IEEE Transactions on Antennas and Propagation [volume 58 number 7]

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Citation preview

JULY 2010

VOLUME 58

NUMBER 7

IETPAK

(ISSN 0018-926X)

Editorial .. ......... ......... ........ ......... ......... ........ ..... ..... ......... ........ ......... ......... ........ ......... T. S. Bird

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PAPERS

Antennas Polymer-Carbon Nanotube Sheets for Conformal Load Bearing Antennas ...... ......... ......... ........ ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... .... Y. Zhou, Y. Bayram, F. Du, L. Dai, and J. L. Volakis A Compact Wideband Leaky-Wave Antenna With Etched Slot Elements and Tapered Structure ....... ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ........ ..... J.-W. Wu, C. F. Jou, and C.-J. Wang A Modified Bow-Tie Antenna for Improved Pulse Radiation .... ......... ........ ......... ......... ........ ......... ......... .. .. ........ ......... ......... .. A. A. Lestari, E. Bharata, A. B. Suksmono, A. Kurniawan, A. G. Yarovoy, and L. P. Ligthart A Compact Parallel-Plane Perpendicular-Current Feed for a Modified Equiangular Spiral Antenna .... ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ........ ......... ... T. W. Eubanks and K. Chang A Broadband Folded Printed Quadrifilar Helical Antenna Employing a Novel Compact Planar Feeding Circuit ........ .. .. ........ ......... ......... ........ ......... ......... ........ ......... M. Caillet, M. Clénet, A. Sharaiha, and Y. M. M. Antar Low-Q Electrically Small Spherical Magnetic Dipole Antennas ......... ........ .......... ......... ........ ........ O. S. Kim Modeling, Design and Characterization of a Very Wideband Slot Antenna With Reconfigurable Band Rejection ....... .. .. ........ ......... ......... ........ ......... ......... ........ .... J. Perruisseau-Carrier, P. Pardo-Carrera, and P. Miskovsky Frequency Selective Surfaces and Their Applications for Nimble-Radiation Pattern Antennas .. ........ ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ........ ......... .... M. N. Jazi and T. A. Denidni UWB, Non Dispersive Radiation From the Planarly Fed Leaky Lens Antenna—Part 1: Theory and Design ... .. A. Neto UWB, Non Dispersive Radiation From the Planarly Fed Leaky Lens Antenna—Part II: Demonstrators and Measurements . ......... ........ ......... ......... ........ ......... ......... ........ ........ A. Neto, S. Monni, and F. Nennie Arrays Beamsteering in Pattern Reconfigurable Arrays Using Directional Modulation . ......... .. M. P. Daly and J. T. Bernhard Analysis and Design of -Plane Scanning Grid Arrays . ......... ......... ........ ......... ......... ........ ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ . A. Iturri-Hinojosa, J. I. Martinez-Lopez, and A. E. Martynyuk Reduction of Long Line Effects in Single-Layer Slotted Waveguide Arrays With an Embedded Partially Corporate Feed .. .. ........ ......... ......... ........ ......... ......... ........ .. M. Ando, Y. Tsunemitsu, M. Zhang, J. Hirokawa, and S. Fujii Minimization of MEMS Breakdowns Effects on the Radiation of a MEMS Based Reconfigurable Reflectarray ........ .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ... H. Salti, E. Fourn, R. Gillard, and H. Legay Band Rejection Methods for Planar Log-Periodic Antennas ..... ......... J. R. Mruk, W. N. Kefauver, and D. S. Filipovic

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(Contents Continued on p. 2165)

(Contents Continued from Front Cover) Electromagnetics and Waves A New Method for Locating the Poles of Green’s Functions in a Lossless or Lossy Multilayered Medium ..... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ..... D. X. Wang, E. K. N. Yung, R. S. Chen, and J. Bao Enhancement of Efficiency of Integral Equation Solutions of Antennas by Incorporation of Network Principles—Part I .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ........ ........ A. W. Schreiber and C. M. Butler Coupled Integral Equations for Microwave Induced Elastic Wave in Elastic Media ..... ..... M. S. Tong and W. C. Chew Imaging Balanced Antipodal Vivaldi Antenna With Dielectric Director for Near-Field Microwave Imaging .... ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ..... J. Bourqui, M. Okoniewski, and E. C. Fear 3D Nonlinear Super-Resolution Microwave Inversion Technique Using Time-Domain Data .... ........ ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ........ ....... M. A. Ali and M. M. Moghaddam Microwave Radar-Based Differential Breast Cancer Imaging: Imaging in Homogeneous Breast Phantoms and Low Contrast Scenarios ...... .... ..... .. M. Klemm, J. A. Leendertz, D. Gibbins, I. J. Craddock, A. Preece, and R. Benjamin Complex Materials On the Fundamental Limitations of Artificial Magnetic Materials ........ ........ A. Kabiri, L. Yousefi, and O. M. Ramahi A Compact Printed Antenna With an Embedded Double-Tuned Metamaterial Matching Network ..... ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ...... M. Selvanayagam and G. V. Eleftheriades

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Numerical EFIE Modeling of High-Definition Multiscale Structures ........ ......... ... F. Vipiana, M. A. Francavilla, and G. Vecchi A Comparative Study of Calderón Preconditioners for PMCHWT Equations ... ......... .... S. Yan, J.-M. Jin, and Z. Nie An Efficient Method to Reduce the Numerical Dispersion in the LOD-FDTD Method Based on the (2, 4) Stencil ..... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ........ Q.-F. Liu, W.-Y. Yin, Z. (D.) Chen, and P.-G. Liu Implementation of Collocated Surface Impedance Boundary Conditions in FDTD ...... ......... ........ ....... G. Kobidze

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Wireless A Reconfigurable PIFA Using a Switchable PIN-Diode and a Fine-Tuning Varactor for USPCS/WCDMA/m-WiMAX/ WLAN . ......... ......... ........ ......... ......... ........ ...... J.-H. Lim, G.-T. Back, Y.-I. Ko, C.-W. Song, and T.-Y. Yun High-Gain Dual-Loop Antennas for MIMO Access Points in the 2.4/5.2/5.8 GHz Bands ....... ........ ......... . S.-W. Su Miniaturization of Planar Monopole Antenna for Ultrawideband Radios ........ ... ....... .. M. Sun, Y. P. Zhang, and Y. Lu Magnetic Induction Communications for Wireless Underground Sensor Networks ..... ......... Z. Sun and I. F. Akyildiz

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COMMUNICATIONS

Planar-Monopole-Fed, Surface-Mounted Quasi-TEM Horn Antenna for UWB Systems ........ ........ ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ....... Y. Ranga, A. K. Verma, and K. P. Esselle A Planar, Differential, and Directive Ultrawideband Antenna ... ......... ........ ......... ......... ........ ......... ......... .. .. ........ ....... A. Locatelli, D. Modotto, F. M. Pigozzo, S. Boscolo, C. De Angelis, A.-D. Capobianco, and M. Midrio Bandwidth Enhancement Method for Low Profile E-Shaped Microstrip Patch Antennas ... . Y. Chen, S. Yang, and Z. Nie Frequency-Scaled UWB Inverted-Hat Antenna .. ........ ......... ......... ........ .. J. Zhao, C.-C. Chen, and J. L. Volakis Reinforced Continuous Carbon-Fiber Composites Using Multi-Wall Carbon Nanotubes for Wideband Antenna Applications ... ......... ........ ......... ....... A. Mehdipour, A. -R. Sebak, C. W. Trueman, I. D. Rosca, and S. V. Hoa 325 GHz Single Layer Sub-Millimeter Wave FSS Based Split Slot Ring Linear to Circular Polarization Convertor .... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... .... M. Euler, V. Fusco, R. Cahill, and R. Dickie A Generalized Synthesis Procedure for Low-Profile, Frequency Selective Surfaces With Odd-Order Bandpass Responses ...... ......... ........ ......... .......... ........ ......... ......... ........ ...... N. Behdad and M. A. Al-Joumayly Numerical Analysis of Propagating and Radiating Properties of Hollow Core Photonic Band Gap Fibres for THz Applications ... ......... ........ ......... ......... ........ ......... ......... ........ ......... ........ L. Vincetti and A. Polemi Analysis of Electromagnetic Scattering and Radiation From Finite Microstrip Structures Using an EFIE-PMCHWT Formulation .... ......... ........ ......... ......... ........ ......... ......... ........ ....... W.-J. Zhao, L.-W. Li, and K. Xiao UHF RFID Systems; Their Susceptibility to Backscattered Signals Induced by Electronic Ballast Driven Fluorescent Lamps . ......... ......... ........ ......... ......... ........ ......... ......... ........ ......... ...... G. Ibrahim and A. Plytage Planar Monopole With a Coupling Feed and an Inductive Shorting Strip for LTE/GSM/UMTS Operation in the Mobile Phone .. ......... ......... ........ ......... ......... ........ ......... ......... ........ ......... ....... C.-T. Lee and K.-L. Wong Preconditioning Matrix Interpolation Technique for Fast Analysis of Scattering Over Broad Frequency Band . ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ........ Z. H. Fan, Z. W. Liu, D. Z. Ding, and R. S. Chen

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CORRECTIONS

Corrections to “Radiation Characteristics of Ingestible Wireless Devices in Human Intestine Following Radio Frequency Exposure at 430, 800, 1200, and 2400 MHz” .. ........ ......... ......... ... L. Xu, M. Q.-H. Meng, Y. Chan, and H. Ren

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IEEE ANTENNAS AND PROPAGATION SOCIETY All members of the IEEE are eligible for membership in the Antennas and Propagation Society and will receive on-line access to this TRANSACTIONS through IEEE Xplore upon payment of the annual Society membership fee of $24.00. Print subscriptions to this TRANSACTIONS are available to Society members for an additional fee of $36.00. For information on joining, write to the IEEE at the address below. Member copies of Transactions/Journals are for personal use only. ADMINISTRATIVE COMMITTEE M. ANDO, President R. D. NEVELS, President Elect M. W. SHIELDS, Secretary-Treasurer 2010 2011 2012 2013 P. DE MAAGT A. AKYURTLU *J. T. BERNHARD G. ELEFTHERIADES W. A. DAVIS G. MANARA H. LING P. PATHAK M. OKONIEWSKI *A. F. PETERSON Honorary Life Members: R. C. HANSEN, W. R. STONE *Past President Committee Chairs and Representatives Antenna Measurements (AMTA): S. SCHNEIDER Antennas & Wireless Propagation Letters Editor-in-Chief: G. LAZZI Applied Computational EM Society (ACES): A. F. PETERSON Awards: A. F. PETERSON Awards and Fellows: C. A. BALANIS Chapter Activities: L. C. KEMPEL CCIR: P. MCKENNA Committee on Man and Radiation: G. LAZZI Constitution and Bylaws: O. KILIC Digital Archive Editor-in-Chief: A. Q. MARTIN Distinguished Lecturers: J. C. VARDAXOGLOU Education: D. F. KELLY EAB Continuing Education: S. R. RENGARAJAN Electronic Design Automation Council: M. VOUVAKIS Electronic Publications Editor-in-Chief: S. R. BEST European Representatives: B. ARBESSER-RASTBURG Fellows Nominations Committee: J. L. VOLAKIS

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION Is the leading international engineering journal on the general topics of electromagnetics, antennas and wave propagation. The journal is devoted to antennas, including analysis, design, development, measurement, and testing; radiation, propagation, and the interaction of electromagnetic waves with discrete and continuous media; and applications and systems pertinent to antennas, propagation, and sensing, such as applied optics, millimeter- and sub-millimeter-wave techniques, antenna signal processing and control, radio astronomy, and propagation and radiation aspects of terrestrial and space-based communication, including wireless, mobile, satellite, and telecommunications. Author contributions of relevant full length papers and shorter Communications are welcomed. See inside back cover for Editorial Board.

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Digital Object Identifier 10.1109/TAP.2010.2056574

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 58, NO. 7, JULY 2010

Editorial – Looking Back on the Past Six Years

T

HIS is my last issue as Editor-in-Chief after two terms and six years in the role. I wish to thank the Antennas and Propagation AdCom for the opportunity to serve two terms as Editor-in-Chief. Whilst I will miss the routine work of forming issues and making decisions on papers, it is a good thing that the Antennas and Propagation Society has regular changeover in its Editors. Change is vital as it prevents staleness and presents opportunities for people to serve and use their gifts for the benefit of IEEE and the Society. A new Editor-in-Chief comes with new ideas and a fresh approach and, to this end, I wish to most warmly introduce Michael Jensen as the new Editor-in-Chief. I know that Michael will continue to further enhance the quality of the IEEE Transactions on Antennas and Propagation (TAP) and will prove to be an excellent choice for this role. As this is my final editorial, it provides an opportunity to reflect on some of the achievements and main issues that arose during my term. Over the past six years, much has happened since the previous Editor-in-Chief, Allen Glisson, signed off in August 2004. For instance, the backlog in publication at that time was eliminated early in my first term due to AdCom authorizing an extraordinary expenditure for additional published pages. In addition, IEEE allowed page budgets to be increased and rules were relaxed on over-quota publication. However, another backlog of about two months has been created due to the change this past twelve months to full electronic publication through the new version of ScholarOne (previously called Manuscript Central - this was reported in the May 2010 editorial). But perhaps the three key statistics are as follows. • The number of pages published in 2004 was 3,200 while in 2009 it had increased to 4,200 (in-line with the increase in the annual page budget over time); • The number of papers submitted has increased from 651 in 2003 to 1347 at the end of 2009; and • The time from submission-to-publication has decreased from an average of 20.9 months in 2004 to 13.7 months in 2009. One of the reasons for the significant increase in the number of papers and pages is a consequence of the wireless revolution that is impacting all our lives to which you, the authors and reviewers, have contributed. The term “wireless revolution,” is now used more and more worldwide to describe the replacement of wires or cables for electronic communications and related applications. Wireless is being applied increasingly for consumer products as well as in business and this is transforming the way humans go about their lives. For example, the recent announcement by the FCC regarding the use of frequencies between spectrum channels (such as the unused frequencies in between television broadcast channels) show how far the revolution has advanced and points towards possible future developments. However, it requires significant changes and improvements in deDigital Object Identifier 10.1109/TAP.2010.2053950

vices such as antennas for receiving and transmitting wireless signals in order to take advantages of available “spaces” in the spectrum. The IEEE and the Antennas and Propagation Society in particular have been one of the key instigators of this wireless revolution. Every month throughout the pages of the TAP, we see new developments and improvements brought on by this technological revolution. Consequently, as wireless has been a leading area for many researchers, this has been reflected by the number, and use made, of papers published in the TAP. Some of these statistics were reported in my editorial given in the May 2010 issue. The changes that are taking place will lead to more innovation, which hopefully, will be reported in these pages! The technological change is somewhat akin to the Clinton Administration’s support for the “Information Superhighway” in the 1990s and the use of the Internet for schools and health care. The result was that the research work on IEEE 802.11 and related technology was highly applicable but needed to be readied for a consumer market. The realization of this is only being achieved today. To respond to the increased demand for wireless, much has been achieved by the IEEE TAP over the past six years. Most noticeable for me has been the increased number of submissions, almost double the number from when I started. At the same time, there has been an increased number of downloads of papers published in the TAP. The number of papers published annually is about 500 but is slowly shifting upwards despite the fact that the acceptance rate is now below 50%. Currently, TAP has the second largest number of downloads from IEEE Xplore out of over 13,000 IEEE publications. In 2009, over 220,000 TAP articles in total were downloaded from IEEE Xplore. As a comparative measure of quality of the articles published in journals, the “Impact Factor” is often quoted. Over the past six years, we have seen the Impact Factor of the TAP increase from below 1 for the base year in 2003 to the most recent figure of 2.011 in 2009. On the organizational front, a new version of the manuscript management software was successfully introduced last year. This has enabled the migration from partial to full electronic publication and papers are now no longer mailed to the IEEE. While presently, it takes longer to compile an issue from the submitted papers than the old method, this will improve with time. In addition, there are no shipping charges for authors or the IEEE. Another change is that the TAP website has migrated from the Editor-in-Chief’s host institution computer to the main Antennas and Propagation Society website (www.ieeeaps.org). As can be imagined, I have had to handle a number of challenging matters over the past six years. None was more challenging than the one related to duplicate submission. The types of duplicate submission include partial and even full duplicates of papers submitted to or published by other journals. It is a problem that seems to have exploded in the 2000s and early

0018-926X/$26.00 © 2010 IEEE

EDITORIAL – LOOKING BACK ON THE PAST SIX YEARS

in my first term as Editor-in-Chief I became very concerned about it. I was fortunate that Associate Editors and reviewers provided me with significant feedback over this issue, which is so wasteful of people’s time and effort. In January 2007, an editorial was published in the TAP that detailed the problem and what was required to overcome it. This included an adherence to IEEE policy. In addition, a one year ban was introduced on authors found guilty of this practice. Repeat offenders have been banned from publishing in all IEEE publications for three years. In the first year, I was dealing with one serious case of duplicate submission about every month or so. After the first year the policy was implemented, instances of duplicate submission had decreased to perhaps two cases per year. Currently, the IEEE TAP has a low level of duplicate submission. On a more positive note, what can be expected in the next few years? In 2011, two joint Special Issues are planned with the IEEE Transactions on Microwave Theory and Techniques (T-MTT). These are on MIMO technology, which will appear in these pages, and one on UWB technology will appear in T-MTT. Other possible changes include the external appearance of the TAP and time-to-publication. Some IEEE journals have become more attractive with the addition of a color graphic on the front cover. AdCom has approved a color cover for TAP but this has been held over until the new Editor-in-Chief can assess the desirability of doing this by our readership. Given the larger size of TAP, AdCom has also approved an increased page budget for the coming year to 4,500 pages to ensure we can maintain or reduce the submission-to-publication time currently averaging at about 12 months. The workload on the volunteer Editor-in-Chief of the IEEE TAP has increased significantly since I commenced this role in 2004. This will need to be assessed at some stage; otherwise it may be unattractive for many potential high-profile candidates with other major responsibilities to accept the Editor-in-Chief role. In this regard I have been very fortunate in having a very understanding family and employer in CSIRO. In addition to this support, I would like to record my thanks to the 64 Associate Editors who have served with me over the past six years. The list is too long to mention them individually here but they are listed on the inside back-page of past TAP. It is not an easy task being an Associate Editor with some now handling over 50 new papers per year as well as revisions of papers. For each new paper assigned to them, appropriate reviewers need to be identified and contacted. Some reviewers do not respond and others are too busy to review the paper. When reviews come in, they have to weigh them up and make a recommendation to the Editor-in-Chief. I have encouraged Associate Editors to have their

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own opinion on papers as, frequently, they are experts in this domain. However, I have tried not to allow this to dominate the overall decision from the opinions provided by the reviewers. One of the innovations I have tried as Editor-in-Chief is to encourage the publication of additional issues on topics of special interest to the Society. Starting in 2005, I have endeavored to publish at least two Special Issues per year with the support of Guest Editors to whom I am especially grateful. These issues continue to provide a useful compendium of articles on important topics. Past examples include “Optical and Terahertz Antenna Technology” and “Large and Multiscale Computational Electromagnetics.” I would hope that this practice of publishing Special Issues continues on a regular basis with future Editors-in-Chief. A final Editorial would be out of place not to mention the significant impact of the Editorial Assistant, Dallas R. Rolph. She has taken the brunt of all correspondence from authors, reviewers and readers, as well as readied every issue for publication before I review the final product. In the first five years, the issues were prepared in a paper format (with computer disks) before being boxed and dispatched to the IEEE in Piscataway, NJ. Now, as outlined in the May 2010 Editorial, this is all accomplished using ScholarOne. The preparation time required for an issue, whether in paper or electronic format, is significant. The role of an Editorial Assistant requires dedication and frequent overtime. For all this work, I thank Dallas on behalf of the Society. Another person who requires thanks is Dawn L. Menendez, the IEEE Associate Editor, who is at the other end of the publication pipeline commenced by authors. She receives the final papers and edits them for final publication in IEEE format. Dawn is dedicated and highly motivated in providing an excellent service for the Society and, like Dallas, frequently works extended hours to prepare issues in time for publication. I have been very fortunate indeed in having excellent support from both Dallas and Dawn in making my job a lot easier. In addition, Dawn will continue to serve the new Editor-in-Chief. The assistance of Sonal Parikh, IEEE Publications Help Desk Supervisor, with ScholarOne is also acknowledged On that note, I wish Michael Jensen all the very best in his new role as Editor-in-Chief. Michael served with me as an Associate Editor and, from this association, I am assured that the TAP is in excellent hands for the future. TREVOR S. BIRD, Editor-in-Chief CSIRO ICT Centre Epping, NSW 1710, Australia

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Trevor S. Bird (S’71–M’76–SM’85–F’97) received the B.App.Sc., M.App.Sc., and Ph.D. degrees from the University of Melbourne, Melbourne, Australia, in 1971, 1973, and 1977, respectively. From 1976 to 1978, he was a Postdoctoral Research Fellow at Queen Mary College, University of London, London, U.K., followed by five years as a Lecturer in the Department of Electrical Engineering, James Cook University, North Queensland, Australia. During 1982 and 1983, he was a Consultant at Plessey Radar, U.K. In December 1983, he joined CSIRO, Sydney, NSW, Australia, where he held several positions and is currently Chief Scientist in the ICT Centre and a CSIRO Fellow. He is also an Adjunct Professor at Macquarie University, Sydney, Australia. He has published widely in the areas of antennas, waveguides, electromagnetics, and satellite communication antennas, and holds 12 patents. Dr. Bird is a Fellow of the Australian Academy of Technological and Engineering Sciences, the Institution of Engineering and Technology (IET), London, U.K., and an Honorary Fellow of the Institution of Engineers, Australia. In 1988, 1992, 1995, and 1996, he received the John Madsen Medal of the Institution of Engineers, Australia, for the best paper published annually in the Journal of Electrical and Electronic Engineering, Australia, and in 2001 he was co-recipient of the H. A. Wheeler Applications Prize Paper Award of the IEEE Antennas and Propagation Society. He was awarded a CSIRO Medal in 1990 for the development of an Optus-B satellite spot beam antenna and again in 1998 for the multibeam antenna feed system for the Parkes radio telescope. He received an IEEE Third Millennium Medal in 2000 for outstanding contributions to the IEEE New South Wales Section. Engineering projects that he played a major role in were given awards by the Society of Satellite Professionals International (New York) in 2004, the Engineers Australia in 2001, and the Communications Research Laboratory, Japan, in 2000. In 2003, he was awarded a Centenary Medal for service to Australian society in telecommunications, and also named Professional Engineer of the Year by the Sydney Division of Engineers Australia. His biography is listed in Who’s Who in Australia. He was a Distinguished Lecturer for the IEEE Antennas and Propagation Society from 1997 to 1999, Chair of the New South Wales joint AP/MTT Chapter from 1995 to 1998, and again in 2003, Chairman of the 2000 Asia Pacific Microwave Conference, Member of the New South Wales Section Committee from 1995 to 2005, and was Vice-Chair and Chair of the Section, from 1999 to 2000 and 2001 to 2002, respectively. He was an Associate Editor of the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION from 2001 to 2004, a member of the Administrative Committee of the IEEE Antennas and Propagation Society from 2003 to 2005, and a member of the College of Experts of the Australian Research Council (ARC) from 2006 to 2007. He has been a member of the technical committee of numerous conferences including JINA, ICAP, AP2000, EuCAP, and the URSI Electromagnetic Theory Symposium. He was appointed Editor-in-Chief of the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION in 2004.

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Polymer-Carbon Nanotube Sheets for Conformal Load Bearing Antennas Yijun Zhou, Member, IEEE, Yakup Bayram, Senior Member, IEEE, Feng Du, Liming Dai, and John L. Volakis, Fellow, IEEE

Abstract—We propose a conductive carbon nanotube (CNT) sheet to realize conformal antennas on polymer substrates. Polymer-ceramic composites (rubber-like structures) have good RF (high dielectric constant and low loss tangent) and desirable mechanical properties (conformal, flexible and lightweight). However, there is a challenge in printing metallization circuits on polymer substrates due to their hydrophobic nature. Also, they are associated with low metal-polymer adhesion, causing peeling under stain or tensile stresses. To address these issues, in this paper, we consider the approach of embedding high density vertically-aligned carbon nanotubes within the polymer composite to achieve a CNT sheet having high structural compatibility. We present the fabrication process to achieve high conductivity CNT sheets and construct a sample polymer-CNT patch antenna, yielding a 5.6 dB gain. This is only 0.8 dB lower than that of an ideal patch made of perfect electric conductor (PEC). Strain and tensile tests are also carried out to evaluate electrical performance of the polymer-CNT sheet as it is bent and stretched. Our measurements show that the proposed conductive polymer-CNT sheet is highly flexible and preserves good conductivity under small bending and stretching. The CNT sheet retains acceptable performances even after 100 bending and 13% stretching. The proposed polymer-CNT sheets are well suited for load bearing antenna applications. Index Terms—Carbon nanotube sheet, load bearing antenna, polymer printing, polymer-ceramic composite, stain and tensile stresses.

I. INTRODUCTION ONFORMAL lightweight polymer-based materials are important for load-bearing antennas and multilayer RF front-ends for small aircrafts and body-worn applications. There is also interest for multilayer three-dimensional RF front-end architectures with each layer bearing different functionalities. Such conformal antenna and multilayer circuit structure call for a new class of materials with desirable electrical/RF (low loss,

C

Manuscript received March 27, 2009; revised May 21, 2009; accepted January 31, 2010. Date of publication April 22, 2010; date of current version July 08, 2010. This work was supported in part by the U.S. Air Force Research Laboratory. Y. Zhou was with the ElectroScience Laboratory, Department of Electrical and Computer Engineering, The Ohio State University, Columbus, OH 43212 USA. He is now with Apple Inc., Cupertino, CA 95014 USA (e-mail: [email protected]). Y. Bayram and J. L. Volakis are with the ElectroScience Laboratory, Department of Electrical and Computer Engineering, The Ohio State University, Columbus, OH 43212 USA. F. Du and L. Dai are with the Chemical Engineering Department, Case Western Researve University, Cleveland, OH 44106 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/TAP.2010.2048852

high permittivity), mechanical (flexible, lightweight, strong shear and tensile rating) as well as thermal properties. Among available materials, polymer composites (such as PDMS-D270 and PDMS-MCT composites) are attractive because they are extremely flexible and not as sensitive to large ) temperature variations. They also have low loss ( up to several GHz and controllable dielectric constants (relative ) [1], [2]. Further, as compared to permittivity of other materials such as those based on liquid crystal polymers (LCP) [3] and low temperature co-fired ceramics (LTCC) [4], PDMS composites can be processed at room temperature. Specifically, for bonding LCP and LTCC layers, they must be for LCPs and 1000 for LTCCs) at temperheated (300 atures that could cause failure to some IC components and fragile wire bonds. With these issues in mind, PDMS composites are well suited for conformal load-bearing antennas and RF systems integration. However, metallization or printing on PDMS composites remains a challenge. Specifically, common lift-off lithography methods using metal evaporation does not work well for PDMS due to poor metal-polymer adhesion [5]. Further, interface incompatibilities can easily cause detachment of the printed layers under bending or tensile stress. In this paper, we propose a novel polymer-printing technology utilizing carbon nanotube (CNTs) sheets. Specifically, multiwalled carbon nanotubes (MWNTs) are vertically grown out of the polymer surface in a similar way as body hair, but ) to in much higher density (about 3 form a CNT sheet with nanotube lengths being a few hundred micro-meters. Since the CNTs are embedded into the polymer, they do not peel-off as is the case with metallization typically done via evaporation. More importantly, by controlling the length and density of carbon nanotubes, high surface conductivity is achieved with concurrent mechanical flexibility, high conformality and good structural compatibility. Below, we first describe the equivalent circuit model of the CNT sheet and its fabrication process. Then, a polymer-CNT patch antenna is “printed” and measured as an application example. The flexibility and stability of the polymer-CNT sheet are subsequently evaluated by carrying out strain and tensile tests. At the end of the paper, we also present measurements for two examples of conformal CNT patch antennas on a cylindrical surface. II. CARBON NANOTUBE SHEET PRINTING ON POLYMERS Carbon nanotubes (CNTs) have drawn significant attention in the RF community due to their superior mechanical properties and potential applications to antennas. Specifically,

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Fig. 2. SEM photograph of the CNT array. (a) Cross-section view of the CNT array. (b) Top view of the CNT array.

A. Circuit Model of the Vertically Aligned CNT Sheet

Fig. 1. Illustration of the vertically aligned polymer-CNT sheet (in actual and model form). (a) Printed polymer-CNT patch. (b) Illustrative model of vertically aligned CNTs. (c) Ohm’s law for a single CNT.

metallic CNTs do not oxidize [6] and are not susceptible to moisture [7], [8]. CNTs are also stable at high temperatures up to 700 [6], a desirable characteristic for harsh and high temperature environments. Further, CNTs are attractive in realizing antennas at millimeter wave, even up to optical frequency range [9]–[13]. For example, it has been reported that a single CNT dipole exhibits significantly slower wave velocities ( , where is the speed of light) above the relaxation frequency of around 53 GHz [9], [11]. However, so far, reported antennas have exhibited low radiation efficiencies due to their high resistive loss [9], [11]. This is common for all nano-radius wires including CNTs, which have large intrinsic resistance (around 6 ), viz. too lossy for most microwave applications. However, CNT ensembles or arrays have shown to have improved surface conductivity [14]. For example, nonaligned CNT ensembles have been reported to reduce sheet resistance down to around 20 [15]. However, even this lower resistance is still too high to realize efficient CNT antennas. Alternatively, e-textiles have been pursued to improve sheet conductivity by weaving the nanotubes within cotton fibers [16]. Nevertheless, flexibility and polymer-CNT adhesion under bending stress are compromised with cotton microfibers. In this paper, we propose to grow vertically aligned CNTs in the polymer substrate [Fig. 1(a)]. Using this approach, we aim to address conductivity and CNT printing issues on polymers.

Fig. 1(a) shows a CNT sheet printed on a PDMS composite substrate. Since the CNTs are grown vertically and embedded inside the polymer substrate, the polymer-CNT sheet can be treated as a composite, where the fillers being the carbon nanotubes. The composite’s conductivity is, of course, dependent on the CNT density. In accordance with percolation theory [17]–[19], the conductivity of the polymer-CNT sheet, , is given by (1) where is the CNT volume density, is the percolation threshold density, and is an exponent related to the conductivity. To obtain an explicit expression for the conductivity, we proceed to model the CNT sheet as an array of touching nanowires [Fig. 1(b)]. This simplified model is valid only for high density CNT sheets, and provided the nanotubes are entangled as shown in Fig. 2(b). In this case, the electric current flows perpendicular to the nanotube stems via the vertically touching CNTs. We can calculate the CNT sheet resistance by using the circuit model in Fig. 3. This is a parallel circuit of resistors, each representing the resistance of individual CNTs in perpendicular direction ( ). Referring to Fig. 3, the CNT surface resistance is calculated to be (2) where is a constant related to the CNT density (in essence the number of CNTs). As shown in Fig. 1(c), the resistance along the perpendicular direction can be calculated by adding up the

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Fig. 3. Model of the CNT array for sheet resistance calculation.

resistance of each segment of length , giving

and cross-sectional area

(3)

with having the effective resistivity of a single CNT. By comparison, when the current flows along the tube’s length, the resistance becomes [see Fig. 1(c)] Fig. 4. Process for growing vertically aligned CNTs.

(4) , then , and this is the primary reason Since for the low values, making the proposed CNT arrangement attractive for antennas and RF printing. As predicted by the above simplified CNT model [Fig. 1(b)] and (3), the CNT density and length are two key parameters to achieve high conductivity. High CNT density (or small spacing distance between CNTs) will increase CNT percolation, leading to higher conductivity. As our fabrication limits for the CNT separation distance are around 100 nm, we tried to compress the CNT arrays to reduce spacing distance down to around 20 nm. Doing so, the corresponding resistance was reduced by 50 times. However, the resulting CNT sample was too small for antenna fabrication. Therefore, as a next step, we will carry out larger area fabrication for the compressed ensembles. Increasing CNT length ( ) can also reduce resistance. However, this holds for highly entangled CNT arrays. In practice, the CNT array is less entangled as we increase the length. Therefore, increasing length may not improve conductivity beyond certain point (around ). In the next sections, we focus on the fabrication and characterization of such vertically aligned CNT array. When the nanotubes are about 200 tall and spaced about 100 nm apart, the achieved DC sheet resistance of the sheet is about 1 . This represents a significant decrease as compared to the single CNT dipole [9] or the nonaligned CNT ensemble [15]. B. Carbon Nanotube Sheet Fabrication Process The vertically aligned CNTs are synthesized via a chemical vapor deposition (CVD) process [20] (see Fig. 4). The process is as follows: First we sputter an array of ferrous particles on a silicon wafer to serve as catalysts for CNT growth. Next the silicon substrate is placed inside a tube furnace (Thermolyne 79400) and methane gases ( ) are blown into the furnace via a carrier argon flow. At high temperature (1000 ), methane gases are decomposed into carbon atoms, aligned along the catalyst

Fig. 5. Process for transferring the CNT sheet onto the polymer composites.

particles into cylinder forms. By controlling the furnace temperature (1000 ) and deposition time (2 hours), we can achieve a vertically aligned CNT array on the silicon wafer as shown in Fig. 2. At the 2nd step we transfer the CNT sheet onto the polymer substrate using a two-stage curing process. First a thin PDMS composite layer is spin-coated onto the CNT sheet as displayed in Fig. 5. After curing, the CNTs are implanted inside the thin polymer layer to form a polymer-coated CNT sheet. The polymer-coated CNT sheet is then detached from the silicon

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Fig. 6. Simulation model and fabricated polymer-CNT patch.

wafer by dissolving on the Si surface using hydrofluoric (HF) acid. During this process, we observe a shrinkage of the polymer, further increasing the CNTs density and improving conductivity. In the final (and 3rd) step, we embed the polymer-coated CNT sheet into a larger customized polymer-ceramic substrate for antenna realization. During this curing stage, the polymer-ceramic substrate cross-links with the coated polymer, leading to a strongly bonded CNT sheet on the polymer-ceramic substrate. III. RF AND MECHANICAL PERFORMANCE EVALUATION We now proceed to characterize the RF and mechanical properties of a fabricated CNT antenna. Specifically, a sample polymer-CNT patch antenna was designed and fabricated as shown in Fig. 6. We then measured the CNT-polymer antenna performance and compared it with simulations for a perfectly electric conductor (PEC) patch on a similar substrate. This was followed by strain and tensile tests to examine the flexibility and stability of the CNT sheet under load bearing conditions. An evaluation of CNT patch under conformal installation was also carried out. A. CNT Microstrip Patch Antenna Referring to Fig. 6, we show a 31 mm 31 mm CNT sheet on a 56 mm 56 mm PDMS-MCT substrate, having a dielecand loss tangent of tric constant of at the resonant frequency of 2.25 GHz. The patch was fed by a coaxial probe soldered to the CNT sheet by conductive epoxy. The polymer-CNT patch was then measured on a 150 mm 150 mm ground plane at the Ohio State University-ElectroScience (OSU-ESL) anechoic chamber. The measurement data were then compared with HFSS simulations for perfectly electric conductor (PEC) patch and a finite con). As shown ductivity patch (surface resistivity: 0.9 in Fig. 7, the measured gain (blue solid curve) agrees well with the finite conductivity patch (dashed curve), verifying the low ) of the polymer-CNT sheet. sheet resistivity (0.9 Further, the radiation pattern [Fig. 7(c)] is that of typical patch antenna. More specifically, the measured gain of the CNT patch was 5.6 dB, i.e., only 0.8 dB lower than that of the simulated PEC patch (dotted curve) of the same dimensions and substrate dielectric properties. Indeed this is a very good RF performance for practical applications.

Fig. 7. Measured RF performance of the polymer-CNT patch antenna. (a) Reflection coefficient (S11). (b) Realized gain. (c) E-plane pattern.

B. Strain and Tensile Tests As load bearing antennas are subject to vibration and temperature change, they are usually deformed by bending or stretching. Therefore, it is critical to characterize their electrical properties under strain and tensile stresses. Specifically, it is desirable that the CNT sheet conductivity remains stable as the substrate it bent or stretched. Here, we only measure the CNT sheet DC resistance under different stain and tensile stresses (which is related to the RF performance of the CNT surface). Fig. 8(a) shows the measurement setup for the bending test. As seen, we clamped a sample polymer-CNT sheet at the two ends and exerted an external force using a universal test machine to deform the polymer substrate. The deformation was evaluated by the degree of bent angle ( ). The DC sheet resistance was subsequently measured and recorded as the sample was deforming. Fig. 8(b) gives the measured sheet resistance versus ap-

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Fig. 8. DC sheet resistance versus strain. (a) Measurement setup. (b) DC sheet resistances versus strain.

plied strain. We observed that the DC sheet resistance was fairly . As exstable within a large range of angles up to pected, the resistance decreases when positive strain is applied since the CNTs are pushed towards each other. In contrast, negative strain further separates the CNT “hairs,” leading to higher resistance. Since the rate of decrease/increase in resistance is slow, we expect that RF performance degradation will also be comparatively slow. It is important to characterize the conductivity of the polymer-CNT sheet under stretching condition as well (not just bending). To do so, we employed the setup shown in Fig. 9(a) and measured the DC sheet resistance as the sample was elongated. In this setup, the degree of elongation is defined , where is the original length of the sample and as refers to the length after stretching. Obviously, stretching led to a decrease in the CNTs density, leading to an increase in resistance as depicted in Fig. 9(b). This behavior also agrees with percolation theory that predicts an exponential relationship between conductivity and CNT density. Nevertheless, the sample resistance was fairly stable within 2% of elongation, a typical maximum stretching for most practical applications. In the future, we expect to improve the CNT sheet conductivity under large strain and tensile stresses by sputtering metal nanoparticles on the nanotubes and by inter-dispersing horizontal CNTs into the vertically aligned CNTs. C. Conformal CNT Patch Antennas We examined two conformal CNT patches mounted on a cylinder surface [21]. As shown in Fig. 10, we attached a polymer-CNT patch on a metal cylinder (80 mm in diameter and 160 mm in length). Referring to Fig. 10(a), the patch is bent along the -plane, implying that the current flows along the circumferential direction. Alternatively [see Fig. 10(b)], when

Fig. 9. DC sheet resistance versus tensile stresses. (a) Measurement setup. (b) DC sheet resistances versus tensile stresses.

Fig. 10. Photograph of the cylindrically mounted polymer-CNT patch antennas. (a) E-plane bending. (b) H-plane bending.

the patch is bent in the -plane, the current flows along the axial direction. We remark that bending led to a 13% stretching in this case. Therefore, the -plane resonance frequency was decreased from 2.25 GHz to 1.95 GHz. This frequency shift can be justified by taking into consideration Young’s modulus of the polymer substrate and the geometry of the platform. The measured reflection coefficient and radiation patterns of the conformal CNT patches were identical to the simulated PEC patch on the same cylinder surface. However, we are most interested in the gain performance as stretching changes the CNT patch conductivity. Indeed, as shown in Fig. 11(a), the -plane bent CNT patch had a gain of 1.7 dB at 1.95 GHz, viz. 3 dB lower than that of a simulated PEC patch in the same bent configuration. This is because the CNT surface resistivity was increased since the bending (100 ) and stretching (13% elongation) reduced the nanotube density. The corresponding -plane CNT patch had a larger measured gain of 2.9 dB at 2.25 GHz,

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ACKNOWLEDGMENT Authors are very grateful to P. Ramesh of The Ohio State University Mechanical Engineering Department for his help with mechanical tests. REFERENCES

Fig. 11. Measured broadside gain of the conformal CNT patches mounted on the cylinder shown in Fig. 10. (a) E-plane bending. (b) H-plane bending.

viz. 1.5 dB lower than the simulated PEC patch on the same cylinder [Fig. 11(b)]. This larger gain is due to that the radiating currents flow vertical along the unbent direction of the CNT patch. For most practical applications, the antennas will not be subjected to such large bending or stretching. Therefore, we expect higher antenna radiation gain as the strain and bending will be smaller.

IV. CONCLUSION We presented a flexible, lightweight and conductive polymer-CNT sheet for conformal load bearing antennas and RF circuits. The CNT sheet is realized by growing a high tall and 100 nm apart) to density of aligned CNTs (200 practically form a conducting sheet on the polymer matrix. As the CNTs are implanted within the polymer substrate, the approach leads to structural integrity under stress, strain and bending. In this paper, we described the fabrication process and presented a circuit model to calculate the CNT sheet conductivity. (as comThe measured patch resistivity was only 0.9 reported with other CNT ensembles [15]. pared to 20 A sample polymer-CNT patch antenna was fabricated and measured to exhibit a gain of 5.6 dB, viz. only 0.8 dB less than that of a simulated ideal patch. Mechanical tests were also carried out to demonstrate the flexibility of the polymer-CNT sheets. Further, two conformal CNT patch antennas were fabricated and measured. The latter had an acceptable gain performance for practical applications, making the proposed polymer-CNT sheets suitable for conformal load bearing antennas.

[1] S. Koulouridis, G. Kizitas, Y. Zhou, D. J. Hansford, and J. L. Volakis, “Polymer-ceramic composites for microwave applications: Fabrication and performance assessment,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 12, pp. 4202–4208, Dec. 2006. [2] Y. Zhou, E. Apaydin, S. Koulouridis, Y. Bayram, D. Hansford, and J. L. Volakis, “High conductivity printing on polymer-ceramic composites,” presented at the IEEE APS/URSI Int. Symp., San Diego, CA, Jul. 2008. [3] D. C. Thompson, M. M. Tentzeris, and J. Papapolymerou, “Packaging of MMICs in multilayer LCP substrates,” in Proc. IEEE MWCL, Jul. 2006, vol. 16, pp. 410–412. [4] L. Katehi, W. Chappell, S. Mohammadi, A. Margomenos, and M. Steer, “Heterogeneous wafer-scale circuit architectures,” IEEE Microw. Mag., vol. 8, no. 1, pp. 52–69, Feb. 2007. [5] E. Apaydin, Y. Zhou, D. Hansford, S. Koulouridis, and J. L. Volakis, “Patterned metal printing on pliable composites for RF design,” presented at the IEEE APS/URSI Int. Symp., San Diego, CA, Jul. 2008. [6] L. Dai, Carbon Nanotechnology: Recent Developments in Chemistry, Physics, Materials Science and Device Applications, 1st ed. The Netherlands: Elsevier Science, 2006. [7] V. A. Basiuk, K. Kobayashi, T. Kaneko, Y. Negishi, E. V. Basiuk, and J.-M. Saniger-Blesa, “Irradiation of single-walled carbon nanotubes with high-energy protons,” Nano Lett., vol. 2, no. 7, pp. 789–791, 2002. [8] P. G. Collins and P. Avouris, “Nanotubes for electronics,” Sci. Am., vol. 283, no. 6, pp. 62–69, 2000. [9] G. W. Hanson, “Fundamental transmitting properties of carbon nanotube antennas,” IEEE Trans. Antennas Propag., vol. 53, no. 11, pp. 3426–3435, Nov. 2005. [10] G. Miano and F. Villone, “An integral formulation for the electrodynamics of metallic carbon nanotubes based on a fluid model,” IEEE Trans. Antennas Propag., vol. 54, no. 10, pp. 2713–2724, Oct. 2006. [11] P. J. Burke, S. Li, and Z. Yu, “Quantitative theory of nanowire and nanotube antenna performance,” IEEE Trans. Nanotechnol., vol. 5, no. 4, pp. 314–334, Jul. 2006. [12] J. Hao and G. W. Hanson, “Infrared and optical properties of carbon nanotube dipole antennas,” IEEE Trans. Nanotechnol., vol. 5, no. 6, Nov. 2006. [13] Y. Huang, W.-Y. Yin, and Q. H. Liu, “Performance prediction of carbon nanotube bundle dipole antennas,” IEEE Trans. Nanotechnol., vol. 7, no. 3, Nov. 2008. [14] A. Yin, H. Chik, and J. Xu, “Postgrowth processing of carbon nanotube arrays-enabling new functionalities and applications,” IEEE Trans. Nanotechnol., vol. 3, no. 1, Mar. 2004. [15] L. Wang, R. Zhou, and H. Xin, “Microwave (8–50 GHz) characterization of multiwalled carbon nanotube papers using rectangular waveguides,” IEEE Trans. Microw. Theory Tech., vol. 56, no. 2, pp. 499–506, Feb. 2008. [16] Y. Bayram, Y. Zhou, J. L. Volakis, B.-S. Shim, and N. A. Kotov, “Textile conductors and polymer-ceramic composites for load bearing antennas,” presented at the IEEE APS/URSI Int. Symp., San Diego, CA, Jul. 2008. [17] D. Stauffer and A. Aharony, Introduction to Percolation Theory. London, U.K.: Taylor and Francis, 1992. [18] J. Ma, J. T. W. Yeow, J. C. L. Chow, and R. B. Barnett, “Effect of percolation on electrical conductivity in a carbon nanotube-based filem radiation sensor,” in Proc. IEEE Conf. on Nanotechnology, Aug. 2008, pp. 259–262. [19] A. M. Lepadatu, E. Rusnac, and I. Stavarache, “Percolation phenomena in silicon-based nanocrystalline systems,” in Proc. IEEE Semiconductor Conf., Oct. 2007, vol. 2, pp. 575–578. [20] L. Dai, A. Patil, X. Gong, Z. Guo, L. Liu, Y. Liu, and D. Zhu, “Aligned nanotubes,” ChemPhysChem, vol. 4, pp. 1150–1169, 2003. [21] L. C. Kempel, J. L. Volakis, and R. Sliva, “Radiation by cavity-backed antennas on a circular cylinder,” in Proc. Inst. Elect. Eng.-H, 1995, pp. 233–239.

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Yijun Zhou (S’04–M’07) was born in Shanghai, China. He received the B.S. degree in electrical engineering from Shanghai Jiao Tong University, in 2004, and the M.S. and Ph.D. degrees from the Ohio State University, Columbus, in 2006 and 2009, respectively. He is currently an Antenna Engineer at Apple Inc., working on small antenna design and RF system integration. Besides novel antenna design, his research also includes polymer-ceramic composite development for RF systems and carbon nanotube printing. He holds two U.S. patents on antenna designs. Dr. Zhou is the winner of 2009 URSI student paper competition.

Yakup Bayram (S’01–M’06–SM’09) was born in Trabzon, Turkey, in 1980. He received the B.S. degree in electrical engineering from Bilkent University, Ankara, Turkey, in 2001, the M.S. and Ph.D. degrees in electrical and computer engineering from The Ohio State University, Columbus, in 2004 and 2006, respectively, and MBA degree from Fisher College of Business, The Ohio State University, Columbus, in 2007. He is currently working at the ElectroScience Laboratory, The Ohio State University, as a Senior Research Engineer. He is also the author of the book Computational Methods for High Frequency Electromagnetic Interference. His past research heavily involved EMI/C of electronics. His most recent and current research interests include developing load bearing, flexible, conformal, lightweight antennas and wireless sensor systems for strain and temperature sensing based on surface acoustic wave (SAW) devices. His recent research has also focused on developing SAW devices at sub-micron scale with e-beam lithography.

Feng Du was born in Wuhai, Inner Mogolia, China. He received the B.S. degree in chemistry and the M.S. degree in polymer physics and chemistry from Nankai University, China, in 2003 and 2006, respectively. After one year of research in PPG coating, he began Ph.D. studies on material engineering at the University of Dayton, Dayton, OH. His areas of research focus on the growth of carbon nanotube with controlled lengths onto varying kinds of substrates and he also has strong interests in instrumentation, electrospinning, membrane, electrical chemistry and carbon nanotube dry adhesive applications. In September 2009, he followed his supervisor and began performing research at Case Western Reserve University, Cleveland, OH. Mr. Du was awarded a multi-year Dayton Area Graduate Studies Institute (DAGSI) Fellowship in 2008.

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Liming Dai, received the B.Sc. degree in chemical engineering from Zhejiang University, China, in 1983 and the Ph.D. degree in chemistry from Australian National University in 1990. He accepted a postdoctoral fellowship in physics from the Cavendish Laboratory at the University of Cambridge, Cambridge, U.K., and two years later became a visiting follow in the Department of Materials Science and Engineering, University of Illinois at Urbana-Champaign. He spent 10 years with the Commonwealth Scientific and Industrial Research Organization (CSIRO), Australia, where he built a world-renowned research team in nanomaterials. From March, 2002 to August, 2004, he was an Associate Professor of polymer engineering at the University of Akron, Akron, OH, and from August 2004 to 2009, he was the Wright Brothers Institute Endowed Chair Professor of Nanomaterials at the University of Dayton, Dayton, OH. He joined Case Western Reserve University, Cleveland, OH, in fall 2009 as the Kent Hale Smith Professor of Engineering in the Case School of Engineering. His expertise lies across several fields, including the synthesis, chemical modification and device fabrication of conjugated polymers, fullerene-containing polymers and carbon nanotubes.

John L. Volakis (S’77–M’82–SM’89–F’96) was born on May 13, 1956 in Chios, Greece and immigrated to the U.S.A. in 1973. He received the B.E. degree (summa cum laude) from Youngstown State University, Youngstown, OH, in 1978, and the M.Sc. and Ph.D. degrees from the Ohio State University, Columbus, in 1979 and 1982, respectively. He started his career at Rockwell International (1982–84), now Boeing Phantom Works. In 1984 he was appointed Assistant Professor at the University of Michigan, Ann Arbor, becoming a full Professor in 1994. He also served as the Director of the Radiation Laboratory from 1998 to 2000. Since January 2003, he is the Roy and Lois Chope Chair Professor of Engineering at the Ohio State University, Columbus, and also serves as the Director of the ElectroScience Laboratory. His primary research deals with antennas, computational methods, electromagnetic compatibility and interference, propagation, design optimization, RF materials, multi-physics engineering and bioelectromagnetics. He has published over 280 articles in major refereed journals, nearly 500 conference papers and 20 book chapters. He coauthored the following five books: Approximate Boundary Conditions in Electromagnetics (Inst. Elect. Eng., London, 1995), Finite Element Method for Electromagnetics (IEEE Press, New York, 1998), Frequency Domain Hybrid Finite Element Methods in Electromagnetics (Morgan & Claypool, 2006), Computational Methods for High Frequency Electromagnetic Interference (Verlag, 2009) and edited the Antenna Engineering Handbook (McGraw-Hill, 2007). He has also written several well-edited coursepacks on introductory and advanced numerical methods for electromagnetics, and has delivered short courses on antennas, numerical methods, and frequency selective surfaces. Dr. Volakis was elected Fellow of the IEEE in 1996, and is a member of the URSI Commissions B and E. He received the University of Michigan (UM) College of Engineering Research Excellence award in 1998 and the UM, Department of Electrical Engineering and Computer Science Service Excellence Award in 2001. He is listed by ISI among the top 250 most referenced authors; He graduated/mentored nearly 60 Ph.D. students/post-docs, and coauthored with them 12 best paper awards at conferences. He was the 2004 President of the IEEE Antennas and Propagation Society and served on the AdCom of the IEEE Antennas and Propagation Society from 1995 to 1998. He also served as Associate Editor for the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION from 1988–1992, Radio Science from 1994–97, and for the IEEE Antennas and Propagation Society Magazine (1992–2006). He currently serves as an associate editor for the J. Electromagnetic Waves and Applications and the URSI Bulletin. He chaired the 1993 IEEE Antennas and Propagation Society Symposium and Radio Science Meeting in Ann Arbor, MI., and co-chaired the same Symposium in 2003 at Columbus, Ohio.

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A Compact Wideband Leaky-Wave Antenna With Etched Slot Elements and Tapered Structure Jin-Wei Wu, Christina F. Jou, and Chien-Jen Wang, Senior Member, IEEE

Abstract—A compact wideband leaky-wave antenna (LWA) with etched slot elements and tapered structure is studied. The proposed antenna is composed of an asymmetric-fed multi-section tapered short leaky-wave antenna with two embedded slots and a ground plane with etched slot elements. Base on the concept of LWA, the asymmetric-fed is utilized to excite the first higher order mode. By etching slot elements on the ground plane, the current distribution of this antenna can be influenced to compact the width of conventional LWA. In order to achieve the impedance matching, this multi-section tapered short leaky-wave antenna is embedded with two rectangular slots. This technique not only improves the impedance matching but also suppresses the back lobe. According to the measured results, the impedance bandwidth achieves about 1.30 GHz for 7-dB return loss, which covers the range from 3.30 to 4.60 GHz, and the scanning angle of the measured main beam is about 36 , which covers the range from 17 to 53 . This short LWA is only about 1.14 0 at 3.4 GHz, and the back lobe can be suppressed by 7.5 dB at 4.3 GHz. Due to the etched slot elements on the ground plane, the frequency of the radiation angle is shifted to lower frequency by 750 MHz, which can compact the width of LWA by more than 20%. Index Terms—Back lobe, cutoff frequency, frequency scanning, leaky-wave antennas (LWAs).

