issue on 2014 IEEE International Conference on Numerical Electromagnetic Modeling and Optimization for RF,

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Microwave, and Terahertz Applications (NEMO2014. Bozzi, M., +, TMTT Jan. 2015 1-2 Electromagnetic pulse Transient Power Loss Density of Electromagnetic Pulse in Debye Media. Huang, K., +, TMTT Jan. 2015 135-140 Electromagnetic shielding Broadband Dielectric Spectroscopy of Composites Filled With Various Carbon Materials. Bellucci, S., +, TMTT Jun. 2015 2024-2031 Robust Pressure-Actuated Liquid Metal Devices Showing Reconfigurable Electromagnetic Effects at GHz Frequencies. Cumby, B. L., +, TMTT Oct. 2015 3122-3130 Electromagnetic wave absorption Fractal Frequency-Selective Surface Embedded Thin Broadband Microwave Absorber Coatings Using Heterogeneous Composites. Panwar, R., +, TMTT Aug. 2015 2438-2448 Investigating the Broadband Microwave Absorption of Nanodiamond Impurities. Cuenca, J. A., +, TMTT Dec. 2015 4110-4118 Electromagnetic wave attenuation Direct -Transform Implementation of the CFS-PML Based on MemoryMinimized Method. Feng, N., +, TMTT Mar. 2015 877-882 Robust Pressure-Actuated Liquid Metal Devices Showing Reconfigurable Electromagnetic Effects at GHz Frequencies. Cumby, B. L., +, TMTT Oct. 2015 3122-3130 Electromagnetic wave polarization A 2.45 GHz Phased Array Antenna Unit Cell Fabricated Using 3-D MultiLayer Direct Digital Manufacturing. Ketterl, T. P., +, TMTT Dec. 2015 4382-4394 Development and Computer-Aided Design of Metal Gratings for Microwave Mesh Polarizers. Alaverdyan, S. A., +, TMTT Aug. 2015 2509-2514 Dynamic-Range Enhancement for a Microwave Photonic Link Based on a Polarization Modulator. Chen, X., +, TMTT Jul. 2015 2384-2389 High-Speed Signal Transmission at W-Band Over Dielectric-Coated Metallic Hollow Fiber. Yu, J., +, TMTT Jun. 2015 1836-1842 Robust Pressure-Actuated Liquid Metal Devices Showing Reconfigurable Electromagnetic Effects at GHz Frequencies. Cumby, B. L., +, TMTT Oct. 2015 3122-3130 Electromagnetic wave propagation Accurate and Stable Matrix-Free Time-Domain Method in 3-D Unstructured Meshes for General Electromagnetic Analysis. Yan, J., +, TMTT Dec. 2015 4201-4214 Application of Coherence Theory to Modeling of Blackbody Radiation at Close Range. Gu, D., +, TMTT May 2015 1475-1488 Computational Time Reversal—A Frontier in Electromagnetic Structure Synthesis and Design. Hoefer, W. J. R., TMTT Jan. 2015 3-10 Modeling of Noisy EM Field Propagation Using Correlation Information. Russer, J. A., +, TMTT Jan. 2015 76-89 Scattering by Conducting Cylinders Below a Dielectric Layer With a Fast Noniterative Approach. Ponti, C., +, TMTT Jan. 2015 30-39 Electromagnetic wave reflection Scattering by Conducting Cylinders Below a Dielectric Layer With a Fast Noniterative Approach. Ponti, C., +, TMTT Jan. 2015 30-39 Electromagnetic wave refraction Polarization Considerations for Scalar Huygens Metasurfaces and Characterization for 2-D Refraction. Wong, J. P. S., +, TMTT Mar. 2015 913-924 Electromagnetic wave scattering Computational Time Reversal—A Frontier in Electromagnetic Structure Synthesis and Design. Hoefer, W. J. R., TMTT Jan. 2015 3-10 Efficient Calculation of the Electromagnetic Scattering by Lossless or Lossy, Prolate or Oblate Dielectric Spheroids. Zouros, G. P., +, TMTT Mar. 2015 864-876 Electromagnetic Scattering by a General Rotationally Symmetric Inhomogeneous Anisotropic Sphere. Zouros, G. P., +, TMTT Oct. 2015 3054-3065 Fast Solution of the Electromagnetic Scattering by Composite Spheroidal–Spherical and Spherical–Spheroidal Configurations. Zouros, G. P., +, TMTT Oct. 2015 3042-3053 Modal Loss Analysis of - and -Plane Filtering Structures. Accatino, L., +, TMTT Jan. 2015 40-47 Non-Reflecting SFBF Termination Inverting From TFSF Discontinuity Decomposition. Tan, T., TMTT Sep. 2015 2710-2719 Scattering by Conducting Cylinders Below a Dielectric Layer With a Fast Noniterative Approach. Ponti, C., +, TMTT Jan. 2015 30-39

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Skew Incidence Plane-Wave Scattering From 2-D Dielectric Periodic Structures: Analysis by the Mortar-Element Method. Tibaldi, A., +, TMTT Jan. 2015 11-19 Time-Domain Electromagnetic Analysis of Multilayer Structures Using the Surface Equivalent Principle and Mixed-Potential Integral Equations. Maftooli, H., +, TMTT Jan. 2015 99-106 Electromagnetic wave transmission Scattering by Conducting Cylinders Below a Dielectric Layer With a Fast Noniterative Approach. Ponti, C., +, TMTT Jan. 2015 30-39 TLM Nodes: A New Look at an Old Problem. Salinas, A., +, TMTT Aug. 2015 2449-2458 Electromagnetic waves Miniaturized Transmission-Line Sensor for Broadband Dielectric Characterization of Biological Liquids and Cell Suspensions. Meyne nee Haase, N., +, TMTT Oct. 2015 3026-3033 Electron beams An Improved Broadband Boundary Condition for the RF Field in Gyrotron Interaction Modeling. Wu, C., +, TMTT Aug. 2015 2459-2467 Electron device testing A 1.3–2.4-GHz 3.1-mW VCO Using Electro-Thermo- Mechanically Tunable Self-Assembled MEMS Inductor on HR Substrate. Bhattacharya, A., +, TMTT Feb. 2015 459-469 Electron gas On the Design of Gyroelectric Resonators and Circulators Using a Magnetically Biased 2-D Electron Gas (2-DEG). Jawad, G. N., +, TMTT May 2015 1512-1517 Electronic design automation Hybrid Nonlinear Modeling Using Adaptive Sampling. Barmuta, P., +, TMTT Dec. 2015 4501-4510 Electronics packaging 3D-Printed Origami Packaging With Inkjet-Printed Antennas for RF Harvesting Sensors. Kimionis, J., +, TMTT Dec. 2015 4521-4532 High Rejection, Self-Packaged Low-Pass Filter Using Multilayer Liquid Crystal Polymer Technology. Cervera, F., +, TMTT Dec. 2015 3920-3928 Electrostatic actuators Monolithic Millimeter-Wave MEMS Waveguide Switch. Vahabisani, N., +, TMTT Feb. 2015 340-351 Electrostatic discharge Generic Electrostatic Discharges Protection Solutions for RF and Millimeter-Wave Applications. Lim, T., +, TMTT Nov. 2015 3747-3759 Electrostatics Electrical Analysis of Cell Membrane Poration by an Intense Nanosecond Pulsed Electric Field Using an Atomistic-to-Continuum Method. Kohler, S., +, TMTT Jun. 2015 2032-2040 Elemental semiconductors 0.8/2.2-GHz Programmable Active Bandpass Filters in InP/Si BiCMOS Technology. Xu, Z., +, TMTT Apr. 2015 1219-1227 160-GHz to 1-THz Multi-Color Active Imaging With a Lens-Coupled SiGe HBT Chip-Set. Statnikov, K., +, TMTT Feb. 2015 520-532 -Band Spatially Combined Power Amplifier Arrays in 45-nm CMOS SOI. Hanafi, B., +, TMTT Jun. 2015 1937-1950 A Stacked-FET Linear SOI CMOS Cellular Antenna Switch With an Extremely Low-Power Biasing Strategy. Im, D., +, TMTT Jun. 2015 19641977 An E-Band Power Amplifier With Broadband Parallel-Series Power Combiner in 40-nm CMOS. Zhao, D., +, TMTT Feb. 2015 683-690 Envelope Tracking of an RF High Power Amplifier With an 8-Level Digitally Controlled GaN-on-Si Supply Modulator. Florian, C., +, TMTT Aug. 2015 2589-2602 Microwave Properties of an Inhomogeneous Optically Illuminated Plasma in a Microstrip Gap. Gamlath, C. D., +, TMTT Feb. 2015 374-383 Supply-Modulated Radar Transmitters With Amplitude-Modulated Pulses. Zai, A., +, TMTT Sep. 2015 2953-2964 Tunable 500–1200-MHz Dual-Band and Wide Bandwidth Notch Filters Using RF Transformers. Ko, C.-H., +, TMTT Jun. 2015 1854-1862 Elliptic filters Propagating Waveguide Filters Using Dielectric Resonators. Tomassoni, C., +, TMTT Dec. 2015 4366-4375 Reflection-Mode Bandstop Filters With Minimum Through-Line Length. Naglich, E. J., +, TMTT Oct. 2015 3479-3486 Synthesis and Design of High-Selectivity Wideband Quasi-Elliptic Bandpass Filters Using Multiconductor Transmission Lines. Sanchez-Martinez, J. J., +, TMTT Jan. 2015 198-208

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 63, NO. 12, DECEMBER 2015

Synthesis of Inline Mixed Coupled Quasi-Elliptic Bandpass Filters Based on Resonators. Zhang, S., +, TMTT Oct. 2015 3487-3493 Encoding Concurrent Multiband Digital Outphasing Transmitter Architecture Using Multidimensional Power Coding. Chung, S., +, TMTT Feb. 2015 598-613 Real-World Implementation Challenges of a Novel Dual-Polarized Compact Printable Chipless RFID Tag. Islam, M. A., +, TMTT Dec. 2015 4581-4591 Endoscopes Propagation, Power Absorption, and Temperature Analysis of UWB Wireless Capsule Endoscopy Devices Operating in the Human Body. Thotahewa, K. M. S., +, TMTT Nov. 2015 3823-3833 Tracking Optimal Efficiency of Magnetic Resonance Wireless Power Transfer System for Biomedical Capsule Endoscopy. Na, K., +, TMTT Jan. 2015 295-304 Energy conservation Theoretical Energy-Conversion Efficiency for Energy-Harvesting Circuits Under Power-Optimized Waveform Excitation. Valenta, C. R., +, TMTT May 2015 1758-1767 Energy efficiency Guest Editorial. KIM, J., +, TMTT Mar. 2015 778-779 Energy harvesting 3D-Printed Origami Packaging With Inkjet-Printed Antennas for RF Harvesting Sensors. Kimionis, J., +, TMTT Dec. 2015 4521-4532 A 2.45-GHz Energy-Autonomous Wireless Power Relay Node. Del Prete, M., +, TMTT Dec. 2015 4511-4520 A Multi-Band Stacked RF Energy Harvester With RF-to-DC Efficiency Up to 84%. Kuhn, V., +, TMTT May 2015 1768-1778 Ambient RF Energy Harvesting From a Two-Way Talk Radio for Flexible Wearable Wireless Sensor Devices Utilizing Inkjet Printing Technologies. Bito, J., +, TMTT Dec. 2015 4533-4543 Breaking the Efficiency Barrier for Ambient Microwave Power Harvesting With Heterojunction Backward Tunnel Diodes. Lorenz, C. H. P., +, TMTT Dec. 2015 4544-4555 Cooperative Integration of Harvesting RF Sections for Passive RFID Communication. Andia Vera, G., +, TMTT Dec. 2015 4556-4566 Low-Input Power-Level CMOS RF Energy-Harvesting Front End. Abouzied, M. A., +, TMTT Nov. 2015 3794-3805 Theoretical Energy-Conversion Efficiency for Energy-Harvesting Circuits Under Power-Optimized Waveform Excitation. Valenta, C. R., +, TMTT May 2015 1758-1767 Energy storage Resonator Voltage Prediction in Microwave Bandpass Filters. Vanin, F. M., +, TMTT Feb. 2015 397-402 EPR spectroscopy A Single-Chip Electron Paramagnetic Resonance Transceiver in 0.13- m SiGe BiCMOS. Yang, X., +, TMTT Nov. 2015 3727-3735 Equivalent circuits (InP) HEMT Small-Signal Equivalent-Circuit Extraction as a Function of Temperature. Alt, A. R., +, TMTT Sep. 2015 2751-2755 A Balanced-to-Unbalanced Microstrip Power Divider With Filtering Function. Xu, K., +, TMTT Aug. 2015 2561-2569 A Broadband and Equivalent-Circuit Model for Millimeter-Wave On-Chip M:N Six-Port Transformers and Baluns. Gao, Z., +, TMTT Oct. 2015 31093121 An Improved Small-Signal Model for SiGe HBT Under OFF-State, Derived From Distributed Network and Corresponding Model Parameter Extraction. Sun, Y., +, TMTT Oct. 2015 3131-3141 An Improved VBIC Large-Signal Equivalent-Circuit Model for SiGe HBT With an Inductive Breakdown Network by -Parameters. Lee, C.-I., +, TMTT Sep. 2015 2756-2763 Balanced Dual-Band Bandpass Filter With Multiple Transmission Zeros Using Doubly Short-Ended Resonator Coupled Line. Yang, L., +, TMTT Jul. 2015 2225-2232 Corrections to “Compact Conical-Line Power Combiner Design Using Circuit Models” [Nov 14 2650-2658]. Beyers, R. D., +, TMTT Jul. 2015 2391 Corrections to “Simple, Fast, and Effective Identification of an Equivalent Ports” [Jan 15 48-55]. Zappelli, Circuit of a Waveguide Junction With L., TMTT Mar. 2015 1108 Design and Modeling of Spoof Surface Plasmon Modes-Based Microwave Slow-Wave Transmission Line. Kianinejad, A., +, TMTT Jun. 2015 18171825 Design of Waveguide Microwave Pulse Compressors Using Equivalent Circuits. Savaidis, S. P., +, TMTT Jan. 2015 125-134

+ Check author entry for coauthors

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Efficient Statistical Simulation of Microwave Devices Via Stochastic Testing-Based Circuit Equivalents of Nonlinear Components. Manfredi, P., +, TMTT May 2015 1502-1511 Exact Synthesis of Full- and Half-Symmetric Rat-Race Ring Hybrids With or Without Impedance Transforming Characteristics. Chou, P.-J., +, TMTT Dec. 2015 3971-3980 Expedited Geometry Scaling of Compact Microwave Passives by Means of Inverse Surrogate Modeling. Koziel, S., +, TMTT Dec. 2015 4019-4026 Free-Positioning Wireless Charging System for Small Electronic Devices Using a Bowl-Shaped Transmitting Coil. Kim, J., +, TMTT Mar. 2015 791-800 Narrowband Coupled-Line Bandstop Filter With Absorptive Stopband. Shao, J.-Y., +, TMTT Oct. 2015 3469-3478 Physics-Based Via and Waveguide Models for Efficient SIW Simulations in Multilayer Substrates. Preibisch, J. B., +, TMTT Jun. 2015 1809-1816 RF Small-Signal and Noise Modeling Including Parameter Extraction of Nanoscale MOSFET From Weak to Strong Inversion. Chalkiadaki, M.-A., +, TMTT Jul. 2015 2173-2184 Simple, Fast, and Effective Identification of an Equivalent Circuit of a Waveguide Junction With Ports. Zappelli, L., TMTT Jan. 2015 48-55 Transient Power Loss Density of Electromagnetic Pulse in Debye Media. Huang, K., +, TMTT Jan. 2015 135-140 Wideband Balanced Network with High Isolation Using Double-Sided Parallel-Strip Line. Feng, W., +, TMTT Dec. 2015 4013-4018 Error statistics High-Speed Signal Transmission at W-Band Over Dielectric-Coated Metallic Hollow Fiber. Yu, J., +, TMTT Jun. 2015 1836-1842 Partitioned Distortion Mitigation in LTE Radio Uplink to Enhance Transmitter Efficiency. Amiri, M. V., +, TMTT Aug. 2015 2661-2671 Performance Estimation for Broadband Multi-Gigabit Millimeter- and SubMillimeter-Wave Wireless Communication Links. Antes, J., +, TMTT Oct. 2015 3288-3299 Estimation theory Material Characterization of Arbitrarily Shaped Dielectrics Based on Reflected Pulse Characteristics. Chan, K.K.M., +, TMTT May 2015 1700-1709 Rapid Yield Estimation and Optimization of Microwave Structures Exploiting Feature-Based Statistical Analysis. Koziel, S., +, TMTT Jan. 2015 107-114 Extrapolation Hybrid Nonlinear Modeling Using Adaptive Sampling. Barmuta, P., +, TMTT Dec. 2015 4501-4510

F Fabrics Textile Microwave Components in Substrate Integrated Waveguide Technology. Moro, R., +, TMTT Feb. 2015 422-432 Fading channels Nonlinear Communication System With Harmonic Diversity. Cheong, P., +, TMTT Dec. 2015 4130-4149 Feature extraction A CMOS Spectrum Sensor Based on Quasi-Cyclostationary Feature Detection for Cognitive Radios. Sepidband, P., +, TMTT Dec. 2015 4098-4109 Computational Feasibility Study of Contrast-Enhanced Thermoacoustic Imaging for Breast Cancer Detection Using Realistic Numerical Breast Phantoms. Wang, X., +, TMTT May 2015 1489-1501 Feedback Multi-Standard Hybrid PLL With Low Phase-Noise Characteristics for GSM/EDGE and LTE Applications. Choi, Y.-C., +, TMTT Oct. 2015 3254-3264 Feedback amplifiers Concurrent Dual-Band Digital Predistortion With a Single Feedback Loop. Liu, Y., +, TMTT May 2015 1556-1568 Transformer-Feedback Interstage Bandwidth Enhancement for MMIC Multistage Amplifiers. Nikandish, G., +, TMTT Feb. 2015 441-448 Feedforward Real-Time Adaptive Transmitter Leakage Cancelling in 5.8-GHz Full-Duplex Transceivers. Maddio, S., +, TMTT Feb. 2015 509-519 Femtocellular radio Asymmetric Broadband Doherty Power Amplifier Using GaN MMIC for Femto-Cell Base-Station. Jee, S., +, TMTT Sep. 2015 2802-2810

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Ferrite filters A High-Power Low-Loss Continuously Tunable Bandpass Filter With Transversely Biased Ferrite-Loaded Coaxial Resonators. Acar, O., +, TMTT Oct. 2015 3425-3432 Ferrite phase shifters An Integrable SIW Phase Shifter in a Partially Magnetized Ferrite LTCC Package. Nafe, A., +, TMTT Jul. 2015 2264-2274 Ferrites Free-Positioning Wireless Charging System for Small Electronic Devices Using a Bowl-Shaped Transmitting Coil. Kim, J., +, TMTT Mar. 2015 791-800 Ferroelectric capacitors Influence of Numerical Method and Geometry Used by Maxwell's Equation Solvers on Simulations of Ferroelectric Thin-Film Capacitors. Furlan, V., +, TMTT Mar. 2015 891-896 Ferroelectric devices High-Tunability and High- -Factor Integrated Ferroelectric Circuits up to Millimeter Waves. De Paolis, R., +, TMTT Aug. 2015 2570-2578 Ferroelectric thin films Influence of Numerical Method and Geometry Used by Maxwell's Equation Solvers on Simulations of Ferroelectric Thin-Film Capacitors. Furlan, V., +, TMTT Mar. 2015 891-896 Field effect MIMIC 130-320-GHz CMOS Harmonic Down-Converters Around and Above the Cutoff Frequency. Khamaisi, B., +, TMTT Jul. 2015 2275-2288 76–81-GHz CMOS Transmitter With a Phase-Locked-Loop-Based Multichirp Modulator for Automotive Radar. Park, J., +, TMTT Apr. 2015 13991408 A 40-nm CMOS E-Band 4-Way Power Amplifier With Neutralized Bootstrapped Cascode Amplifier and Optimum Passive Circuits. Zhao, D., +, TMTT Dec. 2015 4083-4089 A Blocker-Tolerant Current Mode 60-GHz Receiver With 7.5-GHz Bandwidth and 3.8-dB Minimum NF in 65-nm CMOS. Wu, H., +, TMTT Mar. 2015 1053-1062 A mm-Wave Segmented Power Mixer. Dasgupta, K., +, TMTT Apr. 2015 1118-1129 A Wide-Band CMOS to Waveguide Transition at mm-Wave Frequencies With Wire-Bonds. Jameson, S., +, TMTT Sep. 2015 2741-2750 An E-Band Power Amplifier With Broadband Parallel-Series Power Combiner in 40-nm CMOS. Zhao, D., +, TMTT Feb. 2015 683-690 Analysis and Design of a 14.1-mW 50/100-GHz Transformer-Based PLL With Embedded Phase Shifter in 65-nm CMOS. Chao, Y., +, TMTT Apr. 2015 1193-1201 Analysis and Design of Millimeter-Wave Power Amplifier Using Stacked-FET Structure. Kim, Y., +, TMTT Feb. 2015 691-702 Large-Scale Power Combining and Mixed-Signal Linearizing Architectures for Watt-Class mmWave CMOS Power Amplifiers. Bhat, R., +, TMTT Feb. 2015 703-718 Mutual Synchronization for Power Generation and Beam-Steering in CMOS With On-Chip Sense Antennas Near 200 GHz. Sengupta, K., +, TMTT Sep. 2015 2867-2876 Transformer-Based Doherty Power Amplifiers for mm-Wave Applications in 40-nm CMOS. Kaymaksut, E., +, TMTT Apr. 2015 1186-1192 Transmission of Signals With Complex Constellations Using Millimeter-Wave Spatially Power-Combined CMOS Power Amplifiers and Digital Predistortion. Dabag, H.-T., +, TMTT Jul. 2015 2364-2374 Wide Tuning-Range mm-Wave Voltage-Controlled Oscillator Employing an Artificial Magnetic Transmission Line. Yanay, N., +, TMTT Apr. 2015 13421352 Field effect MMIC 160-GHz to 1-THz Multi-Color Active Imaging With a Lens-Coupled SiGe HBT Chip-Set. Statnikov, K., +, TMTT Feb. 2015 520-532 A 0.2–3.6-GHz 10-dBm B1dB 29-dBm IIP3 Tunable Filter for Transmit Leakage Suppression in SAW-Less 3G/4G FDD Receivers. Luo, C., +, TMTT Oct. 2015 3514-3524 A 1.3–2.4-GHz 3.1-mW VCO Using Electro-Thermo- Mechanically Tunable Self-Assembled MEMS Inductor on HR Substrate. Bhattacharya, A., +, TMTT Feb. 2015 459-469 A 5.9-GHz Fully Integrated GaN Frontend Design With Physics-Based RF Compact Model. Choi, P., +, TMTT Apr. 2015 1163-1173 An Integrated 700–1200-MHz Class-F PA With Tunable Harmonic Terminations in 0.13- m CMOS. Sessou, K. K., +, TMTT Apr. 2015 1315-1323 Design and Analysis on Bidirectionally and Passively Coupled QVCO With Nonlinear Coupler. Kuo, N.-C., +, TMTT Apr. 2015 1130-1141 + Check author entry for coauthors

Field effect transistor circuits A 1.1-Gbit/s 10-GHz Outphasing Modulator With 23-dBm Output Power and 60-dB Dynamic Range in 45-nm CMOS SOI. Mehrjoo, M. S., +, TMTT Jul. 2015 2289-2300 Field effect transistors A Novel Load Mismatch Detection and Correction Technique for 3G/4G Load Insensitive Power Amplifier Application. Ji, D., +, TMTT May 2015 1530-1543 A Simple Method to Estimate the Output Power and Efficiency Load–Pull Contours of Class-B Power Amplifiers. Pedro, J. C., +, TMTT Apr. 2015 1239-1249 Active Detuning of MRI Receive Coils with GaN FETs. Twieg, M., +, TMTT Dec. 2015 4169-4177 RF Linearity Performance Potential of Short-Channel Graphene Field-Effect Transistors. Alam, A. U., +, TMTT Dec. 2015 3874-3887 Source Degenerated Derivative Superposition Method for Linearizing RF FET Differential Amplifiers. Shin, H., +, TMTT Mar. 2015 1026-1035 Field programmable gate arrays Concurrent Dual-Band Modeling and Digital Predistortion in the Presence of Unfilterable Harmonic Signal Interference. Rawat, M., +, TMTT Feb. 2015 625-637 Digital Compensation for Transmitter Leakage in Non-Contiguous Carrier Aggregation Applications With FPGA Implementation. Yu, C., +, TMTT Dec. 2015 4306-4318 Efficient Least-Squares 2-D-Cubic Spline for Concurrent Dual-Band Systems. Naraharisetti, N., +, TMTT Jul. 2015 2199-2210 Filtering theory Concurrent Dual-Band Modeling and Digital Predistortion in the Presence of Unfilterable Harmonic Signal Interference. Rawat, M., +, TMTT Feb. 2015 625-637 Guest Editorial. Boria, V. E., +, TMTT Oct. 2015 3321-3323 Filters Dynamic Measurement of Dielectric Properties of Materials at High Temperature During Microwave Heating in a Dual Mode Cylindrical Cavity. Catala-Civera, J. M., +, TMTT Sep. 2015 2905-2914 Finite difference methods Authors’ Reply. Mescia, L., +, TMTT Dec. 2015 4191-4193 Electrical Analysis of Cell Membrane Poration by an Intense Nanosecond Pulsed Electric Field Using an Atomistic-to-Continuum Method. Kohler, S., +, TMTT Jun. 2015 2032-2040 Finite difference time-domain analysis Alternative Method for Making Explicit FDTD Unconditionally Stable. Gaffar, Md., +, TMTT Dec. 2015 4215-4224 Comments on “Fractional Derivative Based FDTD Modeling of Transient Wave Propagation in Havriliak–Negami Media”. Rekanos, I. T., TMTT Dec. 2015 4188-4190 Direct -Transform Implementation of the CFS-PML Based on MemoryMinimized Method. Feng, N., +, TMTT Mar. 2015 877-882 Non-Reflecting SFBF Termination Inverting From TFSF Discontinuity Decomposition. Tan, T., TMTT Sep. 2015 2710-2719 Reduction of Exposure Inhomogeneity for Millimeter-Wave Experiments on Cells In Vitro. Zhao, J., +, TMTT Feb. 2015 533-545 Finite element analysis A Three-Phase Wireless-Power-Transfer System for Online Electric Vehicles With Reduction of Leakage Magnetic Fields. Kim, M., +, TMTT Nov. 2015 3806-3813 An Efficient Hybrid Finite-Element Analysis of Multiple Vias Sharing the Same Anti-Pad in an Arbitrarily Shaped Parallel-Plate Pair. Zhang, Y.-J., +, TMTT Mar. 2015 883-890 An Inverse-Based Multifrontal Block Incomplete LU Preconditioner for the 3-D Finite-Element Eigenvalue Analysis of Lossy Slow-Wave Structures. Wang, H., +, TMTT Jul. 2015 2094-2106 Anomalous Dispersion Characteristics of Periodic Substrate Integrated Waveguides From Microwave to Terahertz. Li, X., +, TMTT Jul. 2015 2142-2153 DC and Imaginary Spurious Modes Suppression for Both Unbounded and Lossy Structures. Zekios, C. L., +, TMTT Jul. 2015 2082-2093 Development and Computer-Aided Design of Metal Gratings for Microwave Mesh Polarizers. Alaverdyan, S. A., +, TMTT Aug. 2015 2509-2514 Direct Finite-Element Solver of Linear Complexity for Large-Scale 3-D Electromagnetic Analysis and Circuit Extraction. Zhou, B., +, TMTT Oct. 2015 3066-3080

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 63, NO. 12, DECEMBER 2015

Electrothermal Effects on Performance of GaAs HBT Power Amplifier During Power Versus Time (PVT) Variation at GSM/DCS Bands. Lin, L., +, TMTT Jun. 2015 1951-1963 Micromachined Room-Temperature Air-Suspended Ni/Cr Nanobolometer. Yang, H.-H., +, TMTT Nov. 2015 3760-3767 Mixed Spectral-Element Method for 3-D Maxwell's Eigenvalue Problem. Liu, N., +, TMTT Feb. 2015 317-325 Mode Filters for Oversized Rectangular Waveguides: A Modal Approach. Ceccuzzi, S., +, TMTT Aug. 2015 2468-2481 MRI-Based Electrical Property Retrieval by Applying the Finite-Element Method (FEM). Huang, S. Y., +, TMTT Aug. 2015 2482-2490 Parametric History Analysis for Material Properties Using Finite Elements and Adaptive Perturbations. Gunel, S., +, TMTT Jan. 2015 90-98 FIR filters Digitally Equalized Doherty RF Front-End Architecture for Broadband and Multistandard Wireless Transmitters. Darraji, R., +, TMTT Jun. 2015 19781988 FM radar A 77-GHz FMCW Radar System Using On-Chip Waveguide Feeders in 65-nm CMOS. Cui, C., +, TMTT Nov. 2015 3736-3746 Multichannel Backscatter Communication and Ranging for Distributed Sensing With an FMCW Radar. Cnaan-On, I., +, TMTT Jul. 2015 2375-2383 Supply-Modulated Radar Transmitters With Amplitude-Modulated Pulses. Zai, A., +, TMTT Sep. 2015 2953-2964 Fourier series 3-D Fourier Series Based Digital Predistortion Technique for Concurrent Dual-Band Envelope Tracking With Reduced Envelope Bandwidth. Lin, Y., +, TMTT Sep. 2015 2764-2775 Fourier transforms 3-D Radiometric Aperture Synthesis Imaging. Salmon, N. A., TMTT Nov. 2015 3579-3587 Time-Domain Electromagnetic Analysis of Multilayer Structures Using the Surface Equivalent Principle and Mixed-Potential Integral Equations. Maftooli, H., +, TMTT Jan. 2015 99-106 Fractals Fractal Frequency-Selective Surface Embedded Thin Broadband Microwave Absorber Coatings Using Heterogeneous Composites. Panwar, R., +, TMTT Aug. 2015 2438-2448 Fraunhofer diffraction 3-D Radiometric Aperture Synthesis Imaging. Salmon, N. A., TMTT Nov. 2015 3579-3587 Frequency control Experimental Control and Design of Low-Frequency Bias Networks for Dynamically Biased Amplifiers. Pelaz, J., +, TMTT Jun. 2015 1923-1936 Frequency converters High-Order Subharmonic Millimeter-Wave Mixer Based on Few-Layer Graphene. Vazquez Antuna, C., +, TMTT Apr. 2015 1361-1369 Frequency dividers A Sub-GHz Wireless Transmitter Utilizing a Multi-Class-Linearized PA and Time-Domain Wideband-Auto I/Q-LOFT Calibration for IEEE 802.11af WLAN. Un, K.-F., +, TMTT Oct. 2015 3228-3241 Analysis of Nonlinearities in Injection-Locked Frequency Dividers. Gui, X., +, TMTT Mar. 2015 945-953 Designs of K-Band Divide-by-2 and Divide-by-3 Injection-Locked Frequency Divider With Darlington Topology. Chien, K.-H., +, TMTT Sep. 2015 2877-2888 Optimized Design of Frequency Dividers Based on Varactor-Inductor Cells. Ponton, M., +, TMTT Dec. 2015 4458-4472 Frequency division multiplexing A 0.2–3.6-GHz 10-dBm B1dB 29-dBm IIP3 Tunable Filter for Transmit Leakage Suppression in SAW-Less 3G/4G FDD Receivers. Luo, C., +, TMTT Oct. 2015 3514-3524 Frequency measurement Design and Analysis of Shielded Vertically Stacked Ring Resonator as Complex Permittivity Sensor for Petroleum Oils. Kulkarni, S., +, TMTT Aug. 2015 2411-2417 Multi-Frequency Measurements for Supply Modulated Transmitters. Schafer, S., +, TMTT Sep. 2015 2931-2941 Qualitative Microwave Imaging With Scattering Parameters Measurements. Akinci, M. N., +, TMTT Sep. 2015 2730-2740

+ Check author entry for coauthors

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Time-Domain System for Millimeter-Wave Material Characterization. Vakili, I., +, TMTT Sep. 2015 2915-2922 Frequency modulation Implementation of Sensor RFID: Carrying Sensor Information in the Modulation Frequency. Islam, Md. M., +, TMTT Aug. 2015 2672-2681 Frequency multipliers 76–81-GHz CMOS Transmitter With a Phase-Locked-Loop-Based Multichirp Modulator for Automotive Radar. Park, J., +, TMTT Apr. 2015 13991408 Efficient Microwave and Millimeter-Wave Frequency Multipliers Using Nonlinear Transmission Lines in CMOS Technology. Adnan, M., +, TMTT Sep. 2015 2889-2896 Frequency response A 1.4–2.3-GHz Tunable Diplexer Based on Reconfigurable Matching Networks. Ko, C. H., +, TMTT May 2015 1595-1602 Concurrent Dual-Band Digital Predistortion With a Single Feedback Loop. Liu, Y., +, TMTT May 2015 1556-1568 Bandpass Filters Using Coupling-Matrix-Based Design of HighAcoustic-Wave Lumped-Element Resonator (AWLR) Modules. Psychogiou, D., +, TMTT Dec. 2015 4319-4328 Enhanced Topology of -Plane Resonators for High-Power Satellite Applications. Peverini, O. A., +, TMTT Oct. 2015 3361-3373 Highly Efficient Concurrent Power Amplifier With Controllable Modes. Sun, Y., +, TMTT Dec. 2015 4051-4060 Hybrid Acoustic-Wave-Lumped-Element Resonators (AWLRs) for HighBandpass Filters With Quasi-Elliptic Frequency Response. Psychogiou, D., +, TMTT Jul. 2015 2233-2244 Synthesis and Design of High-Selectivity Wideband Quasi-Elliptic Bandpass Filters Using Multiconductor Transmission Lines. Sanchez-Martinez, J. J., +, TMTT Jan. 2015 198-208 The Effects of Electrode Configuration on Body Channel Communication Based on Analysis of Vertical and Horizontal Electric Dipoles. Bae, J., +, TMTT Apr. 2015 1409-1420 Triple- and Quadruple-Mode Wideband Bandpass Filter Using Simple Perturbation in Single Metal Cavity. Wong, S.-W., +, TMTT Oct. 2015 34163424 Two-Material Ridge Substrate Integrated Waveguide for Ultra-Wideband Applications. Moscato, S., +, TMTT Oct. 2015 3175-3182 Wideband Differential Bandpass Filters on Multimode Slotline Resonator With Intrinsic Common-Mode Rejection. Guo, X., +, TMTT May 2015 1587-1594 Wideband Microstrip-to-Microstrip Vertical Transitions Via Multiresonant Modes in a Slotline Resonator. Guo, X., +, TMTT Jun. 2015 1902-1909 Frequency selective surfaces Fractal Frequency-Selective Surface Embedded Thin Broadband Microwave Absorber Coatings Using Heterogeneous Composites. Panwar, R., +, TMTT Aug. 2015 2438-2448 Frequency stability Reducing Energy Dissipation in ULP Systems: PLL-Free FBAR-Based Fast Startup Transmitters. Thirunarayanan, R., +, TMTT Apr. 2015 1110-1117 Frequency synthesizers A W-Band 4-GHz Bandwidth Phase-Modulated Pulse Compression Radar Transmitter in 65-nm CMOS. Oh, J., +, TMTT Aug. 2015 2609-2618 An Ultra-Low Phase-Noise 20-GHz PLL Utilizing an Optoelectronic Voltage-Controlled Oscillator. Bluestone, A., +, TMTT Mar. 2015 1046-1052 Multi-Standard Hybrid PLL With Low Phase-Noise Characteristics for GSM/EDGE and LTE Applications. Choi, Y.-C., +, TMTT Oct. 2015 3254-3264 Frequency-domain analysis Comments on “High-Efficiency Class E/F Lumped and Transmission-Line Power Amplifiers”. Cheng, Q.-F., +, TMTT Aug. 2015 2703-2704 Coupled Mode Theory Applied to Resonators in the Presence of Conductors. Elnaggar, S. Y., +, TMTT Jul. 2015 2124-2132 Millimeter-Wave Modulated-Signal and Error-Vector-Magnitude Measurement With Uncertainty. Remley, K. A., +, TMTT May 2015 1710-1720 Time-Domain Electromagnetic Analysis of Multilayer Structures Using the Surface Equivalent Principle and Mixed-Potential Integral Equations. Maftooli, H., +, TMTT Jan. 2015 99-106 Time-Domain System for Millimeter-Wave Material Characterization. Vakili, I., +, TMTT Sep. 2015 2915-2922

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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 63, NO. 12, DECEMBER 2015

G Galerkin method A Nodal Continuous-Discontinuous Galerkin Time-Domain Method for Maxwell's Equations. Angulo, L. D., +, TMTT Oct. 2015 3081-3093 Nonlinear Modeling and Harmonic Recycling of Millimeter-Wave Rectifier Circuit. Ladan, S., +, TMTT Mar. 2015 937-944 Gallium alloys Robust Pressure-Actuated Liquid Metal Devices Showing Reconfigurable Electromagnetic Effects at GHz Frequencies. Cumby, B. L., +, TMTT Oct. 2015 3122-3130 Gallium arsenide A Fully Nonlinear Compact Modeling Approach for High-Frequency Noise in Large-Signal Operated Microwave Electron Devices. Traverso, P. A., +, TMTT Feb. 2015 352-366 A Memoryless Semi-Physical Power Amplifier Behavioral Model Based on the Correlation Between AM–AM and AM–PM Distortions. Glock, S., +, TMTT Jun. 2015 1826-1835 A Novel Load Mismatch Detection and Correction Technique for 3G/4G Load Insensitive Power Amplifier Application. Ji, D., +, TMTT May 2015 1530-1543 Compact Behavioral Models of Nonlinear Active Devices Using Response Surface Methodology. Barmuta, P., +, TMTT Jan. 2015 56-64 Corrections to “Design and Fabrication of Broadband Hybrid GaAs Schottky Diode Frequency Multipliers” [Dec 13 4442-4460]. Hrobak, M., +, TMTT Feb. 2015 553 Electrothermal Effects on Performance of GaAs HBT Power Amplifier During Power Versus Time (PVT) Variation at GSM/DCS Bands. Lin, L., +, TMTT Jun. 2015 1951-1963 InP DHBT Amplifier Modules Operating Between 150–300 GHz Using Membrane Technology. Eriksson, K., +, TMTT Feb. 2015 433-440 Investigation of Intermodulation Distortion of Envelope Tracking Power Amplifier for Linearity Improvement. Moon, K., +, TMTT Apr. 2015 13241333 Transformer-Feedback Interstage Bandwidth Enhancement for MMIC Multistage Amplifiers. Nikandish, G., +, TMTT Feb. 2015 441-448 Gallium compounds 3-D Fourier Series Based Digital Predistortion Technique for Concurrent Dual-Band Envelope Tracking With Reduced Envelope Bandwidth. Lin, Y., +, TMTT Sep. 2015 2764-2775 A 2-W W-Band GaN Traveling-Wave Amplifier With 25-GHz Bandwidth. Schellenberg, J. M., TMTT Sep. 2015 2833-2840 A 5.9-GHz Fully Integrated GaN Frontend Design With Physics-Based RF Compact Model. Choi, P., +, TMTT Apr. 2015 1163-1173 A Broadband GaN pHEMT Power Amplifier Using Non-Foster Matching. Lee, S., +, TMTT Dec. 2015 4406-4414 A Miniature Broadband Doherty Power Amplifier With a Series-Connected Load. Watanabe, S., +, TMTT Feb. 2015 572-579 A New Double Input-Double Output Complex Envelope Amplifier Behavioral Model Taking Into Account Source and Load Mismatch Effects. Zargar, H., +, TMTT Feb. 2015 766-774 A Post-Matching Doherty Power Amplifier Employing Low-Order Impedance Inverters for Broadband Applications. Pang, J., +, TMTT Dec. 2015 4061-4071 Active Detuning of MRI Receive Coils with GaN FETs. Twieg, M., +, TMTT Dec. 2015 4169-4177 Mode Power Amplifier Design ApAn Integrated Continuous Classproach for Microwave Enhanced Portable Diagnostic Applications. Imtiaz, A., +, TMTT Oct. 2015 3007-3015 Bandwidth Enhancement of Three-Stage Doherty Power Amplifier Using Symmetric Devices. Barthwal, A., +, TMTT Aug. 2015 23992410 Concurrent Dual-Band Digital Predistortion With a Single Feedback Loop. Liu, Y., +, TMTT May 2015 1556-1568 Design of X-Band GaN Phase Shifters. Ross, T. N., +, TMTT Jan. 2015 244-255 Digitally Assisted Analog/RF Predistorter With a Small-Signal-Assisted Parameter Identification Algorithm. Huang, H., +, TMTT Dec. 2015 42974305 Envelope Tracking of an RF High Power Amplifier With an 8-Level Digitally Controlled GaN-on-Si Supply Modulator. Florian, C., +, TMTT Aug. 2015 2589-2602 GaN HEMT Noise Model Based on Electromagnetic Simulations. Nalli, A., +, TMTT Aug. 2015 2498-2508 + Check author entry for coauthors

High-Efficiency Harmonic-Peaking Class-EF Power Amplifiers With Enhanced Maximum Operating Frequency. Thian, M., +, TMTT Feb. 2015 659-671 Highly Efficient and Multipaction-Free P-Band GaN High-Power Amplifiers for Space Applications. Ayllon, N., +, TMTT Dec. 2015 4429-4436 Hysteresis and Oscillation in High-Efficiency Power Amplifiers. de Cos, J., +, TMTT Dec. 2015 4284-4296 Investigation of Intermodulation Distortion of Envelope Tracking Power Amplifier for Linearity Improvement. Moon, K., +, TMTT Apr. 2015 13241333 Load Modulation Measurements of X-Band Outphasing Power Amplifiers. Litchfield, M., +, TMTT Dec. 2015 4119-4129 Phase-Noise Analysis of an X-Band Ultra-Low Phase-Noise GaN HEMT Based Cavity Oscillator. Horberg, M., +, TMTT Aug. 2015 2619-2629 Gas sensors Wearable RF Sensor Array Implementing Coupling-Matrix Readout Extraction Technique. Chen, W.-T. S., +, TMTT Dec. 2015 4157-4168 Gaussian processes Hybrid Nonlinear Modeling Using Adaptive Sampling. Barmuta, P., +, TMTT Dec. 2015 4501-4510 Supply-Modulated Radar Transmitters With Amplitude-Modulated Pulses. Zai, A., +, TMTT Sep. 2015 2953-2964 Ge-Si alloys -Band Dual-Polarization Phased-Array Transceiver Front-End in SiGe BiCMOS. Natarajan, A., +, TMTT Jun. 2015 1989-2002 A Broadband 4.5–15.5-GHz SiGe Power Amplifier With 25.5-dBm Peak Saturated Output Power and 28.7% Maximum PAE. Kerherve, E., +, TMTT May 2015 1621-1632 A Reconfigurable K-/Ka-Band Power Amplifier With High PAE in 0.18- m SiGe BiCMOS for Multi-Band Applications. Ma, K., +, TMTT Dec. 2015 4395-4405 A Single-Chip Electron Paramagnetic Resonance Transceiver in 0.13- m SiGe BiCMOS. Yang, X., +, TMTT Nov. 2015 3727-3735 An Improved Small-Signal Model for SiGe HBT Under OFF-State, Derived From Distributed Network and Corresponding Model Parameter Extraction. Sun, Y., +, TMTT Oct. 2015 3131-3141 An Improved VBIC Large-Signal Equivalent-Circuit Model for SiGe HBT With an Inductive Breakdown Network by -Parameters. Lee, C.-I., +, TMTT Sep. 2015 2756-2763 Broadband Circuit Techniques for Multi-Terahertz Gain-BandwidthProduct Low-Power Applications. Gharib, A., +, TMTT Nov. 2015 3701-3712 Consistent Modeling and Power Gain Analysis of Microwave SiGe HBTs in CE and CB Configurations. Alvarez-Botero, G., +, TMTT Dec. 2015 38883895 Fully Monolithic BiCMOS Reconfigurable Power Amplifier for Multi-Mode and Multi-Band Applications. Lee, M.-L., +, TMTT Feb. 2015 614-624 Genetic algorithms Design of a Traveling-Wave Slot Array Power Divider Using the Method of Moments and a Genetic Algorithm. Rengarajan, S. R., +, TMTT Dec. 2015 3981-3987 Design of High-Directivity Wideband Microstrip Directional Coupler With Fragment-Type Structure. Wang, L., +, TMTT Dec. 2015 3962-3970 Fractal Frequency-Selective Surface Embedded Thin Broadband Microwave Absorber Coatings Using Heterogeneous Composites. Panwar, R., +, TMTT Aug. 2015 2438-2448 Geometry Estimating the Inf-Sup Constant in Reduced Basis Methods for Time-Harmonic Maxwell’s Equations. Hess, M. W., +, TMTT Nov. 2015 3549-3557 Influence of Numerical Method and Geometry Used by Maxwell's Equation Solvers on Simulations of Ferroelectric Thin-Film Capacitors. Furlan, V., +, TMTT Mar. 2015 891-896 Radial Transmission-Line Approach for the Analysis of Ring Loaded Slots in Circular Waveguide. Addamo, G., +, TMTT May 2015 1468-1474 Simple and Compact Balanced Bandpass Filters Based on Magnetically Coupled Resonators. Fernandez-Prieto, A., +, TMTT Jun. 2015 1843-1853 Glass Broadband Microwave Characterization of Nanostructured Thin Film With Giant Dielectric Response. Chen, T.-C., +, TMTT Nov. 2015 3768-3774 Dynamic Measurement of Dielectric Properties of Materials at High Temperature During Microwave Heating in a Dual Mode Cylindrical Cavity. Catala-Civera, J. M., +, TMTT Sep. 2015 2905-2914