I. INTRODUCTION ICROSTRIP leaky-wave antennas (LWAs) have been presented nearly thirty years, the structure of which was proposed in 1979 by Menzel [1] and the theory of which was derived in 1986 by Oliner and Lee [2]. LWAs are usually used in the radar system and the satellite communication because they possess the advantages of narrow beam, frequency-scanning capability, wideband bandwidth, and fabrication simplicity [3], [4]. For enhancing the applications of LWA, the frequency-fixed beam-scanning LWAs are proposed [5], [6]. In [5], the structure of microstrip leaky-wave antenna contained many feeding terminals and control switches which achieved the ability of frequency fixed beam-scanning by switching different feeding terminal. In addition to use of the switch, an active microstrip leaky-wave antenna which derived the dual-beam asymmetrically scanning pattern by the active circuit was designed [6]. Although owning many advantages, LWA is faced with a major problem of large size. As well known, the length and

M

Manuscript received February 18, 2009; revised November 12, 2009; accepted February 01, 2010. Date of publication April 22, 2010; date of current version July 08, 2010. This work was supported in part by the National Science Council, Taiwan, under Grants NSC 97-2221-E009-002 and 96-2221E024-001. J.-W. Wu and C. F. Jou are with the Department of Communication Engineering, National Chiao Tung University, Hsinchu, Taiwan, R.O.C. C.-J. Wang is with the Department of Electrical Engineering, National University of Tainan, Tainan, Taiwan, R.O.C. (e-mail: [email protected]). Digital Object Identifier 10.1109/TAP.2010.2048847

the width of LWA are respectively required about four and half wavelengths to radiate effectively. There are two ways to reduce the antenna size: shortening the length and reducing the width. In general, if the length is shortened, the induced back lobes, which are caused by the reflected power, will be increased. For suppressing the back lobes of short LWA, a radiating element was added at the end of short LWA to radiate the remaining power in [7]. Recently, a method of utilizing two patches with short-circuit edges was designed to couple the radiation power, and then suppressed the back lobe [8]. Excluding short LWA, the techniques of compressing the width have been presented in [9], [10]. The electric-magnetic-electric (EME) microstrip was added in the LWA to affect the first higher order mode, and a half width LWA was designed to compact the width of conventional LWA by the image theory [9]. In this paper, see Fig. 1, we propose a novel method to achieve compact size, wide bandwidth, and low back lobes. This antenna is composed of etched slot elements on the ground plane. Although this method can shift the cutoff frequency to lower frequency in order to reduce the width of conventional LWA, these etched slot elements on the ground plane causes the impedance mismatching. Therefore, we embedded two rectangular slots, Slot-A and Slot-B, on the multi-section tapered short LWA. These two slots can achieve the impedance matching and suppress the back lobe. Detail design rules at and results of the short LWA antenna (only about 1.14 3.4 GHz) demonstrate that the impedance bandwidth can be achieved about 33% at the center frequency of 3.95 GHz for 7-dB return loss. The cutoff frequency of this antenna can be shifted about 750 MHz from 4.15 GHz to 3.40 GHz in order to reduce the width of the LWA by more than 20%. The back lobe can be suppressed by 7.5 dB at 4.3 GHz. The design procedure of the proposed antenna, which includes the ground plane with slot elements and the multi-section tapered short LWA with embedded Slot-A and Slot-B, will be discussed in Section II. Section III will illustrate the simulated and experimental results, which includes the radiation patterns and return loss. Finally, a brief conclusion is given in Section IV. II. PROCEDURE OF LEAKY-WAVE ANTENNA DESIGN Fig. 1 shows the proposed configuration of the compact leaky-wave antenna. The antenna is fabricated on FR4 substrate of 4.4, loss tangent (tan ) of with a dielectric constant 0.024, and thickness (H) of 1.6 mm. The total length of the multi-section tapered short leaky-wave antenna is chosen at 3.4 GHz). In order to achieve to be 10.0 cm (about 1.14 good impedance matching condition, the tapered geometry was derived by changing the antenna shape and observing variations of the return loss. The width and length of each section of the

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Fig. 2. Normalized complex propagation constants of the conventional microstrip LWA. H = 1:6 mm, W = 15 mm, and " = 4:4. k is the free space wave number. Fig. 1. Configuration of the proposed leaky-wave antenna.

TABLE I DIMENSIONS OF THE PROPOSED LEAKY-WAVE ANTENNA

, cutoff frequency, and radiation region can be determined by the width of leaky-wave antenna, dielectric conand of stant, and substrate thickness. The theoretical the conventional microstrip LWA as a function of frequency are plotted in Fig. 2. They are calculated by employing a rigorous (Wiener-Hopf) solution [11] and [12]. The cutoff frequency is about 4.15 GHz, and the radiation region is operated from 4.15 and to 4.9 GHz. In [4] and [13], the normalized constant relate directly to the maximum radiation angle between the broadside direction and the main-beam direction, and the . These relations are given by 3-dB radiation beamwidth (1) (2)

tapered LWA are listed in Table I. Here, we embedded two (Slot-A) and rectangular slots with the sizes of (Slot-B) on the leaky-wave antenna. The etched slot elements are on the ground plane, and the with the size of gap between the slots is D. The dimensions of the geometric parameters are also displayed in Table I. In this section, the design procedures of this antenna, which include the etched slot elements on the ground for reducing width of leaky-wave antenna, and the multi-section tapered short leaky-wave antenna with embedded Slot-A and Slot-B for increasing the impedance bandwidth and suppressing the back lobe, are introduced step by step. A. Compact Leaky-Wave Antenna Generally, the cutoff frequency of a conventional leaky-wave antenna is controlled by the normalized complex propagation constant which includes the normalized phase constant and the normalized attenuation constant , where is the free space wavenumber. See Fig. 2, as the normalized attenuation constant equals the normalized phase constant , the cutoff frequency can be defined. When the normalized phase constant is less than one , which is called , the radiation region can be found. The fast wave

and (3) In (3), when 90% of the radiated power is achieved, the length of will be determined. of infinite length, and Fig. 3(a) compares the theoretical the simulated and measured of finite length (about 1.40 at 4.2 GHz) conventional LWA. The characteristics of the finite length conventional LWA were simulated by Ansoft High Frequency Structure Simulator software. Fig. 3(b) illustrates the of infinite length, and the simulated and meatheoretical of finite length conventional LWA. The values of thesured and are determined in (1)–(3) by the values of oretical and . The theoretical, simulated, and meatheoretical sured radiation angles of convention LWA are respectively about 16 , 22 , and 15 at the cutoff frequency of 4.15 GHz; therefore, it can be seen that the length of LWA does not influence the value and much [see (1)]. However, from Fig. 3(b) we can of see that the 3-dB radiation beamwidth, , of the theoretical calculation of infinite-length LWA, and the simulated and measured results of finite length LWA are respectively about 95 , 43 , and 60 at 4.15 GHz. This result agrees very well with the thesis in [13] that the length of LWA can vary the value of and [see (2) and (3)]. Furthermore, since the cutoff frequency

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1 1

Fig. 3. Comparison of the theoretical, simulated, and measured  and  of a conventional LWA: (a) Radiation angle  ; (b) Radiation beamwidth  .

can be controlled by the width of leaky-wave antenna, the width and of LWA can be reduced by reducing the value of or the cutoff frequency. In order to compact the leaky-wave antenna size, the slot eleare etched on the ground plane ments with the size of of the conventional LWA. This method of etching slot elements on the ground plane can change the current distribution on the ground to reduce the frequency of the first higher order mode. and 3-dB radiation beamwidth Therefore, the radiation angle are also varied. Fig. 4(a)–(c), shows the simulated results of the radiation angle, 3-dB radiation beamwidth, and radiation pattern at 4.2 GHz with different number of slot elements. The slot elements are 0, 4, 7, and 10 elements, respectively. For is the results of Fig. 4(a), we can find that the frequency of strongly dependent on the number of the slot elements. As they are increased to 7 elements, the frequency of 22 radiation angle is decreased from 4.15 to 3.33 GHz. Furthermore, the frequency of 22 radiation angle is converted from 3.33 to 3.25 GHz when the number of the slot elements is increased from 7 to 10. In Fig. 4(b), the characteristic of shifting to lower frequency of is similar to that of the . As the cutoff frequency is the and has been varied; shifted to lower frequency, the therefore, the width of LWA is reduced. From Fig. 4(c), due to

Fig. 4. Simulated radiation angle and 3-dB radiation beamwidth of LWA with etched slot elements: (a) Radiation angle  ; (b) Radiation beamwidth  ; (c) Radiation pattern at 4.2 GHz.

1

a change of the propagation constant, the position of the main beam becomes large as the slot elements are increased. The slot lobe appears for the LWAs with the slots. For conventional LWA, if it is operated at lower frequency, obviously, the width

WU et al.: A COMPACT WIDEBAND LWA WITH ETCHED SLOT ELEMENTS AND TAPERED STRUCTURE

Fig. 6. Simulated radiation patterns of the slot widths, 3.70 GHz.

Fig. 5. Simulated surface current distributions: (a) conventional LWA at 4.2 GHz; (b) LWA with 10 slot elements at 3.3 GHz.

of LWA must be increased. However, using this technique of etched slot elements on the ground plane, the LWA can be operated at lower frequency without increasing the width of LWA. From these simulated results, it can clearly be concluded that the cutoff frequency is decreased about 900 MHz from 4.15 to 3.25 GHz. Therefore, by this technique, we can compact the width of conventional LWA by more than 20%. and are changed because the current distributions The are influenced by etching slot elements on the ground plane. The simulated surface current distributions of the conventional LWA at 4.2 GHz and the LWA with 10 etched slot elements on the ground at 3.3 GHz are illustrated in Fig. 5(a) and (b). Comparing the surface current distributions on the LWA of Fig. 5(a) with that of (b), it can be found that the wavelength on the LWA is different. The wavelength of the LWA with 10 etched slot elements on the ground is less than half of that of the conventional LWA. Since the current distributions of ground plane are affected by the slot elements, which are equivalent to the PMCs (perfect magnetic conductor), the wavelength on the LWA is decreased. of This phenomenon is explained that the fast wave by the conventional LWA is changed to the slow wave etching the slot elements on the ground at 4.2 GHz. The cutoff frequency and the radiation region are shifted to the lower frequency; therefore, the width of LWA is reduced. B. Parameter Study of Etched Slot Elements Due to the coupling effect between the LWA and the slot elements on the ground plane, this antenna can excite dual-beam radiation pattern, which includes the radiations of LWA above

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G , in the YZ-plane at

the substrate and radiation below the ground plane with etched slot elements. Fig. 6 exhibits the simulated normalized radiain the tion patterns by adjusting the width of slot elements YZ-plane at 3.7 GHz as the number and length of the slot elements are respectively 10 and 8 mm. The main beam, the back lobe, and the slot lobe resulted from the injection power, the reflected power at the antenna end, and the power leaked from the slots. Because the slots on the ground plane can be treated as the PMCs, the image equivalent magnetic currents were induced below the plane and excited a side slot lobe in the lower semi-space. It could be observed that the main beam at 45 and the lower slot lobe at 135 are symmetrically radiated. As can be seen from Fig. 6, the radiation angle of the main beam at 3.7 GHz is increased from 20 to 44 as the width is increased from 4 mm to 10 mm. The 3-dB radiation beamwidth of the main lobe and the magnitude of the back lobe above the substrate are slightly affected by the width of slot elements. Nevertheless, this gain of back lobe is almost independent of the width of slot. The slot-lobe below the substrate is radiated because the power of the ground is coupled by the LWA and radiates though the slot; consequently, the size of slot can influence the slot-lobe. In this case, the magnitude oft he slot-lobe is enlarged as the width is increased from 4 mm to 7 mm, and it can be found that the radiation angle is depending on the radiation angle of main lobe. The simulated normalized radiation patterns of 3.7 GHz in the are shown YZ-plane at the different length of slot elements in Fig. 7 as other parameters are fixed. As shown in Fig. 7, the 3-dB radiation beamwidth of the main lobe and the magnitude of the back lobe are respectively narrowed and enlarged by increasing the length of the slot, and it can also be seen that the back lobe is mainly varied by the length of the slot. From the results of Figs. 6 and 7, it can be concluded that the large area of the slots is required when the radiation angle of the main beam increases. The simulated return losses of the conventional LWA and the LWA with 10 slot elements on the ground plane are plotted in Fig. 8. The dimensions of the slot and the distance between the two slot elements are displayed in Table I. The 7-dB impedance

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Fig. 7. Simulated radiation patterns of the slot lengths, 3.70 GHz.

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G , in the YZ-plane at

Fig. 8. Comparison the simulated return losses of conventional LWA and LWA with 10 slot elements on the ground plane.

bandwidth of the conventional LWA is about 1.0 GHz from 4.4 to 5.4 GHz. When slot elements are etched on the ground plane, the initially frequency can be decreased from 4.4 to 3.4 GHz; nonetheless, the impedance mismatched from 3.4 to 4.3 GHz is caused by this method. According to above discussions of etching slot elements on the ground plane, we can conclude that the numbers and the dimensions of these slot elements can reduce the frequency of the radiation angle, control the 3-dB radiation beamwidth, influence the back lobe, and excite the slot-lobe. Although reducing the width of LWA, the slot elements cause the impedance mismatching. C. Increasing Bandwidth and Suppressing Back Lobe In order to achieve the impedance matching, the multi-section tapered leaky-wave antenna is utilized. Because the radiated frequency is determined by the width and length of each section

Fig. 9. Comparison the simulated impedance of the LWA of conventional, tapered, and tapered with Slot-A structure.

of the tapered structure, the impedance and the radiation region can be improved [14]. However, this method of the multi-section tapered short leaky-wave antenna results in serious back lobes. To increase the impedance bandwidth further and reduce is emthe serious back lobe, the Slot-A with the sizes of bedded on this multi-section tapered short LWA to improve the is impedance matching, and the Slot-B with the sizes of utilized to suppress the back lobe. In this analysis here, the parameters of etched slot element on the ground plane are fixed. Fig. 9 describe the simulated impedance of the conventional, tapered, and tapered with Slot-A structure. The dimensions of the multi-section tapered short LWA and Slot-A are listed in Table I. According Fig. 9, we can see that the real part impedance of the conventional short LWA is very low, and the imaginary part of the impedance tends to be inductive. When the LWA is changed from conventional to tapered, the low impedance is increased in the real part impedance, and the phenomenon of the imaginary part impedance which is inductive is lowered. Even though the real and the imaginary part impedance are improved by tapered structure, the impedance matching is not optimum. In order to achieve wideband impedance matching, the Slot-A is embedded on this multi-section tapered short LWA. It can be seen from Fig. 9, the real part impedance is changed to almost 50 , and the imaginary part of the impedance is decreased to approach 0 . The location of Slot A must be designed at the Section I of tapered LWA. If Slot A is designed at the other sections, the impedance matching cannot be achieved. Consequently, this method of the multi-section tapered short LWA with embedded Slot-A can improve the impedance bandwidth. The simulated normalized radiation patterns in the YZ-plane of the tapered short LWA with no slot, that with only Slot-A, and that with both Slot-A and Slot-B embedded at 4.3 GHz are compared in Fig. 10. We can see that the magnitude of the back

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Fig. 10. Comparison the simulated radiation patterns of the multi-section tapered short LWA without slot, that with Slot-A, and that with Slot-A and Slot-B at 4.3 GHz.

lobe of the tapered LWA with no slot embedded is only about 1.4 dB lower than the main beam at 4.3 GHz. It was observed that as the frequency was increased, the magnitude of the back lobe could be even larger than the main beam or even substitute for the main beam. As Slot-A was embedded on this tapered short LWA, the magnitude of back lobe can now be suppressed to about 2.5 dB at 4.3 GHz. Therefore, we can see that although embedding Slot-A can improve the impedance matching, but it still cannot suppress the back lobe effectively. To further suppress the back lobe, Slot-B is embedded on this tapered short LWA (as shown in Fig. 1). The location of Slot B is embedded about one wavelength at 4.3 GHz between Slot A and Slot B to suppress the back lobe. Finally, from the simulated results, we can see the magnitude of the back lobe is successfully suppressed by 5.5 dB.

Fig. 11. Simulated and measured radiation patterns of the proposed LWA in the YZ-plane: (a) simulated patterns; (b) measured patterns.

III. RESULTS From the above discussion of antenna design, etching slot elements on the ground can reduce the frequency of the radiation angle, and the multi-section tapered short leaky-wave antenna with embedded Slot-A and Slot-B can achieve both the impedance matching and suppressing the back lobe. Fig. 11(a) and (b) respectively illustrate the simulated and measured normalized radiation patterns in the YZ-plane of the proposed antenna at 3.4, 4.0, and 4.3 GHz. The measured gain of the back lobe is 7.5 dB lower than the main beam at 4.3 GHz. The measured results of the characteristic of the radiation angle, 3-dB radiation beamwidth, and back lobe, are similar to the simulated results [see Fig. 11(b)]. The scanning angle of the measured main beam is 36 from 17 to 53 as the operating frequency increases from 3.4 to 4.3 GHz. In addition, the measured 3-dB

beamwidth of 46 at 4.3 GHz is larger because the main beam and the slot-lobe are combined to increase the 3-dB beamwidth. Comparing the measured results of the conventional short LWA (in Fig. 3) and the proposed LWA [in Fig. 11(b)], it can be inferred that the cutoff frequency of LWA is decreased about 750 MHz from 4.15 to 3.4 GHz; therefore, the width of conventional short LWA can be reduced by more than 20%. The simulated and measured return losses of the conventional LWA and our proposed LWA are exhibited in Fig. 12. It has good agreement between the simulated and measured results of our proposed LWA. Comparing with the impedance bandwidth of about only 24% for the conventional LWA, the measured 7-dB impedance bandwidth of our proposed LWA reaches about 33% with respect to the center frequency at 3.95 GHz. In addition,

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(b). The gains are larger than 4.8 dBi from 3.4 to 4.4 GHz, and the gain variation is less than 1.6 dB. The maximum efficiency is about 60%, theoretically, and the efficiency of our proposed LWA is higher than that of the conventional LWA. It is shown that utilizing our proposed methods can enhance the efficiency for the short LWA. IV. CONCLUSION

Fig. 12. Comparison the simulated and measured return losses of the conventional LWA and proposed LWA.

In this paper, a novel compact leaky-wave antenna has been presented. The width of LWA was reduced by using the method of etching slot elements on the ground; it thus influenced the current distribution of leaky-wave antenna, reducing the frequency of the radiation angle and influencing the back lobe, and excited the slot-lobe. Furthermore, it causes impedance mismatching. As a result, we tapered this short leaky-wave antenna and embedded Slot-A and Slot-B to achieve both the impedance matching and suppressed the back lobe. With these methods, the 7-dB impedance bandwidth can be achieved from 3.30 to 4.60 GHz. The scanning angle of the measured main beam is 36 from 3.40 to 4.30 GHz. This compact LWA with length of only about 1.14 at 3.4 GHz not only successfully reduces the width of a conventional LWA by more than 20%, but also suppresses the back lobe by 7.5 dB at 4.3 GHz. This compact LWA provides a lot of advantages such as compact size, low cost, and easy fabrication. It is suitable for the scanning systems, such as traffic control and collision avoidance system. ACKNOWLEDGMENT The authors are grateful to thank the National Center for High-performance Computing and the Chip Implementation Center (CIC) of the National Applied Research Laboratories, for supports of simulation software and facilities. REFERENCES

Fig. 13. (a) Measured gain of the proposed LWA; (b) simulated radiation efficiency of the conventional LWA and proposed LWA.

the initially frequency is decreased about 1.12 GHz from 4.42 GHz of the conventional LWA to 3.30 GHz of the proposed LWA. From the measured results, it can be seen that this compact antenna, which is formed by the multi-section tapered short leaky-wave antenna with two slots and a ground plane with ten etched slot elements, not only creates a wideband impedance bandwidth and suppresses the back lobe, but also reduces the width of conventional LWA by 20%. The measured gains and the simulated efficiency of the LWAs are shown in Fig. 13(a) and

[1] W. Menzel, “A new travelling-wave antenna in microstrip,” Archiv. Electrnik, Ubertrag Tech., pp. 137T–T140, Apr. 1979, Band 33. [2] A. A. Oliner and K. S. Lee, “The nature of the leakage from higher modes on microstrip line,” in Int. Microw. Symp. Digest, MTT-S, Jun. 1986, vol. 86, no. 1, pp. 57T–T60. [3] C. Luxey and J. M. Laheurte, “Simple design of dual-beam leakywave antennas in microstrips,” Inst. Elect. Eng. Proc. Microw. Antennas Propag., vol. 144, no. 6, pp. 397T–T402, Dec. 1997. [4] J. L. Gómez-Tornero, A. d. l. T. Martínez, D. C. Rebenaque, M. Gugliemi, and A. Álvarez-Melcón, “Design of tapered leaky-wave antennas in hybrid waveguide-planar technology for millimeter waveband applications,” IEEE Trans. Antennas Propag., vol. 53, no. 8, pp. 2563T–T2577, Aug. 2005. [5] Y. Li and Y. Long, “Frequency-fixed beam-scanning microstrip leakywave antenna with multi-terminals,” Electron. Lett., vol. 42, no. 1, pp. 7T–T8, Jan. 2006. [6] C. J. Wang, Y. H. Sheu, and C. F. Jou, “A dual-beam asymmetrically scanning leaky-wave antenna by utilizing a HEMT resistive upconverter,” IEEE Microw. Wireless Compon. Lett., vol. 11, no. 12, pp. 492T–494T, Dec. 2001. [7] C. J. Wang, H. L. Guan, and C. F. Jou, “Two-dimensional scanning leaky-wave antenna by utilizing the phased array,” IEEE Microw. Wireless Compon. Lett., vol. 12, no. 8, pp. 311–313, Aug. 2002. [8] Y. X. Li, Q. Xue, E. K. N. Yung, and Y. L. Long, “Radiation patterns of microstrip leaky-wave antenna with parasitic elements,” Microw. Opt. Technol. Lett., vol. 50, no. 6, pp. 1565–1567, Jun. 2008. [9] C. K. Wu, Y. C. Chen, and C. K. C. Tzuang, “Compressed-width leaky EH mode PBG antenna,” IEEE Microw. Wireless Compon. Lett., vol. 13, no. 8, pp. 343T–344T, Aug. 2003. [10] G. M. Zelinski, G. A. Thiele, M. L. Hastriter, M. J. Havrilla, and A. J. Terzuoli, “Half width leaky wave antennas,” IET Microw. Antennas Propag, vol. 1, no. 2, pp. 341–348, Apr. 2007.

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[11] A. A. Oliner and K. S. Lee, “Microstrip leaky wave strip antennas,” in IEEE AP-S Int. Symp. Dig., Philadelphia, PA, Jun. 1986, pp. 443–446. [12] D. C. Chang and E. F. Kuester, “Total and partial reflection from the end of a parallel-plate waveguide with an extended dielectric loading,” Radio Sci., vol. 16, pp. 1–13, Jan.-Feb. 1981. [13] P. Lampariello, F. Frezza, H. Shigesawa, M. Tsuji, and A. A. Oliner, “A versatile leaky-wave antenna based on stub-loaded rectangular waveguide: Part IT-theory,” IEEE Trans. Antennas Propag., vol. 46, no. 7, pp. 1032T–T1041, Jul. 1998. [14] W. Hong, T. L. Chen, C. Y. Chang, J. W. Sheen, and Y. D. Lin, “Broadband tapered microstrip leaky-wave antenna,” IEEE Trans. Antennas Propag., vol. 51, no. 8, pp. 1922T–T1928, Aug. 2003.

Jin-Wei Wu was born in Tainan, Taiwan, R.O.C., in 1982. He received the B.S. and M.S. degree in electrical engineering from Feng-Chia University, Taichung, Taiwan, in 2004 and 2006, respectively, and the Ph.D. degree in communication engineering from the National Chiao-Tung University, Hsinchu, Taiwan, R.O.C., in 2009. In 2009, he joined Compal Communications, Inc., Taipei, Taiwan, as a Senior Engineer, where he developed built-in antennas for handsets. His research interests include design of microstrip filters and antennas.

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Christina F. Jou was born in Taipei, Taiwan, R.O.C., in 1957. She received the B.S., M.S., and Ph.D. degrees in electrical engineering from the University of California, Los Angeles, in 1980, 1982, 1987, respectively. The subject of her doctoral thesis was the millimeter wave monolithic Schottky diode-grid frequency doubler. From 1987 to 1990, she worked at Hughes Aircraft Company, Torrance, CA, as a Member of the Technical Staff in the Microwave Products Division, where she was responsible for microwave device modeling. In 1990, she joined National Chiao-Tung University, Hsinchu, Taiwan, R.O.C., where she is now an Associate Professor of communication engineering. Her current research is in developing RF and microwave active circuits and MEMS antennas, and filters.

Chien-Jen Wang (M’00–SM’06) was born in Kaohsiung, Taiwan, in 1971. He received the B.S. degree in electrical engineering from the National Sun-Yet-Sen University, Kaohsiung, Taiwan, in 1993 and the Ph.D. degree from the National Chiao-Tung University, Hsinchu, Taiwan, R.O.C., in 2000. In 2000, he joined the Wireless Communication BU, BenQ Corporation, Taipei, Taiwan, as a Project Researcher, where he developed built-in antennas for handsets. In 2001, he joined the Department of Electrical Engineering, Feng-Chia University, Taichung, Taiwan, as an Assistant Professor and, in 2004, an Associate Professor. In 2006, he joined the Department of Electrical Engineering, National University of Tainan, Tainan, Taiwan, as an Associate Professor where, in 2009, he became a Professor. His research activities involve the design and applications of RF/microwave circuits, antennas, and wireless communication systems.

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A Modified Bow-Tie Antenna for Improved Pulse Radiation Andrian Andaya Lestari, Member, IEEE, Endon Bharata, Andriyan Bayu Suksmono, Senior Member, IEEE, Adit Kurniawan, Alexander G. Yarovoy, Senior Member, IEEE, and Leo P. Ligthart, Fellow, IEEE

Abstract—The analysis, design, and realization of a modified bow-tie antenna optimized for impulse ground penetrating radar (GPR) applications is described. The proposed antenna shows improved properties important for GPR, which include its compact size (in comparison with a conventional bow-tie antenna) and ability to radiate UWB pulses with increased amplitude and very small late-time ringing. A substantial increase in the amplitude of the transmitted pulse is achieved by utilizing radiation from discontinuities introduced by the resistive loading employed in the antenna to suppress late-time ringing. By choosing an optimal distance between the antenna’s feed point and the location of the resistive loading, radiations that occur from the antenna’s feed point and the mentioned discontinuities at the resistive loading will combine constructively in the boreside direction of the antenna. As a result, one will observe a substantial increase of the amplitude of the transmitted pulse in the boreside direction. Furthermore, an analytical expression describing approximate time-harmonic current distribution is derived to indicate an optimal resistive loading profile for the proposed antenna. Additionally, the traveling-wave current distribution of the antenna is theoretically analyzed to examine the applicability of the obtained time-harmonic expression for pulse excitation. It has been found that when the antenna is resistively loaded both the time-harmonic and traveling-wave currents decay to approach nearly the same value at the end section of the antenna. As the amount of current at the antenna ends corresponds to the level of reflection which occurs there, the derived expression is found to be useful to indicate an optimal loading profile for the proposed antenna. A theoretical model of the proposed antenna has been developed to perform numerical analysis using a modified NEC-2 code. In addition, an experimental verification has been carried out and both the simulation and experiment confirmed the improved properties of the proposed antenna. Index Terms—Bow-tie antenna, ground penetrating radar (GPR), resistive loading, ultrawideband (UWB) antenna.

I. INTRODUCTION

T

HE wideband nature of bow-tie antennas has always been very attractive for implementation in a wide range of applications. The wideband characteristic of bow-tie antennas was Manuscript received April 12, 2009; revised December 21, 2009; accepted January 25, 2010. Date of publicationApril 22, 2010; date of current version July 08, 2010. This work was supported in part by the International Research Centre for Telecommunications and Radar (IRCTR)—Delft University of Technology, The Netherlands, and Radar & Communication Systems (RCS), Indonesia. A. A. Lestari is with the International Research Centre for Telecom and Radar (IRCTR), Bandung Institute of Technology, Bandung 40132, Indonesia, and also with IRCTR, Delft University of Technology, 2628 CD Delft, The Netherlands (e-mail: [email protected]). E. Bharata, A. B. Suksmono, and A. Kurniawan are with the International Research Centre for Telecom and Radar (IRCTR), Bandung Institute of Technology, Bandung 40132, Indonesia. A. G. Yarovoy and L. P. Ligthart are with the International Research Centre for Telecom and Radar (IRCTR), Delft University of Technology, 2628 CD Delft, The Netherlands. Digital Object Identifier 10.1109/TAP.2010.2048853

already reported in the past by many investigators including Brown and Woodward who carried out an experimental investigation of bow-tie antennas [1], Carrel who was the first to show analytically that the bandwidth of a bow-tie antenna depends on the bow-tie flare angle [2], Lambert et al. [3] and Lee and Smith [4] who improved Carrel’s analytical solution, and Shlager et al. [5] and Leat et al. [6] who developed a numerical model for a bow-tie antenna. In the last couple of decades bow-tie antennas have been introduced in many ultrawideband (UWB) applications for which their bandwidth was enlarged by means of various loading schemes, which include resistive loading [5], reactive loading [7], and combination of those [8]. Ground penetrating radar (GPR) is one of the applications in which resistively-loaded bow-tie antennas are frequently used due to their relatively simple and practical geometry and their ability to transmit UWB transient pulses properly. The antenna proposed in this paper is aimed mainly at this application. For impulse GPR it is generally required that the antenna have sufficiently large bandwidth and a constant phase center. The former is needed to allow transmission of UWB transient pulses with suppressed late-time ringing to avoid masking of targets while the latter is needed to avoid widening of the pulse over time. Late-time ringing is caused by internal reflections in the antenna due to insufficient antenna bandwidth. With respect to this, resistive loading has always been the most popular loading scheme for enlarging antenna bandwidth due to its simplicity. Several types of resistive load commonly applied on GPR antennas include resistive sheets [5], lumped resistors [9], and foam-based absorbers [8], which have been found effective to enlarge antenna bandwidth for suppressing late-time ringing. However, substantial decrease of antenna efficiency is the price that has to be paid when using purely resistive loading. It has been indicated that in this case antenna radiation efficiency might drop to as low as 30% as a large portion of the energy supplied to the antenna is dissipated by the resistive load [10]. To minimize such a great loss in radiation efficiency, non-dissipative loading, i.e., reactive (capacitive or inductive) loading, has been introduced [11], [12]. Unfortunately such reactive loading, usually realized as gaps or slots in the antenna, if not combined with any form of resistive load would not be suitable for impulse GPR applications since it usually exhibits a significant level of late-time ringing which might seriously degrade the GPR performance [10], [12]. Such late-time ringing is most likely the result of distributed discontinuities introduced by the gaps or the slots. In view of the abovementioned problem, in this paper we introduce a modified resistively-loaded bow-tie antenna which has been optimized for an impulse GPR application. The proposed antenna has been designed to enable trans-

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mission of UWB pulses with higher radiation efficiency and lower level of late-time ringing in comparison with other resistively-loaded planar antennas of a comparable or even larger size. This has been achieved by using the principle introduced in [8] in which secondary radiation originating from discontinuities in the antenna is utilized to increase the amplitude of the radiated pulse. Furthermore, in this paper an analytical expression describing approximate time-harmonic current distribution is derived to indicate an optimal resistive loading profile for the proposed antenna. Additionally, the traveling-wave current distribution of the antenna is theoretically analyzed to examine the validity of the obtained time-harmonic expression. This paper is organized as follows. In Section II we describe the design of the proposed antenna. In Section III we derive the analytical expression for approximate time-harmonic current distribution of the proposed antenna. In Section IV we describe the numerical model to evaluate the antenna design with the selected loading profile. Finally, an experimental verification of the antenna design is reported in Section V. This paper is closed with the conclusions presented in Section VI. II. ANTENNA DESIGN The main objectives of the antenna design reported in this paper are as follows. • We wish to design a UWB antenna for transmission of short monocycle pulses with duration of 0.8 ns (central frequency of app. 1 GHz) for a high-resolution GPR. The waveform and spectrum of the pulse measured directly from the GPR system employed in this work are plotted in Fig. 1. • The antenna should have relatively high radiation efficiency and suppressed late-time ringing to improve the GPR performance. • The design should be adequately simple, practical and compact for implementation of the antenna in a commercially-available GPR system. In this work the proposed design is based on a bow-tie antenna. Resistively-loaded planar (dipole) antennas including bow-tie antennas are very attractive and widely used for commercial GPR systems as their planar geometry allows simple implementation in the GPR and ease of operation. Furthermore, the antenna’s casing can be designed to become a shield (to minimize TX-RX antenna coupling and interference) and a reflector (to maximize radiation into the subsurface), and as a result one obtains a practical and cost-effective directive antenna satisfactory for most of commercial GPR systems. Improved directive UWB antennas such as dielectric-filled TEM horn, Vivaldi, and tapered slot antennas are usually less attractive for commercial GPR systems as they tend to be more expensive, more complex in implementation and bulky in shape, especially when shielding is required. Traditionally, GPR makes use of bow-tie antennas loaded with resistive coating, which, as mentioned above, is handicapped with a substantial drop of radiation efficiency. To improve radiation efficiency when using resistive loading for pulse radiation, in this work we apply the method introduced in [8]. By this method, two main sources of radiation are created in

Fig. 1. Monocycle with 0.8 ns duration employed as the exciting pulse: (a) waveform, (b) spectrum.

the antenna, i.e., the main source located at the antenna’s feed point and the secondary source at an artificial discontinuity in the antenna. In this work the antenna is designed to have a secondary source of radiation at the discontinuity in the antenna introduced by the employed resistive loading. The radiation from the secondary source is then utilized to strengthen pulse radiation in the boreside direction, which can be achieved when the distance from the main source (i.e., the feed point) to the secondary source (i.e., the discontinuity caused by the resistive loading) is chosen to be [8] (1) where is the speed of light, is the central frequency of the is the effective relative permittivity of exciting pulse, and the employed substrate (in case of a printed antenna). When (1) is satisfied, radiation from the discontinuity will combine constructively with radiation form the feed point, resulting in a maximum increase in the amplitude of the pulse transmitted in the boreside direction of the antenna. A discontinuity in the antenna can occur as a result of abrupt changes in the antenna geometry (e.g., bends, slots, gaps, etc.) or material (e.g., dielectric, substrate, loading, etc.). Here we attempt to maximize the secondary radiation by designing an abrupt change in both the antenna geometry and material to occur at the same locations.

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Fig. 2. Geometry of a wire bow-tie antenna with 25 cm wires on each arm and 10 angular separation between the neighboring wires [13].

Fig. 3. Geometry of the proposed antenna for realization on FR4: the flare angle of the radiating section is 120 ; angular separation between the neighboring wires in the radiating section is 10 ; distance between the feed point and the bends/loading section is 4 cm; total length and width of the antenna is 23 cm and 7 cm, respectively. The gaps are the locations of chip resistors.

In this way we may expect to further increase the amplitude of the pulse transmitted by the antenna in the boreside direction. Furthermore, in this work we approximate a bow-tie antenna by a wire structure shown in Fig. 2, as suggested in [13]. It has been indicated that such a wire structure is a good approximation for a solid bow-tie antenna with respect to its radiation characteristics [14] and moreover allows simple implementation of resistive loading using lumped resistors when the antenna is realized as a printed antenna on a dielectric substrate. Keeping the abovementioned aspects in mind, the wire bow-tie structure reported in [13] is here modified by bending the wires at a distance of from the feed point according to (1), leading to a geometry shown in Fig. 3. As can be seen, it results in a much more compact geometry which is more amenable to practical implementation in comparison with the original geometry shown in Fig. 2. One may define two different sections in the geometry of the proposed antenna shown in Fig. 3, namely the radiating and the loading sections, which play an important role in the radiation mechanism of the antenna. The former occupies the area which spans from the bends on the right arm to those on the left arm of the antenna. In this part radiation occurs mainly from the primary and the secondary sources, i.e., the feed point and the bends, respectively. Using (1) and assuming the antenna is re, for the exciting pulse in Fig. 1, the alized on FR4 of the radiating section is found to be around 4 cm. length The latter is located between the bends and the wire ends on each arm of the antenna. This part is occupied by resistive loads in the form of lumped resistors mounted across the gaps seen in Fig. 3. It is obvious that such a wire structure simplifies implementation of resistive loading by using lumped resistors. More importantly, it allows one to easily apply any loading profile in the antenna by selection of the resistor’s values. Furthermore, we notice that the discontinuity in the antenna is contributed by the first resistors (those are the resistors nearest to the feed point)

and the wire bends. Therefore, as they are located at the same location we may expect maximum secondary radiation to occur from the discontinuities which would contribute to maximum radiation in the boreside direction of the antenna. It has been demonstrated that the input impedance of a bowtie antenna depends on the flare angle [1]–[4]. Accordingly, the flare angle in the radiating section will give a large contribution to the input impedance of the proposed antenna. Another factor that will contribute to the antenna’s input impedance is the use a dielectric substrate on which the antenna is constructed. One should take it into account when designing the antenna to have a certain value of input impedance since the presence of a dielectric material at the feed point might significantly decrease the antenna’s input impedance. In the case of FR4, it is shown in [14] that the input impedance drops by around 50 . In this work the antenna is designed to exhibit input in the spectrum of the exciting impedance of around 100 pulse in order to match the antenna to the 100-Ohm twin semi-rigid (TSR) line employed as the feed system for the antenna. A feed system using a TSR line has been introduced to feed a balanced antenna without balun [15], [16]. The TSR line employed here comprises two identical 50-Ohm semi-rigid coaxial lines soldered together along their length, resulting in a balanced transmission line with 100-Ohm characteristic impedance. To obtain a match termination of the TSR line, the proposed antenna should therefore have input impedance of 100 within the spectrum of the exciting pulse. Accounting for the aforementioned 50 drop of input impedance caused by FR4, the antenna (without substrate) is designed to exhibit in free space. Using an input impedance of around 150 Carrel’s expressions [2] one can easily calculate that in this case the radiating section of the antenna should have a flare angle of 120 . It is shown in Fig. 3 that the 120 flare angle in the radiating section is realized by 13 wires with angular separation of 10 between the neighboring wires. Moreover, to make the antenna relatively compact, we require that the length of the loading section be smaller than 2 times the length of the radiating section. Thus, for the geometry in Fig. 3 and cm the maximum length of the outermost wires in the loading section is around 9 cm. We note that for such a small antenna the ideal Wu-King loading profile [17] will not work properly with lumped resistors since the sharp increase of the loading values at the end section of the Wu-King profile cannot be approximated appropriately only by a small number of resistors. Therefore, we should find an alternative loading profile that would work effectively for the proposed antenna. For simplicity we shall apply a linear loading profile and our objective is to find the optimal rate of increase of the loading values along the antenna from the feed point towards the antenna end. III. ANALYTICAL EXPRESSION FOR APPROXIMATE CURRENT DISTRIBUTION As resistive loading using a series of lumped resistors will be applied in the proposed antenna, it is advisable to find an expression for the current distribution along the antenna which allows one to determine the optimal loading profile of the resistors. To this end, for simplicity we first assume a wire (cylindrical) dipole and we wish to find an expression for the current

LESTARI et al.: A MODIFIED BOW-TIE ANTENNA FOR IMPROVED PULSE RADIATION

distribution along the dipole. As mentioned above, here we consider a loading profile in which the resistive loading increases linearly towards the antenna end. The loading will be applied to the dipole, which is chosen to be aligned with the -axis with its feed point at the origin in Cartesian coordinates. The dipole is assumed to be loaded along its length with lumped resistive elements in series. The separation between adjacent elements is assumed to be sufficiently small in terms of wavelength. In this case the loading is expressed in impedance per unit length given by

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where (10) Except at the feed point ential equation

the current must satisfy differ-

(11) The solution to (11) can be written as

(2) where is the rate of increase of the resistance (in Ohms/meter) and is the position along the antenna. When a dipole with length and wire radius is fed at by a delta-function generator with EMF (electromotive force) [Volts], assuming the positive time dependence the axial component of the vector potential on the surface of the antenna satisfies the wave equation [17]

(12) and are the constants to be determined by where boundary conditions, and Ai and Bi are the Airy functions. at the wire end, Imposing the boundary conditions we can express (12) as (13)

(3) where where is the wave number in the free space, is the total is the Dirac delta function, and axial current in the antenna, the vector potential is given by

(14) (15)

(4) Since (13) holds for a single wire dipole, the maximum value of the resistor located at the end of the loading section can be approximated by

with (5)

(16) in which (6) where is the source coordinate and is the wire radius. It has been indicated in [17] that the ratio of vector potential to current along the antenna is approximately constant and thus one may write (7) is the expansion parameter at the maximum of current and approximated by , which has also been used for dipoles with purely capacitive loading in [11]. Hence, (3) may be written as

where

(8) where is the intrinsic impedance of the free space. Inserting (2) in (8) leads to (9)

is the number of wires in the loading section. where The selected loading profile determines the amount of current at the end section of the antenna, which in turn determines the level of reflections occurring at the antenna end. For pulse excitation, the time-domain response of the antenna generally consists of a main pulse transmitted directly from the feed point and late-time ringing transmitted mainly from the antenna end as a result of the abovementioned reflections. The level of the late-time ringing corresponds to the amount of current at the end section of the antenna due to the selected loading profile. Therefore, one can find an optimal loading profile which gives the desired level of late-time ringing by adjusting the loading profile to give the same level of current at the end section of the antenna. dB below the peak of the A level of late-time ringing of main pulse should be adequate for most of GPR applications [14]. Accordingly, we prescribe the level of current at the end dB below its maximum value section of the antenna to be at the feed point, for which a suitable loading profile is needed. For the proposed antenna (13) shows that when the last resistor is chosen to be 10 k , it will result in a maximum level of dB at the end section of the antenna within the current of dB level of the spectrum of the exciting 0.8 ns monocycle

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Fig. 4. Current distributions along the proposed antenna due to the linear k according to (13) for the lower dB limit, loading profile for R central frequency, and upper dB limit of the spectrum of the exciting pulse in Fig. 1.

= 10

03

03

Fig. 6. Computed transmit waveforms of the proposed antenna, a conventional (wire) bow-tie antenna with 120 flare angle and 50 cm length, and a dipole of 50 cm length, excited by the monocycle in Fig. 1 with 1 Volt peak-to-peak amplitude. The loading profile indicated in Fig. 4 is applied. The observation point is located in the boreside direction at a distance of 1 m.

in which the time-harmonic distributions are given at the lower dB limit of the spectrum of the exciting pulse. It is shown that both the time-harmonic and traveling-wave distributions indicate more or less the same amount of the remaining current at the end section of the antenna. IV. NUMERICAL MODEL

Fig. 5. Time-harmonic and traveling-wave current distributions along the proposed antenna (without substrate) for different values of R . The time-harmonic distributions are plotted at the lower dB limit of the spectrum of the exciting pulse (420 MHz).

03

shown in Fig. 1(b). The resulting current distributions along the dB limit (420 antenna are plotted in Fig. 4 for the lower dB limit MHz), central frequency (1 GHz), and the upper (1.67 GHz) of the spectrum. It can be seen that the level of curdB level of rent at the end section of the antenna within the dB as prescribed. the spectrum is lower than We notice that (13) holds true for time-harmonic (sinusoidal) excitation of the antenna. To examine the applicability of (13) for pulse/transient excitation we also compute the antenna’s traveling-wave current distribution using the theoretical model described in Section IV for different values of . To this end, pulse excitation using the 0.8 ns monocycle in Fig. 1 is assumed and we compute the amplitude of the pulse as it travels along the antenna. In Fig. 5 we plot the time-harmonic current distribution given by (13) and the computed traveling-wave current distribution for different values of , i.e., 500 , 1 k , and 10 k ,

The proposed antenna with the geometry given in Fig. 3 and the loading profile indicated in Fig. 4 is modeled as a wire structure in free space and analyzed numerically using the NEC-2 code [18] which has been modified to enable time-domain analysis [14]. The wires are assumed to have a diameter of 0.5 mm in order to obtain a comparable current distribution on a strip is satisfied, where of 1 mm width when the relation is the wire diameter and is the strip width [19]. Since we are dealing with a thin wire/strip problem and thus currents along the wires/strips have negligible radial components, the influence of substrate may be neglected in the aforementioned relation. Furthermore, as no substrate is assumed in the wire model, the longer than the length in Fig. 3 to antenna length is made account for the FR4 material used in the antenna realization. The computed transmit waveforms of the antenna with and without the loading are presented in Fig. 6. It can be seen that the application of the loading effectively suppresses the reflection at the antenna end and the following late-time ringing. The level of the ringing with respect to the peak of the main pulse is found to be dB after less than 3 times the pulse duration. lower than Moreover, it significantly increases the amplitude of the pulse by a factor of 1.6. For comparison, the transmit waveforms of a conventional wire bow-tie antenna similar to the one shown in Fig. 2 are computed. The conventional wire bow tie has a flare angle of 120 and a length of 50 cm. The 50 cm length is chosen to have a clear separation in time between the main pulse and end reflection for excitation with the 0.8 ns monocycle. It is important because the main pulse of the conventional bow tie is used in this work as

LESTARI et al.: A MODIFIED BOW-TIE ANTENNA FOR IMPROVED PULSE RADIATION

Fig. 7. Computed input impedance of the proposed antenna.

a benchmark for comparison purposes and therefore it should not be spoiled by the reflection from the antenna end. The traditional loading technique (e.g., resistive coating) attempts at completely suppressing the end reflection and transmitting the main pulse as much as possible for which the end reflection can be suppressed more easily in practice when they are adequately separated from the main pulse. The proposed method makes use of a different approach in which the end reflection is not completely suppressed but partly utilized to enhance the antenna radiation. It is therefore advisable to perform a comparison between the traditional and the proposed loading technique. The computed transmit waveform of the conventional bow-tie antenna is plotted in Fig. 6 where can be seen that the end reflection is clearly separated from the main pulse. The result shows that the peak-to-peak amplitude of the pulse transmitted by the proposed antenna in the boreside direction is around 30% higher than that by the conventional bow tie, indicating the improved characteristic for pulse radiation. Furthermore, when the proposed loading technique is applied to the conventional bow tie, we observe an increase of the peak-to-peak amplitude only by around 20%. This increase is smaller than that of the proposed antenna since in this case there is no contribution from wire bends. Moreover, it is also shown in Fig. 6 that due to the absence of wire bends the peak-to-peak amplitude of the loaded conventional bow tie is approximately 10% smaller than that of the proposed antenna. This concludes that the bends contribute to only 10% of the secondary radiation, while the rest 90% is caused by the discontinuity due to the first resistors. In addition, the result for a dipole of 50 cm length is also presented for inspection. The computed input impedance of the proposed antenna is given in Fig. 7 where can be seen that all high-Q resonances are suppressed and the resistance goes asymptotically to a value slightly below the value of 150 expected by the design. The realization of the antenna as a wire structure might contribute to the slight discrepancy in the predicted input impedance as Carrel’s expressions [2] used to determine the antenna’s flare angle are only valid for solid bow-tie structures. To improve the result, one should develop a new expression which is valid for

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Fig. 8. Computed time-domain radiation pattern of the proposed antenna for excitation with the monocycle in Fig. 1 at a distance of 1 m from the antenna.

a wire bow-tie structure. Furthermore, for pulse transmission it is advisable to introduce the average impedance given by [20] (17) where is the normalized spectrum of the exciting pulse, is the input impedance of the antenna and and are the upper and lower limit of the spectrum of the pulse, respectively. is useful to obtain the input reflection at the feed point of an antenna excited with transient pulses. It was demonstrated in [20] over the range that for this purpose one may assume . Thus, using (17), the dB upper and lower limits of the spectrum of the exciting 0.8 ns monocycle (respectively 1.67 GHz and 420 MHz), and the mentioned assumption, for the wire model of the proposed anwe obtain tenna. This result shows a nearly match termination with the 100-Ohm TSR feed line. However, we note that as the model does not include any dielectric substrate, we may expect to see a smaller value of the average input impedance when realizing the antenna on a dielectric material. Additionally, Fig. 8 presents the computed time-domain radiation pattern of the proposed antenna. The plotted radiation pattern represents the peak-to-peak amplitude of the pulses transmitted by the antenna in the indicated directions. The traditional (frequency-domain) radiation patterns are less useful for pulse radiating antennas as they do not directly give a measure for the strength of the pulses radiated by the antenna. The radiation pattern is computed at a distance of 1 m since in the aimed high-resolution GPR applications the targets are mostly located at a very close range from the antenna, from a few cm to less than 1 m. V. MEASUREMENTS An experimental antenna with chip resistors for the loading has been constructed as a printed antenna on an FR4 material as shown in Fig. 9. Measurements of input impedance and transmitted pulses were carried out using the technique introduced in [15] which employs a TSR line to feed the antenna, and in [16]

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Fig. 9. Experimental antenna constructed as a printed antenna on an FR4 material. Fig. 12. Scaled geometries of different antennas for comparison purposes. From top: the modified bow-tie antenna (length = 23 cm, resistively loaded), a conventional solid bow-tie antenna (length = 50 cm, flare angle = 70 , not loaded), a planar dipole (length = 40 cm, width = 15 cm, not loaded), and a wire dipole (length = 50 cm, not loaded).

Fig. 10. Setup for pulse radiation measurement.

Fig. 13. Comparison of the measured transmit waveforms (at a distance of 1 m in boreside direction) of the antennas shown in Fig. 12.

Fig. 11. Transmit waveform of the experimental antenna at a distance of 1 m in the boreside direction.

which employs a UWB shielded loop antenna [21] as a probe, respectively. The antenna was fed with a TSR line which was connected to a generator exciting the pulse in Fig. 1 according to the setup depicted in Fig. 10. The measurements were carried out in a non reflection-free room by paying attention to the distance from the antenna to the closest surrounding objects. The employed post-processing scheme of the measured data, which includes time windowing to exclude unwanted reflections from the surroundings and a deconvolution procedure to compensate for the probe’s characteristics, is given in detail in [15] and [16]. The measured transmit waveform of the experimental antenna is plotted in Fig. 11 where good agreement with the computed waveform is observed. It is shown that the pulse transmitted

by the antenna exhibits a level of late-time ringing lower than dB below the peak of the pulse after less than 3 times the pulse duration, which agrees with the computed result. To verify the antenna’s improved characteristic for pulse radiation, we perform a comparison between the proposed antenna and several other commonly-used GPR antennas, i.e., a conventional solid bow tie, a planar dipole and a wire dipole. Scaled geometries of these antennas are shown in Fig. 12 where can be seen that the size of the proposed antenna is significantly smaller relative to the others due to the use of FR4. The reason for choosing the 50 cm length for the conventional bow tie and wire dipole has been explained in Section IV. The measured transmit waveforms of these antennas are presented in Fig. 13 and a comparison of their peak-to-peak amplitudes is given in Table I. It is obvious that despite its relatively small size the proposed antenna exhibits the highest peak-to-peak amplitude. The waveform amplitude of the proposed antenna is slightly higher than that of the conventional bow tie (which has considerably larger dimensions), 18% higher than that of the planar dipole

LESTARI et al.: A MODIFIED BOW-TIE ANTENNA FOR IMPROVED PULSE RADIATION

TABLE I COMPARISON OF THE PEAK-TO-PEAK AMPLITUDE OF THE TRANSMIT WAVEFORMS IN FIG. 13

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revealed that the pulses transmitted by the proposed antenna exhibit higher amplitude than those transmitted by other commonly-used planar GPR antennas. However, the antenna’s input impedance has not been accurately predicted as the theoretical expressions used to predict the bow-tie flare angle are valid only for solid bow-tie structures. In order to enable more accurate prediction of the input impedance one needs a new expression describing the relation between the flare angle and input impedance of a wire bow-tie structure. An analytical expression describing approximate time-harmonic current distribution is derived to indicate an optimal linear resistive loading profile for the proposed antenna. Furthermore, the traveling-wave current distribution of the antenna is theoretically analyzed and it is found that when the antenna is resistively loaded both the time-harmonic and traveling-wave currents decay to approach nearly the same value at the end section of the antenna. Therefore, as the current at the antenna end corresponds to the level of reflection which occurs there, the derived expression is useful to estimate the level of late-time ringing and indicate an optimal loading profile for the antenna. The derived expression has been used to find an optimal loading profile for the proposed antenna which gives a level of late-time dB. ringing of less than ACKNOWLEDGMENT

Fig. 14. Measured input impedance of the proposed antenna.

(which is 1.7 times longer and has a much wider surface), and 45% higher than that of the wire dipole (which is 2 times longer). The measured input impedance is presented in Fig. 14. Using (17) and the dB limits of the spectrum of the pulse, the average input impedance of the antenna is found to be 68 , which is significantly lower than 96.5 , the computed result in Section IV. As previously indicated, the use of a dielectric substrate such as FR4 would lead to a drop in input impedance by as much as 50 . When the antenna is fed with the 100-Ohm TSR line, it results in a return loss of 14.5 dB or comparable with VSWR of 1.5 which should still be acceptable for most GPR applications. As mentioned above, since Carrel’s expressions [2] used here to predict the bow-tie flare angle are valid only for solid bow-tie structures, in order to enable more accurate prediction of the input impedance one needs a new expression describing the relation between the flare angle and input impedance of a wire bow-tie structure. VI. CONCLUSION Analysis, design and realization of a modified bow-tie antenna optimized for impulse GPR have been discussed. The antenna shows improved properties important for GPR, which include its compact size and ability to radiate UWB pulses with increased amplitude and very small late-time ringing. A substantial increase in the amplitude of the transmitted pulse in the boreside direction is achieved by using the improved loading technique described in this paper. Measurements have

The authors thank Liarto and D. Yulian from Radar & Communication Systems (RCS), Indonesia, for their assistance in the construction, simulation and measurement of the antennas reported in this paper. The authors are also thankful to the anonymous reviewers for their constructive comments. REFERENCES [1] G. H. Brown and O. M. Woodward, “Experimentally determined radiation characteristics of conical and triangular antennas,” RCA Rev., pp. 425–452, Dec. 1952. [2] R. L. Carrel, “The characteristic impedance of two infinite cones of arbitrary cross section,” IRE Trans. Antennas Propag., vol. 6, pp. 197–201, Apr. 1958. [3] A. P. Lambert, S. M. Booker, and P. D. Smith, “Calculation of the characteristic impedance of TEM horn antennas using the conformal mapping approach,” IEEE Trans. Antennas Propag., vol. 43, no. 1, pp. 47–53, Jan. 1995. [4] R. T. Lee and G. S. Smith, “On the characteristic impedance of the TEM horn antenna,” IEEE Trans. Antennas Propag., vol. 52, no. 1, pp. 315–318, Jan. 2004. [5] K. L. Shlager, G. S. Smith, and J. G. Maloney, “Optimization of bow-tie antennas for pulse radiation,” IEEE Trans. Antennas Propag., vol. 42, no. 7, pp. 975–982, July 1994. [6] C. J. Leat, N. V. Shuley, and G. F. Stickley, “Complex image model for ground-penetrating radar antennas,” IEEE Trans. Antennas Propag., vol. 46, no. 10, pp. 1483–1488, Oct. 1998. [7] A. G. Yarovoy, Y. Erbas, and L. P. Ligthart, “Adaptive bow-tie antenna with increased bandwidth,” in Proc. Eur. Microwave Conf., Milan, Italy, Oct. 2002, pp. 1–4. [8] A. A. Lestari, A. G. Yarovoy, and L. P. Ligthart, “RC-loaded bow-tie antenna for improved pulse radiation,” IEEE Trans. Antennas Propag., vol. 52, no. 10, pp. 2555–2563, Oct. 2004. [9] Y. Nishioka, O. Maeshima, T. Uno, and S. Adachi, “FDTD analysis of resistor-loaded bow-tie antennas covered with ferrite-coated conducting cavity for subsurface radar,” IEEE Trans. Antennas Propag., vol. 47, no. 6, pp. 970–977, Jun. 1999. [10] T. P. Montoya and G. S. Smith, “A study of pulse radiation from several broad-band loaded monopoles,” IEEE Trans. Antennas Propag., vol. 44, no. 8, pp. 1172–1182, Aug. 1996. [11] B. L. J. Rao, J. E. Ferris, and W. E. Zimmerman, “Broadband characteristics of cylindrical antennas with exponentially tapered capacitive loading,” IEEE Trans. Antennas Propag., vol. AP-17, no. 2, pp. 145–151, Mar. 1969.

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[12] A. A. Lestari, A. G. Yarovoy, and L. P. Ligthart, “Capacitively-tapered bowtie antenna,” in Proc. Millennium Conf. Antennas Propag., Davos, Switzerland, Apr. 2000, pp. 1–4. [13] A. A. Lestari, A. G. Yarovoy, and L. P. Ligthart, “Adaptive wire bow-tie antenna for GPR applications,” IEEE Trans. Antennas Propag., vol. 53, no. 5, pp. 1745–1754, May 2005. [14] A. A. Lestari, “Antennas for improved ground penetrating radar: modeling tools, analysis and design,” Ph.D. dissertation, Delft Univ. Technology, Delft, The Netherlands, 2003. [15] A. A. Lestari, A. G. Yarovoy, and L. P. Ligthart, “Ground influence on the input impedance of transient dipole and bow-tie antennas,” IEEE Trans. Antennas Propag., vol. 52, no. 8, pp. 1970–1975, Aug. 2004. [16] A. A. Lestari, A. B. Suksmono, A. Kurniawan, E. Bharata, A. G. Yarovoy, and L. P. Ligthart, “A facility for UWB antenna measurements in time domain,” in Proc. IEEE Int. Workshop Antenna Tech., Singapore, Mar. 2005, pp. 109–112. [17] T. T. Wu and R. W. P. King, “The cylindrical antenna with nonreflecting resistive loading,” IEEE Trans. Antennas Propag., vol. AP-13, pp. 369–373, May 1965. [18] G. J. Burke and A. J. Poggio, “Numerical Electromagnetic Code (NEC)—Method of Moments, Part I: Theory,” NOSC TD-116, Naval Ocean Syst. Center. San Diego, CA, Jan. 1980. [19] C. M. Butler, “The equivalent radius of a narrow conducting strip,” IEEE Trans. Antennas Propag., vol. 30, no. 4, Jul. 1982. [20] R. W. P. King and H. J. Schmitt, “The transient response of linear antennas and loops,” IRE Trans. Antennas Propag., vol. 10, pp. 222–228, May 1962. [21] A. Yarovoy, R. de Jongh, and L. Ligthart, “Ultra-wideband sensor for electromagnetic field measurements in time domain,” Electr. Lett., vol. 36, no. 20, pp. 1679–1680, Sep. 2000.

Andrian Andaya Lestari (M’08) was born in Bogor, Indonesia. He received the M.Sc. (Ingenieur) and Ph.D. degrees in electrical engineering from Delft University of Technology, The Netherlands, in 1993 and 2003, respectively. From 1993 to 1998, he was with a government research agency in Jakarta, Indonesia. He joined the International Research Centre for Telecommunications and Radar (IRCTR) - Delft University of Technology, in 1998. In 2006, he became the Director of the Indonesian Branch of IRCTR (IRCTR-IB) at Bandung Institute of Technology (ITB), Indonesia. He has authored or coauthored over 90 publications, which include patents, technical reports, presentations and articles presented in journals and conferences. His research interests include antennas and radar systems. Currently he is working on the development of the Indonesian maritime radar INDERA.

Endon Bharata received the B.Sc. and M.Eng. degrees in telecommunication engineering from Bandung Institute of Technology (ITB), Indonesia. He worked for some private companies as a radio communication expert between 1980 and 2000. He is currently an Associate Professor at the School of Electrical Engineering and Informatics, Bandung Institute of Technology, Indonesia. His research interest covers communication electronics and microwave, antennas, and communication systems.

Andriyan Bayu Suksmono (M’02–SM’08) received the B.S. degree in physics and the M.S. degree in electrical engineering from the Bandung Institute of Technology (ITB), Indonesia, and the Ph.D. degree in engineering from the University of Tokyo, Japan, in 1990, 1996 and 2002, respectively. He joined ITB as an Instructor (1996–2005), Associate Professor (2005–2009), and Professor (2009-present) at the School of Electrical Engineering and Informatics, ITB. His main research interests are signal processing and imaging.

Dr. Suksmono is a Professional Member of the ACM. He has been granted several international research funds, scholarships, and fellowship, from RCAST—Tokyo University, Monbukagakusho, JSPS, AIGRP, and the Hitachi Foundation. In 2004, he was awarded the Best Paper in Theoretical Development by APNNA for his work in spatio-temporal ultra-wideband neuro-beamforming. He was the recipient of the Outstanding Faculty Award of ITB and the Republic of Indonesia in June 2007 and August 2007, respectively.

Adit Kurniawan graduated from the Bandung Institute of Technology (ITB), Indonesia, in 1986 and received the M.Eng. degree from RMIT, Australia, in 1996 and the Ph.D. degree from the University of South Australia, in 2003, both in telecommunication engineering. He became a faculty member of the Department of Electrical Engineering, ITB, in 1990. His research interests are antenna and wave propagation, cellular communication system, and radio communication. He is currently an Associate Professor and serves as the Head of Telecommunication Engineering Department at the Bandung Institute of Technology.

Alexander G. Yarovoy (M’96–SM’04) graduated with the Diploma (with honors) in radiophysics and electronics and received the Cand. Phys. Math. Sci. and Dr. Phys. Math. Sci. degrees in radiophysics all from Kharkov State University, Ukraine, in 1984, 1987, and 1994, respectively. In 1987, he joined the Department of Radiophysics, Kharkov State University, as a Researcher and became a Professor in 1997. From September 1994 through 1996, he was with the Technical University of Ilmenau, Germany, as a Visiting Researcher. Since 1999, he is with the International Research Centre for Telecommunications and Radar (IRCTR), Delft University of Technology, The Netherlands, where he coordinates all UWB-related projects. His main research interests are in ultrawideband (UWB) technology and its applications (in particular, UWB radars) and applied electromagnetics (in particular, UWB antennas). Prof. Yarovoy is the recipient of a 1996 International Union of Radio Science (URSI) “Young Scientists Award” and co-recipient of the European Microwave Week Radar Award in 2001 for the Paper that Best Advances the State-of-the-Art in Radar Technology. He served as the Co-Chairman and the Technical Program Committee Chair of the 10th International Conference on Ground Penetrating Radar (GPR2004), Delft, and the Secretary of the 1st European Radar Conference (EuRAD’04), Amsterdam, The Netherlands.

Leo P. Ligthart (M’94–SM’95–F’02) was born in Rotterdam, the Netherlands, on September 15, 1946. He received the Engineer’s degree (cum laude) and the Ph.D. degree from Delft University of Technology, The Netherlands, in 1969 and 1985, respectively, and the Doctorates (honoris causa) from Moscow State Technical University of Civil Aviation and Tomsk State University of Control Systems and Radioelectronics, Russia, in 1999 and 2001, respectively. Since 1992, he has held the Chair of Microwave Transmission, Radar and Remote Sensing in the Department of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology. In 1994, he became Director of the International Research Centre for Telecommunications and Radar (IRCTR). His principal areas of specialization include antennas and propagation, radar and remote sensing. He has also been active in satellite, mobile and radio communications. He has written over 400 papers and two radar books. Prof. Ligthart is an Academician of the Russian Academy of Transport and a Fellow of the Institute of Electrical and Electronics Engineers (IEEE) and the Institute of Engineering and Technology (IET), London, U.K.

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A Compact Parallel-Plane Perpendicular-Current Feed for a Modified Equiangular Spiral Antenna Travis Wayne Eubanks, Student Member, IEEE, and Kai Chang, Fellow, IEEE

Abstract—The design and measurement is described of a compact (59.94 mm 59.94 mm 1.14 mm) bidirectional ultrawideband modified equiangular spiral antenna with an integrated feed internally matched to a 50-Ohm microstrip transmission line. An ultrawideband transition from microstrip to parallel-strip line soldered to a short (1.14 mm) twin-line transmission line feeds the spiral. The currents on the feed travel in a direction approximately perpendicular to the direction of the currents on the spiral at the points where the feed passes the spiral in close proximity (0.57 mm). Holes were etched from the metal arms of the spiral to reduce the impedance mismatch caused by coupling between the transmission line feed and the spiral. Measured and simulated radiation patterns and VSWR plots show good performance over the ultrawideband range (3.1–10.6 GHz) with a 2:1 VSWR everywhere in this range except for 3.33–3.95 GHz, which has a 3:1 VSWR. This spiral exhibits an elliptical polarization over the ultrawideband range. Index Terms—Parallel-plane perpendicular-current (PPPC), parallel-strip line, spiral antenna, theory of small reflections, ultrawideband (UWB).

I. INTRODUCTION

J

OHN Dyson showed in the mid-1950’s that equiangular spiral antennas have characteristics associated with infinite structures that allow the antennas to radiate bidirectionally with 98% efficiency, having 20:1 impedance and radiation bandwidths [1]. Knowing that spiral antennas exhibit such broadband behavior with high efficiency, RF engineers have since continued to create ways to feed these antennas that preserve (as much as possible) the radiation and impedance bandwidths from [1], while adapting the antennas to specific applications [2]–[7]. Since the planar spiral antenna with multiple arms has arm terminations closest together near the center of the spiral, some designers choose to feed the spiral from the center at a 90 angle to the spiral’s surface [2], [5]–[7] so that the radiation from the spiral is least affected by the feed network. This three-dimensional feed usually has an absorbing or reflecting cavity behind it to support the feed line mechanically and to force the spiral to radiate unidirectionally. Two-dimensional feeds in planes parallel to the spiral feed the antenna by either connecting the feed line to the arm terminations on the perimeter of the Manuscript received May 11, 2009; revised September 09, 2009; accepted February 01, 2010. Date of publication April 22, 2010; date of current version July 08, 2010. The authors are with the Department of Electrical and Computer Engineering, Texas A&M University, College Station, TX 77843 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/TAP.2010.2048856

Fig. 1. Parallel-plane perpendicular-current feed and modified equiangular spiral antenna from an overhead view.

spiral [4] or by feeding the spiral with a transmission line that follows the metal layer directly beneath the spiral to the center feed point [1], [3]. This paper elaborates on the parallel-plane perpendicular-current (PPPC) feed for a modified equiangular spiral antenna that was originally presented in [8] by describing the operational principles of the feed, the broadband measured impedance and radiation bandwidth, the radiation efficiency, the axial ratio, and the signal fidelity. The PPPC feed is two-dimensional and compact. II. PARALLEL-PLANE PERPENDICULAR-CURRENT FEED This feed receives its name for two reasons. The feed lies in a plane parallel to the spiral’s surface, and the currents traveling down this feed line are approximately perpendicular to the currents on the spiral’s arms where the feed line passes underneath. Placing the feed in a plane parallel to the spiral minimizes the overall volume of the structure. Forcing the currents to cross each other at near perpendicular angles minimizes the interactions of fields from the spiral with fields from the transmission line. With minimized interactions between radiation and transmission line fields, the antenna radiates most efficiently with an optimal return loss. Fig. 1 shows the three metal layers for this structure from an overhead view [8], which are aligned vertically (using the alignment holes in the upper corners and thin rectangular border for guidance) prior to final assembly. In Fig. 1, the substrates between the metal layers were removed to show their alignment. The black sections of Fig. 1 (except for the cartesian coordinate reference) represent the copper metal layers of this structure. Although inevitably the feed line will prevent radiation from the spiral in certain locations due to the proximity of the feed to

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Fig. 2. Microstrip to parallel-strip feed line connection. Region 3 to 2 is tapered microstrip line, and region 2 to 1 is tapered parallel-strip line.

Fig. 3. Microstrip to parallel-strip ground transition. Region 3 to 2 is microstrip ground, and region 2 to 1 is tapered parallel-strip ground, including a circular taper transition at the boundary between the microstrip ground and the parallelstrip ground.

the radiating areas between the spiral’s arms, this antenna structure shows good radiation patterns over the UWB range. The direction forces the spiral’s radiation to feed line in the be lowest along that line. The spiral’s radiation was measured and lines to show the maximal and along the minimal gain of the spiral. A. Motivation for the PPPC Feed Upcoming ultrawideband (UWB) applications inspired the design of the PPPC feed. As consumers’ demand for high datarate wireless connectivity increases, UWB mobile devices become increasingly attractive to investors. The PPPC feed design satisfies the desire to have a low volume equiangular spiral with an integrated and balanced feed network for use in such a UWB mobile device. A UWB balun transforms the unbalanced microstrip line input into a balanced parallel-strip line feed for the antenna, as described in [9]. Fig. 2 shows the middle metal layer [8], which consists of the tapered microstrip line (region 3 to region 2) and the parallelstrip feed line (region 2 to region 1) that connects a microstrip input to the left spiral arm (as seen from the center of the spiral in Fig. 1). A twin-line transmission line guides the fields on this line from region 1 to the center of the spiral through vertical (negative -direction) parallel via holes. Fig. 3 shows the bottom metal layer [8], which converts the microstrip ground into a parallel-strip ground through a circular taper at region 2. The parallel-strip line that results from stacking the middle and bottom layers has the same taper rate for both layers. The twin-line transmission line also connects to the bottom metal layer at region 1 to feed the right spiral arm (as seen from the center of the spiral in Fig. 1). The circular curve at region 1 on the tapered parallel-strip ground (Fig. 3) aids the twin line transmission line by positioning its connection directly beneath the right arm of the spiral. This allows the width of the twin-line transmission line to remain fixed as it connects the transmission line to the spiral arms. Since the equiangular spiral can be designed to operate over the entire UWB range (3.1–10.6 GHz) [1], this antenna may operate in the UWB range if the intermediate transmission line section is designed appropriately (region 2 to region 1 in Figs. 2–3). Fig. 4 shows the metal layer consisting of the

Fig. 4. Spiral metal layer with holes etched out of its arms where the parallelstrip line passes beneath.

equiangular spiral alone [8]. Measured and simulated results show that the PPPC feed minimally affects the spiral’s radiation and impedance bandwidths. B. Connection Between the Spiral and Feed The theory of small reflections shows that a tapered transmission line can impedance match a source to a load over a broadband frequency range. Applying this concept to the parallel-strip feed allowed it to impedance match the spiral antenna to the 50 microstrip input and to prepare the feed for mechanical connection to the spiral’s feed points. After the taper reduced the width of the 50 line to the width of the spiral antenna’s arms at region 1 in Figs. 2–3, a short (1.14 mm) twin line mechanically and electrically connected the parallel-strip feed to the spiral through vertical via-holes. Solder serves as both the mechanical and electrical connection of the twin-line transmission line to the parallel-strip feed and the spiral antenna. As such, the twin-line connection to the parallel-strip feed starts at the narrow end of the circular taper near region 2 in Fig. 3 and ends at the center of the spiral in Fig. 4. Under a microscope, fine needles were used to cut holes 0.4 mm apart into the substrates at the points where the twin-line

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Fig. 5. The attachment of the twin-line transmission line to the parallel-strip feed and the spiral arms. (a) Twin-line connection to the parallel-strip ground line that lies beneath both substrates. (b) Twin-line connection to the parallel-strip feed line that remains between the two substrates. (c) Twin-line passing through both substrates prior to the straightening of the twin-line. (d) Spacing and placement of twin-line holes. (e) Complete spiral without impedance matching holes. (f) Complete spiral with impedance matching holes.

would connect the spiral directly to the parallel-strip feed. After mechanically (and electrically) connecting to the parallel-strip feed and ground lines, the twin-line passed through the small holes to connect to the spiral arms. After the twin-line passed through these holes, the substrate holding the spiral could move flush against the substrate holding the UWB balun while straightening the twin-line between the substrates (since the twin-line passed through vertical holes inside the substrates). Once flush against the balun’s substrate, the spiral and the twin-line were soldered together, and clippers were used removed the extra twin-line. Fig. 5 shows the connection process for the twin-line transmission line on a spiral with and without impedance matching holes. III. SPIRAL ANTENNA DESIGN The design equations for this spiral antenna and integrated feed are derived from several basic concepts. As shown in

[1]–[7], antenna designers generally attempt to isolate the feed lines from the antennas and make energy propagate from the feed to the antenna or from the antenna to the feed efficiently. By isolating these components everywhere except at the points where they connect physically or through desirable coupling, designers may create each component individually and then connect the components together in a cascade. This design method relieves the burden of designing all of the antenna’s components simultaneously.

A. General Spiral Equations After assuming that the cascade design method was possible for this antenna, the polar equations for equiangular spiral antenna arms given in [10] were massaged into parametric equations with impedance matching terms to draw the desired spiral

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Fig. 6. The four spiral arm boundary curves.

in CST Microwave Design Studio with ultrawideband operation. Equations (1)-(4) describe the four two-dimensional parametric curves that compose the spiral arm boundaries.

(1) (2) (3) (4) where , , , and are the Cartesian coordinate references for the spiral arms’ positions in the -direction, , , , and are the Cartesian coordinate references for the spiral arms’ is the radius of the spiral at its positions in the -direction, center, is the initial width of the spiral’s arms, is the spiral expansion coefficient, is the angle of the spiral, and is an impedance matching term which limits the spiral arms’ width. Fig. 6 shows the spatial relationships between the curves given in (1)-(4). The Cartesian coordinate reference used to draw these spiral arm boundaries is not the same as the Cartesian coordinate reference used everywhere else in this paper (see Figs. 2–4). The acid etching facilities at Texas A&M University cannot etch metal with a width less than 0.2 mm effectively, so the minimum spiral arm width ( ) equals 0.2 mm. The minimum central radius of the spiral ( ) equals 0.2 mm because parametric simulations showed that this initial radius gave the spiral an optimal return loss over the UWB range. After building the spiral completely in CST Microwave Design Studio and connecting values were the feed shown in Figs. 2–3, the and chosen parametrically to select the best return loss from the anand tenna. According to these parametric analyses, . B. Parallel-Plane Considerations Since the parallel-strip feed line for this spiral carries fields around it as shown in [9], the conductive surface of the spiral antenna reflects some of those fields from the feed that would otherwise propagate to the spiral’s center. In order to reduce those reflections and also to reduce the coupling from the feed

Fig. 7. Various spiral arm widths minus etching hole diameters (remaining metal widths) at specific angles produce varying return losses over the 4–7 GHz frequency range. The maximum metal width occurs with no etching hole present.

to the spiral, holes were etched out of the spiral’s surface at the places where the feed passed underneath. However, since the spiral cannot radiate without currents propagating through the spiral arms, the hole diameter used to reduce coupling between the spiral and the feed remained limited below the spiral arm width at a certain angle. If the holes became too large, then the spiral’s arms would segment into several sections that could no longer propagate currents. With these considerations, holes were cut from the spiral drawn in CST, and parametric analysis found optimal hole diameters for both of the holes centered above the feed line. Fig. 7 shows the results of this parametric analysis. Since the equiangular spiral should be defined entirely by angles in order to be infinitely wideband (with limitation only from the designed structure size) [1], the hole diameters for both holes were designed as a function of the angle of their centers from the origin so that the spiral’s impedance and radiation bandwidths would not be limited by the holes’ sizes. Effectively, this means that each hole’s diameter relates directly to the spiral arm width at the angle of the hole’s center, which lies directly above the center of the tapered parallel-strip feed. Fig. 7 calls the difference between the spiral arm width and the hole diameter the “remaining metal width”. The smallest metal width (0.076 mm) produced the best average return loss (16.0 dB) over the 4–7 GHz frequency range. However, this metal width was too small to etch. For this reason, the spiral shown in Fig. 5(f) has 30 AWG wires (0.254 mm dia.) connecting the segmented sections of the spiral in the locations where the spiral became thinner than the resolution of the etching lab. This fabrication flaw might have produced the slight variation between the measured and simulated VSWR for the spiral with holes, shown later in Section V.B of the paper. C. Perpendicular Currents As a result of attempting to isolate the fields near the feed line from the fields near the spiral through parametric analysis, the currents through the feed line and the spiral naturally approached perpendicularity between each other. Parametric simulations aided in improving the antenna’s return loss by altering the shape of the spiral and by finding the best positions and shapes for the etching holes. After many of these simulations, the perpendicular current situation gave the best performance. One can see visually in

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Fig. 10. The actual taper w (y ) used to create the parallel-plane perpendicularcurrent feed.

Fig. 7, and it also explains why parametric analysis produced the perpendicular current situation naturally. Fig. 8. The surface currents on a rectangular spiral are forced to travel on the tangent of the circle as they approach the crossing between the spiral and the feed. The tangent to the circle is perpendicular to the feed at the feed’s center.

IV. PARALLEL-STRIP LINE FEED DESIGN In order to match a broadband load to a broadband source of unequal characteristic impedance, one must use a broadband impedance transformer to allow operation of the system through that same broad bandwidth. Since the UWB microstrip to parallel-strip balun given in [9] and the spiral both operate in broad bandwidths, a broadband impedance transformation must match the impedance of the spiral to the 50 microstrip line so that the total antenna and integrated feed may operate in a broadband spectrum. The theory of small reflections, as given in [11] describes the reflection coefficient at the input of a transmission line as a function of the operation frequency , the transition length , and the variation of the characteristic impedance of the transmission line through space . A. Contributions of the Theory of Small Reflections

Fig. 9. The top and bottom surface currents on the equiangular spiral sum vectorially to produce a net current perpendicular to the feed’s current at the point of crossing between the spiral and the feed.

as derived in [11] as a Equation (5) shows the integrable function of the characteristic impedance , which is a function of position . In (6), the integral is performed in the -direction with a phase shift added from the theory of small reflections to find the total reflection coefficient for a transmission line. Equation (7) shows the dependence of in (6) on the frequency and the speed of light . (5)

Fig. 8 that as the diameter of an etching hole approaches the spiral arm width, the currents along the spiral are forced in the direction of the tangent line to the hole at the crossing of the parallel-strip feed and the spiral. The direction of the currents through remaining metal becomes increasingly close to the tangent of the circle as the etched hole diameter approaches the spiral arm width. Fig. 8 idealizes this scenario with a rectangular spiral. Although it seems that the same phenomena cannot hold true for a non-rectangular spiral (since the tangent to the etching hole at the center of the feed becomes slanted for an equiangular spiral), simulations show that the vector sum of the currents on the top and bottom of the spiral lies in a direction approximately perpendicular to the direction of the currents on the feed. Altogether, this forces the fields radiated by the spiral and the fields transmitted by the feed to be non-interactive, or isolated from one another. Fig. 9 shows the surface currents of the spiral antenna, as simulated by CST. When these currents become closer to perpendicular to each other, the return loss improves. This explains why the hole of greatest diameter produced the best return loss, as shown in

(6) (7) The PPPC feed in this paper uses the the transition shown in Fig. 10 to match the UWB balun to the spiral antenna. Since the characteristic impedance of a parallel-strip line depends upon the width of the the line , it also varies with space according to the relationship between and shown in (8), where and have millimeter units. Wheeler explains in [12] that the characteristic impedance of a parallel-strip line has two governing equations, one for wide strips and one for narrow strips. He also explains that the transition between these two equations usually happens when the width of the line equals half the height. (8) The equation for the narrow strip characteristic impedance ((9)) and the equation for the wide strip characteristic impedance ((10)) do not intersect at the transition region

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Fig. 11. Characteristic impedance of the parallel strip-line versus distance in the y -direction.

Fig. 12. Magnitude of the reflection coefficient for the perfectly-matched linearly-tapered parallel-strip line.

for the parallel-strip line in this paper, leaving a discontinuity in the characteristic impedance that gives an infinite value for at that transition. Due to the fact that the derivative of the narrowest point on the parallel-strip line lies at (substrate height ), which almost satisfies the ), wide strip condition according to Wheeler in [12] ( the wide strip equation is used to model this parallel-strip line’s impedance over the entire length of the line (avoiding the ). discontinuity in

in [9]. This means that the complete antenna and integrated feed should operate at frequencies greater than or equal to 3 GHz since the tapered transmission line cannot operate below 3 GHz with less than 10% power reflection. This transmission line meets the requirements for UWB operation since the FCC allotted frequency band for UWB lies between 3.1–10.6 GHz.

(9)

(10) B. Calculating the Reflection Coefficient After substituting in (8) into (10), the characteristic impedance of the parallel-strip line becomes a function of position , as shown in Fig. 11. Then substituting this characteristic impedance into (6) gives the ratio value of for a single frequency . Taking the integral in (6) for many frequency points in the range 0–20 GHz gives the magnitude of the input reflection coefficient versus frequency for the perfectly-matched linearly-tapered transmission line, as shown in Fig. 12. This shows the best possible reflection coefficient through the tapered parallel-strip transmission line, since these calculations assume that the transmission line is perfectly matched on both ends. The return loss through this tapered parallel-strip line , and the return loss remains better than 10 equals . dB for Now knowing the return loss intrinsic to the perfectly-matched linearly-tapered parallel-strip transmission line shown in Fig. 10, one can expect that the total return loss from the antenna specified in Fig. 1 will be worse than the return loss of the tapered transmission line since other losses exist in the spiral specified in [1] and in the UWB transition specified

V. FINAL ANTENNA DESIGN AND PERFORMANCE Since this antenna was designed with cascaded elements to create the final antenna, parametric analysis reduced the coupling between elements in the antenna as much as possible before construction began. After finishing such reductions in simulation, a complete antenna construction allowed for physical measurements that verified the simulated results. These measurements agree with the assumption that all elements could be designed individually and then cascaded together (with moderate parametric analysis for tuning). The antenna’s spiral arms were truncated at a radius of 21 mm to limit the antenna’s size and provide optimal impedance matching for the antenna. The remaining metal width between the etching holes and the outer spiral arms was set to 0.076 mm since that value produced the best return loss parametrically. The tapered microstrip to tapered parallel-strip line that feeds the antenna is 30 mm long, and the total antenna dimensions are 59.94 mm 59.94 mm 1.14 mm. The antenna’s bandwidth is the unity between its impedance and radiation bandwidths. After determining the impedance bandwidth through network analyzer measurements and determining the radiation bandwidth through anechoic chamber measurements, the antenna with etching holes was found to have a bandwidth equal to its impedance bandwidth. The input impedance of the two antennas and the VSWRs of those antennas are shown in Figs. 13–14, respectively. John Dyson showed that equiangular spirals could operate with a 98% radiation efficiency in the mid-1950’s [1], and the designed antenna verifies his result in measurement and simulation. This antenna exhibits its lowest radiation efficiency of 87.3% at 3.0 GHz and its highest radiation efficiency of 98.9% at 7.4 GHz. Fig. 15 shows the radiation efficiency of the antenna with etching holes. The mean displacement error of the . measured radiation efficiency is The radiation efficiency of the spiral was found by calculating the maximum effective aperture size and by measuring the gain.

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Fig. 13. Real and imaginary impedance versus frequency for the antenna (a) without etching holes and (b) with etching holes.

TABLE I MAXIMUM EFFECTIVE APERTURE AREA

Fig. 14. VSWR plots for spiral antennas with and without etching holes.

enclosing those arcs were measured in order to find the maximum effective aperture at those frequencies. The arc lengths, enclosing circle radii, and maximum effective aperture areas at 3, 6, 9, and 12 GHz are given in Table I. A. Impedance Bandwidth

Fig. 15. Measured and simulated radiation efficiency of the antenna with etching holes over the 3–12 GHz range.

The radiation efficiency, gain, and maximum effective aperture size are related by (11) [10], [13], [14]

(11) where is the radiation efficiency, is the wavelength of a specific frequency under consideration, is the maximum meais the maximum effective aperture size. sured gain, and Since an equiangular spiral with an arc length equal to has a lower operating frequency limit equal to [1], the maximum effective aperture of the equiangular spiral at its lower frequency limit is bound by a circle completely enclosing the spiral arc of length . The maximum effective aperture of the spiral decreases with increased frequency since the circle enclosing the arc of length decreases in size as the frequency increases. The arc lengths corresponding to one wavelength at 3, 6, 9, and 12 GHz were calculated, and the radii of the circles

In order to test the hypothesis that the etching holes in the spiral would improve the return loss of the antenna and thereby increase the impedance bandwidth, two spiral antennas were constructed: one with etching holes, and one without etching holes. Fig. 13 shows the real and imaginary measured and simulated impedances for both antennas. The antenna with etching holes oscillates much more regularly around the point in the complex plane , corresponding to a perfect match. Typically the impedance bandwidth lies in the range of frequencies where the return loss remains better than 10 dB, which . Fig. 14 shows the VSWRs corresponds to a for the antennas with and without etching holes in measurement and simulation. The spiral antenna with holes exhibits a better VSWR than the spiral antenna without holes over the UWB range, and the simulated spiral with holes exhibits much lower loss than the fabricated spiral. By observation, one can see that the theory of small reflections accurately predicted the lowest operating frequency limit for the antenna. Fig. 12 showed that the antenna could not operate effectively below 3 GHz, and the measured data in Fig. 14 confirmed that prediction. The simulated VSWR for the antenna with etching holes remained less than 1.5 between 4–12 GHz while the measured VSWR rose to nearly 2 at 6 GHz and 7 GHz. This difference between measurement and simulation might be due to the etching resolution, as discussed previously. The small scale manipulation of solder under a microscope by hand poses another possible source of discrepancy between measured and simulated results.

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Fig. 16. Radiation patterns for the antenna with measured gain shown in dBi. . (b) 3 GHz and  . (c) 6 GHz and  . (a) 3 GHz and  . (d) 6 GHz and 

=0 = 90

= 90

=0

Fig. 17. Radiation patterns for the antenna with measured gain shown in dBi. . (b) 9 GHz and  . (c) 12 GHz and  . (a) 9 GHz and  . (d) 12 GHz and 

=0 = 90

= 90

=0

Nonetheless, the measured VSWR of the antenna with etching holes shows 2:1 VSWR impedance bandwidths between 2.81–3.33 GHz and 3.95–14.80 GHz and a 3:1 VSWR impedance bandwidth between 3.33–3.95 GHz. The antenna without etching holes exhibits 2:1 VSWR impedance bandwidths between 4.00–7.75 GHz, 8.30–9.25 GHz, and 9.90–20.00 GHz and 3:1 VSWR impedance bandwidths elsewhere in the 3.00–9.90 GHz range. Therefore, etching holes into the spiral for the purpose of improving the return loss in the UWB band has succeeded. B. Radiation Bandwidth

Fig. 18. The axial ratio for the spiral with etching holes. This antenna exhibits elliptical polarization from 3–12 GHz.

The frequency range in which an antenna radiates in a desirable way describes the radiation bandwidth of that antenna. Since different applications require different types of radiation, the radiation bandwidth of this antenna shall be defined as the frequency range over which this antenna exhibits bidirectional radiation with greater than or near unity gain in at least one polarization. The spiral’s radiation pattern rotates with changes in frequency since the distance between spiral arms increases with the angle of the spiral’s rotation. Figs. 16 and 17 show the simulated and measured radiation patterns with the coordinate and are given for the reference shown in Figs. 1–4. designed antenna at 3 GHz, 6 GHz, 9 GHz, and 12 GHz at the and . In all of these measurements, planes the gain of the spiral antenna remained above or near 0 dBi in bidirectional broadside radiation with elliptical polarization. Therefore, the radiation pattern does not limit the bandwidth of the antenna in the UWB range (3.1–10.6 GHz).

Measurements showed that both a spiral with etching holes and a spiral without etching holes radiate the same patterns, so Figs. 16 and 17 only show the radiation patterns of a spiral with holes. Since both spirals exhibit the same radiation patterns, the etching holes do not affect the radiation pattern of the spiral with holes through the measured UWB range. Linear polarization is defined by an axial ratio of 10 dB or greater, elliptical polarization is defined by an axial ratio less than 10 dB and greater than 3 dB, and circular polarization is defined by an axial ratio less than 3 dB. For the entire UWB range, this antenna exhibits elliptical polarization. Fig. 18 shows the axial ratio for the spiral over the frequency range 3–12 GHz. The measured results for the axial ratio follow the general trend of the simulated results. Since the radiation pattern does not limit the antenna’s bandwidth in the UWB range, the impedance bandwidth imposes the

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dummy feed and symmetrically placed etching holes. The asymmetric spiral emits a high-fidelity signal in the UWB range, which shows that it would be a good candidate for use in UWB applications. VI. CONCLUSION

Fig. 19. The transmitted signal for both spirals (Trans.), received signal from the asymmetrical spiral (Asym.), and received signal from the symmetrical spiral (Sym.).

TABLE II FIDELITY FACTOR COMPARISON

only restriction on the antenna’s bandwidth. The antenna’s radiation shows good performance for all frequencies between 3–12 GHz. For the purpose of UWB communications, this antenna can radiate well over the entire UWB range. C. Signal Distortion Since the spiral receives and sends different frequency signals at different areas on the antenna, wideband signals undergo phase distortion by the time they are received or transmitted at the spiral’s center feed points. Phase linearization techniques can be used to reduce this distortion [15]. The fidelity factor of an antenna measures the similarity between the transmitted and received signals in order to characterize the antenna’s distortion [16]–[20]. An antenna with little distortion has a fidelity factor near unity. This factor is calculated using (12) [16], (12) where and are the transmitted and received signals, respectively. The antenna under test was excited with a 0.5 ns UWB pulse to cover the frequency range 3–12 GHz. Since the antenna’s feed structure is asymmetrical, which may cause some antennas to have an unbalanced phase center, the same excitation was given to a spiral that had a dummy feed on the opposite side of the actual feed and symmetrical hole modifications on both sides of the spiral. The excitation and far-field received signals for both spirals are plotted together in Fig. 19. The far-field of the spiral is de, where is the fined here as the distance exceeding maximum dimension of the antenna’s aperture, and is the wavelength of the lowest operating frequency [10]. For this antenna, the far-field exists at a distance exceeding 72 mm, and the signals were received at 73 mm. The fidelity factor for both spirals is given in Table II. As seen in Table II, the asymmetric spiral described in this paper has a higher fidelity factor than a similar spiral with a

The parallel-plane perpendicular current feed for a modified equiangular spiral antenna retains the ultrawideband impedance and radiation characteristics of the equiangular spiral while minimizing the volume consumed. This minimal volume allows upcoming UWB technology to utilize the PPPC fed spiral for long or short range communications in remote devices. The novelty of the PPPC feed lies mainly in this answer to the question, “How can an equiangular spiral antenna be fed from the side with a parallel-strip line in order to save space in future portable UWB technology?” Multiple answers to that question do exist [3], and the exploration of those concepts may reveal important stepping stones for technological advances in the future for UWB technology, even including the application of perpendicular current feeds to other existing systems. The antenna in this paper showed good measured performance over the UWB range with a 2:1 VSWR everywhere except 3.33–3.95 GHz with a 3:1 VSWR and a radiation bandwidth exceeding the UWB range. As derived from the theory of small reflections, the reflection coefficient of the tapered parallel-strip line predicted the minimum frequency of operation of the antenna correctly since the UWB balun from the microstrip to parallel-strip line and the spiral both operate effectively below the frequency limit of the designed tapered parallel-strip line. Since this design aimed to support UWB technology, which operates between 3.1–10.6 GHz, the antenna that has the greatest usable bandwidth in that region best suits operation in the UWB range. The spiral antenna with asymmetrical etching holes more effectively uses the UWB frequency range, and therefore it should be preferred over the antenna without etching holes in future UWB technology. ACKNOWLEDGMENT The authors would like to thank Mr. M. Li for all of his dedicated support and thoughtful input. He greatly contributed to the mechanical construction of the spiral antenna and offered many helpful suggestions about feed designs for spiral antennas. The authors would also like to thank Dr. R. D. Nevels for his great ideas on the perpendicular currents model. REFERENCES [1] J. Dyson, “The equiangular spiral antenna,” IRE Trans. Antennas Propag., vol. 7, no. 2, pp. 181–187, Apr. 1959. [2] D. W. Smith and P. E. Mayes, “Spiral antennas over a ground plane,” in Proc. IEEE AP-S Int. Symp., Jul. 1992, vol. 4, pp. 2093–2096. [3] G. H. Huff and T. L. Roach, “Stripline-based spiral antennas with integrated feed structure, impedance transformer, and dyson-style balun,” in Proc. IEEE AP-S Int. Symp., Jun. 2007, pp. 2698–2701. [4] W. Z. Wu, T. H. Chang, and J. F. Kiang, “Broadband slot spiral antenna with external feed and microstrip-to-slotline transition,” in Proc. IEEE AP-S Int. Symp., Jun. 2004, vol. 1, pp. 767–770. [5] H. Nakano, Y. Shinma, and J. Yamauchi, “A monolar spiral antenna and its array above a ground plane-formation of a circularly polarized tilted fan beam,” IEEE Trans. Antennas Propag., vol. 45, no. 10, pp. 1506–1511, Oct. 1997.

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[6] S. Zhaohui, L. Meijia, and D. Zhiyong, “An improved design of microstrip Archimedeam spiral antenna,” in Proc. Int. Conf. on Microwave and Millimeter Wave Tech., Apr. 2007, pp. 1–4. [7] W. H. Tu, M. Y. Li, and K. Chang, “Broadband microstrip-coplanar stripline-fed circularly polarized spiral antenna,” in Proc. IEEE AP-S Int. Symp., Jul. 2006, pp. 3669–3672. [8] T. W. Eubanks and K. Chang, “Modified equiangular spiral antennas side-fed by multi-stage wideband impedance transforming transitions,” in Proc. IEEE AP-S Int. Symp., Jun. 2009, pp. 1–4. [9] S. G. Kim and K. Chang, “Ultrawide-band transitions and new microwave components using double-sided parallel-strip lines,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 9, pp. 2148–2152, Sep. 2004. [10] W. L. Stutzman and G. A. Thiele, Antenna Theory and Design, 2nd ed. New York: Wiley, 1998, pp. 42, 78, 251–253, 413. [11] D. M. Pozar, Microwave Engineering, 3rd ed. New York: Wiley, 2005, pp. 244–263. [12] H. A. Wheeler, “Transmission-line properties of parallel strips separated by a dielectric sheet,” IEEE Trans. Microw. Theory Tech., vol. 13, no. 2, pp. 172–185, Mar. 1965. [13] C. A. Balanis, Antenna Theory: Analysis and Design, 3rd ed. Hoboken, NJ: Wiley., 2005, p. 66. [14] K. Chang, RF and Microwave Wireless Systems. New York: Wiley, 2000, p. 78. [15] J. Volakis and J. Young, “Phase linearization of a broad-band antenna response in time domain,” IEEE Trans. Antennas Propag., vol. 30, no. 2, pp. 309–313, Mar. 1982. [16] A. Mehdipour, K. Mohammadpour-Aghdam, M. R. Kashani-Khatib, and R. Faraji-Dana, “A practical feeder for differential elliptical antennas in ultra wideband applications,” Microw. Opt. Tech. Lett., vol. 50, no. 8, pp. 2103–2107, May 2008. [17] L. Akhoondzadeh-Asl, M. Fardis, A. Abolghasemi, and G. Dadashzadeh, “Frequency and time domain characteristic of a novel notch frequency UWB antenna,” in Prog. Electromag. Rsrch., PIER 80, 2008, pp. 337–348. [18] B. Ahmadi, “A planar eye shape antenna for ultra-wide band applications,” Prog. Electromag. Rsrch. Lett., vol. 11, pp. 31–38, 2009. [19] D.-H. Kwon, “Effect of antenna gain and group delay variations on pulse-preserving capabilities of ultrawideband antennas,” IEEE Trans. Antennas Propag., vol. 54, no. 8, Aug. 2006. [20] D. Lamensdorf and L. Susman, “Baseband-pulse-antenna techniques,” IEEE Antennas Propag. Mag., vol. 36, no. 1, pp. 20–30, Feb. 1994. Travis Wayne Eubanks (S’08) received the B.S.E.E. degree from Texas A&M University, College Station, in 2007, where he is currently working toward the Ph.D. degree. In 2005, he worked for Cooper Cameron Corporation, Houston, TX and created device drivers that would monitor and control sub-sea gate valve controllers to constantly inspect the pressure of oil flowing through sea-floor pipelines in order to prevent catastrophe. He programmed these controllers using Java’s I/O tools and the MODBUS protocol. From 2006 until the present, he has worked for Sandia National Laboratories, Albuquerque, NM, on DC voltage-converting and current-limiting weapons reserve power supplies, synthetic aperture radars for 3D city imaging through thin particle cover from high-altitude (7 km) flight, long-range (greater than 10 miles) coded RFID transceivers for military use, Zigbee wireless communication hubs for user specified local wireless control over automated processes, featureless tagging, tracking, and locating systems, and remotely operated Thermotron temperature controlled environments using the Java Native Interface through a USB port. From 2007–2008, he worked under Dr. Kai Chang as a Research Assistant for the RF and Microwave Department of Texas A&M University, during which time he joined with researchers from Kobe University, Japan, to construct a wireless power rectenna and transmitter for the transmission of power through 148 kilometers of air (between two Hawaiian Islands) to simulate the transmission of such power from a solar power station in space to Earth (shown on Discovery Channel on Sept. 12, 2008). From 2008–2009, he worked as a teaching assistant for the Department of Electrical Engineering at Texas A&M University, and during this time he taught the undergraduate linear circuit theory laboratory and recitation session.

Kai Chang (S’75–M’76–SM’85–F’91) received the B.S.E.E. degree from National Taiwan University, Taipei, Taiwan, R.O.C., in 1970, the M.S. degree from the State University of New York at Stony Brook, in 1972, and the Ph.D. degree from The University of Michigan at Ann Arbor, in 1976. From 1972 to 1976, he was a Research Assistant with the Microwave Solid-State Circuits Group, Cooley Electronics Laboratory, The University of Michigan at Ann Arbor. From 1976 to 1978, he was with Shared Applications Inc., Ann Arbor, where he was involved with computer simulation of microwave circuits and microwave tubes. From 1978 to 1981, he was with the Electron Dynamics Division, Hughes Aircraft Company, Torrance, CA, where he was involved in the research and development of millimeter-wave solid-state devices and circuits, power combiners, oscillators, and transmitters. From 1981 to 1985, he was with TRW Electronics and Defense, Redondo Beach, CA, as a Section Head, where he developed state-of-the-art millimeterwave integrated circuits and subsystems including mixers, voltage-controlled oscillators (VCOs), transmitters, ampliers, modulators, upconverters, switches, multipliers, receivers, and transceivers. In August 1985, he joined the Electrical Engineering Department, Texas A&M University, College Station, as an Associate Professor and became a Professor in 1988. In January 1990, he was appointed Raytheon E-Systems Endowed Professor of Electrical Engineering. In 2006, he was appointed Texas Instruments Endowed Chair. He has authored and coauthored several books, including Microwave Solid-State Circuits and Applications (Wiley, 1994), Microwave Ring Circuits and Antennas (Wiley, 1996; 2nd ed., 2004), Integrated Active Antennas and Spatial Power Combining (Wiley, 1996), RF and Microwave Wireless Systems (Wiley, 2000), and RF and Microwave Circuit and Component Design for Wireless Systems (Wiley, 2002). He has served as the Editor of the four-volume Handbook of Microwave and Optical Components (Wiley, 1989 and 1990; 2nd ed., 2003). He is the Editor of Microwave and Optical Technology Letters and the Wiley Book Series on Microwave and Optical Engineering (over 80 books published). He has authored or coauthored over 450 papers and numerous book chapters in the areas of microwave and millimeter-wave devices, circuits, and antennas. He has graduated over 30 Ph.D. students and over 35 M.S. students. His current interests are microwave and millimeter-wave devices and circuits, microwave integrated circuits, integrated antennas, wideband and active antennas, phased arrays, microwave power transmission, and microwave optical interactions. Dr. Chang has served as technical committee member and Session Chair for the IEEE Microwave Theory and Techniques Society (IEEE MTT-S), the IEEE Antennas and Propagation Society (IEEE AP-S), and numerous international conferences. He was the Vice General Chair for the 2002 IEEE International Symposium on Antennas and Propagation. He was the recipient of the 1984 Special Achievement Award presented by TRW, the 1988 Halliburton Professor Award, the 1989 Distinguished Teaching Award, the 1992 Distinguished Research Award, and the 1996 Texas Engineering Experiment Station (TEES) Fellow Award presented by Texas A&M University.

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A Broadband Folded Printed Quadrifilar Helical Antenna Employing a Novel Compact Planar Feeding Circuit Mathieu Caillet, Member, IEEE, Michel Clénet, Member, IEEE, Ala Sharaiha, Senior Member, IEEE, and Yahia M. M. Antar, Fellow, IEEE

Abstract—A broadband printed quadrifilar helical antenna employing a novel compact feeding circuit is proposed in this paper. This antenna presents an excellent axial ratio over a wide beamwidth, with a 29% bandwidth. A specific feeding circuit based on an aperture-coupled transition and including two 90 surface mount hybrids has been designed to be integrated with the quadrifilar antenna. Over the bandwidth, the measured reflection coefficient of the antenna fed by the wideband compact circuit has been found to be equal to or lower than 12 dB and the maximum gain varies between 1.5 and 2.7 dBic from 1.18 to 1.58 GHz. The half-power beamwidth is 150 , with an axial ratio below 3 dB over this range. The compactness of the feeding circuit allows small element spacing in array arrangements. Index Terms—Antenna feeds, broadband, helical antennas, microstrip antennas, microstrip transitions, planar circuits, satellite navigation systems.

I. INTRODUCTION

M

OST satellite communication and navigation systems transmit signals using circularly polarized waves to benefit from better propagation characteristics through the atmosphere. Circularly polarized (CP) antennas that have a good axial ratio over the operating frequency band and the beamwidth of interest are then required. The navigation applications using any Global Navigation Satellite Systems particularly need antennas exhibiting an excellent axial ratio over a wide frequency band (or multiple bands) and over a wide beamwidth. Interesting antenna candidates that meet some of these requirements are, for instance, the printed stacked patch antenna [1]–[3], the cross printed dipole [4], or the quadrifilar helix antenna [5]. Recently, the folded printed quadrifilar helical antenna (FPQHA) has been proposed [6] and is well suited for use in navigation systems as it exhibits a superior axial ratio over a large frequency bandwidth and over a wide beamwidth. The feeding circuit of this antenna has to provide 4 ports with Manuscript received July 07, 2009; manuscript revised December 03, 2009; accepted January 15, 2010. Date of publication April 26, 2010; date of current version July 08, 2010. M. Caillet and Y. M. M. Antar are with the Royal Military College of Canada, Station Forces Kingston, ON K7K 7B4, Canada (e-mail: [email protected]). M. Clénet is with the Defence Research and Development Canada, Ottawa ON K1A 0K2, Canada. A. Sharaiha is with the Institute of Electronics and Telecommunications, Rennes (IETR), UMR CNRS 6164, University of Rennes 1, 35042 Rennes Cedex, France. Digital Object Identifier 10.1109/TAP.2010.2048865

90 of phase difference between adjacent ports. Conventional power divider and directional coupler circuits were used for the feeding system of the FPQHA. However, these circuits are relatively large in size at low frequencies and have limited frequency bandwidth. Therefore, it would be of interest to investigate a new broadband compact feeding circuit for the FPQHA. Planar printed technology presents an interesting solution to integrate the feeding circuit with the helical antenna, since it does not increase the profile of the antenna, and it is compact and lightweight. Among the possible circuits to achieve a 3-dB power splitter with 180 phase shift, the rat-race coupler, as well as the out-of-phase microstrip aperture-coupled transition are good potential candidates. An aperture-coupled transition offers good frequency bandwidth performance and is a highly integrable structure, even if two substrate layers are required. The proposed new feed network is then composed of a microstrip aperture-coupled transition to realize the 180 phase shift and 90 couplers complete the feed circuit to obtain 90 of phase difference between the 4 ports. The configuration of the proposed antenna consists of a cylindrical FPQHA fed by a planar double layer printed circuit. The novelty of this antenna structure is in the compactness of the feeding circuit, which includes a microstrip aperture-coupled transition confined to the centre of the FPQHA. Integrated with its compact feed, the antenna presents excellent CP performance over a broad beamwidth, across a wide frequency band and is easy to use in array configurations. Because an aperture is required in the ground plane underneath the antenna, the original quadrifilar antenna presented in [6] should be investigated to study the impact of the aperture on the antenna performance. The commercial simulation tool HFSS [7] has been used in this study. Excellent CP performance is targeted across the beamwidth over a 30% frequency band centred at 1.4 GHz. This paper presents the proposed broadband printed quadrifilar helical antenna employing a novel compact feeding circuit. The antenna configuration is described in Section II. Section III focuses on the feed network system design. The measured characteristics of the FPQHA are reported in Section IV. Conclusions and discussions are given in Section V. II. ANTENNA CONFIGURATION The resonant quadrifilar helix antenna (QHA) was originally investigated by Kilgus [8]. This antenna has found many appli-

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Fig. 1. Basic geometry of the folded printed quadrifilar helical antenna.

cations in Global Positioning System (GPS) and Satellite Navigation Systems (SNS) receiving antennas. The significant advantages of this antenna include its relatively compact size, its cardioid shaped pattern with excellent circular polarization coverage, its superior axial ratio and its low cost when using the printed QHA (PQHA) [9]. The geometry of the PQHA is obtained by printing the four arms on a thin, flexible, dielectric . substrate wrapped around a cylindrical foam support One of the current problems of the conventional PQHA is its difficulty in achieving wide bandwidths of operation. The bandwidth is typically 5% to 8%, which could be insufficient for some applications. Several techniques have been described in the literature to extend the QHA’s capability to operate at two frequency bands, using, for example, the mutual coupling effect between two PQHA fitted into each other [10], [11] (L1 and L2 for GPS applications). Other techniques have been proposed to enhance the bandwith of the QHA: for instance, using a conical geometry [12] allows a 18.5% bandwidth. The FPQHA presented in [6] considerably increases the QHA bandwidth, as 30% has been achieved. The basic geometry of the FPQHA is presented in Fig. 1. Each helix element consists of two parallel arms, shorted at the top of the helix. One is connected to the feeding point and the other is grounded. The simulated main characteristics of the FPQHA alone are presented hereafter. Unitary amplitudes and 90 out-of-phase between each feeding point are assumed for the simulation. The geometrical parameters are the same as those of the antenna presented in [6]. The diameter and height of the FPQHA are 36 and 130 mm, respectively. Further simulations reveal that the FPQHA can match the entire SNS bandwidth by slightly tuning its geometrical parameters. The active reflection coeffifrom 1.27 cient of the FPQHA is equal to or lower than to 1.63 GHz, and the maximum antenna gain varies between 2 and 3.5 dBic over the same frequency band (Fig. 2). One can notice that the obtained impedance bandwidth and gain do not cover the lower frequencies of the SNS bands (1.15–1.6 GHz). This has been done intentionally and through several simulations to anticipate the fabrication and measurements, based on previous experience which suggests that measurement results of the QHA tend to be somewhat lower in frequency compared to simulations. Fig. 3 shows the radiation pattern at 1.4 GHz, the

Fig. 2. Simulated active S amplitude/phase.

and maximum gain of the FPQHA fed with ideal

Fig. 3. Simulated radiation patterns of the FPQHA fed with ideal amplitude/ phase at 1.4 GHz.

central frequency. The half-power beamwidth (HPBW) of the right-hand circular polarization (RHCP) is 160 and the crosspolarization rejection is greater than 20 dB over the HPBW. This antenna is usually fed using balun or/and hybrid coupler circuits to provide 90 phase differences between the four ports of the antenna. This type of feeding network is fairly large in size, and its frequency band is limited. To overcome this matter, miniaturized wideband 90 hybrids [13], [14], as well as compact wideband rat-race couplers [15], [16], have been realized using printed technology. Another printed circuit of interest is the aperture-coupled microstrip transition [17], initially introduced to couple a line to a microstrip patch antenna [18]. The aperture-coupled transition has also been used for other applications in microwave circuits [19]. This dual-layer structure has the advantage of providing good broadband performance because of the nature of its geometry. Its design is quite flexible and only two parameters have to be tuned for a desired operating frequency. The aperture-coupled microstrip transition can also be modified to provide two outputs having a 180 phase difference. Another advantage of using a multi-layer structure is to isolate the feeding system from the radiating element, as the ground plane is placed in between them. For these reasons, this circuit has been selected as the 180 power divider of the

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Fig. 5. Simulated axial ratio of the FPQHA without and with a slot etched in the ground plane at 1.4 GHz.