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 63, NO. 12, DECEMBER 2015

Gold A 1.3–2.4-GHz 3.1-mW VCO Using Electro-Thermo- Mechanically Tunable Self-Assembled MEMS Inductor on HR Substrate. Bhattacharya, A., +, TMTT Feb. 2015 459-469 High Power Latching RF MEMS Switches. Bakri-Kassem, M., +, TMTT Jan. 2015 222-232 Graphene Broadband Microwave Attenuator Based on Few Layer Graphene Flakes. Pierantoni, L., +, TMTT Aug. 2015 2491-2497 RF Linearity Performance Potential of Short-Channel Graphene Field-Effect Transistors. Alam, A. U., +, TMTT Dec. 2015 3874-3887 Graphene devices High-Order Subharmonic Millimeter-Wave Mixer Based on Few-Layer Graphene. Vazquez Antuna, C., +, TMTT Apr. 2015 1361-1369 RF Linearity Performance Potential of Short-Channel Graphene Field-Effect Transistors. Alam, A. U., +, TMTT Dec. 2015 3874-3887 Greedy algorithms Behavioral Modeling and Predistortion of Power Amplifiers Under Sparsity Hypothesis. Reina-Tosina, J., +, TMTT Feb. 2015 745-753 Green's function methods Integral-Equation Formulation for the Analysis of Capacitive Waveguide Filters Containing Dielectric and Metallic Arbitrarily Shaped Objects and Novel Applications. Quesada Pereira, F. D., +, TMTT Dec. 2015 38623873 Modeling of Noisy EM Field Propagation Using Correlation Information. Russer, J. A., +, TMTT Jan. 2015 76-89 On the Design of Gyroelectric Resonators and Circulators Using a Magnetically Biased 2-D Electron Gas (2-DEG). Jawad, G. N., +, TMTT May 2015 1512-1517 On the Development and Evaluation of Spatial-Domain Green’s Functions for Multilayered Structures With Conductive Sheets. Koufogiannis, I. D., +, TMTT Jan. 2015 20-29 Qualitative Microwave Imaging With Scattering Parameters Measurements. Akinci, M. N., +, TMTT Sep. 2015 2730-2740 Time-Domain Electromagnetic Analysis of Multilayer Structures Using the Surface Equivalent Principle and Mixed-Potential Integral Equations. Maftooli, H., +, TMTT Jan. 2015 99-106 Gyrators Coupling Matrix Synthesis of Nonreciprocal Lossless Two-Port Networks Using Gyrators and Inverters. Zhang, Q., +, TMTT Sep. 2015 2782-2792 Quality Factor of the Waveguide Re-Entrant Turnstile Junction Circulator. Helszajn, J., +, TMTT May 2015 1603-1608 Gyrotrons An Improved Broadband Boundary Condition for the RF Field in Gyrotron Interaction Modeling. Wu, C., +, TMTT Aug. 2015 2459-2467 Design and Measurement of a Broadband Sidewall Coupler for a W-Band Gyro-TWA. Zhang, L., +, TMTT Oct. 2015 3183-3190 Mode Converter for Gyrotron by the Method for Synthesis of NURBS Technique. Yu, X., +, TMTT Feb. 2015 326-330 H Harmonic analysis An 85-W Multi-Octave Push–Pull GaN HEMT Power Amplifier for HighEfficiency Communication Applications at Microwave Frequencies. Jundi, A., +, TMTT Nov. 2015 3691-3700 Analytical Reflection Coefficient Expressions Utilizing Load-Dependent -Parameters. Gou, Y., +, TMTT Oct. 2015 3142-3152 Efficient Simulation of Solution Curves and Bifurcation Loci in InjectionLocked Oscillators. de Cos, J., +, TMTT Jan. 2015 181-197 Guest Editorial. Draxler, P., TMTT Feb. 2015 557-558 Nonlinear Modeling and Harmonic Recycling of Millimeter-Wave Rectifier Circuit. Ladan, S., +, TMTT Mar. 2015 937-944 Harmonic distortion A Stacked-FET Linear SOI CMOS Cellular Antenna Switch With an Extremely Low-Power Biasing Strategy. Im, D., +, TMTT Jun. 2015 19641977 A Sub-GHz Wireless Transmitter Utilizing a Multi-Class-Linearized PA and Time-Domain Wideband-Auto I/Q-LOFT Calibration for IEEE 802.11af WLAN. Un, K.-F., +, TMTT Oct. 2015 3228-3241 Concurrent Dual-Band Modeling and Digital Predistortion in the Presence of Unfilterable Harmonic Signal Interference. Rawat, M., +, TMTT Feb. 2015 625-637 + Check author entry for coauthors

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Design and Analysis of CMOS High-Speed High Dynamic-Range Trackand-Hold Amplifiers. Liu, Y.-C., +, TMTT Sep. 2015 2841-2853 Extraction of a Multi-Dimensional Polynomial Device Model for an Improved Distortion Contribution Analysis Technique. Aikio, J. P., +, TMTT Jan. 2015 155-164 Nonlinear Behavioral Modeling Dependent on Load Reflection Coefficient Magnitude. Cai, J., +, TMTT May 2015 1518-1529 Harmonic generation 160-GHz to 1-THz Multi-Color Active Imaging With a Lens-Coupled SiGe HBT Chip-Set. Statnikov, K., +, TMTT Feb. 2015 520-532 Third Harmonic Exploitation in Passive UHF RFID. Andiia Vera, G., +, TMTT Sep. 2015 2991-3004 Harmonics suppression A 2.88 mW 9.06 dBm IIP3 Common-Gate LNA With Dual Cross-Coupled Capacitive Feedback. Han, H. G., +, TMTT Mar. 2015 1019-1025 Suppression of Harmonics in Microstrip Filters Using a Combination of Techniques. Huang, F., TMTT Oct. 2015 3453-3461 Wideband Balanced Filters With High Selectivity and Common-Mode Suppression. Chu, Q.-X., +, TMTT Oct. 2015 3462-3468 Health care Mode Power Amplifier Design ApAn Integrated Continuous Classproach for Microwave Enhanced Portable Diagnostic Applications. Imtiaz, A., +, TMTT Oct. 2015 3007-3015 Propagation, Power Absorption, and Temperature Analysis of UWB Wireless Capsule Endoscopy Devices Operating in the Human Body. Thotahewa, K. M. S., +, TMTT Nov. 2015 3823-3833 Hearing aids Free-Positioning Wireless Charging System for Small Electronic Devices Using a Bowl-Shaped Transmitting Coil. Kim, J., +, TMTT Mar. 2015 791-800 Heat transfer A New Broadband Common-Mode Noise Absorption Circuit for High-Speed Differential Digital Systems. Hsiao, C.-Y., +, TMTT Jun. 2015 1894-1901 Helical waveguides Experimental Study of Microwave Pulse Compression Using a Five-Fold Helically Corrugated Waveguide. Zhang, L., +, TMTT Mar. 2015 10901096 HEMT circuits Polymer Multichip Module Process Using 3-D Printing Technologies for D-Band Applications. Merkle, T., +, TMTT Feb. 2015 481-493 Heterojunction bipolar transistors 160-GHz to 1-THz Multi-Color Active Imaging With a Lens-Coupled SiGe HBT Chip-Set. Statnikov, K., +, TMTT Feb. 2015 520-532 A 110–170-GHz Multi-Mode Transconductance Mixer in 250-nm InP DHBT Technology. Yan, Y., +, TMTT Sep. 2015 2897-2904 A Novel Load Mismatch Detection and Correction Technique for 3G/4G Load Insensitive Power Amplifier Application. Ji, D., +, TMTT May 2015 1530-1543 An Improved Small-Signal Model for SiGe HBT Under OFF-State, Derived From Distributed Network and Corresponding Model Parameter Extraction. Sun, Y., +, TMTT Oct. 2015 3131-3141 An Improved VBIC Large-Signal Equivalent-Circuit Model for SiGe HBT With an Inductive Breakdown Network by -Parameters. Lee, C.-I., +, TMTT Sep. 2015 2756-2763 Consistent Modeling and Power Gain Analysis of Microwave SiGe HBTs in CE and CB Configurations. Alvarez-Botero, G., +, TMTT Dec. 2015 38883895 Electrothermal Effects on Performance of GaAs HBT Power Amplifier During Power Versus Time (PVT) Variation at GSM/DCS Bands. Lin, L., +, TMTT Jun. 2015 1951-1963 Fully Integrated D-Band Direct Carrier Quadrature (I/Q) Modulator and Demodulator Circuits in InP DHBT Technology. Carpenter, S., +, TMTT May 2015 1666-1675 InP DHBT Amplifier Modules Operating Between 150–300 GHz Using Membrane Technology. Eriksson, K., +, TMTT Feb. 2015 433-440 InP DHBT Distributed Amplifiers With Up to 235-GHz Bandwidth. Eriksson, K., +, TMTT Apr. 2015 1334-1341 Investigation of Intermodulation Distortion of Envelope Tracking Power Amplifier for Linearity Improvement. Moon, K., +, TMTT Apr. 2015 13241333 High electron mobility transistors (InP) HEMT Small-Signal Equivalent-Circuit Extraction as a Function of Temperature. Alt, A. R., +, TMTT Sep. 2015 2751-2755

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A 5.9-GHz Fully Integrated GaN Frontend Design With Physics-Based RF Compact Model. Choi, P., +, TMTT Apr. 2015 1163-1173 A Broadband GaN pHEMT Power Amplifier Using Non-Foster Matching. Lee, S., +, TMTT Dec. 2015 4406-4414 A Fully Nonlinear Compact Modeling Approach for High-Frequency Noise in Large-Signal Operated Microwave Electron Devices. Traverso, P. A., +, TMTT Feb. 2015 352-366 A Miniature Broadband Doherty Power Amplifier With a Series-Connected Load. Watanabe, S., +, TMTT Feb. 2015 572-579 A Post-Matching Doherty Power Amplifier Employing Low-Order Impedance Inverters for Broadband Applications. Pang, J., +, TMTT Dec. 2015 4061-4071 An 85-W Multi-Octave Push–Pull GaN HEMT Power Amplifier for HighEfficiency Communication Applications at Microwave Frequencies. Jundi, A., +, TMTT Nov. 2015 3691-3700 Analysis and Design of Millimeter-Wave Power Amplifier Using Stacked-FET Structure. Kim, Y., +, TMTT Feb. 2015 691-702 Asymmetric Broadband Doherty Power Amplifier Using GaN MMIC for Femto-Cell Base-Station. Jee, S., +, TMTT Sep. 2015 2802-2810 Bandwidth Enhancement of Three-Stage Doherty Power Amplifier Using Symmetric Devices. Barthwal, A., +, TMTT Aug. 2015 2399-2410 Compact Behavioral Models of Nonlinear Active Devices Using Response Surface Methodology. Barmuta, P., +, TMTT Jan. 2015 56-64 Design of X-Band GaN Phase Shifters. Ross, T. N., +, TMTT Jan. 2015 244-255 GaN HEMT Noise Model Based on Electromagnetic Simulations. Nalli, A., +, TMTT Aug. 2015 2498-2508 GaN Microwave DC–DC Converters. Ramos, I., +, TMTT Dec. 2015 44734482 High-Efficiency Harmonic-Peaking Class-EF Power Amplifiers With Enhanced Maximum Operating Frequency. Thian, M., +, TMTT Feb. 2015 659-671 Hybrid Nonlinear Modeling Using Adaptive Sampling. Barmuta, P., +, TMTT Dec. 2015 4501-4510 Phase-Noise Analysis of an X-Band Ultra-Low Phase-Noise GaN HEMT Based Cavity Oscillator. Horberg, M., +, TMTT Aug. 2015 2619-2629 Transformer-Feedback Interstage Bandwidth Enhancement for MMIC Multistage Amplifiers. Nikandish, G., +, TMTT Feb. 2015 441-448 High K dielectric materials A Transformer-Based Poly-Phase Network for Ultra-Broadband Quadrature Signal Generation. Park, J. S., +, TMTT Dec. 2015 4444-4457 High-frequency effects Anisotropic Microwave Conductivity Dispersion of Horizontally Aligned Multi-Walled Carbon- Nanotube Thin Film on Flexible Substrate. Li, S., +, TMTT Nov. 2015 3588-3594 Microwave Properties of an Inhomogeneous Optically Illuminated Plasma in a Microstrip Gap. Gamlath, C. D., +, TMTT Feb. 2015 374-383 High-frequency transformers Transformer-Based Doherty Power Amplifiers for mm-Wave Applications in 40-nm CMOS. Kaymaksut, E., +, TMTT Apr. 2015 1186-1192 High-frequency transmission lines Reflectionless Filter Structures. Morgan, M. A., +, TMTT Apr. 2015 12631271 Right/Left-Handed Transmission Lines Based on Coupled Transmission Line Sections and Their Application Towards Bandpass Filters. Sorocki, J., +, TMTT Feb. 2015 384-396 High-pass filters Chebyshev Filter Design Using Vias as Quasi-Transmission Lines in Printed Circuit Boards. Hardock, A., +, TMTT Mar. 2015 976-985 High-speed techniques Electrical Analysis of Cell Membrane Poration by an Intense Nanosecond Pulsed Electric Field Using an Atomistic-to-Continuum Method. Kohler, S., +, TMTT Jun. 2015 2032-2040 High-temperature superconductors An Empirical Expression to Predict the Resonant Frequencies of Archimedean Spirals. Hooker, J. W., +, TMTT Jul. 2015 2107-2114 Home appliances Guest Editorial. KIM, J., +, TMTT Mar. 2015 778-779 Humidity sensors Passive Microwave Substrate Integrated Cavity Resonator for Humidity Sensing. El Matbouly, H., +, TMTT Dec. 2015 4150-4156 Hyperthermia High-Efficiency Applicator Based on Printed Circuit Board in MillimeterWave Region. Shiina, T., +, TMTT Oct. 2015 3311-3318 + Check author entry for coauthors

Hysteresis Hysteresis and Oscillation in High-Efficiency Power Amplifiers. de Cos, J., +, TMTT Dec. 2015 4284-4296 I IEEE publishing List of reviewers. reviewers , TMTT Apr. 2015 1431-1442 IIR filters A Low-IF Tag-Based Motion Compensation Technique for Mobile Doppler Radar Life Signs Monitoring. Rahman, A., +, TMTT Oct. 2015 3034-3041 Image color analysis 160-GHz to 1-THz Multi-Color Active Imaging With a Lens-Coupled SiGe HBT Chip-Set. Statnikov, K., +, TMTT Feb. 2015 520-532 Image enhancement Computational Feasibility Study of Contrast-Enhanced Thermoacoustic Imaging for Breast Cancer Detection Using Realistic Numerical Breast Phantoms. Wang, X., +, TMTT May 2015 1489-1501 Image reconstruction Computational Feasibility Study of Contrast-Enhanced Thermoacoustic Imaging for Breast Cancer Detection Using Realistic Numerical Breast Phantoms. Wang, X., +, TMTT May 2015 1489-1501 Image resolution 3-D High-Resolution Imaging Radar at 300 GHz With Enhanced FoV. Grajal, J., +, TMTT Mar. 2015 1097-1107 3-D Radiometric Aperture Synthesis Imaging. Salmon, N. A., TMTT Nov. 2015 3579-3587 Computational Feasibility Study of Contrast-Enhanced Thermoacoustic Imaging for Breast Cancer Detection Using Realistic Numerical Breast Phantoms. Wang, X., +, TMTT May 2015 1489-1501 Image sensors 160-GHz to 1-THz Multi-Color Active Imaging With a Lens-Coupled SiGe HBT Chip-Set. Statnikov, K., +, TMTT Feb. 2015 520-532 Impedance converters A Post-Matching Doherty Power Amplifier Employing Low-Order Impedance Inverters for Broadband Applications. Pang, J., +, TMTT Dec. 2015 4061-4071 A Three-Way Reconfigurable Power Divider/Combiner. Fan, H., +, TMTT Mar. 2015 986-998 A Wideband and Highly Symmetric Multi-Port Parallel Combining Transformer Technology. Yang, H.-S., +, TMTT Nov. 2015 3671-3680 Impedance matching A Broadband GaN pHEMT Power Amplifier Using Non-Foster Matching. Lee, S., +, TMTT Dec. 2015 4406-4414 A Novel Load Mismatch Detection and Correction Technique for 3G/4G Load Insensitive Power Amplifier Application. Ji, D., +, TMTT May 2015 1530-1543 A Three-Way Reconfigurable Power Divider/Combiner. Fan, H., +, TMTT Mar. 2015 986-998 An Integrated Slot-Ring Traveling-Wave Radiator. Bowers, S. M., +, TMTT Apr. 2015 1154-1162 Analytical Design Methodology for Generic Doherty Amplifier Architectures Using Three-Port Input/Output Networks. Akbarpour, M., +, TMTT Oct. 2015 3242-3253 Antenna Impedance Variation Compensation by Exploiting a Digital Doherty Power Amplifier Architecture. Hu, S., +, TMTT Feb. 2015 580-597 Generalized Theory of the Thru-Reflect-Match Calibration Technique. Pulido-Gaytan, M. A., +, TMTT May 2015 1693-1699 Improving Power Utilization Factor of Broadband Doherty Amplifier by Using Bandpass Auxiliary Transformer. Fang, X.-H., +, TMTT Sep. 2015 2811-2820 Longitudinally Independent Matching and Arbitrary Wave Patterning Using -Near-Zero Channels. Soric, J. C., +, TMTT Nov. 2015 3558-3567 Power Synthesis at 110-GHz Frequency Based on Discrete Sources. Zhao, J., +, TMTT May 2015 1633-1644 Reconfigurable Diffractive Antenna Based on Switchable Electrically Induced Transparency. Li, H., +, TMTT Mar. 2015 925-936 RF-Designed High-Power Lamb-Wave Aluminum–Nitride Resonators. Campanella, H., +, TMTT Feb. 2015 331-339 Transformer-Feedback Interstage Bandwidth Enhancement for MMIC Multistage Amplifiers. Nikandish, G., +, TMTT Feb. 2015 441-448 Wideband Balanced Filters With High Selectivity and Common-Mode Suppression. Chu, Q.-X., +, TMTT Oct. 2015 3462-3468

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 63, NO. 12, DECEMBER 2015

Impurities Investigating the Broadband Microwave Absorption of Nanodiamond Impurities. Cuenca, J. A., +, TMTT Dec. 2015 4110-4118 Indium alloys Robust Pressure-Actuated Liquid Metal Devices Showing Reconfigurable Electromagnetic Effects at GHz Frequencies. Cumby, B. L., +, TMTT Oct. 2015 3122-3130 Indium compounds (InP) HEMT Small-Signal Equivalent-Circuit Extraction as a Function of Temperature. Alt, A. R., +, TMTT Sep. 2015 2751-2755 0.8/2.2-GHz Programmable Active Bandpass Filters in InP/Si BiCMOS Technology. Xu, Z., +, TMTT Apr. 2015 1219-1227 A 110–170-GHz Multi-Mode Transconductance Mixer in 250-nm InP DHBT Technology. Yan, Y., +, TMTT Sep. 2015 2897-2904 A Novel Load Mismatch Detection and Correction Technique for 3G/4G Load Insensitive Power Amplifier Application. Ji, D., +, TMTT May 2015 1530-1543 Fully Integrated D-Band Direct Carrier Quadrature (I/Q) Modulator and Demodulator Circuits in InP DHBT Technology. Carpenter, S., +, TMTT May 2015 1666-1675 InP DHBT Amplifier Modules Operating Between 150–300 GHz Using Membrane Technology. Eriksson, K., +, TMTT Feb. 2015 433-440 InP DHBT Distributed Amplifiers With Up to 235-GHz Bandwidth. Eriksson, K., +, TMTT Apr. 2015 1334-1341 Investigation of Intermodulation Distortion of Envelope Tracking Power Amplifier for Linearity Improvement. Moon, K., +, TMTT Apr. 2015 13241333 Indoor navigation A Distributed Positioning System Based on a Predictive Fingerprinting Method Enabling Sub-Metric Precision in IEEE 802.11 Networks. Maddio, S., +, TMTT Dec. 2015 4567-4580 Signal Detection and Noise Modeling of a 1-D Pulse-Based Ultra-Wideband Ranging System and Its Accuracy Assessment. Elkhouly, E., +, TMTT May 2015 1746-1757 Indoor radio Signal Detection and Noise Modeling of a 1-D Pulse-Based Ultra-Wideband Ranging System and Its Accuracy Assessment. Elkhouly, E., +, TMTT May 2015 1746-1757 Inductance A Transformer-Based Poly-Phase Network for Ultra-Broadband Quadrature Signal Generation. Park, J. S., +, TMTT Dec. 2015 4444-4457 Inductive power transmission Advanced Power Control Scheme in Wireless Power Transmission for Human Protection From EM Field. Kim, S.-M., +, TMTT Mar. 2015 847-856 An Investigation of Electromagnetic Radiated Emission and Interference From Multi-Coil Wireless Power Transfer Systems Using Resonant Magnetic Field Coupling. Kong, S., +, TMTT Mar. 2015 833-846 Development of a Communication Scheme for Wireless Power Applications With Moving Receivers. Thoen, B., +, TMTT Mar. 2015 857-863 Efficiency and Optimal Loads Analysis for Multiple-Receiver Wireless Power Transfer Systems. Fu, M., +, TMTT Mar. 2015 801-812 Free-Positioning Wireless Charging System for Small Electronic Devices Using a Bowl-Shaped Transmitting Coil. Kim, J., +, TMTT Mar. 2015 791-800 Resonant Electrical Coupling: Circuit Model and First Experimental Results. Dias Fernandes, R., +, TMTT Sep. 2015 2983-2990 Resonant Inductive Link for Remote Powering of Pacemakers. Monti, G., +, TMTT Nov. 2015 3814-3822 Rigorous Network and Full-Wave Electromagnetic Modeling of Wireless Power Transfer Links. Dionigi, M., +, TMTT Jan. 2015 65-75 Wireless Power Systems for Mobile Devices Supporting Inductive and Resonant Operating Modes. Riehl, P. S., +, TMTT Mar. 2015 780-790 Inductors A 1.3–2.4-GHz 3.1-mW VCO Using Electro-Thermo- Mechanically Tunable Self-Assembled MEMS Inductor on HR Substrate. Bhattacharya, A., +, TMTT Feb. 2015 459-469 An Integrated Slot-Ring Traveling-Wave Radiator. Bowers, S. M., +, TMTT Apr. 2015 1154-1162 Low-Input Power-Level CMOS RF Energy-Harvesting Front End. Abouzied, M. A., +, TMTT Nov. 2015 3794-3805 Optimized Design of Frequency Dividers Based on Varactor-Inductor Cells. Ponton, M., +, TMTT Dec. 2015 4458-4472

+ Check author entry for coauthors

4643

Infrared imaging Micromachined Room-Temperature Air-Suspended Ni/Cr Nanobolometer. Yang, H.-H., +, TMTT Nov. 2015 3760-3767 Inhomogeneous media A Linear Complexity Direct Volume Integral Equation Solver for Full-Wave 3-D Circuit Extraction in Inhomogeneous Materials. Omar, S., +, TMTT Mar. 2015 897-912 Electromagnetic Scattering by a General Rotationally Symmetric Inhomogeneous Anisotropic Sphere. Zouros, G. P., +, TMTT Oct. 2015 3054-3065 Injection locked oscillators Comparison of Injection-Locked and Coupled Oscillator Arrays for Beamforming. Lo, Y.-T., +, TMTT Apr. 2015 1353-1360 Design and Tuning of Coupled-LC mm-Wave Subharmonically InjectionLocked Oscillators. Mangraviti, G., +, TMTT Jul. 2015 2301-2312 Efficient Simulation of Solution Curves and Bifurcation Loci in InjectionLocked Oscillators. de Cos, J., +, TMTT Jan. 2015 181-197 Ink jet printing Ambient RF Energy Harvesting From a Two-Way Talk Radio for Flexible Wearable Wireless Sensor Devices Utilizing Inkjet Printing Technologies. Bito, J., +, TMTT Dec. 2015 4533-4543 Integral equations A Linear Complexity Direct Volume Integral Equation Solver for Full-Wave 3-D Circuit Extraction in Inhomogeneous Materials. Omar, S., +, TMTT Mar. 2015 897-912 Design of a Traveling-Wave Slot Array Power Divider Using the Method of Moments and a Genetic Algorithm. Rengarajan, S. R., +, TMTT Dec. 2015 3981-3987 Electromagnetic Scattering by a General Rotationally Symmetric Inhomogeneous Anisotropic Sphere. Zouros, G. P., +, TMTT Oct. 2015 3054-3065 Integral-Equation Formulation for the Analysis of Capacitive Waveguide Filters Containing Dielectric and Metallic Arbitrarily Shaped Objects and Novel Applications. Quesada Pereira, F. D., +, TMTT Dec. 2015 38623873 On the Development and Evaluation of Spatial-Domain Green’s Functions for Multilayered Structures With Conductive Sheets. Koufogiannis, I. D., +, TMTT Jan. 2015 20-29 Time-Domain Electromagnetic Analysis of Multilayer Structures Using the Surface Equivalent Principle and Mixed-Potential Integral Equations. Maftooli, H., +, TMTT Jan. 2015 99-106 Integrated circuit design A 1.1-Gbit/s 10-GHz Outphasing Modulator With 23-dBm Output Power and 60-dB Dynamic Range in 45-nm CMOS SOI. Mehrjoo, M. S., +, TMTT Jul. 2015 2289-2300 A Pulsed Dynamic Load Modulation Technique for High-Efficiency Linear Transmitters. Jeon, M.-S., +, TMTT Sep. 2015 2854-2866 Analysis and Design of Millimeter-Wave Power Amplifier Using Stacked-FET Structure. Kim, Y., +, TMTT Feb. 2015 691-702 CMOS Broadband Programmable Gain Active Balun With 0.5-dB Gain Steps. Hur, B., +, TMTT Aug. 2015 2650-2660 Millimeter-Wave Low-Noise Amplifier Design in 28-nm Low-Power Digital CMOS. Fritsche, D., +, TMTT Jun. 2015 1910-1922 Polymer Multichip Module Process Using 3-D Printing Technologies for D-Band Applications. Merkle, T., +, TMTT Feb. 2015 481-493 Transformer-Feedback Interstage Bandwidth Enhancement for MMIC Multistage Amplifiers. Nikandish, G., +, TMTT Feb. 2015 441-448 Integrated circuit interconnections Polymer Multichip Module Process Using 3-D Printing Technologies for D-Band Applications. Merkle, T., +, TMTT Feb. 2015 481-493 Substrate Integrated Waveguide Directional Couplers for Compact ThreeDimensional Integrated Circuits. Doghri, A., +, TMTT Jan. 2015 209-221 Integrated circuit manufacture CMOS Broadband Programmable Gain Active Balun With 0.5-dB Gain Steps. Hur, B., +, TMTT Aug. 2015 2650-2660 High-Tunability and High- -Factor Integrated Ferroelectric Circuits up to Millimeter Waves. De Paolis, R., +, TMTT Aug. 2015 2570-2578 Integrated circuit metallization Polymer Multichip Module Process Using 3-D Printing Technologies for D-Band Applications. Merkle, T., +, TMTT Feb. 2015 481-493 Integrated circuit modeling Corrections to “Compact Conical-Line Power Combiner Design Using Circuit Models” [Nov 14 2650-2658]. Beyers, R. D., +, TMTT Jul. 2015 2391 Millimeter-Wave Low-Noise Amplifier Design in 28-nm Low-Power Digital CMOS. Fritsche, D., +, TMTT Jun. 2015 1910-1922

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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 63, NO. 12, DECEMBER 2015

Integrated circuit noise A Stacked-FET Linear SOI CMOS Cellular Antenna Switch With an Extremely Low-Power Biasing Strategy. Im, D., +, TMTT Jun. 2015 19641977 Integrated circuit packaging 60-GHz Substrate Materials Characterization Using the Covered Transmission-Line Method. Papio Toda, A., +, TMTT Mar. 2015 1063-1075 InP DHBT Amplifier Modules Operating Between 150–300 GHz Using Membrane Technology. Eriksson, K., +, TMTT Feb. 2015 433-440 Polymer Multichip Module Process Using 3-D Printing Technologies for D-Band Applications. Merkle, T., +, TMTT Feb. 2015 481-493 Integrated circuit technology A Pulsed Dynamic Load Modulation Technique for High-Efficiency Linear Transmitters. Jeon, M.-S., +, TMTT Sep. 2015 2854-2866 Integrated circuit testing Common-Base/Common-Gate Millimeter-Wave Power Detectors. Serhan, A., +, TMTT Dec. 2015 4483-4491 Integrated circuits High-Tunability and High- -Factor Integrated Ferroelectric Circuits up to Millimeter Waves. De Paolis, R., +, TMTT Aug. 2015 2570-2578 Intensity measurement Near-Field Microwave Distribution Measurement With a Point Detector Base on Thermoacoustic Effect. Ding, W., +, TMTT Oct. 2015 3272-3276 Interconnections Textile Microwave Components in Substrate Integrated Waveguide Technology. Moro, R., +, TMTT Feb. 2015 422-432 Interference (signal) Generalized Coupled-Line All-Pass Phasers. Gupta, S., +, TMTT Mar. 2015 1007-1018 Interference suppression Concurrent Dual-Band Modeling and Digital Predistortion in the Presence of Unfilterable Harmonic Signal Interference. Rawat, M., +, TMTT Feb. 2015 625-637 Dynamic Bandpass Filter Shape and Interference Cancellation Control Utilizing Bandpass–Bandstop Filter Cascade. Lee, T.-C., +, TMTT Aug. 2015 2526-2539 Partitioned Distortion Mitigation in LTE Radio Uplink to Enhance Transmitter Efficiency. Amiri, M. V., +, TMTT Aug. 2015 2661-2671 Real-Time Adaptive Transmitter Leakage Cancelling in 5.8-GHz Full-Duplex Transceivers. Maddio, S., +, TMTT Feb. 2015 509-519 Intermodulation A Tunable RF Front-End With Narrowband Antennas for Mobile Devices. Bahramzy, P., +, TMTT Oct. 2015 3300-3310 Nonlinear Communication System With Harmonic Diversity. Cheong, P., +, TMTT Dec. 2015 4130-4149 Intermodulation distortion A Varactor-Based Variable Attenuator Design With Enhanced Linearity Performance. Cheng, K.-K. M., +, TMTT Oct. 2015 3191-3198 Dynamic-Range Enhancement for a Microwave Photonic Link Based on a Polarization Modulator. Chen, X., +, TMTT Jul. 2015 2384-2389 Highly Linear Fully Integrated Wideband RF PA for LTE-Advanced in 180-nm SOI. Francois, B., +, TMTT Feb. 2015 649-658 Investigation of Intermodulation Distortion of Envelope Tracking Power Amplifier for Linearity Improvement. Moon, K., +, TMTT Apr. 2015 13241333 Investigation of RF Avalanche Inductive Effect on Reduction of Intermodulation Distortion of MOSFETs Using Volterra Series Analysis. Lee, C.-I., +, TMTT Feb. 2015 367-373 RF Linearity Performance Potential of Short-Channel Graphene Field-Effect Transistors. Alam, A. U., +, TMTT Dec. 2015 3874-3887 Inverse problems Expedited Geometry Scaling of Compact Microwave Passives by Means of Inverse Surrogate Modeling. Koziel, S., +, TMTT Dec. 2015 4019-4026 Inverse transforms 3-D Radiometric Aperture Synthesis Imaging. Salmon, N. A., TMTT Nov. 2015 3579-3587 Time-Domain Electromagnetic Analysis of Multilayer Structures Using the Surface Equivalent Principle and Mixed-Potential Integral Equations. Maftooli, H., +, TMTT Jan. 2015 99-106 Inverters Automated Design of Common-Mode Suppressed Balanced Wideband Bandpass Filters by Means of Aggressive Space Mapping. Sans, M., +, TMTT Dec. 2015 3896-3908 + Check author entry for coauthors

Compact Filtering Rat-Race Hybrid With Wide Stopband. Wang, K.-X., +, TMTT Aug. 2015 2550-2560 Coupling Matrix Synthesis of Nonreciprocal Lossless Two-Port Networks Using Gyrators and Inverters. Zhang, Q., +, TMTT Sep. 2015 2782-2792 Modeling of Inline Transitions Between Different Waveguides as Impedance Inverters for the Use in Novel Filter Designs. Strauss, G., +, TMTT Nov. 2015 3663-3670 Invisibility cloaks Planar Distributed Full-Tensor Anisotropic Metamaterials for Transformation Electromagnetics. Nagayama, T., +, TMTT Dec. 2015 3851-3861 Iron compounds Fractal Frequency-Selective Surface Embedded Thin Broadband Microwave Absorber Coatings Using Heterogeneous Composites. Panwar, R., +, TMTT Aug. 2015 2438-2448 Self-Biased Y-Junction Circulators Using Lanthanum- and Cobalt-Substituted Strontium Hexaferrites. Laur, V., +, TMTT Dec. 2015 4376-4381 Iterative methods Direct Finite-Element Solver of Linear Complexity for Large-Scale 3-D Electromagnetic Analysis and Circuit Extraction. Zhou, B., +, TMTT Oct. 2015 3066-3080 Fractal Frequency-Selective Surface Embedded Thin Broadband Microwave Absorber Coatings Using Heterogeneous Composites. Panwar, R., +, TMTT Aug. 2015 2438-2448 Qualitative Microwave Imaging With Scattering Parameters Measurements. Akinci, M. N., +, TMTT Sep. 2015 2730-2740 J Jamming Low-Loss Ultrawideband Programmable RF Photonic Phase Filter for Spread Spectrum Pulse Compression. Kim, H.-J., +, TMTT Dec. 2015 4178-4187 Jitter A CML Ring Oscillator-Based Supply-Insensitive PLL With On-Chip Calibrations. Gui, X., +, TMTT Jan. 2015 233-243 Multi-Standard Hybrid PLL With Low Phase-Noise Characteristics for GSM/EDGE and LTE Applications. Choi, Y.-C., +, TMTT Oct. 2015 3254-3264 L Laminates Design of Multilayered Epsilon-Near-Zero Microwave Planar Sensor for Testing of Dispersive Materials. Jha, A. K., +, TMTT Aug. 2015 2418-2426 Lanthanum compounds Self-Biased Y-Junction Circulators Using Lanthanum- and Cobalt-Substituted Strontium Hexaferrites. Laur, V., +, TMTT Dec. 2015 4376-4381 Large-scale systems Coupled Mode Theory Applied to Resonators in the Presence of Conductors. Elnaggar, S. Y., +, TMTT Jul. 2015 2124-2132 Laser beam cutting A Configurable Coupling Structure for Broadband Millimeter-Wave SplitBlock Networks. Koenen, C., +, TMTT Dec. 2015 3954-3961 LC circuits 76–81-GHz CMOS Transmitter With a Phase-Locked-Loop-Based Multichirp Modulator for Automotive Radar. Park, J., +, TMTT Apr. 2015 13991408 A 47.6–71.0-GHz 65-nm CMOS VCO Based on Magnetically Coupled -Type LC Network. Jia, H., +, TMTT May 2015 1645-1657 A Low Phase-Noise Wide Tuning-Range Quadrature Oscillator Using a Transformer-Based Dual-Resonance LC Ring. Bajestan, M. M., +, TMTT Apr. 2015 1142-1153 Design and Analysis on Bidirectionally and Passively Coupled QVCO With Nonlinear Coupler. Kuo, N.-C., +, TMTT Apr. 2015 1130-1141 Designs of K-Band Divide-by-2 and Divide-by-3 Injection-Locked Frequency Divider With Darlington Topology. Chien, K.-H., +, TMTT Sep. 2015 2877-2888 Transformer-Based Doherty Power Amplifiers for mm-Wave Applications in 40-nm CMOS. Kaymaksut, E., +, TMTT Apr. 2015 1186-1192 Tuning-Range Enhancement Through Deterministic Mode Selection in RF Quadrature Oscillators. Bagheri, M., +, TMTT Nov. 2015 3713-3726

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 63, NO. 12, DECEMBER 2015

Lead A Technique to Evaluate MRI-Induced Electric Fields at the Ends of Practical Implanted Lead. Feng, S., +, TMTT Jan. 2015 305-313 Lead bonding 160-GHz to 1-THz Multi-Color Active Imaging With a Lens-Coupled SiGe HBT Chip-Set. Statnikov, K., +, TMTT Feb. 2015 520-532 A Wide-Band CMOS to Waveguide Transition at mm-Wave Frequencies With Wire-Bonds. Jameson, S., +, TMTT Sep. 2015 2741-2750 Leaky wave antennas Time-Domain System for Millimeter-Wave Material Characterization. Vakili, I., +, TMTT Sep. 2015 2915-2922 Least mean squares methods Concurrent Dual-Band Modeling and Digital Predistortion in the Presence of Unfilterable Harmonic Signal Interference. Rawat, M., +, TMTT Feb. 2015 625-637 Least squares approximations Efficient Least-Squares 2-D-Cubic Spline for Concurrent Dual-Band Systems. Naraharisetti, N., +, TMTT Jul. 2015 2199-2210 Linearization and Imbalance Correction Techniques for Broadband Outphasing Power Amplifiers. Hwang, T., +, TMTT Jul. 2015 2185-2198 Lens antennas 160-GHz to 1-THz Multi-Color Active Imaging With a Lens-Coupled SiGe HBT Chip-Set. Statnikov, K., +, TMTT Feb. 2015 520-532 Lenses 160-GHz to 1-THz Multi-Color Active Imaging With a Lens-Coupled SiGe HBT Chip-Set. Statnikov, K., +, TMTT Feb. 2015 520-532 Longitudinally Independent Matching and Arbitrary Wave Patterning Using -Near-Zero Channels. Soric, J. C., +, TMTT Nov. 2015 3558-3567 Light emitting diodes Ambient RF Energy Harvesting From a Two-Way Talk Radio for Flexible Wearable Wireless Sensor Devices Utilizing Inkjet Printing Technologies. Bito, J., +, TMTT Dec. 2015 4533-4543 Light polarization Polarization Considerations for Scalar Huygens Metasurfaces and Characterization for 2-D Refraction. Wong, J. P. S., +, TMTT Mar. 2015 913-924 Linear algebra Corrections to “Simple, Fast, and Effective Identification of an Equivalent Ports” [Jan 15 48-55]. Zappelli, Circuit of a Waveguide Junction With L., TMTT Mar. 2015 1108 Simple, Fast, and Effective Identification of an Equivalent Circuit of a Waveguide Junction With Ports. Zappelli, L., TMTT Jan. 2015 48-55 Linearization techniques A Varactor-Based Variable Attenuator Design With Enhanced Linearity Performance. Cheng, K.-K. M., +, TMTT Oct. 2015 3191-3198 DC and Imaginary Spurious Modes Suppression for Both Unbounded and Lossy Structures. Zekios, C. L., +, TMTT Jul. 2015 2082-2093 Linearization and Imbalance Correction Techniques for Broadband Outphasing Power Amplifiers. Hwang, T., +, TMTT Jul. 2015 2185-2198 Lipid bilayers Electrical Analysis of Cell Membrane Poration by an Intense Nanosecond Pulsed Electric Field Using an Atomistic-to-Continuum Method. Kohler, S., +, TMTT Jun. 2015 2032-2040 Liquid crystal polymers High Rejection, Self-Packaged Low-Pass Filter Using Multilayer Liquid Crystal Polymer Technology. Cervera, F., +, TMTT Dec. 2015 3920-3928 Present and Future Trends in Filters and Multiplexers. Snyder, R. V., +, TMTT Oct. 2015 3324-3360 Liquid metals Robust Pressure-Actuated Liquid Metal Devices Showing Reconfigurable Electromagnetic Effects at GHz Frequencies. Cumby, B. L., +, TMTT Oct. 2015 3122-3130 Liver The Development of Forceps-Type Microwave Tissue Coagulator for Surgical Operation. Endo, Y., +, TMTT Jun. 2015 2041-2049 Load modeling Guest Editorial. Draxler, P., TMTT Feb. 2015 557-558 Load regulation Efficiency and Optimal Loads Analysis for Multiple-Receiver Wireless Power Transfer Systems. Fu, M., +, TMTT Mar. 2015 801-812 Loading Ultra-Miniature SIW Cavity Resonators and Filters. Pourghorban Saghati, A., +, TMTT Dec. 2015 4329-4340

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Logic gates A 2.45-GHz Energy-Autonomous Wireless Power Relay Node. Del Prete, M., +, TMTT Dec. 2015 4511-4520 Long Term Evolution A Highly Efficient LTE Pulse-Modulated Polar Transmitter Using Wideband Power Recycling. Yang, H.-S., +, TMTT Dec. 2015 4437-4443 A Novel Load Mismatch Detection and Correction Technique for 3G/4G Load Insensitive Power Amplifier Application. Ji, D., +, TMTT May 2015 1530-1543 A Prototype SAW-Less LTE Transmitter With a High-Linearity Modulator Using BPF-Based I/Q Summing and a Triple-Layer Marchand Balun. Nakamura, T., +, TMTT Dec. 2015 4090-4097 A Pulsed Dynamic Load Modulation Technique for High-Efficiency Linear Transmitters. Jeon, M.-S., +, TMTT Sep. 2015 2854-2866 A Tunable RF Front-End With Narrowband Antennas for Mobile Devices. Bahramzy, P., +, TMTT Oct. 2015 3300-3310 A Wideband Pulse-Modulated Polar Transmitter Using Envelope Correction for LTE Applications. Liang, K.-F., +, TMTT Aug. 2015 2603-2608 Asymmetric Broadband Doherty Power Amplifier Using GaN MMIC for Femto-Cell Base-Station. Jee, S., +, TMTT Sep. 2015 2802-2810 Behavioral Modeling and Predistortion of Power Amplifiers Under Sparsity Hypothesis. Reina-Tosina, J., +, TMTT Feb. 2015 745-753 Broadband CMOS Stacked RF Power Amplifier Using Reconfigurable Interstage Network for Wideband Envelope Tracking. Park, S., +, TMTT Apr. 2015 1174-1185 Concurrent Multiband Digital Outphasing Transmitter Architecture Using Multidimensional Power Coding. Chung, S., +, TMTT Feb. 2015 598-613 Digital Mitigation of Transmitter-Induced Receiver Desensitization in Carrier Aggregation FDD Transceivers. Kiayani, A., +, TMTT Nov. 2015 36083623 Digitally Equalized Doherty RF Front-End Architecture for Broadband and Multistandard Wireless Transmitters. Darraji, R., +, TMTT Jun. 2015 19781988 Fully Monolithic BiCMOS Reconfigurable Power Amplifier for Multi-Mode and Multi-Band Applications. Lee, M.-L., +, TMTT Feb. 2015 614-624 Highly Efficient Concurrent Power Amplifier With Controllable Modes. Sun, Y., +, TMTT Dec. 2015 4051-4060 Highly Linear Fully Integrated Wideband RF PA for LTE-Advanced in 180-nm SOI. Francois, B., +, TMTT Feb. 2015 649-658 Linearization and Imbalance Correction Techniques for Broadband Outphasing Power Amplifiers. Hwang, T., +, TMTT Jul. 2015 2185-2198 Multi-Standard Hybrid PLL With Low Phase-Noise Characteristics for GSM/EDGE and LTE Applications. Choi, Y.-C., +, TMTT Oct. 2015 3254-3264 Partitioned Distortion Mitigation in LTE Radio Uplink to Enhance Transmitter Efficiency. Amiri, M. V., +, TMTT Aug. 2015 2661-2671 Spectra-Folding Feedback Architecture for Concurrent Dual-Band Power Amplifier Predistortion. Ma, Y., +, TMTT Oct. 2015 3164-3174 Loop antennas Mode Power Amplifier Design ApAn Integrated Continuous Classproach for Microwave Enhanced Portable Diagnostic Applications. Imtiaz, A., +, TMTT Oct. 2015 3007-3015 Losses Design of X-Band GaN Phase Shifters. Ross, T. N., +, TMTT Jan. 2015 244-255 High Power Latching RF MEMS Switches. Bakri-Kassem, M., +, TMTT Jan. 2015 222-232 Low noise amplifiers (InP) HEMT Small-Signal Equivalent-Circuit Extraction as a Function of Temperature. Alt, A. R., +, TMTT Sep. 2015 2751-2755 -Band Dual-Polarization Phased-Array Transceiver Front-End in SiGe BiCMOS. Natarajan, A., +, TMTT Jun. 2015 1989-2002 A 2.88 mW 9.06 dBm IIP3 Common-Gate LNA With Dual Cross-Coupled Capacitive Feedback. Han, H. G., +, TMTT Mar. 2015 1019-1025 A Fully Nonlinear Compact Modeling Approach for High-Frequency Noise in Large-Signal Operated Microwave Electron Devices. Traverso, P. A., +, TMTT Feb. 2015 352-366 Efficient Statistical Simulation of Microwave Devices Via Stochastic Testing-Based Circuit Equivalents of Nonlinear Components. Manfredi, P., +, TMTT May 2015 1502-1511 Millimeter-Wave Low-Noise Amplifier Design in 28-nm Low-Power Digital CMOS. Fritsche, D., +, TMTT Jun. 2015 1910-1922

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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 63, NO. 12, DECEMBER 2015

RF Input Matching Design for Closed-Loop Direct Delta–Sigma Receivers. Ostman, K. B., +, TMTT Apr. 2015 1370-1379 Silicon-Based True-Time-Delay Phased-Array Front-Ends at Ka-Band. Ma, Q., +, TMTT Sep. 2015 2942-2952 Transformer-Feedback Interstage Bandwidth Enhancement for MMIC Multistage Amplifiers. Nikandish, G., +, TMTT Feb. 2015 441-448 Low-noise amplifiers Corrections to “Unified Theory of Linear Noisy Two-Ports” [Nov 13 39863997]. Dietrich, J. L., TMTT Feb. 2015 554 Low-pass filters A Millimeter-Wave WPAN Adaptive Phased Array Control Method Using Low-Frequency Part of Signal for Self-Directed System. Ta, T. T., +, TMTT Aug. 2015 2682-2691 A Post-Matching Doherty Power Amplifier Employing Low-Order Impedance Inverters for Broadband Applications. Pang, J., +, TMTT Dec. 2015 4061-4071 Chebyshev Filter Design Using Vias as Quasi-Transmission Lines in Printed Circuit Boards. Hardock, A., +, TMTT Mar. 2015 976-985 Exact Design of a New Class of Generalized Chebyshev Low-Pass Filters Using Coupled Line/Stub Sections. Musonda, E., +, TMTT Dec. 2015 43554365 High Rejection, Self-Packaged Low-Pass Filter Using Multilayer Liquid Crystal Polymer Technology. Cervera, F., +, TMTT Dec. 2015 3920-3928 Integral-Equation Formulation for the Analysis of Capacitive Waveguide Filters Containing Dielectric and Metallic Arbitrarily Shaped Objects and Novel Applications. Quesada Pereira, F. D., +, TMTT Dec. 2015 38623873 Low-power electronics A Stacked-FET Linear SOI CMOS Cellular Antenna Switch With an Extremely Low-Power Biasing Strategy. Im, D., +, TMTT Jun. 2015 19641977 An 8-bit 100-GS/s Distributed DAC in 28-nm CMOS for Optical Communications. Huang, H., +, TMTT Apr. 2015 1211-1218 Broadband Circuit Techniques for Multi-Terahertz Gain-BandwidthProduct Low-Power Applications. Gharib, A., +, TMTT Nov. 2015 3701-3712 Improving Power Utilization Factor of Broadband Doherty Amplifier by Using Bandpass Auxiliary Transformer. Fang, X.-H., +, TMTT Sep. 2015 2811-2820 Millimeter-Wave Low-Noise Amplifier Design in 28-nm Low-Power Digital CMOS. Fritsche, D., +, TMTT Jun. 2015 1910-1922 Reducing Energy Dissipation in ULP Systems: PLL-Free FBAR-Based Fast Startup Transmitters. Thirunarayanan, R., +, TMTT Apr. 2015 1110-1117 Lumped parameter networks An LTCC Coupled Resonator Decoupling Network for Two Antennas. Qian, K., +, TMTT Oct. 2015 3199-3207 Large-Scale Power Combining and Mixed-Signal Linearizing Architectures for Watt-Class mmWave CMOS Power Amplifiers. Bhat, R., +, TMTT Feb. 2015 703-718 Reflectionless Filter Structures. Morgan, M. A., +, TMTT Apr. 2015 12631271

M Magnetic anisotropy Self-Biased Y-Junction Circulators Using Lanthanum- and Cobalt-Substituted Strontium Hexaferrites. Laur, V., +, TMTT Dec. 2015 4376-4381 Magnetic circuits A 47.6–71.0-GHz 65-nm CMOS VCO Based on Magnetically Coupled -Type LC Network. Jia, H., +, TMTT May 2015 1645-1657 Compact Multi-Band Bandpass Filters With Mixed Electric and Magnetic Coupling Using Multiple-Mode Resonator. Xu, J., +, TMTT Dec. 2015 3909-3919 Magnetic devices Dispersion Modeling and Analysis for Multilayered Open Coaxial Waveguides. Nordebo, S., +, TMTT Jun. 2015 1791-1799 Magnetic field integral equations Determination of Normalized Magnetic Eigenfields in Microwave Cavities. Helsing, J., +, TMTT May 2015 1457-1467 Radial Transmission-Line Approach for the Analysis of Ring Loaded Slots in Circular Waveguide. Addamo, G., +, TMTT May 2015 1468-1474

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Magnetic fields An Investigation of Electromagnetic Radiated Emission and Interference From Multi-Coil Wireless Power Transfer Systems Using Resonant Magnetic Field Coupling. Kong, S., +, TMTT Mar. 2015 833-846 Development of the Optimization Framework for Low-Power Wireless Power Transfer Systems. Lee, S. B., +, TMTT Mar. 2015 813-820 Free-Positioning Wireless Charging System for Small Electronic Devices Using a Bowl-Shaped Transmitting Coil. Kim, J., +, TMTT Mar. 2015 791-800 Self-Biased Y-Junction Circulators Using Lanthanum- and Cobalt-Substituted Strontium Hexaferrites. Laur, V., +, TMTT Dec. 2015 4376-4381 Synthesis and Design of Programmable Subwavelength Coil Array for NearField Manipulation. Gao, F., +, TMTT Sep. 2015 2971-2982 Time-Domain Electromagnetic Analysis of Multilayer Structures Using the Surface Equivalent Principle and Mixed-Potential Integral Equations. Maftooli, H., +, TMTT Jan. 2015 99-106 Magnetic leakage Self-Biased Y-Junction Circulators Using Lanthanum- and Cobalt-Substituted Strontium Hexaferrites. Laur, V., +, TMTT Dec. 2015 4376-4381 Magnetic materials Integral-Equation Formulation for the Analysis of Capacitive Waveguide Filters Containing Dielectric and Metallic Arbitrarily Shaped Objects and Novel Applications. Quesada Pereira, F. D., +, TMTT Dec. 2015 38623873 Magnetic permeability Fractal Frequency-Selective Surface Embedded Thin Broadband Microwave Absorber Coatings Using Heterogeneous Composites. Panwar, R., +, TMTT Aug. 2015 2438-2448 Planar Distributed Full-Tensor Anisotropic Metamaterials for Transformation Electromagnetics. Nagayama, T., +, TMTT Dec. 2015 3851-3861 Magnetic resonance Advanced Power Control Scheme in Wireless Power Transmission for Human Protection From EM Field. Kim, S.-M., +, TMTT Mar. 2015 847-856 Efficiency and Optimal Loads Analysis for Multiple-Receiver Wireless Power Transfer Systems. Fu, M., +, TMTT Mar. 2015 801-812 Resonant Electrical Coupling: Circuit Model and First Experimental Results. Dias Fernandes, R., +, TMTT Sep. 2015 2983-2990 Magnetic resonance imaging Active Detuning of MRI Receive Coils with GaN FETs. Twieg, M., +, TMTT Dec. 2015 4169-4177 Mammography Computational Feasibility Study of Contrast-Enhanced Thermoacoustic Imaging for Breast Cancer Detection Using Realistic Numerical Breast Phantoms. Wang, X., +, TMTT May 2015 1489-1501 Manifolds Efficient Design of Waveguide Manifold Multiplexers Based on Low-Order EM Distributed Models. Cogollos, S., +, TMTT Aug. 2015 2540-2549 Masks Behavioral Modeling and Predistortion of Power Amplifiers Under Sparsity Hypothesis. Reina-Tosina, J., +, TMTT Feb. 2015 745-753 Matched filters A 1.4–2.3-GHz Tunable Diplexer Based on Reconfigurable Matching Networks. Ko, C. H., +, TMTT May 2015 1595-1602 Materials testing 60-GHz Substrate Materials Characterization Using the Covered Transmission-Line Method. Papio Toda, A., +, TMTT Mar. 2015 1063-1075 Design of Multilayered Epsilon-Near-Zero Microwave Planar Sensor for Testing of Dispersive Materials. Jha, A. K., +, TMTT Aug. 2015 2418-2426 Material Characterization of Arbitrarily Shaped Dielectrics Based on Reflected Pulse Characteristics. Chan, K.K.M., +, TMTT May 2015 1700-1709 Single-Compound Complementary Split-Ring Resonator for Simultaneously Measuring the Permittivity and Thickness of Dual-Layer Dielectric Materials. Lee, C.-S., +, TMTT Jun. 2015 2010-2023 Mathematical model A Transformer-Based Poly-Phase Network for Ultra-Broadband Quadrature Signal Generation. Park, J. S., +, TMTT Dec. 2015 4444-4457 Corrections to “Compact Conical-Line Power Combiner Design Using Circuit Models” [Nov 14 2650-2658]. Beyers, R. D., +, TMTT Jul. 2015 2391 Matrix algebra Accurate and Stable Matrix-Free Time-Domain Method in 3-D Unstructured Meshes for General Electromagnetic Analysis. Yan, J., +, TMTT Dec. 2015 4201-4214

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 63, NO. 12, DECEMBER 2015

Alternative Method for Making Explicit FDTD Unconditionally Stable. Gaffar, Md., +, TMTT Dec. 2015 4215-4224 Analytical Reflection Coefficient Expressions Utilizing Load-Dependent -Parameters. Gou, Y., +, TMTT Oct. 2015 3142-3152 Coupling Matrix Synthesis of Nonreciprocal Lossless Two-Port Networks Using Gyrators and Inverters. Zhang, Q., +, TMTT Sep. 2015 2782-2792 Coupling-Matrix-Based Design of HighBandpass Filters Using Acoustic-Wave Lumped-Element Resonator (AWLR) Modules. Psychogiou, D., +, TMTT Dec. 2015 4319-4328 Generalized Theory of the Thru-Reflect-Match Calibration Technique. Pulido-Gaytan, M. A., +, TMTT May 2015 1693-1699 Mode Filters for Oversized Rectangular Waveguides: A Modal Approach. Ceccuzzi, S., +, TMTT Aug. 2015 2468-2481 Novel Coupling Matrix Synthesis for Single-Layer Substrate-Integrated Evanescent-Mode Cavity Tunable Bandstop Filter Design. Saeedi, S., +, TMTT Dec. 2015 3929-3938 On the Development and Evaluation of Spatial-Domain Green’s Functions for Multilayered Structures With Conductive Sheets. Koufogiannis, I. D., +, TMTT Jan. 2015 20-29 Parametric History Analysis for Material Properties Using Finite Elements and Adaptive Perturbations. Gunel, S., +, TMTT Jan. 2015 90-98 Resonator Voltage Prediction in Microwave Bandpass Filters. Vanin, F. M., +, TMTT Feb. 2015 397-402 Wideband Balanced Network with High Isolation Using Double-Sided Parallel-Strip Line. Feng, W., +, TMTT Dec. 2015 4013-4018 Matrix decomposition An Inverse-Based Multifrontal Block Incomplete LU Preconditioner for the 3-D Finite-Element Eigenvalue Analysis of Lossy Slow-Wave Structures. Wang, H., +, TMTT Jul. 2015 2094-2106 Matrix inversion A Linear Complexity Direct Volume Integral Equation Solver for Full-Wave 3-D Circuit Extraction in Inhomogeneous Materials. Omar, S., +, TMTT Mar. 2015 897-912 Maximum likelihood estimation A Distributed Positioning System Based on a Predictive Fingerprinting Method Enabling Sub-Metric Precision in IEEE 802.11 Networks. Maddio, S., +, TMTT Dec. 2015 4567-4580 Behavioral Modeling and Predistortion of Power Amplifiers Under Sparsity Hypothesis. Reina-Tosina, J., +, TMTT Feb. 2015 745-753 Maxwell equations A Nodal Continuous-Discontinuous Galerkin Time-Domain Method for Maxwell's Equations. Angulo, L. D., +, TMTT Oct. 2015 3081-3093 Estimating the Inf-Sup Constant in Reduced Basis Methods for Time-Harmonic Maxwell’s Equations. Hess, M. W., +, TMTT Nov. 2015 3549-3557 Influence of Numerical Method and Geometry Used by Maxwell's Equation Solvers on Simulations of Ferroelectric Thin-Film Capacitors. Furlan, V., +, TMTT Mar. 2015 891-896 Mixed Spectral-Element Method for 3-D Maxwell's Eigenvalue Problem. Liu, N., +, TMTT Feb. 2015 317-325 Non-Reflecting SFBF Termination Inverting From TFSF Discontinuity Decomposition. Tan, T., TMTT Sep. 2015 2710-2719 Planar Distributed Full-Tensor Anisotropic Metamaterials for Transformation Electromagnetics. Nagayama, T., +, TMTT Dec. 2015 3851-3861 The Effects of Electrode Configuration on Body Channel Communication Based on Analysis of Vertical and Horizontal Electric Dipoles. Bae, J., +, TMTT Apr. 2015 1409-1420 TLM Nodes: A New Look at an Old Problem. Salinas, A., +, TMTT Aug. 2015 2449-2458 Mean square error methods 3-D Fourier Series Based Digital Predistortion Technique for Concurrent Dual-Band Envelope Tracking With Reduced Envelope Bandwidth. Lin, Y., +, TMTT Sep. 2015 2764-2775 A 220–320-GHz Vector-Sum Phase Shifter Using Single Gilbert-Cell Structure With Lossy Output Matching. Kim, Y., +, TMTT Jan. 2015 256-265 A New Double Input-Double Output Complex Envelope Amplifier Behavioral Model Taking Into Account Source and Load Mismatch Effects. Zargar, H., +, TMTT Feb. 2015 766-774 Multi-Standard Hybrid PLL With Low Phase-Noise Characteristics for GSM/EDGE and LTE Applications. Choi, Y.-C., +, TMTT Oct. 2015 3254-3264 Measurement errors Single-Compound Complementary Split-Ring Resonator for Simultaneously Measuring the Permittivity and Thickness of Dual-Layer Dielectric Materials. Lee, C.-S., +, TMTT Jun. 2015 2010-2023 + Check author entry for coauthors

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Measurement standards Generalized Theory of the Thru-Reflect-Match Calibration Technique. Pulido-Gaytan, M. A., +, TMTT May 2015 1693-1699 Measurement uncertainty Accuracy and Bandwidth Optimization of the Over-Determined Offset-Short Reflectometer Calibration. Lewandowski, A., +, TMTT Mar. 2015 1076-1089 Accurate Evaluation Technique of Complex Permittivity for Low-Permittivity Dielectric Films Using a Cavity Resonator Method in 60-GHz Band. Shimizu, T., +, TMTT Jan. 2015 279-286 Determination of Reference-Plane Invariant, Thickness-Independent, and Broadband Constitutive Parameters of Thin Materials. Hasar, U. C., +, TMTT Jul. 2015 2313-2321 Evaluation of Uncertainty in Temporal Waveforms of Microwave Transistors. Avolio, G., +, TMTT Jul. 2015 2353-2363 Medical image processing Computational Feasibility Study of Contrast-Enhanced Thermoacoustic Imaging for Breast Cancer Detection Using Realistic Numerical Breast Phantoms. Wang, X., +, TMTT May 2015 1489-1501 Synthesis and Design of Programmable Subwavelength Coil Array for NearField Manipulation. Gao, F., +, TMTT Sep. 2015 2971-2982 Medical signal detection A High-Sensitivity Fully Passive Neurosensing System for Wireless Brain Signal Monitoring. Lee, C. W. L., +, TMTT Jun. 2015 2060-2068 Medical signal processing Channel Imbalance Effects and Compensation for Doppler Radar Physiological Measurements. Yavari, E., +, TMTT Nov. 2015 3834-3842 Propagation, Power Absorption, and Temperature Analysis of UWB Wireless Capsule Endoscopy Devices Operating in the Human Body. Thotahewa, K. M. S., +, TMTT Nov. 2015 3823-3833 Meetings Guest Editorial. Rodenbeck, C. T., TMTT Dec. 2015 4199-4200 Guest Editorial. Alomainy, A., +, TMTT Oct. 2015 3005-3006 Guest Editorial. Gharpurey, R., TMTT Apr. 2015 1109 Guest Editorial. Ghorbani, K., +, TMTT Aug. 2015 2397-2398 Guest Editorial. KIM, J., +, TMTT Mar. 2015 778-779 Guest Editorial [Mini-Special Issue on 2014 IEEE International Conference on Numerical Electromagnetic Modeling and Optimization for RF, Microwave, and Terahertz Applications (NEMO2014. Bozzi, M., +, TMTT Jan. 2015 1-2 Metals Ultra-Miniature SIW Cavity Resonators and Filters. Pourghorban Saghati, A., +, TMTT Dec. 2015 4329-4340 Metamaterials Energy Coupled Mode Theory for Electromagnetic Resonators. Elnaggar, S. Y., +, TMTT Jul. 2015 2115-2123 Method of moments An Analysis of Multistrip Line Configuration on Elliptical Cylinder. Kusiek, A., +, TMTT Jun. 2015 1800-1808 An Empirical Expression to Predict the Resonant Frequencies of Archimedean Spirals. Hooker, J. W., +, TMTT Jul. 2015 2107-2114 Design of a Traveling-Wave Slot Array Power Divider Using the Method of Moments and a Genetic Algorithm. Rengarajan, S. R., +, TMTT Dec. 2015 3981-3987 Skew Incidence Plane-Wave Scattering From 2-D Dielectric Periodic Structures: Analysis by the Mortar-Element Method. Tibaldi, A., +, TMTT Jan. 2015 11-19 Microchannel flow A Miniaturized Microfluidically Reconfigurable Coplanar Waveguide Bandpass Filter With Maximum Power Handling of 10 Watts. Pourghorban Saghati, A., +, TMTT Aug. 2015 2515-2525 Microcontrollers Ambient RF Energy Harvesting From a Two-Way Talk Radio for Flexible Wearable Wireless Sensor Devices Utilizing Inkjet Printing Technologies. Bito, J., +, TMTT Dec. 2015 4533-4543 Microfabrication A 1.6–2.3-GHz RF MEMS Reconfigurable Quadrature Coupler and Its Application to a 360 Reflective-Type Phase Shifter. Gurbuz, O. D., +, TMTT Feb. 2015 414-421 Modelling and Measurements of the Microwave Dielectric Properties of Microspheres. Abduljabar, A. A., +, TMTT Dec. 2015 4492-4500 Microfluidics Adaptive Coupling of Resonators for Efficient Microwave Heating of Microfluidic Systems. Abduljabar, A. A., +, TMTT Nov. 2015 3681-3690

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Microfluidically Tunable Microstrip Filters. Diedhiou, D. L., +, TMTT Jul. 2015 2245-2252 Miniaturized Transmission-Line Sensor for Broadband Dielectric Characterization of Biological Liquids and Cell Suspensions. Meyne nee Haase, N., +, TMTT Oct. 2015 3026-3033 Modelling and Measurements of the Microwave Dielectric Properties of Microspheres. Abduljabar, A. A., +, TMTT Dec. 2015 4492-4500 Whispering-Gallery-Mode Resonator Technique With Microfluidic Channel for Permittivity Measurement of Liquids. Gubin, A. I., +, TMTT Jun. 2015 2003-2009 Micromachining Micromachined Room-Temperature Air-Suspended Ni/Cr Nanobolometer. Yang, H.-H., +, TMTT Nov. 2015 3760-3767 Millimeter-Wave Near-Field Probe Designed for High-Resolution Skin Cancer Diagnosis. Topfer, F., +, TMTT Jun. 2015 2050-2059 Reliability Analysis of Ku-Band 5-bit Phase Shifters Using MEMS SP4T and SPDT Switches. Dey, S., +, TMTT Dec. 2015 3997-4012 Micromechanical devices A 1.3–2.4-GHz 3.1-mW VCO Using Electro-Thermo- Mechanically Tunable Self-Assembled MEMS Inductor on HR Substrate. Bhattacharya, A., +, TMTT Feb. 2015 459-469 A 1.6–2.3-GHz RF MEMS Reconfigurable Quadrature Coupler and Its Application to a 360 Reflective-Type Phase Shifter. Gurbuz, O. D., +, TMTT Feb. 2015 414-421 RF-Designed High-Power Lamb-Wave Aluminum–Nitride Resonators. Campanella, H., +, TMTT Feb. 2015 331-339 Microsensors Micromachined Room-Temperature Air-Suspended Ni/Cr Nanobolometer. Yang, H.-H., +, TMTT Nov. 2015 3760-3767 Miniaturized Transmission-Line Sensor for Broadband Dielectric Characterization of Biological Liquids and Cell Suspensions. Meyne nee Haase, N., +, TMTT Oct. 2015 3026-3033 Microstrip antenna arrays -Band Spatially Combined Power Amplifier Arrays in 45-nm CMOS SOI. Hanafi, B., +, TMTT Jun. 2015 1937-1950 A 2.45 GHz Phased Array Antenna Unit Cell Fabricated Using 3-D MultiLayer Direct Digital Manufacturing. Ketterl, T. P., +, TMTT Dec. 2015 4382-4394 A 37.5-mW 8-dBm-EIRP 15.5 -HPBW 338-GHz Terahertz Transmitter Using SoP Heterogeneous System Integration. Li, C.-H., +, TMTT Feb. 2015 470-480 Microstrip antennas 3D-Printed Origami Packaging With Inkjet-Printed Antennas for RF Harvesting Sensors. Kimionis, J., +, TMTT Dec. 2015 4521-4532 Compact Printable Chipless RFID Systems. Islam, M. A., +, TMTT Nov. 2015 3785-3793 Textile Microwave Components in Substrate Integrated Waveguide Technology. Moro, R., +, TMTT Feb. 2015 422-432 Microstrip circuits Microfluidically Tunable Microstrip Filters. Diedhiou, D. L., +, TMTT Jul. 2015 2245-2252 Microstrip components Dielectric Characterization of Ultra-Thin Low-Loss Build-Up Substrate for System-in-Package (SiP) Modules. Ho, C.-Y., +, TMTT Sep. 2015 29232930 Microstrip couplers Design of High-Directivity Wideband Microstrip Directional Coupler With Fragment-Type Structure. Wang, L., +, TMTT Dec. 2015 3962-3970 Microstrip filters A Balanced-to-Unbalanced Microstrip Power Divider With Filtering Function. Xu, K., +, TMTT Aug. 2015 2561-2569 A Four-Way Microstrip Filtering Power Divider With Frequency-Dependent Couplings. Chen, F.-J., +, TMTT Oct. 2015 3494-3504 Automated Design of Common-Mode Suppressed Balanced Wideband Bandpass Filters by Means of Aggressive Space Mapping. Sans, M., +, TMTT Dec. 2015 3896-3908 Microfluidically Tunable Microstrip Filters. Diedhiou, D. L., +, TMTT Jul. 2015 2245-2252 Rapid Yield Estimation and Optimization of Microwave Structures Exploiting Feature-Based Statistical Analysis. Koziel, S., +, TMTT Jan. 2015 107-114 Reliable Microwave Modeling by Means of Variable-Fidelity Response Features. Koziel, S., +, TMTT Dec. 2015 4247-4254 + Check author entry for coauthors

Suppression of Harmonics in Microstrip Filters Using a Combination of Techniques. Huang, F., TMTT Oct. 2015 3453-3461 Temporal Coupled-Mode Theory and the Combined Effect of Dual Orthogonal Resonant Modes in Microstrip Bandpass Filters. Yu, F., +, TMTT Feb. 2015 403-413 Microstrip lines A Novel 1 4 Coupler for Compact and High-Gain Power Amplifier MMICs Around 250 GHz. Diebold, S., +, TMTT Mar. 2015 999-1006 Broadband Microwave Attenuator Based on Few Layer Graphene Flakes. Pierantoni, L., +, TMTT Aug. 2015 2491-2497 Design and Modeling of Spoof Surface Plasmon Modes-Based Microwave Slow-Wave Transmission Line. Kianinejad, A., +, TMTT Jun. 2015 18171825 Microstrip Device for Broadband (15–65 GHz) Measurement of Dielectric Properties of Nematic Liquid Crystals. Deo, P., +, TMTT Apr. 2015 13881398 Modeling of Inline Transitions Between Different Waveguides as Impedance Inverters for the Use in Novel Filter Designs. Strauss, G., +, TMTT Nov. 2015 3663-3670 Planar Distributed Full-Tensor Anisotropic Metamaterials for Transformation Electromagnetics. Nagayama, T., +, TMTT Dec. 2015 3851-3861 Wideband Differential Bandpass Filters on Multimode Slotline Resonator With Intrinsic Common-Mode Rejection. Guo, X., +, TMTT May 2015 1587-1594 Microstrip resonators Adaptive Coupling of Resonators for Efficient Microwave Heating of Microfluidic Systems. Abduljabar, A. A., +, TMTT Nov. 2015 3681-3690 Automated Design of Common-Mode Suppressed Balanced Wideband Bandpass Filters by Means of Aggressive Space Mapping. Sans, M., +, TMTT Dec. 2015 3896-3908 Corrections to “Design and Fabrication of Broadband Hybrid GaAs Schottky Diode Frequency Multipliers” [Dec 13 4442-4460]. Hrobak, M., +, TMTT Feb. 2015 553 Microstrip Whispering-Gallery-Mode Resonator. Bunyaev, S. A., +, TMTT Sep. 2015 2776-2781 Microstrip transitions Coaxial End-Launched and Microstrip to Partial -Plane Waveguide Transitions. Kloke, K. H., +, TMTT Oct. 2015 3103-3108 Design and Validation of Microstrip Gap Waveguides and Their Transitions to Rectangular Waveguide, for Millimeter-Wave Applications. Brazalez, A. A., +, TMTT Dec. 2015 4035-4050 Mode Substrate Integrated Wideband Excitation Technology of Waveguide (SIW) and Its Applications. Wu, P., +, TMTT Jun. 2015 1863-1874 Wideband Microstrip-to-Microstrip Vertical Transitions Via Multiresonant Modes in a Slotline Resonator. Guo, X., +, TMTT Jun. 2015 1902-1909 Microswitches High Power Latching RF MEMS Switches. Bakri-Kassem, M., +, TMTT Jan. 2015 222-232 High- Tunable Waveguide Filters Using Ohmic RF MEMS Switches. Pelliccia, L., +, TMTT Oct. 2015 3381-3390 Monolithic Millimeter-Wave MEMS Waveguide Switch. Vahabisani, N., +, TMTT Feb. 2015 340-351 Reliability Analysis of Ku-Band 5-bit Phase Shifters Using MEMS SP4T and SPDT Switches. Dey, S., +, TMTT Dec. 2015 3997-4012 Microwave amplifiers A Fully Nonlinear Compact Modeling Approach for High-Frequency Noise in Large-Signal Operated Microwave Electron Devices. Traverso, P. A., +, TMTT Feb. 2015 352-366 A K-Band Reconfigurable Pulse-Compression Automotive Radar Transmitter in 90-nm CMOS. Tan, K.-W., +, TMTT Apr. 2015 1380-1387 Analytical Reflection Coefficient Expressions Utilizing Load-Dependent -Parameters. Gou, Y., +, TMTT Oct. 2015 3142-3152 Design and Analysis of 24-GHz Active Isolator and Quasi-Circulator. Chang, J.-F., +, TMTT Aug. 2015 2638-2649 Microwave antenna arrays Concurrent Detection of Vibration and Distance Using Unmodulated CW Doppler Vibration Radar With An Adaptive Beam-Steering Antenna. Nieh, C.-M., +, TMTT Jun. 2015 2069-2078 Microwave antennas 160-GHz to 1-THz Multi-Color Active Imaging With a Lens-Coupled SiGe HBT Chip-Set. Statnikov, K., +, TMTT Feb. 2015 520-532 A Compact Dual-Channel Transceiver for Long-Range Passive Embedded Monitoring. Nassar, I. T., +, TMTT Jan. 2015 287-294

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Near-Field Microwave Distribution Measurement With a Point Detector Base on Thermoacoustic Effect. Ding, W., +, TMTT Oct. 2015 3272-3276 Real-Time Adaptive Transmitter Leakage Cancelling in 5.8-GHz Full-Duplex Transceivers. Maddio, S., +, TMTT Feb. 2015 509-519 Reconfigurable Diffractive Antenna Based on Switchable Electrically Induced Transparency. Li, H., +, TMTT Mar. 2015 925-936 Textile Microwave Components in Substrate Integrated Waveguide Technology. Moro, R., +, TMTT Feb. 2015 422-432 Microwave bipolar transistors 160-GHz to 1-THz Multi-Color Active Imaging With a Lens-Coupled SiGe HBT Chip-Set. Statnikov, K., +, TMTT Feb. 2015 520-532 Consistent Modeling and Power Gain Analysis of Microwave SiGe HBTs in CE and CB Configurations. Alvarez-Botero, G., +, TMTT Dec. 2015 38883895 Microwave circuits A Varactor-Based Variable Attenuator Design With Enhanced Linearity Performance. Cheng, K.-K. M., +, TMTT Oct. 2015 3191-3198 Breaking the Efficiency Barrier for Ambient Microwave Power Harvesting With Heterojunction Backward Tunnel Diodes. Lorenz, C. H. P., +, TMTT Dec. 2015 4544-4555 Design and Modeling of Spoof Surface Plasmon Modes-Based Microwave Slow-Wave Transmission Line. Kianinejad, A., +, TMTT Jun. 2015 18171825 Design of Waveguide Microwave Pulse Compressors Using Equivalent Circuits. Savaidis, S. P., +, TMTT Jan. 2015 125-134 Expedited Geometry Scaling of Compact Microwave Passives by Means of Inverse Surrogate Modeling. Koziel, S., +, TMTT Dec. 2015 4019-4026 Optimized Design of Frequency Dividers Based on Varactor-Inductor Cells. Ponton, M., +, TMTT Dec. 2015 4458-4472 Power Synthesis at 110-GHz Frequency Based on Discrete Sources. Zhao, J., +, TMTT May 2015 1633-1644 Textile Microwave Components in Substrate Integrated Waveguide Technology. Moro, R., +, TMTT Feb. 2015 422-432 Theoretical Energy-Conversion Efficiency for Energy-Harvesting Circuits Under Power-Optimized Waveform Excitation. Valenta, C. R., +, TMTT May 2015 1758-1767 Microwave circulators Quality Factor of the Waveguide Re-Entrant Turnstile Junction Circulator. Helszajn, J., +, TMTT May 2015 1603-1608 Microwave communication Guest Editorial. Ghorbani, K., +, TMTT Aug. 2015 2397-2398 Microwave communications Guest Editorial. Rodenbeck, C. T., TMTT Dec. 2015 4199-4200 Microwave detectors A Compact L-Band Orthomode Transducer for Radio Astronomical Receivers at Cryogenic Temperature. Valente, G., +, TMTT Oct. 2015 32183227 Design of Multilayered Epsilon-Near-Zero Microwave Planar Sensor for Testing of Dispersive Materials. Jha, A. K., +, TMTT Aug. 2015 2418-2426 Modelling and Measurements of the Microwave Dielectric Properties of Microspheres. Abduljabar, A. A., +, TMTT Dec. 2015 4492-4500 Near-Field Microwave Distribution Measurement With a Point Detector Base on Thermoacoustic Effect. Ding, W., +, TMTT Oct. 2015 3272-3276 Passive Microwave Substrate Integrated Cavity Resonator for Humidity Sensing. El Matbouly, H., +, TMTT Dec. 2015 4150-4156 Microwave devices -Mode An Isolated Radial Power Divider via Circular Waveguide Transducer. Chu, Q.-X., +, TMTT Dec. 2015 3988-3996 Broadband Microwave Attenuator Based on Few Layer Graphene Flakes. Pierantoni, L., +, TMTT Aug. 2015 2491-2497 Compact Behavioral Models of Nonlinear Active Devices Using Response Surface Methodology. Barmuta, P., +, TMTT Jan. 2015 56-64 High Power Latching RF MEMS Switches. Bakri-Kassem, M., +, TMTT Jan. 2015 222-232 Microwave field effect transistors 160-GHz to 1-THz Multi-Color Active Imaging With a Lens-Coupled SiGe HBT Chip-Set. Statnikov, K., +, TMTT Feb. 2015 520-532 A Broadband GaN pHEMT Power Amplifier Using Non-Foster Matching. Lee, S., +, TMTT Dec. 2015 4406-4414 Millimeter-Wave Low-Noise Amplifier Design in 28-nm Low-Power Digital CMOS. Fritsche, D., +, TMTT Jun. 2015 1910-1922 + Check author entry for coauthors

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Microwave filters A 0.2–3.6-GHz 10-dBm B1dB 29-dBm IIP3 Tunable Filter for Transmit Leakage Suppression in SAW-Less 3G/4G FDD Receivers. Luo, C., +, TMTT Oct. 2015 3514-3524 A 1.4–2.3-GHz Tunable Diplexer Based on Reconfigurable Matching Networks. Ko, C. H., +, TMTT May 2015 1595-1602 A Miniaturized Microfluidically Reconfigurable Coplanar Waveguide Bandpass Filter With Maximum Power Handling of 10 Watts. Pourghorban Saghati, A., +, TMTT Aug. 2015 2515-2525 A New Broadband Common-Mode Noise Absorption Circuit for High-Speed Differential Digital Systems. Hsiao, C.-Y., +, TMTT Jun. 2015 1894-1901 Advanced Butler Matrices With Integrated Bandpass Filter Functions. Tornielli di Crestvolant, V., +, TMTT Oct. 2015 3433-3444 An Ultra-Compact Common-Mode Bandstop Filter With Modified-T Circuits in Integrated Passive Device (IPD) Process. Hsiao, C.-Y., +, TMTT Nov. 2015 3624-3631 An Ultra-Low Phase-Noise 20-GHz PLL Utilizing an Optoelectronic Voltage-Controlled Oscillator. Bluestone, A., +, TMTT Mar. 2015 1046-1052 Chebyshev Filter Design Using Vias as Quasi-Transmission Lines in Printed Circuit Boards. Hardock, A., +, TMTT Mar. 2015 976-985 Cognition-Driven Formulation of Space Mapping for Equal-Ripple Optimization of Microwave Filters. Zhang, C., +, TMTT Jul. 2015 2154-2165 Design and Multiphysics Analysis of Direct and Cross-Coupled SIW Combline Filters Using Electric and Magnetic Couplings. Sirci, S., +, TMTT Dec. 2015 4341-4354 Design of Compact Wideband Manifold-Coupled Multiplexers. Carceller, C., +, TMTT Oct. 2015 3398-3407 Enhanced Topology of -Plane Resonators for High-Power Satellite Applications. Peverini, O. A., +, TMTT Oct. 2015 3361-3373 Guest Editorial. Boria, V. E., +, TMTT Oct. 2015 3321-3323 High Rejection, Self-Packaged Low-Pass Filter Using Multilayer Liquid Crystal Polymer Technology. Cervera, F., +, TMTT Dec. 2015 3920-3928 K-Band Frequency Tunable Substrate-Integrated- Waveguide Resonator Filter With Enhanced Stopband Attenuation. Lee, B., +, TMTT Nov. 2015 3632-3640 Ka-Band Dual-Mode Super Filters and Multiplexers. Yassini, B., +, TMTT Oct. 2015 3391-3397 Microwave Bandpass Filters Using Re-Entrant Resonators. Musonda, E., +, TMTT Mar. 2015 954-964 Radial Transmission-Line Approach for the Analysis of Ring Loaded Slots in Circular Waveguide. Addamo, G., +, TMTT May 2015 1468-1474 Rapid Yield Estimation and Optimization of Microwave Structures Exploiting Feature-Based Statistical Analysis. Koziel, S., +, TMTT Jan. 2015 107-114 Reconfigurable Multi-Band Microwave Filters. Gomez-Garcia, R., +, TMTT Apr. 2015 1294-1307 Reflection-Mode Bandstop Filters With Minimum Through-Line Length. Naglich, E. J., +, TMTT Oct. 2015 3479-3486 Reflectionless Filter Structures. Morgan, M. A., +, TMTT Apr. 2015 12631271 Resonator Voltage Prediction in Microwave Bandpass Filters. Vanin, F. M., +, TMTT Feb. 2015 397-402 Synthesis of Cross-Coupled Prototype Filters Including Resonant and NonResonant Nodes. Tamiazzo, S., +, TMTT Oct. 2015 3408-3415 Textile Microwave Components in Substrate Integrated Waveguide Technology. Moro, R., +, TMTT Feb. 2015 422-432 Triple- and Quadruple-Mode Wideband Bandpass Filter Using Simple Perturbation in Single Metal Cavity. Wong, S.-W., +, TMTT Oct. 2015 34163424 Microwave frequency converters Efficient Microwave and Millimeter-Wave Frequency Multipliers Using Nonlinear Transmission Lines in CMOS Technology. Adnan, M., +, TMTT Sep. 2015 2889-2896 Microwave generation 160-GHz to 1-THz Multi-Color Active Imaging With a Lens-Coupled SiGe HBT Chip-Set. Statnikov, K., +, TMTT Feb. 2015 520-532 Microwave heating Adaptive Coupling of Resonators for Efficient Microwave Heating of Microfluidic Systems. Abduljabar, A. A., +, TMTT Nov. 2015 3681-3690 Dynamic Measurement of Dielectric Properties of Materials at High Temperature During Microwave Heating in a Dual Mode Cylindrical Cavity. Catala-Civera, J. M., +, TMTT Sep. 2015 2905-2914

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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 63, NO. 12, DECEMBER 2015

High-Efficiency Applicator Based on Printed Circuit Board in MillimeterWave Region. Shiina, T., +, TMTT Oct. 2015 3311-3318 The Development of Forceps-Type Microwave Tissue Coagulator for Surgical Operation. Endo, Y., +, TMTT Jun. 2015 2041-2049 Microwave imaging 160-GHz to 1-THz Multi-Color Active Imaging With a Lens-Coupled SiGe HBT Chip-Set. Statnikov, K., +, TMTT Feb. 2015 520-532 Qualitative Microwave Imaging With Scattering Parameters Measurements. Akinci, M. N., +, TMTT Sep. 2015 2730-2740 Microwave integrated circuits A 1.1-Gbit/s 10-GHz Outphasing Modulator With 23-dBm Output Power and 60-dB Dynamic Range in 45-nm CMOS SOI. Mehrjoo, M. S., +, TMTT Jul. 2015 2289-2300 Millimeter-Wave Low-Noise Amplifier Design in 28-nm Low-Power Digital CMOS. Fritsche, D., +, TMTT Jun. 2015 1910-1922 Microwave isolators Design and Analysis of 24-GHz Active Isolator and Quasi-Circulator. Chang, J.-F., +, TMTT Aug. 2015 2638-2649 Microwave materials Fractal Frequency-Selective Surface Embedded Thin Broadband Microwave Absorber Coatings Using Heterogeneous Composites. Panwar, R., +, TMTT Aug. 2015 2438-2448 Investigating the Broadband Microwave Absorption of Nanodiamond Impurities. Cuenca, J. A., +, TMTT Dec. 2015 4110-4118 Material Characterization of Arbitrarily Shaped Dielectrics Based on Reflected Pulse Characteristics. Chan, K.K.M., +, TMTT May 2015 1700-1709 Parametric History Analysis for Material Properties Using Finite Elements and Adaptive Perturbations. Gunel, S., +, TMTT Jan. 2015 90-98 Microwave measurement An Accurate Radially Stratified Approach for Determining the Complex Permittivity of Liquids in a Cylindrical Microwave Cavity. Barmatz, M. B., +, TMTT Feb. 2015 504-508 Anisotropic Microwave Conductivity Dispersion of Horizontally Aligned Multi-Walled Carbon- Nanotube Thin Film on Flexible Substrate. Li, S., +, TMTT Nov. 2015 3588-3594 Design of Multilayered Epsilon-Near-Zero Microwave Planar Sensor for Testing of Dispersive Materials. Jha, A. K., +, TMTT Aug. 2015 2418-2426 Determination of Reference-Plane Invariant, Thickness-Independent, and Broadband Constitutive Parameters of Thin Materials. Hasar, U. C., +, TMTT Jul. 2015 2313-2321 Evaluation of Uncertainty in Temporal Waveforms of Microwave Transistors. Avolio, G., +, TMTT Jul. 2015 2353-2363 Microstrip Device for Broadband (15–65 GHz) Measurement of Dielectric Properties of Nematic Liquid Crystals. Deo, P., +, TMTT Apr. 2015 13881398 Modelling and Measurements of the Microwave Dielectric Properties of Microspheres. Abduljabar, A. A., +, TMTT Dec. 2015 4492-4500 Near-Field Microwave Distribution Measurement With a Point Detector Base on Thermoacoustic Effect. Ding, W., +, TMTT Oct. 2015 3272-3276 Photonic Approach to Wide-Frequency-Range High-Resolution Microwave/Millimeter-Wave Doppler Frequency Shift Estimation. Zou, X., +, TMTT Apr. 2015 1421-1430 Qualitative Microwave Imaging With Scattering Parameters Measurements. Akinci, M. N., +, TMTT Sep. 2015 2730-2740 Whispering-Gallery-Mode Resonator Technique With Microfluidic Channel for Permittivity Measurement of Liquids. Gubin, A. I., +, TMTT Jun. 2015 2003-2009 Microwave metamaterials Longitudinally Independent Matching and Arbitrary Wave Patterning Using -Near-Zero Channels. Soric, J. C., +, TMTT Nov. 2015 3558-3567 Polarization Considerations for Scalar Huygens Metasurfaces and Characterization for 2-D Refraction. Wong, J. P. S., +, TMTT Mar. 2015 913-924 Right/Left-Handed Transmission Lines Based on Coupled Transmission Line Sections and Their Application Towards Bandpass Filters. Sorocki, J., +, TMTT Feb. 2015 384-396 Microwave mixers A 0.12-mm 2.4-GHz CMOS Inductorless High Isolation Subharmonic Mixer With Effective Current-Reuse Transconductance. Chong, W. K., +, TMTT Aug. 2015 2427-2437 A K-Band Reconfigurable Pulse-Compression Automotive Radar Transmitter in 90-nm CMOS. Tan, K.-W., +, TMTT Apr. 2015 1380-1387 Microwave oscillators A CML Ring Oscillator-Based Supply-Insensitive PLL With On-Chip Calibrations. Gui, X., +, TMTT Jan. 2015 233-243 + Check author entry for coauthors