Fig. 4. Geometry’s exploded view of the compact feeding circuit integrated with the Folded Printed Quadrifilar Helical Antenna.

feeding system. Fig. 4 presents an exploded view of the antenna geometry. III. THE COMPACT WIDEBAND FEEDING SYSTEM The feeding system has to provide constant magnitudes and 90 phase differences to the four arms of the FPQHA over the operating frequency band. The design procedure of the feeding system and its measurement results are described in this section. A. Design and Fabrication The key concept used to integrate the feeding system with the FPQHA consists of a compact aperture-coupled microstrip transition enclosed in the bottom section of the antenna, whose diameter is 36 mm. The conventional configuration of this transition includes two layers of substrates topped by microstrip lines (possibly a patch) and a slot etched in the ground plane. The feeding line of the transition is located on the upper substrate and the outputs are on the lower substrate (Fig. 4). A quarter-wavelength serial stub is required to match the feeding . A quarter-wavelength line is placed on top of the line to . slot between the two outputs to match the T-junction to The outputs of this dual-layer structure provide 180 phase difference. The FPQHA usually remains directly on a ground plane. Because a substrate is required on top of the ground plane for the aperture-coupled microstrip transition, the feeding line footprint of the transition should then be limited to the bottom section of the antenna. This means that the antenna port cannot be on the same layer as the transition feeding line. To overcome this, the antenna port is located on the lower substrate and a microstrip to coaxial transition is used to connect the antenna feeding line

to the transition feeding line. In such a configuration, the microstrip line on the upper layer is short and can be enclosed in the bottom section of the antenna. To reduce the aperture dimensions and improve the coupling as well, the geometry of the slot can be changed from linear to a dogbone (or H) shape [20]. This also offers the advantage of reducing the back radiation. In addition, the use of a high perfor the feeding network almittivity constant material lows to further reduce the size of the aperture to fit at the bottom of the centre part of the helical antenna. Based on these considerations, an H-shape aperture-coupled transition has been investigated to be integrated with the FPQHA while limiting its footprint to the center part of the antenna. In particular, the effects of the slot on the ground plane have been investigated, as a full ground plane (no slot) was used in the original design of the FPQHA. The main differences have been observed for the level of the back radiation, and the axial ratio. Indeed, the presence of a slot in the ground plane increases by 2.5 dB the level of the back radiation at 1.4 GHz. Fig. 5 shows the effect of the slot etched in the ground plane on the FPQHA axial ratio for a full ground plane and a 0.5 mm wide slot. One can notice an increase of the axial ratio of about 1 dB in the boresight region. Very similar results have been obtained with 1 and 1.5 mm wide slots. These effects do not radically degrade the performance of the FPQHA, and are considered acceptable. The final slot geometry is composed of mirrored C-shaped arms (10 mm high, and 4.5 mm wide) placed on both sides of a linear slot (17 mm long). This geometry allows to further reduce the occupied area while providing very similar performance. To complete the CP antenna feeding circuit, two commercial surface mount 90 hybrids [21] have been positioned on both sides of the aperture-slot transition. Grounded pads are required resistors need to be soldered to the for the SMT hybrids and isolated port of the 90 hybrids. This grounding is realized using plated thru holes. The feeding circuit remains on the bottom substrate (Fig. 4). From the antenna port on the bottom layer, a microstrip to coaxial transition allows connection to a line placed on the upper substrate. This line excites the aperture-slot transition that couples to a microstrip line printed on the bottom

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Fig. 8. Measured results of the output phase differences of the FPQHA feeding circuit.

Fig. 6. The FPQHA feeding circuit prototype. The edge of the square board is 50.8 mm (2”) long.

Fig. 9. Fabricated antenna prototype.

Fig. 7. Measured results of the S-parameter magnitude of the FPQHA feeding circuit.

layer, whose outputs have a 180 phase difference. Commercial surface mount (SMT) 90 hybrids [21] are connected to both outputs of the aperture-slot transition to allow for a four port circuit having a 90 phase sequential rotation. The fabricated feeding circuit is shown in Fig. 6. B. Measurement Results The fabricated feeding circuit shown in Fig. 6 was measured to verify its performance over the frequency band of interest. Fig. 7 presents the measured reflection coefficient and output magnitudes. The reflection coefficient is below from 1.15 to 1.6 GHz, and the output magnitudes exhibit a maximum unbalance of 0.6 dB over the same bandwidth. Furthermore, Fig. 8 presents the output phase differences as a function of frequency. The maximum phase variation is 3 over the frequency band. The above results indicate that the obtained measured performance of the QHA feeding circuit is sufficient, and its characterization with the QHA is the subject of Section IV.

Fig. 10. Measured reflection coefficient of the FPQHA fed by the wideband feeding system.

IV. CHARACTERIZATION OF THE ANTENNA This section focuses on the presentation of the measured results obtained with a fabricated FPQHA prototype integrated with the compact wideband feeding circuit. Fig. 9 presents the fabricated prototype of the FPQHA employing the compact wideband feeding circuit presented in Section III. The reflection coefficient of the fabricated antenna was meaover the SNS frequency bands, sured. It is lower than as shown on Fig. 10.

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TABLE I SUMMARY OF THE RADIATION CHARACTERISTICS OF THE FPQHA WITH THE WIDEBAND FEEDING SYSTEM AT F1 (1.225 GHZ), F2 (1.375 GHZ) AND F3 (1.575 GHZ)

Fig. 12. Measured maximum gain of the FPQHA as a function of the frequency.

Fig. 11. Radiation patterns of the FPQHA fed by the wideband aperture-slot feeding system: (a) F1 = 1:225 GHz, (b) F2 = 1:375 GHz, and (c) F3 = 1:575 GHz.

The radiation patterns of the FPQHA with the wideband slot feeding system were measured in a far-field anechoic chamber at the Communications Research Centre in Ottawa, Canada. A linearly polarized antenna was used as the transmitting antenna, and two orthogonal measurements were carried out in magnitude and phase. The radiation patterns were measured in three , 45 , and 90 over a 1.125–1.625 GHz frequency planes: contains the probe range with a 50 MHz step. The plane feed. Measurements for three frequencies, ,

and , are shown in Fig. 11. Note that F1 corresponds to L2 GPS band and F3 corresponds to L1 GPS band. F2 is the centre frequency of the bandwidth considered for radiation pattern measurement. One can first notice that all the patterns present a wide beamwidth with an almost constant gain and low axial ratio. The radiation characteristics were extracted for each frequency and plane cut. They are summarized in Table I. The axial ratio (AR) is computed from the magnitude and phase captured in two orthogonal planes by first calculating the tilt angle representing the spatial orientation of the ellipse [22]. The minor and major axes of the ellipse can then be obtained, and the AR is the ratio of the major axis over the minor axis. The antenna gain in circular polarization is the modulus of the two orthogonal measured magnitudes. The maximum gain in CP is about 1.8, 2.3 and 1.5 dBic at F1, F2 and F3, respectively (Fig. 12). There is however a slight gain drop in the boresight direction, which is more pronounced when the frequency increases, as it can be seen in Fig. 11. In the boresight direction, the gain in CP is 1.5, 1.3 and 0 dBic at F1, F2 and F3, respectively. The half-power beamwidth (HPBW) increases slightly with frequency, being 145 at F1, 160 at F2 and 180 at F3. The HPBWs in the three planes are of the same order. The axial ratio (AR) has been deduced from measurements in two orthogonal cuts. The AR in the boresight direction is greater than 2 dB over the frequency range, being 1.5 dB at F1, 0.7 dB at F2 and 2.0 dB at F3 (Fig. 13). The AR does not increase quickly when one moves away from boresight. The beamwidth where the AR is lower than 3 dB is about 180 at the three frequencies under consideration, varying from 200 for F1 and F2, to 150

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ACKNOWLEDGMENT The authors would like to thank Taconic Advanced Dielectric Division for providing laminate substrate samples, and the staff at Communications Research Centre in Ottawa for their assistance in circuit fabrication and antenna testing. REFERENCES

Fig. 13. Measured axial ratio of the FPQHA at boresight as a function of the frequency.

for F3. As pointed out previously, the introduction of a slot in the ground plane may increase the back radiation level, so it is important to check its level. The front-to-back ratio reaches 8 dB at F1, 15 dB at F2 and 6 dB at F3. Overall, the antenna exhibits excellent radiation characteristics, i.e., a constant gain and a low axial ratio over a wide frequency range and over a wide beamwidth. Its performance exceeds the capabilities of other small antennas designed for these applications such as the stacked-patch [3] and dielectric resonator [23] antennas, especially in terms of achieving valuable performance over a wide beamwidth. This makes the presented antenna an outstanding candidate for use in SNS applications.

V. CONCLUSION In this paper, a broadband printed quadrifilar helical antenna employing a novel compact feeding circuit has been designed and implemented. This antenna is well suited for use in satellite navigation systems as it exhibits an excellent axial ratio over a large frequency bandwidth and over a wide beamwidth. The measured results of a compact feeding circuit based on an aperture-coupled transition and including two 90 SMT hybrids have first been addressed. The reflection coefficient is below between 1.15 and 1.6 GHz, the maximum output magnitude imbalance is 0.6 dB, and the maximum output phase imbalance is 3 over the same bandwidth. Measured results of the folded printed quadrifilar helical antenna integrated with its compact feeding circuit show good overall performance. The reflection coefficient of the FPQHA and the gain varies between is equal to or lower than 1.5 and 2.7 dBic over a 29% bandwidth, from 1.18 to 1.58 GHz. The HPBW of the RHCP is in the range of 150 , with an axial ratio below 3 dB over the HPBW. The maximum back radiation level is 6 dB. Future extensions of this work are the design of a compact FPQHA using dielectric to load the antenna centre part [11] for example, and the study of the FPQHA integration into an array configuration.

[1] D. M. Pozar and S. M. Duffy, “A dual-band circularly polarized aperture-coupled stacked microstrip antenna for global positioning satellite,” IEEE Trans. Antennas Propag., vol. 45, no. 11, pp. 1618–1625, Nov. 1997. [2] Y. Zhou, C.-C. Chen, and J. L. Volakis, “Single-fed circularly polarized antenna element with reduced coupling for GPS arrays,” IEEE Trans. Antennas Propag., vol. 56, no. 5, pp. 1469–1472, May 2008. [3] E. G. Doust, M. Clénet, V. Hemmati, and J. Wight, “An aperture-coupled circularly polarized stacked microstrip antenna for GPS frequency bands L1, L2, and L5,” presented at the IEEE AP-S Int. Symp., Jul. 2008. [4] J. Jin, X.-M. Wan, W. Wang, and X.-L. Liang, “Broad beamwidth circularly polarized printed antenna for GPS applications,” in Proc. IEEE AP-S Int. Symp., Jun. 2007, pp. 2638–2641. [5] J. M. Tranquilla and S. R. Best, “A study of the quadrifilar helix antenna for global positioning system (GPS) applications,” IEEE Trans. Antennas Propag., vol. 38, no. 10, pp. 1545–1550, Oct. 1990. [6] Y. Letestu and A. Sharaiha, “Broadband folded printed quadrifilar helical antenna,” IEEE Trans. Antennas Propag., vol. 54, no. 5, pp. 1600–1604, May 2006. [7] “High Frequency Structure Simulator v. 11.0,” Ansoft Corp, 2008 [Online]. Available: www.ansoft.com [8] C. Kilgus, “Resonant quadrafilar helix,” IEEE Trans. Antennas Propag., vol. 17, no. 3, pp. 349–351, May 1969. [9] A. Sharaiha and C. Terret, “Analysis of quadrifilar resonant printed helix antenna for mobile communications,” IEE Proc.-H, vol. 140, no. 4, pp. 269–273, Aug. 1993. [10] A. Sharaiha and C. Terret, “Overlapping quadrifilar resonant helix,” Electron. Lett., vol. 26, no. 14, pp. 1090–1092, Jul. 1990. [11] Q.-X. Chu and S. Liu, “A novel dielectric-loaded dual-band GPS antenna for handset applications,” presented at the IEEE AP-S Int. Symp., Jun. 2008. [12] S. Yang, S. H. Tan, Y. B. Gan, and C. W. See, “Broadband conical printed quadrifilar antenna with integrated feed network,” Microw. Opt. Technol. Lett., vol. 35, no. 6, pp. 491–493, Dec. 2002. [13] Y.-H. Chun and J.-S. Hong, “Compact wide-band branch-line hybrids,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 2, pp. 704–709, Feb. 2006. [14] C.-W. Tang and M.-G. Chen, “Synthesizing microstrip branch-line couplers with predetermined compact size and bandwidth,” IEEE Trans. Microw. Theory Tech., vol. 55, no. 9, pp. 1926–1934, Sep. 2007. [15] T. T. Mo, Q. Xue, and C. H. Chan, “A broadband compact microstrip rat-race hybrid using a novel CPW inverter,” IEEE Trans. Microw. Theory Tech., vol. 55, no. 1, pp. 161–167, Jan. 2007. [16] M. Caillet, M. Clénet, A. Sharaiha, and Y. M. M. Antar, “A compact wide-band rat-race hybrid using microstrip lines,” IEEE Microw. Wireless Compon. Lett., vol. 19, no. 4, pp. 191–193, Apr. 2009. [17] B. Schiek and J. Kohler, “An improved microstrip-to-microslot transition,” IEEE Trans. Microw. Theory Tech., vol. 24, no. 4, pp. 231–233, Apr. 1976. [18] D. M. Pozar, “A microstrip antenna aperture coupled to a microstrip line,” Electron. Lett., vol. 21, no. 2, pp. 49–50, Jan. 1985. [19] M. W. Katsube, Y. M. M. Antar, A. Ittipiboon, and M. Cuhaci, “A novel aperture coupled microstrip magic-T,” IEEE Microw. Guided Wave Lett., vol. 2, pp. 245–246, Jun. 1992. [20] D. M. Pozar and S. D. Targonski, “Improved coupling for aperture coupled microstrip antennas,” Electron. Lett., vol. 27, no. 13, pp. 1129–1131, Jun. 1991. [21] 3-dB/90 Hybrid Coupler, Model XC1400P-03S, Anaren [Online]. Available: www.anaren.com [22] C. A. Balanis, Antenna Theory: Analysis and Design, 2nd ed. New York: Wiley, 1997. [23] K.-W. Khoo, Y.-X. Guo, and L. C. Ong, “Wideband circularly polarized dielectric resonator antenna,” IEEE Trans. Antennas Propag., vol. 55, no. 7, pp. 1929–1932, Jul. 2007.

CAILLET et al.: A BROADBAND FPQHA EMPLOYING A NOVEL COMPACT PLANAR FEEDING CIRCUIT

Mathieu Caillet (S’06–M’07) was born in Besançon, France, in 1980. He received the Engineering and M.S. degrees in signal processing and telecommunications from the University of Rennes 1, France, in 2003 and the Ph.D. degree from the Rennes Institute of Electronics and Telecommunications, France, in 2006. He is now a Research Assistant in the Electrical and Computer Engineering Department of the Royal Military College of Canada at Kingston, Ontario, Canada. His current research interests include the analysis and development of an array processing module for a phased array antenna simulation tool, and new concepts of compact antennas and circuits.

Michel Clénet (M’99) was born in Nantes, France, in 1968. He received the Master in Sciences and Technology (MST) degree in signal processing and the Diplôme d’Études Approfondies (DEA) degree in telecommunications from the University of Rennes I, France, in 1991 and 1992 respectively, and the Ph.D. degree from the University of Nantes, Nantes, France, in 1997. In 1993, he joined the Electronic and Computer Systems (SEI) Laboratory at IRESTE, Nantes, where he was involved in research on antenna systems for mobile communications. He developed several prototypes for adaptive antenna applications. From 1997 to 1999, he was a Postdoctoral Fellow at the University of Manitoba, Winnipeg, Canada, where he worked on microstrip antennas, arrays and horns. Since 1999, he has been with Defence Research and Development Canada (DRDC), Ottawa, Canada, where he has been working on array signal processing, RF systems, planar antennas, arrays and related technologies, for satellite communication applications. He is currently working on controlled reception pattern antenna systems for GPS applications.

Ala Sharaiha (SM’09) received the Ph.D. and Habilitation à Diriger la Recherche (HDR) degrees in telecommunication from the University of Rennes 1, France, in 1990 and 2001, respectively. Currently, he is a Professor at the University of Rennes 1, Rennes, France and a Researcher in the Antennas and High Frequency Group at the institute of Telecommunication of Rennes, where he is the responsible of a research theme concerning the new concepts and architecture of antennas design. Main research activities include broadband and UWB antennas, miniaturization, printed spiral and helical antennas, antennas

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for mobile communications, etc. Conducted and involved in more than 15 development projects for private companies and participates in the European Network of Excellence ACE (Antenna Center of Excellence) in the small antenna WP. He is the author and coauthor of 30 international papers, 90 conference presentations and holds eight European patents. Prof. Sharaiha is a reviewer for the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, and IET Letters. He was the conference Chairman of the 11th International Canadian Conference ANTEM (Antenna Technology and Applied ElectroMagnetics), held at Saint-Malo in France, 2005.

Yahia M. M. Antar (S’73–M’76–SM’85–F’00) received the B.Sc. (Hons.) degree from Alexandria University, Alexandria, Egypt, in 1966 and the M.Sc. and Ph.D. degrees from the University of Manitoba, Manitoba, ON, Canada, in 1971 and 1975, respectively, all in electrical engineering. In May 1979, he joined the Division of Electrical Engineering, National Research Council of Canada, Ottawa, where he worked on polarization radar applications in remote sensing of precipitation, radio wave propagation, electromagnetic scattering and radar cross section investigations. In November 1987, he joined the staff of the Department of Electrical and Computer Engineering at the Royal Military College of Canada in Kingston, where he has held the position of Professor since 1990. He has authored or coauthored over 160 journal papers and 300 Conference papers, and holds several patents. He holds an adjunct appointment at the University of Manitoba, and has a cross appointment at Queen’s University in Kingston. He also serves, since November 2008, as Associate Director of the Defence and Security Research Institute (DSRI). Dr. Antar is a Fellow of the IEEE, a Fellow of the Engineering Institute of Canada (FEIC), an Associate Editor (Features) of the IEEE ANTENNAS AND PROPAGATION MAGAZINE, served as Associate Editor of the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, and is a member of the Editorial Board of the RFMiCAE Journal. In May 2002, he was awarded a Tier 1 Canada Research Chair position in Electromagnetic Engineering which has been renewed in 2009. In 2003, he received the 2003 Royal Military College “Excellence in Research” Prize. He was elected to the Board of the International Union of Radio Science (URSI) as Vice President in August 2008 and to the IEEE AP Society ADCOM in December 2009. He chaired conferences and given plenary talks in many conferences, and supervised or co-supervised over 70 Ph.D. and M.Sc. theses at the Royal Military College and at Queen’s University, of which several have received the Governor General of Canada Gold Medal as well as best paper awards in major symposia. He served as the Chairman of the Canadian National Commission for Radio Science (CNC/URSI 1999–2008), Commission B National Chair (1993–1999).

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Low-Q Electrically Small Spherical Magnetic Dipole Antennas Oleksiy S. Kim

Abstract—Three novel electrically small antenna configurations radiating a TE10 spherical mode corresponding to a magnetic dipole are presented and investigated: multiarm spherical helix (MSH) antenna, spherical split ring resonator (S-SRR) antenna, and spherical split ring (SSR) antenna. All three antennas are self-resonant, with the input resistance tuned to 50 ohms by an excitation curved dipole/monopole. A prototype of the SSR antenna has been fabricated and measured, yielding results that are consistent with the numerical simulations. Radiation quality factors ( ) of these electrically small antennas (in all cases 0 26) approach the limit of 3.0 times the Chu lower bound for a given antenna size, which is in line with a theoretical prediction made by Wheeler in 1958. Index Terms—Chu limit, electrically small antennas, quality factor, magnetic dipole, split-ring resonator (SRR), surface integral equation.

I. INTRODUCTION

F

UNDAMENTAL electromagnetic properties of electrically small antennas (ESA) were first explored by Wheeler [1] and Chu [2] more than 60 years ago. Whereas Wheeler focuses on limitations peculiar to electrically small electric and magnetic dipole antennas, Chu develops a more sophisticated theory based on spherical TM and TE modes radiated by a generalized omnidirectional ESA. Subsequently revisited and corrected by a number of authors [3]–[6], Chu’s theory establishes a lower bound for a radiation quality factor achievable by a small antenna occupying a certain volume. The quality factor relates the reactive energy to the radiated power, and for a single-resonance ESA it is inversely proportional to the antenna frequency bandwidth. Chu assumes that the reactive electric (magnetic) energy is stored entirely outside a minimum sphere of radius and thus derives an ultimate lower bound for an electrically small TM-mode (TE-mode) antenna. Any passive antenna inscribed in a sphere cannot perform better than that. More realistic of radius configurations are considered by Thal in [7], where he starts with an impressed electric current on a spherical surface and allows the field not only outside but also inside the sphere to satisfy the boundary condition. It is not surprising that Thal’s bounds are higher than those by Chu. For instance, Thal shows that for an electric dipole (TM mode) antenna Manuscript received July 02, 2009; revised October 03, 2009; accepted January 11, 2010. Date of publication April 26, 2010; date of current version July 08, 2010. This work was supported by the Danish Research Council for Technology and Production Sciences within the TopAnt project. The author is with the Department of Electrical Engineering, Electromagnetic Systems, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark (e-mail: [email protected]). Digital Object Identifier 10.1109/TAP.2010.2048863

Fig. 1. Geometries of spherical magnetic dipole (TE mode) antennas: (a) Multiarm spherical helix (MSH) antenna; (b) spherical split-ring resonator (S-SRR) antenna; (c) spherical split ring (SSR) antenna.

as , where is the free space propagation constant. This result is confirmed by simulations and measurements of real antennas designed by Best [8], [9]. What is more interesting is that Thal’s bounds for electric and magnetic dipole antennas are not equal. According to Thal, for an electrically small magnetic . In fact, the latter dipole (TE mode) antenna result was also predicted by Wheeler in 1958 [10]. Recently, a 16-slot electrically small TE -mode antenna yielding the was reported by Best [11]. quality factor This paper presents three novel electrically small antenna configurations (Fig. 1) designed to radiate the TE spherical mode corresponding to a magnetic dipole (z-directed in Fig. 1). These antennas are a multiarm spherical helix (MSH) antenna, a spherical split-ring resonator (S-SRR) antenna, and a spherical split ring (SSR) antenna. Being quite different in geometry, all three antennas are self-resonant with no external lumped

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KIM: LOW-Q ELECTRICALLY SMALL SPHERICAL MAGNETIC DIPOLE ANTENNAS

elements used to ensure the resonance. Basically, each antenna is a spherical resonator excited by a curved dipole, whose length is varied appropriately to match the antenna to a feed line in a way similar to [12], [13]. The TE -mode antennas presented in this paper not only validate the Wheeler-Thal lower bound for magnetic dipole antennas, but also provide a necessary basis for designing low- ESA that outperform electric dipole antennas. As shown in [14], a magnetic dipole antenna augmented with a magnetic core yields the quality factor approaching the Chu lower bound. In this paper, numerical results are obtained using a surface integral equation (SIE) technique combined with a higher-order method of moments [15]. The antennas are assumed to be lossless with a delta-gap generator as a signal source. The quality factor is calculated from the antenna input impedance as [16]

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(3b) where and are the external stored magnetic energy and the radiated power of higher-order magnetic modes (TE spherical modes), respectively. For an electrically small , the magnetic dipole antenna, besides the radiated power higher-order TM modes contribute predominantly to the stored electric energy, and thus negligibly change the numerator in (3). On the other hand, the stored magnetic energy is defined by the fundamental TE mode as well as by the higher-order TE modes that, unlike the higher-order TM modes, increase the quality factor [5], and therefore must be suppressed in a well-designed magnetic dipole antenna. In this case, the bound (3) can be simplified as (4)

(1) is the angular frequency at the resonance. where In terms of comparing the quality factors of practical antennas with the lower bound, it is important to recognize that the presence of higher-order modes affects the quality factor, and this effect must be accounted for not only in the calculations of the antenna itself, but also in the bound it is compared with. In the next section of this paper, a brief note on the evaluation of the quality factor lower bound for a magnetic dipole antenna in is given. the presence of higher-order modes The next three sections contain results of parametric investigations for each of the three antenna configurations, respecis approached tively. It is shown how the bound by changing appropriate antenna geometry parameters as well as how the resonance frequency and the input resistance at resonance are tuned to the desired values. Experimental results for a fabricated SSR antenna are also presented. II. QUALITY FACTOR LOWER BOUND AND HIGHER-ORDER MODES The quality factor lower bound for an electrically small magnetic dipole non-resonant antenna tuned to a resonance by a lossless reactive element and/or by distributed reactive fields is given by [4], [6] (2) where and are the time-average stored magnetic energy external to the antenna sphere of radius and the radiated power of the magnetic dipole mode (TE spherical mode), respectively. In the presence of higher-order modes the bound can be exactly computed using expressions provided by Fante [5]. However, this requires knowledge of the whole spectrum of spherical modes radiated by an antenna. In many cases, a somewhat easier approach can be undertaken. To account for higher-order modes the expression (2) is modified as (3a)

where is the power of the TE mode relative to the total radiated power. Thus, to compute the lower bound it is sufficient to evaluate a single spectrum component—the amplitude of the TE mode. The expression (4) for a magnetic dipole TE mode antenna is valid under three conditions: 1) the antenna is electrically small, so that TM modes contribute negligibly to the stored magnetic energy; 2) higher-order TE modes are suppressed enough to be neglected; 3) externally to the antenna, the stored magnetic energy ex. ceeds the stored electric energy As shown below, all antennas presented in this paper fulfill the first two conditions, whereas the third one is only met by the S-SRR and SSR antennas. The third condition is violated by some magnetic dipole antennas, in which due to higher-order TM modes the stored electric energy outside the antenna is superior to the corresponding stored magnetic energy. If such an antenna is self-resonant, e.g., the MSH antenna, the overall energy balance is restored by the surplus of the stored magnetic energy inside the antenna. In this case, an expression dual to (3a) must be applied, although the radiated power is by far dominated by the main TE mode. It is noted, that the considerations presented in this section are by duality applicable for electric dipole antennas. III. MULTIARM SPHERICAL HELIX (MSH) ANTENNA The TE MSH antenna is a modification of a spherical helix antenna developed by Best [9]. The original configuration [Fig. 2(a)] radiates the TM spherical mode, since the driving voltage is applied vertically in the middle of one of the arms. Due to the symmetry and small electrical dimensions, the far-field contributions from the -components of the electric mutually cancel, thus leaving only the current on the wires -component of the electric far-field (and -component of the magnetic far-field). In the TE MSH antenna, top and bottom parts of the arms are disconnected, and a curved dipole is placed at the equator of the antenna sphere (Fig. 2(b)). The driving voltage is now applied horizontally at the midpoint of the excitation dipole. In

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TABLE I CHARACTERISTICS OF THE TE

MSH ANTENNA

Fig. 3. Input impedance of the TE of turns in each arm.

Fig. 2. Multiarm spherical helix (MSH) antenna: (a) TM (b) TE (magnetic dipole).

(electric dipole);

this case, the far-field contributions from the -components of cancel, and the resulting radiated fields the electric current are those of the desired TE spherical mode. and number of arms , the For a given frequency antenna is tuned to the resonance by changing the number of in the arms as shown in Fig. 3, where the anturns MHz is plotted for four tenna input impedance at antenna configurations having , and arms. All mm, and the wire antenna configurations have radius radius is set to 0.5 mm. Thus, the antennas occupy a spherical mm, or at 300 MHz. volume of radius Observing Fig. 3 one may note that the quality factor decreases as the number of arms multiplied. From Table I, which summarizes the geometry parameters for self-resonant antenna configurations and corresponding quality factors , it is seen that the quality factor indeed decreases approaching .

MSH antenna as a function of the number

Besides the number of arms and the number of turns in each arm, there is another important antenna geometry parameter—the length of the curved excitation dipole. In this paper, it is quantified in angular units and denoted by [see Fig. 2(b)]. It controls the antenna input resistance at resonance and makes matching of the antenna to external circuits a fairly straightforward task. For instance, the results presented chosen in Fig. 3 and Table I, are obtained with the length so that for each number of arms the antenna is matched to 50 ohms at the resonance. Fig. 4(a) shows the dependence of the on the angle with the number of antenna input resistance arms as a parameter. For a fixed number of turns (see Table I for the values), a change in the length of the excitation dipole causes a little shift in the resonance frequency as depicted in Fig. 4(b). By adjusting the number of turns the deviation in the resonance frequency is easily compensated. The presented antenna is electrically small and its radiation pattern closely reproduces that of an elementary magnetic dipole with the directivity 1.76 dB. A spherical wave expansion of the antenna far-fields shows that next most significant spherical modes after the fundamental TE mode are TM and TM . The radiated power of these modes normalized to the total radiated power is given in Table I. As the number of arms increases, the relative radiated power of the TM mode decreases, whereas the TM mode stays constant at a level, which is so high that the stored electric energy external to the antenna exceeds the external stored magnetic energy. Since the antenna is self-resonant, the energy balance is by necessity recovered by the opposite energy difference inside the antenna.

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Fig. 5. Spherical split-ring resonator (S-SRR) antenna on a ground plane.

Fig. 4. Input resistance at resonance (a) and the resonance frequency (b) of the TE MSH antenna as a function of the excitation dipole length.

However, the lower bound must now be computed using the stored electric energy, and this is done by applying the exact expressions [5, Eq. (7)]. As shown in Table I, due to the presence of the relatively strong TM mode the lowest achievable quality factor is noticeably higher than that of the . Consequently, the ratio TE mode alone becomes less than 3.0. IV. SPHERICAL SPLIT-RING RESONATOR (S-SRR) ANTENNA The S-SRR antenna consists of a spherical split-ring resonator and a curved excitation dipole [Fig. 1(b)] arranged so that mostly -directed electric surface currents of the desired TE mode are excited. Unlike the previous case, a symmetry along the XZ-plane allows the antenna to be placed on a metal ground plane as sketched in Fig. 5. The S-SRR is a conformal to a sphere variation of a broadside coupled split-ring resonator [17], [18]. Due to a large overlapping area of two spherical surfaces the S-SRR can be easily made electrically small. Results below are presented for the S-SRR antenna on an infinite perfectly electrically conducting (PEC) ground plane; and the

Fig. 6. Properties of the S-SRR antenna as a function of angle : (a) ratio Q=Q and the relative radiated power of the TM mode; (b) input resistance at resonance and the resonance frequency.

geometrical parameters are as follows: mm, mm, mm, mm, and the radius of the monopole is 0.5 mm. In terms of low it is desirable to distribute the electric cur, that is to rent over the entire spherical surface of radius . Howallow the S-SRR to cover the whole sphere ever, this blocks the magnetic flux over the antenna crossection and thus diminishes the electric current on the antenna surface. Therefore, there should be expected an optimal coverage yielding a minimum . Indeed, the dependence of on the angle plotted in Fig. 6(a) exhibits an the ratio optimum at .

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Fig. 8. Spherical split ring (SSR) antenna on a ground plane.

Fig. 7. Input resistance at resonance and the resonance frequency of the S-SRR antenna as a function of the excitation monopole length.

The resonance frequency variation versus [Fig. 6(b)] . shows the similar behavior yielding minimum at Although the location of this minimum does not coincide , the difference in with the optimum for the ratio and is minor, the resonance frequency for the resonance frequency being only 1.5 MHz. For MHz, and the electrical size of the antenna is is . Fig. 6(b) also illustrates the dependence of the antenna input at resonance on the angle . For this plot as resistance well as for the simulations above, the length of the excitation monopole, which likewise the excitation dipole in the MSH antenna (Section III) controls the input impedance, is chosen to , so that ohms for the optimal . be In the spherical wave spectrum of the antenna, TM is the only most significant higher-order mode, whereas TM —the strongest higher-order mode in the spectrum of the MSH antenna (Section III)—in this case is totally suppressed due to absence of -directed currents in the XZ-plane. The TM mode is however very pronounced and thus noticeably influences the , as shown in Fig. 6(a). The S-SRR antenna fulfills ratio all three conditions specified in Section II, and therefore, the ex. An expression (4) is applied to compute the lower bound cellent agreement with the ratio obtained using the exact expression [5, Eq. (7)] validates the approach introduced in Section II. The tuning properties of the S-SRR antenna are demonstrated and the input rein Fig. 7, where the resonance frequency sistance at resonance are plotted versus the length of the . A weak variation of the resomonopole for a fixed nance frequency is observed, while a broad variation of the input resistance allows the antenna to be matched to a wide range of feed lines. exhibited by the In summary, the minimum ratio S-SRR antenna is close to that of the 4-arm MSH antenna (Section III). On the other hand, the symmetry in the XZ plane eliminates the TM mode and enables the S-SRR antenna to operate on a ground plane. V. SPHERICAL SPLIT RING (SSR) ANTENNA In this novel antenna configuration, the spherical resonator is composed of individual wire split rings distributed evenly in

[Fig. 1(c)]. Every two neighbor rings are flipped with respect to each other and, thus, operate as a conventional SRR. Combined with other rings they constitute a multielement SRR. This arrangement ensures a more uniform current distribution over the antenna spherical surface as well as a great reduction of the resonance frequency as compared to a single two-element SRR and, a fortiori, a single split ring. The number of the rings are chosen to be odd, so that the central split ring serves as an excitation dipole with arm lengths adjusted to match the antenna to a feed line. As in the previous case, the SSR antenna possesses the symmetry in the XZ-plane and, consequently, an ability to operate on a ground plane (Fig. 8). For a given radius of the spherical resonator , the resonance frequency is essentially controlled by the number of split rings ; finer adjustments can be made via changing the gap width in the rings. The number of split rings is determined using the following expression (5) where is an angular separation between two neighbor rings (Fig. 8). A. Numerical Results Here, results are presented for the SSR antenna on an infinite PEC ground plane. Some of the geometrical parameters are mm, mm, and the radius of the fixed as follows: wires is 0.5 mm. The separation angle is varied to elucidate the dependence of the antenna quality factor on the number of split rings. The result presented in Fig. 9(a) shows that as the split rings get closer to each other and their number increases, the monotonically decreases. And so does the relative ratio radiated power of the parasitic TM mode. As compared to the S-SRR antenna (Section IV), its level is highly reduced, and its influence on the ratio is minor [Fig. 9(a)]. Again, the TM mode is totally suppressed due to absence of -directed wires. Variations of the resonance frequency and the input resisversus the angle are plotted in Fig. 9(b). tance at resonance In these simulations the length of the excitation monopole (the , which yields central split ring) is fixed to ohms input impedance for , or . If

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Fig. 11. Fabricated prototype the SSR antenna.

Fig. 9. Properties of the SSR antenna as a function of angle : (a) ratio Q=Q and the relative radiated power of the TM mode; (b) input resistance at resonance and the resonance frequency.

Fig. 12. Predicted and measured reflection coefficient of the manufactured SSR antenna.

B. Measured Results

Fig. 10. Input resistance at resonance and the resonance frequency of the SSR antenna as a function of the excitation monopole length. : .

=49

is varied, it changes the input resistance as illustrated in Fig. 10. Corresponding changes in the resonance frequency also shown in Fig. 10 are within %. comparable to that The SSR antenna yields the ratio of the MSH antenna (Section III), and at the same time, it can be used on a ground plane. Furthermore, among all presented antennas it exhibits the best characteristics in terms of radiation purity of the TE mode.

To facilitate the fabrication of an SSR antenna prototype, , and the the number of split rings was reduced to wire of diameter 1.63 mm was selected. With the excitation , the SIE simulations predict the monopole length ohms and the resonance frequency input impedance MHz, which corresponds to the electrical size . A supplementary simulation taking into account finite conductivity (copper) of the wires was carried out in the commercially available CST Microwave Studio, and the results are consistent with the SIE predictions. The fabricated prototype (Fig. 11) measured on a 1.5 m circular ground plane yields the ohms and the resonance frequency input impedance nearly coinciding with the SIE result, as illustrated in Fig. 12 and summarized in Table II. Results of the radiation measurements performed at the DTU-ESA Spherical Near-field Antenna Test Facility are shown in Fig. 13 along with the radiation pattern obtained by the numerical simulations of the antenna on an infinite ground plane (note a change in the coordinate system). The effect of the finite-size ground plane is immediately recognized. The radiation pattern exhibits almost perfect left-right symmetry with a deep null in the crosspolarization at the boresight.

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TABLE II CHARACTERISTICS THE MANUFACTURED SRR ANTENNA

TABLE III CHARACTERISTICS THE TE

ANTENNAS

The antenna input resistance at resonance is a function of the excitation dipole (monopole) length. Thus, it is easily adjusted to match the antenna to a given feed line, no matter how small the antenna is, and without any extra matching network. Moreover, this can be done nearly independent of the resonance frequency tuning, which is accomplished by adjusting the spherical resonator geometrical parameters. In this paper, the , and all are matched antennas have an electrical size to 50 ohms. The characteristics of the antennas are summarized in Table III. The presented numerical results show that all three antennas yield the radiation quality factor close to 3.0 times the Chu lower bound, which agrees with the theoretical prediction for an ideal electrically small magnetic dipole antenna made by Wheeler in 1958. ACKNOWLEDGMENT The author thanks F. Persson and Dr. S. Pivnenko, both from the Technical University of Denmark, for fabrication and measurements of the SSR antenna prototype. REFERENCES

= 403

Fig. 13. Radiation pattern of the SSR antenna at f MHz: (a) predicted, on an infinite ground plane; (b) measured, on a 1.5 m circular ground plane.

VI. CONCLUSION Three novel electrically small self-resonant antennas radiating the TE spherical mode are presented. The antennas are named after the spherical resonators they are based on: • multiarm spherical helix (MSH) antenna; • spherical split-ring resonator (S-SRR) antenna; • spherical split ring (SSR) antenna. Theoretically, each of the resonators can be made arbitrarily small at a given frequency. The lower limit is set by a required frequency bandwidth. Each antenna is excited by a curved dipole (or monopole) located in the antenna equatorial plane.

[1] H. A. Wheeler, “Fundamental limitations of small antennas,” in Proc. IRE, 1947, vol. 35, no. 12, pp. 1479–1484. [2] L. J. Chu, “Physical limitations of omni-directional antennas,” J. Appl. Phys., vol. 19, no. 12, pp. 1163–1175, 1948. [3] R. F. Harrington, J. Res. National Bureau of Standards-D, Radio Propag., vol. 64D, no. 1, pp. 1–12, 1960. [4] R. Collin and S. Rothschild, “Evaluation of antenna Q,” IEEE Trans. Antennas Propag., vol. 12, no. 1, pp. 23–27, Jan. 1964. [5] R. L. Fante, “Quality factor of general ideal antennas,” IEEE Trans. Antennas Propag., vol. 17, no. 2, pp. 151–155, Mar. 1969. [6] J. S. McLean, “A re-examination of the fundamental limits on the radiation Q of electrically small antennas,” IEEE Trans. Antennas Propag., vol. 44, no. 5, pp. 672–676, May 1996. [7] H. L. Thal, “New radiation Q limits for spherical wire antennas,” IEEE Trans. Antennas Propag., vol. 54, no. 10, pp. 2757–2763, Oct. 2006. [8] S. R. Best, “The radiation properties of electrically small folded spherical helix antennas,” IEEE Trans. Antennas Propag., vol. 52, no. 4, pp. 953–960, Apr. 2004. [9] S. R. Best, “Low Q electrically small linear and elliptical polarized spherical dipole antennas,” IEEE Trans. Antennas Propag., vol. 53, no. 3, pp. 1047–1053, Mar. 2005. [10] H. A. Wheeler, “The spherical coil as an inductor, shield, or antenna,” in Proc. IRE, 1958, vol. 46, no. 9, pp. 1595–1602.

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[11] S. R. Best, “A low Q electrically small magnetic (TE mode) dipole,” IEEE Antennas Wireless Propag. Lett., vol. 8, pp. 572–575, 2009. [12] O. S. Kim and O. Breinbjerg, “Miniaturised self-resonant split-ring resonator antenna,” Electron. Lett., vol. 45, no. 4, pp. 196–197, Feb. 2009. [13] O. S. Kim and O. Breinbjerg, “Miniaturized planar split-ring resonator antenna,” presented at the IEEE Antennas Propag. Soc. Int. Symp., Charleston, SC, Jun. 1–5, 2009. [14] O. S. Kim, O. Breinbjerg, and A. D. Yaghjian, “Electrically small magnetic dipole antennas with quality factors approaching the Chu lower bound,” IEEE Trans. Antennas Propag., vol. 58, no. 6, pp. 1898–1906, Jun. 2010. [15] E. Jørgensen, J. L. Volakis, P. Meincke, and O. Breinbjerg, “Higher order hierarchical Legendre basis functions for electromagnetic modeling,” IEEE Trans. Antennas Propag., vol. 52, no. 11, pp. 2985–2995, Nov. 2004. [16] A. D. Yaghjian and S. R. Best, “Impedance, bandwidth, and Q of antennas,” IEEE Trans. Antennas Propag., vol. 53, no. 4, pp. 1298–1324, Apr. 2005.

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[17] R. Marqués, F. Medina, and R. Rafii-El-Idrissi, “Role of bianisotropy in negative permeability and left-handed metamaterials,” Phys. Rev. B, vol. 65, no. 14, pp. 144 440/1–144 440/6, Apr. 2002. [18] P. Gay-Balmaz and O. J. F. Martin, “Efficient isotropic magnetic resonators,” Appl. Phys. Lett., vol. 81, no. 5, pp. 939–941, Jul. 2002. Oleksiy S. Kim received the M.S. and Ph.D. degrees in electrical engineering from the National Technical University of Ukraine, Kiev, in 1996 and 2000, respectively. In 2000, he joined the Antenna and Electromagnetics Group at the Technical University of Denmark (DTU), Kgs. Lyngby. He is currently an Associate Professor with the Department of Electrical Engineering, Electromagnetic Systems Group, DTU. His research interests include computational electromagnetics, metamaterials, electrically small antennas, photonic bandgap and plasmonic structures.

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Modeling, Design and Characterization of a Very Wideband Slot Antenna With Reconfigurable Band Rejection Julien Perruisseau-Carrier, Member, IEEE, Pablo Pardo-Carrera, and Pavel Miskovsky

Abstract—An antenna exhibiting a very wide bandwidth with reconfigurable rejection within the band is presented. The proposed topology is versatile in terms of the number of available antenna states and location of the rejection frequencies, and also allows the operation of the antenna in an “all-pass” state. First, a physical interpretation of the rejection mechanism and its corresponding circuit model are presented and validated. The proposed antenna concept is then demonstrated on a 4-state slot bow-tie antenna operating from 1.5 to 5 GHz with various rejection frequencies. PIN diodes are used as switching elements, with particular care taken to minimize power consumption. Simulated and measured return loss, radiation patterns and gain of the fully operational antenna are presented. Finally, we characterize and discuss the overall efficiency—considered here as the most relevant parameter to characterize the antenna filtering performance—both theoretically and experimentally, thereby highlighting the benefit of the proposed topology. Index Terms—Band rejection, frequency reconfiguration, filtering antenna, reconfigurable antenna, wideband.

I. INTRODUCTION N RECENT years, there has been growing effort in the development of frequency-reconfigurable antennas, from which a good overview can be found in, e.g., [1], [2]. This interest is pushed by the need for frequency-agile front-ends in future microwave systems, which will support an ever growing number of functionalities such as radars, communication, direction and spectrum “sniffing” or control. Moreover, personal wireless or vehicle-to-vehicle communication devices must typically support a large number of standards and associated frequencies (e.g., UMTS, Bluetooth, WiFi, WiMAX, DSRC). Finally, the availability of performing reconfigurable front-ends is one of the most challenging aspects to the successful implementation of software-defined and cognitive radio systems [3], [4]. Frequency reconfiguration in conventional front-end architectures might be achieved in different ways. It is generally accepted that switching between different components is a poor solution as the number of frequencies increases, mainly for

I

Manuscript received August 04, 2009; revised December 23, 2009; accepted January 28, 2010. Date of publication April 26, 2010; date of current version July 08, 2010. This work was supported in part by the Spanish Government in the framework of the m:Vía project (TSI-020301-2008-3) and the Torres Quevedo Grants PTQ-08-01-06434 and PTQ08-01-06438. The authors are with the Centre Tecnològic de Telecomunicacions de Catalunya (CTTC), Barcelona, Spain (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/TAP.2010.2048872

system size and inter antennas coupling considerations. As a result, the system should preferably consist of the combination of reconfigurable filters, antennas, and LNAs. Considering the different architectures that can be envisioned in such systems [1], [3], [4], it has become clear that achieving the reconfigurable filtering function at the antenna level can be beneficial in terms of system simplicity and size. However, it can be difficult in practice to obtain sufficient rejection and selectivity working at the antenna level only. Nevertheless, the antenna filtering capability would in that case significantly relax the constraints on the reconfigurable filters, as explained in [1], [3]. In the case of software-defined radio architectures, wideband filtering at the antenna level can be beneficial prior to low-noise amplification LNAs and downconversion to the software-defined stage. In this context, a significant number of antennas with a reconfigurable passband have been designed, some examples of which can be found in [1]–[11]. The antenna presented here exhibits a different functionality, namely, a very wideband response with dynamically-reconfigurable rejection within the band, as well as an “all-pass” state where no frequency is rejected (note that such a capability was partially obtained in [14], [15], as discussed in more detail in Section II). In comparison with the aforementioned tunable passband antennas, this characteristic presents the advantages of: (i) the possibility to support more than one standard at a time while rejecting an interferer and (ii) not requiring a reconfigurable matching network or particular attention to matching issues, since stable antenna impedance outside the stopband is easily achieved with common wideband antenna topologies. Moreover, the proposed approach presents the very interesting feature that strong currents flow through the diodes only at the rejected frequency, hence preserving good efficiency for a reconfigurable antenna. Nevertheless, a drawback of this solution is that a wid band antenna cannot be as small as a reconfigurable narrowband one, although the size of the antenna presented here is only about at the lowest matched frequency (1.65 GHz). Finally, the proposed antenna architecture allows easily selecting the required number of states, namely, of different stopband frequencies, as well as their location in the passband. Initial results of this work were presented in the conference paper of [12]. Here, we also discuss in detail the physical modeling of the structure, and characterize it in terms of radiation patterns, gain, efficiency, and non-linearities. We provide analyses on issues such as the effect of the PIN diode non-ideal behavior on the return loss, or the miniaturization of the antenna through its band-rejection resonator loading. Finally, we

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Fig. 1. General topology of the slot bow-tie antenna. (a) Fixed antenna topology. (b) Right side of the reconfigurable antenna with PIN diodes and biasing scheme. The DC-block capacitors are marked with “1” and the RF-block inductors with “2.” The dimensions are  ;c mm, : mm, : mm, : mm, d mm, mm, d mm, d L W : mm and n : mm. mm, n

g = 0 1 CPW = 3 5 = = 45 =03

= 22 = 8 =3 = 10 =07

d = 19 3 = 14

postulate that the filtering capability of such an antenna should be assessed in terms of overall efficiency rather than return loss only, and characterize experimentally the antenna efficiency using a time and cost effective method. II. PRINCIPLE OF THE RECONFIGURABLE ANTENNA The proposed reconfigurable antenna is based on the planar monolayer antenna shown in Fig. 1(a), whose basic topology was initially proposed in [13] in a non-reconfigurable case. The antenna consists of CPW-fed wideband slot bow-tie, and a slot etched along the bow-tie upper edge provides the rejection of a certain band (the physical explanation of this rejection, not provided in [13], is addressed in the next section). It will be shown that this topology allows a very simple mechanism for the reconfigurable band rejection capability, by electrically shorting the slot at variable distances from the antenna symmetry axis using e.g., PIN diodes, such as depicted in Fig. 1(b). It is noticeable that a reconfigurable antenna with band-rejection was already presented in [14]. However, the structure presented here is based on a CPW-fed slot antenna, and reconfiguration is achieved using PIN instead of varactor diodes. A first main difference in terms of antenna performance is that the tuning range obtained here is very large, whereas [14] achieves a limited control of the rejection frequency. Second, the approach presented in this paper allows to operate the antenna in an “all-pass” state, namely, without rejection band. Another work worth mentioning here is the antenna recently published in [15], which allows the on/off switching of a fixed-frequency rejection band. The increment in terms of functionality achieved here is that the rejection frequency can also be frequency-tuned. Finally, in this work we also provide significant new contributions in the field of band-rejecting antennas in terms of modeling and characterization. III. ANALYSIS OF THE BASIC ANTENNA STRUCTURE A. Introduction This section provides the analysis and corresponding model of the antenna structure formed by the bow-tie and a slot of a given half-length [see Fig. 1(a)]. Due to the reconfiguration

Fig. 2. (a) Complementary “metal” antenna employed for the analysis: balanced-fed metal bow-tie dipole with wire resonator. The diagram represents the half structure sufficient for the analysis, as well as the decomposition of the total input current into antenna and TL mode. (b) Odd-mode model of the half metal antenna.

mechanism mentioned in the previous section (dynamic control of ), such an analysis allows modeling the proposed reconfigurable implementation. The validity of the model is then demonstrated based on the observation of surface currents and input antenna impedances of the antenna with and without slot at different frequencies. B. Analysis and Circuit Model Complementary “Metal” Antenna Analysis: In order to study the slot antenna of Fig. 1, it is convenient to first analyze the complementary structure and subsequently apply the “duality” principle [16, p. 616]. This complementary antenna, which will be referred to here as the “metal” antenna, is depicted in Fig. 2(a). The balanced excitation of the antenna makes it possible to analyze only half of the structure. This is similar to the wellknown odd/even mode analysis, but here only the odd mode exists as a result of the balanced excitation imposed on this symmetrical structure. From Fig. 2(a) we deduce that the input of the actual metal antenna is twice that of its impedance model since “odd-mode” half model (1) where and are the voltage and current at the antenna input, respectively. The half-antenna is then analyzed based on the assumption, which will be verified later, that the structure supports two different modes, in a similar fashion as in the Gamma or Tee matching networks analysis [16], [17]. The first mode corresponds to the radiation of the bow-tie antenna (hereafter called “antenna” mode) and is similar to the mode supported by the metal bow-tie without wire resonator. The second mode is a transmission line (TL) mode occurring between the bow-tie edge and the wire, as shown in Fig. 2(a). This mode superposition is translated in Fig. 2(a) into the decomposition of the total current at the bow-tie driving point into an antenna mode and TL mode current , with . By current

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Fig. 3. Reduced circuit models of the whole (a) metal antenna (b) slot antenna. In the case of the slot antenna, Z corresponds to the input impedance of a TL of length d terminated by a short-circuit.

definition of a TL mode, the wire carries the TL mode return . current As a result, the circuit model for the half-structure (odd-mode) is such as depicted in Fig. 2(b). The input is a shunt connection impedance of the half-antenna and , where is the input impedance of the of the whole metal bow-tie without resonator and input impedance of the open-ended TL. Using (1), the input impedance of the complete complementary “metal” antenna is thus given by (2) (2) It is interesting to note that, in this dual metal case, the TLs on each side of the antenna symmetry axis are in series, hence in (2). Graphically, (2) corresponds to the simple circuit model of Fig. 3(a). Slot Antenna Analysis: As explained at the beginning of the section, our interest rather lies in the input impedance of the slot, complementary structure of the metal antenna. This impedance can be obtained using Booker’s Formula (3), which links the input impedances of complementary antennas ([16], p. 616). In and , where the (3), these impedances are referred to as subscripts “S” and “M” stand for “slot” and “metal,” respectively, whereas is the free space impedance (with some approximation here due to the presence of the dielectric substrate ) of relative permittivity (3) Introducing (2) in (3), and subsequently applying again Booker’s formula to the impedances and , yields

Fig. 4. Input impedance and reflection coefficient the antenna with and without slot.

The validity of this model will be demonstrated based on the observation of surface currents and input antenna impedances of the antenna with and without slot. For compactness, this is done together with the presentation of the initials steps of the design of the reconfigurable antenna in Section V. IV. GENERAL DESIGN APPROACH Observation of (4) suggests that a broadband matched antenna with a reconfigurable rejection band can be designed according to the following three steps. First, the broadband bow-tie antenna without slot is designed. Its input impedance in (4). Second, the slot is inserted to corresponds to create, together with the bow-tie edge, a TL of very high input at the desired rejection frequency. Since impedance the TL is terminated by a short-circuit, the impedance becomes large when the electrical length of the TL is about a quarter guided wavelength. Thus, the total length of the slot determines the stopband frequency when all PIN diodes are in OFF state. Third, the PIN diodes are inserted in the slot together with the required biasing scheme [Fig. 1(b)]. The number and positions of the PIN diodes pairs determine the number and location of the available rejection frequencies, respectively. These design steps are further described in the next sections. V. FIXED ANTENNA DESIGN AND MODEL VALIDATION

(4) Equation (4) provides the input impedance of the complete band-rejection slot antenna as a function of the slot bow-tie , and the input impedance impedance without slot of the TL of length formed by the half slot and the bow-tie edge. The corresponding circuit model is shown Fig. 3(b). The antenna and TL impedances are now in series, in contrast with the metal case, which is due to the impedance “inversion” in now corresponds to a Booker’s formula (3). Similarly, TL terminated by a short-circuit.

The first design step thus consists in designing the unloaded (i.e., without slot) broadband bow-tie antenna. Here, it was optimized for matching to 50 to avoid the need for a matching network, using a 1.524 mm thick Arlon CuClad217 substrate . The corresponding simulated input impedance and matching are shown in Fig. 4, showing good matching from 2 to 8 GHz. The slot, forming the TL resonator together with the bow-tie antenna edge, is then introduced in the structure. Fig. 4 shows that this results in a strong rejection band centered at about 3 GHz, corresponding here to a slot half-length mm. A second lower rejection is observed at about 9 GHz. These observations can be linked to the model of Section II as follows. First,

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Fig. 6. Modeled matching of the antenna in the four operational states, using the actual measured diode model (- -) and removing the losses in the diode model (- - - ). Fig. 5. Simulated surface current complex magnitude without [(a) 3 GHz, (b) 9 GHz] and with resonator [(c) 3 GHz, (d) 9 GHz].

let us note that antenna input impedances of the antenna without and with the slot shown in Fig. 4 correspond to and in (4), respectively, by definition of these variables in the model. According to (4), or equivalently, to the circuit model of Fig. 3, this difference corresponds to half of the input impedance of the TL. First we observe that the two stop bands occur when the TL resonates and its input impedance becomes very large. We can then estimate the electrical length of the TL at the resonant frequencies. Assuming that the effective relevant permittivity of the TL mode is the average of the substrate and air permittivites , the TL length in terms of the guided wavelength is and at 3 and 9 GHz, respectively. The length of the TL resonator is thus very close to and at the resonant frequencies, where the input impedance becomes very large. This confirms the theoretical prediction of Section III that the rejection mechanism can be modeled by the serial connection of the input impedance of the short-ended TL with the unloaded antenna impedance. Finally, the same conclusions can be drawn from the computed surface currents of Fig. 5 at the rejection frequencies, where typical and standing waves are observed on TL formed by the slot and bow-tie edge. It is noticeable that these results differ from previous interpretations of similar phenomena by other authors. First, it is stated in [13]—which presented the antenna topology employed here in a non-reconfigurable case—that the slot half-length is about at the resonant frequency. This is true but this value corresponds to the half-slot length in terms of the free space wavelength. However, we showed that the slot electrical length relevant to explain the rejection mechanism should be expressed in terms of the TL mode created by the slot, and is thus . The fact that the slot half-length in [13] is in terms of the free-space wavelength is only due to the fact that the relative permittivity of the substrate in that work is , hence a ratio of about 2 between free space and guided wavelength. Another work proposes a conceptual circuit model for a similar rejection mechanism. In [14], the stopband is modeled

by the shunt connection of a resonator with the antenna, the impedance of the resonator being zero at the rejection frequency. It appears that this model is not consistent with the observation that the input impedance of the antenna is very large at the rejection frequency (see Fig. 4). VI. RECONFIGURABLE ANTENNA A. Description and Modeling Since the rejection frequency is determined by the half-slot length , it can be dynamically reconfigured in a simple manner by short-circuiting the slot at variable locations. Here, the concept is demonstrated using three pairs of Aeroflex-Metelics MPN7310 PIN diodes (A, B, C) shorting the slot as shown in Fig. 1. From a design point-of-view, the locations of the diodes for a given set of rejection frequencies are easily determined since approximately corresponds to a quarter guided wavelength at the rejection frequency. Nevertheless, a simulation-based tuning is then necessary to take into account the non-ideal diode characteristic, and to provide all antenna radiation characteristics. Here, Ansoft HFSS is used as full-wave simulator, and the diodes are represented in the simulations by equivalent impedances previously extracted from TRL-calibrated diodes measurements. The diode impedance in OFF state corresponds pH, and to a RLC series network with fF, while the ON state is well modeled by a resistance in series with pH. B. Input Return Loss 1) Simulation Results: Fig. 6 shows the reflection coefficient of the antenna in its four operational states. When all diodes are OFF (state ), the rejection band is determined by the total slot length, and is centered at 2.4 GHz. When the “A” , the effective length of the diode pair is actuated slot is reduced and the rejection frequency is shifted to 3 GHz. Similarly, switching the B diode pair further reduces the slot . Finally, length to achieve rejection at 3.6 GHz since the diode pair “C” is placed close enough to the antenna centre for the corresponding rejection frequency to be out of the

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Fig. 7. Picture of the fabricated reconfigurable antenna.

band of interest, the antenna response in state is of “all-pass” type. 2) Slot Effect on Antenna Size: It should be noted that the slot effective length also has an impact on the lower matched frequency (see Fig. 6). Such an effect was already observed in the simulations presented in Fig. 4, and can be understood by the input impedance plot in the same figure: the imaginary parts of the TL and unloaded antenna impedances are of opposite sign below the resonant frequency, resulting in better matching of the loaded antenna. As a result, in the reconfigurable antenna state with lowest rejection frequency (000), the antenna is dB-matched down to 1.65 GHz, whereas this frequency is 2.25 GHz in state 001 corresponding to the effective removal of the slot. This substantial reduction of about 30% results in a small size for a wideband antenna (its maximal dimension, 45 mm, is at 1.65 GHz). 3) Effect of the Diodes Resistance on the Return Loss: The impact of the diode losses on the results can be assessed by cancelling the real part of the diodes measured impedance. As can be seen in Fig. 6, this loss is the main limitation to the rejecdB and dB for tion levels obtained, which are about lossless and real diodes, respectively. The model of Section III explains this phenomenon by the fact that the loss introduced by the diodes along and at the termination of TL “smooth” the TL input impedance around the resonance, leading to lower rejection levels. Nevertheless, it is important to note that the lower reflection loss does not necessarily correspond to a degradation of the antenna performance in terms of its band filtering capability, which is better represented by the overall antenna efficiency, as discussed in detail in Section IV.E. 4) Experimental Validation: The fully operational reconfigurable antenna was fabricated and is shown in Fig. 7. Antenna dimensions and substrate characteristics were provided in Fig. 1 and Section V, respectively. The vias consist of 0.6 mm wide holes drilled in the substrate, covered by conductive epoxy. The reflection coefficients in the various states were measured and are presented in Fig. 8 in comparison with the simulation results previously shown in Fig. 6. A good agreement is obtained between simulation and measurements, considering the various sources of imprecision in the fabricated antenna such as the modeling and variability of the diodes, the DC-blocking SMD elements, the external DC wires, and the CPW narrow slot width (100 m).

Fig. 8. Reflection coefficient in the four operating states. The graphs shows modeled results ( ) and measurements for diode ON state forward bias currents of 10 mA (- - - ) and 1 mA (1 1 1), which are almost exactly superimposed.

C. Power Consumption diodes The proposed antenna topology comprises for operational reconfigurable states (see Section VI.B), namely, 6 diodes and 4 states in the case of the presented demonstrator. However, since the four operation states of the antenna are 000, 001, 010, 100, where “1” represents one pair of diode in the ON state, there is on average only 0.75 pair of diode dissipating DC power. Moreover, the power consumption can be further reduced by operating the PIN diodes with the minimum biasing current sufficient for the antenna to preserve good performance. Indeed, PIN diodes present an inherent tradeoff between the biasing current and the RF series resistance in ON state, which are approximately inversely proportional. Fig. 8 shows the measured reflection coefficient of the antenna when the diodes are biased in ON state with 10 mA and 1 mA forward currents, respectively. The curves are often indistinguishable but some degradation in the rejection level is observed for the smaller current value. In the dB worst case, state 010, the rejection level degrades from to dB. However, the total average DC current drawn is mA, which corresponds to a total now antenna power consumption of only 1.1 mW. All experimental results presented hereafter are obtained using this reduced ON biasing current of 1 mA per diode. D. Radiation Patterns and Gain The antenna radiation patterns have been simulated and measured at different frequencies and for each of the four

PERRUISSEAU-CARRIER et al.: MODELING, DESIGN AND CHARACTERIZATION OF A VERY WIDEBAND SLOT ANTENNA

Fig. 9. Radiation patterns at two different non-rejected frequencies in state 000, including DC biasing cables. By symmetry, the simulated cross-polarization is zero in the E plane. Similar patterns are obtained for the other states matched at the same frequencies (not shown here).

antenna states. Since the TL resonator is very weakly excited out of the rejection frequencies, similar radiation patterns are obtained for the different antenna states at a given frequency. Therefore we only show in Fig. 9 the radiation patterns at two different frequencies matched in a given state, namely, above and below the rejection frequency of state 000 (1.8 GHz and 4.0 GHz, see Fig. 8). Although good agreement is obtained between simulation and measurement in, e.g., the co-polarized field in the E-plane at 4 GHz, significant discrepancies and high measured cross-polarization levels are also observed. These are necessarily due to the fabricated antenna imperfection, since the cross-polarization is large in the E-plane despite the antenna symmetry. Similarly, the measured co-polarized pattern is not symmetrical in the H-plane. The main cause for the degraded measured patterns is the presence of the DC feeding cables attached to the antenna and visible in Fig. 7. This is evidenced by Fig. 10, which shows the results obtained in state 000 after removing the cables from the antenna, thereby achieving much lower measured cross-polarization and closer agreement between measurements and simulation (the cables were not introduced in the simulations). In some applications where the antenna is to be used as a single non-directive radiator, the patterns degradation due to the cables is not critical. From a more general perspective, and as for any fixed or reconfigurable antenna, the radiation patterns in operation would depend on the eventual location of the antenna within the radio system and should be studied accordingly, which is beyond the scope of this work. Nevertheless, the

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Fig. 10. Radiation patterns at two different non-rejected frequencies in state 000 (same as Fig. 9), without DC biasing cables.

antenna integration or its characterization in free space without the spurious effect of external DC cables would be facilitated by the use of a chip component having a single digital feed line to control the various diodes (see, e.g., [18]). The remaining line could then be driven along the antenna CPW feed to avoid any detrimental effect on the radiation. The simulated and measured antenna peak realized gains are presented in Fig. 11, where the effect of the band rejection is clearly observed. A fair agreement is obtained between simulation and measurement, with gains generally between 0 dB and 5 dB outside the rejection bands. Although the antenna gain is shown here for completeness, a more relevant parameter to characterize the presented antenna is the antenna efficiency discussed in detail in the next section. E. Radiation and Overall Efficiencies This section presents and discusses the performance of the antenna in terms of radiation and overall efficiency. First, in (5) and (6) are recalled the definitions of the radiation and efficiencies as functions of the power incident , overall , radiated , and dissipated , by the anaccepted tenna [16, p. 60] (5) (6) The efficiency of reconfigurable antennas is often not characterized, although it is a critical issue because of the significant

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Fig. 11. Gain in the four states of the reconfigurable antenna, simulated (- - - ) and measured (----- ).

Fig. 13. Overall efficiency in the four states of the reconfigurable antenna, simulated (- - - ) and measured using the method of [19] with a 1 mA diodes ON biasing current (----- ). The shaded zones shows the frequencies where the measurement method is particularly inaccurate (see text). Fig. 12. Simulated radiation efficiency in the four states of the reconfigurable antenna.

loss that can be associated with current crowding linked with the control topology [2] and the high currents flowing through the control elements such as PIN diodes. Although gain measurement provides some information on this issue, the overall efficiency is more relevant parameter to characterize a non-directive antenna. Moreover, it should be noted that the overall antenna efficiency is the most relevant indicator of the filtering performance of the antenna, since it directly relates incident and radiated power of the antenna. Thus, the overall efficiency accounts for both return and dissipation losses, and is therefore a better metric of the antenna filtering performance than the return loss alone. This is especially important in the case of the presented antenna, since we will show in this section that the dissipation loss at the rejection frequency is beneficial to the antenna filtering performance. 1) Radiation Efficiency: The radiation efficiency (5) is linked dissipated in the antenna, thereby into the total power cluding dissipation loss in all materials and surface-mounted components. This parameter is directly obtained from the fullwave simulations and is depicted in Fig. 12 in the four antenna states. It is generally between 80% and 90%, but reduces very significantly at the rejection frequencies, namely, where strong mismatch was observed in Fig. 6. Here it should be recalled that radiation efficiency excludes, by definition, mismatch return loss. Thus the minima observed here are not just another

representation of the mismatch observed in Fig. 6. In fact, the large mismatch and low radiation efficiency occurring at the rejection frequencies are two distinct consequences of the resonance of the TL resonator. In the case of the radiation efficiency shown in Fig. 12, the phenomenon can be simply understood as follows. At the rejection frequencies, on the one increases due to the strong curhand the dissipated power rents excited around the resonator and through the diodes, while gets on the other hand the power radiated by the antenna lower. Both phenomena have a cumulative effect in (5), which lead to the nulls in radiation efficiency observed at the rejection frequencies. This “parallelism” between return loss and radiation efficiency is particular to the proposed antenna operation mechanism and is beneficial to its performance. Indeed, outside the return loss rejection frequencies, where an effective radiator is desired, the resonator and diodes support low currents, and good radiation efficiency is obtained. On the contrary, at the rejection frequency, the currents in the resonator and PIN diodes are high and the radiation efficiency is poor, which improves the rejection phenomenon. 2) Overall Efficiency: As explained above, the overall efficiency allows effectively assessing the reconfigurable filtering capability of the presented antenna, since it include both return and dissipation losses. Fig. 13 shows the simulated overall efficiency in the four states, which falls below 10% or lower in the stopband, while levels between 60% and 90% are obtained at the antenna matched frequencies.

PERRUISSEAU-CARRIER et al.: MODELING, DESIGN AND CHARACTERIZATION OF A VERY WIDEBAND SLOT ANTENNA

The measurement of radiation efficiency is in general a complex or expensive process; thus some approximate but simpler methods have been developed, as explained in the introduction of [19]. Here we used the strategy proposed in [19], which was shown to allow the approximate characterization of the antenna efficiency of very wideband antennas as required here, in a rather simple and inexpensive process. The measured overall efficiency is then obtained by (6), using the measured reflection coefficient and radiation efficiency. The measured efficiency in the four states is shown in Fig. 13. The shaded zones show the regions where the measurement method limitations prevent obtaining satisfactory measurements. The higher shaded zone corresponds to frequencies above the first resonant mode of the Wheeler cap used in the measurement, where the filtering algorithm is not able to correctly remove the efficiency notches, as explained in [19]. Concerning the zone below 2 GHz, some tests not detailed here showed that the measurement inaccuracy is mainly due to the DC biasing cables. In the zone of reliable measurement, between 2.0 GHz and about 4.25 GHz, a rather good agreement between simulations and measurements is obtained, considering: (i) the known limited precision of the method and the remaining influence of the cables; (ii) the complexity of the reconfigurable antenna and its biasing network; and (iii) the fact the overall efficiency is obtained using (6) and hence includes both the discrepancies in the radiation efficiency and in the return loss characterization. The main difference in this zone between simulated and measured results consists in the slightly lower measured overall efficiency, which however remains between 50% and 70%. F. Non-Linearities The third order intercept points IP3 were measured at 1.8 GHz and 4.0 GHz (these are the same frequencies as the radiation patterns of Figs. 9 and 10) with a tone separation of 1 MHz, and for different diode currents and antenna operation states. The measured transmitted IP3 levels at 1.8 GHz and 4.0 GHz are 35.6 dBm and 40 dBm, respectively, in state 000. The intermodulation levels are similar in other antenna states. For example, in state 001, the measured transmitted IP3 is 44 dBm at 4.0 GHz (the intermodulation at 1.8 GHz was not measured in this state since the antenna is not matched at this frequency, see Fig. 8). Finally, no compression was evidenced up to a transmitted power of 24 dBm, which was the maximum measurable power in the available test setup. VII. CONCLUSION We have presented and fully characterized an antenna exhibiting a wide bandwidth and the dynamic control of a rejection band, showing very large reconfiguration range as well as the availability of an “all-pass” state. The proposed topology, whose concept was demonstrated here on a PIN diodes 4-states implementation, is versatile in terms of the number of available antenna states and location of the rejection frequencies. Another important contribution of this work consists in the developed conceptual model of the antenna, which was validated and used for the design and analysis of the structure. Moreover, it

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was shown that the proposed topology allows preserving good radiation efficiency for a reconfigurable antenna, and that the losses in the resonator are beneficial to the rejection in terms of overall efficiency. Potential further work concerning such reconfigurable rejection capabilities includes the control of the rejection bandwidth or the choice of the number of bands that can be simultaneously rejected. REFERENCES [1] S. Yang, C. Zhang, H. Pan, A. Fathy, and V. Nair, “Frequency-reconfigurable antennas for multiradio wireless platforms,” IEEE Microw. Mag., vol. 10, pp. 66–83, 2008. [2] J. T. Bernhard, Reconfigurable Antennas. San Rafael, CA: Morgan & Claypool, 2007. [3] P. S. Hall, P. Gardner, J. Kelly, E. Ebrahimi, M. R. Hamid, F. Ghanem, F. J. Herraiz-Martinez, and D. Segovia-Vargas, “Reconfigurable antenna challenges for future radio systems,” in Proc. 3rd Eur. Conf. on Antennas and Propagation, Berlin, Germany, 2009, pp. 949–955. [4] S.-H. Oh, J. T. Aberle, S. Anantharaman, K. Arai, H. L. Chong, and S. C. Koay, “Electronically tunable antenna pair and novel RF front-end architecture for software-defined radios,” EURASIP J. Appl. Signal Processing, vol. 2005, pp. 2701–2707, 2005. [5] D. E. Anagnostou, Z. Guizhen, M. T. Chryssomallis, J. C. Lyke, G. E. Ponchak, J. Papapolymerou, and C. G. Christodoulou, “Design, fabrication, and measurements of an RF-MEMS-based self-similar reconfigurable antenna,” IEEE Trans. Antennas Propag., vol. 54, pp. 422–432, 2006. [6] N. Yang, C. Caloz, and K. Wu, “Fixed-beam frequency-tunable phase-reversal coplanar stripline antenna array,” IEEE Trans. Antennas Propag., vol. 57, pp. 671–681, 2009. [7] C. R. White and G. M. Rebeiz, “Single- and dual-polarized tunable slot-ring antennas,” IEEE Trans. Antennas Propag., vol. 57, pp. 19–26, 2009. [8] K. Van Caekenberghe and K. Sarabandi, “A 2-bit Ka-band RF MEMS frequency tunable slot antenna,” IEEE Antennas Wireless Propag. Lett., vol. 7, pp. 179–182, 2008. [9] G. H. Huff, J. Feng, S. Zhang, and J. T. Bernhard, “A novel radiation pattern and frequency reconfigurable single turn square spiral microstrip antenna,” IEEE Microw. Wireless Compon. Lett., vol. 13, pp. 57–59, 2003. [10] N. Behdad and K. Sarabandi, “Dual-band reconfigurable antenna with a very wide tunability range,” IEEE Trans. Antennas Propag., vol. 54, pp. 409–416, 2006. [11] D. Peroulis, K. Sarabandi, and L. P. B. Katehi, “Design of reconfigurable slot antennas,” IEEE Trans. Antennas Propag., vol. 53, pp. 645–654, 2005. [12] P. Pardo and J. Perruisseau-Carrier, “A very wideband antenna with dynamically-controllable band rejection,” presented at the Loughborough Antennas and Propagation Conf., Loughborough, U.K., 2009. [13] Y. Kim and D. H. Kwon, “CPW-fed planar ultra wideband antenna having a frequency band notch function,” Electron. Lett., vol. 40, pp. 403–405, 2004. [14] J. Won-Seok, L. Sang-Yun, L. Won-Gyu, L. Ho, and Y. Jong-Won, “Tunable band-notched ultra wideband (UWB) planar monopole antennas using varactor,” in Proc. 38th Eur. Microw. Conf., 2008, pp. 266–268. [15] S. Nikolaou, N. D. Kingsley, G. E. Ponchak, J. Papapolymerou, and M. M. Tentzeris, “UWB elliptical monopoles with a reconfigurable band notch using MEMS switches actuated without bias lines,” IEEE Trans. Antennas Propag., vol. 57, pp. 2242–2251, 2009. [16] C. A. Balanis, Antenna Theory: Analysis and Design, 2nd ed. New York: Wiley, 1997. [17] J. Perruisseau-Carrier, D. L. d. Rio, and J. R. Mosig, “A new integrated match for CPW-fed slot antennas,” Microw. Opt. Technol. Lett., vol. 42, pp. 444–448, Sep. 2004. [18] T. H. Hand and S. A. Cummer, “Controllable magnetic metamaterial using digitally addressable split-ring resonators,” IEEE Antennas Wireless Propag. Lett., vol. 8, pp. 262–265, 2009. [19] P. Miskovsky, J. M. Gonzalez-Arbesu, and J. Romeu, “Antenna radiation efficiency measurement in an ultrawide frequency range,” IEEE Antennas Wireless Propag. Lett., vol. 8, pp. 72–75, 2009.

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Julien Perruisseau-Carrier (S’07–M’09) was born in Lausanne, Switzerland, in 1979. He received the M.Sc. and Ph.D. degrees from the Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, in 2003 and 2007, respectively. In 2003, he was a Visiting Researcher with the Communication Group at the University of Birmingham, Birmingham, U.K. From 2004 to 2007, he was with the Laboratory of Electromagnetics and Acoustics (LEMA), Ecole Polytechnique Fédérale de Lausanne (EPFL), where he completed his Ph.D. degree while working on various European Union funded projects. Since December 2007, he has been a Research Associate at the Centre Tecnològic de Telecomunicacions de Catalunya (CTTC), Barcelona, Spain. He has authored more than 50 journal and international conference papers. His research interest mainly concerns reconfigurable microwave devices. In particular, he has been involved in the development of dynamically-reconfigurable reflectarrays, antennas, and metamaterials. Dr. Perruisseau-Carrier was the recipient of the Young Scientist Award presented at the URSI-EMTS 2007, International Symposium on Electromagnetic Theory, Ottawa, Canada and of the Raj Mittra Travel Grant 2010 presented by the IEEE Antennas and Propagation Society.

Pablo Pardo-Carrera was born in Madrid, Spain, in 1980. He received the B.Sc. and M.Sc. degrees in engineering from the Ramon Lull University (URL), Barcelona, Spain, in 2003 and 2006, respectively. From 2006 to 2007, he was with Altran (previously Berata) Switzerland, Zurich, and Altran Est., Strasbourg, France, where he was involved in automotive and space projects. Since October 2007, he has been a Research Engineer at the Centre Tecnològic de Telecomunicacions de Catalunya (CTTC), Barcelona, Spain. His research interests mainly concerns active and passive microwave circuits and broadband reconfigurable antennas.

Pavel Miskovsky was born in P˘ríbram, Czech Republic, in 1979. He received the B.Sc. degree in engineering from the École Nationale Supérieure des Télécommunications (ENST), France, in 2003, the M.Sc. degree in engineering from the Czech Technical University (CTU), Czech Republic, in 2004, and the Ph.D. degree in electrical engineering from the Technical University of Catalonia (UPC), Barcelona, Spain, in 2010. Since 2006, he has been a Research Assistant at the Centre Tecnologic de Telecomunicacions de Catalunya (CTTC), where he is involved in national and industry-funded projects. His research interests include UWB and reconfigurable antennas and antenna characterization and measurement methods. Dr. Miskovsky was granted a Ph.D. fellowship for 2004 to 2005 by the CTTC.

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Frequency Selective Surfaces and Their Applications for Nimble-Radiation Pattern Antennas Mahmoud Niroo Jazi, Student Member, IEEE, and Tayeb A. Denidni, Senior Member, IEEE

Abstract—Two different active frequency selective screens are proposed to develop a new class of reconfigurable-agile radiation-pattern antennas. High frequency PIN-Diodes are precisely incorporated into the screens to reconfigure electromagnetic (EM) response of the surfaces imitating blocking-transparent window for the incident EM waves. The DC-feed loading in the first screen and the PIN-Diode parasitic effects are carefully examined to achieve the desired performance. The constraints of DC-feed lines for the first cylindrical screen are also clarified, and then a second surface is proposed to surmount them providing more functionality compared to the first one. The new structure is used to construct a nimble-radiation pattern antenna which introduces an agile configuration by sweeping the radiation pattern over all 360 azimuth angles. Furthermore, it is also able to reconfigure its radiation pattern to an omnidirectional state covering instantaneously the azimuth plane. Measurement and simulation results show that the proposed structures provide reconfigurable-agile in terms radiation patterns over a minimum bandwidth of of matching and desired radiation pattern.

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Index Terms—Active frequency selective surfaces, agile-radiation pattern, DC-feed loading effect, PIN-Diodes, reconfigurable antennas.

I. INTRODUCTION

D

EMANDS on low cost, high quality, robust and high data rate communication systems have proliferated an attractive emerging research topic on reconfigurable antennas [1]. In the recent decade, reconfigurable antennas have been extensively exploited in the intelligent systems to mitigate detriments of the conventional antennas and demerits of the smart or adaptive antenna-array systems [2]–[6]. For instance, planar phased array technology restricts both scan angles and operation because of the limitations of individual array elements and antenna element spacing. On the other hand, adaptive antenna systems often require a complex adaptive feed network to weight each antenna element according to the desired beamforming algorithm [7]. In addition, there is no any smartness in the antenna elements limiting the overall performances of the communication system. Therefore, reconfigurable antennas have recently been exploited in the smart antenna array in order to introduce, of course in some extent, intellectuality into the antenna elements providing more flexibility and robustness along with adaptive

Manuscript received August 19, 2009; revised December 03, 2009; accepted January 25, 2010. Date of publication April 26, 2010; date of current version July 08, 2010. The authors are with the INRS-EMT, Université de Québec, Montreal, QC H5A 1K6, Canada (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/TAP.2010.2048877

controlling network to accommodate changing in the operating requirements [8]. More attractive is the ability of reconfigurable structures to deliver in part the same functionality of multi-element-system topologies by just one single antenna leading to a significant saving in cost, volume and resource maintenance. Therefore, all these remarkable merits have received a great eminence among antenna designers to develop a broad range of new multifunctional antenna structures. In particular, because of the synergy between the concept of reconfiguration and the EM behavior of artificial materials, the reconfigurable structures based on these materials have received growing attention [9]–[14]. Broadly classified as artificial materials, frequency selective surfaces (FSSs) introduce anomalous electromagnetic (EM) behavior that has well been exploited in antenna applications [15]. Nowadays, it is well known that a screen constructed of continuous strips creates a stop-band for the incident EM waves polarized along the strips [15], [16]. Furthermore, by cascading some layers of these screens, an electromagnetic bandgap (EBG) regime can be created for the waves excited inside this medium [17]. However, by introducing a reconfigurable defect with a particular pattern inside the structure, an agile radiation pattern antenna can be realized [18]. Recently in [19], an EBG-based agile antenna has been proposed by cascading four layers of continuous strips in which the defect has been created by introducing capacitive loaded strips. By moving the position of the defect, this antenna is able to sweep its radiation beam. Moreover, by using the linkage between the EM responses of the continuous and discontinuous strips in two different bandwidths [20], [21], or by changing the defect pattern [22], it is possible to reduce the number of active elements in order to achieve less power consumption. In [23], a prototype based almost on the same concept proposed in [19] has been practically implemented in which high frequency PIN-Diodes are integrated into the structure. In this structure, the periodicities of the capacitive loaded strips have been deliberately chosen in which the undesired parasitic elements of the PIN-Diodes do not degrade the performance of the antenna. Furthermore, as the basic concept of the structure, applying this part of the EM response of the cascaded FSS layers introduces more bandwidth. In the same perspective, without much more improvement, still a large number of diodes are required in this configuration, which results in higher cost, more complexity and may reduce the overall antenna performances. In this paper, following to the authors’ recent contributions [24], [25], a class of new reconfigurable radiation-pattern antennas is introduced with one layer of FSS sheet reducing the number of active elements. This results in lower cost, more power saving, compactness, robustness and, hence, is easier in

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implementation and maintenance. In order to accomplish this objective, two FSS sheets with different wave-propagation behavior are proposed and developed. The constraints and potentials of each one are carefully examined and their merits for radiation pattern reconfiguration are introduced. In addition, the practical restrictions imposed by the PIN-Diodes including the DC-feed network and undesired natural parasitic elements of the active elements are analytically and experimentally investigated. Finally, simulation and experimental results are presented and discussed. II. CAPACITIVE LOADED STRIPS AND AGILE ACTIVE FREQUENCY SELECTIVE SURFACES It is well-known that a grid of inductive continuous strips periodically aligned in a plane treats like a partially reflective surface (PRS) below a cut off frequency to the incident EM waves polarized along the strips, while it is transparent at high frequencies [17]. On the other hand, inserting some periodic discontinuities along the strips introduce a dual EM response which make the surface transparent at low frequencies. Moreover, this capacitive surface creates a stop-band which its center frequency is proportional to the dimensions of constructive unit cell created by short strips [15]. In fact, around this frequency, the unit cell can be modeled as an LC resonant circuit with a length of about at the center of this frequency band. L and C are mainly related to the length of the resonant dipole and the gap discontinuity, respectively. This exotic behavior provides three practical states, which can be exploited in reconfigurable structures with more flexibility. Therefore, these properties were hereby applied to develop a new class of reconfigurable radiation pattern antennas with more functionality. In these designs, a low loss flexible substrate of and thickness of 0.254 mm is used to RO3003 with create a cylindrical shape agile FSS surface. High frequency PIN-Diodes of GMP4201 are incorporated into the unit cells to reconfigure the EM response of the screen. All simulations here are carried out using CST Microwave Studio simulator. Two different unit cells are introduced in the following sub sections and their performances are carefully examined. A. Proposed Unit Cells The first configuration is introduced to produce a reconfigurable radiation pattern antenna based on the stop-band created by a surface comprising a grid of parallel capacitive loaded strips. The proposed unit cell and its calculated transmission coefficient are depicted in Fig. 1. The calculated results are based on the Floquet theorem, which are performed using CST Microwave Studio simulator. In this structure, by reconfiguring the periodicity of the unit cell, the position of the stop-band is changed using a high frequency PIN-Diode integrated into the unit cell. Indeed, activating or deactivating the diode changes the effective inductance and capacitance of the resonant strips L and C. The effective values of these elements for the Case-B and ), are about half of the ones in Case-A ( as shown in Fig. 1(b); this leads to double the stop-band center frequency. Therefore, in the ideal case, the EM response of the screen constructed from this unit cell can mimic an opaque or

Fig. 1. First proposed unit cell and its EM response to the TM incident waves. (a) First proposed unit cell and its electric circuit model. (b) Transmission coefficient response of the first proposed unit cell.

transparent surface at the desired bandwidth by connecting the discontinuities or keeping them discontinuous, respectively. In order to bias the PIN-Diode integrated into the unit cell, DC-feed lines are used. The loading effect of these lines is examined in Fig. 2. Basically, because of changing the total L and C in the resonant circuit model of the proposed unit cell, the loading effect of these lines impacts the EM response of the unit cell undesirably shifting down the position of the stop-band. Nevertheless, the effective inductance is the main parameter that contributes to alter the stop-band position. As it can be noticed in this figure, the loading effect of the discontinuous case is more affecting the stop-band position compared to the continuous one. In this case, the capacitance is considerably changed along with inductance resulting in a greater shift. Therefore, it can be concluded that even though the structure provides the desired transparency and opaque surface for the incident EM waves, the DC-feed lines severely impact

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Fig. 3. Second proposed unit cell and its EM response to the TM incident waves. (a) Second proposed unit cell. (b) Transmission coefficient response of the second proposed unit cell. Fig. 2. Loading effect of DC-feed line on the EM response. (a) First proposed unit cell and its DC-feed lines. (b) Calculated transmission coefficient.

the position of the stop-band. This causes to reduce the desired transparency of this state. Furthermore, the DC-feed network limits the application of the surface to a particular reconfigurable configuration. To overcome this issues a second unit cell is proposed. The second unit cell shown in Fig. 3 is designed to implement an agile as well as reconfigurable radiation-pattern antenna using a cylindrical active FSS surface to cover all 360 azimuth angles. When the active element is forward biased, ideally, there is no interaction at high frequencies with the incident EM waves passing through the screen constructed with this unit cell. On the other hand, for the reverse biased case, the surface will block the incident wave, by creating an opaque surface. However, as the main advantage, this structure alleviates the practical feeding constraint of the active elements in the previous proposed unit cell. In addition, in this configuration two stubs are added to the strips as extra parameters to tune the band-stop position providing more degrees of freedom to tune agile antenna performances in terms of radiation pattern and impedance matching. Although, the other dimensions of and h also impact the response of the FSS screen, Fig. 4 demonstrates the effect of stub

Fig. 4. Effect of sublength on transmission coefficient.

length as the main parameter on the EM response of the unit cell.

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Fig. 6. Proposed nimble-radiation pattern antenna configuration.

Fig. 5. Active element mode used in the simulations and its effect on the EM response of the unit cell. (a) Actual PIN-Diode electrical circuit model used in the simulation. (b) Simulated transmission coefficient of the unit cell shown in Fig. 1(b).

B. Active Element Integration High frequency PIN-Diodes, in spite of their nonlinearity demerit, are one of the most commonly used active elements applied to reconfigure the EM response of an FSS texture. Fig. 5(a) depicts the applied electrical circuit model of the GMP4201 PIN-Diode in the simulation [26]. In the forward biased case, the diode mainly represents a small resistance, which has negligible effect on the desired response of the FSS surface. Because of their small value, the series self inductance of the diode in this case has been neglected. However, when it is reverse biased, the parasitic capacitance considerably deviates the position of the surface stop-band by altering the total effective capacitance of the unit cell. Therefore, it is required to consider its effect in the design process. As a potential bonus in this part of examination, one can deduce an interesting point by applying this effect to change the center frequency of the band-stop. Indeed, by using variable capacitance one can reconfigure the band-stop over a wide frequency range. This promises a more attractive application as a multi-functional antenna to be able to reconfigure frequency as well as radiation pattern. III. RECONFIGURABLE-AGILE ANTENNAS In this section, a step by step design procedure is performed to design a class of new reconfigurable radiation-pattern antennas

based on the two proposed unit cells. Two new antennas based on the configuration shown in Fig. 6, Antenna-I and II are proposed to provide more functionality compared to the flat FSS reflector introduced in [24] by the authors. When a flat FSS screen is reformed to a curved structure, its EM response can be altered according to the new lattice pattern, incident angle of EM waves and the radius of the curvature [27]. Here, because of no variation in the incidence angles of EM waves emanating from the dipole at the center of the cylinder, almost the same EM responses are expected in the two proposed cylindrical reflectors. However, the finite dimension of FSS screen can affect a little the EM response of the surface compared to the infinite case. The cylindrical active FSS surface used in Antenna-I is constructed from the first proposed unit cell. This structure is able to provide two directive radiation patterns in opposite directions as well as a nearly omnidirectional pattern. Because of the required DC-feed lines, this structure cannot sweep the beam over the all azimuth angles. In addition, these lines undesirably deteriorate the radiation pattern in the omnidirectional state. Therefore, Antenna-II, named nimble-radiation pattern antenna, comprised of the second unit cell is proposed to alleviate the feed network constraints, and to introduce more functionality. In this case, not only the antenna can sweep the beam over the whole azimuth plane as an agile structure but also can provide an omnidirectional radiation pattern as well to reconfigure the pattern from directive case to omnidirectional case. In this work, both antennas are designed in the same way. The unit cell dimensions, radius of the cylinder and dipole sizes are crucial parameters and can significantly affect the antenna characteristics. The initial dimensions of the unit cell are determined for the desired band-stop around 2.45 GHz. An efficient directive radiation pattern for a semi-cylindrical solid reflector illuminated by a simple dipole requires a radius in the range – , in which is the free space wavelength at 2.45 of GHz. Therefore, R is chosen in this range as an initial value. According to the estimated radius for the cylinder and the peri, the required columns to construct odicity of the agile cylindrical FSS surface is fixed to 10. Finally, for both antennas, comprehensive parametric studies on the dimensions were carried out to analyze the performances of , , , in terms of matching, bandwidth, back-lobe and desired radiation pattern reconfiguration. In order to tune Antenna-II performance, the stub sizes should be optimized as well as other

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Fig. 7. Parametric study of antenna parameters performed for various R values: (a) reflection coefficient, (b) gain, (c) E-plane radiation pattern, (d) H-plane radiation pattern.

TABLE I FINAL DIMENSIONS OF ANTENNAS-I AND II

parameters. However, the radius of the cylinder is the main parameter that affects all antenna characteristics in both structures. Table I shows the final dimensions of Antennas-I and II. Fig. 7 shows a parametric study performed for different values of r, demonstrating its impact on the radiation performances of Antenna-I. The return loss bandwidth of the directional radiation pattern is about 175 MHz. The simulated realized gain of the proposed configuration, predicts more than 10 dB gain over a bandwidth of 150 MHz, which is significantly affected by the radius of the cylinder. This amount of gain was achieved just with one layer of FSS structure. Moreover, it seems that by changing the FSS configurations, it is possible to further reduce the number of active elements for the same

performance, which leads to smaller power consumption. Some asymmetry noticed in the E-plane radiation pattern is mainly due to the required parallel DC-feed lines on the sides of the cylinder that are required to bias the diodes. In addition, as it would be expected, when all the diodes are deactivated, these lines degrade the H-plane radiation pattern as well. Therefore, this leads to not be a completely omnidirectional pattern. When the antenna pattern is reconfigured to be omnidirectional, the return loss diagram is affected, which is mainly due to the coupling effect of the cylindrical FSS texture on the dipole antenna. Alternatively, in Antenna-II, the construction of the applied agile cylindrical reflector is consisted of the second proposed unit cell. The design procedure of this antenna is similar to Antenna-I. Fig. 8 shows parametric study performed for R and in terms of matching, gain and radiation pattern. As it can be noticed, the radius is the main parameter that controls the antenna characteristics. However, the stub sizes can be used to tune the back lobe and in some extent the main radiation pattern of the antenna. The return loss bandwidth predicted by the

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Fig. 8. Parametric study of antenna parameters performed for various L values: (a) reflection coefficient, (b) gain, (c) E-plane radiation pattern for different R values, (d) H-plane radiation pattern for different R values, (e) E-plane radiation pattern for different L values, (f) H-plane radiation pattern for different L values.

simulation is about 100 MHz for directive case while for omnidirectional case it seems that the structure does not have good matching bandwidth around the desired frequency. Because of the coupling effect of the cylindrical FSS, there is still some shift in the return loss diagram for omnidirectional radiation pattern case. However, the proposed nimble configuration ameliorates

the radiation pattern degradation provided by DC-feed line of Antenna-I and also when all diodes are on, it provides omnidirectional pattern. Moreover, it is able to create an agile radiation pattern covering all azimuth angles by selecting 5 columns of 10 at each time. This leads to sweep 360 azimuth area in 10 steps. Mainly because of smaller cylinder radius and the gap , the

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TABLE II RADIATION CHARACTERISTICS OF ANTENNAS-I AND II

gain of this antenna is smaller than the one of Antenna-I, and it is expected to be around 8 dB. The final characteristics of both Antenna-I and II are compared in Table II. IV. IMPLEMENTATION, EXPERIMENTAL RESULTS AND DISCUSSION First, the performances of one of the active FSS screens constructed using the first unit cell were carried out by measuring the transmission coefficient. This sheet is designed to operate at the desired frequency in which the DC-feed line and parasitic effect are compensated. Two broadband horn antennas are used in a measurement setup. The setup is calibrated for the case without FSS sheet to eliminate the directional coupling between antennas as well as the multipath phenomenon. In order to achieve more accurate measurement result, the sheet dimensions should be large enough to capture all the power introduced by the horn antennas at the sheet surface. The transmission coefficients are carried out for four different cases of Fig. 9(a). As it can be observed in Fig. 9(b), the first measurement performed for the passive structure well confirms the simulation prediction. The simulation in this figure was performed for a unit cell without considering the DC-feed line and parasitic effects to examine each case. Inclusion of PINDiode into the unit cell significantly lowers the stop-band center frequency. Furthermore, as it is expected, loading effect of the DC-feed lines also shifts further down the stop-band. When the sheet is activated, the measurement results show a good stop-band around the desired frequency confirming the integrity of the design process. In addition, these measurement results prove the potential of the proposed structure to create an agile FSS screen by considering the undesired parasitic elements and DC-feed loading effect. Antenna-II was also designed and implemented without compensating the PIN-Diodes parasitic effect. Therefore, the PIN-Diodes of column 6–10 in Fig. 10(b) are removed in the fabricated prototype to achieve the desired performance for directional radiation pattern while for the omnidirectional case all diodes are replaced with copper tape to connect the strips. Fig. 10 shows the distributed configurations of the cylindrical shape agile FSS screens prepared for fabrication. A simple dipole antenna is used in both structures as an excitation element. High frequency PIN-Diodes biased with DC-feed network are connected to the FSS grid using RF-Chock inductors. RF-Chocks separate the biasing feed network form the FSS screen over the desired antenna bandwidth. Ridged foam is

Fig. 9. Evaluating the performances of a FSS screen based on the first proposed unit cell. (a) Four different FSS screens constructed using 24 4 elements of these unit cells. (b) Measured transmission coefficient compared to the simulation.

2

used as a stand to fix the dipole antenna in the middle of the cylinder. The photos of the fabricated antennas are depicted in Fig. 11. To examine the performances of the proposed design, first, the return losses of both antennas was measured. Then, some measurements were performed for directive H-plane radiation pattern of each antenna at different frequencies to find the best radiation pattern in terms of desired main beam, realized gain, side lobe and back lobe level. Finally, other patterns were measured to evaluate the radiation performances in other planes as well as omnidirectional case. Fig. 12 shows the measured results of Antenna-I compared to the ones measured for the applied dipole in this configuration. As it can be noticed, the wideband dipole is efficiently working above 2.6 GHz; whereas when it is placed at the center of the cylindrical FSS it operates effectively around 2.45 GHz. The measured return loss for this structure demonstrates better matching compared to the simulation. In addition, deactivating the diodes leads to a little shift in the return loss curve which it has been predicted by simulations. Its

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Fig. 11. Photos of fabricated antennas: (a) Antenna-I and (b) Antenna-II. Fig. 10. Distributed configurations of the proposed active FSS screens used to implement the antennas. (a) Antenna-I and the implemented dipole antenna. (b) Antenna-II.

E- and H-plane radiation patterns at the frequency of 3.2 GHz are compared to the ones related to the Antenna-I. Some asymmetric is noticed in the E- and H-planes of the dipole antenna which is mainly because of the RF cable and the SMA connector used in the antenna implementation. However, its H-plane pattern is uniformly radiating over all angles. The measured E- and H-plane radiation patterns of Antenna-I demonstrate the best performance at the frequency of 2.45 GHz, which confirms the integrity of the proposed concept. It is clear that the proposed configuration can provide a directional radiation pattern with back lobe level better than 17 dB and 14 dB for H- and E-plane patterns, respectively. Because of scattering from the aperture edge, this level is a little degrading at the other angles in the back plane. The difference between these two planes is mainly because of the measurement errors. As it would be expected, the parallel DC-feeds on the sides affect the E-plane radiation pattern in the directional case as well as H-plane pattern when all diodes are off. The achieved characteristics for this antenna are compared to the simulations in Tab. II. The same measurement process is followed for Antenna-II to evaluate its performances. As it was mentioned earlier, in these

measurements performed for directional case, PIN-Diodes of columns 6–10 are removed. Therefore, this part well operates as a blocking surface at this frequency, while when columns 1–5 which are integrated with activated diodes is expected to be transparent. For the omnidirectional case, all diodes are removed and the strips are connected by copper tape. Fig. 13 shows the measured return loss of this structure, which similar to Antenna-I, it is better than the simulation and matches to input impedance over a large frequency bandwidth in both directional and omnidirectional cases. However, the best directive radiation pattern for this antenna was achieved at the frequency of 2.35 GHz. As it can be observed in Fig. 13(a) and (c), this structure provides a back lobe level better than 20 dB in the H-plane while in some angles the E-plane is not as good as the H-plane. Moreover, the measured E-plane pattern for omnidirectional case shows some undesired radiation in the Z direction. This is due to the fact that the stop-band of discontinuous strips are more close to the blocking regime of continuous strips at low frequencies, which results in reducing the transparency of continuous strips around the operating bandwidth. This causes to capture some RF energy inside the cylinder and, directions of the cylinder. hence, leaking out from the Z and Therefore, in order to obtain right performance, the stop-band of discontinuous wires should be far enough from the stop-band

JAZI AND DENIDNI: FSSs AND THEIR APPLICATIONS FOR NIMBLE-RADIATION PATTERN ANTENNAS

Fig. 12. Measured results for Antenna-I and the dipole applied to excite this configuration: (a) Measured reflection coefficient, (b) measured E-plane pattern, (c) measured H-plane pattern.

of the continuous ones. The measurement results of Antenna-II are compared to those of Antenna-I and listed in Tab. II.

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Fig. 13. Measured results for Antenna-II: (a) Measured reflection coefficient, (b) measured H-plane at 2.35 GHz, (c) measured E-plane at 2.35 GHz.

Finally, the gain of Antenna-I and II were measured using the comparison gain measurement method. The gain of the antenna is the can be calculated from the formula (1) in which

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through the antenna design procedure. However, as a potential bonus, it can be deduced that if variable capacitors are integrated into the proposed FSS, this will introduce a multi function reconfigurable antenna. The research is ongoing in this subject to propose new multifunction antennas with better performances. REFERENCES

Fig. 14. Measured gains for Antenna-I and II compared to the simulation.

received power by antenna under test. and are also the received power and gain of the standard horn antenna (1) Fig. 14 shows the measured gains for two antennas at different frequencies. Antenna-I presents better performances compared to the Antenna-II which is believed this is due to the better operation of each part of the structure at its desired frequency regime. As it can be seen from the E-plane measurement for Antenna-II, some gain reduction would be expected. This is mainly due to the fact that the antenna does not effectively operate according to the expected EM behavior for each part of the FSS screen. This can be alleviated by optimizing the structure according to the achieved experimental results. V. CONCLUSION A new class of reconfigurable-agile (nimble) antennas has been successfully proposed, exploiting exotic behaviors of two different active frequency selective screens. The constraints and potential of each nimble FSS screen have been examined when active elements are integrated into the FSS structures. The effects of DC-feed line loading and PIN-Diode parasitic elements on the frequency response of the screens have also been inspected both theoretically and practically. The results demonstrate that the DC-feed line required to bias the active elements impacts the frequency response of the FSS sheet by effectively changing the equivalent inductance and capacitance related to the electrical circuit model of the resonant strips. In addition, the biasing network of the diodes restricts the potentials and applications of the structure to particular reconfigurable configurations. Furthermore, the parasitic capacitance of the diodes severely affects the FSS response as well, leading to change the stop-band position to the lower frequencies. Depending on the operating regime of the FSS frequency response, this causes to restrict the frequency operation of the proposed structures to a limited design range. Therefore, in order to achieve the desired performances, it is recommended to consider all these issues

[1] J. T. Bernhard, Reconfigurable Antennas. San Rafael, CA: Morgan & Claypool, 2007. [2] J. C. Liberti and T. S. Rappaport, Smart Antennas for Wireless Communications: IS-95 and Third Generation CDMA Applications. Englewood Cliffs, NJ: Prentice Hall, 1999. [3] J. T. Aberle, S. H. Oh, D. T. Auckland, and S. D. Rogers, “Reconfigurable antennas for portable wireless devices,” IEEE Antennas Propag. Mag., vol. 45, no. 6, pp. 148–154, Dec. 2003. [4] A. T. Denidni, G. Y. Delisle, and M. Lecours, “Performance enhancement of adaptive phased arrays for wireless indoor communication systems,” in Proc. Canadian Conf. on Elect. and Comm. Eng., Sep. 1994, vol. 1, pp. 238–241. [5] A. T. Denidni and G. Y. Delisle, “A nonlinear algorithm for output power maximization of an indoor adaptive phased array,” IEEE Trans. Electromagn. Compat., vol. 37, no. 2, pp. 201–209, May 1995. [6] J. T. Bernhard, “Reconfigurable multifunction antennas: Next steps for the future,” Proc. Int. Symp. on Microw. Antennas Propag. and EMC Tech., pp. K2-1–K2-4, Aug. 2007. [7] C. B. Dietrich, W. L. Stutzman, B. K. Kim, and K. Dietze, “Smart antennas in wireless communications: Base-station diversity and handset beamforming,” IEEE Antennas Propag. Mag., vol. 42, no. 5, pp. 142–151, Oct. 2000. [8] B. A. Cetiner, H. Jafarkhkani, J. Y. Qian, H. J. Yoo, A. Grau, and F. D. Flaviis, “Multifunctional reconfigurable MEMS integrated antennas for adaptive MIMO systems,” IEEE Commun. Mag., vol. 42, no. 12, pp. 62–70, Dec. 2004. [9] T. K. Chang, R. J. Langley, and E. A. Parker, “Active frequency selective surfaces,” Proc.Inst. Elect. Eng. Microw. Antennas Propag., vol. 143, no. 1, pp. 62–66, Feb. 1996. [10] A. Qurir, S. N. Burokur, and A. de Lustrac, “Electronically reconfigurable metamaterial for compact directive cavity antennas,” Electron. Lett., vol. 43, no. 13, pp. 698–700, Jun. 2007. [11] F. Costa, A. Monorchio, S. Talarico, and F. M. Valeri, “An active high impedance surface for low profile tunable and steerable antennas,” Antennas Wireless Propag. Lett., vol. 7, pp. 676–680, Sep. 2008. [12] Y. E. Eremli, K. Sertel, R. A. Gilbert, D. E. Wrigh, and J. L. Volakis, “Frequency selective surfaces to enhance performance of broad band reconfigurable arrays,” IEEE Trans. Antennas Propag., vol. 50, no. 12, pp. 1716–1724, Dec. 2002. [13] G. M. Coutts, R. R. Mansour, and S. K. Chaudhuri, “Microelectromechanical systems tunable frequency-selective surfaces and electromagnetic-bandgap structures on rigid-flex substrates,” IEEE Trans. Microw. Theory Tech., vol. 56, no. 7, pp. 1737–1746, Jul. 2008. [14] D. Sievenpiper, J. Schaffner, R. Loo, G. Tangonan, S. Ontiveros, and R. Harold, “A tunable impedance surface performing as a reconfigurable beam steering reflector,” IEEE Trans. Antennas Propag., vol. 50, no. 3, pp. 384–390, Mar. 2002. [15] B. A. Munk, Frequency Selective Surfaces Theory and Design. New York: Wiley, 2000. [16] B. A. Munk, R. G. Kouyoumian, and L. Peters, “Reflection properties of periodic surfaces of loaded dipole,” IEEE Trans. Antennas Propag., vol. 19, no. 5, pp. 612–617, Sep. 1971. [17] S. Tretyakov, Analytical Modeling in Applied Electromagnetics. Boston, MA: Artech House, 2003. [18] G. Poilasne, P. Pouliguen, K. Mahdjoubu, L. Desclos, and C. Terret, “Active metallic photonic band-gap materials (MPBG): Experimental results on beam shaper,” IEEE Trans. Antennas Propag., vol. 48, no. 1, pp. 117–119, Jan. 2000. [19] H. Boutayeb, T. A. Denidni, K. Mahdjoubi, A. C. Tarot, A. R. Sebak, and L. Talbi, “Analysis and design of a cylindrical EBG-based directive antenna,” IEEE Trans. Antennas Propag., vol. 54, no. 1, pp. 211–219, Jan. 2006. [20] H. Boutayeb and T. A. Denidni, “Technique for reducing power supply in reconfigurable cylindrical electromagnetic structures,” IEEE Antennas Wireless Propag. Lett., vol. 5, no. 1, pp. 424–425, Dec. 2006. [21] A. Edalati, T. A. Denidni, and H. Boutayeb, “Reduction of active elements in agile EBG antennas using their second band-gap,” presented at the IEEE Antennas Propag. Society Int. Symp., Jul. 2008.

JAZI AND DENIDNI: FSSs AND THEIR APPLICATIONS FOR NIMBLE-RADIATION PATTERN ANTENNAS

[22] A. Edalati and T. A. Denidni, “Analysis of different defect configurations in CEBG structures for directive patterns,” in Proc. IEEE Antennas Propag. Society Int. Symp., Jun. 2007, pp. 185–188. [23] M. A. Habib, M. N. Jazi, A. Djaiz, M. Nedil, and T. A. Denidni, “Switched-beam antenna based on EBG periodic structures,” in Proc. IEEE Int. Microwave Symp., Jun. 2009, pp. 813–816. [24] M. N. Jazi, M. A. Habib, and T. A. Denidni, “Reconfigurable radiation pattern antenna based on active frequency selective surfaces,” presented at the IEEE Antennas Propag. Society Int. Symp., Jun. 2009. [25] M. N. Jazi, M. A. Habib, and T. A. Denidni, “Electronically switching radiation pattern antenna using an active cylindrical frequency selective surface,” presented at the IEEE Antennas Propag. Society Int. Symp., Jun. 2009. [26] GMP4200 PIN-Diode Series [Online]. Available: http://www.microsemi.com/datasheets/gmp4200%20series.pdf [27] B. Philips, E. A. Parker, and R. J. Langley, “Finite curved frequency selective surfaces,” Electron. Lett., vol. 29, no. 10, pp. 882–883, May 1993. Mahmoud Niroo Jazi (S’08) received the B.S. degree in electrical engineering from Azad University of Najafaband, Isfahan-Iran, in 2000, and the M.S. degree in electrical engineering from Urmia University, Urmia, Iran, in 2004. He is currently working toward the Ph.D. degree at Institute National de la Recherche (INRS), Montreal, Canada. He was with the Information Communication Institute and Technology (ICTI), Isfahan University of Technology (IUT), as a Research Engineer, from April 2004 to June 2007. During this period, he was involved in the Antennas and Microwave Research Group to develop and implement some practical communication systems. His research areas of interest broadly include antennas, passive and active microwave circuits, and numerical methods in electromagnetic and radar systems. His major subjects are focused on ultrawideband dielectric-resonator antennas, and particularly on periodic structures and their applications in reconfigurable antennas.

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Tayeb A. Denidni (M’98–SM’04) received the B.Sc. degree in electronic engineering from the University of Setif, Setif, Algeria, in 1986, and the M.Sc. and Ph.D. degrees in electrical engineering from Laval University, Quebec City, QC, Canada, in 1990 and 1994, respectively. From 1994 to 1996, he was an Assistant Professor with the Engineering Department, Université du Quebec, Rimouski (UQAR), Quebec, Canada, where, from 1996 to 2000, he was promoted to Associate Professor and then founded the Telecommunications Laboratory. Since August 2000, he has been with the Personal Communications Staff, Institut National de la Recherche Scientifique (INRS), Université du Quebec, Montreal, Canada. He founded the RF laboratory, INRS-EMT, Montreal, for graduate student research in the design, fabrication, and measurement of antennas. He possesses ten years of experience with antennas and microwave systems and is leading a large research group consisting of two research scientists, five Ph.D. students, and three M.S. students. Over the past ten years, he has graduated numerous graduate students. He has served as the Principal Investigator on numerous research projects on antennas for wireless communications. Currently he is actively involved in a major project in wireless of PROMPT-Quebec (Partnerships for Research on Microelectronics, Photonics and Telecommunications). His current research interests include planar microstrip filters, dielectric resonator antennas, electromagnetic-bandgap (EBG) antennas, antenna arrays, and microwave and RF design for wireless applications. He has authored over 100 papers in refereed journals. He has also authored or coauthored over 130 papers and invited presentations in numerous national and international conferences and symposia. Dr. Denidni is a member of the Order of Engineers of the Province of Quebec, Canada. He is also a member of URSI (Commission C). From 2006 to 2007, he was an Associate Editor for the IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS and, since 2008, for the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION.