A W-Band 4-GHz Bandwidth Phase-Modulated Pulse Compression Radar Transmitter in 65-nm CMOS. Oh, J., +, TMTT Aug. 2015 2609-2618 An Ultra-Low Phase-Noise 20-GHz PLL Utilizing an Optoelectronic Voltage-Controlled Oscillator. Bluestone, A., +, TMTT Mar. 2015 1046-1052 Designs of K-Band Divide-by-2 and Divide-by-3 Injection-Locked Frequency Divider With Darlington Topology. Chien, K.-H., +, TMTT Sep. 2015 2877-2888 GaN Microwave DC–DC Converters. Ramos, I., +, TMTT Dec. 2015 44734482 Global Stability Analysis of Coupled-Oscillator Systems. Suarez, A., +, TMTT Jan. 2015 165-180 Microwave phase shifters A New Compact High-Power Microwave Phase Shifter. Chang, C., +, TMTT Jun. 2015 1875-1882 Adaptive Coupling of Resonators for Efficient Microwave Heating of Microfluidic Systems. Abduljabar, A. A., +, TMTT Nov. 2015 3681-3690 Reliability Analysis of Ku-Band 5-bit Phase Shifters Using MEMS SP4T and SPDT Switches. Dey, S., +, TMTT Dec. 2015 3997-4012 Silicon-Based True-Time-Delay Phased-Array Front-Ends at Ka-Band. Ma, Q., +, TMTT Sep. 2015 2942-2952 Microwave photonics Dynamic-Range Enhancement for a Microwave Photonic Link Based on a Polarization Modulator. Chen, X., +, TMTT Jul. 2015 2384-2389 Low-Loss Ultrawideband Programmable RF Photonic Phase Filter for Spread Spectrum Pulse Compression. Kim, H.-J., +, TMTT Dec. 2015 4178-4187 Microwave Properties of an Inhomogeneous Optically Illuminated Plasma in a Microstrip Gap. Gamlath, C. D., +, TMTT Feb. 2015 374-383 Photonic Approach to Wide-Frequency-Range High-Resolution Microwave/Millimeter-Wave Doppler Frequency Shift Estimation. Zou, X., +, TMTT Apr. 2015 1421-1430 Simple Broadband Quasi-Optical Spatial Multiplexer in Substrate Integrated Technology. Gomez-Tornero, J. L., +, TMTT May 2015 1609-1620 Microwave power amplifiers A Broadband 4.5–15.5-GHz SiGe Power Amplifier With 25.5-dBm Peak Saturated Output Power and 28.7% Maximum PAE. Kerherve, E., +, TMTT May 2015 1621-1632 A Broadband GaN pHEMT Power Amplifier Using Non-Foster Matching. Lee, S., +, TMTT Dec. 2015 4406-4414 A Miniature Broadband Doherty Power Amplifier With a Series-Connected Load. Watanabe, S., +, TMTT Feb. 2015 572-579 A Simple Method to Estimate the Output Power and Efficiency Load–Pull Contours of Class-B Power Amplifiers. Pedro, J. C., +, TMTT Apr. 2015 1239-1249 A W-Band 4-GHz Bandwidth Phase-Modulated Pulse Compression Radar Transmitter in 65-nm CMOS. Oh, J., +, TMTT Aug. 2015 2609-2618 An Integrated 700–1200-MHz Class-F PA With Tunable Harmonic Terminations in 0.13- m CMOS. Sessou, K. K., +, TMTT Apr. 2015 1315-1323 Mode Power Amplifier Design ApAn Integrated Continuous Classproach for Microwave Enhanced Portable Diagnostic Applications. Imtiaz, A., +, TMTT Oct. 2015 3007-3015 Efficient Statistical Simulation of Microwave Devices Via Stochastic Testing-Based Circuit Equivalents of Nonlinear Components. Manfredi, P., +, TMTT May 2015 1502-1511 GaN Microwave DC–DC Converters. Ramos, I., +, TMTT Dec. 2015 44734482 Improving Power Utilization Factor of Broadband Doherty Amplifier by Using Bandpass Auxiliary Transformer. Fang, X.-H., +, TMTT Sep. 2015 2811-2820 Load Modulation Measurements of X-Band Outphasing Power Amplifiers. Litchfield, M., +, TMTT Dec. 2015 4119-4129 Modeling of Deterministic Output Emissions of Power Amplifiers Into Adjacent Receive Bands. Farsi, S., +, TMTT Apr. 2015 12501262 Silicon-Based True-Time-Delay Phased-Array Front-Ends at Ka-Band. Ma, Q., +, TMTT Sep. 2015 2942-2952 The Doherty Power Amplifier: Review of Recent Solutions and Trends. Camarchia, V., +, TMTT Feb. 2015 559-571 Microwave power transistors GaN Microwave DC–DC Converters. Ramos, I., +, TMTT Dec. 2015 44734482

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 63, NO. 12, DECEMBER 2015

Microwave power transmission Breaking the Efficiency Barrier for Ambient Microwave Power Harvesting With Heterojunction Backward Tunnel Diodes. Lorenz, C. H. P., +, TMTT Dec. 2015 4544-4555 Theoretical Energy-Conversion Efficiency for Energy-Harvesting Circuits Under Power-Optimized Waveform Excitation. Valenta, C. R., +, TMTT May 2015 1758-1767 Microwave propagation Comments on “Fractional Derivative Based FDTD Modeling of Transient Wave Propagation in Havriliak–Negami Media”. Rekanos, I. T., TMTT Dec. 2015 4188-4190 Microwave receivers A 0.2–3.6-GHz 10-dBm B1dB 29-dBm IIP3 Tunable Filter for Transmit Leakage Suppression in SAW-Less 3G/4G FDD Receivers. Luo, C., +, TMTT Oct. 2015 3514-3524 A Compact L-Band Orthomode Transducer for Radio Astronomical Receivers at Cryogenic Temperature. Valente, G., +, TMTT Oct. 2015 32183227 Silicon-Based True-Time-Delay Phased-Array Front-Ends at Ka-Band. Ma, Q., +, TMTT Sep. 2015 2942-2952 Microwave resonators Adaptive Coupling of Resonators for Efficient Microwave Heating of Microfluidic Systems. Abduljabar, A. A., +, TMTT Nov. 2015 3681-3690 Determination of Normalized Magnetic Eigenfields in Microwave Cavities. Helsing, J., +, TMTT May 2015 1457-1467 K-Band Frequency Tunable Substrate-Integrated- Waveguide Resonator Filter With Enhanced Stopband Attenuation. Lee, B., +, TMTT Nov. 2015 3632-3640 Modelling and Measurements of the Microwave Dielectric Properties of Microspheres. Abduljabar, A. A., +, TMTT Dec. 2015 4492-4500 Ultra-Compact (80 mm ) Differential-Mode Ultra-Wideband (UWB) Bandpass Filters With Common-Mode Noise Suppression. Velez, P., +, TMTT Apr. 2015 1272-1280 Whispering-Gallery-Mode Resonator Technique With Microfluidic Channel for Permittivity Measurement of Liquids. Gubin, A. I., +, TMTT Jun. 2015 2003-2009 Microwave technology Power Synthesis at 110-GHz Frequency Based on Discrete Sources. Zhao, J., +, TMTT May 2015 1633-1644 Reliable Microwave Modeling by Means of Variable-Fidelity Response Features. Koziel, S., +, TMTT Dec. 2015 4247-4254 Microwave theory and techniques Authors’ Reply. Mescia, L., +, TMTT Dec. 2015 4191-4193 Ultra-Miniature SIW Cavity Resonators and Filters. Pourghorban Saghati, A., +, TMTT Dec. 2015 4329-4340 Microwave transistors A Fully Nonlinear Compact Modeling Approach for High-Frequency Noise in Large-Signal Operated Microwave Electron Devices. Traverso, P. A., +, TMTT Feb. 2015 352-366 Evaluation of Uncertainty in Temporal Waveforms of Microwave Transistors. Avolio, G., +, TMTT Jul. 2015 2353-2363 Multi-Frequency Measurements for Supply Modulated Transmitters. Schafer, S., +, TMTT Sep. 2015 2931-2941 Millimeter wave amplifiers A K-Band Reconfigurable Pulse-Compression Automotive Radar Transmitter in 90-nm CMOS. Tan, K.-W., +, TMTT Apr. 2015 1380-1387 A Novel 1 4 Coupler for Compact and High-Gain Power Amplifier MMICs Around 250 GHz. Diebold, S., +, TMTT Mar. 2015 999-1006 Design and Measurement of a Broadband Sidewall Coupler for a W-Band Gyro-TWA. Zhang, L., +, TMTT Oct. 2015 3183-3190 Design and Validation of Microstrip Gap Waveguides and Their Transitions to Rectangular Waveguide, for Millimeter-Wave Applications. Brazalez, A. A., +, TMTT Dec. 2015 4035-4050 InP DHBT Amplifier Modules Operating Between 150–300 GHz Using Membrane Technology. Eriksson, K., +, TMTT Feb. 2015 433-440 InP DHBT Distributed Amplifiers With Up to 235-GHz Bandwidth. Eriksson, K., +, TMTT Apr. 2015 1334-1341 Millimeter-Wave Low-Noise Amplifier Design in 28-nm Low-Power Digital CMOS. Fritsche, D., +, TMTT Jun. 2015 1910-1922 Polymer Multichip Module Process Using 3-D Printing Technologies for D-Band Applications. Merkle, T., +, TMTT Feb. 2015 481-493 Silicon-Based True-Time-Delay Phased-Array Front-Ends at Ka-Band. Ma, Q., +, TMTT Sep. 2015 2942-2952

+ Check author entry for coauthors

4651

Transformer-Feedback Interstage Bandwidth Enhancement for MMIC Multistage Amplifiers. Nikandish, G., +, TMTT Feb. 2015 441-448 Millimeter wave antenna arrays A Configurable Coupling Structure for Broadband Millimeter-Wave SplitBlock Networks. Koenen, C., +, TMTT Dec. 2015 3954-3961 Mutual Synchronization for Power Generation and Beam-Steering in CMOS With On-Chip Sense Antennas Near 200 GHz. Sengupta, K., +, TMTT Sep. 2015 2867-2876 Transmission of Signals With Complex Constellations Using Millimeter-Wave Spatially Power-Combined CMOS Power Amplifiers and Digital Predistortion. Dabag, H.-T., +, TMTT Jul. 2015 2364-2374 Millimeter wave antennas An Integrated Slot-Ring Traveling-Wave Radiator. Bowers, S. M., +, TMTT Apr. 2015 1154-1162 Design and Validation of Microstrip Gap Waveguides and Their Transitions to Rectangular Waveguide, for Millimeter-Wave Applications. Brazalez, A. A., +, TMTT Dec. 2015 4035-4050 Time-Domain System for Millimeter-Wave Material Characterization. Vakili, I., +, TMTT Sep. 2015 2915-2922 Millimeter wave circuits High-Efficiency Applicator Based on Printed Circuit Board in MillimeterWave Region. Shiina, T., +, TMTT Oct. 2015 3311-3318 High-Tunability and High- -Factor Integrated Ferroelectric Circuits up to Millimeter Waves. De Paolis, R., +, TMTT Aug. 2015 2570-2578 Monolithic Millimeter-Wave MEMS Waveguide Switch. Vahabisani, N., +, TMTT Feb. 2015 340-351 Nonlinear Modeling and Harmonic Recycling of Millimeter-Wave Rectifier Circuit. Ladan, S., +, TMTT Mar. 2015 937-944 Millimeter wave circulators On the Design of Gyroelectric Resonators and Circulators Using a Magnetically Biased 2-D Electron Gas (2-DEG). Jawad, G. N., +, TMTT May 2015 1512-1517 Self-Biased Y-Junction Circulators Using Lanthanum- and Cobalt-Substituted Strontium Hexaferrites. Laur, V., +, TMTT Dec. 2015 4376-4381 Millimeter wave couplers A Novel 1 4 Coupler for Compact and High-Gain Power Amplifier MMICs Around 250 GHz. Diebold, S., +, TMTT Mar. 2015 999-1006 Design of a Traveling-Wave Slot Array Power Divider Using the Method of Moments and a Genetic Algorithm. Rengarajan, S. R., +, TMTT Dec. 2015 3981-3987 Millimeter wave detectors Common-Base/Common-Gate Millimeter-Wave Power Detectors. Serhan, A., +, TMTT Dec. 2015 4483-4491 Millimeter wave devices Monolithic Millimeter-Wave MEMS Waveguide Switch. Vahabisani, N., +, TMTT Feb. 2015 340-351 Millimeter wave directional couplers Substrate Integrated Waveguide Directional Couplers for Compact ThreeDimensional Integrated Circuits. Doghri, A., +, TMTT Jan. 2015 209-221 Millimeter wave field effect transistors Analysis and Design of Millimeter-Wave Power Amplifier Using Stacked-FET Structure. Kim, Y., +, TMTT Feb. 2015 691-702 Millimeter-Wave Low-Noise Amplifier Design in 28-nm Low-Power Digital CMOS. Fritsche, D., +, TMTT Jun. 2015 1910-1922 Millimeter wave filters Enhanced Topology of -Plane Resonators for High-Power Satellite Applications. Peverini, O. A., +, TMTT Oct. 2015 3361-3373 Ka-Band Dual-Mode Super Filters and Multiplexers. Yassini, B., +, TMTT Oct. 2015 3391-3397 Millimeter wave frequency converters 130-320-GHz CMOS Harmonic Down-Converters Around and Above the Cutoff Frequency. Khamaisi, B., +, TMTT Jul. 2015 2275-2288 Efficient Microwave and Millimeter-Wave Frequency Multipliers Using Nonlinear Transmission Lines in CMOS Technology. Adnan, M., +, TMTT Sep. 2015 2889-2896 Millimeter wave imaging 3-D Radiometric Aperture Synthesis Imaging. Salmon, N. A., TMTT Nov. 2015 3579-3587 Millimeter-Wave Near-Field Probe Designed for High-Resolution Skin Cancer Diagnosis. Topfer, F., +, TMTT Jun. 2015 2050-2059 Millimeter wave integrated circuits 60-GHz Substrate Materials Characterization Using the Covered Transmission-Line Method. Papio Toda, A., +, TMTT Mar. 2015 1063-1075

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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 63, NO. 12, DECEMBER 2015

-Band Dual-Polarization Phased-Array Transceiver Front-End in SiGe BiCMOS. Natarajan, A., +, TMTT Jun. 2015 1989-2002 A Broadband and Equivalent-Circuit Model for Millimeter-Wave On-Chip M:N Six-Port Transformers and Baluns. Gao, Z., +, TMTT Oct. 2015 31093121 A W-Band Power Amplifier Utilizing a Miniaturized Marchand Balun Combiner. Jia, H., +, TMTT Feb. 2015 719-725 Air-Filled Substrate Integrated Waveguide for Low-Loss and High PowerHandling Millimeter-Wave Substrate Integrated Circuits. Parment, F., +, TMTT Apr. 2015 1228-1238 Design and Tuning of Coupled-LC mm-Wave Subharmonically InjectionLocked Oscillators. Mangraviti, G., +, TMTT Jul. 2015 2301-2312 Generic Electrostatic Discharges Protection Solutions for RF and Millimeter-Wave Applications. Lim, T., +, TMTT Nov. 2015 3747-3759 InP DHBT Amplifier Modules Operating Between 150–300 GHz Using Membrane Technology. Eriksson, K., +, TMTT Feb. 2015 433-440 Millimeter wave materials Time-Domain System for Millimeter-Wave Material Characterization. Vakili, I., +, TMTT Sep. 2015 2915-2922 Millimeter wave measurement Accurate Evaluation Technique of Complex Permittivity for Low-Permittivity Dielectric Films Using a Cavity Resonator Method in 60-GHz Band. Shimizu, T., +, TMTT Jan. 2015 279-286 Microstrip Device for Broadband (15–65 GHz) Measurement of Dielectric Properties of Nematic Liquid Crystals. Deo, P., +, TMTT Apr. 2015 13881398 Millimeter-Wave Modulated-Signal and Error-Vector-Magnitude Measurement With Uncertainty. Remley, K. A., +, TMTT May 2015 1710-1720 Photonic Approach to Wide-Frequency-Range High-Resolution Microwave/Millimeter-Wave Doppler Frequency Shift Estimation. Zou, X., +, TMTT Apr. 2015 1421-1430 Time-Domain System for Millimeter-Wave Material Characterization. Vakili, I., +, TMTT Sep. 2015 2915-2922 Millimeter wave mixers 130-320-GHz CMOS Harmonic Down-Converters Around and Above the Cutoff Frequency. Khamaisi, B., +, TMTT Jul. 2015 2275-2288 A 110–170-GHz Multi-Mode Transconductance Mixer in 250-nm InP DHBT Technology. Yan, Y., +, TMTT Sep. 2015 2897-2904 A K-Band Reconfigurable Pulse-Compression Automotive Radar Transmitter in 90-nm CMOS. Tan, K.-W., +, TMTT Apr. 2015 1380-1387 A mm-Wave Segmented Power Mixer. Dasgupta, K., +, TMTT Apr. 2015 1118-1129 Fully Integrated D-Band Direct Carrier Quadrature (I/Q) Modulator and Demodulator Circuits in InP DHBT Technology. Carpenter, S., +, TMTT May 2015 1666-1675 High-Order Subharmonic Millimeter-Wave Mixer Based on Few-Layer Graphene. Vazquez Antuna, C., +, TMTT Apr. 2015 1361-1369 Millimeter wave oscillators 130-320-GHz CMOS Harmonic Down-Converters Around and Above the Cutoff Frequency. Khamaisi, B., +, TMTT Jul. 2015 2275-2288 A 47.6–71.0-GHz 65-nm CMOS VCO Based on Magnetically Coupled -Type LC Network. Jia, H., +, TMTT May 2015 1645-1657 A Blocker-Tolerant Current Mode 60-GHz Receiver With 7.5-GHz Bandwidth and 3.8-dB Minimum NF in 65-nm CMOS. Wu, H., +, TMTT Mar. 2015 1053-1062 A G-Band Standing-Wave Push–Push VCO Using a Transmission-Line Resonator. Koo, H., +, TMTT Mar. 2015 1036-1045 A W-Band 4-GHz Bandwidth Phase-Modulated Pulse Compression Radar Transmitter in 65-nm CMOS. Oh, J., +, TMTT Aug. 2015 2609-2618 A Wide-Band CMOS to Waveguide Transition at mm-Wave Frequencies With Wire-Bonds. Jameson, S., +, TMTT Sep. 2015 2741-2750 An Integrated Slot-Ring Traveling-Wave Radiator. Bowers, S. M., +, TMTT Apr. 2015 1154-1162 Design and Tuning of Coupled-LC mm-Wave Subharmonically InjectionLocked Oscillators. Mangraviti, G., +, TMTT Jul. 2015 2301-2312 Mutual Synchronization for Power Generation and Beam-Steering in CMOS With On-Chip Sense Antennas Near 200 GHz. Sengupta, K., +, TMTT Sep. 2015 2867-2876 Wide Tuning-Range mm-Wave Voltage-Controlled Oscillator Employing an Artificial Magnetic Transmission Line. Yanay, N., +, TMTT Apr. 2015 13421352 Millimeter wave phase shifters -Band Dual-Polarization Phased-Array Transceiver Front-End in SiGe BiCMOS. Natarajan, A., +, TMTT Jun. 2015 1989-2002 + Check author entry for coauthors

-Band Dual-Polarization Phased-Array Transceiver Front-End in SiGe BiCMOS. Natarajan, A., +, TMTT Jun. 2015 1989-2002 A 220–320-GHz Vector-Sum Phase Shifter Using Single Gilbert-Cell Structure With Lossy Output Matching. Kim, Y., +, TMTT Jan. 2015 256-265 A 40-nm CMOS E-Band 4-Way Power Amplifier With Neutralized Bootstrapped Cascode Amplifier and Optimum Passive Circuits. Zhao, D., +, TMTT Dec. 2015 4083-4089 A Reconfigurable K-/Ka-Band Power Amplifier With High PAE in 0.18- m SiGe BiCMOS for Multi-Band Applications. Ma, K., +, TMTT Dec. 2015 4395-4405 A W-Band 4-GHz Bandwidth Phase-Modulated Pulse Compression Radar Transmitter in 65-nm CMOS. Oh, J., +, TMTT Aug. 2015 2609-2618 A W-Band Power Amplifier Utilizing a Miniaturized Marchand Balun Combiner. Jia, H., +, TMTT Feb. 2015 719-725 An E-Band Power Amplifier With Broadband Parallel-Series Power Combiner in 40-nm CMOS. Zhao, D., +, TMTT Feb. 2015 683-690 Analysis and Design of a 14.1-mW 50/100-GHz Transformer-Based PLL With Embedded Phase Shifter in 65-nm CMOS. Chao, Y., +, TMTT Apr. 2015 1193-1201 Analysis and Design of Millimeter-Wave Power Amplifier Using Stacked-FET Structure. Kim, Y., +, TMTT Feb. 2015 691-702 Large-Scale Power Combining and Mixed-Signal Linearizing Architectures for Watt-Class mmWave CMOS Power Amplifiers. Bhat, R., +, TMTT Feb. 2015 703-718 Silicon-Based True-Time-Delay Phased-Array Front-Ends at Ka-Band. Ma, Q., +, TMTT Sep. 2015 2942-2952 Transformer-Based Doherty Power Amplifiers for mm-Wave Applications in 40-nm CMOS. Kaymaksut, E., +, TMTT Apr. 2015 1186-1192 Transmission of Signals With Complex Constellations Using Millimeter-Wave Spatially Power-Combined CMOS Power Amplifiers and Digital Predistortion. Dabag, H.-T., +, TMTT Jul. 2015 2364-2374 Millimeter wave radar 3-D High-Resolution Imaging Radar at 300 GHz With Enhanced FoV. Grajal, J., +, TMTT Mar. 2015 1097-1107 Millimeter wave receivers A Blocker-Tolerant Current Mode 60-GHz Receiver With 7.5-GHz Bandwidth and 3.8-dB Minimum NF in 65-nm CMOS. Wu, H., +, TMTT Mar. 2015 1053-1062 A Hardware Efficient Implementation of a Digital Baseband Receiver for High-Capacity Millimeter-Wave Radios. He, Z., +, TMTT May 2015 16831692 Silicon-Based True-Time-Delay Phased-Array Front-Ends at Ka-Band. Ma, Q., +, TMTT Sep. 2015 2942-2952 Millimeter wave resonators A G-Band Standing-Wave Push–Push VCO Using a Transmission-Line Resonator. Koo, H., +, TMTT Mar. 2015 1036-1045 Millimeter waves Performance Estimation for Broadband Multi-Gigabit Millimeter- and SubMillimeter-Wave Wireless Communication Links. Antes, J., +, TMTT Oct. 2015 3288-3299 Reduction of Exposure Inhomogeneity for Millimeter-Wave Experiments on Cells In Vitro. Zhao, J., +, TMTT Feb. 2015 533-545 MIM devices High-Tunability and High- -Factor Integrated Ferroelectric Circuits up to Millimeter Waves. De Paolis, R., +, TMTT Aug. 2015 2570-2578 MIMIC A Novel 1 4 Coupler for Compact and High-Gain Power Amplifier MMICs Around 250 GHz. Diebold, S., +, TMTT Mar. 2015 9991006 Millimeter-Wave Low-Noise Amplifier Design in 28-nm Low-Power Digital CMOS. Fritsche, D., +, TMTT Jun. 2015 1910-1922 Polymer Multichip Module Process Using 3-D Printing Technologies for D-Band Applications. Merkle, T., +, TMTT Feb. 2015 481-493 Silicon-Based True-Time-Delay Phased-Array Front-Ends at Ka-Band. Ma, Q., +, TMTT Sep. 2015 2942-2952 Transformer-Feedback Interstage Bandwidth Enhancement for MMIC Multistage Amplifiers. Nikandish, G., +, TMTT Feb. 2015 441-448 Mirrors Design and Characterization of a 170-GHz Resonant Diplexer for HighPower ECRH Systems. Wu, Z., +, TMTT Oct. 2015 3537-3546 MIS devices Extraction of a Multi-Dimensional Polynomial Device Model for an Improved Distortion Contribution Analysis Technique. Aikio, J. P., +, TMTT Jan. 2015 155-164

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Mixed analog digital integrated circuits -Parameters: A Novel Framework for Characterization and Behavioral Modeling of Mixed-Signal Systems. Ribeiro, D. C., +, TMTT Oct. 2015 3277-3287 A Reconfigurable 50-Mb/s-1 Gb/s Pulse Compression Radar Signal Processor With Offset Calibration in 90-nm CMOS. Li, J., +, TMTT Jan. 2015 266-278 Large-Scale Power Combining and Mixed-Signal Linearizing Architectures for Watt-Class mmWave CMOS Power Amplifiers. Bhat, R., +, TMTT Feb. 2015 703-718 MMIC A Novel Load Mismatch Detection and Correction Technique for 3G/4G Load Insensitive Power Amplifier Application. Ji, D., +, TMTT May 2015 1530-1543 Design and Analysis of 24-GHz Active Isolator and Quasi-Circulator. Chang, J.-F., +, TMTT Aug. 2015 2638-2649 On the Accurate Measurement and Calibration of S-Parameters for Millimeter Wavelengths and Beyond. Seelmann-Eggebert, M., +, TMTT Jul. 2015 2335-2342 Reflectionless Filter Structures. Morgan, M. A., +, TMTT Apr. 2015 12631271 Silicon-Based True-Time-Delay Phased-Array Front-Ends at Ka-Band. Ma, Q., +, TMTT Sep. 2015 2942-2952 MMIC amplifiers A 2-W W-Band GaN Traveling-Wave Amplifier With 25-GHz Bandwidth. Schellenberg, J. M., TMTT Sep. 2015 2833-2840 Millimeter-Wave Low-Noise Amplifier Design in 28-nm Low-Power Digital CMOS. Fritsche, D., +, TMTT Jun. 2015 1910-1922 Phase-Noise Analysis of an X-Band Ultra-Low Phase-Noise GaN HEMT Based Cavity Oscillator. Horberg, M., +, TMTT Aug. 2015 2619-2629 Source Degenerated Derivative Superposition Method for Linearizing RF FET Differential Amplifiers. Shin, H., +, TMTT Mar. 2015 1026-1035 Supply-Modulated Radar Transmitters With Amplitude-Modulated Pulses. Zai, A., +, TMTT Sep. 2015 2953-2964 Transformer-Feedback Interstage Bandwidth Enhancement for MMIC Multistage Amplifiers. Nikandish, G., +, TMTT Feb. 2015 441-448 MMIC mixers 160-GHz to 1-THz Multi-Color Active Imaging With a Lens-Coupled SiGe HBT Chip-Set. Statnikov, K., +, TMTT Feb. 2015 520-532 Fully Integrated D-Band Direct Carrier Quadrature (I/Q) Modulator and Demodulator Circuits in InP DHBT Technology. Carpenter, S., +, TMTT May 2015 1666-1675 MMIC oscillators A 1.3–2.4-GHz 3.1-mW VCO Using Electro-Thermo- Mechanically Tunable Self-Assembled MEMS Inductor on HR Substrate. Bhattacharya, A., +, TMTT Feb. 2015 459-469 Tuning-Range Enhancement Through Deterministic Mode Selection in RF Quadrature Oscillators. Bagheri, M., +, TMTT Nov. 2015 3713-3726 MMIC phase shifters -Band Dual-Polarization Phased-Array Transceiver Front-End in SiGe BiCMOS. Natarajan, A., +, TMTT Jun. 2015 1989-2002 Design of X-Band GaN Phase Shifters. Ross, T. N., +, TMTT Jan. 2015 244-255 MMIC power amplifiers -Band Spatially Combined Power Amplifier Arrays in 45-nm CMOS SOI. Hanafi, B., +, TMTT Jun. 2015 1937-1950 -Band Dual-Polarization Phased-Array Transceiver Front-End in SiGe BiCMOS. Natarajan, A., +, TMTT Jun. 2015 1989-2002 A Novel 1 4 Coupler for Compact and High-Gain Power Amplifier MMICs Around 250 GHz. Diebold, S., +, TMTT Mar. 2015 999-1006 A Reconfigurable K-/Ka-Band Power Amplifier With High PAE in 0.18- m SiGe BiCMOS for Multi-Band Applications. Ma, K., +, TMTT Dec. 2015 4395-4405 Analysis and Design of Millimeter-Wave Power Amplifier Using Stacked-FET Structure. Kim, Y., +, TMTT Feb. 2015 691-702 Asymmetric Broadband Doherty Power Amplifier Using GaN MMIC for Femto-Cell Base-Station. Jee, S., +, TMTT Sep. 2015 2802-2810 Load Modulation Measurements of X-Band Outphasing Power Amplifiers. Litchfield, M., +, TMTT Dec. 2015 4119-4129 Multi-Frequency Measurements for Supply Modulated Transmitters. Schafer, S., +, TMTT Sep. 2015 2931-2941 Mobile antennas A Tunable RF Front-End With Narrowband Antennas for Mobile Devices. Bahramzy, P., +, TMTT Oct. 2015 3300-3310 + Check author entry for coauthors

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Mobile communication Guest Editorial. KIM, J., +, TMTT Mar. 2015 778-779 Mobile handsets A Tunable RF Front-End With Narrowband Antennas for Mobile Devices. Bahramzy, P., +, TMTT Oct. 2015 3300-3310 Wireless Power Systems for Mobile Devices Supporting Inductive and Resonant Operating Modes. Riehl, P. S., +, TMTT Mar. 2015 780-790 Mobile radio A Pulsed Dynamic Load Modulation Technique for High-Efficiency Linear Transmitters. Jeon, M.-S., +, TMTT Sep. 2015 2854-2866 Modal analysis Dispersion Modeling and Analysis for Multilayered Open Coaxial Waveguides. Nordebo, S., +, TMTT Jun. 2015 1791-1799 Modal Loss Analysis of - and -Plane Filtering Structures. Accatino, L., +, TMTT Jan. 2015 40-47 Mode matching Mode Filters for Oversized Rectangular Waveguides: A Modal Approach. Ceccuzzi, S., +, TMTT Aug. 2015 2468-2481 Modulation A New Double Input-Double Output Complex Envelope Amplifier Behavioral Model Taking Into Account Source and Load Mismatch Effects. Zargar, H., +, TMTT Feb. 2015 766-774 Modulators A 1.1-Gbit/s 10-GHz Outphasing Modulator With 23-dBm Output Power and 60-dB Dynamic Range in 45-nm CMOS SOI. Mehrjoo, M. S., +, TMTT Jul. 2015 2289-2300 A Prototype SAW-Less LTE Transmitter With a High-Linearity Modulator Using BPF-Based I/Q Summing and a Triple-Layer Marchand Balun. Nakamura, T., +, TMTT Dec. 2015 4090-4097 Dynamic-Range Enhancement for a Microwave Photonic Link Based on a Polarization Modulator. Chen, X., +, TMTT Jul. 2015 2384-2389 Fully Integrated D-Band Direct Carrier Quadrature (I/Q) Modulator and Demodulator Circuits in InP DHBT Technology. Carpenter, S., +, TMTT May 2015 1666-1675 Supply-Modulated Radar Transmitters With Amplitude-Modulated Pulses. Zai, A., +, TMTT Sep. 2015 2953-2964 Modules Bandpass Filters Using Coupling-Matrix-Based Design of HighAcoustic-Wave Lumped-Element Resonator (AWLR) Modules. Psychogiou, D., +, TMTT Dec. 2015 4319-4328 Highly Efficient and Multipaction-Free P-Band GaN High-Power Amplifiers for Space Applications. Ayllon, N., +, TMTT Dec. 2015 4429-4436 Molecular biophysics Miniaturized Transmission-Line Sensor for Broadband Dielectric Characterization of Biological Liquids and Cell Suspensions. Meyne nee Haase, N., +, TMTT Oct. 2015 3026-3033 Molecular dynamics method Electrical Analysis of Cell Membrane Poration by an Intense Nanosecond Pulsed Electric Field Using an Atomistic-to-Continuum Method. Kohler, S., +, TMTT Jun. 2015 2032-2040 Monopole antennas A Compact Dual-Channel Transceiver for Long-Range Passive Embedded Monitoring. Nassar, I. T., +, TMTT Jan. 2015 287-294 Monte Carlo methods Accuracy and Bandwidth Optimization of the Over-Determined Offset-Short Reflectometer Calibration. Lewandowski, A., +, TMTT Mar. 2015 1076-1089 Comparison of Injection-Locked and Coupled Oscillator Arrays for Beamforming. Lo, Y.-T., +, TMTT Apr. 2015 1353-1360 Millimeter-Wave Modulated-Signal and Error-Vector-Magnitude Measurement With Uncertainty. Remley, K. A., +, TMTT May 2015 1710-1720 Rapid Yield Estimation and Optimization of Microwave Structures Exploiting Feature-Based Statistical Analysis. Koziel, S., +, TMTT Jan. 2015 107-114 Mos analog integrated circuits Power Adaptive Digital Predistortion for Wideband RF Power Amplifiers With Dynamic Power Transmission. Guo, Y., +, TMTT Nov. 2015 35953607 MOSFET A Stacked-FET Linear SOI CMOS Cellular Antenna Switch With an Extremely Low-Power Biasing Strategy. Im, D., +, TMTT Jun. 2015 19641977 Analysis and Design of Millimeter-Wave Power Amplifier Using Stacked-FET Structure. Kim, Y., +, TMTT Feb. 2015 691-702

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Consistent DC and RF MOSFET Modeling Using an -Parameter Measurement-Based Parameter Extraction Method in the Linear Region. ZarateRincon, F., +, TMTT Dec. 2015 4255-4262 High-Frequency Noise Modeling of MOSFETs for Ultra Low-Voltage RF Applications. Chan, L. H. K., +, TMTT Jan. 2015 141-154 Investigation of RF Avalanche Inductive Effect on Reduction of Intermodulation Distortion of MOSFETs Using Volterra Series Analysis. Lee, C.-I., +, TMTT Feb. 2015 367-373 Millimeter-Wave Low-Noise Amplifier Design in 28-nm Low-Power Digital CMOS. Fritsche, D., +, TMTT Jun. 2015 1910-1922 RF Small-Signal and Noise Modeling Including Parameter Extraction of Nanoscale MOSFET From Weak to Strong Inversion. Chalkiadaki, M.-A., +, TMTT Jul. 2015 2173-2184 Motion compensation A Low-IF Tag-Based Motion Compensation Technique for Mobile Doppler Radar Life Signs Monitoring. Rahman, A., +, TMTT Oct. 2015 3034-3041 Multi-wall carbon nanotubes Anisotropic Microwave Conductivity Dispersion of Horizontally Aligned Multi-Walled Carbon- Nanotube Thin Film on Flexible Substrate. Li, S., +, TMTT Nov. 2015 3588-3594 Multichip modules Polymer Multichip Module Process Using 3-D Printing Technologies for D-Band Applications. Merkle, T., +, TMTT Feb. 2015 481-493 Multiconductor transmission lines Synthesis and Design of High-Selectivity Wideband Quasi-Elliptic Bandpass Filters Using Multiconductor Transmission Lines. Sanchez-Martinez, J. J., +, TMTT Jan. 2015 198-208 Multidimensional systems Extraction of a Multi-Dimensional Polynomial Device Model for an Improved Distortion Contribution Analysis Technique. Aikio, J. P., +, TMTT Jan. 2015 155-164 Multifrequency antennas A Tunable RF Front-End With Narrowband Antennas for Mobile Devices. Bahramzy, P., +, TMTT Oct. 2015 3300-3310 Multilayers High Rejection, Self-Packaged Low-Pass Filter Using Multilayer Liquid Crystal Polymer Technology. Cervera, F., +, TMTT Dec. 2015 3920-3928 Multiplexing Guest Editorial. Boria, V. E., +, TMTT Oct. 2015 3321-3323 Multiplexing equipment A 1.4–2.3-GHz Tunable Diplexer Based on Reconfigurable Matching Networks. Ko, C. H., +, TMTT May 2015 1595-1602 Design and Characterization of a 170-GHz Resonant Diplexer for HighPower ECRH Systems. Wu, Z., +, TMTT Oct. 2015 3537-3546 Design of Compact Wideband Manifold-Coupled Multiplexers. Carceller, C., +, TMTT Oct. 2015 3398-3407 Efficient Design of Compact Contiguous-Channel SIW Multiplexers Using the Space-Mapping Method. Hao, Z.-C., +, TMTT Nov. 2015 3651-3662 Efficient Design of Waveguide Manifold Multiplexers Based on Low-Order EM Distributed Models. Cogollos, S., +, TMTT Aug. 2015 2540-2549 Ka-Band Dual-Mode Super Filters and Multiplexers. Yassini, B., +, TMTT Oct. 2015 3391-3397 Present and Future Trends in Filters and Multiplexers. Snyder, R. V., +, TMTT Oct. 2015 3324-3360 Simple Broadband Quasi-Optical Spatial Multiplexer in Substrate Integrated Technology. Gomez-Tornero, J. L., +, TMTT May 2015 1609-1620 Multiport networks A Wideband and Highly Symmetric Multi-Port Parallel Combining Transformer Technology. Yang, H.-S., +, TMTT Nov. 2015 3671-3680 N Nanocomposites Fractal Frequency-Selective Surface Embedded Thin Broadband Microwave Absorber Coatings Using Heterogeneous Composites. Panwar, R., +, TMTT Aug. 2015 2438-2448 Nanofabrication Micromachined Room-Temperature Air-Suspended Ni/Cr Nanobolometer. Yang, H.-H., +, TMTT Nov. 2015 3760-3767 Nanomedicine Computational Feasibility Study of Contrast-Enhanced Thermoacoustic Imaging for Breast Cancer Detection Using Realistic Numerical Breast Phantoms. Wang, X., +, TMTT May 2015 1489-1501 + Check author entry for coauthors

Nanoparticles Broadband Microwave Characterization of Nanostructured Thin Film With Giant Dielectric Response. Chen, T.-C., +, TMTT Nov. 2015 3768-3774 Fractal Frequency-Selective Surface Embedded Thin Broadband Microwave Absorber Coatings Using Heterogeneous Composites. Panwar, R., +, TMTT Aug. 2015 2438-2448 Nanoporous materials Electrical Analysis of Cell Membrane Poration by an Intense Nanosecond Pulsed Electric Field Using an Atomistic-to-Continuum Method. Kohler, S., +, TMTT Jun. 2015 2032-2040 Nanosensors High-Speed Antenna-Coupled Terahertz Thermocouple Detectors and Mixers. Russer, J. A., +, TMTT Dec. 2015 4236-4246 Micromachined Room-Temperature Air-Suspended Ni/Cr Nanobolometer. Yang, H.-H., +, TMTT Nov. 2015 3760-3767 Nanowires High-Speed Antenna-Coupled Terahertz Thermocouple Detectors and Mixers. Russer, J. A., +, TMTT Dec. 2015 4236-4246 Near-field communication Mutual Synchronization for Power Generation and Beam-Steering in CMOS With On-Chip Sense Antennas Near 200 GHz. Sengupta, K., +, TMTT Sep. 2015 2867-2876 Negative impedance converters A Broadband GaN pHEMT Power Amplifier Using Non-Foster Matching. Lee, S., +, TMTT Dec. 2015 4406-4414 Negative resistance circuits A 47.6–71.0-GHz 65-nm CMOS VCO Based on Magnetically Coupled -Type LC Network. Jia, H., +, TMTT May 2015 1645-1657 Nematic liquid crystals Microstrip Device for Broadband (15–65 GHz) Measurement of Dielectric Properties of Nematic Liquid Crystals. Deo, P., +, TMTT Apr. 2015 13881398 Network analysis An Ultra-Compact Common-Mode Bandstop Filter With Modified-T Circuits in Integrated Passive Device (IPD) Process. Hsiao, C.-Y., +, TMTT Nov. 2015 3624-3631 Author's Reply. Grebennikov, A., TMTT Aug. 2015 2705 Network analyzers Accuracy and Bandwidth Optimization of the Over-Determined Offset-Short Reflectometer Calibration. Lewandowski, A., +, TMTT Mar. 2015 1076-1089 Generalized Theory of the Thru-Reflect-Match Calibration Technique. Pulido-Gaytan, M. A., +, TMTT May 2015 1693-1699 Qualitative Microwave Imaging With Scattering Parameters Measurements. Akinci, M. N., +, TMTT Sep. 2015 2730-2740 The Effects of Electrode Configuration on Body Channel Communication Based on Analysis of Vertical and Horizontal Electric Dipoles. Bae, J., +, TMTT Apr. 2015 1409-1420 Time-Domain Optoelectronic Vector Network Analysis on Coplanar Waveguides. Bieler, M., +, TMTT Nov. 2015 3775-3784 Network synthesis Bandpass Filters Using Coupling-Matrix-Based Design of HighAcoustic-Wave Lumped-Element Resonator (AWLR) Modules. Psychogiou, D., +, TMTT Dec. 2015 4319-4328 Exact Synthesis of Full- and Half-Symmetric Rat-Race Ring Hybrids With or Without Impedance Transforming Characteristics. Chou, P.-J., +, TMTT Dec. 2015 3971-3980 Optimized Design of Frequency Dividers Based on Varactor-Inductor Cells. Ponton, M., +, TMTT Dec. 2015 4458-4472 Network topology A Post-Matching Doherty Power Amplifier Employing Low-Order Impedance Inverters for Broadband Applications. Pang, J., +, TMTT Dec. 2015 4061-4071 An Ultra-Compact Common-Mode Bandstop Filter With Modified-T Circuits in Integrated Passive Device (IPD) Process. Hsiao, C.-Y., +, TMTT Nov. 2015 3624-3631 Asymmetric Broadband Doherty Power Amplifier Using GaN MMIC for Femto-Cell Base-Station. Jee, S., +, TMTT Sep. 2015 2802-2810 Transformer-Based Doherty Power Amplifiers for mm-Wave Applications in 40-nm CMOS. Kaymaksut, E., +, TMTT Apr. 2015 1186-1192 Neurophysiology A High-Sensitivity Fully Passive Neurosensing System for Wireless Brain Signal Monitoring. Lee, C. W. L., +, TMTT Jun. 2015 2060-2068

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Wireless Fully Passive Multichannel Recording of Neuropotentials Using Photo-Activated RF Backscattering Methods. Schwerdt, H. N., +, TMTT Sep. 2015 2965-2970 Nickel High Power Latching RF MEMS Switches. Bakri-Kassem, M., +, TMTT Jan. 2015 222-232 Micromachined Room-Temperature Air-Suspended Ni/Cr Nanobolometer. Yang, H.-H., +, TMTT Nov. 2015 3760-3767 Noise measurement Corrections to “Unified Theory of Linear Noisy Two-Ports” [Nov 13 39863997]. Dietrich, J. L., TMTT Feb. 2015 554 GaN HEMT Noise Model Based on Electromagnetic Simulations. Nalli, A., +, TMTT Aug. 2015 2498-2508 Nonlinear distortion A General Digital Predistortion Architecture Using Constrained Feedback Bandwidth for Wideband Power Amplifiers. Liu, Y., +, TMTT May 2015 1544-1555 Analysis of Weakly Nonlinear Effect for Varactor-Tuned Bandpass Filter. Ge, C., +, TMTT Nov. 2015 3641-3650 Partitioned Distortion Mitigation in LTE Radio Uplink to Enhance Transmitter Efficiency. Amiri, M. V., +, TMTT Aug. 2015 2661-2671 Nonlinear functions Efficient Simulation of Solution Curves and Bifurcation Loci in InjectionLocked Oscillators. de Cos, J., +, TMTT Jan. 2015 181-197 Nonlinear network analysis Generalized Stability Criteria for Power Amplifiers Under Mismatch Effects. Suarez, A., +, TMTT Dec. 2015 4415-4428 Hysteresis and Oscillation in High-Efficiency Power Amplifiers. de Cos, J., +, TMTT Dec. 2015 4284-4296 Nonlinear Behavioral Modeling Dependent on Load Reflection Coefficient Magnitude. Cai, J., +, TMTT May 2015 1518-1529 Notch filters An FBAR/CMOS Frequency/Phase Discriminator and Phase Noise Reduction System. Imani, A., +, TMTT May 2015 1658-1665 Tunable 4-Pole Dual-Notch Filters for Cognitive Radios and Carrier Aggregation Systems. Cho, Y.-H., +, TMTT Apr. 2015 1308-1314 Tunable 500–1200-MHz Dual-Band and Wide Bandwidth Notch Filters Using RF Transformers. Ko, C.-H., +, TMTT Jun. 2015 1854-1862 Numerical analysis An Improved Broadband Boundary Condition for the RF Field in Gyrotron Interaction Modeling. Wu, C., +, TMTT Aug. 2015 2459-2467 Application of Coherence Theory to Modeling of Blackbody Radiation at Close Range. Gu, D., +, TMTT May 2015 1475-1488 Computational Feasibility Study of Contrast-Enhanced Thermoacoustic Imaging for Breast Cancer Detection Using Realistic Numerical Breast Phantoms. Wang, X., +, TMTT May 2015 1489-1501 Dispersion Modeling and Analysis for Multilayered Open Coaxial Waveguides. Nordebo, S., +, TMTT Jun. 2015 1791-1799 Fast Solution of the Electromagnetic Scattering by Composite Spheroidal–Spherical and Spherical–Spheroidal Configurations. Zouros, G. P., +, TMTT Oct. 2015 3042-3053 Influence of Numerical Method and Geometry Used by Maxwell's Equation Solvers on Simulations of Ferroelectric Thin-Film Capacitors. Furlan, V., +, TMTT Mar. 2015 891-896 Resonant Modes of Disk-Loaded Cylindrical Structures With Open Boundaries. Chelis, I. G., +, TMTT Jun. 2015 1781-1790 The Development of Forceps-Type Microwave Tissue Coagulator for Surgical Operation. Endo, Y., +, TMTT Jun. 2015 2041-2049 Numerical models Guest Editorial [Mini-Special Issue on 2014 IEEE International Conference on Numerical Electromagnetic Modeling and Optimization for RF, Microwave, and Terahertz Applications (NEMO2014. Bozzi, M., +, TMTT Jan. 2015 1-2

O

OFDM modulation A Sub-GHz Wireless Transmitter Utilizing a Multi-Class-Linearized PA and Time-Domain Wideband-Auto I/Q-LOFT Calibration for IEEE 802.11af WLAN. Un, K.-F., +, TMTT Oct. 2015 3228-3241 Behavioral Modeling and Predistortion of Power Amplifiers Under Sparsity Hypothesis. Reina-Tosina, J., +, TMTT Feb. 2015 745-753 + Check author entry for coauthors

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Oils Design and Analysis of Shielded Vertically Stacked Ring Resonator as Complex Permittivity Sensor for Petroleum Oils. Kulkarni, S., +, TMTT Aug. 2015 2411-2417 Optical communication equipment An 8-bit 100-GS/s Distributed DAC in 28-nm CMOS for Optical Communications. Huang, H., +, TMTT Apr. 2015 1211-1218 Optical correlation 3-D Radiometric Aperture Synthesis Imaging. Salmon, N. A., TMTT Nov. 2015 3579-3587 Optical fiber communication High-Speed Signal Transmission at W-Band Over Dielectric-Coated Metallic Hollow Fiber. Yu, J., +, TMTT Jun. 2015 1836-1842 Optical fiber dispersion Broadband and Precise Microwave Time Reversal Using a Single Linearly Chirped Fiber Bragg Grating. Zhang, J., +, TMTT Jul. 2015 2166-2172 Optical filters Dynamic-Range Enhancement for a Microwave Photonic Link Based on a Polarization Modulator. Chen, X., +, TMTT Jul. 2015 2384-2389 Optical microscopes 3-D Radiometric Aperture Synthesis Imaging. Salmon, N. A., TMTT Nov. 2015 3579-3587 Optical modulation High-Speed Signal Transmission at W-Band Over Dielectric-Coated Metallic Hollow Fiber. Yu, J., +, TMTT Jun. 2015 1836-1842 Optical pulse compression Low-Loss Ultrawideband Programmable RF Photonic Phase Filter for Spread Spectrum Pulse Compression. Kim, H.-J., +, TMTT Dec. 2015 4178-4187 Optical pulse generation Time-Domain Optoelectronic Vector Network Analysis on Coplanar Waveguides. Bieler, M., +, TMTT Nov. 2015 3775-3784 Optical waveguides Simple Broadband Quasi-Optical Spatial Multiplexer in Substrate Integrated Technology. Gomez-Tornero, J. L., +, TMTT May 2015 1609-1620 Optimization Bayesian Optimization for Broadband High-Efficiency Power Amplifier Designs. Chen, P., +, TMTT Dec. 2015 4263-4272 Cognition-Driven Formulation of Space Mapping for Equal-Ripple Optimization of Microwave Filters. Zhang, C., +, TMTT Jul. 2015 2154-2165 Development of the Optimization Framework for Low-Power Wireless Power Transfer Systems. Lee, S. B., +, TMTT Mar. 2015 813-820 Efficient Design of Compact Contiguous-Channel SIW Multiplexers Using the Space-Mapping Method. Hao, Z.-C., +, TMTT Nov. 2015 3651-3662 Optimized Design of a Dual-Band Power Amplifier With SiC VaractorBased Dynamic Load Modulation. Sanchez-Perez, C., +, TMTT Aug. 2015 2579-2588 Rapid Yield Estimation and Optimization of Microwave Structures Exploiting Feature-Based Statistical Analysis. Koziel, S., +, TMTT Jan. 2015 107-114 Oscillators A 0.12-mm 2.4-GHz CMOS Inductorless High Isolation Subharmonic Mixer With Effective Current-Reuse Transconductance. Chong, W. K., +, TMTT Aug. 2015 2427-2437 Phase-Noise Analysis of an X-Band Ultra-Low Phase-Noise GaN HEMT Based Cavity Oscillator. Horberg, M., +, TMTT Aug. 2015 2619-2629

P P-i-n diodes A Three-Way Reconfigurable Power Divider/Combiner. Fan, H., +, TMTT Mar. 2015 986-998 Active Detuning of MRI Receive Coils with GaN FETs. Twieg, M., +, TMTT Dec. 2015 4169-4177 Pacemakers A Technique to Evaluate MRI-Induced Electric Fields at the Ends of Practical Implanted Lead. Feng, S., +, TMTT Jan. 2015 305-313 Resonant Inductive Link for Remote Powering of Pacemakers. Monti, G., +, TMTT Nov. 2015 3814-3822 Parallel plate waveguides Time-Domain Electromagnetic Analysis of Multilayer Structures Using the Surface Equivalent Principle and Mixed-Potential Integral Equations. Maftooli, H., +, TMTT Jan. 2015 99-106

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Parameter estimation Digitally Assisted Analog/RF Predistorter With a Small-Signal-Assisted Parameter Identification Algorithm. Huang, H., +, TMTT Dec. 2015 42974305 Estimation of Nonhomogeneous and Multi-Section Twisted-Pair Transmission-Line Parameters. Lindqvist, F., +, TMTT Nov. 2015 3568-3578 Partial differential equations Estimating the Inf-Sup Constant in Reduced Basis Methods for Time-Harmonic Maxwell’s Equations. Hess, M. W., +, TMTT Nov. 2015 3549-3557 Particle swarm optimization Mode Filters for Oversized Rectangular Waveguides: A Modal Approach. Ceccuzzi, S., +, TMTT Aug. 2015 2468-2481 Passive filters A New Broadband Common-Mode Noise Absorption Circuit for High-Speed Differential Digital Systems. Hsiao, C.-Y., +, TMTT Jun. 2015 1894-1901 A Prototype SAW-Less LTE Transmitter With a High-Linearity Modulator Using BPF-Based I/Q Summing and a Triple-Layer Marchand Balun. Nakamura, T., +, TMTT Dec. 2015 4090-4097 Passive networks 130-320-GHz CMOS Harmonic Down-Converters Around and Above the Cutoff Frequency. Khamaisi, B., +, TMTT Jul. 2015 2275-2288 -Band Dual-Polarization Phased-Array Transceiver Front-End in SiGe BiCMOS. Natarajan, A., +, TMTT Jun. 2015 1989-2002 A 40-nm CMOS E-Band 4-Way Power Amplifier With Neutralized Bootstrapped Cascode Amplifier and Optimum Passive Circuits. Zhao, D., +, TMTT Dec. 2015 4083-4089 A Wideband and Highly Symmetric Multi-Port Parallel Combining Transformer Technology. Yang, H.-S., +, TMTT Nov. 2015 3671-3680 Millimeter-Wave Low-Noise Amplifier Design in 28-nm Low-Power Digital CMOS. Fritsche, D., +, TMTT Jun. 2015 1910-1922 Patient monitoring A Low-IF Tag-Based Motion Compensation Technique for Mobile Doppler Radar Life Signs Monitoring. Rahman, A., +, TMTT Oct. 2015 3034-3041 Pattern recognition Wearable RF Sensor Array Implementing Coupling-Matrix Readout Extraction Technique. Chen, W.-T. S., +, TMTT Dec. 2015 4157-4168 Percolation Broadband Dielectric Spectroscopy of Composites Filled With Various Carbon Materials. Bellucci, S., +, TMTT Jun. 2015 2024-2031 Permeability Electromagnetic Scattering by a General Rotationally Symmetric Inhomogeneous Anisotropic Sphere. Zouros, G. P., +, TMTT Oct. 2015 3054-3065 Permittivity Broadband Microwave Characterization of Nanostructured Thin Film With Giant Dielectric Response. Chen, T.-C., +, TMTT Nov. 2015 3768-3774 Dielectric Constant Estimation of a Carbon Nanotube Layer on the Dielectric Rod Waveguide at Millimeter Wavelengths. Nefedova, I. I., +, TMTT Oct. 2015 3265-3271 Electromagnetic Scattering by a General Rotationally Symmetric Inhomogeneous Anisotropic Sphere. Zouros, G. P., +, TMTT Oct. 2015 3054-3065 Extraction of Dielectric and Rough Conductor Loss of Printed Circuit Board Using Differential Method at Microwave Frequencies. Zhu, X.-C., +, TMTT Feb. 2015 494-503 Fractal Frequency-Selective Surface Embedded Thin Broadband Microwave Absorber Coatings Using Heterogeneous Composites. Panwar, R., +, TMTT Aug. 2015 2438-2448 Influence of Numerical Method and Geometry Used by Maxwell's Equation Solvers on Simulations of Ferroelectric Thin-Film Capacitors. Furlan, V., +, TMTT Mar. 2015 891-896 Millimeter-Wave Near-Field Probe Designed for High-Resolution Skin Cancer Diagnosis. Topfer, F., +, TMTT Jun. 2015 2050-2059 Miniaturized Transmission-Line Sensor for Broadband Dielectric Characterization of Biological Liquids and Cell Suspensions. Meyne nee Haase, N., +, TMTT Oct. 2015 3026-3033 Modelling and Measurements of the Microwave Dielectric Properties of Microspheres. Abduljabar, A. A., +, TMTT Dec. 2015 4492-4500 MRI-Based Electrical Property Retrieval by Applying the Finite-Element Method (FEM). Huang, S. Y., +, TMTT Aug. 2015 2482-2490 Printable Planar Dielectric Waveguides Based on High-Permittivity Films. Rashidian, A., +, TMTT Sep. 2015 2720-2729 Propagation, Power Absorption, and Temperature Analysis of UWB Wireless Capsule Endoscopy Devices Operating in the Human Body. Thotahewa, K. M. S., +, TMTT Nov. 2015 3823-3833 + Check author entry for coauthors

Real-World Implementation Challenges of a Novel Dual-Polarized Compact Printable Chipless RFID Tag. Islam, M. A., +, TMTT Dec. 2015 4581-4591 Two-Material Ridge Substrate Integrated Waveguide for Ultra-Wideband Applications. Moscato, S., +, TMTT Oct. 2015 3175-3182 Permittivity measurement 60-GHz Substrate Materials Characterization Using the Covered Transmission-Line Method. Papio Toda, A., +, TMTT Mar. 2015 1063-1075 Accurate Evaluation Technique of Complex Permittivity for Low-Permittivity Dielectric Films Using a Cavity Resonator Method in 60-GHz Band. Shimizu, T., +, TMTT Jan. 2015 279-286 An Accurate Radially Stratified Approach for Determining the Complex Permittivity of Liquids in a Cylindrical Microwave Cavity. Barmatz, M. B., +, TMTT Feb. 2015 504-508 Design and Analysis of Shielded Vertically Stacked Ring Resonator as Complex Permittivity Sensor for Petroleum Oils. Kulkarni, S., +, TMTT Aug. 2015 2411-2417 Design of Multilayered Epsilon-Near-Zero Microwave Planar Sensor for Testing of Dispersive Materials. Jha, A. K., +, TMTT Aug. 2015 2418-2426 Dynamic Measurement of Dielectric Properties of Materials at High Temperature During Microwave Heating in a Dual Mode Cylindrical Cavity. Catala-Civera, J. M., +, TMTT Sep. 2015 2905-2914 Investigating the Broadband Microwave Absorption of Nanodiamond Impurities. Cuenca, J. A., +, TMTT Dec. 2015 4110-4118 Microstrip Device for Broadband (15–65 GHz) Measurement of Dielectric Properties of Nematic Liquid Crystals. Deo, P., +, TMTT Apr. 2015 13881398 Modelling and Measurements of the Microwave Dielectric Properties of Microspheres. Abduljabar, A. A., +, TMTT Dec. 2015 4492-4500 Single-Compound Complementary Split-Ring Resonator for Simultaneously Measuring the Permittivity and Thickness of Dual-Layer Dielectric Materials. Lee, C.-S., +, TMTT Jun. 2015 2010-2023 Whispering-Gallery-Mode Resonator Technique With Microfluidic Channel for Permittivity Measurement of Liquids. Gubin, A. I., +, TMTT Jun. 2015 2003-2009 Personal area networks A Millimeter-Wave WPAN Adaptive Phased Array Control Method Using Low-Frequency Part of Signal for Self-Directed System. Ta, T. T., +, TMTT Aug. 2015 2682-2691 Perturbation techniques Dynamic Measurement of Dielectric Properties of Materials at High Temperature During Microwave Heating in a Dual Mode Cylindrical Cavity. Catala-Civera, J. M., +, TMTT Sep. 2015 2905-2914 Parametric History Analysis for Material Properties Using Finite Elements and Adaptive Perturbations. Gunel, S., +, TMTT Jan. 2015 90-98 Petroleum Design and Analysis of Shielded Vertically Stacked Ring Resonator as Complex Permittivity Sensor for Petroleum Oils. Kulkarni, S., +, TMTT Aug. 2015 2411-2417 Phantoms A Technique to Evaluate MRI-Induced Electric Fields at the Ends of Practical Implanted Lead. Feng, S., +, TMTT Jan. 2015 305-313 Computational Feasibility Study of Contrast-Enhanced Thermoacoustic Imaging for Breast Cancer Detection Using Realistic Numerical Breast Phantoms. Wang, X., +, TMTT May 2015 1489-1501 Phase control A 1.1-Gbit/s 10-GHz Outphasing Modulator With 23-dBm Output Power and 60-dB Dynamic Range in 45-nm CMOS SOI. Mehrjoo, M. S., +, TMTT Jul. 2015 2289-2300 Polarization Considerations for Scalar Huygens Metasurfaces and Characterization for 2-D Refraction. Wong, J. P. S., +, TMTT Mar. 2015 913-924 Power Synthesis at 110-GHz Frequency Based on Discrete Sources. Zhao, J., +, TMTT May 2015 1633-1644 Phase estimation Low Complexity Coefficient Estimation for Concurrent Dual-Band Digital Predistortion. Qian, H., +, TMTT Oct. 2015 3153-3163 Phase locked loops 76–81-GHz CMOS Transmitter With a Phase-Locked-Loop-Based Multichirp Modulator for Automotive Radar. Park, J., +, TMTT Apr. 2015 13991408 A CML Ring Oscillator-Based Supply-Insensitive PLL With On-Chip Calibrations. Gui, X., +, TMTT Jan. 2015 233-243 A K-Band Reconfigurable Pulse-Compression Automotive Radar Transmitter in 90-nm CMOS. Tan, K.-W., +, TMTT Apr. 2015 1380-1387

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 63, NO. 12, DECEMBER 2015

An Ultra-Low Phase-Noise 20-GHz PLL Utilizing an Optoelectronic Voltage-Controlled Oscillator. Bluestone, A., +, TMTT Mar. 2015 1046-1052 Analysis and Design of a 14.1-mW 50/100-GHz Transformer-Based PLL With Embedded Phase Shifter in 65-nm CMOS. Chao, Y., +, TMTT Apr. 2015 1193-1201 Multi-Standard Hybrid PLL With Low Phase-Noise Characteristics for GSM/EDGE and LTE Applications. Choi, Y.-C., +, TMTT Oct. 2015 3254-3264 Reducing Energy Dissipation in ULP Systems: PLL-Free FBAR-Based Fast Startup Transmitters. Thirunarayanan, R., +, TMTT Apr. 2015 1110-1117 Spur Reduction Techniques With a Switched-Capacitor Feedback Differential PLL and a DLL-Based SSCG in UHF RFID Transmitter. Lee, I.-Y., +, TMTT Apr. 2015 1202-1210 Phase locked oscillators Reducing Energy Dissipation in ULP Systems: PLL-Free FBAR-Based Fast Startup Transmitters. Thirunarayanan, R., +, TMTT Apr. 2015 1110-1117 Phase modulation A Memoryless Semi-Physical Power Amplifier Behavioral Model Based on the Correlation Between AM–AM and AM–PM Distortions. Glock, S., +, TMTT Jun. 2015 1826-1835 A W-Band 4-GHz Bandwidth Phase-Modulated Pulse Compression Radar Transmitter in 65-nm CMOS. Oh, J., +, TMTT Aug. 2015 2609-2618 Theory and Implementation of RF-Input Outphasing Power Amplification. Barton, T. W., +, TMTT Dec. 2015 4273-4283 Phase noise 76–81-GHz CMOS Transmitter With a Phase-Locked-Loop-Based Multichirp Modulator for Automotive Radar. Park, J., +, TMTT Apr. 2015 13991408 A 47.6–71.0-GHz 65-nm CMOS VCO Based on Magnetically Coupled -Type LC Network. Jia, H., +, TMTT May 2015 1645-1657 A Low Phase-Noise Wide Tuning-Range Quadrature Oscillator Using a Transformer-Based Dual-Resonance LC Ring. Bajestan, M. M., +, TMTT Apr. 2015 1142-1153 A W-Band 4-GHz Bandwidth Phase-Modulated Pulse Compression Radar Transmitter in 65-nm CMOS. Oh, J., +, TMTT Aug. 2015 2609-2618 An FBAR/CMOS Frequency/Phase Discriminator and Phase Noise Reduction System. Imani, A., +, TMTT May 2015 1658-1665 An Ultra-Low Phase-Noise 20-GHz PLL Utilizing an Optoelectronic Voltage-Controlled Oscillator. Bluestone, A., +, TMTT Mar. 2015 1046-1052 Design and Tuning of Coupled-LC mm-Wave Subharmonically InjectionLocked Oscillators. Mangraviti, G., +, TMTT Jul. 2015 2301-2312 Designs of K-Band Divide-by-2 and Divide-by-3 Injection-Locked Frequency Divider With Darlington Topology. Chien, K.-H., +, TMTT Sep. 2015 2877-2888 Multi-Standard Hybrid PLL With Low Phase-Noise Characteristics for GSM/EDGE and LTE Applications. Choi, Y.-C., +, TMTT Oct. 2015 3254-3264 Performance Estimation for Broadband Multi-Gigabit Millimeter- and SubMillimeter-Wave Wireless Communication Links. Antes, J., +, TMTT Oct. 2015 3288-3299 Phase-Noise Analysis of an X-Band Ultra-Low Phase-Noise GaN HEMT Based Cavity Oscillator. Horberg, M., +, TMTT Aug. 2015 2619-2629 Phase shift keying A 15-Gb/s 8-PSK Demodulator With Comparator-Based Carrier Synchronization. He, Z., +, TMTT Aug. 2015 2630-2637 Phase shifters A K-Band CMOS UWB Four-Channel Radar Front-End With Coherent Pulsed Oscillator Array. Lee, S., +, TMTT May 2015 17351745 Accurate Parametric Electrical Model for Slow-Wave CPW and Application to Circuits Design. Bautista, A., +, TMTT Dec. 2015 4225-4235 Phased array radar A K-Band CMOS UWB Four-Channel Radar Front-End With Coherent Pulsed Oscillator Array. Lee, S., +, TMTT May 2015 1735-1745 Photodetectors Dynamic-Range Enhancement for a Microwave Photonic Link Based on a Polarization Modulator. Chen, X., +, TMTT Jul. 2015 2384-2389 Low-Loss Ultrawideband Programmable RF Photonic Phase Filter for Spread Spectrum Pulse Compression. Kim, H.-J., +, TMTT Dec. 2015 4178-4187

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Physiological models Computational Feasibility Study of Contrast-Enhanced Thermoacoustic Imaging for Breast Cancer Detection Using Realistic Numerical Breast Phantoms. Wang, X., +, TMTT May 2015 1489-1501 Piecewise linear techniques Decomposed Vector Rotation-Based Behavioral Modeling for Digital Predistortion of RF Power Amplifiers. Zhu, A., TMTT Feb. 2015 737-744 Planar antennas On the Development and Evaluation of Spatial-Domain Green’s Functions for Multilayered Structures With Conductive Sheets. Koufogiannis, I. D., +, TMTT Jan. 2015 20-29 Reconfigurable Diffractive Antenna Based on Switchable Electrically Induced Transparency. Li, H., +, TMTT Mar. 2015 925-936 Planar waveguides Printable Planar Dielectric Waveguides Based on High-Permittivity Films. Rashidian, A., +, TMTT Sep. 2015 2720-2729 Plasma radiofrequency heating Design and Characterization of a 170-GHz Resonant Diplexer for HighPower ECRH Systems. Wu, Z., +, TMTT Oct. 2015 3537-3546 Polarization Compact Orthomode Transducer Polarizer Based on a Tilted-Waveguide T-Junction. Esteban, J., +, TMTT Oct. 2015 3208-3217 Real-World Implementation Challenges of a Novel Dual-Polarized Compact Printable Chipless RFID Tag. Islam, M. A., +, TMTT Dec. 2015 4581-4591 Poles and zeros A Novel Compact -Plane Waveguide Filter With Multiple Transmission Zeroes. Jin, J. Y., +, TMTT Oct. 2015 3374-3380 An Ultra-Compact Common-Mode Bandstop Filter With Modified-T Circuits in Integrated Passive Device (IPD) Process. Hsiao, C.-Y., +, TMTT Nov. 2015 3624-3631 Automated Design of Common-Mode Suppressed Balanced Wideband Bandpass Filters by Means of Aggressive Space Mapping. Sans, M., +, TMTT Dec. 2015 3896-3908 Compact Tunable Filtering Power Divider With Constant Absolute Bandwidth. Gao, L., +, TMTT Oct. 2015 3505-3513 Hysteresis and Oscillation in High-Efficiency Power Amplifiers. de Cos, J., +, TMTT Dec. 2015 4284-4296 Reflection-Mode Bandstop Filters With Minimum Through-Line Length. Naglich, E. J., +, TMTT Oct. 2015 3479-3486 Synthesis of Inline Mixed Coupled Quasi-Elliptic Bandpass Filters Based on Resonators. Zhang, S., +, TMTT Oct. 2015 3487-3493 Wideband Balanced Filters With High Selectivity and Common-Mode Suppression. Chu, Q.-X., +, TMTT Oct. 2015 3462-3468 Polymerization Polymer Multichip Module Process Using 3-D Printing Technologies for D-Band Applications. Merkle, T., +, TMTT Feb. 2015 481-493 Polymers Wearable RF Sensor Array Implementing Coupling-Matrix Readout Extraction Technique. Chen, W.-T. S., +, TMTT Dec. 2015 4157-4168 Polynomial approximation DC and Imaginary Spurious Modes Suppression for Both Unbounded and Lossy Structures. Zekios, C. L., +, TMTT Jul. 2015 2082-2093 Polynomials 3-D Fourier Series Based Digital Predistortion Technique for Concurrent Dual-Band Envelope Tracking With Reduced Envelope Bandwidth. Lin, Y., +, TMTT Sep. 2015 2764-2775 An Improved Broadband Boundary Condition for the RF Field in Gyrotron Interaction Modeling. Wu, C., +, TMTT Aug. 2015 2459-2467 Concurrent Dual-Band Digital Predistortion With a Single Feedback Loop. Liu, Y., +, TMTT May 2015 1556-1568 Corrections to “Simple, Fast, and Effective Identification of an Equivalent Ports” [Jan 15 48-55]. Zappelli, Circuit of a Waveguide Junction With L., TMTT Mar. 2015 1108 Extraction of a Multi-Dimensional Polynomial Device Model for an Improved Distortion Contribution Analysis Technique. Aikio, J. P., +, TMTT Jan. 2015 155-164 Mixed Spectral-Element Method for 3-D Maxwell's Eigenvalue Problem. Liu, N., +, TMTT Feb. 2015 317-325 Simple, Fast, and Effective Identification of an Equivalent Circuit of a Waveguide Junction With Ports. Zappelli, L., TMTT Jan. 2015 48-55 The Mixed Spectral-Element Method for Anisotropic, Lossy, and Open Waveguides. Liu, N., +, TMTT Oct. 2015 3094-3102

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Ports (Computers) A Transformer-Based Poly-Phase Network for Ultra-Broadband Quadrature Signal Generation. Park, J. S., +, TMTT Dec. 2015 4444-4457 Power amplifiers 3-D Fourier Series Based Digital Predistortion Technique for Concurrent Dual-Band Envelope Tracking With Reduced Envelope Bandwidth. Lin, Y., +, TMTT Sep. 2015 2764-2775 A 1.1-Gbit/s 10-GHz Outphasing Modulator With 23-dBm Output Power and 60-dB Dynamic Range in 45-nm CMOS SOI. Mehrjoo, M. S., +, TMTT Jul. 2015 2289-2300 A Broadband 1-to- Power Divider/Combiner With Isolation and Reflection Cancellation. Darwish, A. M., +, TMTT Jul. 2015 2253-2263 A Memoryless Semi-Physical Power Amplifier Behavioral Model Based on the Correlation Between AM–AM and AM–PM Distortions. Glock, S., +, TMTT Jun. 2015 1826-1835 A New Double Input-Double Output Complex Envelope Amplifier Behavioral Model Taking Into Account Source and Load Mismatch Effects. Zargar, H., +, TMTT Feb. 2015 766-774 A Post-Matching Doherty Power Amplifier Employing Low-Order Impedance Inverters for Broadband Applications. Pang, J., +, TMTT Dec. 2015 4061-4071 Advanced Butler Matrices With Integrated Bandpass Filter Functions. Tornielli di Crestvolant, V., +, TMTT Oct. 2015 3433-3444 Antenna Impedance Variation Compensation by Exploiting a Digital Doherty Power Amplifier Architecture. Hu, S., +, TMTT Feb. 2015 580-597 Author's Reply. Grebennikov, A., TMTT Aug. 2015 2705 Bandwidth Enhancement of Three-Stage Doherty Power Amplifier Using Symmetric Devices. Barthwal, A., +, TMTT Aug. 2015 2399-2410 Behavioral Modeling and Predistortion of Power Amplifiers Under Sparsity Hypothesis. Reina-Tosina, J., +, TMTT Feb. 2015 745-753 Broadband Sequential Power Amplifier With Doherty-Type Active Load Modulation. Nghiem, X. A., +, TMTT Sep. 2015 2821-2832 Closed-Loop Digital Predistortion (DPD) Using an Observation Path With Limited Bandwidth. Braithwaite, R. N., TMTT Feb. 2015 726-736 Comments on “High-Efficiency Class E/F Lumped and Transmission-Line Power Amplifiers”. Cheng, Q.-F., +, TMTT Aug. 2015 2703-2704 Concurrent Dual-Band Digital Predistortion With a Single Feedback Loop. Liu, Y., +, TMTT May 2015 1556-1568 Efficient Least-Squares 2-D-Cubic Spline for Concurrent Dual-Band Systems. Naraharisetti, N., +, TMTT Jul. 2015 2199-2210 Envelope Tracking of an RF High Power Amplifier With an 8-Level Digitally Controlled GaN-on-Si Supply Modulator. Florian, C., +, TMTT Aug. 2015 2589-2602 Experimental Control and Design of Low-Frequency Bias Networks for Dynamically Biased Amplifiers. Pelaz, J., +, TMTT Jun. 2015 1923-1936 Generalized Stability Criteria for Power Amplifiers Under Mismatch Effects. Suarez, A., +, TMTT Dec. 2015 4415-4428 Guest Editorial. Draxler, P., TMTT Feb. 2015 557-558 Improved Reactance-Compensation Technique for the Design of Wideband Suboptimum Class-E Power Amplifiers. Zhou, J., +, TMTT Sep. 2015 27932801 Linearization and Imbalance Correction Techniques for Broadband Outphasing Power Amplifiers. Hwang, T., +, TMTT Jul. 2015 21852198 Output Impedance Mismatch Effects on the Linearity Performance of Digitally Predistorted Power Amplifiers. Zenteno, E., +, TMTT Feb. 2015 754-765 Spectra-Folding Feedback Architecture for Concurrent Dual-Band Power Amplifier Predistortion. Ma, Y., +, TMTT Oct. 2015 3164-3174 Power aware computing Power Adaptive Digital Predistortion for Wideband RF Power Amplifiers With Dynamic Power Transmission. Guo, Y., +, TMTT Nov. 2015 35953607 Power cables Dispersion Modeling and Analysis for Multilayered Open Coaxial Waveguides. Nordebo, S., +, TMTT Jun. 2015 1791-1799 Power combiners -Band Spatially Combined Power Amplifier Arrays in 45-nm CMOS SOI. Hanafi, B., +, TMTT Jun. 2015 1937-1950 A 110–170-GHz Multi-Mode Transconductance Mixer in 250-nm InP DHBT Technology. Yan, Y., +, TMTT Sep. 2015 2897-2904 A 2-W W-Band GaN Traveling-Wave Amplifier With 25-GHz Bandwidth. Schellenberg, J. M., TMTT Sep. 2015 2833-2840

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A 40-nm CMOS E-Band 4-Way Power Amplifier With Neutralized Bootstrapped Cascode Amplifier and Optimum Passive Circuits. Zhao, D., +, TMTT Dec. 2015 4083-4089 A Broadband 1-to- Power Divider/Combiner With Isolation and Reflection Cancellation. Darwish, A. M., +, TMTT Jul. 2015 2253-2263 A Broadband 4.5–15.5-GHz SiGe Power Amplifier With 25.5-dBm Peak Saturated Output Power and 28.7% Maximum PAE. Kerherve, E., +, TMTT May 2015 1621-1632 A Compact L-Band Orthomode Transducer for Radio Astronomical Receivers at Cryogenic Temperature. Valente, G., +, TMTT Oct. 2015 32183227 A Three-Way Reconfigurable Power Divider/Combiner. Fan, H., +, TMTT Mar. 2015 986-998 A W-Band Power Amplifier Utilizing a Miniaturized Marchand Balun Combiner. Jia, H., +, TMTT Feb. 2015 719-725 An E-Band Power Amplifier With Broadband Parallel-Series Power Combiner in 40-nm CMOS. Zhao, D., +, TMTT Feb. 2015 683-690 An Integrated Slot-Ring Traveling-Wave Radiator. Bowers, S. M., +, TMTT Apr. 2015 1154-1162 Analytical Design Methodology for Generic Doherty Amplifier Architectures Using Three-Port Input/Output Networks. Akbarpour, M., +, TMTT Oct. 2015 3242-3253 Corrections to “Compact Conical-Line Power Combiner Design Using Circuit Models” [Nov 14 2650-2658]. Beyers, R. D., +, TMTT Jul. 2015 2391 Corrections to “Compact Multi-Port Power Combination/Distribution With Inherent Bandpass Filter Characteristics” [Nov 14 2659-2672]. Rosenberg, U., +, TMTT Jul. 2015 2390 Design of a Traveling-Wave Slot Array Power Divider Using the Method of Moments and a Genetic Algorithm. Rengarajan, S. R., +, TMTT Dec. 2015 3981-3987 Efficient Design of Compact Contiguous-Channel SIW Multiplexers Using the Space-Mapping Method. Hao, Z.-C., +, TMTT Nov. 2015 3651-3662 Theory and Implementation of RF-Input Outphasing Power Amplification. Barton, T. W., +, TMTT Dec. 2015 4273-4283 Wideband Balanced Network with High Isolation Using Double-Sided Parallel-Strip Line. Feng, W., +, TMTT Dec. 2015 4013-4018 Power control Advanced Power Control Scheme in Wireless Power Transmission for Human Protection From EM Field. Kim, S.-M., +, TMTT Mar. 2015 847-856 An Efficiency-Enhanced Stacked 2.4-GHz CMOS Power Amplifier With Mode Switching Scheme for WLAN Applications. Yin, Y., +, TMTT Feb. 2015 672-682 Power conversion harmonics GaN Microwave DC–DC Converters. Ramos, I., +, TMTT Dec. 2015 44734482 Power converters Envelope Tracking of an RF High Power Amplifier With an 8-Level Digitally Controlled GaN-on-Si Supply Modulator. Florian, C., +, TMTT Aug. 2015 2589-2602 Power dividers A Balanced-to-Unbalanced Microstrip Power Divider With Filtering Function. Xu, K., +, TMTT Aug. 2015 2561-2569 A Broadband 1-to- Power Divider/Combiner With Isolation and Reflection Cancellation. Darwish, A. M., +, TMTT Jul. 2015 2253-2263 A Four-Way Microstrip Filtering Power Divider With Frequency-Dependent Couplings. Chen, F.-J., +, TMTT Oct. 2015 3494-3504 A Three-Way Reconfigurable Power Divider/Combiner. Fan, H., +, TMTT Mar. 2015 986-998 Adaptive Coupling of Resonators for Efficient Microwave Heating of Microfluidic Systems. Abduljabar, A. A., +, TMTT Nov. 2015 3681-3690 -Mode An Isolated Radial Power Divider via Circular Waveguide Transducer. Chu, Q.-X., +, TMTT Dec. 2015 3988-3996 Compact Tunable Filtering Power Divider With Constant Absolute Bandwidth. Gao, L., +, TMTT Oct. 2015 3505-3513 Corrections to “Compact Multi-Port Power Combination/Distribution With Inherent Bandpass Filter Characteristics” [Nov 14 2659-2672]. Rosenberg, U., +, TMTT Jul. 2015 2390 Design of a Traveling-Wave Slot Array Power Divider Using the Method of Moments and a Genetic Algorithm. Rengarajan, S. R., +, TMTT Dec. 2015 3981-3987 Wideband Balanced Network with High Isolation Using Double-Sided Parallel-Strip Line. Feng, W., +, TMTT Dec. 2015 4013-4018

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 63, NO. 12, DECEMBER 2015

Power electronics Power Synthesis at 110-GHz Frequency Based on Discrete Sources. Zhao, J., +, TMTT May 2015 1633-1644 Power harmonic filters Guest Editorial. Boria, V. E., +, TMTT Oct. 2015 3321-3323 Power transfer Guest Editorial. KIM, J., +, TMTT Mar. 2015 778-779 Power transformers The Effects of Electrode Configuration on Body Channel Communication Based on Analysis of Vertical and Horizontal Electric Dipoles. Bae, J., +, TMTT Apr. 2015 1409-1420 Power utilization Improving Power Utilization Factor of Broadband Doherty Amplifier by Using Bandpass Auxiliary Transformer. Fang, X.-H., +, TMTT Sep. 2015 2811-2820 Principal component analysis 3-D Distributed Memory Polynomial Behavioral Model for Concurrent Dual-Band Envelope Tracking Power Amplifier Linearization. Gilabert, P. L., +, TMTT Feb. 2015 638-648 Printed circuit design A Miniaturized Microfluidically Reconfigurable Coplanar Waveguide Bandpass Filter With Maximum Power Handling of 10 Watts. Pourghorban Saghati, A., +, TMTT Aug. 2015 2515-2525 Printed circuits 160-GHz to 1-THz Multi-Color Active Imaging With a Lens-Coupled SiGe HBT Chip-Set. Statnikov, K., +, TMTT Feb. 2015 520-532 -Band Spatially Combined Power Amplifier Arrays in 45-nm CMOS SOI. Hanafi, B., +, TMTT Jun. 2015 1937-1950 A 77-GHz FMCW Radar System Using On-Chip Waveguide Feeders in 65-nm CMOS. Cui, C., +, TMTT Nov. 2015 3736-3746 A Single-Chip Electron Paramagnetic Resonance Transceiver in 0.13- m SiGe BiCMOS. Yang, X., +, TMTT Nov. 2015 3727-3735 A Wide-Band CMOS to Waveguide Transition at mm-Wave Frequencies With Wire-Bonds. Jameson, S., +, TMTT Sep. 2015 2741-2750 Air-Filled Substrate Integrated Waveguide for Low-Loss and High PowerHandling Millimeter-Wave Substrate Integrated Circuits. Parment, F., +, TMTT Apr. 2015 1228-1238 Chebyshev Filter Design Using Vias as Quasi-Transmission Lines in Printed Circuit Boards. Hardock, A., +, TMTT Mar. 2015 976-985 Design of Compact Reflection-Type Phase Shifters With High Figure-ofMerit. Burdin, F., +, TMTT Jun. 2015 1883-1893 Extraction of Dielectric and Rough Conductor Loss of Printed Circuit Board Using Differential Method at Microwave Frequencies. Zhu, X.-C., +, TMTT Feb. 2015 494-503 High-Efficiency Applicator Based on Printed Circuit Board in MillimeterWave Region. Shiina, T., +, TMTT Oct. 2015 3311-3318 High-Performance Coplanar Waveguide to Empty Substrate Integrated Coaxial Line Transition. Belenguer, A., +, TMTT Dec. 2015 4027-4034 Low-Input Power-Level CMOS RF Energy-Harvesting Front End. Abouzied, M. A., +, TMTT Nov. 2015 3794-3805 Polarization Considerations for Scalar Huygens Metasurfaces and Characterization for 2-D Refraction. Wong, J. P. S., +, TMTT Mar. 2015 913-924 Substrate Integrated Waveguide Directional Couplers for Compact ThreeDimensional Integrated Circuits. Doghri, A., +, TMTT Jan. 2015 209-221 Tunable 500–1200-MHz Dual-Band and Wide Bandwidth Notch Filters Using RF Transformers. Ko, C.-H., +, TMTT Jun. 2015 1854-1862 Programmable filters 0.8/2.2-GHz Programmable Active Bandpass Filters in InP/Si BiCMOS Technology. Xu, Z., +, TMTT Apr. 2015 1219-1227 Low-Loss Ultrawideband Programmable RF Photonic Phase Filter for Spread Spectrum Pulse Compression. Kim, H.-J., +, TMTT Dec. 2015 4178-4187 Prosthetics A High-Sensitivity Fully Passive Neurosensing System for Wireless Brain Signal Monitoring. Lee, C. W. L., +, TMTT Jun. 2015 2060-2068 Resonant Inductive Link for Remote Powering of Pacemakers. Monti, G., +, TMTT Nov. 2015 3814-3822 Proteins Miniaturized Transmission-Line Sensor for Broadband Dielectric Characterization of Biological Liquids and Cell Suspensions. Meyne nee Haase, N., +, TMTT Oct. 2015 3026-3033 Protocols Wireless Power Systems for Mobile Devices Supporting Inductive and Resonant Operating Modes. Riehl, P. S., +, TMTT Mar. 2015 780-790 + Check author entry for coauthors

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Pseudonoise codes A K-Band Reconfigurable Pulse-Compression Automotive Radar Transmitter in 90-nm CMOS. Tan, K.-W., +, TMTT Apr. 2015 1380-1387 A W-Band 4-GHz Bandwidth Phase-Modulated Pulse Compression Radar Transmitter in 65-nm CMOS. Oh, J., +, TMTT Aug. 2015 2609-2618 Pulse amplitude modulation Supply-Modulated Radar Transmitters With Amplitude-Modulated Pulses. Zai, A., +, TMTT Sep. 2015 2953-2964 Pulse compression A K-Band Reconfigurable Pulse-Compression Automotive Radar Transmitter in 90-nm CMOS. Tan, K.-W., +, TMTT Apr. 2015 1380-1387 A Reconfigurable 50-Mb/s-1 Gb/s Pulse Compression Radar Signal Processor With Offset Calibration in 90-nm CMOS. Li, J., +, TMTT Jan. 2015 266-278 A W-Band 4-GHz Bandwidth Phase-Modulated Pulse Compression Radar Transmitter in 65-nm CMOS. Oh, J., +, TMTT Aug. 2015 2609-2618 Design of Waveguide Microwave Pulse Compressors Using Equivalent Circuits. Savaidis, S. P., +, TMTT Jan. 2015 125-134 Experimental Study of Microwave Pulse Compression Using a Five-Fold Helically Corrugated Waveguide. Zhang, L., +, TMTT Mar. 2015 10901096 Pulse generators A K-Band Reconfigurable Pulse-Compression Automotive Radar Transmitter in 90-nm CMOS. Tan, K.-W., +, TMTT Apr. 2015 1380-1387 Pulse measurement Time-Domain Optoelectronic Vector Network Analysis on Coplanar Waveguides. Bieler, M., +, TMTT Nov. 2015 3775-3784 Pulse modulation A Highly Efficient LTE Pulse-Modulated Polar Transmitter Using Wideband Power Recycling. Yang, H.-S., +, TMTT Dec. 2015 4437-4443 Pulse width modulation A Pulsed Dynamic Load Modulation Technique for High-Efficiency Linear Transmitters. Jeon, M.-S., +, TMTT Sep. 2015 2854-2866 A Wideband Pulse-Modulated Polar Transmitter Using Envelope Correction for LTE Applications. Liang, K.-F., +, TMTT Aug. 2015 2603-2608 Concurrent Multiband Digital Outphasing Transmitter Architecture Using Multidimensional Power Coding. Chung, S., +, TMTT Feb. 2015 598-613 PWM rectifiers A Highly Efficient LTE Pulse-Modulated Polar Transmitter Using Wideband Power Recycling. Yang, H.-S., +, TMTT Dec. 2015 4437-4443