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UWB, Non Dispersive Radiation From the Planarly Fed Leaky Lens Antenna— Part 1: Theory and Design Andrea Neto, Member, IEEE

Abstract—An efficient directive antenna is described that can be used to realize essentially non dispersive links over extremely large bandwidths. The antenna is a significantly enhanced version of previously proposed Leaky Lens antennas that use a frequency independent leaky slot radiation mechanism. A theoretical breakthrough now allows the use of this mechanism also in the presence of purely planar structures. This step allows the realization of the feed of a leaky lens antenna in a unique planar structure that is then glued to a standard circularly symmetric elliptical dielectric lens, as integrated technology requires in the mm and sub-mm wave domains. The first part of this sequence deals with a theoretical breakthrough, the consequent antenna concept and a description of the basic physical mechanisms inside and outside the lens antenna. It is shown that Leaky Lens antennas have the potential to be used to realize antenna links over bands exceeding a decade with minimal dispersion, high efficiency and high directivity. The second part of this sequence deals with the demonstration of these claims via the measurement of two prototypes. Index Terms—Dispersive channels, electromagnetic theory, lens antennas, ultrawideband antennas, ultrawideband radiation.

I. INTRODUCTION NE of the key parts of high frequency (mm or sub-mm waves) sensing systems is the integrated antenna that couples the incoming radiation into the receiver. The combinations of elliptical dielectric lenses and slot or dipole feeds have been used for decades in harmonic or pulsed sensing systems. Resonant feeds were introduced by [1] and by now gained a significant level of maturity, [2]–[5]. So far most of the studies presented in the literature involve antennas with 10%–15% operational bandwidth and good efficiencies. In recent years, however, the request for wider bands has been systematically driven by the desire for higher range resolution in radars or larger frequency characterization in spectrometers. In order to improve the usable bandwidth of dielectric lenses a particular leaky wave feed structure was proposed in [6], and [7] and the combination of feed and lens was called leaky lens antenna. While the antenna in [6] would operate over a band width of about an octave, the extension proposed in [7] leads to a decade of bandwidth (BW). However these previous leaky lenses were 3D structure with feed lines extending in different

O

Manuscript received October 20, 2009; revised January 05, 2010; accepted January 13, 2010. Date of publication April 26, 2010; date of current version July 08, 2010. The author was with the TNO Defence, Security and Safety, Den Haag 2597 AK, The Netherlands. He is now with the Department of Electrical Engineering (EEMCS), Technical University of Delft, 2628 CD Delft, The Netherlands (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/TAP.2010.2048879

planes and thus not suited to be realized in integrated or printed circuit board (PCB) technology. Moreover, they presented asymmetric radiation patterns with high side lobe levels. This paper presents an important breakthrough. The excellent performances of [7], derive from the very weak dispersivity intrinsic in the leaky wave slot radiation mechanism [8], [9]. The breakthrough is the realization that the velocity of propagation along a slot printed between two dielectric media can be accelerated acting locally on the reactive energy that surrounds the slot, without significantly reducing the characteristic low dispersivity of this type of radiation/propagation. Thanks to this theoretical insight it was possible to design an enhanced version of the UWB leaky lens antenna. The new antenna can be realized in planar integrated or printed technology. Next, it can be glued to a standard circularly symmetric lens, like those routinely used in mm and sub-mm wave technology i.e. as the ones in [1]–[5]. The novel antenna concept promises impedance matching over decades of bandwidth, very high efficiency, which is only limited by ohmic losses in the dielectric, directive and circularly symmetric patterns, and excellent pulse preservation properties which render it potentially suited for both pulsed and harmonic broad band instruments. For readers also interested in the practical realizability, a prototype demonstrator of the antenna has been designed to operate in the band (20 GHz–60 GHz) and some results of numerical simulations are presented at the end of this paper. The prototype has then been manufactured with printed circuit board technology. The details of the prototype and the consequent characterization, which validates the discussion in this paper, is presented in Part 2 of this sequence [10]. II. PLANARLY FED DIELECTRIC LENSES Fig. 1 shows a cross section of an elliptical dielectric lens and the direct rays emerging from a focal slot. The eccentricity of the ellipse that focuses in broadside part of the rays emerging from the lower focus is defined by the dielectric constant of the . Only the rays impinging on the dielectric air lens, section are focused in the far field, interface above the line while rays that impinge on the interface below the are lost in spill over since they are scattered in useless directions. A. Focused Feeds In reception, a sub-wavelength antenna is able to capture power incoming in the focus area. The focus radius depends on the focal distance to diameter ratio, F/D, of the system: with the wavelength in the dielecessentially tric. The F/D of these lenses cannot be approximated easily. However, a single pixel detection scheme would use the lens

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NETO: UWB, NON DISPERSIVE RADIATION FROM THE PLANARLY FED LEAKY LENS ANTENNA–PART 1

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Fig. 1. Cross section of an elliptical dielectric lens antenna. Also the transmitted ray picture that focuses energy toward broad side is shown.

relatively efficiently if the dimension of the feed was in the or smaller, when . order Resonant dipoles and slots are used to realize efficient integrated mixers in the spectroscopy domain. The twin slot configuration from [2], with the length of each of the slots being about one wavelength in the dielectric, is probably the most known design. In these cases all the available power from the local oscillators and the incoming signal is effectively used. Such efficient designs present narrow usable bandwidths. The author of the present paper recently designed an extension of the double slot of [2] in order to achieve an octave bandwidth of operation. This could only be achieved at the price of the efficiency decreasing to about 75% associated to an impedance mismatch. Moreover, an additional cost is that the radiation pattern from the slots becomes almost omnidirectional thus inducing important spill over losses due to rays impinging below the line in Fig. 1. The details of these results are not reported for the sake of brevity. Note that, for all resonant antennas located at an interface between two media, a denser dielectric contrast means more power is radiated toward the denser dielectric. Higher dielectric contrast corresponds to Higher front to back ratio. B. Planar Leaky Wave Slots: Standard and Enhanced A different strategy for the excitation of these same lenses is proposed here. The aim is to achieve an equivalent F/D of these lenses larger than 1 over a broad band. The original idea to adopt a leaky slot type of feed, as in [8] (in the following indicated as standard leaky wave slot), in a circularly symmetric elliptical lens antenna drove the present work. The leaky slot would guarantee the broad bandwidth and, hopefully, the circular symmetry of the lens should lead to reasonably symmetric patterns, while maintaining a compatibility of the feed manufacture with integrated technology. A simplified ray picture of the near field radiated by a “standard” leaky slot printed at the interface between air and a dense dielectric, is shown in Fig. 2. The region of co-existence of the leaky wave and the space wave, as well as the region where only space waves exist are highlighted in Fig. 2. The picture also shows the leaky wave . As highlighted in section IV of [8] leaky wave raangle, diation is a much larger phenomenon than space wave radiation when the slot is narrow in terms of the wavelength. The leaky wave mode is associated to distributed radiation which occurs ONLY in the denser medium, whatever is the dielectric contrast,

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Fig. 2. Side view ( -plane cut) of the near field ray picture, highlighting leaky , for a standard leaky waves existence zones, and the leaky wave angle, wave slot.

Fig. 3. Representation of the ray propagation inside an elliptical dielectric lens ( = 10). Picture associated to the radiation from: (a) a standard leaky wave slot, (b) an enhanced leaky wave slot.



provided there is one. Thus the front to back ratio in leaky slots is typically much higher than in resonant type of feeds, and independent from the dielectric contrast. When the observation point is moved to the far field, with respect to the slot’s finite radiating length, the leaky wave cannot be explicitly observed anymore, since it attenuates exponentially as a function of . However, a different but still useful ray picture can be derived resorting to the space waves only. The far field ray picture, associated to this same slot inside a dielectric lens is shown in Fig. 3(a). This figure shows a simplified two dimensional cut, representing the plane of a dense, , elliptical lens, fed by the standard leaky wave slot. The center of the slot would be located at the lower focus of the elliptical lens so that the two separate beams, associated to , could be separately traced leaky waves propagating along to the radiating aperture, A. The angle characterizing the stan, defines the width and dard leaky wave, here indicated as the center location of the zones on the lens which are active. can be evaluated analytically as shown in [8]. The angle , is a typical value over a large frequency band for . As deslots printed between air and a dielectric with scribed in Appendix A the 3 dB beam widths in the dielectric can also be calculated analytically. The beams of rays inside the dielectric can be imagined 12 wide which can be representative for this type of slots. Following the rays to the aperture A, one can identify a distribution which can be thought of as the superposition of two separate contributions. Let us assume that

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have to be enhanced, i.e. be larger. Fig. 3(b) shows the ray pic.A ture in the case the angle of the leaky wave was simple tracking of the geometrical rays shows that, in this case, the aperture distribution is well represented when the parameand . ters and are taken as Resorting again to (1) to estimate the pattern one finds the results in Fig. 4(b). In this enhanced case the side lobes are always lower than 10 dB thanks to the fact that the spatial separation of the ray bundles on A is much lower and these same bundles impinge on the dielectric-air interface almost normally. would give rise to One can note that any angle side lobes higher than 10 dB. Since the radiation can be described as due to an array structure (composed of two elements), when the lens diameter becomes larger in terms of the wavelength grating lobes will eventually emerge. However the peak level of these grating lobes will be low as it is modulated by the element factor of this array. The element factor becomes more directive for larger lenses. Overall it appears that thus 70 should be considered a minimum angle, as a rule of thumb. III. ENHANCED LEAKY WAVE RADIATION: THE BREAKTHROUGH

Fig. 4. Simplified, normalized, H-plane secondary radiation patterns due to the lenses and feed represented in Fig. 3. (a) a standard leaky wave slot feed (d  ,t  ), (b) an enhanced leaky wave slot feed (d  ).  ,t

5

= 10 =4

=2

=

the separation between the two contributions is indicated with and that, for the sake of simplicity, each of the distributions is triangular with width . Given these approximations, the analytical evaluation of the secondary radiation pattern, after the lens, can be performed by simple Fourier transformation of the aperture distribution in Fig. 3, leading to:

(1) Note that here indicates the distance of the observation point from the center of the radiating aperture A, and is a complex constant, unimportant at this point, which accounts for the amplitude of the excitation, the propagation and reflections inside plane. If one subthe lens and the field distribution in the and a pattern stitutes as in Fig. 4(a) emerges, indicating that a large number of side lobes essentially renders this type of lens useless. The interference between the two separate bundles of energy emerging from the focal point gives rise to this. In order to obtain a unique secondary main beam and much lower side lobes, using a double leaky wave source, the angle of the leaky waves with respect to the slot plane, , would

of radiation of each leaky wave in Fig. 2 is asThe angle sociated to the real part of the propagation constant of the leaky wave propagating along the slot. In previous leaky lens structure [6] and [7] it was assumed that the propagation constant associated to this type of radiation is mainly the average of the propagation constant in the two dielectric media in contact through the slot. Apart from secondary dispersion effects, the propagation constant of the slot was assumed to be where , for , 2, were the propagation constants in the (with characterizing the two media of dielectric constant less dense medium). Increasing the dielectric contrast would always lead to an upper boundary of 45 for the leaky wave angle . Thus a separation of at least 90 between the two separate beams, as in Figs. 2 and 3(a), associated to a central feed of the slot is to be expected if the slot separates two different homogeneous dielectrics. However, if is not the average between and but can be designed to assume a desired value things could look differently. If the separation between the two beams in the dense dielectric is much smaller. In implies waves propagating in the dielectric at angle, fact . This means that when waves are propagating with free space velocity of the less dense medium along the interface between the two media, waves propagate parallel to the critical angle in the denser dielectric. As an example, if on a slot separating free space and silicon , was propagating a wave with propagation constant equal to that of free space, the angle of leaky radiation in the dielectric would be 73 . , the angle would be about 60 . It In the case of quartz is not difficult to alter the slot’s geometry in order to render its propagation constant similar to the one of the free space in the less dense medium, . It is sufficient to introduce a small air separation between the slot and the dense dielectric as indiis very small with respect cated in Fig. 5(a). If the slot width , the distributed capacitance assoto the wavelength and ciated to the slot is dominated by the very-near fields and thus by

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can be obtained. The propagation constant in the slot can be expressed as (2)

Fig. 5. (a) Canonical problem of a slot, of width w with separation layer, h. (b) Schematic drawing of the electric field configuration.

air. Consequently the real part of propagation constant is essentially that of free space, see Fig. 5(b). The imaginary part of the propagation constant is associated to radiation in the dielectric. Power is increasingly leaving the slot as the wave propagates. In fact the pointing vector is not parallel to the slot but directed toward the dielectric in the presence of a dielectric contrast. Note that the introduction of a separation layer is just one way to alter the propagation constant and one of the most simple to realize at microwave frequencies. However, under-etching the slot in a dense crystal, or introducing a separation layer of low dielectric constant between the slot and the densest dielectric are equivalent implementation procedures. In the rest of this paper we will refer to this type of radiation as to the enhanced leaky lens radiation, in contrast with the previous “standard” leaky lens radiation. For the interested reader, the link with Cherenkov radiation is explained in Appendix B. A. Green’s Function Investigations The overall behavior of the leaky lens radiation has been described in the previous paragraph. A parametric investigation of the structure based on a rigorous Green’s Function (GF) analysis is of use when one wishes to actually design an antenna using the enhanced leaky slot. In this paragraph the dispersion equation and the radiation patterns are investigated using the formalism and calculational tools described in [8], and [9] and the specific extension to generic stratifications in [11]. It will be assumed that . This choice is just for the sake of fixing some variables. In practice the fine tuning of the ratio of and depends on a third parameter, the thickness choice for of the metal. This latter parameter is not easy to introduce in our evaluation of the GF, thus it is neglected in the present analysis. 1) Dispersion Study: The approximate but accurate solution of the dispersion equation that identifies the leaky wave pole

where D is the function reported in [11, Eq. (21)]. is an initial guess of the real part of the propagation constant. would certainly be a good initial guess, however since the numerical evaluation of the derivative in (2) would imply the evaluation of the denominator function extremely close to a branch singularity in the complex domain. In the following numerical examples the initial point . The results are still excellent in comparwas taken to be ison with much heavier full wave simulations performed with commercial tools. The angle of radiation and the normalized attenuation constant as a function of the frequency are shown in Fig. 6(a) and (b) respectively. The assumed dielectric contrast is and while . For comparison also are reported the results associated to the case in which in order to appreciate the importance of the small separation layers. Considering the real part of the propagation constant, one can observe that the expected radiation angle tends asymptotically to the critical angle in the dielectric (72 ). From the observation of the attenuation constant one can realize that it decreases significantly as the slot is more separated from the dielectric in terms of the wavelength (high frequencies). This is because when the slot is farther away from the dielectric interface in terms of the wavelength, is large, the portion of the field distributed inside the dielectric is lower and thus the propagation constant tends to be the one of free space. 2) Radiation Pattern in the Dense Dielectric: In this section the radiation from the slots whose dispersion has been investigated in Section III-A-1 is studied. In particular the radiation patterns in absence of the dielectric lens are considered, assuming both the dielectric media, and the slot infinitely extended. To evaluate the far fields, the same procedure as presented in [9] has been used, with the difference that this time the implemented Spectral Domain Magnetic Field GF includes the separation layer between the ground plane containing the slots and the denser dielectric. This spectral domain GF can be evaluated as discussed in [11]. Assuming the slot to be oriented along , , Fig. 7(a), (b), (c) show the normalized total magnetic fields in the , the and the diagonal planes respectively, as a function of the observation , . The different curves in angle in the case of . Note also that the each figure refer to different values of angles from to 90 refer to radiation in the denser dielec, and 90 , 180 refer tric, while the angle ranging to radiation in the free space. The behavior of the filed in the plane, Fig. 7(a) is congruent with the dispersion analysis in Section III-A-1: two beams are systematically found pointing at relatively small angles from broadside. As the values of become larger the beams are more directive and pointing more clearly toward the critical angle. The behavior of the field in the plane, Fig. 7(b), is similar at least for certain values of the

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Fig. 6. Leaky wave propagation constant as a function of the frequency: leaky (a) and normalized attenuation constant (b). The dielectric wave angle, constants are  and  . The continuous lines are pertinent to h : , while the dashed lines are pertinent to slots parameters w w : and h .

=1 = 10 = = 0 5 mm = 0 5 mm =0

parameter . This might come as a surprise to the reader, but in fact this was to be expected. The feed in the slot also excites a cylindrically spreading TM wave propagating away from the feed and that is initially bounded between the ground plane and the dense dielectric . This propagation occurs with a phase velocity that is essentially the one of free space. In order to have continuity of the tangent fields at the air dielectric interface the waves in the denser dielectric, have to propagate toward the critical angle, thus realizing a directive beam in the dielectric not only in the direction of the slot ( -plane) but also in the other directions. In this plane the width of the slot plays a minor role and the parameter is more important. Note that the pattern in -plane is approximately equivalent to the radiation pattern of an electric dipole printed at the interface between two different dielectric, see [1, Fig. 5]. For very small values of in terms of the wavelength, the radiation pattern in the -plane tends to recover the shape it would have if the separation layer was equal to zero. This implies that a very small separation in terms of the wavelength can be sufficient to alter the propagation along the slot, because the important effect is the local reactive energy in the surrounding of the slots, but could

Fig. 7. The total magnetic field radiated in the far field by a set of different slots h are shown as a function , and with w printed among  of the elevation angles,  . (a) represents the H plane, (b) the E plane and (c) the diagonal plane.

=1

= 10

=

not be enough to render directive the radiation in the -plane. For completeness also the patterns in the diagonal plane are reported in Fig. 7. IV. ANTENNA DESIGN The design of circularly symmetric lenses fed by sub-wavelength antennas has been described in many excellent contributions mentioned in the introduction, specifically [12] is a recent reference that discusses some of efficiency tradeoffs in standard centrally fed dielectric lens antenna. However, feeding such lens

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Fig. 8. CAD drawing of the enhanced UWB leaky lens design, highlighting the dielectric layers and the metallic holder.

with long leaky wave slots introduces a number of novel characteristics. In order to highlight them, the design of a specific implementation of a planar UWB leaky lens antenna is described. The antenna is designed to operate efficiently in the band 20–60 GHz. On the basis of this design, a prototype has been manufactured and the results of the measurement campaign are presented in [10]. A. Lens Design Based on the considerations in Section III, the dielectric constant of the lens was chosen . The elliptical shape of the lens was synthesized as the union of an hemisphere of diamand a cylindrical dielectric slab base of height eter , in the present case . A CAD drawing of the designed structure is shown in Fig. 8. The dielectric layers of the lens are made transparent for higher visibility. The dielectric lens is inserted into a metallic plate, thick enough to support the weight of the lens, in which a circular hole of 22 mm diameter has been cut. Most of the peculiar properties of the planar UWB leaky lens, when compared to lenses fed by resonant feeds, stem from the fact that the effective F/D of the lens is relatively larger than for standard lenses. That is because the radiation pattern in the lens is more directive with respect to the cases mentioned in Section II-A, and this implies that only the upper part of the lens is effectively used. As shown in the Appendix A, the equivalent F/D ratio for a circularly symmetric elliptical dielectric lens, with , fed by an enhanced leaky wave slot, is above 1 and increases as a function of the frequency. A larger F/D for the same lens clearly implies that the aperture efficiency is lower (a lower gain that the physical area would suggest). However the highest possible gain is rarely an incentive in higher frequencies, since the dimensions are very small. 1) No Spill Over: The main advantage of the rays illuminating the central part of the lens is that the amount of power, associated to rays emerging directly from the slot, that impinges at the dielectric air interface below the line in Fig. 1 is almost negligible. This implies that there is small amount of power lost in spill over. In standard lens antennas fed by sub-wavelength antennas, the only way to achieve low spill over is to either use array types of feeds which further diminish the bandwidth, or to use non elliptical lenses, which also lead to a lower directivity.

Fig. 9. Characterization of a plane wave normally incident at the interface between a dense dielectric and the three matching layers. Continuous line represents the reflection coefficient in dB while the dashed line represents the transmission efficiency in linear scale.

2) Reflection at the Dielectric Air Interface: As explained [13] and [14] the double reflections at the dielectric-air interface normally play a major role in characterizing the input impedance of the antenna as well as its radiation pattern. However, in the present case only the upper part of the lens is active. As explained in Fig. 2(b) of [13] the top region of the lens does not contribute to the refocusing of doubly reflected rays. As a consequence, the new configuration of circularly symmetric lenses is not expected to suffer from resonances associated to doubly reflected rays even if a dense dielectric is used. However, as also explained in [4] the first reflections can be an important cause of performance degradation. 3) Dielectric Layers: When possible, it is better to include matching layers [16] to diminish all reflections. In the present case the antenna was expected to operate over a very broad band, thus a three-layers structure is proposed. The matching layers , , were chosen to be of heights and dielectric constants , , . Fig. 9 shows the reflection coefficient associated to a plane wave normally incident to the dielectric stratification. It is apparent that a reduction of the reflection coefficient from 6 dB to 10 dB can be obtained over most of the band from 12 to 80 GHz. Also the transmission efficiency associated to the same plane wave is reported in Fig. 9. A transmission higher than 90% can be obtained over the same band. The matching layers included in the design are also visible in Fig. 8. 4) Front-to-Back Ratio: Normally sub-wavelength or resonant slots printed at the interface between two dielectrics radiate with front-to-back ratios proportional to the dielectric contrast ( corresponding to 15 dB). From the curves in as Fig. 7 one can observe that the front-to-back ratios for the magnetic fields are moderate if one considers the radiation in the lens. However the rays propagating with angles close to 17 , the critical angle, are also directed toward broadside by the focusing lens. Accordingly, one can expect that the eventual front-to-back ratio for the magnetic fields

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V. DISPERSIVITY OF A LINK WITH TWO LEAKY LENSES A detailed discussion on the performance of this antenna will be presented in [10] based on the measurements of hardware demonstrators. Here, we will discuss the potentials for this antenna to be used as basic element for a non distorting radiated link. The link between a transmitter and a receiver does not distort a short time domain pulse if the S12 parameter of the link in the frequency domain presents • linear phase variation (no dispersivity); • constant amplitude (no amplitude distortion). A. Phase Center and Phase Linearity

Fig. 10. The enhanced UWB leaky lens prototype. TABLE I GEOMETRICAL SPECIFICATIONS OF THE UWB LEAKY LENS

The qualitative behavior of the phase of the field inside the lens but far from the feed is the same as that shown in [9]. The propagation constant in the dielectric and the distance of the observation point from the feed point relate to the phase as . This represents a spherical spreading in the lens. Moreover, in Section II-B the -plane radiation pattern, including the lens, was discussed. If matching layers are used, the transition between dense dielectric and air is practically reflection-less. Since all the rays arrive at the radiating aperture, see Fig. 12, with the same electrical path length, one can use the central ray to estimate their phase. Thus in the approximate equation (1) for the far field radiated by the lens, one can substitute the expression of the phase of the aperture field as radiated by the source (3) differs from in (1). in (3) is where the subscript in a real function for a symmetric distribution. The only variation of the phase of the far field as a function of the frequency and of the observation point can be expressed as (4)

of the overall system will be higher than 15 dB everywhere, corfrom Fig. 7. responding to B. Details of the Feed Some of the geometrical details of the structure, excluding the metallic holder are shown in Fig. 10. Below the metallic thick plate a printed circuit board is glued, which is composed dielectric layer of dielectric constant , metallized of a thin, on the side where the radiating slot is etched. The slot’s and , respectively. The metallic width and length are holding block keeps the slot’s plane at m of distance from the bottom of the lens. A micro-strip line, shorted to the slot’s plane via a vertical metallic pin, feeds the slot and is also depicted in , corresponding to 80 Fig. 10. The micro-strip width is characteristic impedance. Note that the slot’s width is not constant. It is tapered to about 100 in corresponding of the micro-strip transition. This minimizes the localized reactive energy and improves the matching significantly. The dimensioning of the planar UWB leaky lens are summarized in Table I. . Note that, unlike the examples in Section III,

We note that this expression is valid in the far field with respect to the radiating antenna and that is taken at the center of the top of the lens. For quasi optical systems, the far field , where D is the diameter of region is defined as the entire aperture. Thus the far field region is at greater distance for higher frequencies. However, in the present leaky lens case, the equivalent diameter of the radiating aperture decreases for higher frequencies due to the higher attenuation of the leaky wave and thus the far field zone remains essentially at constant distance for all frequencies. The dependence from the frequency in (4) can be highlighted (5) This last equation shows that • the phase center is constant for all frequencies and observation points in the main beam. It is located on top of the lens as shown Fig. 11; • the antenna can be described as non dispersive, since the variation of the phase as a function of the frequency is linear. Overall, if the far field radiated by an antenna can be expressed as a radiation integral from a planar aperture distribu-

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Fig. 11. Phase center location for the planar leaky lens.

tion with constant phase, the phase center of the antenna does not move as a function of the frequency. If the phase of the distribution also depends linearly from the frequency then the link is dispersion less. Differences With TEM Horns: These properties do not apply for the most widely used antennas for UWB applications that require low dispersivity, TEM horns (or derived types like the Vivaldi). These horns, like all horns, are characterized by phase centres that move as a function of the frequency. The reason why they are considered weakly dispersive antennas is that their performance is typically observed in the broadside direction, see Fig. 12(a). For simplicity we can assume that the frequency spectrum can be divided in two bands only. Also we can assume that the high frequency components emerge as rays from the high frequency phase center while low frequency components emerge as rays from a point further along the tapering, the low frequency phase center . Before emerging as rays, the waves are guided with a phase velocity of a coplanar line . In Fig. 12(a) and (b), the paths from the antenna feeding point to the observation points followed by the high frequency rays are indicated by the solid lines. The paths followed by the low frequency rays are indicated by a dotted line. For observation points at broadside, , the high frequency and the low frequency waves arrive to the observer after having followed the same path length: as anticipated the low frequency waves are partly guided and partly radiated while the high frequency waves can be considered entirely radiated. But for TEM horns . So high frequency rays and low frequency waves arrive to the observation point with the same phase delay. This shows that in the broadside case the dependence of the phase from the frequency is linear even if the phase center moves. This only happens at broadside, as is evident when observing Fig. 12(b), which depicts the situation for observation points not at broadside. The path lengths for high frequency, solid line, and low frequency, dotted line, differ. In other terms, it would not be possible to obtain a correct representation of the far field radiated by an horn based on the radiation integral from a planar aperture distribution with constant phase, as was done in the case of the leaky lens. B. Calculated Gains and Directivities The antenna presented in the previous section has been analyzed by means of the commercial code CST, [17] based on the FDTD method. Two configurations, with and without matching layers, have been investigated. The only parameters which are important to finalize the theoretical discussion are the calculated

Fig. 12. Phase center location for TEM horns: top Figures indicates weak dispersivity at broadside; bottom figures shows high dispersivity off broadside, but still in the main beam.

Fig. 13. Calculated gain and directivity for the leaky lenses with and without matching layers as a function of the frequency.

gain and directivity. Fig. 13 shows the calculated gain and directivity for the antenna described in Section IV, with and without the matching layers.

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The important aspect is that, with matching layers, the achieved gain increases almost linearly with frequency in the band from 15 GHz to 70 GHz. This is unusual for dielectric lens antennas. As anticipated, this is due to the fact that as the frequency increases the slot feed becomes more directive and only the central part of the lens is illuminated. , in an antenna link is proThe power received, portional to the transmitted power, via . If an impulse . Note is not by an antenna link: it leads to that the condition for a pulse not to be distorted by a radiated link is on the product of the two gains in transmit and receive. Accordingly, also a design in which the gain in transmit is constant with frequency and the one in receive grows quadratically in frequency leads to non distorting links. The lens shape of leaky lenses can be tuned to different needs depending on the application provided the phase linearity property is not altered. VI. CONCLUSION The leaky lens radiation mechanism, introduced in [8] and extended in this paper, is the only practical exploitation at microwaves of the well known Cherenkov radiation, with properties that are essentially frequency independent. Specifically, this paper demonstrates for the first time that this mechanism can also be used to realize feeds for dielectric lens antennas in completely planar technology. The first prototypes implementing this antenna concept will be presented in the second part of this paper [10] and further concluding remarks will follow based on the analysis of the achieved results. However, it should be already clear that the antenna concept is a real function enabling breakthrough. It allows efficient UWB radiation, constant phase centres, very low dispersivity and gain linearly increasing with frequency. These properties indicate the possibility of realizing radiated links between two antennas characterized by extremely large relative bandwidths with virtually no distortion. Despite the fact that the issue was not discussed in the paper, it is apparent that there are significant margin of improvements in the efficiency of the structure once the shape of the lens would become a design parameter. APPENDIX A F/D OF THE LENS The 3 DB beam width in the dielectric can easily be related to the imaginary part of propagation constant of the leaky wave, indicated as in Fig. 6. In fact, given that the far field radiated by a leaky wave is proportional in first approximation to the leaky wave pole as (6)

defines the area of the lens Assuming that the angle which is excited, it is straight forward to define an equivalent F/D for the present lenses according to the picture in 3(b). One can assume that the equivalent focal distance of the lens remains is the portion aperture distribution F while the diameter which is excited with field levels higher than 3 dB. This region of space can be geometrically tracked to , where is the beam width it results in the dielectric. Overall in the case of which implies the equivalent . APPENDIX B LINK TO CHERENKOV RADIATION Cherenkov radiation is the mechanism by which an electrically charged particle radiates when moving with uniform velocity higher than the speed of light in the hosting medium. Even if here there are no particles moving at relativistic speed a relationship between Cherenkov radiation and the phenomenon described in this paper, and more in depth in [8] and [9], probably exists. Its discussion is outside the scope of the present work. However we will just remind the reader that a charge, q, moving along x with constant speed can be associated to an electric current as in [15, p. 494–499]

Taking the Fourier transform of this current to represent it in the frequency domain gives rise to

This is a propagating wave and does not show an obvious link to leaky waves. However, in relativistic electrodynamics, it is well accepted that when the power is radiated the charge velocity decreases in reason of its reduced kinetic energy. When a arbitrarily small exponential deceleration in the charge’s speed the associated current can be exis included, pressed as

The integration inside the Diracs function can be performed analytically leading to

where the small argument approximation of the exponential has been used, because the deceleration is assumed to be small. Taking the Fourier transform of the decreasing current leads to a representation in the frequency domain

the 3 dB beam-width in the dielectric can be easily demonstrated to be (7) Considering that a representative value for is for the considered example of , it results

, .

Thus the spectral representation of the current associated to a decelarating charge is the same as that of a current exponentially decreasing in amplitude. Clearly there is a connection between the phenomenon of field amplitude decay in leaky waves and charge deceleration. This link is not obvious.

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REFERENCES [1] D. B. Rutledge and M. S. Muha, “Imaging antenna arrays,” IEEE Trans. Antennas Propag., vol. 30, no. 4, pp. 535–540, Jul. 1982. [2] D. F. Filippovic, S. S. Gearhart, and G. M. Rebeiz, “Double slot on extended hemispherical and elliptical silicon dielectric lenses,” IEEE Trans. Microw. Theory Tech., vol. 41, no. 10, pp. 1738–1749, Oct. 1993. [3] X. Wu, G. Eleftheriades, and T. E. van Deventer-Perkins, “Design and characterization of single and multiple beam MM-wave circularly polarized substrate lens antennas for wireless communications,” IEEE Trans. Microw. Theory Tech., vol. 49, no. 3, pp. 431–441, March 2001. [4] A. V. Boriskin, G. Godi, R. Sauleau, and A. I. Nosich, “Small hemielliptic dielectric lens antenna analysis in 2-D: Boundary integral equations versus geometrical and physical optics,” IEEE Trans. Antennas Propag., vol. 56, no. 2, pp. 485–492, Feb. 2008. [5] P. Focardi, W. R. McGrath, and A. Neto, “Design guidelines for terahertz mixers and detectors,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 5, pp. 1653–1661, May 2005. [6] A. Neto, S. Bruni, G. Gerini, and M. Sabbadini, “The leaky lens: A broad band, fixed beam leaky wave antenna,” IEEE Trans. Antennas Propag., vol. 53, no. 10, pp. 3240–3246, Oct. 2005. [7] S. Bruni, A. Neto, and F. Marliani, “The UWB leaky lens antenna,” IEEE Trans. Antennas Propag., vol. 55, no. 10, pp. 2642–2653, Oct. 2007. [8] A. Neto and S. Maci, “Green’s function of an infinite slot printed between two homogeneous dielectrics. Part I: Magnetic currents,” IIEEE Trans. Antennas Propag., vol. 51, no. 7, pp. 1572–1581, Jul. 2003. [9] S. Maci and A. Neto, “Green’s function of an infinite slot line printed between two homogeneous dielectrics—Part II: Uniform asymptotic fields,” IEEE Trans. Antennas Propag., vol. 52, no. 3, pp. 666–676, Mar. 2004. [10] A. Neto, S. Monni, and F. Nennie, “UWB, non dispersive radiation from the planarly fed leaky lens antenna—Part II: Demonstrators and measurements,” IEEE Trans. Antennas Propag., vol. 58, no. 7, pp. –, Jul. 2010. [11] S. Bruni, N. Llombart, A. Neto, G. Gerini, and S. Maci, “Problemmatched basis functions for microstrip coupled slot antennas based on transmission line Green’s functions,” IIEEE Trans. Antennas Propag., vol. 53, no. 11, pp. 3556–3567, Nov. 2005. [12] A. V. Boriskin, R. Sauleau, and A. I. Nosich, “Performance of hemielliptic dielectric lens antennas with optimal edge illumination,” IEEE Trans. Antennas Propag., vol. 57, no. 7, pp. 2193–2198, Jul. 2009.

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[13] A. Neto, S. Maci, and P. J. de Maagt, “Reflections inside an elliptical dielectric lens antenna,” IEE Proc. Microw., Antennas Propag., vol. 145, no. 3, pp. 243–248, Jun. 1998. [14] A. Neto, D. Pasqualini, A. Toccafondi, and S. Maci, “Mutual coupling between slots under an elliptical dielectric lens,” IEEE Trans. Antennas Propag., vol. 47, no. 10, pp. 1504–1507, Oct. 1999. [15] L. Felsen and N. Marcuvitz, Radiation and Scattering of Waves. New York: IEEE Press, 1994. [16] N. T. Nguyen, R. Sauleau, and C. J. M. Perez, “Very broadband extended hemispherical lenses: Role of matching layers for bandwidth enlargement,” IEEE Trans. Antennas Propag., vol. 57, no. 7, pp. 1907–1913, Jul. 2009. [17] “CST Microwave Studio, User Manual Version 5.0,” CST GmbH, Darmstadt, Germany.

Andrea Neto (M’00) received the Laurea degree (summa cum laude) in electronic engineering from the University of Florence, Italy, in 1994 and the Ph.D. degree in electromagnetics from the University of Siena, Italy, in 2000. Part of his Ph.D. was developed at the European Space Agency Research and Technology Center, Noordwijk, The Netherlands. From 1998 to 2000, he worked for the Antenna Section, European Space Agency Research and Technology Center, Noordwijk, The Netherlands. In the years 2000–2001, he was a Postdoctoral Researcher at California Institute of Technology, Pasadena, working for the Sub-mm wave Advanced Technology Group. From 2002 to January 2010, was a Senior Antenna Scientist at TNO Defence, Security and Safety, The Hague, The Netherlands. In February 2010, he was appointed Full Professor of Applied Electromagnetism at the Department of Electrical Engineering (EEMCS), Technical University of Delft, Delft, The Netherlands. His research interests are in the analysis and design of antennas, with emphasis on arrays, dielectric lens antennas, wide band antennas and EBG structures. Prof. Neto was co-recipient of the H.A. Wheeler Award for the Best Applications Paper of the year 2008 in the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION. He presently serves as an Associate Editor of IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS (AWPL).

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 58, NO. 7, JULY 2010

UWB, Non Dispersive Radiation From the Planarly Fed Leaky Lens Antenna—Part II: Demonstrators and Measurements Andrea Neto, Member, IEEE, Stefania Monni, Member, IEEE, and Frans Nennie

Abstract—We provide for the first time the experimental characterization of a planarly fed ultrawideband leaky lens antenna. The paper includes the description and the experimental characterization of two antenna prototypes with radiating element realized in printed circuit board technology. The impedance parameters and the radiation patterns of the antennas have been measured showing excellent pattern quality and efficiency. The link between two antennas has also been characterized in the frequency and time domains in terms of mutual coupling impulse response respectively. Unprecedented performance in terms of pulse fidelity are demonstrated suggesting very high potentials of these antennas for all applications that require preservation of narrow pulses. Index Terms—Dispersive channels, electromagnetic theory, lens antennas, ultrawideband antennas, ultrawideband radiation.

I. INTRODUCTION OR most radar and communication applications that require a wide frequency bandwidth the linearity of the phase of the antenna transfer function is of great importance. If the antenna is dispersive (i.e., the phase does not vary linearly with frequency) compensations at system level must be included, such as subdivisions of the bands, digital signal processing, inclusions of filters, etc. [1]. The most linear phase responses are associated to antennas derived from TEM-like horns. For instance the Vivaldi antenna, which is a low cost implementation of TEM horns, is a very successful example, see [2]. However, it is well known that its phase center moves along the longitudinal axis. This implies that the phase linearity is only limited to the broadside direction. The stability of the phase center as a function of the frequency is only a necessary condition for the linearity of the phase in all observation directions. The most successful wideband antennas that present fixed phase centers are often derived from spirals or from the log periodic concept. As an example, the Eleven antenna [3] has recently been proposed for decade bandwidth

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Manuscript received October 20, 2009; revised January 05, 2010; accepted January 13, 2010. Date of publication April 26, 2010; date of current version July 08, 2010. A. Neto was with the TNO Defence, Security and Safety, Den Haag 2597 AK, The Netherlands. He is now with the Department of Electrical Engineering (EEMCS), Technical University of Delft, 2628 CD Delft, The Netherlands (e-mail: [email protected]). S. Monni and F. Nennie are with the TNO Defence, Security and Security, Den Haag 2597 AK, The Netherlands (e-mail: [email protected]; frans. [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/TAP.2010.2048880

(BW) reflector’s excitation. However, as shown in [2] the log periodic concept is intrinsically associated to a non linear phase variation of the transfer function. The same applies for spirals. Overall, it appears that no antennas are presently known capable of radiating non dispersively over the entire main beam and over very large bandwidths. When the attention is shifted from a single antenna to a radiated link, the linearity of the phase of the antenna transfer function is not sufficient for the reception of a non distorted replica of the input impulse. Also the amplitude of the spectrum of the transmitted impulse must be preserved. The planarly fed leaky lens antenna, described in paper [4], appears to be well performing with respect to both dispersivity and amplitude distortion. In [4], the concept and design of the antenna was presented. In this paper, corresponding hardware prototypes are described and experimentally characterized. To demonstrate the ultra-wide bandwidth performance while retaining manageable lens dimensions, 12 GHz has been chosen as lowest operating frequency. The planar feed has been realized in standard printed circuit board (PCB) technology. Both types of antennas discussed in [4], with and without matching layers, have been manufactured. The matching layers reduce the reflection at the dielectric/air interface and this is therefore the preferred implementation of the Leaky Lens antenna design. However, for applications at sub-mm wave frequencies the realization of the matching layers poses serious technological challenges. Thus, the performance degradation of the planarly fed leaky lens antenna without the matching layers has also been quantified. A link between two prototypes has been experimentally characterized. From the measured S-parameters, the pulse preserving property of the antenna link demonstrates the phase linearity and phase center stability of each antenna as well as the spectral amplitude preservation of the link. While the phase preserving properties arise from the Enhanced Leaky Lens radiation mechanism [4], the spectral amplitude preservation is strictly related to the specific geometry chosen for the dielectric lens. The paper is structured as follows. After a short description of the prototypes in Sections II, III presents the S-parameter measurement results for both structures, with and without matching layers, covering the band from 5 to 70 GHz. Section IV describes the impulse response of the links between two antennas. Time gating is applied to this response in Section V to highlight the dominant wave phenomena characterizing the links. The

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Fig. 2. Measurement setup for the characterization of the transmit-receive antenna link.

Fig. 1. The planarly fed UWB leaky lens antenna prototype.

measured antenna radiation patterns are plotted in Section VI for the frequency range 33–75 GHz. Considerations on the results are provided in Section VII. II. PROTOTYPE DESCRIPTION A 3D radar imaging system operating with 30 GHz bandwidth is currently being designed at TNO. In the frame of this project, a planarly fed Leaky Lens antenna will be integrated on the printed circuit board where the TX/RX front-end circuitry will be hosted. As preliminary step, two prototypes of the antenna have been designed and manufactured to characterize the antenna performance independently from the rest of the system. According to the design guidelines presented in [4] the prototypes have been manufactured to operate efficiently as transmitter and receiver in the frequency band 30 to 60 GHz. The dielectric lens has been made of a material for microwave applithat is commercially available cations in cylindrical rods of up to 100 mm of diameter. The material could be machined at TNO workshop with sufficient accuracy. The relevant dimensions of the lens and of the feeding structure in the PCB can be found in [4] and will not be repeated here for the sake of brevity. Fig. 1 shows the lateral and top view of one of the prototypes. In Fig. 1(a) the holder consisting of a thick metal plate (1 mm) is also visible on top of a plastic block that was introduced to provide support to the antenna PCB. Because of the high front-to-back ratio of the planarly fed leaky lens antenna, this structure does not significantly affect the radiation , was inserted to performance. A slab of foam material,

maintain a constant separation between the lens and the ground plane where the slot is etched and ensure the enhanced radiation mechanism. The micro-strip extends at the side of the lens, where it is fed through a mini-SMP coaxial cable connector. To protect the mini-SMP, 1.85 mm connector savers are used. As outlined in [4], to match the 80 antenna impedance to the 50 impedance of the connector the micro-strip width has accordingly been tapered from 200 to 300 . The overall distance between the coaxial connector and the center of the slot is about 4 cm. After measuring the performance of the two antenna prototypes, two sets of curved matching layers conformal to the original lens have been milled away from three dielectric roads of , 3.5, 2.5 and . The nominal permittivity details of the stratification were described in [4, Sec. IV-A.3]. The matching layers have then been glued to each other and to the lens of the original antennas and new measurements have been carried out. III. SCATTERING PARAMETERS The antenna scattering parameters have been measured using an Agilent vector network analyzer, which is able to perform measurements up to 70 GHz. The reflection behavior of each antenna has been investigated in terms of S11. The performance of the two manufactured antennas will be shown in Fig. 3. The transmit-receive antenna link has been characterized in terms of S12 with the measurement set up depicted in Fig. 2. The antennas were placed at about 20 cm distance, measured between the two strip-slot transitions. The antenna alignment was optimized to provide maximum mutual coupling. The antenna scattering parameters will be discussed separately for the implementation without matching layers and with matching layers. A. Without Matching Layers The measured scattering parameters of the two antennas, S11 and S22, are shown in Fig. 3(a) and (b) respectively. The measurements were performed with the same setup used to characterize the antenna link in Fig. 2. However, since the distance between the two antennas is relatively large and the S12 is in

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Fig. 4. Measured S12 parameter for antennas (1) and (2) without matching layers.

Fig. 3. Measured Sii parameters for antennas (1) in a) and (2) in b) without matching layers, dashed lines. For both antennas also the results pertinent to the case in which the reflections at the connectors are gated out are included, continuous lines.

the order of , it is believed that the SII parameters provide a very good approximation of the reflection coefficient for each one of the two antennas in isolation. The amplitudes of all SII parameters are plotted in dB’s as a function of the frequency in the range 5–70 GHz. The resolution obtained with this frequency range is so high, that the location of the strongest reflection could easily be identified by performing the inverse Fourier transform (IFT) of the frequency domain data and observing the time domain data. This reflection was, as expected, associated to the connector- strip transition. Accordingly, it has been possible to gate out this transition effect to characterize the matching of the two antennas without the effect of the connector. Fig. 3(a) and (b) also presents the results pertinent to this gated situation (continuous line). The curves obtained after time gating show very good matching performance for both antennas with SII lower than from 15 GHz on. The rapid oscillation as a function of the frequency can be associated to reflections inside the dielectric lenses. Simulations performed with the commercial FDTD-based software package CST Microwave Studio [5], not

reported for brevity, are in excellent agreement with these measured results. The simulations actually indicate that this same structure should remain matched with SII better than up to at least 100 GHz (the increase of the computational burden did not allow performing the simulations for higher frequencies). When the connector effect is considered, the matching deteriorates significantly: the oscillations in the SII parameters can be tracked to standing waves between the slot and the connector. Notably, the impact of the connectors differs significantly in the two antennas. Being the designs exactly the same it is apparent that the soldering of the coaxial connector to the PCB is the most unreliable part of this antenna design. However, the use of such connector will not be necessary in the final integrated design. In Fig. 4 the amplitude of the measured S12 is plotted as a function of the frequency. The S12 parameter presents significant oscillations due to the reflections inside the lens and due to the mismatch associated to the transition from coaxial cable to strip. Moreover the S12 is impacted by the ohmic losses due to the strip lines lengths and by the ohmic losses in the dielectric composing the lenses. B. Estimated Efficiency Without Matching Layers The causes of reduced efficiency for the antenna prototypes without matching layers can be identified and quantified by means of measurements and simulations as follows. • Ohmic losses in the dielectric lens, varying from 0.5 dB at 20 GHz to 1.5 dB at 70 GHz (calculated using the nominal value of the loss provided by the material manufacturer); • Mismatch losses at the connector, measured with the Sii parameters; • Ohmic losses in the strip line, varying from 0.5 dB at 20 GHz to 1.5 dB at 70 GHz (calculated using the nominal value of the loss in the dielectric as provided by the manufacturer). These losses, partly calculated and partly measured, are summarized in Fig. 5, which shows the estimated efficiency of antenna (1). It should be noted that the antennas eventually will be used without strips and connectors.

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Fig. 7. Measured S12 parameter for antennas (1) and (2) with matching layers. Fig. 5. Overall expected loss of efficiency in dB for antenna (1).

the losses due to mismatch at the connector are for these antennas essentially the same as those discussed for the case of no matching layers. However, an increase of 2 dB in the transmission efficiency at the dielectric-air interface implies that the radiation pattern is better behaved in the sense that more power is radiated into the main beam rather than in the side lobes. This will be explicitly shown in Section VI. IV. TIME DOMAIN FROM FREQUENCY DOMAIN

Fig. 6. Sii parameters for antenna (1) with matching layers.

The link between a transmitting and a receiving antenna can be characterized in terms of its complex transfer function , where and are the spectra of the received and transmitted voltages. The , is linked coupling parameter in the frequency domain, to the complex transfer function of the antennas involved in the link by [2]

C. With Matching Layers The two antenna prototypes equipped with matching layers have then been characterized. The S11 parameter of antenna (1) is shown in Fig. 6. In this case only the curve pertinent to the situation in which the connectors are gated out is presented. Also in this case excellent matching performance with S11 from 12 GHz on is observed. The rapid oslower than cillation as a function of the frequency is significantly reduced in amplitude with respect to the corresponding case in absence of matching layers. Again simulations performed with CST, not reported for brevity, are in very good agreement with these measured results. Fig. 7 shows the amplitude of the measured S12 as a function of the frequency. In the whole frequency range the S12 is at least 5 dB higher than the value obtained without matching layers. Moreover, the oscillations are now much weaker, with the S12 to ) from 15 amplitude varying in a 7 dB band ( to 70 GHz.

(1) where and are the transfer functions of transmit and receive antenna and is distance between these antennas. In this section the impulse response of the link is derived over a 65 GHz BW, from 5 to 70 GHz, by means of . the IFT of the measured A parameter frequently used to quantify the pulse distortion is the fidelity factor. It is in general defined with respect to a predefined reference signal [6], [7]:

D. Estimated Efficiency With Matching Layers

In the following, the reference signal will be a sinc associated to the mentioned 65 GHz band, which can be expressed as

Based on the comparison between measurements with and without matching layers, one can clearly establish that the presence of matching layers ensures an increase in gain of the order of 2–3 dB per antenna. This does not imply a much higher efficiency of the antenna in terms of losses. The ohmic losses and

where

and

.

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Fig. 8. Normalized time domain representation of the S12 parameter for the antennas with matching layers.

Fig. 9. Comparison between the measured impulse response of the combined antennas and an ideal 65 GHz bandwidth (5–70 GHz) pulse delayed by 1.35 ns. The pulse is visible in the inset.

A. With Matching Layers Fig. 8 shows the time domain representation, normalized to the maximum, of the amplitude of the S12 parameter measured with the setup in Fig. 2 for the case in which the lenses are covered by matching layers. The main peak of the signal arrives to the receiver after approximately 1.35 ns corresponding to 404 mm of equivalent free space propagation. This propagation time can be explained accounting for 14 cm of free-space propagation plus 6.4 cm of propagation in the two lenses (equivalent to 18.5 cm in free space) and 8 cm of micro-strip and coaxial cables propagation. A second peak of amplitude 22 dB smaller than the first peak appears 0.3 ns after this, corresponding to approximately 9.2 cm of free space propagation. It can be associated to single reflections inside the lens, as highlighted in the inset of the figure. This effect could be considered as a measure of the ringing. If as reference for defining the ringing an amplitude of for the secondary peak is considered, also in this respect the leaky lens antenna outperforms the Vivaldi and the log-periodic antennas reported in [2]. Since there are no other important images arriving at later times, the statement in [4, Sec. IV.A.2] that the planarly fed leaky lens antenna does not support double reflections inside the lens thanks to its directive pattern is fully validated. A comparison between the response of the antenna link in time domain and the reference signal, delayed of 1.35 ns to present the maximum in correspondence of the main peak of the link impulse response is shown in Fig. 9. Note that the scale is expanded with respect to that in Fig. 8. The curves show impressive similarity and one can observe that the half power width of the measured pulse is only 0.002 ns longer than that of the reference signal (0.015 ns instead of 0.013 ns). To more rigorously quantify the pulse distortion introduced by the combined antennas the fidelity factor has been calculated. For the entire mea, and ) the fidelity sured band ( factor of the link between two leaky lenses with matching layers is 0.94. To the best of our knowledge such a high fidelity factor on a frequency BW 1:14 has never been reported for radiated links. Impulse radiating antennas have been reported to present

Fig. 10. Comparison between the measured impulse response of the combined antennas and an ideal 55 GHz bandwidth (15–70 GHz) delayed pulse.

high fidelity factors, on smaller bands, but always when used in conjunction with resistive loadings (see [8] for a comparison). In the present case a non desired resistive loading is also present, due to the ohmic losses in the dielectric, in the micro-strip and in the connectors. However, this loading actually decreases the fidelity factor since it is the main cause for the diminished antenna efficiency and for the reduced S12 amplitude in the high frequency portion of the band. A lossless leaky lens antenna link would provide a constant S12 link for even higher frequencies. This will become clearer after the examination of the results of Section V. When one considers only the frequencies above the threshold of 15 GHz, after which the matching layers start to function, (see [4, Sec. IV]), the fidelity factors becomes 0.97, as visible in Fig. 10. The frequency band with fidelity higher than 0.97 is in fact 1:5. Note that comparable performance in terms of fidelity have been shown by Vivaldi antennas on BW in the order of 1:3 [7], but only in the broadside direction.

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Fig. 11. On the right scale: optimal delay that should be introduced to recover 16 GHz BW pulses centered at different frequencies. On the left scale: corresponding phase center variation with respect to the average.

At the time of writing this paper, TNO measurement set up did not allow us to perform S-parameter measurements at frequencies higher than 70 GHz. However it can be observed that the S12 starts decreasing in the higher portion of the band due to increase in the losses. Nevertheless simulations carried out using CST Microwave Studio have shown that one can obtain, in relative BW higher than 1:7, the fidelity factor larger than 0.97. B. Phase Center Stability With Matching Layers As explained in [4, Sec. V], the excellent dispersivity properties that were presented in the previous Figures are due to both the linear growth of the gain and the linear variation of the phase of the received signal as a function of the frequency. While the gain can be derived from the amplitude of the , the phase variation over a certain frequency band can be read from the position of the peak of the link impulse response. Fig. 11 shows on the right scale the distance between the two antennas composing the link as derived from the position of the peak of the received signal in time domain over different frequency bands. Thus, for by only retaining the instance, performing the IFT of frequency components from 5 to 21 GHz, one would observe that the peak of the received signal would arrive at a moment which corresponds to 402.5 mm of propagation in free space. Similarly performing the IFT on the band 55 to 70 GHz, the peak of the received signal would arrive after a time that corresponds to 404 mm of free space propagation. Dividing this phase delay by two, one can readily observe that the corresponding variation of the phase center in each of the antennas is less than . Considering that the slot width is 0.5 mm, one can state that the phase center does not move with frequency. This experimental demonstration only holds for broadside links. However, since the antenna behaves accordingly to the dominant ray picture provided in Fig. 12 [4, Sec. V], the phase center stability can be implied for at least the entire main beam. Note that this antenna is the only one, to our knowledge, which is at the same time efficient, weakly dispersive and with stable phase center. Uniting this property with the intrinsic directivity, one can use the leaky lenses to excite a reflector with high F/D, maintaining the low dispersivity. Accordingly a focal plane arrangement, can be used to generate multiple secondary beams, hundreds, without significant off-focus degradation. This was not possible until now, with any other feed. The time domain link impulse response in the absence of matching layers is discussed in Appendix A.

Fig. 12. Zoomed time window were most of the link impulse response is concentrated. The responses for both antenna links, with (solid line) and without (dashed line) matching layers are plotted.

V. FREQUENCY DOMAIN FROM TIME DOMAIN The investigation of the time domain representation of the S12 parameter allows one to identify the critical time domain zones in which the dominant wave mechanisms can be recognized. Fig. 12 shows a zoomed time window in which most of the S12 signal is concentrated. The two curves correspond to the links including antennas with (solid line) and without (dashed line) matching layers. Note that here the amplitudes are normalized to the maximum of the signal in of the the presence of matching layers, to fully appreciate the relative difference between the two signal intensities and qualities. It is apparent that for both links the bulk portion of the signal arrives to the receiver between 1.3 and 1.4 ns. Also it is relatively simple to identify the zone between 1.6 and 1.7 ns as the window where contributions arrive to the receiver after having undergone a single reflection at the dielectric-air interface and on the ground plane. Finally we can associate the zone between 1.4 and 1.6 ns as the zone where further contributions associated to multiple reflections inside the lens or between the connector and the slot in antennas (1) and (2) are concentrated. This subdivision suggests to adopt different gating of the time domain signals to highlight the frequency signature of each contribution. Fig. 13 shows the spectral signature of the main peaks of the impulse response for the two antennas. A time gate between 0 and 1.38 ns (window 1) is applied to neglect all contributions following the main peak. It is apparent that the amplitude difference between the links with and without matching layer is essentially spread through the entire frequency range from 5 to to with matching layers 70 GHz. A 6 dB band ( and to without matching layers) extends from 10 to 70 GHz for both links. This is the core graph that highlights the potentials of the leaky lens antenna for low dispersivity as claimed in this series of articles. If ohmic losses were lower the dispersivity would also be lower. In fact one can observe that while the tapering at the beginning of the spectrum is

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Fig. 13. Frequency domain spectrum after windowing 1 for both links, including antennas with (solid line) and without (dashed line) matching layers.