Q Q factor A 1.3–2.4-GHz 3.1-mW VCO Using Electro-Thermo- Mechanically Tunable Self-Assembled MEMS Inductor on HR Substrate. Bhattacharya, A., +, TMTT Feb. 2015 459-469 A High-Power Low-Loss Continuously Tunable Bandpass Filter With Transversely Biased Ferrite-Loaded Coaxial Resonators. Acar, O., +, TMTT Oct. 2015 3425-3432 An FBAR/CMOS Frequency/Phase Discriminator and Phase Noise Reduction System. Imani, A., +, TMTT May 2015 1658-1665 Compact Quad-Mode Bandpass Filter Using Modified Coaxial Cavity Resonator With Improved -Factor. Wang, X., +, TMTT Mar. 2015 965-975 Compact Tunable Filtering Power Divider With Constant Absolute Bandwidth. Gao, L., +, TMTT Oct. 2015 3505-3513 Bandpass Filters Using Coupling-Matrix-Based Design of HighAcoustic-Wave Lumped-Element Resonator (AWLR) Modules. Psychogiou, D., +, TMTT Dec. 2015 4319-4328 Design and Characterization of a 170-GHz Resonant Diplexer for HighPower ECRH Systems. Wu, Z., +, TMTT Oct. 2015 3537-3546 Extraction of Dielectric and Rough Conductor Loss of Printed Circuit Board Using Differential Method at Microwave Frequencies. Zhu, X.-C., +, TMTT Feb. 2015 494-503 High- Tunable Waveguide Filters Using Ohmic RF MEMS Switches. Pelliccia, L., +, TMTT Oct. 2015 3381-3390 High-Tunability and High- -Factor Integrated Ferroelectric Circuits up to Millimeter Waves. De Paolis, R., +, TMTT Aug. 2015 2570-2578 Microstrip Whispering-Gallery-Mode Resonator. Bunyaev, S. A., +, TMTT Sep. 2015 2776-2781 Passive Microwave Substrate Integrated Cavity Resonator for Humidity Sensing. El Matbouly, H., +, TMTT Dec. 2015 4150-4156

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Quality Factor of the Waveguide Re-Entrant Turnstile Junction Circulator. Helszajn, J., +, TMTT May 2015 1603-1608 RF-Designed High-Power Lamb-Wave Aluminum–Nitride Resonators. Campanella, H., +, TMTT Feb. 2015 331-339 Whispering-Gallery-Mode Resonator Technique With Microfluidic Channel for Permittivity Measurement of Liquids. Gubin, A. I., +, TMTT Jun. 2015 2003-2009 Quadrature amplitude modulation A 1.1-Gbit/s 10-GHz Outphasing Modulator With 23-dBm Output Power and 60-dB Dynamic Range in 45-nm CMOS SOI. Mehrjoo, M. S., +, TMTT Jul. 2015 2289-2300 A Hardware Efficient Implementation of a Digital Baseband Receiver for High-Capacity Millimeter-Wave Radios. He, Z., +, TMTT May 2015 16831692 A Highly Efficient LTE Pulse-Modulated Polar Transmitter Using Wideband Power Recycling. Yang, H.-S., +, TMTT Dec. 2015 4437-4443 A Novel Load Mismatch Detection and Correction Technique for 3G/4G Load Insensitive Power Amplifier Application. Ji, D., +, TMTT May 2015 1530-1543 A Pulsed Dynamic Load Modulation Technique for High-Efficiency Linear Transmitters. Jeon, M.-S., +, TMTT Sep. 2015 2854-2866 A Sub-GHz Wireless Transmitter Utilizing a Multi-Class-Linearized PA and Time-Domain Wideband-Auto I/Q-LOFT Calibration for IEEE 802.11af WLAN. Un, K.-F., +, TMTT Oct. 2015 3228-3241 A Wideband Pulse-Modulated Polar Transmitter Using Envelope Correction for LTE Applications. Liang, K.-F., +, TMTT Aug. 2015 2603-2608 An Efficiency-Enhanced Stacked 2.4-GHz CMOS Power Amplifier With Mode Switching Scheme for WLAN Applications. Yin, Y., +, TMTT Feb. 2015 672-682 Fully Integrated D-Band Direct Carrier Quadrature (I/Q) Modulator and Demodulator Circuits in InP DHBT Technology. Carpenter, S., +, TMTT May 2015 1666-1675 Fully Monolithic BiCMOS Reconfigurable Power Amplifier for Multi-Mode and Multi-Band Applications. Lee, M.-L., +, TMTT Feb. 2015 614-624 High-Speed Signal Transmission at W-Band Over Dielectric-Coated Metallic Hollow Fiber. Yu, J., +, TMTT Jun. 2015 1836-1842 Investigation of Intermodulation Distortion of Envelope Tracking Power Amplifier for Linearity Improvement. Moon, K., +, TMTT Apr. 2015 13241333 Millimeter-Wave Modulated-Signal and Error-Vector-Magnitude Measurement With Uncertainty. Remley, K. A., +, TMTT May 2015 1710-1720 Transmission of Signals With Complex Constellations Using Millimeter-Wave Spatially Power-Combined CMOS Power Amplifiers and Digital Predistortion. Dabag, H.-T., +, TMTT Jul. 2015 2364-2374 Quadrature phase shift keying A mm-Wave Segmented Power Mixer. Dasgupta, K., +, TMTT Apr. 2015 1118-1129 High-Speed Signal Transmission at W-Band Over Dielectric-Coated Metallic Hollow Fiber. Yu, J., +, TMTT Jun. 2015 1836-1842 Performance Estimation for Broadband Multi-Gigabit Millimeter- and SubMillimeter-Wave Wireless Communication Links. Antes, J., +, TMTT Oct. 2015 3288-3299 R Radar antennas 3-D High-Resolution Imaging Radar at 300 GHz With Enhanced FoV. Grajal, J., +, TMTT Mar. 2015 1097-1107 Radar applications Material Characterization of Arbitrarily Shaped Dielectrics Based on Reflected Pulse Characteristics. Chan, K.K.M., +, TMTT May 2015 1700-1709 Radar clutter Multichannel Backscatter Communication and Ranging for Distributed Sensing With an FMCW Radar. Cnaan-On, I., +, TMTT Jul. 2015 2375-2383 Radar imaging 3-D High-Resolution Imaging Radar at 300 GHz With Enhanced FoV. Grajal, J., +, TMTT Mar. 2015 1097-1107 Radar receivers A Reconfigurable 50-Mb/s-1 Gb/s Pulse Compression Radar Signal Processor With Offset Calibration in 90-nm CMOS. Li, J., +, TMTT Jan. 2015 266-278 + Check author entry for coauthors

Multi-Band Software-Defined Coherent Radar Based on a Single Photonic Transceiver. Scotti, F., +, TMTT Feb. 2015 546-552 Radar resolution A Reconfigurable 50-Mb/s-1 Gb/s Pulse Compression Radar Signal Processor With Offset Calibration in 90-nm CMOS. Li, J., +, TMTT Jan. 2015 266-278 A W-Band 4-GHz Bandwidth Phase-Modulated Pulse Compression Radar Transmitter in 65-nm CMOS. Oh, J., +, TMTT Aug. 2015 2609-2618 Radar signal processing Gesture Sensing Using Retransmitted Wireless Communication Signals Based on Doppler Radar Technology. Wang, F.-K., +, TMTT Dec. 2015 4592-4602 Radar transmitters A K-Band Reconfigurable Pulse-Compression Automotive Radar Transmitter in 90-nm CMOS. Tan, K.-W., +, TMTT Apr. 2015 1380-1387 A W-Band 4-GHz Bandwidth Phase-Modulated Pulse Compression Radar Transmitter in 65-nm CMOS. Oh, J., +, TMTT Aug. 2015 2609-2618 Multi-Band Software-Defined Coherent Radar Based on a Single Photonic Transceiver. Scotti, F., +, TMTT Feb. 2015 546-552 Supply-Modulated Radar Transmitters With Amplitude-Modulated Pulses. Zai, A., +, TMTT Sep. 2015 2953-2964 Radial basis function networks Compact Behavioral Models of Nonlinear Active Devices Using Response Surface Methodology. Barmuta, P., +, TMTT Jan. 2015 56-64 Hybrid Nonlinear Modeling Using Adaptive Sampling. Barmuta, P., +, TMTT Dec. 2015 4501-4510 Radio frequency A Transformer-Based Poly-Phase Network for Ultra-Broadband Quadrature Signal Generation. Park, J. S., +, TMTT Dec. 2015 4444-4457 Radio links A Hardware Efficient Implementation of a Digital Baseband Receiver for High-Capacity Millimeter-Wave Radios. He, Z., +, TMTT May 2015 16831692 Partitioned Distortion Mitigation in LTE Radio Uplink to Enhance Transmitter Efficiency. Amiri, M. V., +, TMTT Aug. 2015 2661-2671 Wireless Power Systems for Mobile Devices Supporting Inductive and Resonant Operating Modes. Riehl, P. S., +, TMTT Mar. 2015 780-790 Radio networks Performance Estimation for Broadband Multi-Gigabit Millimeter- and SubMillimeter-Wave Wireless Communication Links. Antes, J., +, TMTT Oct. 2015 3288-3299 Resonant Inductive Link for Remote Powering of Pacemakers. Monti, G., +, TMTT Nov. 2015 3814-3822 Radio receivers 3-D Radiometric Aperture Synthesis Imaging. Salmon, N. A., TMTT Nov. 2015 3579-3587 A 2.45-GHz Energy-Autonomous Wireless Power Relay Node. Del Prete, M., +, TMTT Dec. 2015 4511-4520 A CMOS Spectrum Sensor Based on Quasi-Cyclostationary Feature Detection for Cognitive Radios. Sepidband, P., +, TMTT Dec. 2015 4098-4109 A Compact L-Band Orthomode Transducer for Radio Astronomical Receivers at Cryogenic Temperature. Valente, G., +, TMTT Oct. 2015 32183227 A Prototype SAW-Less LTE Transmitter With a High-Linearity Modulator Using BPF-Based I/Q Summing and a Triple-Layer Marchand Balun. Nakamura, T., +, TMTT Dec. 2015 4090-4097 A Tunable RF Front-End With Narrowband Antennas for Mobile Devices. Bahramzy, P., +, TMTT Oct. 2015 3300-3310 Development of a Communication Scheme for Wireless Power Applications With Moving Receivers. Thoen, B., +, TMTT Mar. 2015 857-863 Partitioned Distortion Mitigation in LTE Radio Uplink to Enhance Transmitter Efficiency. Amiri, M. V., +, TMTT Aug. 2015 2661-2671 RF Input Matching Design for Closed-Loop Direct Delta–Sigma Receivers. Ostman, K. B., +, TMTT Apr. 2015 1370-1379 The Effects of Electrode Configuration on Body Channel Communication Based on Analysis of Vertical and Horizontal Electric Dipoles. Bae, J., +, TMTT Apr. 2015 1409-1420 Radio spectrum management A CMOS Spectrum Sensor Based on Quasi-Cyclostationary Feature Detection for Cognitive Radios. Sepidband, P., +, TMTT Dec. 2015 4098-4109 Radio transceivers A Compact Dual-Channel Transceiver for Long-Range Passive Embedded Monitoring. Nassar, I. T., +, TMTT Jan. 2015 287-294

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A Low-IF Tag-Based Motion Compensation Technique for Mobile Doppler Radar Life Signs Monitoring. Rahman, A., +, TMTT Oct. 2015 3034-3041 Concurrent Dual-Band Modeling and Digital Predistortion in the Presence of Unfilterable Harmonic Signal Interference. Rawat, M., +, TMTT Feb. 2015 625-637 Digital Compensation for Transmitter Leakage in Non-Contiguous Carrier Aggregation Applications With FPGA Implementation. Yu, C., +, TMTT Dec. 2015 4306-4318 Multi-Band Software-Defined Coherent Radar Based on a Single Photonic Transceiver. Scotti, F., +, TMTT Feb. 2015 546-552 Nonlinear Communication System With Harmonic Diversity. Cheong, P., +, TMTT Dec. 2015 4130-4149 Real-Time Adaptive Transmitter Leakage Cancelling in 5.8-GHz Full-Duplex Transceivers. Maddio, S., +, TMTT Feb. 2015 509-519 Radio transmitters 76–81-GHz CMOS Transmitter With a Phase-Locked-Loop-Based Multichirp Modulator for Automotive Radar. Park, J., +, TMTT Apr. 2015 13991408 A 2.45-GHz Energy-Autonomous Wireless Power Relay Node. Del Prete, M., +, TMTT Dec. 2015 4511-4520 A 37.5-mW 8-dBm-EIRP 15.5 -HPBW 338-GHz Terahertz Transmitter Using SoP Heterogeneous System Integration. Li, C.-H., +, TMTT Feb. 2015 470-480 A Highly Efficient LTE Pulse-Modulated Polar Transmitter Using Wideband Power Recycling. Yang, H.-S., +, TMTT Dec. 2015 4437-4443 A Prototype SAW-Less LTE Transmitter With a High-Linearity Modulator Using BPF-Based I/Q Summing and a Triple-Layer Marchand Balun. Nakamura, T., +, TMTT Dec. 2015 4090-4097 A Pulsed Dynamic Load Modulation Technique for High-Efficiency Linear Transmitters. Jeon, M.-S., +, TMTT Sep. 2015 2854-2866 A Sub-GHz Wireless Transmitter Utilizing a Multi-Class-Linearized PA and Time-Domain Wideband-Auto I/Q-LOFT Calibration for IEEE 802.11af WLAN. Un, K.-F., +, TMTT Oct. 2015 3228-3241 A Tunable RF Front-End With Narrowband Antennas for Mobile Devices. Bahramzy, P., +, TMTT Oct. 2015 3300-3310 A Wideband Pulse-Modulated Polar Transmitter Using Envelope Correction for LTE Applications. Liang, K.-F., +, TMTT Aug. 2015 2603-2608 Concurrent Multiband Digital Outphasing Transmitter Architecture Using Multidimensional Power Coding. Chung, S., +, TMTT Feb. 2015 598-613 Digitally Equalized Doherty RF Front-End Architecture for Broadband and Multistandard Wireless Transmitters. Darraji, R., +, TMTT Jun. 2015 19781988 Efficient Least-Squares 2-D-Cubic Spline for Concurrent Dual-Band Systems. Naraharisetti, N., +, TMTT Jul. 2015 2199-2210 Multi-Frequency Measurements for Supply Modulated Transmitters. Schafer, S., +, TMTT Sep. 2015 2931-2941 Partitioned Distortion Mitigation in LTE Radio Uplink to Enhance Transmitter Efficiency. Amiri, M. V., +, TMTT Aug. 2015 2661-2671 Single-Model Single-Feedback Digital Predistortion for Concurrent Multi-Band Wireless Transmitters. Yu, C., +, TMTT Jul. 2015 2211-2224 Source Degenerated Derivative Superposition Method for Linearizing RF FET Differential Amplifiers. Shin, H., +, TMTT Mar. 2015 1026-1035 Spur Reduction Techniques With a Switched-Capacitor Feedback Differential PLL and a DLL-Based SSCG in UHF RFID Transmitter. Lee, I.-Y., +, TMTT Apr. 2015 1202-1210 The Effects of Electrode Configuration on Body Channel Communication Based on Analysis of Vertical and Horizontal Electric Dipoles. Bae, J., +, TMTT Apr. 2015 1409-1420 Radio-over-fiber Analysis of Dual Wavelength Linearization Technique for Radio-Over-Fiber Systems With Electro-Absorption Modulator. Zhu, R., +, TMTT Aug. 2015 2692-2702 Radioastronomy A Compact L-Band Orthomode Transducer for Radio Astronomical Receivers at Cryogenic Temperature. Valente, G., +, TMTT Oct. 2015 32183227 Radiocommunication Development of a Communication Scheme for Wireless Power Applications With Moving Receivers. Thoen, B., +, TMTT Mar. 2015 857-863 Radiofrequency amplifiers Envelope Tracking of an RF High Power Amplifier With an 8-Level Digitally Controlled GaN-on-Si Supply Modulator. Florian, C., +, TMTT Aug. 2015 2589-2602 + Check author entry for coauthors

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Radiofrequency filters A High-Power Low-Loss Continuously Tunable Bandpass Filter With Transversely Biased Ferrite-Loaded Coaxial Resonators. Acar, O., +, TMTT Oct. 2015 3425-3432 A Tunable RF Front-End With Narrowband Antennas for Mobile Devices. Bahramzy, P., +, TMTT Oct. 2015 3300-3310 Hybrid Acoustic-Wave-Lumped-Element Resonators (AWLRs) for HighBandpass Filters With Quasi-Elliptic Frequency Response. Psychogiou, D., +, TMTT Jul. 2015 2233-2244 Radiofrequency identification A Low-IF Tag-Based Motion Compensation Technique for Mobile Doppler Radar Life Signs Monitoring. Rahman, A., +, TMTT Oct. 2015 3034-3041 Compact Printable Chipless RFID Systems. Islam, M. A., +, TMTT Nov. 2015 3785-3793 Cooperative Integration of Harvesting RF Sections for Passive RFID Communication. Andia Vera, G., +, TMTT Dec. 2015 4556-4566 Guest Editorial. Alomainy, A., +, TMTT Oct. 2015 3005-3006 Implementation of Sensor RFID: Carrying Sensor Information in the Modulation Frequency. Islam, Md. M., +, TMTT Aug. 2015 2672-2681 Real-World Implementation Challenges of a Novel Dual-Polarized Compact Printable Chipless RFID Tag. Islam, M. A., +, TMTT Dec. 2015 4581-4591 Spur Reduction Techniques With a Switched-Capacitor Feedback Differential PLL and a DLL-Based SSCG in UHF RFID Transmitter. Lee, I.-Y., +, TMTT Apr. 2015 1202-1210 Third Harmonic Exploitation in Passive UHF RFID. Andiia Vera, G., +, TMTT Sep. 2015 2991-3004 Radiofrequency integrated circuits A 0.12-mm 2.4-GHz CMOS Inductorless High Isolation Subharmonic Mixer With Effective Current-Reuse Transconductance. Chong, W. K., +, TMTT Aug. 2015 2427-2437 CMOS Broadband Programmable Gain Active Balun With 0.5-dB Gain Steps. Hur, B., +, TMTT Aug. 2015 2650-2660 Digitally Assisted CMOS RF Detectors With Self-Calibration for Variability Compensation. Barabino, N., +, TMTT May 2015 1676-1682 Guest Editorial. Gharpurey, R., TMTT Apr. 2015 1109 High Power Latching RF MEMS Switches. Bakri-Kassem, M., +, TMTT Jan. 2015 222-232 Modeling of Inline Transitions Between Different Waveguides as Impedance Inverters for the Use in Novel Filter Designs. Strauss, G., +, TMTT Nov. 2015 3663-3670 Radiofrequency interference A New Broadband Common-Mode Noise Absorption Circuit for High-Speed Differential Digital Systems. Hsiao, C.-Y., +, TMTT Jun. 2015 1894-1901 An Investigation of Electromagnetic Radiated Emission and Interference From Multi-Coil Wireless Power Transfer Systems Using Resonant Magnetic Field Coupling. Kong, S., +, TMTT Mar. 2015 833-846 An Ultra-Compact Common-Mode Bandstop Filter With Modified-T Circuits in Integrated Passive Device (IPD) Process. Hsiao, C.-Y., +, TMTT Nov. 2015 3624-3631 The Effects of Electrode Configuration on Body Channel Communication Based on Analysis of Vertical and Horizontal Electric Dipoles. Bae, J., +, TMTT Apr. 2015 1409-1420 Radiofrequency measurement Digitally Assisted CMOS RF Detectors With Self-Calibration for Variability Compensation. Barabino, N., +, TMTT May 2015 1676-1682 Radiofrequency oscillators A Sub-GHz Wireless Transmitter Utilizing a Multi-Class-Linearized PA and Time-Domain Wideband-Auto I/Q-LOFT Calibration for IEEE 802.11af WLAN. Un, K.-F., +, TMTT Oct. 2015 3228-3241 Nonlinear Communication System With Harmonic Diversity. Cheong, P., +, TMTT Dec. 2015 4130-4149 Radiofrequency power amplifiers A General Digital Predistortion Architecture Using Constrained Feedback Bandwidth for Wideband Power Amplifiers. Liu, Y., +, TMTT May 2015 1544-1555 A Pulsed Dynamic Load Modulation Technique for High-Efficiency Linear Transmitters. Jeon, M.-S., +, TMTT Sep. 2015 2854-2866 A Sub-GHz Wireless Transmitter Utilizing a Multi-Class-Linearized PA and Time-Domain Wideband-Auto I/Q-LOFT Calibration for IEEE 802.11af WLAN. Un, K.-F., +, TMTT Oct. 2015 3228-3241 An Efficiency-Enhanced Stacked 2.4-GHz CMOS Power Amplifier With Mode Switching Scheme for WLAN Applications. Yin, Y., +, TMTT Feb. 2015 672-682

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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 63, NO. 12, DECEMBER 2015

Broadband CMOS Stacked RF Power Amplifier Using Reconfigurable Interstage Network for Wideband Envelope Tracking. Park, S., +, TMTT Apr. 2015 1174-1185 Decomposed Vector Rotation-Based Behavioral Modeling for Digital Predistortion of RF Power Amplifiers. Zhu, A., TMTT Feb. 2015 737-744 Digitally Assisted Analog/RF Predistorter With a Small-Signal-Assisted Parameter Identification Algorithm. Huang, H., +, TMTT Dec. 2015 42974305 Electrothermal Effects on Performance of GaAs HBT Power Amplifier During Power Versus Time (PVT) Variation at GSM/DCS Bands. Lin, L., +, TMTT Jun. 2015 1951-1963 Extraction of a Multi-Dimensional Polynomial Device Model for an Improved Distortion Contribution Analysis Technique. Aikio, J. P., +, TMTT Jan. 2015 155-164 Low Complexity Coefficient Estimation for Concurrent Dual-Band Digital Predistortion. Qian, H., +, TMTT Oct. 2015 3153-3163 Optimized Design of a Dual-Band Power Amplifier With SiC VaractorBased Dynamic Load Modulation. Sanchez-Perez, C., +, TMTT Aug. 2015 2579-2588 Radiofrequency power transmission Advanced Power Control Scheme in Wireless Power Transmission for Human Protection From EM Field. Kim, S.-M., +, TMTT Mar. 2015 847-856 Development of a Communication Scheme for Wireless Power Applications With Moving Receivers. Thoen, B., +, TMTT Mar. 2015 857-863 Development of the Optimization Framework for Low-Power Wireless Power Transfer Systems. Lee, S. B., +, TMTT Mar. 2015 813-820 Enhanced Analysis and Design Method of Dual-Band Coil Module for NearField Wireless Power Transfer Systems. Kung, M.-L., +, TMTT Mar. 2015 821-832 Free-Positioning Wireless Charging System for Small Electronic Devices Using a Bowl-Shaped Transmitting Coil. Kim, J., +, TMTT Mar. 2015 791-800 Radiometry 3-D Radiometric Aperture Synthesis Imaging. Salmon, N. A., TMTT Nov. 2015 3579-3587 Radionavigation A Distributed Positioning System Based on a Predictive Fingerprinting Method Enabling Sub-Metric Precision in IEEE 802.11 Networks. Maddio, S., +, TMTT Dec. 2015 4567-4580 Signal Detection and Noise Modeling of a 1-D Pulse-Based Ultra-Wideband Ranging System and Its Accuracy Assessment. Elkhouly, E., +, TMTT May 2015 1746-1757 Radiotelescopes A Compact L-Band Orthomode Transducer for Radio Astronomical Receivers at Cryogenic Temperature. Valente, G., +, TMTT Oct. 2015 32183227 RC circuits 0.8/2.2-GHz Programmable Active Bandpass Filters in InP/Si BiCMOS Technology. Xu, Z., +, TMTT Apr. 2015 1219-1227 Readout electronics Wearable RF Sensor Array Implementing Coupling-Matrix Readout Extraction Technique. Chen, W.-T. S., +, TMTT Dec. 2015 4157-4168 Receivers Digital Mitigation of Transmitter-Induced Receiver Desensitization in Carrier Aggregation FDD Transceivers. Kiayani, A., +, TMTT Nov. 2015 36083623 Receiving antennas A Compact Dual-Channel Transceiver for Long-Range Passive Embedded Monitoring. Nassar, I. T., +, TMTT Jan. 2015 287-294 Real-Time Adaptive Transmitter Leakage Cancelling in 5.8-GHz Full-Duplex Transceivers. Maddio, S., +, TMTT Feb. 2015 509-519 Reconfigurable architectures A 1.4–2.3-GHz Tunable Diplexer Based on Reconfigurable Matching Networks. Ko, C. H., +, TMTT May 2015 1595-1602 Rectangular waveguides Anisotropic Microwave Conductivity Dispersion of Horizontally Aligned Multi-Walled Carbon- Nanotube Thin Film on Flexible Substrate. Li, S., +, TMTT Nov. 2015 3588-3594 Anomalous Dispersion Characteristics of Periodic Substrate Integrated Waveguides From Microwave to Terahertz. Li, X., +, TMTT Jul. 2015 2142-2153 Coaxial End-Launched and Microstrip to Partial -Plane Waveguide Transitions. Kloke, K. H., +, TMTT Oct. 2015 3103-3108 + Check author entry for coauthors

Compact Orthomode Transducer Polarizer Based on a Tilted-Waveguide T-Junction. Esteban, J., +, TMTT Oct. 2015 3208-3217 Design and Validation of Microstrip Gap Waveguides and Their Transitions to Rectangular Waveguide, for Millimeter-Wave Applications. Brazalez, A. A., +, TMTT Dec. 2015 4035-4050 Design of a Traveling-Wave Slot Array Power Divider Using the Method of Moments and a Genetic Algorithm. Rengarajan, S. R., +, TMTT Dec. 2015 3981-3987 Efficient Design of Waveguide Manifold Multiplexers Based on Low-Order EM Distributed Models. Cogollos, S., +, TMTT Aug. 2015 2540-2549 Mode Filters for Oversized Rectangular Waveguides: A Modal Approach. Ceccuzzi, S., +, TMTT Aug. 2015 2468-2481 Near-Field Microwave Distribution Measurement With a Point Detector Base on Thermoacoustic Effect. Ding, W., +, TMTT Oct. 2015 3272-3276 Propagating Waveguide Filters Using Dielectric Resonators. Tomassoni, C., +, TMTT Dec. 2015 4366-4375 Rectennas A Multi-Band Stacked RF Energy Harvester With RF-to-DC Efficiency Up to 84%. Kuhn, V., +, TMTT May 2015 1768-1778 Rectifiers A 2.45-GHz Energy-Autonomous Wireless Power Relay Node. Del Prete, M., +, TMTT Dec. 2015 4511-4520 A Multi-Band Stacked RF Energy Harvester With RF-to-DC Efficiency Up to 84%. Kuhn, V., +, TMTT May 2015 1768-1778 Breaking the Efficiency Barrier for Ambient Microwave Power Harvesting With Heterojunction Backward Tunnel Diodes. Lorenz, C. H. P., +, TMTT Dec. 2015 4544-4555 GaN Microwave DC–DC Converters. Ramos, I., +, TMTT Dec. 2015 44734482 Low-Input Power-Level CMOS RF Energy-Harvesting Front End. Abouzied, M. A., +, TMTT Nov. 2015 3794-3805 Rectifying circuits Nonlinear Modeling and Harmonic Recycling of Millimeter-Wave Rectifier Circuit. Ladan, S., +, TMTT Mar. 2015 937-944 Reflectometers Accuracy and Bandwidth Optimization of the Over-Determined Offset-Short Reflectometer Calibration. Lewandowski, A., +, TMTT Mar. 2015 1076-1089 Regression analysis Development and Computer-Aided Design of Metal Gratings for Microwave Mesh Polarizers. Alaverdyan, S. A., +, TMTT Aug. 2015 2509-2514 Relay networks (telecommunication) A 2.45-GHz Energy-Autonomous Wireless Power Relay Node. Del Prete, M., +, TMTT Dec. 2015 4511-4520 Reliability Passive Microwave Substrate Integrated Cavity Resonator for Humidity Sensing. El Matbouly, H., +, TMTT Dec. 2015 4150-4156 Qualitative Microwave Imaging With Scattering Parameters Measurements. Akinci, M. N., +, TMTT Sep. 2015 2730-2740 Resistors A New Broadband Common-Mode Noise Absorption Circuit for High-Speed Differential Digital Systems. Hsiao, C.-Y., +, TMTT Jun. 2015 1894-1901 Broadband Microwave Attenuator Based on Few Layer Graphene Flakes. Pierantoni, L., +, TMTT Aug. 2015 2491-2497 Resonant frequency Ultra-Miniature SIW Cavity Resonators and Filters. Pourghorban Saghati, A., +, TMTT Dec. 2015 4329-4340 Resonator filters A 1.4–2.3-GHz Tunable Diplexer Based on Reconfigurable Matching Networks. Ko, C. H., +, TMTT May 2015 1595-1602 A 2.45 GHz Phased Array Antenna Unit Cell Fabricated Using 3-D MultiLayer Direct Digital Manufacturing. Ketterl, T. P., +, TMTT Dec. 2015 4382-4394 A High-Power Low-Loss Continuously Tunable Bandpass Filter With Transversely Biased Ferrite-Loaded Coaxial Resonators. Acar, O., +, TMTT Oct. 2015 3425-3432 A Miniaturized Microfluidically Reconfigurable Coplanar Waveguide Bandpass Filter With Maximum Power Handling of 10 Watts. Pourghorban Saghati, A., +, TMTT Aug. 2015 2515-2525 A Novel Compact -Plane Waveguide Filter With Multiple Transmission Zeroes. Jin, J. Y., +, TMTT Oct. 2015 3374-3380

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 63, NO. 12, DECEMBER 2015

Advanced Butler Matrices With Integrated Bandpass Filter Functions. Tornielli di Crestvolant, V., +, TMTT Oct. 2015 3433-3444 Balanced Dual-Band Bandpass Filter With Multiple Transmission Zeros Using Doubly Short-Ended Resonator Coupled Line. Yang, L., +, TMTT Jul. 2015 2225-2232 Compact Multi-Band Bandpass Filters With Mixed Electric and Magnetic Coupling Using Multiple-Mode Resonator. Xu, J., +, TMTT Dec. 2015 3909-3919 Compact Tunable Filtering Power Divider With Constant Absolute Bandwidth. Gao, L., +, TMTT Oct. 2015 3505-3513 Design and Characterization of a 170-GHz Resonant Diplexer for HighPower ECRH Systems. Wu, Z., +, TMTT Oct. 2015 3537-3546 Design of Compact Wideband Manifold-Coupled Multiplexers. Carceller, C., +, TMTT Oct. 2015 3398-3407 Direct Coupled Resonator Filters Realized by Gap Waveguide Technology. Ahmadi, B., +, TMTT Oct. 2015 3445-3452 Dynamic Bandpass Filter Shape and Interference Cancellation Control Utilizing Bandpass–Bandstop Filter Cascade. Lee, T.-C., +, TMTT Aug. 2015 2526-2539 Efficient Design of Waveguide Manifold Multiplexers Based on Low-Order EM Distributed Models. Cogollos, S., +, TMTT Aug. 2015 2540-2549 Enhanced Topology of -Plane Resonators for High-Power Satellite Applications. Peverini, O. A., +, TMTT Oct. 2015 3361-3373 Guest Editorial. Boria, V. E., +, TMTT Oct. 2015 3321-3323 K-Band Frequency Tunable Substrate-Integrated- Waveguide Resonator Filter With Enhanced Stopband Attenuation. Lee, B., +, TMTT Nov. 2015 3632-3640 Ka-Band Dual-Mode Super Filters and Multiplexers. Yassini, B., +, TMTT Oct. 2015 3391-3397 Microwave Bandpass Filters Using Re-Entrant Resonators. Musonda, E., +, TMTT Mar. 2015 954-964 Modeling of Inline Transitions Between Different Waveguides as Impedance Inverters for the Use in Novel Filter Designs. Strauss, G., +, TMTT Nov. 2015 3663-3670 Narrowband Coupled-Line Bandstop Filter With Absorptive Stopband. Shao, J.-Y., +, TMTT Oct. 2015 3469-3478 Reflection-Mode Bandstop Filters With Minimum Through-Line Length. Naglich, E. J., +, TMTT Oct. 2015 3479-3486 Resonator Voltage Prediction in Microwave Bandpass Filters. Vanin, F. M., +, TMTT Feb. 2015 397-402 Simple and Compact Balanced Bandpass Filters Based on Magnetically Coupled Resonators. Fernandez-Prieto, A., +, TMTT Jun. 2015 1843-1853 Superconducting Ultra-Wideband (UWB) Bandpass Filter Design Based on Quintuple/Quadruple/ Triple-Mode Resonator. Lu, X., +, TMTT Apr. 2015 1281-1293 Suppression of Harmonics in Microstrip Filters Using a Combination of Techniques. Huang, F., TMTT Oct. 2015 3453-3461 Synthesis of Cross-Coupled Prototype Filters Including Resonant and NonResonant Nodes. Tamiazzo, S., +, TMTT Oct. 2015 3408-3415 Synthesis of Inline Mixed Coupled Quasi-Elliptic Bandpass Filters Based on Resonators. Zhang, S., +, TMTT Oct. 2015 3487-3493 Temporal Coupled-Mode Theory and the Combined Effect of Dual Orthogonal Resonant Modes in Microstrip Bandpass Filters. Yu, F., +, TMTT Feb. 2015 403-413 Tunable 500–1200-MHz Dual-Band and Wide Bandwidth Notch Filters Using RF Transformers. Ko, C.-H., +, TMTT Jun. 2015 1854-1862 Wideband Balanced Filters With High Selectivity and Common-Mode Suppression. Chu, Q.-X., +, TMTT Oct. 2015 3462-3468 Wideband Differential Bandpass Filters on Multimode Slotline Resonator With Intrinsic Common-Mode Rejection. Guo, X., +, TMTT May 2015 1587-1594 Resonators A 37.5-mW 8-dBm-EIRP 15.5 -HPBW 338-GHz Terahertz Transmitter Using SoP Heterogeneous System Integration. Li, C.-H., +, TMTT Feb. 2015 470-480 Compact Printable Chipless RFID Systems. Islam, M. A., +, TMTT Nov. 2015 3785-3793 Design and Analysis of Shielded Vertically Stacked Ring Resonator as Complex Permittivity Sensor for Petroleum Oils. Kulkarni, S., +, TMTT Aug. 2015 2411-2417 Design and In Vitro Interference Test of Microwave Noninvasive Blood Glucose Monitoring Sensor. Choi, H., +, TMTT Oct. 2015 3016-3025 Energy Coupled Mode Theory for Electromagnetic Resonators. Elnaggar, S. Y., +, TMTT Jul. 2015 2115-2123 + Check author entry for coauthors

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On the Design of Gyroelectric Resonators and Circulators Using a Magnetically Biased 2-D Electron Gas (2-DEG). Jawad, G. N., +, TMTT May 2015 1512-1517 On the Radiation Properties of Split-Ring Resonators (SRRs) at the Second Resonance. Zuffanelli, S., +, TMTT Jul. 2015 2133-2141 Real-World Implementation Challenges of a Novel Dual-Polarized Compact Printable Chipless RFID Tag. Islam, M. A., +, TMTT Dec. 2015 4581-4591 Resonant Inductive Link for Remote Powering of Pacemakers. Monti, G., +, TMTT Nov. 2015 3814-3822 Tunable 4-Pole Dual-Notch Filters for Cognitive Radios and Carrier Aggregation Systems. Cho, Y.-H., +, TMTT Apr. 2015 1308-1314 Wideband Microstrip-to-Microstrip Vertical Transitions Via Multiresonant Modes in a Slotline Resonator. Guo, X., +, TMTT Jun. 2015 1902-1909 Response surface methodology Compact Behavioral Models of Nonlinear Active Devices Using Response Surface Methodology. Barmuta, P., +, TMTT Jan. 2015 56-64 Hybrid Nonlinear Modeling Using Adaptive Sampling. Barmuta, P., +, TMTT Dec. 2015 4501-4510 Rapid Yield Estimation and Optimization of Microwave Structures Exploiting Feature-Based Statistical Analysis. Koziel, S., +, TMTT Jan. 2015 107-114 Ridge waveguides Modeling of Inline Transitions Between Different Waveguides as Impedance Inverters for the Use in Novel Filter Designs. Strauss, G., +, TMTT Nov. 2015 3663-3670 Two-Material Ridge Substrate Integrated Waveguide for Ultra-Wideband Applications. Moscato, S., +, TMTT Oct. 2015 3175-3182 RLC circuits Hybrid Acoustic-Wave-Lumped-Element Resonators (AWLRs) for HighBandpass Filters With Quasi-Elliptic Frequency Response. Psychogiou, D., +, TMTT Jul. 2015 2233-2244 Road pricing (tolls) Real-Time Adaptive Transmitter Leakage Cancelling in 5.8-GHz Full-Duplex Transceivers. Maddio, S., +, TMTT Feb. 2015 509-519 Road vehicle radar 76–81-GHz CMOS Transmitter With a Phase-Locked-Loop-Based Multichirp Modulator for Automotive Radar. Park, J., +, TMTT Apr. 2015 13991408 A K-Band Reconfigurable Pulse-Compression Automotive Radar Transmitter in 90-nm CMOS. Tan, K.-W., +, TMTT Apr. 2015 1380-1387 Rough surfaces Extraction of Dielectric and Rough Conductor Loss of Printed Circuit Board Using Differential Method at Microwave Frequencies. Zhu, X.-C., +, TMTT Feb. 2015 494-503 RSSI A Distributed Positioning System Based on a Predictive Fingerprinting Method Enabling Sub-Metric Precision in IEEE 802.11 Networks. Maddio, S., +, TMTT Dec. 2015 4567-4580

S

S-matrix theory A New Compact High-Power Microwave Phase Shifter. Chang, C., +, TMTT Jun. 2015 1875-1882 Anomalous Dispersion Characteristics of Periodic Substrate Integrated Waveguides From Microwave to Terahertz. Li, X., +, TMTT Jul. 2015 2142-2153 Generalized Stability Criteria for Power Amplifiers Under Mismatch Effects. Suarez, A., +, TMTT Dec. 2015 4415-4428 Modal Loss Analysis of - and -Plane Filtering Structures. Accatino, L., +, TMTT Jan. 2015 40-47 Multiport Scattering Matrix Determination From One-Port Measurements. Lin, Y.-C., +, TMTT Jul. 2015 2343-2352 S-parameters (InP) HEMT Small-Signal Equivalent-Circuit Extraction as a Function of Temperature. Alt, A. R., +, TMTT Sep. 2015 2751-2755 -Parameters: A Novel Framework for Characterization and Behavioral Modeling of Mixed-Signal Systems. Ribeiro, D. C., +, TMTT Oct. 2015 3277-3287 A Balanced-to-Unbalanced Microstrip Power Divider With Filtering Function. Xu, K., +, TMTT Aug. 2015 2561-2569

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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 63, NO. 12, DECEMBER 2015

A Broadband and Equivalent-Circuit Model for Millimeter-Wave On-Chip M:N Six-Port Transformers and Baluns. Gao, Z., +, TMTT Oct. 2015 31093121 An Improved Small-Signal Model for SiGe HBT Under OFF-State, Derived From Distributed Network and Corresponding Model Parameter Extraction. Sun, Y., +, TMTT Oct. 2015 3131-3141 An Improved VBIC Large-Signal Equivalent-Circuit Model for SiGe HBT With an Inductive Breakdown Network by -Parameters. Lee, C.-I., +, TMTT Sep. 2015 2756-2763 Analytical Reflection Coefficient Expressions Utilizing Load-Dependent -Parameters. Gou, Y., +, TMTT Oct. 2015 3142-3152 Anisotropic Microwave Conductivity Dispersion of Horizontally Aligned Multi-Walled Carbon- Nanotube Thin Film on Flexible Substrate. Li, S., +, TMTT Nov. 2015 3588-3594 Broadband Microwave Characterization of Nanostructured Thin Film With Giant Dielectric Response. Chen, T.-C., +, TMTT Nov. 2015 3768-3774 Compact Orthomode Transducer Polarizer Based on a Tilted-Waveguide T-Junction. Esteban, J., +, TMTT Oct. 2015 3208-3217 Consistent DC and RF MOSFET Modeling Using an -Parameter Measurement-Based Parameter Extraction Method in the Linear Region. ZarateRincon, F., +, TMTT Dec. 2015 4255-4262 Dielectric Characterization of Ultra-Thin Low-Loss Build-Up Substrate for System-in-Package (SiP) Modules. Ho, C.-Y., +, TMTT Sep. 2015 29232930 Exact Synthesis of Full- and Half-Symmetric Rat-Race Ring Hybrids With or Without Impedance Transforming Characteristics. Chou, P.-J., +, TMTT Dec. 2015 3971-3980 GaN HEMT Noise Model Based on Electromagnetic Simulations. Nalli, A., +, TMTT Aug. 2015 2498-2508 Modal Loss Analysis of - and -Plane Filtering Structures. Accatino, L., +, TMTT Jan. 2015 40-47 Mode Filters for Oversized Rectangular Waveguides: A Modal Approach. Ceccuzzi, S., +, TMTT Aug. 2015 2468-2481 Modeling of Inline Transitions Between Different Waveguides as Impedance Inverters for the Use in Novel Filter Designs. Strauss, G., +, TMTT Nov. 2015 3663-3670 On the Accurate Measurement and Calibration of S-Parameters for Millimeter Wavelengths and Beyond. Seelmann-Eggebert, M., +, TMTT Jul. 2015 2335-2342 Qualitative Microwave Imaging With Scattering Parameters Measurements. Akinci, M. N., +, TMTT Sep. 2015 2730-2740 Triple- and Quadruple-Mode Wideband Bandpass Filter Using Simple Perturbation in Single Metal Cavity. Wong, S.-W., +, TMTT Oct. 2015 34163424 Safety Computational Feasibility Study of Contrast-Enhanced Thermoacoustic Imaging for Breast Cancer Detection Using Realistic Numerical Breast Phantoms. Wang, X., +, TMTT May 2015 1489-1501 Sample and hold circuits Design and Analysis of CMOS High-Speed High Dynamic-Range Trackand-Hold Amplifiers. Liu, Y.-C., +, TMTT Sep. 2015 2841-2853 Sampling methods Compact Behavioral Models of Nonlinear Active Devices Using Response Surface Methodology. Barmuta, P., +, TMTT Jan. 2015 56-64 Hybrid Nonlinear Modeling Using Adaptive Sampling. Barmuta, P., +, TMTT Dec. 2015 4501-4510 Qualitative Microwave Imaging With Scattering Parameters Measurements. Akinci, M. N., +, TMTT Sep. 2015 2730-2740 Sapphire Microstrip Whispering-Gallery-Mode Resonator. Bunyaev, S. A., +, TMTT Sep. 2015 2776-2781 Whispering-Gallery-Mode Resonator Technique With Microfluidic Channel for Permittivity Measurement of Liquids. Gubin, A. I., +, TMTT Jun. 2015 2003-2009 Satellite communication An Integrable SIW Phase Shifter in a Partially Magnetized Ferrite LTCC Package. Nafe, A., +, TMTT Jul. 2015 2264-2274 Enhanced Topology of -Plane Resonators for High-Power Satellite Applications. Peverini, O. A., +, TMTT Oct. 2015 3361-3373 Schottky diodes A 1.4–2.3-GHz Tunable Diplexer Based on Reconfigurable Matching Networks. Ko, C. H., +, TMTT May 2015 1595-1602

+ Check author entry for coauthors

Breaking the Efficiency Barrier for Ambient Microwave Power Harvesting With Heterojunction Backward Tunnel Diodes. Lorenz, C. H. P., +, TMTT Dec. 2015 4544-4555 Corrections to “Design and Fabrication of Broadband Hybrid GaAs Schottky Diode Frequency Multipliers” [Dec 13 4442-4460]. Hrobak, M., +, TMTT Feb. 2015 553 Search problems Design of High-Directivity Wideband Microstrip Directional Coupler With Fragment-Type Structure. Wang, L., +, TMTT Dec. 2015 3962-3970 Seebeck effect High-Speed Antenna-Coupled Terahertz Thermocouple Detectors and Mixers. Russer, J. A., +, TMTT Dec. 2015 4236-4246 Semiconductor device breakdown An Improved VBIC Large-Signal Equivalent-Circuit Model for SiGe HBT With an Inductive Breakdown Network by -Parameters. Lee, C.-I., +, TMTT Sep. 2015 2756-2763 Investigation of RF Avalanche Inductive Effect on Reduction of Intermodulation Distortion of MOSFETs Using Volterra Series Analysis. Lee, C.-I., +, TMTT Feb. 2015 367-373 Semiconductor device measurement On the Accurate Measurement and Calibration of S-Parameters for Millimeter Wavelengths and Beyond. Seelmann-Eggebert, M., +, TMTT Jul. 2015 2335-2342 Semiconductor device models A 5.9-GHz Fully Integrated GaN Frontend Design With Physics-Based RF Compact Model. Choi, P., +, TMTT Apr. 2015 1163-1173 A Simple Method to Estimate the Output Power and Efficiency Load–Pull Contours of Class-B Power Amplifiers. Pedro, J. C., +, TMTT Apr. 2015 1239-1249 An Improved Small-Signal Model for SiGe HBT Under OFF-State, Derived From Distributed Network and Corresponding Model Parameter Extraction. Sun, Y., +, TMTT Oct. 2015 3131-3141 An Improved VBIC Large-Signal Equivalent-Circuit Model for SiGe HBT With an Inductive Breakdown Network by -Parameters. Lee, C.-I., +, TMTT Sep. 2015 2756-2763 Compact Behavioral Models of Nonlinear Active Devices Using Response Surface Methodology. Barmuta, P., +, TMTT Jan. 2015 56-64 Consistent DC and RF MOSFET Modeling Using an -Parameter Measurement-Based Parameter Extraction Method in the Linear Region. ZarateRincon, F., +, TMTT Dec. 2015 4255-4262 Consistent Modeling and Power Gain Analysis of Microwave SiGe HBTs in CE and CB Configurations. Alvarez-Botero, G., +, TMTT Dec. 2015 38883895 GaN HEMT Noise Model Based on Electromagnetic Simulations. Nalli, A., +, TMTT Aug. 2015 2498-2508 High-Frequency Noise Modeling of MOSFETs for Ultra Low-Voltage RF Applications. Chan, L. H. K., +, TMTT Jan. 2015 141-154 Hybrid Nonlinear Modeling Using Adaptive Sampling. Barmuta, P., +, TMTT Dec. 2015 4501-4510 RF Linearity Performance Potential of Short-Channel Graphene Field-Effect Transistors. Alam, A. U., +, TMTT Dec. 2015 3874-3887 RF Small-Signal and Noise Modeling Including Parameter Extraction of Nanoscale MOSFET From Weak to Strong Inversion. Chalkiadaki, M.-A., +, TMTT Jul. 2015 2173-2184 Semiconductor device noise GaN HEMT Noise Model Based on Electromagnetic Simulations. Nalli, A., +, TMTT Aug. 2015 2498-2508 High-Frequency Noise Modeling of MOSFETs for Ultra Low-Voltage RF Applications. Chan, L. H. K., +, TMTT Jan. 2015 141-154 Semiconductor device testing Efficient Statistical Simulation of Microwave Devices Via Stochastic Testing-Based Circuit Equivalents of Nonlinear Components. Manfredi, P., +, TMTT May 2015 1502-1511 Semiconductor materials A Reconfigurable K-/Ka-Band Power Amplifier With High PAE in 0.18- m SiGe BiCMOS for Multi-Band Applications. Ma, K., +, TMTT Dec. 2015 4395-4405 Semiconductor plasma Microwave Properties of an Inhomogeneous Optically Illuminated Plasma in a Microstrip Gap. Gamlath, C. D., +, TMTT Feb. 2015 374-383 Sensitivity analysis Millimeter-Wave Modulated-Signal and Error-Vector-Magnitude Measurement With Uncertainty. Remley, K. A., +, TMTT May 2015 1710-1720

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 63, NO. 12, DECEMBER 2015

Sensor arrays Wearable RF Sensor Array Implementing Coupling-Matrix Readout Extraction Technique. Chen, W.-T. S., +, TMTT Dec. 2015 4157-4168 Sensors 3D-Printed Origami Packaging With Inkjet-Printed Antennas for RF Harvesting Sensors. Kimionis, J., +, TMTT Dec. 2015 4521-4532 Servomotors A New Compact High-Power Microwave Phase Shifter. Chang, C., +, TMTT Jun. 2015 1875-1882 Shapes (structures) Analysis of Axisymmetric Waveguide Components by a Multi-Domain Spectral Method. Tibaldi, A., +, TMTT Jan. 2015 115-124 Sheet materials Free-Positioning Wireless Charging System for Small Electronic Devices Using a Bowl-Shaped Transmitting Coil. Kim, J., +, TMTT Mar. 2015 791-800 Shift registers A W-Band 4-GHz Bandwidth Phase-Modulated Pulse Compression Radar Transmitter in 65-nm CMOS. Oh, J., +, TMTT Aug. 2015 2609-2618 Signal detection A CMOS Spectrum Sensor Based on Quasi-Cyclostationary Feature Detection for Cognitive Radios. Sepidband, P., +, TMTT Dec. 2015 4098-4109 Concurrent Detection of Vibration and Distance Using Unmodulated CW Doppler Vibration Radar With An Adaptive Beam-Steering Antenna. Nieh, C.-M., +, TMTT Jun. 2015 2069-2078 Signal Detection and Noise Modeling of a 1-D Pulse-Based Ultra-Wideband Ranging System and Its Accuracy Assessment. Elkhouly, E., +, TMTT May 2015 1746-1757 Signal processing Simple Broadband Quasi-Optical Spatial Multiplexer in Substrate Integrated Technology. Gomez-Tornero, J. L., +, TMTT May 2015 1609-1620 Single-Model Single-Feedback Digital Predistortion for Concurrent MultiBand Wireless Transmitters. Yu, C., +, TMTT Jul. 2015 2211-2224 Spectra-Folding Feedback Architecture for Concurrent Dual-Band Power Amplifier Predistortion. Ma, Y., +, TMTT Oct. 2015 3164-3174 Transmission of Signals With Complex Constellations Using Millimeter-Wave Spatially Power-Combined CMOS Power Amplifiers and Digital Predistortion. Dabag, H.-T., +, TMTT Jul. 2015 2364-2374 Silicon 0.8/2.2-GHz Programmable Active Bandpass Filters in InP/Si BiCMOS Technology. Xu, Z., +, TMTT Apr. 2015 1219-1227 160-GHz to 1-THz Multi-Color Active Imaging With a Lens-Coupled SiGe HBT Chip-Set. Statnikov, K., +, TMTT Feb. 2015 520-532 -Band Spatially Combined Power Amplifier Arrays in 45-nm CMOS SOI. Hanafi, B., +, TMTT Jun. 2015 1937-1950 A 1.3–2.4-GHz 3.1-mW VCO Using Electro-Thermo- Mechanically Tunable Self-Assembled MEMS Inductor on HR Substrate. Bhattacharya, A., +, TMTT Feb. 2015 459-469 A Single-Chip Electron Paramagnetic Resonance Transceiver in 0.13- m SiGe BiCMOS. Yang, X., +, TMTT Nov. 2015 3727-3735 A Stacked-FET Linear SOI CMOS Cellular Antenna Switch With an Extremely Low-Power Biasing Strategy. Im, D., +, TMTT Jun. 2015 19641977 An E-Band Power Amplifier With Broadband Parallel-Series Power Combiner in 40-nm CMOS. Zhao, D., +, TMTT Feb. 2015 683-690 Envelope Tracking of an RF High Power Amplifier With an 8-Level Digitally Controlled GaN-on-Si Supply Modulator. Florian, C., +, TMTT Aug. 2015 2589-2602 Generic Electrostatic Discharges Protection Solutions for RF and Millimeter-Wave Applications. Lim, T., +, TMTT Nov. 2015 3747-3759 Microwave Properties of an Inhomogeneous Optically Illuminated Plasma in a Microstrip Gap. Gamlath, C. D., +, TMTT Feb. 2015 374-383 Millimeter-Wave Near-Field Probe Designed for High-Resolution Skin Cancer Diagnosis. Topfer, F., +, TMTT Jun. 2015 2050-2059 Tunable 500–1200-MHz Dual-Band and Wide Bandwidth Notch Filters Using RF Transformers. Ko, C.-H., +, TMTT Jun. 2015 1854-1862 Silicon compounds A 5.9-GHz Fully Integrated GaN Frontend Design With Physics-Based RF Compact Model. Choi, P., +, TMTT Apr. 2015 1163-1173 Optimized Design of a Dual-Band Power Amplifier With SiC VaractorBased Dynamic Load Modulation. Sanchez-Perez, C., +, TMTT Aug. 2015 2579-2588

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4665

Silicon-on-insulator -Band Spatially Combined Power Amplifier Arrays in 45-nm CMOS SOI. Hanafi, B., +, TMTT Jun. 2015 1937-1950 A 0.2–3.6-GHz 10-dBm B1dB 29-dBm IIP3 Tunable Filter for Transmit Leakage Suppression in SAW-Less 3G/4G FDD Receivers. Luo, C., +, TMTT Oct. 2015 3514-3524 A 1.1-Gbit/s 10-GHz Outphasing Modulator With 23-dBm Output Power and 60-dB Dynamic Range in 45-nm CMOS SOI. Mehrjoo, M. S., +, TMTT Jul. 2015 2289-2300 A mm-Wave Segmented Power Mixer. Dasgupta, K., +, TMTT Apr. 2015 1118-1129 A Novel Load Mismatch Detection and Correction Technique for 3G/4G Load Insensitive Power Amplifier Application. Ji, D., +, TMTT May 2015 1530-1543 A Pulsed Dynamic Load Modulation Technique for High-Efficiency Linear Transmitters. Jeon, M.-S., +, TMTT Sep. 2015 2854-2866 A Stacked-FET Linear SOI CMOS Cellular Antenna Switch With an Extremely Low-Power Biasing Strategy. Im, D., +, TMTT Jun. 2015 19641977 Highly Linear Fully Integrated Wideband RF PA for LTE-Advanced in 180-nm SOI. Francois, B., +, TMTT Feb. 2015 649-658 Large-Scale Power Combining and Mixed-Signal Linearizing Architectures for Watt-Class mmWave CMOS Power Amplifiers. Bhat, R., +, TMTT Feb. 2015 703-718 RF-Designed High-Power Lamb-Wave Aluminum–Nitride Resonators. Campanella, H., +, TMTT Feb. 2015 331-339 Silver Broadband Microwave Characterization of Nanostructured Thin Film With Giant Dielectric Response. Chen, T.-C., +, TMTT Nov. 2015 3768-3774 Silver alloys Triple- and Quadruple-Mode Wideband Bandpass Filter Using Simple Perturbation in Single Metal Cavity. Wong, S.-W., +, TMTT Oct. 2015 34163424 Single-wall carbon nanotubes Computational Feasibility Study of Contrast-Enhanced Thermoacoustic Imaging for Breast Cancer Detection Using Realistic Numerical Breast Phantoms. Wang, X., +, TMTT May 2015 1489-1501 Skin Millimeter-Wave Near-Field Probe Designed for High-Resolution Skin Cancer Diagnosis. Topfer, F., +, TMTT Jun. 2015 2050-2059 Slot antennas An Integrated Slot-Ring Traveling-Wave Radiator. Bowers, S. M., +, TMTT Apr. 2015 1154-1162 Compact Printable Chipless RFID Systems. Islam, M. A., +, TMTT Nov. 2015 3785-3793 Slot lines Mode Substrate Integrated Wideband Excitation Technology of Waveguide (SIW) and Its Applications. Wu, P., +, TMTT Jun. 2015 1863-1874 Wideband Microstrip-to-Microstrip Vertical Transitions Via Multiresonant Modes in a Slotline Resonator. Guo, X., +, TMTT Jun. 2015 1902-1909 Slow wave structures Accurate Parametric Electrical Model for Slow-Wave CPW and Application to Circuits Design. Bautista, A., +, TMTT Dec. 2015 4225-4235 An Inverse-Based Multifrontal Block Incomplete LU Preconditioner for the 3-D Finite-Element Eigenvalue Analysis of Lossy Slow-Wave Structures. Wang, H., +, TMTT Jul. 2015 2094-2106 Design and Modeling of Spoof Surface Plasmon Modes-Based Microwave Slow-Wave Transmission Line. Kianinejad, A., +, TMTT Jun. 2015 18171825 Dispersion Equations of a Rectangular Tape Helix Slow-Wave Structure. Wei, W., +, TMTT May 2015 1445-1456 Software radio -Parameters: A Novel Framework for Characterization and Behavioral Modeling of Mixed-Signal Systems. Ribeiro, D. C., +, TMTT Oct. 2015 3277-3287 Broadband CMOS Stacked RF Power Amplifier Using Reconfigurable Interstage Network for Wideband Envelope Tracking. Park, S., +, TMTT Apr. 2015 1174-1185 Multi-Band Software-Defined Coherent Radar Based on a Single Photonic Transceiver. Scotti, F., +, TMTT Feb. 2015 546-552

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Space division multiple access A Distributed Positioning System Based on a Predictive Fingerprinting Method Enabling Sub-Metric Precision in IEEE 802.11 Networks. Maddio, S., +, TMTT Dec. 2015 4567-4580 Space division multiplexing A Distributed Positioning System Based on a Predictive Fingerprinting Method Enabling Sub-Metric Precision in IEEE 802.11 Networks. Maddio, S., +, TMTT Dec. 2015 4567-4580 High-Speed Signal Transmission at W-Band Over Dielectric-Coated Metallic Hollow Fiber. Yu, J., +, TMTT Jun. 2015 1836-1842 Sparse matrices A Linear Complexity Direct Volume Integral Equation Solver for Full-Wave 3-D Circuit Extraction in Inhomogeneous Materials. Omar, S., +, TMTT Mar. 2015 897-912 Spatiotemporal phenomena Electrical Analysis of Cell Membrane Poration by an Intense Nanosecond Pulsed Electric Field Using an Atomistic-to-Continuum Method. Kohler, S., +, TMTT Jun. 2015 2032-2040 Special issues and sections Guest Editorial. Boria, V. E., +, TMTT Oct. 2015 3321-3323 Guest Editorial. Rodenbeck, C. T., TMTT Dec. 2015 4199-4200 Guest Editorial. Alomainy, A., +, TMTT Oct. 2015 3005-3006 Guest Editorial. Gharpurey, R., TMTT Apr. 2015 1109 Guest Editorial. Draxler, P., TMTT Feb. 2015 557-558 Guest Editorial. Ghorbani, K., +, TMTT Aug. 2015 2397-2398 Guest Editorial. KIM, J., +, TMTT Mar. 2015 778-779 Guest Editorial [Mini-Special Issue on 2014 IEEE International Conference on Numerical Electromagnetic Modeling and Optimization for RF, Microwave, and Terahertz Applications (NEMO2014. Bozzi, M., +, TMTT Jan. 2015 1-2 Spectral analysis A W-Band 4-GHz Bandwidth Phase-Modulated Pulse Compression Radar Transmitter in 65-nm CMOS. Oh, J., +, TMTT Aug. 2015 2609-2618 Analysis of Axisymmetric Waveguide Components by a Multi-Domain Spectral Method. Tibaldi, A., +, TMTT Jan. 2015 115-124 Investigating the Broadband Microwave Absorption of Nanodiamond Impurities. Cuenca, J. A., +, TMTT Dec. 2015 4110-4118 Skew Incidence Plane-Wave Scattering From 2-D Dielectric Periodic Structures: Analysis by the Mortar-Element Method. Tibaldi, A., +, TMTT Jan. 2015 11-19 The Mixed Spectral-Element Method for Anisotropic, Lossy, and Open Waveguides. Liu, N., +, TMTT Oct. 2015 3094-3102 Spectral-domain analysis On the Development and Evaluation of Spatial-Domain Green’s Functions for Multilayered Structures With Conductive Sheets. Koufogiannis, I. D., +, TMTT Jan. 2015 20-29 Splines (mathematics) -toCircular Mode Converter Design. A Universal Solution to Yu, X. H., +, TMTT Dec. 2015 3845-3850 Efficient Least-Squares 2-D-Cubic Spline for Concurrent Dual-Band Systems. Naraharisetti, N., +, TMTT Jul. 2015 2199-2210 Mode Converter for Gyrotron by the Method for Synthesis of NURBS Technique. Yu, X., +, TMTT Feb. 2015 326-330 Spread spectrum communication Low-Loss Ultrawideband Programmable RF Photonic Phase Filter for Spread Spectrum Pulse Compression. Kim, H.-J., +, TMTT Dec. 2015 4178-4187 Spread spectrum radar A W-Band 4-GHz Bandwidth Phase-Modulated Pulse Compression Radar Transmitter in 65-nm CMOS. Oh, J., +, TMTT Aug. 2015 2609-2618 Stability Global Stability Analysis of Coupled-Oscillator Systems. Suarez, A., +, TMTT Jan. 2015 165-180 Statistical analysis Efficient Statistical Simulation of Microwave Devices Via Stochastic Testing-Based Circuit Equivalents of Nonlinear Components. Manfredi, P., +, TMTT May 2015 1502-1511 Rapid Yield Estimation and Optimization of Microwave Structures Exploiting Feature-Based Statistical Analysis. Koziel, S., +, TMTT Jan. 2015 107-114 Reliable Microwave Modeling by Means of Variable-Fidelity Response Features. Koziel, S., +, TMTT Dec. 2015 4247-4254

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Statistical distributions A Distributed Positioning System Based on a Predictive Fingerprinting Method Enabling Sub-Metric Precision in IEEE 802.11 Networks. Maddio, S., +, TMTT Dec. 2015 4567-4580 Stochastic processes Efficient Statistical Simulation of Microwave Devices Via Stochastic Testing-Based Circuit Equivalents of Nonlinear Components. Manfredi, P., +, TMTT May 2015 1502-1511 Strip line filters Reflection-Mode Bandstop Filters With Minimum Through-Line Length. Naglich, E. J., +, TMTT Oct. 2015 3479-3486 Tunable 1.25–2.1-GHz 4-Pole Bandpass Filter With Intrinsic Transmission Zero Tuning. Yang, T., +, TMTT May 2015 1569-1578 Strip lines An Analysis of Multistrip Line Configuration on Elliptical Cylinder. Kusiek, A., +, TMTT Jun. 2015 1800-1808 Wideband Balanced Network with High Isolation Using Double-Sided Parallel-Strip Line. Feng, W., +, TMTT Dec. 2015 4013-4018 Strontium Printable Planar Dielectric Waveguides Based on High-Permittivity Films. Rashidian, A., +, TMTT Sep. 2015 2720-2729 Strontium compounds Present and Future Trends in Filters and Multiplexers. Snyder, R. V., +, TMTT Oct. 2015 3324-3360 Self-Biased Y-Junction Circulators Using Lanthanum- and Cobalt-Substituted Strontium Hexaferrites. Laur, V., +, TMTT Dec. 2015 4376-4381 Submillimeter wave antennas 160-GHz to 1-THz Multi-Color Active Imaging With a Lens-Coupled SiGe HBT Chip-Set. Statnikov, K., +, TMTT Feb. 2015 520-532 A 37.5-mW 8-dBm-EIRP 15.5 -HPBW 338-GHz Terahertz Transmitter Using SoP Heterogeneous System Integration. Li, C.-H., +, TMTT Feb. 2015 470-480 High-Speed Antenna-Coupled Terahertz Thermocouple Detectors and Mixers. Russer, J. A., +, TMTT Dec. 2015 4236-4246 Submillimeter wave circuits -Mode An Isolated Radial Power Divider via Circular Waveguide Transducer. Chu, Q.-X., +, TMTT Dec. 2015 3988-3996 Submillimeter wave detectors High-Speed Antenna-Coupled Terahertz Thermocouple Detectors and Mixers. Russer, J. A., +, TMTT Dec. 2015 4236-4246 Submillimeter wave generation 160-GHz to 1-THz Multi-Color Active Imaging With a Lens-Coupled SiGe HBT Chip-Set. Statnikov, K., +, TMTT Feb. 2015 520-532 Submillimeter wave imaging 160-GHz to 1-THz Multi-Color Active Imaging With a Lens-Coupled SiGe HBT Chip-Set. Statnikov, K., +, TMTT Feb. 2015 520-532 Micromachined Room-Temperature Air-Suspended Ni/Cr Nanobolometer. Yang, H.-H., +, TMTT Nov. 2015 3760-3767 Submillimeter wave integrated circuits 160-GHz to 1-THz Multi-Color Active Imaging With a Lens-Coupled SiGe HBT Chip-Set. Statnikov, K., +, TMTT Feb. 2015 520-532 Submillimeter wave measurement Micromachined Room-Temperature Air-Suspended Ni/Cr Nanobolometer. Yang, H.-H., +, TMTT Nov. 2015 3760-3767 Submillimeter wave mixers 160-GHz to 1-THz Multi-Color Active Imaging With a Lens-Coupled SiGe HBT Chip-Set. Statnikov, K., +, TMTT Feb. 2015 520-532 High-Speed Antenna-Coupled Terahertz Thermocouple Detectors and Mixers. Russer, J. A., +, TMTT Dec. 2015 4236-4246 Submillimeter wave oscillators A 37.5-mW 8-dBm-EIRP 15.5 -HPBW 338-GHz Terahertz Transmitter Using SoP Heterogeneous System Integration. Li, C.-H., +, TMTT Feb. 2015 470-480 Submillimeter wave receivers 160-GHz to 1-THz Multi-Color Active Imaging With a Lens-Coupled SiGe HBT Chip-Set. Statnikov, K., +, TMTT Feb. 2015 520-532 Submillimeter wave transistors 160-GHz to 1-THz Multi-Color Active Imaging With a Lens-Coupled SiGe HBT Chip-Set. Statnikov, K., +, TMTT Feb. 2015 520-532 Submillimeter waves Performance Estimation for Broadband Multi-Gigabit Millimeter- and SubMillimeter-Wave Wireless Communication Links. Antes, J., +, TMTT Oct. 2015 3288-3299

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 63, NO. 12, DECEMBER 2015

Substrate integrated waveguides Air-Filled Substrate Integrated Waveguide for Low-Loss and High PowerHandling Millimeter-Wave Substrate Integrated Circuits. Parment, F., +, TMTT Apr. 2015 1228-1238 An Integrable SIW Phase Shifter in a Partially Magnetized Ferrite LTCC Package. Nafe, A., +, TMTT Jul. 2015 2264-2274 Anomalous Dispersion Characteristics of Periodic Substrate Integrated Waveguides From Microwave to Terahertz. Li, X., +, TMTT Jul. 2015 2142-2153 Design and Multiphysics Analysis of Direct and Cross-Coupled SIW Combline Filters Using Electric and Magnetic Couplings. Sirci, S., +, TMTT Dec. 2015 4341-4354 Design and Validation of Microstrip Gap Waveguides and Their Transitions to Rectangular Waveguide, for Millimeter-Wave Applications. Brazalez, A. A., +, TMTT Dec. 2015 4035-4050 Design of Multilayered Epsilon-Near-Zero Microwave Planar Sensor for Testing of Dispersive Materials. Jha, A. K., +, TMTT Aug. 2015 2418-2426 Efficient Design of Compact Contiguous-Channel SIW Multiplexers Using the Space-Mapping Method. Hao, Z.-C., +, TMTT Nov. 2015 3651-3662 Extraction of Dielectric and Rough Conductor Loss of Printed Circuit Board Using Differential Method at Microwave Frequencies. Zhu, X.-C., +, TMTT Feb. 2015 494-503 High-Performance Coplanar Waveguide to Empty Substrate Integrated Coaxial Line Transition. Belenguer, A., +, TMTT Dec. 2015 4027-4034 K-Band Frequency Tunable Substrate-Integrated- Waveguide Resonator Filter With Enhanced Stopband Attenuation. Lee, B., +, TMTT Nov. 2015 3632-3640 Mechanical Tuning of Substrate Integrated Waveguide Filters. Mira, F., +, TMTT Dec. 2015 3939-3946 Passive Microwave Substrate Integrated Cavity Resonator for Humidity Sensing. El Matbouly, H., +, TMTT Dec. 2015 4150-4156 Physics-Based Via and Waveguide Models for Efficient SIW Simulations in Multilayer Substrates. Preibisch, J. B., +, TMTT Jun. 2015 1809-1816 Present and Future Trends in Filters and Multiplexers. Snyder, R. V., +, TMTT Oct. 2015 3324-3360 Simple Broadband Quasi-Optical Spatial Multiplexer in Substrate Integrated Technology. Gomez-Tornero, J. L., +, TMTT May 2015 1609-1620 Substrate Integrated Waveguide Directional Couplers for Compact ThreeDimensional Integrated Circuits. Doghri, A., +, TMTT Jan. 2015 209-221 Textile Microwave Components in Substrate Integrated Waveguide Technology. Moro, R., +, TMTT Feb. 2015 422-432 Two-Material Ridge Substrate Integrated Waveguide for Ultra-Wideband Applications. Moscato, S., +, TMTT Oct. 2015 3175-3182 Mode Substrate Integrated Wideband Excitation Technology of Waveguide (SIW) and Its Applications. Wu, P., +, TMTT Jun. 2015 1863-1874 Substrates 60-GHz Substrate Materials Characterization Using the Covered Transmission-Line Method. Papio Toda, A., +, TMTT Mar. 2015 1063-1075 Microwave Properties of an Inhomogeneous Optically Illuminated Plasma in a Microstrip Gap. Gamlath, C. D., +, TMTT Feb. 2015 374-383 Ultra-Miniature SIW Cavity Resonators and Filters. Pourghorban Saghati, A., +, TMTT Dec. 2015 4329-4340 Supercapacitors Development of a Communication Scheme for Wireless Power Applications With Moving Receivers. Thoen, B., +, TMTT Mar. 2015 857-863 Superconducting filters Superconducting Ultra-Wideband (UWB) Bandpass Filter Design Based on Quintuple/Quadruple/ Triple-Mode Resonator. Lu, X., +, TMTT Apr. 2015 1281-1293 Superconducting resonators An Empirical Expression to Predict the Resonant Frequencies of Archimedean Spirals. Hooker, J. W., +, TMTT Jul. 2015 2107-2114 Surface acoustic wave filters A Highly Efficient LTE Pulse-Modulated Polar Transmitter Using Wideband Power Recycling. Yang, H.-S., +, TMTT Dec. 2015 4437-4443 A Prototype SAW-Less LTE Transmitter With a High-Linearity Modulator Using BPF-Based I/Q Summing and a Triple-Layer Marchand Balun. Nakamura, T., +, TMTT Dec. 2015 4090-4097 Surface acoustic wave resonator filters Hybrid Acoustic-Wave-Lumped-Element Resonators (AWLRs) for HighBandpass Filters With Quasi-Elliptic Frequency Response. Psychogiou, D., +, TMTT Jul. 2015 2233-2244

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4667

Surface acoustic wave resonators Coupling-Matrix-Based Design of HighBandpass Filters Using Acoustic-Wave Lumped-Element Resonator (AWLR) Modules. Psychogiou, D., +, TMTT Dec. 2015 4319-4328 Surface conductivity Anisotropic Microwave Conductivity Dispersion of Horizontally Aligned Multi-Walled Carbon- Nanotube Thin Film on Flexible Substrate. Li, S., +, TMTT Nov. 2015 3588-3594 Dielectric Constant Estimation of a Carbon Nanotube Layer on the Dielectric Rod Waveguide at Millimeter Wavelengths. Nefedova, I. I., +, TMTT Oct. 2015 3265-3271 On the Development and Evaluation of Spatial-Domain Green’s Functions for Multilayered Structures With Conductive Sheets. Koufogiannis, I. D., +, TMTT Jan. 2015 20-29 Surface mount technology Bandpass Filters Using Coupling-Matrix-Based Design of HighAcoustic-Wave Lumped-Element Resonator (AWLR) Modules. Psychogiou, D., +, TMTT Dec. 2015 4319-4328 Surface plasmons Design and Modeling of Spoof Surface Plasmon Modes-Based Microwave Slow-Wave Transmission Line. Kianinejad, A., +, TMTT Jun. 2015 18171825 Surgery The Development of Forceps-Type Microwave Tissue Coagulator for Surgical Operation. Endo, Y., +, TMTT Jun. 2015 2041-2049 Switched capacitor networks A 1.6–2.3-GHz RF MEMS Reconfigurable Quadrature Coupler and Its Application to a 360 Reflective-Type Phase Shifter. Gurbuz, O. D., +, TMTT Feb. 2015 414-421 Spur Reduction Techniques With a Switched-Capacitor Feedback Differential PLL and a DLL-Based SSCG in UHF RFID Transmitter. Lee, I.-Y., +, TMTT Apr. 2015 1202-1210 Switched filters Design of X-Band GaN Phase Shifters. Ross, T. N., +, TMTT Jan. 2015 244-255 Switches A Stacked-FET Linear SOI CMOS Cellular Antenna Switch With an Extremely Low-Power Biasing Strategy. Im, D., +, TMTT Jun. 2015 19641977 Synchronization A Hardware Efficient Implementation of a Digital Baseband Receiver for High-Capacity Millimeter-Wave Radios. He, Z., +, TMTT May 2015 16831692 A W-Band 4-GHz Bandwidth Phase-Modulated Pulse Compression Radar Transmitter in 65-nm CMOS. Oh, J., +, TMTT Aug. 2015 2609-2618 Efficient Simulation of Solution Curves and Bifurcation Loci in InjectionLocked Oscillators. de Cos, J., +, TMTT Jan. 2015 181-197 Hysteresis and Oscillation in High-Efficiency Power Amplifiers. de Cos, J., +, TMTT Dec. 2015 4284-4296 Improving Power Utilization Factor of Broadband Doherty Amplifier by Using Bandpass Auxiliary Transformer. Fang, X.-H., +, TMTT Sep. 2015 2811-2820 Mutual Synchronization for Power Generation and Beam-Steering in CMOS With On-Chip Sense Antennas Near 200 GHz. Sengupta, K., +, TMTT Sep. 2015 2867-2876 System-in-package Dielectric Characterization of Ultra-Thin Low-Loss Build-Up Substrate for System-in-Package (SiP) Modules. Ho, C.-Y., +, TMTT Sep. 2015 29232930 System-on-chip Digitally Assisted CMOS RF Detectors With Self-Calibration for Variability Compensation. Barabino, N., +, TMTT May 2015 1676-1682 System-on-package A 37.5-mW 8-dBm-EIRP 15.5 -HPBW 338-GHz Terahertz Transmitter Using SoP Heterogeneous System Integration. Li, C.-H., +, TMTT Feb. 2015 470-480 T Telecommunication channels A Compact Dual-Channel Transceiver for Long-Range Passive Embedded Monitoring. Nassar, I. T., +, TMTT Jan. 2015 287-294

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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 63, NO. 12, DECEMBER 2015

Concurrent Multiband Digital Outphasing Transmitter Architecture Using Multidimensional Power Coding. Chung, S., +, TMTT Feb. 2015 598-613 Telecommunication network topology A 37.5-mW 8-dBm-EIRP 15.5 -HPBW 338-GHz Terahertz Transmitter Using SoP Heterogeneous System Integration. Li, C.-H., +, TMTT Feb. 2015 470-480 Telecommunication power management Digitally Equalized Doherty RF Front-End Architecture for Broadband and Multistandard Wireless Transmitters. Darraji, R., +, TMTT Jun. 2015 19781988 Telecommunication power supplies Ambient RF Energy Harvesting From a Two-Way Talk Radio for Flexible Wearable Wireless Sensor Devices Utilizing Inkjet Printing Technologies. Bito, J., +, TMTT Dec. 2015 4533-4543 Telecommunication traffic A Hardware Efficient Implementation of a Digital Baseband Receiver for High-Capacity Millimeter-Wave Radios. He, Z., +, TMTT May 2015 16831692 Telecommunication transmission lines Estimation of Nonhomogeneous and Multi-Section Twisted-Pair Transmission-Line Parameters. Lindqvist, F., +, TMTT Nov. 2015 3568-3578 TLM Nodes: A New Look at an Old Problem. Salinas, A., +, TMTT Aug. 2015 2449-2458 Telemedicine Resonant Inductive Link for Remote Powering of Pacemakers. Monti, G., +, TMTT Nov. 2015 3814-3822 Temperature control High-Efficiency Applicator Based on Printed Circuit Board in MillimeterWave Region. Shiina, T., +, TMTT Oct. 2015 3311-3318 Temperature distribution Electrothermal Effects on Performance of GaAs HBT Power Amplifier During Power Versus Time (PVT) Variation at GSM/DCS Bands. Lin, L., +, TMTT Jun. 2015 1951-1963 MRI-Based Electrical Property Retrieval by Applying the Finite-Element Method (FEM). Huang, S. Y., +, TMTT Aug. 2015 2482-2490 The Development of Forceps-Type Microwave Tissue Coagulator for Surgical Operation. Endo, Y., +, TMTT Jun. 2015 2041-2049 Temperature sensors Micromachined Room-Temperature Air-Suspended Ni/Cr Nanobolometer. Yang, H.-H., +, TMTT Nov. 2015 3760-3767 Tensors Electromagnetic Scattering by a General Rotationally Symmetric Inhomogeneous Anisotropic Sphere. Zouros, G. P., +, TMTT Oct. 2015 3054-3065 Terahertz wave detectors High-Speed Antenna-Coupled Terahertz Thermocouple Detectors and Mixers. Russer, J. A., +, TMTT Dec. 2015 4236-4246 Terahertz wave devices Broadband Circuit Techniques for Multi-Terahertz Gain-BandwidthProduct Low-Power Applications. Gharib, A., +, TMTT Nov. 2015 3701-3712 Terahertz wave generation 160-GHz to 1-THz Multi-Color Active Imaging With a Lens-Coupled SiGe HBT Chip-Set. Statnikov, K., +, TMTT Feb. 2015 520-532 Terahertz wave imaging 160-GHz to 1-THz Multi-Color Active Imaging With a Lens-Coupled SiGe HBT Chip-Set. Statnikov, K., +, TMTT Feb. 2015 520-532 Micromachined Room-Temperature Air-Suspended Ni/Cr Nanobolometer. Yang, H.-H., +, TMTT Nov. 2015 3760-3767 Thermal analysis High Power Latching RF MEMS Switches. Bakri-Kassem, M., +, TMTT Jan. 2015 222-232 Thermal noise A Compact L-Band Orthomode Transducer for Radio Astronomical Receivers at Cryogenic Temperature. Valente, G., +, TMTT Oct. 2015 32183227 Thermal printers Real-World Implementation Challenges of a Novel Dual-Polarized Compact Printable Chipless RFID Tag. Islam, M. A., +, TMTT Dec. 2015 4581-4591 Thermal resistance measurement Micromachined Room-Temperature Air-Suspended Ni/Cr Nanobolometer. Yang, H.-H., +, TMTT Nov. 2015 3760-3767

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Thermoacoustics Computational Feasibility Study of Contrast-Enhanced Thermoacoustic Imaging for Breast Cancer Detection Using Realistic Numerical Breast Phantoms. Wang, X., +, TMTT May 2015 1489-1501 Near-Field Microwave Distribution Measurement With a Point Detector Base on Thermoacoustic Effect. Ding, W., +, TMTT Oct. 2015 3272-3276 Thermocouples High-Speed Antenna-Coupled Terahertz Thermocouple Detectors and Mixers. Russer, J. A., +, TMTT Dec. 2015 4236-4246 Thick film devices A 2.45 GHz Phased Array Antenna Unit Cell Fabricated Using 3-D MultiLayer Direct Digital Manufacturing. Ketterl, T. P., +, TMTT Dec. 2015 4382-4394 Thick films Printable Planar Dielectric Waveguides Based on High-Permittivity Films. Rashidian, A., +, TMTT Sep. 2015 2720-2729 Thickness measurement Determination of Reference-Plane Invariant, Thickness-Independent, and Broadband Constitutive Parameters of Thin Materials. Hasar, U. C., +, TMTT Jul. 2015 2313-2321 Single-Compound Complementary Split-Ring Resonator for Simultaneously Measuring the Permittivity and Thickness of Dual-Layer Dielectric Materials. Lee, C.-S., +, TMTT Jun. 2015 2010-2023 Thin film capacitors Influence of Numerical Method and Geometry Used by Maxwell's Equation Solvers on Simulations of Ferroelectric Thin-Film Capacitors. Furlan, V., +, TMTT Mar. 2015 891-896 Thin film devices An FBAR/CMOS Frequency/Phase Discriminator and Phase Noise Reduction System. Imani, A., +, TMTT May 2015 1658-1665 InP DHBT Amplifier Modules Operating Between 150–300 GHz Using Membrane Technology. Eriksson, K., +, TMTT Feb. 2015 433-440 Three-dimensional integrated circuits Substrate Integrated Waveguide Directional Couplers for Compact ThreeDimensional Integrated Circuits. Doghri, A., +, TMTT Jan. 2015 209-221 Three-dimensional printing 3D-Printed Origami Packaging With Inkjet-Printed Antennas for RF Harvesting Sensors. Kimionis, J., +, TMTT Dec. 2015 4521-4532 Polymer Multichip Module Process Using 3-D Printing Technologies for D-Band Applications. Merkle, T., +, TMTT Feb. 2015 481-493 Time-domain analysis A Nodal Continuous-Discontinuous Galerkin Time-Domain Method for Maxwell's Equations. Angulo, L. D., +, TMTT Oct. 2015 3081-3093 A Sub-GHz Wireless Transmitter Utilizing a Multi-Class-Linearized PA and Time-Domain Wideband-Auto I/Q-LOFT Calibration for IEEE 802.11af WLAN. Un, K.-F., +, TMTT Oct. 2015 3228-3241 Accurate and Stable Matrix-Free Time-Domain Method in 3-D Unstructured Meshes for General Electromagnetic Analysis. Yan, J., +, TMTT Dec. 2015 4201-4214 Authors’ Reply. Mescia, L., +, TMTT Dec. 2015 4191-4193 Comments on “High-Efficiency Class E/F Lumped and Transmission-Line Power Amplifiers”. Cheng, Q.-F., +, TMTT Aug. 2015 2703-2704 Material Characterization of Arbitrarily Shaped Dielectrics Based on Reflected Pulse Characteristics. Chan, K.K.M., +, TMTT May 2015 1700-1709 Millimeter-Wave Modulated-Signal and Error-Vector-Magnitude Measurement With Uncertainty. Remley, K. A., +, TMTT May 2015 1710-1720 Time-Domain Electromagnetic Analysis of Multilayer Structures Using the Surface Equivalent Principle and Mixed-Potential Integral Equations. Maftooli, H., +, TMTT Jan. 2015 99-106 Time-Domain Optoelectronic Vector Network Analysis on Coplanar Waveguides. Bieler, M., +, TMTT Nov. 2015 3775-3784 Time-Domain System for Millimeter-Wave Material Characterization. Vakili, I., +, TMTT Sep. 2015 2915-2922 Time-of-arrival estimation Signal Detection and Noise Modeling of a 1-D Pulse-Based Ultra-Wideband Ranging System and Its Accuracy Assessment. Elkhouly, E., +, TMTT May 2015 1746-1757 Tin alloys Robust Pressure-Actuated Liquid Metal Devices Showing Reconfigurable Electromagnetic Effects at GHz Frequencies. Cumby, B. L., +, TMTT Oct. 2015 3122-3130

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 63, NO. 12, DECEMBER 2015

Titanium Fractal Frequency-Selective Surface Embedded Thin Broadband Microwave Absorber Coatings Using Heterogeneous Composites. Panwar, R., +, TMTT Aug. 2015 2438-2448 Titanium compounds Printable Planar Dielectric Waveguides Based on High-Permittivity Films. Rashidian, A., +, TMTT Sep. 2015 2720-2729 Transceivers -Band Dual-Polarization Phased-Array Transceiver Front-End in SiGe BiCMOS. Natarajan, A., +, TMTT Jun. 2015 1989-2002 A Single-Chip Electron Paramagnetic Resonance Transceiver in 0.13- m SiGe BiCMOS. Yang, X., +, TMTT Nov. 2015 3727-3735 Digital Mitigation of Transmitter-Induced Receiver Desensitization in Carrier Aggregation FDD Transceivers. Kiayani, A., +, TMTT Nov. 2015 36083623 Modeling of Deterministic Output Emissions of Power Amplifiers Into Adjacent Receive Bands. Farsi, S., +, TMTT Apr. 2015 1250-1262 Transducers A Compact L-Band Orthomode Transducer for Radio Astronomical Receivers at Cryogenic Temperature. Valente, G., +, TMTT Oct. 2015 32183227 -Mode An Isolated Radial Power Divider via Circular Waveguide Transducer. Chu, Q.-X., +, TMTT Dec. 2015 3988-3996 Compact Orthomode Transducer Polarizer Based on a Tilted-Waveguide T-Junction. Esteban, J., +, TMTT Oct. 2015 3208-3217 Transfer functions Bandpass Filters Using Coupling-Matrix-Based Design of HighAcoustic-Wave Lumped-Element Resonator (AWLR) Modules. Psychogiou, D., +, TMTT Dec. 2015 4319-4328 Experimental Control and Design of Low-Frequency Bias Networks for Dynamically Biased Amplifiers. Pelaz, J., +, TMTT Jun. 2015 1923-1936 Transformer windings A Broadband and Equivalent-Circuit Model for Millimeter-Wave On-Chip M:N Six-Port Transformers and Baluns. Gao, Z., +, TMTT Oct. 2015 31093121 Transformers A Broadband and Equivalent-Circuit Model for Millimeter-Wave On-Chip M:N Six-Port Transformers and Baluns. Gao, Z., +, TMTT Oct. 2015 31093121 A New Distributed Parameter Broadband Matching Method for Power Amplifier via Real Frequency Technique. Dai, Z., +, TMTT Feb. 2015 449-458 A Wideband and Highly Symmetric Multi-Port Parallel Combining Transformer Technology. Yang, H.-S., +, TMTT Nov. 2015 3671-3680 An 85-W Multi-Octave Push–Pull GaN HEMT Power Amplifier for HighEfficiency Communication Applications at Microwave Frequencies. Jundi, A., +, TMTT Nov. 2015 3691-3700 Improving Power Utilization Factor of Broadband Doherty Amplifier by Using Bandpass Auxiliary Transformer. Fang, X.-H., +, TMTT Sep. 2015 2811-2820 Transformer-Feedback Interstage Bandwidth Enhancement for MMIC Multistage Amplifiers. Nikandish, G., +, TMTT Feb. 2015 441-448 Tunable 500–1200-MHz Dual-Band and Wide Bandwidth Notch Filters Using RF Transformers. Ko, C.-H., +, TMTT Jun. 2015 1854-1862 Wideband Microstrip-to-Microstrip Vertical Transitions Via Multiresonant Modes in a Slotline Resonator. Guo, X., +, TMTT Jun. 2015 1902-1909 Transient analysis Comments on “Fractional Derivative Based FDTD Modeling of Transient Wave Propagation in Havriliak–Negami Media”. Rekanos, I. T., TMTT Dec. 2015 4188-4190 Transients Transient Power Loss Density of Electromagnetic Pulse in Debye Media. Huang, K., +, TMTT Jan. 2015 135-140 Transmission line matrix methods 60-GHz Substrate Materials Characterization Using the Covered Transmission-Line Method. Papio Toda, A., +, TMTT Mar. 2015 1063-1075 Transmission line theory Wideband Microstrip-to-Microstrip Vertical Transitions Via Multiresonant Modes in a Slotline Resonator. Guo, X., +, TMTT Jun. 2015 1902-1909 Transmission lines A G-Band Standing-Wave Push–Push VCO Using a Transmission-Line Resonator. Koo, H., +, TMTT Mar. 2015 1036-1045