Fig. 14. Frequency domain spectrum after windowing 2 for both links, including antennas with (solid line) and without (dashed line) matching layers.

Fig. 16. E -plane Co-polarized component of the field radiated by the lens including matching layers: (a) frequencies 35 to 50 GHz, (b) frequencies 55 to 75 GHz.

VI. RADIATION PATTERNS MEASUREMENTS

Fig. 15. Frequency domain spectrum after windowing 3 for both links, including antennas with (solid line) and without (dashed line) matching layers.

very similar for the links with and without matching layers, the antennas with matching layers are characterized by noticeably higher losses at high frequencies. With the window 2, the contributions associated to the connectors are included. In Fig. 14, a ripple of intensity 1–2 dB and with approximately 4 GHz period appears for both antenna links, independently from the presence of the matching layers. When finally the contribution associated to the lens-air interface is introduced (window 3) it appears that the reflections at this interface are essentially insignificant for the antenna with matching layers, Fig. 15. However they are very important for the antenna without matching layers, as they induce 6–8 dB oscillations.

The measurements of the radiation patterns have been performed at the Near Field Antenna Test Range of TNO in the frequency band 33–75 GHz. Both co- and cross-polarized components in the and planes have been measured for two antennas, one with matching layers and the other without matching layers. A. Co-Polarized Patterns With Matching Layers The co-polarized radiation patterns in the -plane are shown in Fig. 16(a) and (b) for the case with matching layers. The normalized co-polarized radiation patterns in the -plane are plotted in Fig. 17(a) and (b), with matching layers. The radiation patterns are circularly symmetric with side lobes below 15 dB on the main planes, except for the -plane in the higher frequency range. In this case the patterns also appear less symmetric, probably due to an inaccurate alignment of the near field probe with the antenna. The radiation patterns pertinent to the antennas without matching layers are presented in Appendix B.

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Fig. 18. Gains as a function of the frequency for the antenna without matching layers (dashed line) and the antenna with matching layers (solid line). Note that the scale is the same as in Fig. 12 of [4] for easy comparisons.

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Fig. 17. -plane Co-polar component of the radiated field by the lens including matching layers: (a) frequencies 35 to 50 GHz, (b) frequencies 55 to 75 GHz.

B. Gains The absolute gains of both antennas have been measured as a function of the frequency by comparison with reference standard gain horns. These gains are reported in Fig. 18 for the antennas with and without matching layers. The front-to-back ratio has also been separately measured and it has found to be higher than 25 dB at all frequencies, with and without matching layers. This is also in agreement with predictions from [4, Sec. IV.B.4]. C. Cross Polarization The antennas radiate a non negligible amount of power in cross polarization. The exact shape of the patterns is of little significance, but for all antennas with and without matching layers, and for all frequencies, the distribution of the cross polarized fields (according to the third Ludwig definition) is qualitatively described by the schematic drawing shown in the inset of Fig. 19. Four cross-polarized lobes emerge in the diagonal planes. For the case of lenses with matching layers, the maximum level of cross-polarized field with respect to the maximum of the co-polarized field at the same frequency is

Fig. 19. Maximum cross-polarized field as a function of the frequency for the antenna with matching layer, normalized to the maximum co-polarized fields at the same frequency.

shown in Fig. 19 as a function of the frequency. The maximum of cross-polarized fields is lower than 9 dB for all frequencies. VII. CONCLUSION The measurements of the hardware presented in this paper show that the planarly fed UWB leaky lens antenna has, over a BW 1:5: • directive radiation patterns that are circularly symmetric, • low (with respect to other UWB non dispersive antennas) cross-polarization levels, variation), • constant phase center (less than • efficiency higher than 50% (85% in an integrated system). The increase of efficiency from 50% to 85% in an integrated system is due to the absence of the connectors and -strip lines. A link realized using two leaky lens antennas has demonbeing the strated a pulse fidelity F higher than 0.94 (with maximum) on the band 5–70 GHz. This pulse fidelity, over the full 3 dB beamwidth and on such a large bandwidth, is much on higher than ever reported for any radiated link (

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Fig. 20. Normalized time domain representation of the S12 in the presence of matching layers.

Fig. 21. Comparison between the measured impulse response and an ideal 65 GHz BW (5–70 GHz) pulse delayed by a time corresponding to 399 mm. In the inset the pulse is visible.

a 1–3 BW is often considered excellent). This pulse fidelity is indeed comparable to the one of TEM-guided links at low frequencies, opening a wide range of opportunities for system designers. Since the link is composed of two nominally identical antennas, each of the two antennas essentially radiates non dispersively. The present Leaky Lens antenna, as it is also directive, can be used as feed for reflector systems capable of operating over decade bandwidths, even if imaging with hundreds of beams is required. Moreover, minor design adaptations can lead to an omnidirectional antenna (only the shape of the lens needs to be changed). This would render the concept suited for short-range communications and SAR systems. Finally, the antenna is very inexpensive and simple to manufacture. APPENDIX A TIME DOMAIN LINK RESPONSE WITHOUT MATCHING LAYERS Fig. 20 shows the time domain representation, normalized to the maximum, of the S12 parameter when the two antennas of the link do not include matching layers. The main received signal arrives to the receiver after 1.33 ns corresponding to approximately 399 mm of equivalent free space propagation, (it was 404 mm in the case of the matching layers). The difference corresponds to the matching layers thickness. A second peak can be observed 0.3 ns after the main peak. 0.3 ns approximately correspond to 9 cm in free space and thus to 3 cm in the dielectric. Accordingly, this image can be associated to single reflections in the lens. The amplitude of this second peak is 15 dB lower than the main one. Also in this case the antenna would be indicated as ringing free according to recent indications in the literature [2]. Fig. 21 shows an expanded view of the pulse received and the reference signal, in order to highlight that the pulse is more distorted than in absence of the matching layers (compare to Fig. 9). In particular the pulse is slightly wider and the fidelity . When the attention is moved factor on the band is to the band 15 to 70 GHz, Fig. 22 the pulse preservation im. Thus proves significantly and can be quantified by the lower portion of the band, suffers most significantly from the

Fig. 22. Comparison between the measured impulse response and an ideal 55 GHz BW (15–70 GHz) delayed pulse.

Fig. 23. On the right scale: optimal delay that should be introduced to recover 16 GHz BW pulses centerd at different frequencies. On the left scale: corresponding phase center variation with respect to the average.

pulse dispersion associated to the reflections at the dielectric-air interface.

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Fig. 24. E -plane Co-polarized component of the field radiated by the lens without matching layers: (a) frequencies 35 to 45 GHz, (b) frequencies 50 to 75 GHz.

Phase Center Stability Without Matching Layers: Fig. 23 shows on the right scale the distance between the two antennas as measured using different frequency bands, while the left scale shows the phase center movement. The variation of the phase center in each of the antennas is 0.75 mm, in the lowest band, from 5 to 21 GHz, but then stabilizes to levels comparable to the antenna with matching layers for the higher frequencies. Thus, again it appears that the dispersivity introduced by the absence of matching layers is mostly confined at lower frequencies. APPENDIX B RADIATION PATTERNS WITHOUT MATCHING LAYERS The normalized co-polarized radiation patterns in the -plane are shown in Fig. 24(a) and (b) for the case without matching layers. The normalized corresponding co-polarized radiation patterns in the -plane are shown in Fig. 25(a) and (b). Also in this case the patterns are mostly symmetric with respect to broadside. While for low frequencies the patterns are relatively large, the beam width decreases with frequency. The measured side-lobes are lower than .

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Fig. 25. -plane Co-polarized component of the field radiated by the lens without matching layers: (a) frequencies 35 to 45 GHz, (b) frequencies 50 to 75 GHz.

REFERENCES [1] J. D. Taylor, “Ultra-wideband antenna technology,” in Introduction to Ultra-Wideband Radar Systems. Boca Raton, FL: CRC Press, 1995. [2] W. Sörgel and W. Wiesbeck, “Influence of the antennas on the ultrawideband transmission,” EURASIP J. Appl. Signal Processing, no. 3, pp. 296–305, 2005. [3] R. Olsson, P. S. Kildal, and S. Weinreb, “The eleven antenna: A compact low-profile decade bandwidth dual polarized feed for reflector antennas,” IEEE Trans. Antennas Propag., vol. 54, pp. 368–375, Feb. 2006. [4] A. Neto, “UWB, non dispersive radiation from the planarly fed leaky lens antenna. Part 1: Theory and design,” EEE Trans. Antennas Propag., vol. 58, no. 7, p. , Jul. 2010. [5] CST Microwave Studio, User Manual Version 5.0. Darmstadt, Germany: CST GmbH. [6] A. Mehdipour, K. Mohammadpour-Aghdam, and R. Faraji-Dana, “Complete dispersion analysis of Vivaldi antenna for ultra wideband applications,” in Progr. Electromagn. Res., to be published. [7] E. Pancera and W. Wiesbeck, “Correlation properties of the pulse transmitted by UWB antennas,” presented at the Proc. 11th Int. Conf. on EM in Advanced Applications, Torino, Italy, Sep. 18, 2009. [8] M. Manteghi and Y. Rahmat-Samii, “On the characterization of a reflector impulse radiating antenna (IRA): Full wave analysis and measured results,” IEEE Trans. Antennas Propag., vol. 54, pp. 812–822, Mar. 2006.

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Andrea Neto (M’00) received the Laurea degree (summa cum laude) in electronic engineering from the University of Florence, Italy, in 1994 and the Ph.D. degree in electromagnetics from the University of Siena, Italy, in 2000. Part of his Ph.D. was developed at the European Space Agency Research and Technology Center, Noordwijk, The Netherlands. From 1998 to 2000, he worked for the Antenna Section, European Space Agency Research and Technology Center, Noordwijk, The Netherlands. In the years 2000–2001, he was a Postdoctoral Researcher at California Institute of Technology, Pasadena, working for the Sub-mm wave Advanced Technology Group. From 2002 to January 2010, was a Senior Antenna Scientist at TNO Defence, Security and Safety, The Hague, The Netherlands. In February 2010, he was appointed Full Professor of Applied Electromagnetism at the Department of Electrical Engineering (EEMCS), Technical University of Delft, Delft, The Netherlands. His research interests are in the analysis and design of antennas, with emphasis on arrays, dielectric lens antennas, wide band antennas and EBG structures. Prof. Neto was co-recipient of the H.A. Wheeler Award for the Best Applications Paper of the year 2008 in the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION. He presently serves as an Associate Editor of IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS (AWPL).

Stefania Monni (S’01–M’06) received the M.Sc. degree (summa cum laude) in electronic engineering from the University of Cagliari, Italy, in 1999 and the Ph.D. degree in electronic engineering from the Technical University of Eindhoven, The Netherlands, in 2005. In 1999 and 2000, she worked at the Radio Frequency System Division, European Space Research and Technology Centre (ESA-ESTEC), as an undergraduate and graduate trainee, respectively. From 2001 until 2005, she has carried out her Ph.D. research at the Netherlands Organization for Applied Scientific Research (TNO), The Hague, The Netherlands, where she is currently employed. Her main research interests concern analysis and design techniques for phased array antennas and frequency selective surfaces, wide band antennas and digital beam forming for active and passive radars.

Frans Nennie joined the Defence Safety and Security Branch, TNO, Dutch National Center for Applied Research, Den Haag The Netherlands, in 1974, where he still works as a Microwave Engineer. Originally, he worked on the design of front ends for phased arrays. He then joined the Radar Cross Section Group, where he was mostly involved in the development of the TNO coherent Radar. In 2001, he joined the Antenna Group, where he is responsible for the measurements and the measurement facilities. He is actively involved in all advanced development engineering programs. His research interests span the entire microwave regime. More recently he is specifically involved in the development of mm wave imaging systems.

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Beamsteering in Pattern Reconfigurable Arrays Using Directional Modulation Michael P. Daly, Graduate Student Member, IEEE, and Jennifer T. Bernhard, Fellow, IEEE

Abstract—An array with pattern-reconfigurable elements is used to generate a digital modulation by switching the elements for every symbol. This technique is known as directional modulation. Because the modulation is generated at the antenna level, it gives control over the directions in which data is sent, unlike baseband modulation which transmits the same data in all directions at different power levels. A procedure for determining how to switch the elements to transmit only in a specified direction is outlined. Results indicate that compared to a traditional reconfigurable array, the directional modulation array allows information to be sent over a narrower beamwidth. Additionally, the method provides more selectivity in the possible transmit angles. Measured and calculated results from a four-element reconfigurable array are presented. Index Terms—Digital modulation, reconfigurable antenna, reconfigurable array, secure communication.

I. INTRODUCTION

A

NTENNA arrays are advantageous because they can focus radiation in a narrower beamwidth than a single element and they have the ability to electronically steer the radiation pattern. Beamsteering efficiently uses transmitted power by sending most of the power toward a desired receiver. Communication is more secure because less of the signal is broadcast in other directions. Reconfigurable arrays implement beamsteering without the use of phase shifters, which add cost and size to the system. Of the previous work on reconfigurable arrays, most arrays consist of a single driven element steered by changing the electrical characteristics of parasitic elements [1]–[7], although there are some investigations of beamsteering for arrays with multiple driven reconfigurable elements [8], [9]. Some drawbacks of reconfigurable arrays are that their beamsteering capability is limited compared to phased arrays, and it is not always clear how to configure the elements to steer a beam in a certain direction. Directional modulation (DM) presents an alternative means of beamsteering [10]. DM is one of several techniques that synthesize a digital modulation fully or partially in the RF portion of the transmitter [10]–[16]. This is in contrast to a traditional array transmitter, in which a digital modulation

Manuscript received June 17, 2009; revised November 06, 2009; accepted December 23, 2009. Date of publication March 29, 2010; date of current version July 08, 2010. This work was supported by an NDSEG Fellowship. The authors are with the Electromagnetics Laboratory, Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801 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/TAP.2010.2046854

Fig. 1. Block diagrams of a simplified traditional reconfigurable array transmitter with baseband and RF portions (top) and the reconfigurable array DM transmitter (bottom).

is created at baseband and then passed through a static RF portion. DM offers more beamsteering freedom and a clear method to synthesize information in a certain direction. DM is also called near-field modulation in [14] and near-field direct antenna modulation in [15] where it was demonstrated for a parasitic array with a single driven element. While a parasitic array can have the same performance benefits as an array with driven elements, the design procedure for synthesis of a digital modulation is more complicated with a parasitic array. Either trial-and-error measurements [14] or a model of the array’s electromagnetic characteristics [15] must be used. In contrast, the design procedure is greatly simplified with an array of driven reconfigurable elements because once the active element patterns are found, simple calculations are used to find the combinations of elements that generate a desired modulation in a specific direction [10]. The design procedure discussed in [10] will be used here. A continuous wave (CW) signal is fed to each element and for each digital symbol, the elements are switched in such a way to change the amplitude and phase of the radiated field in the desired direction to correspond to that symbol. Fig. 1 gives a block diagram of this DM transmitter, compared to a traditional reconfigurable array whose modulation is generated in

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baseband and then upconverted to the carrier frequency before going into the antenna elements. DM offers an improvement over the traditional transmitter not in steering the radiation pattern, but rather by steering the information beam, meaning the beamwidth over which decodable information is sent. Unlike baseband modulation, DM can distort a digital modulation’s constellation diagram in undesired transmit angles, making the information hard to decode for any eavesdropping receiver not in the direction of the desired receiver [10], [14], [15]. While DM offers no improvement for the power efficiency aspect of beamsteering, the security aspect is greatly improved over a traditional transmitter. This improvement in security by using DM will be demonstrated in this paper using a reconfigurable array. Section II gives a description of the reconfigurable array. Next, Section III explains the design procedure for implementing directional modulation and how security will be quantitatively measured. Finally, Section IV gives calculations from measured data to show that the information beam can be steered in a more secure manner using DM over baseband modulation.

2

Fig. 2. Reconfigurable 4 1 array. All elements in broadside mode (top) and endfire mode (bottom) (adapted from [18]).

II. A PATTERN RECONFIGURABLE ARRAY The four-element array used in this paper is shown in a diagram in Fig. 2 and on a test fixture inside an anechoic chamber in Fig. 3. Each element is a square spiral microstrip antenna [17]. Only the polarization will be considered for all pattern measurements. In this polarization, each element can reconfigure between an endfire pattern and a pattern that is nearly broadplane. As shown in side, when measuring in the azimuthal Fig. 2, an element is broadside when a switch is closed at the top of the spiral and the lower switch is open. An endfire pattern is achieved when the top switch location is open and the bottom switch is closed. This element was demonstrated in [17] using RF MEMS switches, but for this paper the array switches are hardwired for proof of concept. The measured active element patterns for both modes of configuration are shown in Fig. 4. The elements have half-wavelength spacing at the operating frequency of 6.9 GHz, and all modes of configuration have a VSWR of less than 2 at the operating frequency. The superposition of active element patterns is used in the design of DM to determine how each element should be configured [10]. To confirm that adding the patterns in Fig. 4 will yield the correct total radiation pattern, several measurements with all four elements driven were made. Both the measured pattern magnitude and phase were compared to the summation of the active element patterns for the corresponding modes (broadside to were or endfire). Only azimuthal angles from measured, corresponding to the half plane in front of the array. Figs. 5 and 6 shows the comparison between the measured total pattern and summation of active element patterns when all elements are in broadside mode and endfire mode, respectively. There is good agreement in both modes in both the magnitude and phase. As a side note, one of the sidelobes of the all broadside radiation pattern is 10 dB higher than the other due to the fact that the broadside active element patterns are slightly tilted in the direction of the higher sidelobe. It is not enough to conclude that any total array pattern can be predicted by the active element patterns by only testing the

Fig. 3. The reconfigurable array inside an anechoic chamber. Switches are hardwired for proof of concept.

Fig. 4. Normalized measured active element patterns in both modes of configuration and for vertical polarization only. Elements 1 and 2 on top row, and elements 3 and 4 on bottom row.

previous two cases. This is because the broadside active element patterns were measured while their neighboring elements were also in broadside mode, and the endfire active element patterns similarly were measured while their neighboring elements

DALY AND BERNHARD: BEAMSTEERING IN PATTERN RECONFIGURABLE ARRAYS USING DIRECTIONAL MODULATION

Fig. 5. Normalized measured radiation pattern with all elements in broadside mode (“Together”) and the superposition of broadside active element patterns (“Separate”).

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Fig. 7. Normalized measured radiation pattern with elements 1 and 3 in broadside mode and elements 2 and 4 in endfire mode (“Together”) and the superposition of the corresponding active element patterns (“Separate”).

and third are configured to endfire. The patterns obtained from the summation of the corresponding active element patterns are also shown in Figs. 7 and 8. The measured patterns and the summed active element patterns still exhibit good agreement. From this, we can conclude that the mutual coupling effects of neighboring elements are approximately the same whether those neighboring elements are in broadside or endfire mode. If this were not the case, then every switching combination would have to be measured and the simplification from using driven elements would be lost. Now that the active element patterns are known, Section III will detail the design process for DM on a reconfigurable array. III. DIRECTIONAL MODULATION FOR BEAMSTEERING

Fig. 6. Normalized measured radiation pattern with all elements in endfire mode (“Together”) and the superposition of endfire active element patterns (“Separate”).

were also in endfire mode. But if mutual coupling is significant, one element’s pattern will be influenced its neighbors’ modes (broadside or endfire). One way to determine the extent of the coupling is to measure array patterns when some of the elements are in broadside mode and some are in endfire. Figs. 7 and 8 show measured patterns for two of these cases. In Fig. 7, the first and third element are configured to broadside and the second and fourth are configured to endfire. In Fig. 8, the first and fourth element are configured to broadside and the second

DM is implemented by the repeated switching of elements to synthesize digital symbols. This section details how to find the best switching combinations for a specific set of symbols and in a specific transmit direction. As in [10], a four-symbol (4-ary) modulation scheme will be used by the DM transmitter and the traditional transmitter will use QPSK. The DM transmitter can create a more arbitrary constellation diagram than the traditional transmitter because the modulation is done at the antenna level [10]. As will be shown, the distortion of the modulation can be increased in undesired transmit directions and lowered toward the desired transmit direction. Five separate cases will be considered with the desired re, or from array broadside. ceiver at The location of any eavesdroppers is unknown so that goal will be to minimize the transmission of useful information to any other direction beside that of the desired receiver. We will assume a line-of-sight (LOS) from the transmitter to the receiver, although this technique can be used for channels with multipath

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TABLE I BEST SETS OF ELEMENT CONFIGURATIONS FOR TRANSMISSION TO A DESIRED ANGLE FOR THE DM TRANSMITTER. “B” MEANS BROADSIDE, “E” MEANS ENDFIRE, AND “O” MEANS THE ELEMENT WAS TURNED OFF

Fig. 8. Normalized measured radiation pattern with elements 1 and 4 in broadside mode and elements 2 and 3 in endfire mode (“Together”) and the superposition of the corresponding active element patterns (“Separate”).

as well [10]. The metric to assess the security and calculate an information beam is the bit error rate (BER). Calculations of BER based on measured radiation patterns for the traditional array and a closed-form approximation for the DM array are given in [10]. Each desired receiver location requires a separate design process. For each of the four digital symbols, a separate set of element configurations is used to synthesize the symbol in DM. We assume that each of the four elements can be configured combinations for to broadside, endfire, or off. This gives combinations to synthesize all four a single symbol, and symbols. An exhaustive search is performed over these combinations, evaluating the BER in the directions from to in 1 increments. This search took about 20 hours on a PC running Matlab [19]. This exhaustive search approach is similar to the approach of the designs in [15], although in our case we need only calculate a sum for each combination rather than take a new measurement. After calculating 181 BERs for each combination, a cost was assigned to the combination based on the following equation (1) There was a 20 “don’t care” region around the desired angle where the BER could transition from low to high, and these BERs were not included among the undesired angles in the calculation in (1). For each of the five simulations, the best set of configurations is reported in Table I. A closed-form lower bound for BER was used for the repeated BER calculations during the exhaustive search [10]. After the search found the best candidates, BER simulations were run for each of the five cases and for 1 increments from

TABLE II BEST SET OF ELEMENT CONFIGURATIONS FOR TRANSMISSION TO A DESIRED ANGLE FOR THE TRADITIONAL TRANSMITTER. “B” MEANS BROADSIDE, “E” MEANS ENDFIRE, AND “O” MEANS THE ELEMENT WAS TURNED OFF

to from broadside. At minimum, 10 million bits were simulated for each angle, and simulations became as long as billions of bits if the estimated BER was much lower. The configurations for beamsteering of the traditional array transmitter were also found by an exhaustive search, with (1) used as the criterion. In this case, there is only one configuration necessary since the modulation is done in baseband, and so there are only possibilities to consider. The best configuration for each of the five transmit angles is shown in Table II. One configuration from Table II that is intuitively obvious is the all-broadside mode for a desired receiver at 0 . One would expect that configuring all elements to broadside is the best way to achieve as low as possible of a BER toward broadside and as high as possible everywhere else. Section II gave a mathematical justification of the beamsteering choices for the traditional and DM transmitters. In Section III, these results will be confirmed graphically. The BER curves as a function of direction will show information beams, where the information is easiest to decode. Also radiation patterns and constellation diagrams for specific cases will be shown to better contrast DM with baseband modulation performance. IV. CALCULATED RESULTS This section combines the measured active element patterns from Section II and the configurations found using the procedure from Section III and calculates performance results. The

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Fig. 9. Theoretical lower bound and simulated BER for the DM transmitter, and the BER for the traditional transmitter when the desired receiver is 30 from array broadside.

0

case when the desired receiver is at from array broadside will be analyzed in more detail to give insight into how DM successfully controls BER. Then the results from the other four cases will be presented. Fig. 9 shows simulated BERs and BERs calculated from a closed-form expression for the DM and traditional transmitters. Both the closed-form lower bound expression and the simulated BER are plotted for the DM transmitter. As mentioned earlier, the traditional array BER is a function of the magnitude of the radiation pattern. The traditional array BER in the desired diinitially was lower than the simulated BER from rection the DM array because the traditional array beamforming directs the maximum possible power (for this reconfigurable array) toward the desired receiver. In order to fairly compare the security of both schemes, where a high BER is desired in all other directions, the power of the traditional array was reduced until the two BERs were the same in the desired direction. In other words, both arrays must send the same low BER toward the desired receiver but they also want to send out as little total power as possible so the undesired transmit regions have high BERs. In this case, it meant reducing the transmitted power from the traditional array by 1.26 dB. As is evident from Fig. 9, the DM transmitter outperforms a traditional baseband modulation transmitter in this security aspect. Both arrays form an information beam toward the desired receiver, but the traditional array also has other unwanted areas where the BER is low. An explanation for this can be discerned from Fig. 10. In this figure, the radiation pattern for the traditional array is plotted, along with the radiation patterns formed from each of the four DM symbols. There is a large sidelobe that almost reaches the in the traditional array pattern at same magnitude as the mainlobe. From the limited beamsteering options of the traditional reconfigurable array, this configuration (given in Table II) gave the largest mainlobe (toward ) to sidelobe ratio. Additional insight into DM performance gains can be found by examining the constellation diagrams. Fig. 11 shows the constellations transmitted by both arrays in the desired direction . The DM constellation is almost the same as the constellation generated from baseband modulation, with a slight phase rotation that any ordinary receiver can correct. The DM constellation is composed of configurations whose radiation patterns

Fig. 10. Calculated radiation patterns resulting from all four DM modes of configuration for communication to a receiver at 30 . Also shown is the radiation pattern of the traditional transmitter when steered toward 30 .

0

0

Fig. 11. Constellation diagrams of the signals from the DM and traditional arrays transmitted to 30 . The intended receiver also is at 30 .

0

0

in the desired direction have approximately the same amplitude and differ in phase from one another by about 90 . The similar constellations from both transmitters produce the same BER in this direction. On the other hand, the constellations in Fig. 12 explain why the DM array can achieve a high BER in undesired directions even while having relatively high radiation pattern magnitudes. Fig. 12 shows the constellations that an eavesdropper at broadside would see. From Fig. 10, the broadside radiation pattern magnitudes of all four DM symbols are higher by as much as 10 dB than the magnitude of the radiation pattern at broadside from the traditional array. Yet, from Fig. 9, the broadside BER of the DM array is about two orders of magnitude higher than the broadside BER of the traditional array. The reason for this can be seen in Fig. 12. This constellation diagram reflects the fact that the traditional array has a lower radiation pattern magnitude, because the constellation points all lie closer to the origin than the DM constellation points. However, the DM constellation points, while larger in magnitude, are shifted in phase so that they are clustered closer together. This shift in relative phase position of the constellation points for different transmit angles

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Fig. 12. Constellation diagrams of the signals from the DM and traditional arrays transmitted to broadside. The intended receiver is at 30 .

0

Fig. 13. Theoretical lower bound and simulated BER for the DM transmitter, and the BER for the traditional transmitter when the desired receiver is 60 from array broadside.

0

Fig. 15. Theoretical lower bound and simulated BER for the DM transmitter, and the BER for the traditional transmitter when the desired receiver is +30 from array broadside.

Fig. 16. Theoretical lower bound and simulated BER for the DM transmitter, and the BER for the traditional transmitter when the desired receiver is +60 from array broadside.

4.14 dB, and 1.53 dB, respectively. The power reduction is especially significant in the case when the desired receiver was at broadside because the traditional array transmits with all four elements in broadside mode, generating the maximum possible pattern magnitude of any configuration. This is the case where the traditional array would have the best performance because it does not have to steer its beam. Yet its sidelobe BER performance is only slightly better than the DM array, and the DM array has a narrower information beamwidth, meaning there is a steeper transition from the low BER region to the high BER region. This narrower information beamwidth occurs in each of the other four desired transmit directions as well. Fig. 14. Theoretical lower bound and simulated BER for the DM transmitter, and the BER for the traditional transmitter when the desired receiver is at array broadside.

is only possible when using directional modulation and not possible with baseband modulation. In this case, the additional degree of freedom with DM is able to scramble the signal in sidelobe directions even when sidelobe levels are high. The BER curves for the other four cases are plotted in Figs. 13–16. As mentioned earlier, the power of the traditional array was lowered until the BER in the desired direction matched that of the DM array. For the cases of the desired , broadside, , and , the power receiver at of the traditional array was reduced by 1.84 dB, 12.28 dB,

V. CONCLUSION Directional modulation has been presented for the first time using an array of reconfigurable, actively-fed elements. The reconfigurable elements, rather than baseband hardware, synthesize a digital signal. Unlike previous research using a single driven element in a parasitic array [14], [15], an array of reconfigurable elements is used which simplifies and shortens the design procedure. Instead of using phase shifters as in [10], modulation is carried out using only the antenna elements. A four-element array using DM outperformed an identical array using traditional baseband modulation by synthesizing a narrower information beam in the desired direction. In most cases in this paper, the DM array had a higher BER in unwanted transmit directions compared to the traditional array. More work is needed

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to design DM arrays that always avoid transmitting low BER signals in any undesired direction. REFERENCES [1] R. F. Harrington, “Reactively controlled directive arrays,” IEEE Trans. Antennas Propag., vol. 26, no. 3, pp. 390–395, May 1978. [2] S. L. Preston, D. V. Thiel, J. W. Lu, S. G. O’Keefe, and T. S. Bird, “Electronic beam steering using switched parasitic patch elements,” Electron. Lett., vol. 33, no. 1, pp. 7–8, 1997. [3] R. Schlub, D. V. Thiel, J. W. Lu, and S. G. O’Keefe, “Dual-band six element switched parasitic array for smart antenna cellular communications systems,” Electron. Lett., vol. 36, no. 16, pp. 1342–1343, 2000. [4] R. Schlub, J. Lu, and T. Ohira, “Seven-element ground skirt monopole ESPAR antenna design from a genetic algorithm and the finite element method,” IEEE Trans. Antennas Propag., vol. 51, no. 11, pp. 3033–3039, 2003. [5] D. V. Thiel, “Switched parasitic antennas and controlled reactance parasitic antennas: A systems comparison,” in Proc. IEEE Antennas Propag. Soc. Int. Symp., 2004, vol. 3, pp. 3211–3214. [6] S. Zhang, G. H. Huff, J. Feng, and J. T. Bernhard, “A pattern reconfigurable microstrip parasitic array,” IEEE Trans. Antennas Propag., vol. 52, no. 10, pp. 2773–2776, Oct. 2004. [7] A. Hirata, E. Taillefer, H. Yamada, and T. Ohira, “Handheld direction of arrival finder with electronically steerable parasitic array radiator using the reactance-domain multiple signal classification algorithm,” IET Microw. Antennas Propag., vol. 4, no. 1, pp. 815–821, 2007. [8] S. Zhang and J. T. Bernhard, “Performance study of a reconfigurable microstrip parasitic array (RMPA) phased array,” in Proc. IEEE Antennas Propag. Soc. Int. Symp., 2006, pp. 2305–2308. [9] T. L. Roach and J. T. Bernhard, “Investigation of sidelobe level performance in phased arrays with pattern reconfigurable elements,” in IEEE Antennas Propag. Soc. Int. Symp., 2007, pp. 105–108. [10] M. P. Daly and J. T. Bernhard, “Directional modulation technique for phased arrays,” IEEE Trans. Antennas Propag., vol. 57, pp. 2633–2640, Sept. 2009. [11] S. D. Keller, W. D. Palmer, and W. T. Joines, “Electromagnetic modeling and simulation of a directly-modulated L-band microstrip patch antenna,” in Proc. Int. Symp. on Antennas and Propag., Jun. 2007, pp. 4489–4492. [12] E. Baghdady, “Directional signal modulation by means of switched spaced antennas,” IEEE Trans. Commun., vol. 38, pp. 399–403, Apr. 1990. [13] C. M. Elam and D. A. Leavy, “Secure Communication Using Array Transmitter,” U.S. Patent 6 275 679, Aug. 14, 2001. [14] A. Babakhani, D. B. Rutledge, and A. Hajimiri, “A near-field modulation technique using antenna reflector switching,” in IEEE Int. Solid State Circuits Conf., Feb. 2008, pp. 188–189. [15] A. Babakhani, D. B. Rutledge, and A. Hajimiri, “Transmitter architectures based on near-field direct antenna modulation,” IEEE J. SolidState Circuits, vol. 12, no. 43, pp. 2674–2692, Dec. 2008. [16] M. P. Daly and J. T. Bernhard, “Reconfigurable array for multidirectional and secure communication,” in Proc. Allerton Antennas Symp., Monticello, IL, 2008, pp. 116–131. [17] G. H. Huff and J. T. Bernhard, “Integration of packaged RF MEMS switches with radiation pattern reconfigurable square spiral microstrip antennas,” IEEE Trans. Antennas Propag., vol. 54, pp. 464–469, Feb. 2006. [18] K. Hietpas, “Beam steering in phased arrays using a pattern reconfigurable antenna,” Master’s thesis, University of Illinois at UrbanaChampaign, IL, 2004. [19] MATLAB Version 7.0.4.365 (R14) Service Pack 2, Natick, MA: TheMathworks, Inc. 2005.

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Michael P. Daly (S’09) was born in San Juan, Puerto Rico on October 31, 1984. He received the B.S. (with highest honors) and M.S. degrees in electrical engineering at the University of Illinois at Urbana-Champaign (UIUC), in 2007 and 2008, respectively, where he is currently working toward his Ph.D. degree. His research interests include reconfigurable antennas, arrays, and digital communications. Mr. Daly is the recipient of an NDSEG fellowship.

Jennifer T. Bernhard (S’89–M’95–SM’01–F’10) was born on May 1, 1966, in New Hartford, NY. She received the B.S.E.E. degree from Cornell University, Ithaca, NY, in 1988, and the M.S. and Ph.D. degrees in electrical engineering from Duke University, Durham, NC, in 1990 and 1994, respectively, with support from a National Science Foundation Graduate Fellowship. While at Cornell, she was a McMullen Dean’s Scholar and participated in the Engineering Co-op Program, working at IBM Federal Systems Division in Owego, New York. During the 1994–95 academic year she held the position of Postdoctoral Research Associate with the Departments of Radiation Oncology and Electrical Engineering at Duke University, where she developed RF and microwave circuitry for simultaneous hyperthermia (treatment of cancer with microwaves) and MRI (magnetic resonance imaging) thermometry. At Duke, she was also an organizing member of the Women in Science and Engineering (WISE) Project, a graduate student-run organization designed to improve the climate for graduate women in engineering and the sciences. From 1995–1999, she was an Assistant Professor in the Department of Electrical and Computer Engineering at the University of New Hampshire, where she held the Class of 1944 Professorship. Since 1999, she has been with the Electromagnetics Laboratory in the Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, where she is now a Professor. In 1999 and 2000, she was a NASA-ASEE Summer Faculty Fellow at NASA Glenn Research Center in Cleveland, OH. She is also an Illinois College of Engineering Willett Faculty Scholar and a Research Professor in Illinois’ Micro and Nanotechnology Laboratory, the Coordinated Science Laboratory, and the Information Trust Institute. Her industrial experience includes work as a research engineer with Avnet Development Labs and, more recently, as a private consultant for members of the wireless communication and sensors community. Her research interests include reconfigurable and wideband microwave antennas and circuits, wireless sensors and sensor networks, high speed wireless data communication, electromagnetic compatibility, and electromagnetics for industrial, agricultural, and medical applications, and has two patents on technology in these areas. Prof. Bernhard is a member of URSI Commissions B and D, Tau Beta Pi, Eta Kappa Nu, Sigma Xi, and ASEE. She is a Fellow of the IEEE and served as an elected member of the IEEE Antennas and Propagation Society’s Administrative Committee from 2004–2006. She received the NSF CAREER Award in 2000. She and her students received the 2004 H. A. Wheeler Applications Prize Paper Award from the IEEE Antenna and Propagation Society for their paper published in the March 2003 issue of the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION. She served as an Associate Editor for the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION from 2001–2007 and the IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS from 2001–2005. She was President Elect and President of the IEEE Antennas and Propagation Society in 2007 and 2008, respectively. She is also a member of the editorial board of Smart Structures and Systems.

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Analysis and Design of E -Plane Scanning Grid Arrays Alejandro Iturri-Hinojosa, Jose I. Martinez-Lopez, and Alexander E. Martynyuk

Abstract—A quasi-optical beam steering multilayer lens with scanning in -plane is analyzed. A full-wave mathematical model is developed to predict the scanning characteristics of the lens. The model is used to optimize the performance of a three-bit beam steering lens. It is demonstrated that the calculated conversion coefficients for the optimized lens are better than 2 1 dB in the frequency band from 27.5 to 32.5 GHz for transmission elevation angles up to 28 . A two-bit lens that corrects the phase front at the aperture of a short -plane sectoral horn has been designed, fabricated and tested to verify the model. Measured radiation pattern of the -plane sectoral horn with correcting lens agrees well with the predictions based on the model. Index Terms—Antenna array mutual coupling, antenna arrays, beam steering, phased arrays.

I. INTRODUCTION OWADAYS we can observe a growing interest in electronically scanning phased array antennas operating at microwave frequencies for radar and telecommunication applications. One of the problems that delays the commercial application of phased arrays is the elevated cost of these antennas [1]. Many promising designs have been developed to reduce cost and weight of the antenna. One of the methods that potentially results in a low-cost low-weight beam-steering array is the usage of quasi-optical structures at microwave frequencies. These structures avoid limitations such as high insertion loss and expensive fabrication costs of conventional microwave and millimeter-wave combining circuits when the frequency of operation increases [2]. Several types of quasi-optical arrays have been designed and fabricated [3]–[5]. One of the approaches that offers low-cost, low-weight and simple design is the RADANT technique proposed by Chekroun [6]. This technique uses a diode-loaded controlled medium for providing phase shifting (Fig. 1). Thus, a RADANT lens can be seen as an artificial dielectric with a controlled refractive index that ensures electronic scanning of the transmitted wavefront. To

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Manuscript received February 07, 2009; revised September 05, 2009; accepted January 25, 2010. Date of publication April 22, 2010; date of current version July 08, 2010. This work was supported in part by CONACYT 79832 and PAPIIT IN1042063 projects. A. Iturri-Hinojosa and A. E. Martynyuk are with the Faculty of Engineering, National Autonomous University of Mexico (UNAM), Coyoacan C.P. 04510, Mexico (e-mail: [email protected]; [email protected]). J. I. Martinez-Lopez is with the ElectroScience Laboratory, Ohio State University, Columbus, OH 43212 USA on leave from the Faculty of Engineering, National Autonomous University of Mexico (UNAM), Coyoacan C.P. 04510, Mexico. 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/TAP.2010.2048846

Fig. 1. Classic RADANT lens with one-dimensional scanning in E -plane.

control this refractive index, switching diodes are placed one behind the other in the direction of propagation. The propagation velocity of the signal transmitted through the lens depends on the states of the diodes. The design of the classic -plane scanning RADANT lens contains horizontal metal strips with diodes. This configuration ensures the same diode biasing in the row. By varying the states of the diodes from row to row it is possible to steer the beam in one plane. On the other hand, the -plane scanning lens contains vertical wires loaded with diodes. Then, the cascading of one -plane and one -plane RADANT lens leads to the complete two plane scanning [7]. Thus, the RADANT technique can be considered a mature technology for use in real systems. Therefore, the need for a model that aids the design of quasi-optical structures is of primary importance to reduce time and cost. Different models of quasi-optical systems have been developed [8], [9]. These models treat the quasi-optical array as an infinite periodic structure with the unit cell containing only one element. However, in real scanning quasi-optical arrays the neighboring elements have different configurations to allow the beam steering. So, the non uniform configuration of the elements along the array destroys the original periodicity and changes significantly the mutual coupling between the elements. On the other hand, mathematical models for finite quasi-optical arrays have been developed [10], [11]. Nevertheless, these models are based on a complete formulation of the electromagnetic problem for all the elements, demanding considerable computation resources in the case of large arrays and multilayered structures. Thus, in this work we have developed a full-wave electromagnetic model for an infinite periodic multilayered array with differently-configured elements. This mathematical model permits us to obtain the scanning characteristics of the multilayered quasi-optical RADANT—type arrays. Our model was used to design and optimize the performance of a three-bit beam steering quasi-optical array with p-i-n diode

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Fig. 2. (a) Cell of the grid array, (b) equivalent circuit for the grid array with p-i-n diodes in the forward states and (c) in the reverse states.

switches. To verify this mathematical model, an -plane sectoral horn with a two-bit correcting lens that improves the phase distribution at the horn aperture has been designed, fabricated and tested. The measured radiation pattern of the -plane sectoral horn with correcting lens is similar to the radiation characteristics predicted by the mathematical model.

Fig. 3. Pair of grid arrays separated by air gap as a section of loaded-line phase shifter for the case of (a) forward and (b) reverse diode states and equivalent circuits for the case of (c) forward and (d) reverse diode states.

II. PRINCIPLE OF OPERATION Consider the classic quasi-optical beam steering lens based on p-i-n diode switches shown in Fig. 1. The incident -polarized plane wave travels in the positive -direction. After passing through several grid layers (or grid arrays) in cascade, this wave is converted into a transmitted wave traveling in a desired direction determined by proper p-i-n diode biasing. Each grid array contains cells loaded with p-i-n diodes. These cells are situated at the nodes of a periodic rectangular grid with -dimension equal to and -dimension equal to . The cell geometry is shown in Fig. 2(a). This cell can be considered as capacitive horizontal metal strips separated by a distance and loaded with a p-i-n diode switch. Additional strip conductors are used to solder the beam-lead p-i-n diode. All cells are printed on a dielectric substrate with relative permittivity and dielectric thickness of . According to [12], the single grid array represents a shunt reactance for the incident -polarized plane wave. This reactance can be set to inductive or capacitive depending on the state of the p-i-n diode switches. When all p-i-n diodes in the grid array are in the low-impedance state (or on-state), the reactance is inductive, and when all these diodes are in the high-impedance state (or off-state) the reactance becomes capacitive. The equivalent circuits of the grid array with p-i-n diodes in low-impedance and high-impedance states are shown in is deterFig. 2(b) and (c), respectively. The capacitance mined by the geometry of the metal strips. The inductance is an additional lumped inductance to tune the circuit. This inductance also takes into account the effect of additional and are intrinsic resistances metal strips. Resistances of the p-i-n diode in the on- and off-state, respectively. The is the capacitance of the diode in the off-state. capacitance The equivalent circuit also contains a transmission line that takes into account the dielectric substrate. The characteristic impedance of the transmission line is equal to the intrinsic impedance of the dielectric medium and the length is equal to the thickness of the dielectric substrate.

Fig. 4. Beam steering E -plane lens based on pairs of grid arrays.

An elementary section of a loaded-line phase shifter can be built from a pair of grid arrays with the same diode biasing separated by a distance . Frequently, the section of the loaded-line phase shifter is tuned to provide the differential phase shift of radians, where is the number of bits in the digital identical phase shifter. Thus, a cascade connection of sections provides a complete -bit phase shifter. The equivalent circuits for a pair of grid arrays are shown in and are the grid array susceptances for Fig. 3(a) and (b). the case of forward and reverse diode states, respectively. The represents the air gap between the pair transmission line of grid arrays. Fig. 3(c) and (d) show the equivalent circuits for the pair of grid arrays considering that all p-i-n diodes are in the forward and reverse states, respectively. Therefore, for steering a beam in a desired direction, a phase variation across the transmitting aperture is needed. Thus, by stacking several above-mentioned pairs of grid arrays, the linearly progressive phase shifts can be provided [12]. Consequently, a proper biasing of the p-i-n diodes is needed to obtain the required linear phase taper to redirect the transmitted wave as it is shown in Fig. 4. Then, the phase front of the transmitted wave will no longer be parallel to the plane of the incident wave. Instead, the resulting beam will be steered at a transmission pairs of grid arrays can be elevation angle . Thus, considered as an -bit beam steering -plane lens.

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Fig. 5. Geometry of the grid array (or grid layer). The “large” cell of this grid array contains four “small” cells.

III. MATHEMATICAL MODEL A. General Considerations A full-wave mathematical model has been built to predict the performance and optimize the parameters of the RADANT—type lens. The approach used was similar to the one described in [13]. Three constraints related to the geometry of the lens are considered to simplify the analysis. 1) The “small” cell that contains one switching element has the same size in all the layers of the lens; however, its internal geometry may change from layer to layer; 2) The same rectangular grid in the - plane is employed in all the layers; 3) “Small” cells of different layers are perfectly aligned with respect to their centers. If the biases across all p-i-n diodes in one grid array are the same, this layer can be analyzed as a periodic structure with a unit cell equal to the “small” cell. In this case, when the size of the “small” cell is limited to avoid the appearance of grating lobes, the transmitted wave would have the same direction of propagation as the incident wave. Now consider a normally-incident -polarized plane wave as an excitation source and assume that it travels toward the lens in the positive -direction (Fig. 1). To redirect the transmitted wave plane is in a direction determined by (scanning in the assumed), a linear phase taper must be applied. The incremental is ensured by controlling the states of the p-i-n diodes phase in the adjacent “small” cells in the -direction. The different p-i-n diode states in adjacent “small” cells in -direction destroy the initial periodicity of the array. Thus, the “small” cell can no longer be considered as the unit periodic , a new cell of the grid array. However, for certain values of periodic structure appears with a “large” unit cell containing one adjacent “small” cells in “small” cell in the -direction and the -direction (Fig. 5). To achieve this new periodicity, the incremental phase shift between any two adjacent cells in the -direction must be set to (1)

is the total number of phase shifts introduced by where the “large” cell along the -direction. can be approximated with a desired In fact, all possible tolerance by (1). However, for almost all , it is impossible to achieve a precise value due to the discrete phase values introduced by digital phase shifters. Thus, the required linear phase taper is approximated by step functions. Therefore, Floquet’s theorem can be applied to analyze the periodic infinite grid array. According to Floquet’s theorem, the electromagnetic field in front of and behind the infinite grid array is presented as a sum of Floquet modes or plane waves. The condition (1) ensures that two Floquet modes are linearlypolarized plane waves propagating in the desired direction determined by . Thus, the mathematical model has been developed to calculate the conversion efficiency of the incident -polarized wave to the plane wave traveling in the desired direction. The mathematical model of the multilayer lens has been built by characterizing each layer using a generalized scattering matrix (GSM) approach [14], [15] and a posterior cascading procedure resulting in the total GSM of the whole lens. Then this total GSM can be used to obtain the characteristics of the entire lens. The efficient computational method presented in [16] has been used to accelerate the cascading procedure. B. Mathematical Model of a Single Layer and Cascading Procedure Each single layer (or grid layer) of the lens can be considered as an infinite array that contains “small” cells printed on a dielectric substrate. Two reference planes were defined as it is shown in Fig. 5 to calculate the GSM of a single layer. The order of the GSM is equal to the number of Floquet modes included in the cascading process. So, to obtain the GSM of a single layer, the scattering of every Floquet mode taken into account needs to be analyzed. Then, a system of integral equations was formulated to analyze the scattering of the Floquet modes by the single layer. Assume that a plane wave corresponding to a certain incident Floquet mode of unit magnitude is scattered by the single layer in the plane of the lens. The unknown tangential electric field of the grid can be presented as a sum of two components (2) where is the electric field that appears considering that the incident wave excites the single layer without switching eleis the electric field that exists due to the electric ments and currents that flow across the switching elements in the single layer. The switching element contains one p-i-n diode and one tuning inductance . is calculated following At first, the tangential electric field the same approach presented in [13]. The unit cell of the grid array is the first “small” cell of the “large” cell. So, the solution is found only for this “small” cell and then is expanded to the other cells of the “large” cell using Floquet’s theorem. Application of the boundary conditions for the tangential electric field over the “small” cell and application of the continuity condition for the tangential magnetic field over the slot lead to the

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first equation in the system of integral equations. This equation is the Fredholm integral equation similar to the one obtained in [17]

(3) where is the tangential electric field that appears in the first “small” cell of the “large” cell of the single layer without is the complete system of Floquet switching elements; is the incident modes corresponding to the “small” cell; is the admittance of the Floquet mode ; Floquet mode; is the modified admittance of the Floquet mode that takes into account the properties of the dielectric substrate; is the aperture area of the first “small” cell, are the local Cartesian coordinates with origin at the center of the first “small” cell and denotes the complex conjugation. Then, the integral equation with respect to the unknown elecwas obtained as a result of the application of the tric field continuity condition for the tangential magnetic field across all slots contained in the “large” cell. An important consideration is that the tangential magnetic field is not continuous in the regions where electric currents flow across the switching elements. As a result of this discontinuity, the second integral equation of the system contains the electric currents

(4) where is the complete system of the Floquet modes correis the admittance of the Flosponding to the “large” cell; ; is the modified admittance of the Floquet quet mode mode that takes into account the dielectric substrate; is the total area of all slots contained in the “large” cell, is the induced electric current across the switching element in the th is the vector function that “small” cell of the “large” cell and into the corresponding electric converts the electric current current density . Equation (4) is valid only over the surface of all the slots that the “large” cell contains. When the dimensions of the switching elements are negligible with respect to the wavelength and each switching element has the form of a rectangle of width and length equal can be to the distance between metal strips , the function expressed in the following form:

(5)

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and are the local Cartesian coordinates with origin where is the unit vector in at the center of the th “small” cell, -direction and is the Heaviside unit step function. The left side of the integral (4) contains the unknown induced currents . Therefore, additional equations are needed in order to resolve (4). In the case when the size of the switching elements is negligible with respect to the wavelength , Ohm’s law can be applied to each switching element to obtain these additional equations

(6)

is the total tangential electric field in the th “small” where is the line path where exists and is the impedance cell, of the switching element installed at the th “small” cell. The integral (3), (4) and the system of (6) were resolved simultaneously in the same manner as the system of the integral equations for the loaded ring slot resonators in [13] using the method of Galerkin. Special functions that take into account the singularity of electric field at the perfect conductor edge were used as the basis and weighting functions to approximate the electric field at the slot [18]. The and -directed vector basis functions and are the Chebyshev polynomials of and second kind, respectively, the first , respecwhich are divided and multiplied by tively. The resulting expressions are in turn multiplied by a sine , where . or a cosine with argument This system of basis functions allows us to approximate the standing-wave-like electric field that appears in the slot line due to the p-i-n diodes connected in parallel. The special transversal was calcuwave number lated for each basis function in order to arrange these functions according to their spatial frequency. The number of basis functions necessary to approximate the electric field in the “small” cell was determined according to the minimal characteristic dimension of the “small” cell. This dimension corresponds to the width of the switching element . was calculated Then the maximum wavenumber and all basis functions with less than were taken into account. The above-mentioned procedure is repeated for any of the incident Floquet modes taking into account in the cascading process to obtain the GSM of the single layer. When the GSMs of all layers are known, the cascade connection of generalized scattering parameters is used to obtain the total GSM of the whole lens using the procedure described in [16]. When the total GSM of the lens is known, it is possible to evaluate the to introduce the conversion coefficient efficiency of the mode conversion. This conversion coefficient can be calculated as a ratio between the power density of the transmitted Floquet mode (or transmitted linearly-polarized plane wave) traveling in the desired direction and the power

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density of the incident Floquet mode that represents the incident linearly-polarized wave [13]

(7) where is the index corresponding to the incident Floquet is the index corresponding to the transmitted Floquet mode, is the corremode traveling in the desired direction and spondent element of the GSM. IV. RESULTS OF NUMERICAL SIMULATIONS A three-bit beam steering lens containing fourteen equal grid arrays has been designed and optimized at 30 GHz using the developed mathematical model. This three-bit lens can be considered as a cascade connection of seven identical 45-degree phase shifters. The pair of grid arrays is equivalent to a 45-degree loaded line spatial phase shifter. A. Optimization of a Pair of Grid Arrays First, our mathematical model and the method of equivalent circuits (similar to the one described in [12]) were used to determine the internal geometry of the “small” cell of the grid array. Therefore, the geometry of the pair of grid arrays was optimized to obtain the 45-degree matched loaded line phase shifter with minimized levels of return and insertion loss and reduced level of the parasitic amplitude modulation near the frequency of 30 GHz. As a result of the parametric optimization, the geometry of , , the “small” cell is given by: and . The tuning inductance was set to 0.27 nH. Parameters of the HPND 4005 p-i-n diode , and are considered in the calculation. It is assumed that grids are printed on a substrate with a thickness of 0.102 mm and a relative permittivity of 2.4. The optimized distance of 1.7 mm between the grid arrays in the pair was obtained. B. Scanning Characteristics of the Optimized 3-Bit Beam Steering Lens The optimized pair of grid arrays was used as the basic building block of the 3-bit beam steering lens. With the use of the developed mathematical model, the scanning characteristics of the multilayer array containing 14 identical grid arrays were obtained. Initially, the distances between the grid arrays in the multilayer array were set to 1.7 mm. The results of the numerical simulation for different transmission elevation angles are shown in Fig. 6. First, the lens was configured to ensure of 10 at 30 GHz. For this case the “large” cell of the 3-bit lens contains 64 adjacent “small” cells in the -direction. The required biases for all 896 (14 64) diodes in the simulated structure were set in order to introduce the desired linear phase taper. The conversion coefficient for this configin the frequency band from 25 to uration is better than 35 GHz. The 3-bit beam steering lens was also configured to ensure of 47 , 36 , 29 and 22 at 30 GHz with of 16, 20, 24 and

Fig. 6. Conversion coefficient L and transmission elevation angle lated for different configurations of the 3-bit beam steering lens.



calcu-

32, respectively. However, the conversion coefficients obtained (Fig. 6). for these configurations are worse than As indicated in [13], one of the reasons for the degradation of the conversion coefficient is the power interchange between the different propagating high-order Floquet modes on the layers of the lens. Also, for large transmission elevation angles, the phase velocities of the propagating Floquet modes are significantly different from the phase velocity of the normally incident wave. Thus, the previously-mentioned optimization of the geometry is helpful only for small transmission angles. Therefore, an additional optimization was performed to obtain better conversion coefficients for large transmission angles. The distances between grid arrays were used as the optimization parameters in order to achieve improved values of conversion coefficients for different “large” cell configurations. After this new optimization, the distances (starting from the first layer that receives the electromagnetic wave) were set to 2, 2.9, 1.8, 3.1, 2, 3, 2.4, 2.7, 2.1, 2.5, 1.6, 3 and 1.7 mm, respectively. As a result, a considerable improvement of conversion coefficients was obtained for large transmission angles. Calculated in the frequency conversion coefficients are better than band from 27.5 to 32.5 GHz for the case of transmission angles up to 28 (Fig. 7). A total of fourteen basis functions were used to approximate the electric field in each “small” cell, including one (cosine) and thirteen functions function ( , sine and cosine). During the calculations the number of Floquet modes taken into account in the cascading procedure was increased in increments of 25 until convergence was achieved. It was ensures the reasonable accuracy of the found that calculated results. Six propagating and 94 evanescent Floquet modes of the “large” cell were considered in the cascading , while 26 propagating and procedure for the case of 74 evanescent Floquet modes were taken into account for the . The contribution of an evanescent Floquet case of mode to the interaction between closely-spaced grid arrays is mainly determined by the magnitude of its transmission coeffi-

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Fig. 7. Conversion coefficient L and transmission elevation angle  calculated for the different configurations of the 3-bit beam steering lens with optimized distances between layers. Fig. 8. lens.

cient through the air gap between the grid arrays. It was found, that all Floquet modes with transmission coefficient magniwere taken into account during tudes greater than the cascading procedure. The magnitudes of the transmission coefficients were calculated for the smallest air gap of 1.6 mm at the highest frequency of 35 GHz. V. EXPERIMENTAL VERIFICATION A waveguide simulator was used to verify the developed mathematical model. A two-bit lens was designed and installed at the cross-section of an overmoded rectangular waveguide to correct the phase distribution at the aperture of the -plane sectoral horn. It is a well-known fact [19], [20] that the quadratic phase distribution with a significant phase deviation is typical for the . When short -plane sectoral horns with a large flare angle maximum phase deviation increases, the pattern widens and becomes flatter around the main lobe. For severe phase deviations, the main maximum does not occur on the axis of the horn. Therefore, a two-bit -plane correcting lens formed with six grid arrays was designed, fabricated and installed at the cross section of the overmoded rectangular waveguide with and height . Printed grid width arrays were installed at the cross-section of specially fabricated support structures with thicknesses equal to the optimized distances . The disassembled view of the lens is shown in Fig. 8. Each grid array consists of 16 “small” cells with identical internal geometry and arranged along the -axis. The pair of grid arrays forms sixteen 90-degree fixed phase shifters arranged along the -axis. The cross-section of the overmoded rectangular waveguide has the same size as the “large” unit cell of the equivalent infinite periodic structure optimized during the design process. The operation of the lens was optimized at 30 GHz to correct the quadratic phase distribution at the aperture of the short -plane sectoral horn with an aperture width and height equal to and , respectively, and a total flare angle of 106.3 . As a result of the optimization procedure, similar

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E -plane sectoral horn with the disassembled quasi-optical correcting

to the one described above, the geometry of the “small” cell , and has been defined as follows: . The grid arrays of the lens were fabricated on a dielectric substrate with relative permittivity of 2.4 and thickness of 0.102 mm. The distance between layers in the pair of grid arrays was set to 2.6 mm to form a 90-degree fixed phase shifters. The distance between pairs of grid arrays was set to 1.5 mm. Two cascaded “small” cells without loading were used to delay the phase of the transmitted wave with respect to the one transmitted through two cascaded “small” cells loaded with inductors. These inducdiameter gold wire with length tors were fabricated from 25 of 1.4 mm. The loaded and unloaded “small” cells were arranged along the lens in order to correct the phase deviation at the aperture of the -plane sectoral horn. As a result, the first pair of grid arrays (the nearest to the feeding short -plane sectoral horn) contains 10 “small” cells in each grid array loaded with inductors. Two blocks of five loaded cells are situated at the ends of each grid array to compensate the maximum phase delay near the upper and bottom wall of the horn as it is shown in Fig. 9(a) The second pair of grid arrays contains two blocks of three loaded “small” cells at the ends of each grid array [Fig. 9(b)], while the third pair contains only one loaded “small” cell at the ends of each grid array [Fig. 9(c)]. The fabricated horn with correcting lens is shown in Fig. 10. The amplitude and phase distributions at the aperture of the -plane sectoral horn used in the experiments as well as the radiation pattern has been calculated at 30 GHz according to the method described in [20]. The calculated amplitude and phase distributions at the horn aperture are presented in Fig. 11. A significant phase deviation of 240 can be observed at the aperture of the horn. The calculated radiation pattern of the horn is presented in Fig. 12. The severe degradation of the pattern including the destruction of the main lobe can be explained from the huge phase deviation at the aperture. The calculated directivity in the horn axis direction was 7.5 dB. On the same

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Fig. 9. Fabricated panels for (a) the first pair of grid arrays, (b) the second pair of grid arrays and (c) the third pair of grid arrays.