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4669

A New Distributed Parameter Broadband Matching Method for Power Amplifier via Real Frequency Technique. Dai, Z., +, TMTT Feb. 2015 449-458 A W-Band Power Amplifier Utilizing a Miniaturized Marchand Balun Combiner. Jia, H., +, TMTT Feb. 2015 719-725 An Improved Small-Signal Model for SiGe HBT Under OFF-State, Derived From Distributed Network and Corresponding Model Parameter Extraction. Sun, Y., +, TMTT Oct. 2015 3131-3141 Broadband Synthetic Transmission-Line N-Path Filter Design. Thomas, C. M., +, TMTT Oct. 2015 3525-3536 Chebyshev Filter Design Using Vias as Quasi-Transmission Lines in Printed Circuit Boards. Hardock, A., +, TMTT Mar. 2015 976-985 Design and Characterization of a 170-GHz Resonant Diplexer for HighPower ECRH Systems. Wu, Z., +, TMTT Oct. 2015 3537-3546 Design and Modeling of Spoof Surface Plasmon Modes-Based Microwave Slow-Wave Transmission Line. Kianinejad, A., +, TMTT Jun. 2015 18171825 Design of Compact Reflection-Type Phase Shifters With High Figure-ofMerit. Burdin, F., +, TMTT Jun. 2015 1883-1893 Efficient Design of Waveguide Manifold Multiplexers Based on LowOrder EM Distributed Models. Cogollos, S., +, TMTT Aug. 2015 2540-2549 InP DHBT Amplifier Modules Operating Between 150–300 GHz Using Membrane Technology. Eriksson, K., +, TMTT Feb. 2015 433-440 Large-Scale Power Combining and Mixed-Signal Linearizing Architectures for Watt-Class mmWave CMOS Power Amplifiers. Bhat, R., +, TMTT Feb. 2015 703-718 Miniaturized Transmission-Line Sensor for Broadband Dielectric Characterization of Biological Liquids and Cell Suspensions. Meyne nee Haase, N., +, TMTT Oct. 2015 3026-3033 Radial Transmission-Line Approach for the Analysis of Ring Loaded Slots in Circular Waveguide. Addamo, G., +, TMTT May 2015 1468-1474 Simple, Fast, and Effective Identification of an Equivalent Circuit of a Waveguide Junction With Ports. Zappelli, L., TMTT Jan. 2015 48-55 Transmitting antennas A Compact Dual-Channel Transceiver for Long-Range Passive Embedded Monitoring. Nassar, I. T., +, TMTT Jan. 2015 287-294 Real-Time Adaptive Transmitter Leakage Cancelling in 5.8-GHz Full-Duplex Transceivers. Maddio, S., +, TMTT Feb. 2015 509-519 Transparency Reconfigurable Diffractive Antenna Based on Switchable Electrically Induced Transparency. Li, H., +, TMTT Mar. 2015 925-936 Traveling wave amplifiers A 2-W W-Band GaN Traveling-Wave Amplifier With 25-GHz Bandwidth. Schellenberg, J. M., TMTT Sep. 2015 2833-2840 Design and Measurement of a Broadband Sidewall Coupler for a W-Band Gyro-TWA. Zhang, L., +, TMTT Oct. 2015 3183-3190 Trees (mathematics) DC and Imaginary Spurious Modes Suppression for Both Unbounded and Lossy Structures. Zekios, C. L., +, TMTT Jul. 2015 2082-2093 Tumors Computational Feasibility Study of Contrast-Enhanced Thermoacoustic Imaging for Breast Cancer Detection Using Realistic Numerical Breast Phantoms. Wang, X., +, TMTT May 2015 1489-1501 Millimeter-Wave Near-Field Probe Designed for High-Resolution Skin Cancer Diagnosis. Topfer, F., +, TMTT Jun. 2015 2050-2059 MRI-Based Electrical Property Retrieval by Applying the Finite-Element Method (FEM). Huang, S. Y., +, TMTT Aug. 2015 2482-2490 Tuning Tunable 1.25–2.1-GHz 4-Pole Bandpass Filter With Intrinsic Transmission Zero Tuning. Yang, T., +, TMTT May 2015 1569-1578 Tunnel diodes Breaking the Efficiency Barrier for Ambient Microwave Power Harvesting With Heterojunction Backward Tunnel Diodes. Lorenz, C. H. P., +, TMTT Dec. 2015 4544-4555 Twisted pair cables Estimation of Nonhomogeneous and Multi-Section Twisted-Pair Transmission-Line Parameters. Lindqvist, F., +, TMTT Nov. 2015 3568-3578 Two-port networks Multiport Scattering Matrix Determination From One-Port Measurements. Lin, Y.-C., +, TMTT Jul. 2015 2343-2352

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UHF amplifiers A Novel Load Mismatch Detection and Correction Technique for 3G/4G Load Insensitive Power Amplifier Application. Ji, D., +, TMTT May 2015 1530-1543 A Post-Matching Doherty Power Amplifier Employing Low-Order Impedance Inverters for Broadband Applications. Pang, J., +, TMTT Dec. 2015 4061-4071 Analytical Design Methodology for Generic Doherty Amplifier Architectures Using Three-Port Input/Output Networks. Akbarpour, M., +, TMTT Oct. 2015 3242-3253 RF Input Matching Design for Closed-Loop Direct Delta–Sigma Receivers. Ostman, K. B., +, TMTT Apr. 2015 1370-1379 UHF antennas A 2.45 GHz Phased Array Antenna Unit Cell Fabricated Using 3-D MultiLayer Direct Digital Manufacturing. Ketterl, T. P., +, TMTT Dec. 2015 4382-4394 A Compact Dual-Channel Transceiver for Long-Range Passive Embedded Monitoring. Nassar, I. T., +, TMTT Jan. 2015 287-294 A Distributed Positioning System Based on a Predictive Fingerprinting Method Enabling Sub-Metric Precision in IEEE 802.11 Networks. Maddio, S., +, TMTT Dec. 2015 4567-4580 Textile Microwave Components in Substrate Integrated Waveguide Technology. Moro, R., +, TMTT Feb. 2015 422-432 Third Harmonic Exploitation in Passive UHF RFID. Andiia Vera, G., +, TMTT Sep. 2015 2991-3004 UHF circuits Optimized Design of Frequency Dividers Based on Varactor-Inductor Cells. Ponton, M., +, TMTT Dec. 2015 4458-4472 Textile Microwave Components in Substrate Integrated Waveguide Technology. Moro, R., +, TMTT Feb. 2015 422-432 UHF couplers Design of High-Directivity Wideband Microstrip Directional Coupler With Fragment-Type Structure. Wang, L., +, TMTT Dec. 2015 3962-3970 UHF detectors Modelling and Measurements of the Microwave Dielectric Properties of Microspheres. Abduljabar, A. A., +, TMTT Dec. 2015 4492-4500 UHF devices High Power Latching RF MEMS Switches. Bakri-Kassem, M., +, TMTT Jan. 2015 222-232 Implementation of Sensor RFID: Carrying Sensor Information in the Modulation Frequency. Islam, Md. M., +, TMTT Aug. 2015 2672-2681 UHF diodes A 2.45-GHz Energy-Autonomous Wireless Power Relay Node. Del Prete, M., +, TMTT Dec. 2015 4511-4520 UHF field effect transistors A 2.45-GHz Energy-Autonomous Wireless Power Relay Node. Del Prete, M., +, TMTT Dec. 2015 4511-4520 UHF filters A 0.2–3.6-GHz 10-dBm B1dB 29-dBm IIP3 Tunable Filter for Transmit Leakage Suppression in SAW-Less 3G/4G FDD Receivers. Luo, C., +, TMTT Oct. 2015 3514-3524 A Highly Efficient LTE Pulse-Modulated Polar Transmitter Using Wideband Power Recycling. Yang, H.-S., +, TMTT Dec. 2015 4437-4443 A Post-Matching Doherty Power Amplifier Employing Low-Order Impedance Inverters for Broadband Applications. Pang, J., +, TMTT Dec. 2015 4061-4071 An Ultra-Compact Common-Mode Bandstop Filter With Modified-T Circuits in Integrated Passive Device (IPD) Process. Hsiao, C.-Y., +, TMTT Nov. 2015 3624-3631 Balanced Dual-Band Bandpass Filter With Multiple Transmission Zeros Using Doubly Short-Ended Resonator Coupled Line. Yang, L., +, TMTT Jul. 2015 2225-2232 Broadband Synthetic Transmission-Line N-Path Filter Design. Thomas, C. M., +, TMTT Oct. 2015 3525-3536 Compact Tunable Filtering Power Divider With Constant Absolute Bandwidth. Gao, L., +, TMTT Oct. 2015 3505-3513 Suppression of Harmonics in Microstrip Filters Using a Combination of Techniques. Huang, F., TMTT Oct. 2015 3453-3461 Textile Microwave Components in Substrate Integrated Waveguide Technology. Moro, R., +, TMTT Feb. 2015 422-432 + Check author entry for coauthors

Tunable 1.25–2.1-GHz 4-Pole Bandpass Filter With Intrinsic Transmission Zero Tuning. Yang, T., +, TMTT May 2015 1569-1578 Tunable 4-Pole Noncontiguous 0.7–2.1-GHz Bandpass Filters Based on Dual Zero-Value Couplings. Cho, Y.-H., +, TMTT May 2015 1579-1586 Tunable 500–1200-MHz Dual-Band and Wide Bandwidth Notch Filters Using RF Transformers. Ko, C.-H., +, TMTT Jun. 2015 1854-1862 UHF integrated circuits Analysis of Far-Out Spurious Noise and its Reduction in Envelope-Tracking Power Amplifier. Kim, J., +, TMTT Dec. 2015 4072-4082 Fully Monolithic BiCMOS Reconfigurable Power Amplifier for Multi-Mode and Multi-Band Applications. Lee, M.-L., +, TMTT Feb. 2015 614-624 Investigation of Intermodulation Distortion of Envelope Tracking Power Amplifier for Linearity Improvement. Moon, K., +, TMTT Apr. 2015 13241333 Power Adaptive Digital Predistortion for Wideband RF Power Amplifiers With Dynamic Power Transmission. Guo, Y., +, TMTT Nov. 2015 35953607 UHF mixers Narrowband Coupled-Line Bandstop Filter With Absorptive Stopband. Shao, J.-Y., +, TMTT Oct. 2015 3469-3478 UHF oscillators A 2.45-GHz Energy-Autonomous Wireless Power Relay Node. Del Prete, M., +, TMTT Dec. 2015 4511-4520 Tuning-Range Enhancement Through Deterministic Mode Selection in RF Quadrature Oscillators. Bagheri, M., +, TMTT Nov. 2015 3713-3726 UHF phase shifters A 1.6–2.3-GHz RF MEMS Reconfigurable Quadrature Coupler and Its Application to a 360 Reflective-Type Phase Shifter. Gurbuz, O. D., +, TMTT Feb. 2015 414-421 A 2.45 GHz Phased Array Antenna Unit Cell Fabricated Using 3-D MultiLayer Direct Digital Manufacturing. Ketterl, T. P., +, TMTT Dec. 2015 4382-4394 Design of Compact Reflection-Type Phase Shifters With High Figure-ofMerit. Burdin, F., +, TMTT Jun. 2015 1883-1893 UHF power amplifiers 3-D Distributed Memory Polynomial Behavioral Model for Concurrent Dual-Band Envelope Tracking Power Amplifier Linearization. Gilabert, P. L., +, TMTT Feb. 2015 638-648 A Highly Efficient LTE Pulse-Modulated Polar Transmitter Using Wideband Power Recycling. Yang, H.-S., +, TMTT Dec. 2015 4437-4443 A New Distributed Parameter Broadband Matching Method for Power Amplifier via Real Frequency Technique. Dai, Z., +, TMTT Feb. 2015 449-458 An 85-W Multi-Octave Push–Pull GaN HEMT Power Amplifier for HighEfficiency Communication Applications at Microwave Frequencies. Jundi, A., +, TMTT Nov. 2015 3691-3700 Analysis of Far-Out Spurious Noise and its Reduction in Envelope-Tracking Power Amplifier. Kim, J., +, TMTT Dec. 2015 4072-4082 Asymmetric Broadband Doherty Power Amplifier Using GaN MMIC for Femto-Cell Base-Station. Jee, S., +, TMTT Sep. 2015 2802-2810 Bayesian Optimization for Broadband High-Efficiency Power Amplifier Designs. Chen, P., +, TMTT Dec. 2015 4263-4272 Digitally Equalized Doherty RF Front-End Architecture for Broadband and Multistandard Wireless Transmitters. Darraji, R., +, TMTT Jun. 2015 19781988 Fully Monolithic BiCMOS Reconfigurable Power Amplifier for Multi-Mode and Multi-Band Applications. Lee, M.-L., +, TMTT Feb. 2015 614-624 High-Efficiency Harmonic-Peaking Class-EF Power Amplifiers With Enhanced Maximum Operating Frequency. Thian, M., +, TMTT Feb. 2015 659-671 Highly Efficient and Multipaction-Free P-Band GaN High-Power Amplifiers for Space Applications. Ayllon, N., +, TMTT Dec. 2015 4429-4436 Highly Efficient Concurrent Power Amplifier With Controllable Modes. Sun, Y., +, TMTT Dec. 2015 4051-4060 Highly Linear Fully Integrated Wideband RF PA for LTE-Advanced in 180-nm SOI. Francois, B., +, TMTT Feb. 2015 649-658 Hysteresis and Oscillation in High-Efficiency Power Amplifiers. de Cos, J., +, TMTT Dec. 2015 4284-4296 Investigation of Intermodulation Distortion of Envelope Tracking Power Amplifier for Linearity Improvement. Moon, K., +, TMTT Apr. 2015 13241333 Multi-Frequency Measurements for Supply Modulated Transmitters. Schafer, S., +, TMTT Sep. 2015 2931-2941

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 63, NO. 12, DECEMBER 2015

Power Adaptive Digital Predistortion for Wideband RF Power Amplifiers With Dynamic Power Transmission. Guo, Y., +, TMTT Nov. 2015 35953607 Source Degenerated Derivative Superposition Method for Linearizing RF FET Differential Amplifiers. Shin, H., +, TMTT Mar. 2015 1026-1035 Supply-Modulated Radar Transmitters With Amplitude-Modulated Pulses. Zai, A., +, TMTT Sep. 2015 2953-2964 Theory and Implementation of RF-Input Outphasing Power Amplification. Barton, T. W., +, TMTT Dec. 2015 4273-4283 UHF radio propagation A Distributed Positioning System Based on a Predictive Fingerprinting Method Enabling Sub-Metric Precision in IEEE 802.11 Networks. Maddio, S., +, TMTT Dec. 2015 4567-4580 UHF resonators A Single-Chip Electron Paramagnetic Resonance Transceiver in 0.13- m SiGe BiCMOS. Yang, X., +, TMTT Nov. 2015 3727-3735 An FBAR/CMOS Frequency/Phase Discriminator and Phase Noise Reduction System. Imani, A., +, TMTT May 2015 1658-1665 An LTCC Coupled Resonator Decoupling Network for Two Antennas. Qian, K., +, TMTT Oct. 2015 3199-3207 Modelling and Measurements of the Microwave Dielectric Properties of Microspheres. Abduljabar, A. A., +, TMTT Dec. 2015 4492-4500 RF-Designed High-Power Lamb-Wave Aluminum–Nitride Resonators. Campanella, H., +, TMTT Feb. 2015 331-339 UHF transistors Multi-Frequency Measurements for Supply Modulated Transmitters. Schafer, S., +, TMTT Sep. 2015 2931-2941 Ultra wideband antennas 160-GHz to 1-THz Multi-Color Active Imaging With a Lens-Coupled SiGe HBT Chip-Set. Statnikov, K., +, TMTT Feb. 2015 520-532 Calibrated Layer-Stripping Technique for Level and Permittivity Measurement With UWB Radar in Metallic Tanks. Maunder, A., +, TMTT Jul. 2015 2322-2334 Propagation, Power Absorption, and Temperature Analysis of UWB Wireless Capsule Endoscopy Devices Operating in the Human Body. Thotahewa, K. M. S., +, TMTT Nov. 2015 3823-3833 Ultra wideband communication Concurrent Dual-Band Modeling and Digital Predistortion in the Presence of Unfilterable Harmonic Signal Interference. Rawat, M., +, TMTT Feb. 2015 625-637 Low-Loss Ultrawideband Programmable RF Photonic Phase Filter for Spread Spectrum Pulse Compression. Kim, H.-J., +, TMTT Dec. 2015 4178-4187 Propagation, Power Absorption, and Temperature Analysis of UWB Wireless Capsule Endoscopy Devices Operating in the Human Body. Thotahewa, K. M. S., +, TMTT Nov. 2015 3823-3833 Signal Detection and Noise Modeling of a 1-D Pulse-Based Ultra-Wideband Ranging System and Its Accuracy Assessment. Elkhouly, E., +, TMTT May 2015 1746-1757 Ultra-Compact (80 mm ) Differential-Mode Ultra-Wideband (UWB) Bandpass Filters With Common-Mode Noise Suppression. Velez, P., +, TMTT Apr. 2015 1272-1280 Ultra wideband radar A K-Band Reconfigurable Pulse-Compression Automotive Radar Transmitter in 90-nm CMOS. Tan, K.-W., +, TMTT Apr. 2015 1380-1387 Calibrated Layer-Stripping Technique for Level and Permittivity Measurement With UWB Radar in Metallic Tanks. Maunder, A., +, TMTT Jul. 2015 2322-2334 Ultra wideband technology Two-Material Ridge Substrate Integrated Waveguide for Ultra-Wideband Applications. Moscato, S., +, TMTT Oct. 2015 3175-3182

V Vacuum switches High Power Latching RF MEMS Switches. Bakri-Kassem, M., +, TMTT Jan. 2015 222-232 Varactors -Band Dual-Polarization Phased-Array Transceiver Front-End in SiGe BiCMOS. Natarajan, A., +, TMTT Jun. 2015 1989-2002

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4671

A Varactor-Based Variable Attenuator Design With Enhanced Linearity Performance. Cheng, K.-K. M., +, TMTT Oct. 2015 3191-3198 Accurate Parametric Electrical Model for Slow-Wave CPW and Application to Circuits Design. Bautista, A., +, TMTT Dec. 2015 4225-4235 Analysis of Weakly Nonlinear Effect for Varactor-Tuned Bandpass Filter. Ge, C., +, TMTT Nov. 2015 3641-3650 Compact Tunable Filtering Power Divider With Constant Absolute Bandwidth. Gao, L., +, TMTT Oct. 2015 3505-3513 Design of Compact Reflection-Type Phase Shifters With High Figure-ofMerit. Burdin, F., +, TMTT Jun. 2015 1883-1893 Optimized Design of a Dual-Band Power Amplifier With SiC VaractorBased Dynamic Load Modulation. Sanchez-Perez, C., +, TMTT Aug. 2015 2579-2588 Optimized Design of Frequency Dividers Based on Varactor-Inductor Cells. Ponton, M., +, TMTT Dec. 2015 4458-4472 Tunable 4-Pole Noncontiguous 0.7–2.1-GHz Bandpass Filters Based on Dual Zero-Value Couplings. Cho, Y.-H., +, TMTT May 2015 1579-1586 Tunable 500–1200-MHz Dual-Band and Wide Bandwidth Notch Filters Using RF Transformers. Ko, C.-H., +, TMTT Jun. 2015 1854-1862 Varistors Corrections to “Design and Fabrication of Broadband Hybrid GaAs Schottky Diode Frequency Multipliers” [Dec 13 4442-4460]. Hrobak, M., +, TMTT Feb. 2015 553 Vectors Application of Coherence Theory to Modeling of Blackbody Radiation at Close Range. Gu, D., +, TMTT May 2015 1475-1488 Behavioral Modeling and Predistortion of Power Amplifiers Under Sparsity Hypothesis. Reina-Tosina, J., +, TMTT Feb. 2015 745-753 Decomposed Vector Rotation-Based Behavioral Modeling for Digital Predistortion of RF Power Amplifiers. Zhu, A., TMTT Feb. 2015 737-744 Millimeter-Wave Modulated-Signal and Error-Vector-Magnitude Measurement With Uncertainty. Remley, K. A., +, TMTT May 2015 1710-1720 Qualitative Microwave Imaging With Scattering Parameters Measurements. Akinci, M. N., +, TMTT Sep. 2015 2730-2740 VHF amplifiers A General Digital Predistortion Architecture Using Constrained Feedback Bandwidth for Wideband Power Amplifiers. Liu, Y., +, TMTT May 2015 1544-1555 Vias An Efficient Hybrid Finite-Element Analysis of Multiple Vias Sharing the Same Anti-Pad in an Arbitrarily Shaped Parallel-Plate Pair. Zhang, Y.-J., +, TMTT Mar. 2015 883-890 Chebyshev Filter Design Using Vias as Quasi-Transmission Lines in Printed Circuit Boards. Hardock, A., +, TMTT Mar. 2015 976-985 Two-Material Ridge Substrate Integrated Waveguide for Ultra-Wideband Applications. Moscato, S., +, TMTT Oct. 2015 3175-3182 Voltage multipliers Nonlinear Modeling and Harmonic Recycling of Millimeter-Wave Rectifier Circuit. Ladan, S., +, TMTT Mar. 2015 937-944 Voltage-controlled oscillators 76–81-GHz CMOS Transmitter With a Phase-Locked-Loop-Based Multichirp Modulator for Automotive Radar. Park, J., +, TMTT Apr. 2015 13991408 A 1.3–2.4-GHz 3.1-mW VCO Using Electro-Thermo- Mechanically Tunable Self-Assembled MEMS Inductor on HR Substrate. Bhattacharya, A., +, TMTT Feb. 2015 459-469 A 47.6–71.0-GHz 65-nm CMOS VCO Based on Magnetically Coupled -Type LC Network. Jia, H., +, TMTT May 2015 1645-1657 A G-Band Standing-Wave Push–Push VCO Using a Transmission-Line Resonator. Koo, H., +, TMTT Mar. 2015 1036-1045 A Low Phase-Noise Wide Tuning-Range Quadrature Oscillator Using a Transformer-Based Dual-Resonance LC Ring. Bajestan, M. M., +, TMTT Apr. 2015 1142-1153 A Wide-Band CMOS to Waveguide Transition at mm-Wave Frequencies With Wire-Bonds. Jameson, S., +, TMTT Sep. 2015 2741-2750 An FBAR/CMOS Frequency/Phase Discriminator and Phase Noise Reduction System. Imani, A., +, TMTT May 2015 1658-1665 An Ultra-Low Phase-Noise 20-GHz PLL Utilizing an Optoelectronic Voltage-Controlled Oscillator. Bluestone, A., +, TMTT Mar. 2015 1046-1052 Design and Analysis on Bidirectionally and Passively Coupled QVCO With Nonlinear Coupler. Kuo, N.-C., +, TMTT Apr. 2015 1130-1141

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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 63, NO. 12, DECEMBER 2015

Design and Tuning of Coupled-LC mm-Wave Subharmonically InjectionLocked Oscillators. Mangraviti, G., +, TMTT Jul. 2015 2301-2312 Multi-Standard Hybrid PLL With Low Phase-Noise Characteristics for GSM/EDGE and LTE Applications. Choi, Y.-C., +, TMTT Oct. 2015 3254-3264 Wide Tuning-Range mm-Wave Voltage-Controlled Oscillator Employing an Artificial Magnetic Transmission Line. Yanay, N., +, TMTT Apr. 2015 13421352 Volterra equations Extraction of a Multi-Dimensional Polynomial Device Model for an Improved Distortion Contribution Analysis Technique. Aikio, J. P., +, TMTT Jan. 2015 155-164 Modeling of Deterministic Output Emissions of Power Amplifiers Into Adjacent Receive Bands. Farsi, S., +, TMTT Apr. 2015 1250-1262 Volterra series Analysis of Weakly Nonlinear Effect for Varactor-Tuned Bandpass Filter. Ge, C., +, TMTT Nov. 2015 3641-3650 Investigation of RF Avalanche Inductive Effect on Reduction of Intermodulation Distortion of MOSFETs Using Volterra Series Analysis. Lee, C.-I., +, TMTT Feb. 2015 367-373 Source Degenerated Derivative Superposition Method for Linearizing RF FET Differential Amplifiers. Shin, H., +, TMTT Mar. 2015 1026-1035 W Water Electrical Analysis of Cell Membrane Poration by an Intense Nanosecond Pulsed Electric Field Using an Atomistic-to-Continuum Method. Kohler, S., +, TMTT Jun. 2015 2032-2040 Waveform generators Millimeter-Wave Modulated-Signal and Error-Vector-Magnitude Measurement With Uncertainty. Remley, K. A., +, TMTT May 2015 1710-1720 Waveguide antenna arrays A Configurable Coupling Structure for Broadband Millimeter-Wave SplitBlock Networks. Koenen, C., +, TMTT Dec. 2015 3954-3961 Waveguide components Analysis of Axisymmetric Waveguide Components by a Multi-Domain Spectral Method. Tibaldi, A., +, TMTT Jan. 2015 115-124 Design of Waveguide Microwave Pulse Compressors Using Equivalent Circuits. Savaidis, S. P., +, TMTT Jan. 2015 125-134 Waveguide couplers Design and Analysis on Bidirectionally and Passively Coupled QVCO With Nonlinear Coupler. Kuo, N.-C., +, TMTT Apr. 2015 1130-1141 Design and Measurement of a Broadband Sidewall Coupler for a W-Band Gyro-TWA. Zhang, L., +, TMTT Oct. 2015 3183-3190 Load Modulation Measurements of X-Band Outphasing Power Amplifiers. Litchfield, M., +, TMTT Dec. 2015 4119-4129 Waveguide filters A Miniaturized Microfluidically Reconfigurable Coplanar Waveguide Bandpass Filter With Maximum Power Handling of 10 Watts. Pourghorban Saghati, A., +, TMTT Aug. 2015 2515-2525 A Novel Compact -Plane Waveguide Filter With Multiple Transmission Zeroes. Jin, J. Y., +, TMTT Oct. 2015 3374-3380 Design and Multiphysics Analysis of Direct and Cross-Coupled SIW Combline Filters Using Electric and Magnetic Couplings. Sirci, S., +, TMTT Dec. 2015 4341-4354 Efficient Design of Waveguide Manifold Multiplexers Based on Low-Order EM Distributed Models. Cogollos, S., +, TMTT Aug. 2015 2540-2549 High- Tunable Waveguide Filters Using Ohmic RF MEMS Switches. Pelliccia, L., +, TMTT Oct. 2015 3381-3390 High-Performance Coplanar Waveguide to Empty Substrate Integrated Coaxial Line Transition. Belenguer, A., +, TMTT Dec. 2015 4027-4034 Integral-Equation Formulation for the Analysis of Capacitive Waveguide Filters Containing Dielectric and Metallic Arbitrarily Shaped Objects and Novel Applications. Quesada Pereira, F. D., +, TMTT Dec. 2015 38623873 K-Band Frequency Tunable Substrate-Integrated- Waveguide Resonator Filter With Enhanced Stopband Attenuation. Lee, B., +, TMTT Nov. 2015 3632-3640 Mechanical Tuning of Substrate Integrated Waveguide Filters. Mira, F., +, TMTT Dec. 2015 3939-3946 Modal Loss Analysis of - and -Plane Filtering Structures. Accatino, L., +, TMTT Jan. 2015 40-47 + Check author entry for coauthors

Mode Filters for Oversized Rectangular Waveguides: A Modal Approach. Ceccuzzi, S., +, TMTT Aug. 2015 2468-2481 Modeling of Inline Transitions Between Different Waveguides as Impedance Inverters for the Use in Novel Filter Designs. Strauss, G., +, TMTT Nov. 2015 3663-3670 Propagating Waveguide Filters Using Dielectric Resonators. Tomassoni, C., +, TMTT Dec. 2015 4366-4375 Waveguide junctions Simple, Fast, and Effective Identification of an Equivalent Circuit of a Waveguide Junction With Ports. Zappelli, L., TMTT Jan. 2015 48-55 Waveguide transitions A Wide-Band CMOS to Waveguide Transition at mm-Wave Frequencies With Wire-Bonds. Jameson, S., +, TMTT Sep. 2015 2741-2750 Coaxial End-Launched and Microstrip to Partial -Plane Waveguide Transitions. Kloke, K. H., +, TMTT Oct. 2015 3103-3108 Monolithic Millimeter-Wave MEMS Waveguide Switch. Vahabisani, N., +, TMTT Feb. 2015 340-351 Polymer Multichip Module Process Using 3-D Printing Technologies for D-Band Applications. Merkle, T., +, TMTT Feb. 2015 481-493 Waveguides A 77-GHz FMCW Radar System Using On-Chip Waveguide Feeders in 65-nm CMOS. Cui, C., +, TMTT Nov. 2015 3736-3746 The Mixed Spectral-Element Method for Anisotropic, Lossy, and Open Waveguides. Liu, N., +, TMTT Oct. 2015 3094-3102 Wearable antennas Textile Microwave Components in Substrate Integrated Waveguide Technology. Moro, R., +, TMTT Feb. 2015 422-432 Wearable computers Ambient RF Energy Harvesting From a Two-Way Talk Radio for Flexible Wearable Wireless Sensor Devices Utilizing Inkjet Printing Technologies. Bito, J., +, TMTT Dec. 2015 4533-4543 Whispering gallery modes Whispering-Gallery-Mode Resonator Technique With Microfluidic Channel for Permittivity Measurement of Liquids. Gubin, A. I., +, TMTT Jun. 2015 2003-2009 Wide band gap semiconductors A 2-W W-Band GaN Traveling-Wave Amplifier With 25-GHz Bandwidth. Schellenberg, J. M., TMTT Sep. 2015 2833-2840 A 5.9-GHz Fully Integrated GaN Frontend Design With Physics-Based RF Compact Model. Choi, P., +, TMTT Apr. 2015 1163-1173 A Broadband GaN pHEMT Power Amplifier Using Non-Foster Matching. Lee, S., +, TMTT Dec. 2015 4406-4414 A Miniature Broadband Doherty Power Amplifier With a Series-Connected Load. Watanabe, S., +, TMTT Feb. 2015 572-579 A New Double Input-Double Output Complex Envelope Amplifier Behavioral Model Taking Into Account Source and Load Mismatch Effects. Zargar, H., +, TMTT Feb. 2015 766-774 A Post-Matching Doherty Power Amplifier Employing Low-Order Impedance Inverters for Broadband Applications. Pang, J., +, TMTT Dec. 2015 4061-4071 Active Detuning of MRI Receive Coils with GaN FETs. Twieg, M., +, TMTT Dec. 2015 4169-4177 An 85-W Multi-Octave Push–Pull GaN HEMT Power Amplifier for HighEfficiency Communication Applications at Microwave Frequencies. Jundi, A., +, TMTT Nov. 2015 3691-3700 Mode Power Amplifier Design ApAn Integrated Continuous Classproach for Microwave Enhanced Portable Diagnostic Applications. Imtiaz, A., +, TMTT Oct. 2015 3007-3015 Design of X-Band GaN Phase Shifters. Ross, T. N., +, TMTT Jan. 2015 244-255 Digitally Assisted Analog/RF Predistorter With a Small-Signal-Assisted Parameter Identification Algorithm. Huang, H., +, TMTT Dec. 2015 42974305 Envelope Tracking of an RF High Power Amplifier With an 8-Level Digitally Controlled GaN-on-Si Supply Modulator. Florian, C., +, TMTT Aug. 2015 2589-2602 GaN HEMT Noise Model Based on Electromagnetic Simulations. Nalli, A., +, TMTT Aug. 2015 2498-2508 GaN Microwave DC–DC Converters. Ramos, I., +, TMTT Dec. 2015 44734482 High-Efficiency Harmonic-Peaking Class-EF Power Amplifiers With Enhanced Maximum Operating Frequency. Thian, M., +, TMTT Feb. 2015 659-671

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 63, NO. 12, DECEMBER 2015

Highly Efficient and Multipaction-Free P-Band GaN High-Power Amplifiers for Space Applications. Ayllon, N., +, TMTT Dec. 2015 4429-4436 Hysteresis and Oscillation in High-Efficiency Power Amplifiers. de Cos, J., +, TMTT Dec. 2015 4284-4296 Investigation of Intermodulation Distortion of Envelope Tracking Power Amplifier for Linearity Improvement. Moon, K., +, TMTT Apr. 2015 13241333 Load Modulation Measurements of X-Band Outphasing Power Amplifiers. Litchfield, M., +, TMTT Dec. 2015 4119-4129 Optimized Design of a Dual-Band Power Amplifier With SiC VaractorBased Dynamic Load Modulation. Sanchez-Perez, C., +, TMTT Aug. 2015 2579-2588 Wideband amplifiers A 40-nm CMOS E-Band 4-Way Power Amplifier With Neutralized Bootstrapped Cascode Amplifier and Optimum Passive Circuits. Zhao, D., +, TMTT Dec. 2015 4083-4089 A Broadband 1-to- Power Divider/Combiner With Isolation and Reflection Cancellation. Darwish, A. M., +, TMTT Jul. 2015 2253-2263 A Broadband GaN pHEMT Power Amplifier Using Non-Foster Matching. Lee, S., +, TMTT Dec. 2015 4406-4414 A General Digital Predistortion Architecture Using Constrained Feedback Bandwidth for Wideband Power Amplifiers. Liu, Y., +, TMTT May 2015 1544-1555 A Miniature Broadband Doherty Power Amplifier With a Series-Connected Load. Watanabe, S., +, TMTT Feb. 2015 572-579 A New Distributed Parameter Broadband Matching Method for Power Amplifier via Real Frequency Technique. Dai, Z., +, TMTT Feb. 2015 449-458 A New Double Input-Double Output Complex Envelope Amplifier Behavioral Model Taking Into Account Source and Load Mismatch Effects. Zargar, H., +, TMTT Feb. 2015 766-774 A Reconfigurable K-/Ka-Band Power Amplifier With High PAE in 0.18- m SiGe BiCMOS for Multi-Band Applications. Ma, K., +, TMTT Dec. 2015 4395-4405 Bandwidth Enhancement of Three-Stage Doherty Power Amplifier Using Symmetric Devices. Barthwal, A., +, TMTT Aug. 2015 2399-2410 Bayesian Optimization for Broadband High-Efficiency Power Amplifier Designs. Chen, P., +, TMTT Dec. 2015 4263-4272 Broadband Sequential Power Amplifier With Doherty-Type Active Load Modulation. Nghiem, X. A., +, TMTT Sep. 2015 2821-2832 Digitally Equalized Doherty RF Front-End Architecture for Broadband and Multistandard Wireless Transmitters. Darraji, R., +, TMTT Jun. 2015 19781988 Efficient Least-Squares 2-D-Cubic Spline for Concurrent Dual-Band Systems. Naraharisetti, N., +, TMTT Jul. 2015 2199-2210 Improved Reactance-Compensation Technique for the Design of Wideband Suboptimum Class-E Power Amplifiers. Zhou, J., +, TMTT Sep. 2015 27932801 Improving Power Utilization Factor of Broadband Doherty Amplifier by Using Bandpass Auxiliary Transformer. Fang, X.-H., +, TMTT Sep. 2015 2811-2820 Linearization and Imbalance Correction Techniques for Broadband Outphasing Power Amplifiers. Hwang, T., +, TMTT Jul. 2015 2185-2198 Millimeter-Wave Low-Noise Amplifier Design in 28-nm Low-Power Digital CMOS. Fritsche, D., +, TMTT Jun. 2015 1910-1922 Polymer Multichip Module Process Using 3-D Printing Technologies for D-Band Applications. Merkle, T., +, TMTT Feb. 2015 481-493 Transformer-Feedback Interstage Bandwidth Enhancement for MMIC Multistage Amplifiers. Nikandish, G., +, TMTT Feb. 2015 441-448 Wireless channels 3-D Radiometric Aperture Synthesis Imaging. Salmon, N. A., TMTT Nov. 2015 3579-3587

+ Check author entry for coauthors

4673

Digitally Equalized Doherty RF Front-End Architecture for Broadband and Multistandard Wireless Transmitters. Darraji, R., +, TMTT Jun. 2015 19781988 Highly Efficient Concurrent Power Amplifier With Controllable Modes. Sun, Y., +, TMTT Dec. 2015 4051-4060 Partitioned Distortion Mitigation in LTE Radio Uplink to Enhance Transmitter Efficiency. Amiri, M. V., +, TMTT Aug. 2015 2661-2671 Performance Estimation for Broadband Multi-Gigabit Millimeter- and SubMillimeter-Wave Wireless Communication Links. Antes, J., +, TMTT Oct. 2015 3288-3299 Third Harmonic Exploitation in Passive UHF RFID. Andiia Vera, G., +, TMTT Sep. 2015 2991-3004 Wireless Fully Passive Multichannel Recording of Neuropotentials Using Photo-Activated RF Backscattering Methods. Schwerdt, H. N., +, TMTT Sep. 2015 2965-2970 Wireless Power Systems for Mobile Devices Supporting Inductive and Resonant Operating Modes. Riehl, P. S., +, TMTT Mar. 2015 780-790 Wireless communication Guest Editorial. Boria, V. E., +, TMTT Oct. 2015 3321-3323 Guest Editorial. Alomainy, A., +, TMTT Oct. 2015 3005-3006 Guest Editorial. KIM, J., +, TMTT Mar. 2015 778-779 Wireless LAN A Distributed Positioning System Based on a Predictive Fingerprinting Method Enabling Sub-Metric Precision in IEEE 802.11 Networks. Maddio, S., +, TMTT Dec. 2015 4567-4580 A Multi-Band Stacked RF Energy Harvester With RF-to-DC Efficiency Up to 84%. Kuhn, V., +, TMTT May 2015 1768-1778 A Sub-GHz Wireless Transmitter Utilizing a Multi-Class-Linearized PA and Time-Domain Wideband-Auto I/Q-LOFT Calibration for IEEE 802.11af WLAN. Un, K.-F., +, TMTT Oct. 2015 3228-3241 An Efficiency-Enhanced Stacked 2.4-GHz CMOS Power Amplifier With Mode Switching Scheme for WLAN Applications. Yin, Y., +, TMTT Feb. 2015 672-682 Fully Monolithic BiCMOS Reconfigurable Power Amplifier for Multi-Mode and Multi-Band Applications. Lee, M.-L., +, TMTT Feb. 2015 614-624 Guest Editorial. Draxler, P., TMTT Feb. 2015 557-558 Wireless sensor networks A High-Sensitivity Fully Passive Neurosensing System for Wireless Brain Signal Monitoring. Lee, C. W. L., +, TMTT Jun. 2015 2060-2068 A Multi-Band Stacked RF Energy Harvester With RF-to-DC Efficiency Up to 84%. Kuhn, V., +, TMTT May 2015 1768-1778 Ambient RF Energy Harvesting From a Two-Way Talk Radio for Flexible Wearable Wireless Sensor Devices Utilizing Inkjet Printing Technologies. Bito, J., +, TMTT Dec. 2015 4533-4543 Wiring A Stacked-FET Linear SOI CMOS Cellular Antenna Switch With an Extremely Low-Power Biasing Strategy. Im, D., +, TMTT Jun. 2015 19641977

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Z transforms Direct -Transform Implementation of the CFS-PML Based on MemoryMinimized Method. Feng, N., +, TMTT Mar. 2015 877-882

Editors-in-Chief Dominique Schreurs c/o Mrs. Enas Kandil, Editorial Assistant KU Leuven, Div. ESAT-TELEMIC Kasteelpark Arenberg 10 B-3000 Leuven Belgium E-mail: [email protected] or [email protected]

Jenshan Lin c/o Mrs. Marcia Hensley, Editorial Assistant University of Florida 1064 Center Drive, NEB 559 Gainesville, FL 32611 USA E-mail: [email protected] or [email protected]fl.edu

Information for Authors The IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES focuses on that part of engineering and theory associated with microwave/millimeter-wave components, devices, circuits, and systems involving the generation, modulation, demodulation, control, transmission, and detection of microwave signals. This includes scientific, technical, and industrial, activities. Microwave theory and techniques relates to electromagnetic waves usually in the frequency region between a few MHz and a THz; other spectral regions and wave types are included within the scope of the Society whenever basic microwave theory and techniques can yield useful results. Generally, this occurs in the theory of wave propagation in structures with dimensions comparable to a wavelength, and in the related techniques for analysis and design. I. Paper Submission in Electronic Form Authors need to visit the website http://www.mtt.org/transactions/34-author-information-transactions.html for the author instructions. To reduce time from submission to publication of papers, the editorial office accepts manuscripts only in electronic form as .pdf files and all communications with authors will be via email. The files must not be larger than 1MB and no *.zip files are accepted. Submissions should be submitted through the ScholarOne Manuscripts site at: http://mc.manuscriptcentral.com/tmtt-ieee and use the templates provided under http://www.ieee.org/publications_standards/publications/authors/authors_journals.html (Template for all Transactions (except IEEE Transactions on Magnetics), two-column template; can also be requested from the editorial office). Figures, graphs and all other necessary information for reviewing the manuscript must be included in this file (as opposed to being attached to it as separate files) and placed at appropriate locations within the text rather than at the end: • The abstract must be self-contained, without abbreviations, footnotes, or references. It should be no more than 250 words. It must be written as one paragraph, and should not contain displayed mathematical equations or tabular material. • IEEE supports the publication of author names in the native language alongside the English versions of the names in the author list of an article. For more information, please visit the IEEE Author Digital Tool Box at: http://www.ieee.org/publications_standards/publications/authors/auth_names_native_lang.pdf • Figures should be large enough to be easily readable on a computer screen and on paper when printed out. • A photograph of any component or circuit presented must be included. • If, at the decision of the Editor, the component or circuit can be fabricated, measured characteristics must be included. • All papers with theoretical contributions must have independent verification with measurement-based validation strongly preferred. • Instrument screen captures are not suitable for publication and the data should be replotted. • The print version of the paper will be in black and white, but color figures may be used in the electronic version of the paper. • Axes should be labeled with large lettering. • Whenever possible, theory and corresponding experimental results should be printed on the same graph for easy comparison. • Follow the Guidelines for Author-Supplied Electronic Text and Graphics available for download at the above website. • The minimum paper length is 4 pages, excluding the authors’ photos and biographies. Short papers of three pages or less should be sent to the IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS. The font size is specified in the templates. TeX and LaTeX users must use scalable fonts rather than bitmapped fonts to allow easy reading of .pdf files on the computer screen. • This publication accepts graphical abstracts, which must be peer reviewed. For more information about graphical abstracts and their specifications, please visit: http://www.ieee.org/publications_standards/publications/graphical_abstract.pdf Note: Manuscripts that are related to material submitted to or published at conferences are considered only if the content is significantly updated or contains material of substantially complementary nature. Authors must reference all of their previous papers that are similar. Please attach .pdf files of previous papers and clearly state (on a separate page) the difference with respect to the current submission. Failure to disclose prior papers by the authors that are similar will be rejected. II. Final Submission Format After a manuscript has been accepted for publication, the author will be requested to provide an electronic copy of the final version of the manuscript in pdf format; Microsoft Word is the preferred format for this final submission, although TEX and LATEX formats are also acceptable. Note: Although we require a .pdf file of the manuscript for the review process, this format is not acceptable (neither is .ps) for the final submission. Some additional guidelines must, however, be followed for the submission of the final manuscript in electronic form: • Include all macros (/def) that are required to produce your manuscript (TEX and LATEX). • IEEE Transaction/Journal style dictates a 21-pica (3.5 inch) column width. If mathematical expressions are produced with this in mind, they are more aesthetically pleasing in the final version. • Figures and tables must be submitted as separate files in .ps, .eps, .doc or .tiff format III. Open Access This publication is a hybrid journal, allowing either Traditional manuscript submission or Open Access (author-pays OA) manuscript submission. Upon submission, if you choose to have your manuscript be an Open Access article, you commit to pay the discounted $1,750 OA fee if your manuscript is accepted for publication in order to enable unrestricted public access. If you would like your manuscript to be a Traditional submission, your article will be available to qualified subscribers and purchasers via IEEE Xplore. No OA payment is required for Traditional submission. IV. Page Charges for Traditional Submissions Papers will be reviewed for their technical merit, and decisions to publish will be made independently of an author’s ability to pay page charges. Page charges of $110 (U.S.) per printed page will be requested on papers of seven printed pages or less. Overlength page charges of $200 per page are mandatory for each page in excess of seven pages. This is effective for any paper published after August 1, 2014 onward. If the author’s organization agrees to honor the total page charge, which includes the page charges on the first seven pages plus the mandatory overlength charge, the author will receive 100 reprints. If the supporting organization honors only the mandatory charge, no free reprints will be sent. Digital Object Identifier 10.1109/TMTT.2015.2503943