Fig. 12. Calculated and measured 30 GHz.

E -plane patterns of the horn antenna at

the input of the waveguide due to the complex field distribution at the aperture of the horn. Thus, many incident Floquet modes appear at the input of the equivalent infinite periodic structure. can be repAs a result, the incident tangential electric field resented as (8)

Fig. 10. The fabricated horn with 2-bit correcting lens.

are the magnitudes of the incident Floquet modes where and is the propagation constant of the corresponding Floquet mode. can be calculated using the The magnitudes of the modes orthonormality properties of the Floquet modes over the “large” unit cell of the structure (9)

Fig. 11. Calculated magnitude and phase of the electric field at the aperture of the horn antenna at 30 GHz.

Fig. 12 the measured radiation pattern of the fabricated horn is presented. When the -plane sectoral horn is connected to the overmoded rectangular waveguide with installed lens, many propagating and non-propagating waveguide modes are excited at

is the tangential electric field at the aperture where of the horn. The calculated magnitudes of the first twenty propagating Floquet modes arranged according to their tangential wavenumat the input of the lens are presented in Fig. 13. The bers sum of the first and the third Floquet modes forms the incident mode of the overmoded rectangular waveguide with uniform amplitude-phase distribution along the -axis. The other and propagating Floquet modes form the high-order modes of significant magnitudes that cause large phase deviation at the horn aperture. Our model was used to calculate the transmission of the incident Floquet modes through the lens. The calculated magnitudes of the transmitted Floquet modes are shown in Fig. 14. The magnitude of the first and third Floquet modes (corresponding to the mode) increase significantly, while the magnitudes of the undesired high-order modes are effectively suppressed. Thus, this lens is equivalent to a multimode converter that pumps up , modes into the the power of the undesired high-order

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Fig. 15. Calculated magnitude and phase of the electric field at the aperture of the 2-bit correcting lens at 30 GHz.

Fig. 13. Calculated magnitudes of the propagating Floquet modes at the aperture of the horn antenna at 30 GHz.

Fig. 16. Calculated and measured E -plane patterns of the horn with 2-bit correcting lens at 30 GHz.

Fig. 14. Calculated magnitudes of the propagating Floquet modes at the aperture of the lens at 30 GHz.

mode with uniform amplitude-phase distribution along -axis. The calculated amplitude-phase distribution at the output aperture of the lens is shown in Fig. 15. Note that at the output of the lens the phase deviation at the aperture was reduced to 47 . The improvement in the amplitude and phase distributions leads to the correction of the radiation pattern. The calculated radiation pattern of the horn with correcting lens is presented in Fig. 16. A half power beamwidth of 12 was obtained for the field pattern. A directivity of 14.2 dB was calculated. In the same figure the measured radiation pattern of the fabricated horn-lens system is presented. Good agreement is observed between the calculated and measured radiation patterns. VI. CONCLUSION A full-wave mathematical model for the quasi-optical beam steering lens with scanning in -plane was developed. This

model was used to design a three-bit beam steering lens containing 14 identical grid arrays. Different configurations of grid arrays for the -plane lens were simulated. Transmission elevation angles up to 28 for the transmitted linearly-polarized wave . were achieved with conversion coefficients better than Furthermore, the model was verified using a six-layer correcting lens. This fabricated 2-bit lens installed at the aperture of an -plane sectoral horn improves the amplitude and phase distribution of the field at the aperture, making possible a field pattern with better directivity. The measured radiation pattern agrees well with the theoretical calculations performed using the developed mathematical model. ACKNOWLEDGMENT The authors would like to thank Dr. J. Rodriguez-Cuevas and D. Mendoza-Rosales for assistance in fabrication of correcting lens. REFERENCES [1] E. Brookner, “Phased arrays around the world,” in Proc. IEEE Int. Symp. Phased Arrays Syst. Tech. (PAST’03), Boston, MA, Oct. 2003, pp. 1–8.

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[2] T. K. Wu, Frequency Selective Surface and Grid Array. New York: Wiley-Interscience, 1995. [3] H. R. Phelan, “Spiraphase-a new, low cost, lightweight phased array,” Microw. J., vol. 19, no. 12, pp. 41–46, Dec. 1976. [4] J. B. L. Rao, G. V. Trunk, and D. P. Patel, “Two low cost phased arrays,” in Proc. IEEE Int. Symp. Phased Array Syst. Tech.(PAST’96), Boston, MA, Oct. 15–18, 1996, pp. 119–124. [5] J. R. Mathew, R. A. Meger, J. A. Gregor, D. P. Murphy, R. E. Pechacek, R. F. Fernsler, and W. M. Manheimer, “Electronically steerable plasma mirror,” in Proc. IEEE Int. Symp. Phased Array Syst. Tech. (PAST’96), Boston, MA, Oct. 15–18, 1996, pp. 58–62. [6] C. Chekroun, D. Herric, Y. Michel, R. Pauchard, and P. Vidal, “Radant: New method of electronic scanning,” Microw. J., vol. 24, no. 2, pp. 45–53, Feb. 1981. [7] E. Brookner, “Major advances in phased arrays: Part II,” Microw. J., vol. 40, no. 6, pp. 84–92, Jun. 1997. [8] C. Chen, “Transmission of microwaves through perforated flat plates,” IEEE Trans. Microw. Theory Tech., vol. 21, no. 1, pp. 1–6, Jan. 1973. [9] J. P. Montgomery, “Scattering by an infinite periodic array of thin conductors on a dielectric sheet,” IEEE Trans. Antennas Propag., vol. 23, no. 1, pp. 70–75, Jan. 1975. [10] R. Kastner and R. Mittra, “Iterative analysis of finite sized planar frequency selective surfaces with rectangular patches or perforations,” IEEE Trans. Antennas Propag., vol. 35, no. 4, pp. 372–377, Apr. 1987. [11] T. W. Nuteson, M. B. Steer, K. Naishadham, W. Mink, and J. Harvey, “Electromagnetic modeling of finite grid structures in quasi-optical systems,” in IEEE MTT-S Int. Microw. Symp. Dig., San Francisco, CA, Jun. 1996, vol. 3, pp. 1251–1254. [12] J. Mazotta, M. DeLisio, and J. C. Chiao, “Quasi-optical discrete beam steering grids,” in IEEE MTT-S Int. Microw. Symp. Dig., Anaheim, CA, Jun. 1999, vol. 4, pp. 1825–1828. [13] A. E. Martynyuk, J. I. Martinez-Lopez, and N. A. Martynyuk, “Spiraphase-type reflectarrays based on loaded ring slot resonators,” IEEE Trans. Antennas Propag., vol. 52, no. 1, pp. 142–153, Jan. 2004. [14] R. C. Hall, R. Mittra, and K. M. Mitzner, “Analysis of multilayered periodic structures using generalized scattering matrix theory,” IEEE Trans. Antennas Propag., vol. 36, no. 4, pp. 511–517, Apr. 1988. [15] R. Mittra, C. H. Chan, and T. Cwik, “Techniques for analyzing frequency selective surfaces-a review,” Proc. IEEE, vol. 76, pp. 1593–1615, Dec. 1988. [16] C. Wan and J. A. Encinar, “Efficient computation of generalized scattering matrix for analyzing multilayered periodic structures,” IEEE Trans. Antennas Propag., vol. 43, no. 11, pp. 1233–1242, Nov. 1995. [17] N. Amitay, V. Galindo, and C. P. Wu, Theory and Analysis of Phased Array Antennas. New York: Wiley-Interscience, 1972. [18] A. Frenkel, “On entire-domain basis functions with square-root edge singularity,” IEEE Trans. Antennas Propag., vol. 37, no. 9, pp. 1211–1214, Sep. 1989. [19] C. A. Balanis, Antenna Theory—Analysis and Design. New York: Wiley, 1982.

[20] E. V. Jull and L. E. Allan, “Gain of an E -plane sectoral horn—a failure of the Kirchhoff theory and a new proposal,” IEEE Trans. Antennas Propag., vol. 22, no. 2, pp. 221–226, Mar. 1974.

Alejandro Iturri-Hinojosa was born in La Paz, Bolivia, on January 20, 1973. He received the degree in electronic engineering from Universidad Mayor de San Andres, La Paz, in 2000, the M.Sc. degree from the Polytechnic Institute of Mexico (IPN), Mexico City, in 2003, and is currently working toward the Ph.D. degree at the National Autonomous University of Mexico (UNAM), Mexico City. His research interests include phased arrays antennas and microwave communication systems.

Jose I. Martinez-Lopez was born in Mexico City, Mexico. He received the B.S., M.Eng., and Ph.D. degrees in electrical engineering from the National Autonomous University of Mexico (UNAM), Mexico City, in 1994, 1998, and 2005, respectively. He is currently a Professor of electrical engineering at UNAM. In 2006, he was with the Schlumberger Technology Center, Sugar Land, TX, developing antennas for deep induction array tools for oil industry. Since September 2009, he has been with the ElectroScience Laboratory at the Ohio State University, Columbus, as a Visiting Scholar. His current research interests are antenna arrays, and microwave and millimeter-wave circuits.

Alexander E. Martynyuk was born in Kiev, Ukraine. He received the M.Sc. degree in radio engineering in 1988 from the Kiev Polytechnic Institute, Ukraine, and the Ph.D. degree in 1993 from the same institute for his work on millimeter-wave devices and subsystems. From 1988 to 1995, he was with the Faculty of Radio Engineering of the Kiev Polytechnic Institute. Since 1995, he has been with the National Autonomous University of Mexico (UNAM), Mexico City, where he is currently a Professor on the Faculty of Engineering. His current research interests include microwave and millimeter-wave devices, antenna arrays and millimeter-wave communications.

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Reduction of Long Line Effects in Single-Layer Slotted Waveguide Arrays With an Embedded Partially Corporate Feed Makoto Ando, Fellow, IEEE, Yasuhiro Tsunemitsu, Member, IEEE, Miao Zhang, Member, IEEE, Jiro Hirokawa, Senior Member, IEEE, and Shusuke Fujii

Abstract—Single-layer slotted waveguide arrays have various advantages such as low cost and mass productivity for fabrication, high gain and efficiency especially in millimeter wave band. They have traveling wave operation and the bandwidth becomes inherently narrower due to the long line effect as the antenna gain increases. This paper proposes the partially corporate feed in the single-layer structure, which inherits the advantage of low cost in fabrication. The bandwidth enhancement as well as the degradation due to the non radiating area in the aperture is assessed. The feasibility/potential of the embedded partially corporate feed is demonstrated by the experiments using the E- to H-plane power divider with very small blockage. Index Terms—Millimeter wave antenna arrays, planar arrays, slot arrays, traveling wave, waveguide arrays.

Fig. 1. An alternating phase-fed single-layer slotted waveguide array (centerfeed).

I. INTRODUCTION

V

ARIOUS wireless communication systems using high gain and wideband antennas have been developed in millimeter wave band such as fixed wireless access (FWA) [1]. A single-layer slotted waveguide array [1], [2] as shown in Fig. 1 consists of only two components, which are the slot plate and the base plate. It is one of the promising candidates for these systems because it has high gain, high efficiency in millimeter wave bands and very low cost due to the simple structure. The high performance in 76 GHz band already supported the potential of these unique arrays in millimeter wave [3]. It works in travelling wave operation with the series feed which is advantageous in terms of design simplicity and low transmission loss [1], [4], [5]. Unfortunately, the bandwidth is inversely proportional to the length of waveguide in travelling wave operation [6]; there is trade-off between antenna gain and bandwidth in the design of single-layer slotted waveguide array; the system specification can not always be met.

Manuscript received June 25, 2009; revised October 28, 2009; accepted November 14, 2009. Date of publication March 01, 2010; date of current version July 08, 2010. This work was supported in part by the “The research and development project for expansion of radio spectrum resources” of the Ministry of Internal Affairs and Communications, Japan. M. Ando, M. Zhang, and J. Hirokawa are with the Department of Electrical and Electronic Engineering, Tokyo Institute of Technology, Tokyo 152-8552, Japan (e-mail: [email protected]; [email protected]; [email protected]). Y. Tsunemitsu is with the Research & Development Center, Japan Radio Co., Ltd., Tokyo 181-8510, Japan (e-mail: [email protected]). S. Fujii was with the Tokyo Institute of Technology, Tokyo 152-8552, Japan. He is now with the Bank of Tokyo Mitsubishi UFJ, Ltd., Tokyo, Japan (e-mail: [email protected]). Digital Object Identifier 10.1109/TAP.2010.2044346

The partially corporate feed is a well known technique for bandwidth enhancement of series fed arrays. The key challenge here is to embed the corporate feed in the layer of the base plate; the array is still single-layer and inherits the advantage of the single-layer waveguide arrays such as mass productivity and high efficiency. Long line effects should be suppressed in two directions (2D) in the aperture; that is along the directions of the feed waveguide and the radiation waveguide in Fig. 1 [7]. Partially corporate feeds for 1D suppression of long line effect have already been introduced in the end feed waveguide [8], [9]. Our objective is to realize broadband single-layer slotted waveguide arrays by two-dimensionally embedding partially corporate feed in the aperture [10], [11]. In this paper, the bandwidth enhancement of the partially corporate feed is assessed in terms of array factor first. To reduce the computational cost for large sized arrays, the radiating elements are replaced with the small dipoles, whose excitation phase varies with the frequency simply due to the change in guided wavelength. Furthermore, the electromagnetic perturbation due to slots is neglected. In this model, the non-radiating area in the aperture or the “blocking area” increases as the corporate feed become prevalent. Large blocking area results in high side-lobe levels and gain reduction of the array. Then the basic and general design criterion for this unique array is assessed with the blocking effects into account. Secondly, waveguide junctions with acceptably small blocking width are proposed for the embedded corporate feed. The electromagnetic design is conducted from the hardware design point of view [10]. Two arrays with small and medium size are fabricated in 25 GHz and 39 GHz bands, respectively. The basic operation

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Fig. 3. Approximation models evaluating the bandwidth associated with the long line effects. (a) Center-feed and (b) partially corporate feed (Corp4).

III. BANDWIDTH ENHANCEMENT OF ARRAY DIRECTIVITY BY INTRODUCING CORPORATE FEED IN THE APERTURE

Fig. 2. Partially corporate feed in a single-layer slotted waveguide array antenna. (a) Center-feed. (b) Partially corporate feed (divided into 4 units: Corp4). (c) Partially corporate feed (divided into 16 units: Corp16).

is verified. The feasibility of embedded partially corporate feed for widening the bandwidth is confirmed [10]. II. EMBEDDED PARTIALLY CORPORATE FEED Fig. 2(b) and (c) show the structure of partially corporate feed embedded in the aperture. Whole the aperture is divided into 4 (Corp4) and 16 units (Corp16) where the number of cascaded cross-junctions and the length of radiating waveguide in each unit is reduced to 1/2 and 1/4, respectively [10]; the long line effect is suppressed two-dimensionally. The “blocking area” increases as the corporate feed become prevalent from Center (a) to Corp4 (b) and Corp16 (c) in Fig. 2. To reduce the “blocking area”, the feed waveguide is arranged with its narrow wall facing to the array aperture. At the same time, E-plane T-junctions and E- to H-plane T- and cross-junctions are specially designed for very small narrow wall width in Section V.

The potential of bandwidth enhancement by introducing partially corporate feed in the aperture is assessed by simple array theory. Fig. 3 shows the approximation models where slots are replaced with small dipole elements and the frequency dependence of the array factor is discussed. The element spacing is . The total number of elements is set to be . The phase error of each element due to long line effects, at shifted frequency, is calculated for the distance from in-phase port of the corporate feed by taking the change of wave length in the waveguide into account. The blocking area over the aperalong the partially ture is defined by the additional spacing corporate feed as is indicated in Fig. 3. The minimum value depends upon the physical dimensions of the feeding for waveguide. is set to zero and As the first step, the additional spacing the effect of blocking is neglected. The bandwidth enhancement by introducing the partially corporate feed is evaluated. The frequency characteristics of directivity are calculated for three types of feeds (Center, Corp4 and Corp16) and presented in the dotted lines in Fig. 4 for various size of the aperture or the . For the center-feed single-layer number of array elements ) bearray, the bandwidth becomes narrower as the array (or comes larger. Therefore, the bandwidth and the gain are related to each other and can not be specified independently. One envelope curve is drawn in the solid line from a set of directivity curves for different aperture sizes for each type of feed. It indicates the upper limit of the available bandwidth vs. the direc-

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Fig. 6. Aperture efficiency as functions of additional spacing. Fig. 4. Frequency characteristics of the highest directivity for various feeds. Each dotted line indicates the frequency characteristics of the directivity for the specific aperture size. The bold solid line is the envelope for the group of dotted lines showing the highest directivity attained by optimizing the aperture size. A, B and C indicate the widest 40 dB directivity bandwidths, realized for Corp16, Corp4 and Center feed respectively.

Fig. 5. Frequency characteristics of the directivity for various feeds and the degradation due to additional spacings.

tivity. For example, for the directivity of 40 dB, the bandwidth is narrower than two points indicated by (C) in Fig. 4. The 4% bandwidth can never been met for the center-feed array irrespective of the aperture size. Fig. 4 also includes the directivity as well as the envelope curves for the arrays with partially corporate feeds. The envelope of the Corp4 and Corp16 is wide banded than that of the center feed; we could push the limits and realize high directivity and wide bandwidth at the same time. For example, at the directivity of 40 dB, the bandwidth limitation of about 2% (C) for the center-feed is enhanced to about 4% (B) and 9% (A) by adopting partially corporate feeds of Corp4 and Corp16, respectively in Fig. 4. IV. DEGRADATION DUE TO NON-RADIATING AREA ABOVE THE EMBEDDED PARTIALLY CORPORATE FEED IN THE APERTURE In practical implementation, embedding the corporate feed in the aperture of single-layer slotted waveguide array causes the non-radiating area associated with the physical dimensions of the feed waveguide and junctions [12]–[14]. The degradation is assessed by the simplified dipole models as functions of the between elements along the feed waveadditional spacing guide, as shown in Fig. 3. The directivity curves for partially corporate feed are lowered by the additional spacing as is shown in Fig. 5. For the arrays with the same number of slots, the prevalence of corporate feed results in larger degradation, while those with the same number of corporate units, the degradation becomes notable for the smaller arrays. It is noted that increase of slightly increases the aperture size and

Fig. 7. Radiation patterns of arrays with partially corporate feed for various spacing.

could enhance the directivity, but in reality, the power loss in growing sidelobes is more dominant and the total gain is reduced in Fig. 5. Fig. 6 summarizes the efficiency degradation for as functions of , at the center frequency. In the conventional H-plane coupler center-feed single-layer slotted is about 0.9 to waveguide array, the additional spacing [12], [13]. The radiation patterns for are shown in Fig. 7 for Corp4. All the far sidelobes are growing up and result in the efficiency reduction. From Fig. 6, the H-plane couloses the gain about 1.2 dB and 3 dB for pler with Corp4 and Corp16 respectively. If the additional spacing is smaller than about , which is realized by introducing the E- to H-plane junction discussed later, the gain reduction is less than 0.5 dB and 1 dB respectively. The sidelobes are in Fig. 7 which accounts for also reduced for the higher directivity, though some sidelobes remain high in E-plane. These imply that the embedding partially corporate feed in the single-layer slotted waveguide arrays is promising provided that the feeding waveguide with additional spacing is adopted. smaller than

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Fig. 10. Reflection Characteristics of each component as well as the whole array. Fig. 8. A 39 GHz Model Array with partially corporate feed Corp4 (400 slots).

Fig. 9. Waveguide components for partially corporate E- to H-plane feed with narrow blockage. (a) Reflection canceling stair (b) E-plane T-junction (c) E- to H-plane cross-junction (d) E- to H-plane T-junction.

V. DESIGN AND MEASUREMENTS OF AN ARRAY WITH AN EMBEDDED PARTIALLY CORPORATE FEED The array with embedded partially corporate feed as in Fig. 8 is fabricated at 39 GHz for the gain of 33 dBi. This is not large enough to highlight the bandwidth enhancement effects of this unique array, as is predicted in Fig. 4. But the basic concept of the array is verified, especially the feasibility of the embedded corporate feed. The aperture consists of four units (Corp4). In each unit, the number of the radiating waveguides is 20 each with 5 radiating slots. Fig. 9(a) briefly schematizes the design of radiating waveguides with slots. The novel structure consists of a set of shunt slot and a broad wall stair which makes a reflection cancelling unit element in the array [16]. It provides us the lower

sidelobes than the standard shunt slot [17]. Total number of slots in the array is 400 (P.Corp.400). The EM design for the various components in the partially corporate feed consisting of E- to H-plane cross-junction as is shown in Fig. 9, is conducted by the FEM analysis (HFSS) [15]. from The wall width b is set to be as small as possible the electrical and mechanical point of views and the reflection [10], [14]. To assess the design of can be kept below the power divider itself, the reflection from the radiation waveguides through the E-to H-plane cross-junctions is neglected first. The reflection of the T-junction in Fig. 9(b) is predicted by HFSS in Fig. 10. The reflection from the partially corporate feed (Corp4) is calculated by connecting the S matrices for the cascaded T junctions. It grows slightly but still remains lower than over the bandwidth of 4%. Fig. 10 also includes the prediction of the reflection from a 10 way power divider consisting of four cascaded E- to H-plane cross-junctions in Fig. 9(c) and and low enough. one shorted end Fig. 9(d). It is below The predicted uniformity of the 10-way power divider is reasonable with the division error smaller than 0.6 dB and 63.7 degree at 39 GHz band (38.0 GHz to 39.5 GHz) for FWA in Japan. As the final evaluation of the whole array with the slots, the reflection from the P.Corp.400 array is analyzed by HFSS and is presented also in Fig. 10. The accumulated reflection is perturbed over due to the reflection from slots but is kept below 4%. If the lower reflection is specified, the fine tuning with the slot coupling taken into account seems indispensable. The measured performance is summarized. The array overall reflection is measured and is presented in Fig. 10. The reflection over 2% bandwidth. Fig. 11 compares the anis below tenna gain. To demonstrate the bandwidth widening effects, the bandwidth of the array at 39 GHz (P.Corp.400) is compared with that of the center feed array with almost the same aperture size; it is observed that the former is wider than the latter. About 1 dB discrepancy of the gain is observed between the prediction and the measurement. The smaller array with 192 slots is also designed using partially corporate feed (P.Corp.192) and measured. Since it is not high gain and is inherently wide banded, the bandwidth enhancement is not clear. However, the better agreement of the measurement and the prediction observed in the Fig. 11, demonstrate the validity of this unique design of the array.

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of the concept are verified by the measurement using small and medium size arrays with embedded partially corporate feed. The partially corporate feed brings about the new design freedom for the single layer waveguide arrays with the travelling wave operation in principle, where the antenna gain and the bandwidth can be independently specified. The advantage of partially corporate feed should be demonstrated for the larger arrays in the future. ACKNOWLEDGMENT The authors acknowledge many years of leadership by Prof. N. Goto. The authors wish to thank JRC for collaboration and fabrication of the model antennas. Fig. 11. Measured and Predicted Antenna Gain of partially corporate feed arrays (Corp4).

Fig. 12. Measured radiation patterns of test array P.Corp.400. (a) E-plane f : (b) H-plane f : .

39 0 (GHz)

= 39 0 (GHz)

=

The E- and H- plane radiation patterns of P.Corp.400 are presented in Fig. 12. The far sidelobes in E-plane are relatively high due to the blocking but it is acceptable in terms of the efficiency. All the measurement results are reasonably predicted by the HFSS and the basic concepts discussed in Sections II and III are supported. VI. CONCLUSION A wideband single-layer slotted waveguide array with an embedded partially corporate feed is proposed as the candidate for the high gain and the wideband antennas for the millimeter wave systems. The bandwidth enhancement of the array as well as the design criterion of this unique array is assessed by using the simple array model, with the change of the guided wavelength taken into account. The degradation associated with the increasing non-radiating area in the aperture above the embedded feed is also evaluated. The feasibility and the reality

REFERENCES [1] Y. Kimura, Y. Miura, T. Shirosaki, T. Taniguchi, Y. Kazama, J. Hirokawa, M. Ando, and T. Shirouzu, “A low-cost and very compact wireless terminal integrated on the back of a waveguide planar array for 26 GHz band fixed wireless access (FWA) systems,” IEEE Trans. Antennas Propag., vol. 53, no. 8, pt. 1, pp. 2456–2463, Aug. 2005. [2] N. Goto, A Waveguide-Fed Printed Antenna 1989, IEICE Tech. Rep., AP89-3. [3] Y. Kimura, M. Takahashi, J. Hirokawa, M. Ando, and M. Haneishi, “An alternating-phase fed single-layer slotted waveguide array in 76 GHz band and its sidelobe suppression,” IEICE Trans. Electron., vol. E88-C, no. 10, pp. 1952–1960, Oct. 2005. [4] M. Ando and J. Hirokawa, “Single-layer slotted waveguide arrays for DBS reception and higher frequency applications,” Electromagnetics, vol. 19, no. 1, pp. 0023–48, Jan.-Feb. 1999. [5] [Online]. Available: http://www.jrc.co.jp/eng/product/26g_fwa/index. html [6] L. Pazin and Y. Leviatan, “Effect of amplitude tapering and frequencydependent phase errors on radiation characteristics of radial waveguide fed non-resonant array antennas,” IEE Microw. Antennas Propag., vol. 151, no. 4, Aug. 2004. [7] A. C. Ludwig, “Low sidelobe aperture distributions for blocked and unblocked circular apertures,” IEEE Trans. Antennas Propag., vol. AP-30, no. 5, pp. 933–946, Sep. 1982. [8] M. Zhang, J. Hirokawa, M. Ando, and N. Goto, “A three-way power divider for partially parallel feed in single-layer slotted waveguide arrays,” IEICE Trans, Commun., vol. E88-B, no. 11, pp. 4339–4345, Nov. 2005. [9] M. Zhang, J. Hirokawa, and M. Ando, “A four-way divider for partially-corporate feed in an alternating-phase fed single-layer slotted waveguide array,” IEEE Trans. Antennas Propag., vol. 56, no. 6, pp. 1790–1794, Jun. 2008. [10] S. Fujii, Y. Tsunemitsu, G. Yoshida, N. Goto, J. Hirokawa, and M. Ando, “Partially corporate feed using E-plane coupler in a single-layer slotted waveguide array,” in IEICE Tech. Rep., AP2007-150, Jan. 2008, pp. 163–168. [11] S. Fujii, Y. Tsunemitsu, G. Yoshida, N. Goto, M. Zhang, J. Hirokawa, and M. Ando, “A wideband single-layer slotted waveguide array with an embedded partially corporate feed,” presented at the ISAP2008, Taipei, Taiwan, Oct. 2008, TP-C27, Paper No. 1645382. [12] S. Park, J. Hirokawa, and M. Ando, “A planar cross-junction power divider for the center feed in single-layer slotted waveguide arrays,” IEICE Trans. Commun., vol. E85-B, no. 11, pp. 2476–2481, Nov. 2002. [13] S. Park, Y. Tsunemitsu, J. Hirokawa, and M. Ando, “Center feed single layer slotted waveguide array,” IEEE Trans. Antennas Propag., vol. 54, no. 5, pp. 1474–1480, May 2006. [14] Y. Tsunemitsu, S. Matsumoto, Y. Kazama, J. Hirokawa, and M. Ando, “Reduction of aperture blockage in the center-feed alternating-phase fed single-layer slotted waveguide array antenna by E- to H-plane cross-junction power dividers,” IEEE Trans. Antennas Propag., vol. 56, no. 6, pp. 1787–1790, Jun. 2008. [15] HFSS Version 10 Manual. California: Ansoft Corporation, 2007. [16] Y. Tsunemitsu, J. Hirokawa, M. Ando, Y. Kazama, and N. Goto, “Single-Layer slotted waveguide array with reflection cancelling stairs,” in Proc. IEEE AP-S Int. Symp. and USNC/URSI National Radio Science Meeting, Session: 405.6, Albuquerque, NM, Jul. 9–14, 2006, pp. 3149–3152. [17] S. H. Park, J. Hirokawa, and M. Ando, “Simple analysis of a slot and a reflection-cancelling post in a rectangular waveguide using only the axial uniform currents on the post surface,” IEICE Trans. Commun., vol. E86-B, no. 8, pp. 2482–2487, Aug. 2003.

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Makoto Ando (SM’01–F’03) was born in Hokkaido, Japan, on February 16, 1952. He received the B.S., M.S., and D.E. degrees in electrical engineering from Tokyo Institute of Technology, Tokyo, Japan in 1974, 1976 and 1979, respectively. From 1979 to 1983, he worked at Yokosuka Electrical Communication Laboratory, NTT, and was engaged in the development of antennas for satellite communication. He was a Research Associate at Tokyo Institute of Technology from 1983 to 1985, and is currently a Professor. His main interests have been high frequency diffraction theory such as physical optics and geometrical theory of diffraction. His research also covers the design of reflector antennas and waveguide planar arrays for DBS and VSAT. Latest interest includes the design of high gain millimeter-wave antennas. Dr. Ando received the Young Engineers Award of IEICE Japan in 1981, the Achievement Award and the Paper Awards from IEICE Japan in 1993 and 2009. He also received the 5th Telecom Systems Award in 1990, the 8th Inoue Prize for Science in 1992, the Meritorious Award of the Minister of Internal Affairs and Communications and the Chairman of the Broad of ARIB in 2004 and the Award in Information Promotion Month 2006, the Minister of Internal Affairs and Communications. He served as the guest editor-in-chief of more than six special issues in IEICE, Radio Science and IEEE AP. He was the general chair of the 2004 URSI EMT symposium in Pisa and of the ISAP 2007 in Niigata. He served as the Chair of the Technical Committee of Electromagnetic theory (2004–2005) and Antennas and Propagation (2005–2007) in IEICE. He served as a member of Administrative Committee of IEEE Antennas and Propagation Society 2004–2006 and also a member of Scientific Council for Antenna Centre of Excellence—ACE in EU’s 6’th framework programme since 2004. He served as the Chair of Commission B of URSI 2002–2005. He was the 2007 President of Electronics Society IEICE and the 2009 President of IEEE Antennas and Propagation Society. He is currently serving as the Program Officer for engineering science group in Research Center for Science Systems, JSPS. He is the Fellow IEEE and IEICE.

Yasuhiro Tsunemitsu (S’05–M’07) was born in Kanagawa, Japan, on September 1, 1976. He received the B.S. degree in electrical engineering from Takushoku University, Tokyo, Japan in 2000, the M.S. degree in electrical and electronic engineering from Yokohama National University, Yokohama, Japan in 2002, and the D.E. degree in electrical and electronic engineering from Tokyo Institute of Technology, Tokyo, Japan in 2007. Since 2002, he has worked at Japan Radio Co., Ltd. His current research area is in analysis of slotted waveguide array antennas. Dr. Tsunemitsu received the First Prize and Business Plan Award presented at the 3rd IEEE Tokyo Young Researchers Workshop in 2006. He received the Young Researcher Encouragement Prize from IEICE Antenna and Propagation Society in 2007. He received the IEEE AP-S Japan Chapter Young Engineer Award from IEEE Japan Chapter Antennas and Propagation Society in 2008. He is a member of The Institute of Electronics, Information and Communication Engineers (IEICE) JAPAN, The Institute of Electrical and Electronics Engineers (IEEE), The Applied Computational Electromagnetics Society (ACES), and The Institution of Engineering and Technology (IET).

Miao Zhang (S’05–M’09) was born in Liaoning, China, on June 5, 1979. He received the B.S., M.S., and D.E. degrees in electrical and electronic engineering from Tokyo Institute of Technology, Tokyo, Japan in 2003, 2005 and 2008, respectively. From 2005 to 2008, he was a Research Fellow of the Japan Society for the Promotion of Science (JSPS). His current research interests include electromagnetic analysis and planar waveguide arrays. He received the Best Letter Award from Communication Society of IEICE Japan in 2009.

Jiro Hirokawa (S’89–M’90–SM’03) was born in Tokyo, Japan, on May 8, 1965. He received the B.S., M.S., and D.E. degrees in electrical and electronic engineering from Tokyo Institute of Technology (Tokyo Tech.), Tokyo, Japan, in 1988, 1990, and 1994, respectively. He was a Research Associate from 1990 to 1996, and is currently an Associate Professor at Tokyo Tech. From 1994 to 1995, he was with the antenna group at Chalmers University of Technology, Gothenburg, Sweden, as a Postdoctoral Fellow, on leave from Tokyo Tech. His research area has been in analyzes of slotted waveguide array antennas. Dr. Hirokawa is a Member of the Institute of Electronics, Information and Communication Engineers (IEICE), Japan. He received an IEEE AP-S Tokyo Chapter Young Engineer Award in 1991, a Young Engineer Award from IEICE in 1996, a Tokyo Tech. Award for Challenging Research in 2003, and a Young Scientist Award from the Minister of Education, Cultures, Sports, Science and Technology of Japan in 2005.

Shusuke Fujii was born in Fukuoka, Japan, on April 6, 1984. He received the B.S. and M.S. degrees in electrical and electronic engineering from Tokyo Institute of Technology (Tokyo Tech.), Tokyo, Japan in 2007 and 2009, respectively. He works for the Bank of Tokyo Mitsubishi UFJ, Ltd., Tokyo, Japan. Mr. Fujii received the JRC special prize at the 4th IEEE Tokyo Young Researchers Workshop in 2007.

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Minimization of MEMS Breakdowns Effects on the Radiation of a MEMS Based Reconfigurable Reflectarray Hassan Salti, Erwan Fourn, Raphaël Gillard, and Hervé Legay

Abstract—We present an investigation of MEMS breakdowns effects on the radiation pattern of a MEMS based reconfigurable reflectarray. In addition, a correction procedure is proposed to minimize phase errors due to breakdowns. It takes advantage of the numerous possibilities offered by the refectarray’s cell to achieve a given phase shift. Furthermore, a systematic methodology is proposed to assess cell’s robustness to breakdowns by defining a cumulative root mean square error accounting for any possible MEMS failure. It is shown to provide a convenient means of comparing different possible cell topologies. Finally, it is also used to minimize the number of MEMS in the cell while preserving the necessary redundancy to limit phase errors. Index Terms—Breakdowns, MEMS, reconfigurable reflectarray, robustness.

Fig. 1. MEMS controlled planar phase-shifting cell used in Ku-band and manufactured on alumina substrate (relative permittivity: 9.8; thickness: 254  ).

m

I. INTRODUCTION reflectarray consists of a feeding antenna illuminating a planar microstrip array, whose radiation is controlled by the phase shift at each element in the aperture [1]. Recently, many researches have been carried out to control dynamically the phase shift at each element in the array in order to obtain reconfigurable reflectarrays [2], [3]. MEMS based phase-shifting cells are key elements for such applications [4] due to the excellent radio-frequency (RF) properties of MEMS technology (low insertion loss, low power consummation, high isolation, etc.). MEMS are usually used as switches to control the physical length of resonating elements such as stubs or slots [5], [6]. However, the level of reliability of RF MEMS is still a major issue. Their use in reflectarrays, especially in harsh environments like space, is still problematic due to their relatively low life time [7]. MEMS breakdowns can then be responsible for severe phase errors in the radiation aperture resulting in large deformations in the radiation patterns. It has been shown that the effect of MEMS breakdowns can be reduced by increasing the number of MEMS in the cell [8]. This

A

Manuscript received June 16, 2009; revised January 27, 2010; accepted January 31, 2010. Date of publication April 26, 2010; date of current version July 08, 2010. This work was supported by the Research Minister of France within the context of the ANR project (Agence Nationale de la Recherche) entitled R3MEMS. H. Salti, E. Fourn, and R. Gillard are with the Electronic and Telecommunications Institute of Rennes IETR, INSA of Rennes, 35043 Rennes, France (e-mail: [email protected]). H. Legay is with the Research and Development Department, Thales Alenia Space, 31037 Toulouse, France (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/TAP.2010.2048861

creates redundancy that permits to achieve the same phase shift with different combinations of MEMS states. Unfortunately, this also increases the complexity of the design, especially the biasing and control of the switches. Consequently, a trade-off has to be found between redundancy and complexity. In a first section of this paper, we investigate the effects of MEMS breakdowns on the radiation pattern of a MEMS based reconfigurable reflectarray. Hence, we define the maximum percentage of MEMS breakdowns beyond which radiation pattern’s deterioration is unacceptable. Then, we prove that by using a phase error correction procedure we can largely increase this percentage. This procedure uses the phase redundancy in the phase shifting cell. Its efficiency directly relies on the cell capability to yield the same phase with different MEMS combinations. This property is very dependant on the number of MEMS in each cell and also on their position. In a second section, we propose a methodology to assess the performance of the phase shifting cell and more precisely its robustness with regards to possible MEMS breakdowns. Indeed, a quantitative factor is defined that quantifies the average phase error for any combination of MEMS breakdowns and any desired phase shift. Then, this quantitative factor is used to optimize the position and number of MEMS in a cell while preserving the necessary redundancy for minimizing the effects of MEMS breakdowns. II. PHASE-SHIFT ELEMENT The phase shifting element used in this paper is a realistic cell published in [5] and validated in [8]. It consists of a patch element loaded with two slots controlled by a set of 10 MEMS switches (cf. Fig. 1). MEMS switches are used to control the length of the slots thus adjusting the phase of the reflected wave.

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Fig. 4. Reflectarray configuration (F

0:8).

= 753:6 mm; D = 942 mm; F=D =

Fig. 2. Cell’s characteristic.

Fig. 5. Breakdowns effect on radiation pattern (typical example).

Fig. 3. Redundancy in the shift cell.

Assuming all MEMS working properly, the position of these MEMS has been optimized in [9], [10] in order to provide a smooth coverage of the required 360 phase range. Fig. 2 ildiflustrates the obtained phase shifts for the ferent MEMS combinations. In the following, this curve representing phase shifts versus MEMS combinations is named « Cell’s Characteristic (CC) ». The proposed phase shifting cell presents a remarkable redundancy since one phase shift could be achieved with various different MEMS combinations. Fig. 3 shows the number of possible combinations to achieve any phase shift in the inassuming a accuracy. All phase shifts can terval be reached with at least three different combinations and more than 200 solutions are available for some of them. This redundancy is very useful for minimizing MEMS breakdowns effects (as will be shown in the following). III. MEMS BREAKDOWNS EFFECTS ON RADIATION’S PATTERN A. Test Case Reflectarray In order to assess the effect of MEMS breakdowns on the array radiation pattern, a typical test-case reflectarray is defined. It consists of a circular reflectarray containing 1436 phase-shifting elements working at 14 GHz central frequency. , the diameter The inter-element spacing is and where F is the of the array is

distance from the horn phase centre to the centre of the array. For simplicity, the array is illuminated by a central horn with a 12 dB tapering at the outline of the array (cf. Fig. 4). The phase law in the radiation aperture is fixed for broadside radiation. The needed phase shift on each cell is approximated to the nearest phase-shift in the CC. The corresponding normalized array factor is given in Fig. 5 (No breakdowns curve) and will be considered in the following as the reference for the estimation of the radiation pattern’s deformation. B. Introducing MEMS Breakdowns Phase shifts in the radiation aperture are achieved by choosing the appropriate combination of MEMS switches in each phase shifting cell. The phase law is so translated to a combinations’ law that defines the state of all MEMS switches in the aperture (each combination contains the state of the 10 MEMS for one cell). Without any breakdowns, this combinations’ law produces the specified phase law and so the specified radiation pattern. In our study, capacitive MEMS are used. For such switches, we expect only two main configurations of failure as in [11]. The first one is that the cantilever beam of the MEMS actuates and returns to the up-state position, irrespective of the polarity of the applied voltage. The second failure mechanism is due to charge injection in the dielectric layer and results in the beam remaining in the down-state position when the actuation voltage is removed [12]. Hence, when MEMS breakdowns occur, some MEMS switches are fixed on an unchangeable state (Up or Down) and they are no longer available for phase control. This means that the combinations’ law does not produce

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the desired phase law anymore. On the contrary, an erroneous phase law results with random errors (up to 180 for the worst cases) in all cells with faulty MEMS. We note here that capacitive MEMS can suffer from other failure mechanisms such as partial sticking. As a result, intermediate values of the capacitance (between the up and down state) may be obtained. In most cases, these faulty intermediate states can be brought close to one of the two considered breakdowns. For instance, partial sticking can usually be forced to down-state failure by applying an additional voltage. More generally, the problem of intermediate states can be addressed by introducing and . It is some level of uncertainty on the values of shown in [13] that the sensitivity of the result to these interme) can be largely diate states (especially the tolerance on improved by eliminating MEMS combinations with larger frequency dispersions.

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Fig. 6. Deterioration curves before and after introducing correction algorithm.

C. Effects of Breakdowns on the Radiation Pattern In simulations, MEMS breakdowns are accounted for by enforcing a percentage of arbitrary fixed states in combinations’ law (the position and state of fixed MEMS are chosen arbitrary). The resulting array factor is calculated and compared to the reference array factor. Fig. 5 shows an example of the pattern’s deterioration after introducing 15% of MEMS breakdowns in the reflectarray. We see that 15% of random breakdowns result in a severe degradation of the radiation pattern. However, the modification of the radiation pattern depends on the very repartition of phase errors in the aperture. It is not only related to the number of fixed MEMS but also to their position and states. As a consequence, two identical percentages of MEMS breakdowns with different repartitions can result in different repartitions of phase errors and finally to different modifications of the radiation pattern. As a result, a statistical analysis is required. D. Deterioration Curves The proposed statistical analysis is carried out as follows. For a given percentage of breakdowns, 100 random repartitions are considered and the corresponding array factors are calculated. The percentage of patterns that do not comply with specified requirements is then determined. For the present study, a pattern is said to be out of specifications if: — side lobes are higher than 18 dB; — reduction in main lobe (compared to the reference case) is larger than 0.3 dB. A “deterioration curve” is then defined as the percentage of wrong repartitions (that give an unacceptable radiation pattern’s modification) versus the percentage of breakdowns. Fig. 6 (without correction) shows a quick increase in the percentage of radiations out of specifications when the percentage of breakdowns gets larger than 1.5%. As the transition is very sharp, this value can be seen as the absolute maximum percentage of acceptable MEMS breakdowns. This number is quite small. In some extent, this is due to the large number of MEMS in each cell: if we assume a uniform distribution of breakdowns, 1.5% breakdowns correspond to 15% faulty cells (for which the achieved phase is random). On the other hand, we can take benefit of the large number of MEMS

per cell to derive a phase correction procedure as explained in the next section. E. Phase Correction Procedure The proposed correction procedure consists in minimizing phase errors by updating the state of the remaining normally working MEMS in each erroneous cell. In fact, a cell containing P breakdowns still has N-P commendable MEMS (where N is the total number of MEMS in the combinations to tune the phase. As cell), which gives a result, a reduced cell’s characteristic (RCC) can be defined to replace the original CC. Then, the correction procedure consists in choosing from the RCC the combination that best fits the required phase. to In other words, if the achieved phase shift moves from due to breakdowns, the state of available MEMS is modified is replaced by where is the smallest until achievable phase error with (10-P) operating MEMS in the cell. As an example, Fig. 7 shows the RCC for a cell containing breakdowns. As can be seen, only 128 combinations are available (instead of 1024 initially). Moreover, due to the non uniform distribution of errors, the achievable phase range is also affected. For instance, a gap can be observed between is 301 and 328 and so the best approximation of . Most of other phases can be reached with a very good accuracy. Fig. 6 shows the application of the correction procedure to the studied array. It shows that the maximum acceptable number of MEMS breakdowns can be moved from 1.5% to 23%. This proves the effectiveness of our algorithm and the importance of redundancy in MEMS-based reconfigurable reflectarray’s cell. An important issue is that the correction procedure can only be used if the position and state of the faulty MEMS can be identified. Recently many researches have been carried out to assess the reliability of MEMS switches and detect their failures. Some of them use RF test signals and a superimposed bias voltage [14], others use low frequency techniques where the monitoring is done through the bias input [15], [16]. These last techniques are very interesting and promising especially as they have no impact on the initial RF design.

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Fig. 7. Reduced cell’s characteristic (RCC) of a cell with P = 3 breakdowns.

Fig. 8. Strongly distorted RCC with large gap between 252 and 360 of a cell with P = 3 breakdowns.

On the other hand, it is essential to notice that this study focus on reflectarrays for spatial communications for which reconfiguration is only expected to occur four to five times in an average 20 years lifetime [8], [17]. In such applications, MEMS failure detection and correction can be a slow process fully compatible with onboard processing.

The RMSE is finally defined as the averaged error when successively trying to produce all the possible phase, as in

IV. REFLECTARRAY CELL’S ROBUSTNESS The proposed correction procedure relies on the redundancy that makes it possible to reach the same phase using different MEMS combinations. This property is very dependant on the cell topology itself (number and position of MEMS). We now propose a systematic methodology to assess the potentialities of a candidate cell and finally optimize its topology. To do so, a quantitative criterion is defined to assess the robustness of the cell.

(1) A breakdown combination that leads to a large error corresponds to a strongly distorted RCC (as the one shown in Fig. 8 where a large gap in the phase range is observed). 2) Step 2: Calculating CRMSE: At the end of step 1, we values of RMSE noted (associated to have ). The second step of the calculation simply the different consists in defining the global CRMSE, as in

(2)

A. Cumulative Root Mean Square Error Cumulative Root Mean Square Errors (CRMSE) is defined as the mean phase error resulting from all random combinations of P faulty MEMS in a given phase shifting cell. It is computed as the averaging of phase errors for all possible required phases when P arbitrary breakdowns are encountered. P breakdowns in an N-MEMS cell generate equi-probable different combinations of breakdowns and so RCC (noted where “ ” is an index that ). In practice, a 2-step calculation is varies from 1 to required in order to calculate the resultant mean phase error. 1) Step1: Defining RMSE of an RCC: The first step consists in defining the root mean square error (RMSE) for any . To do so, we successively consider all posof the and we evaluate the nearest sible required phases achieved values that can be obtained from . In this paper, we assume a 1 accuracy which means the cell can be asked to produce any of the 360 values in the set . As we have seen in Section III-E, is the phase that best matches among available phases associated to the considered . the

B. CRMSE as Criterion of Robustness By definition, the CMRSE quantifies the average phase error that can be expected from a given phase shifting cell and for a given number of faulty MEMS in the cell whatever the targeted phase and whatever the fixed state and location of the faulty MEMS. In a large reflectarray, it is assumed that all phases are equi-probable and that the distribution of MEMS breakdowns is uniform over the radiating aperture. As a consequence, thanks to ergodism, the CMRSE should also reflect the performance of any large reflectarray built by using the considered phase shifting cell. In order to enforce this conclusion, three different cells with 9 MEMS have been defined. These cells derive from the initial 10-MEMS cell by eliminating one different MEMS in each (cf. Fig. 9). We then define three different reflectarrays, each of them being built with only one of the three considered cells. The geometry and configuration of the reflectarrays are the same as for the test-case reflectarray (presented in the Section III-A). For each case, the deterioration curve is plotted in Fig. 10(a) in order to estimate the acceptable percentage of MEMS breakdowns. It

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Fig. 9. Different cell’s configurations (N = 9).

Fig. 11. CRMSE of all DC (N = 10, M = 9, P = 1 to 5).

This is an important conclusion as the analysis of the cell (using CRMSE) can be done independently of the configuration of the array. It only requires a few minutes while the statistical analysis of random errors in an array requires up to 6 hours (using a 2 GHz Pentium 4 with 2 GBytes of RAM). Furthermore, if we go deeper in the analysis of Fig. 10(b), and intersects at we can see that CRMSE curves of . This means that these cells present the same efficiency when only one breakdown is present (whatever the location of behaves better for a larger number this breakdown) while of breakdowns. Hence, should be preferred in cases where MEMS reliability is poor. At the contrary, it should be noticed that no intersection can be seen in deterioration curves [Fig. 10(a)]. This is because the sharp transitions in these curves is observed for percentages larger than 11,1% (which corresponds to one average breakdown in each cell). V. OPTIMIZING PHASE SHIFT CELL’S ROBUSTNESS

Fig. 10. Robustness of three different phase-shifting cells, (a) deterioration curves, (b) CRMSE.

shows that the maximum percentage of permitted breakdowns is 11% for reflectarray using , 17% for reflectarray using and 22% for that using . Secondly, we determine the CRMSE for each of these cells when the number of breakdowns in the cell varies from 1 to 5 is the most robust one while (Fig. 10(b)). It shows that is the worst. This result is consistent with the one obtained by analyzing the array. As a consequence, the CRMSE can be seen as an actual criterion to estimate the robustness of a MEMS-based phase-shifting cell and of the derived reflectarrays.

Since CRMSE appears as a reliable criterion to assess cell’s robustness, it can be used in an optimization process in order to choose appropriate positions and number of MEMS in a phaseshifting cell while preserving the necessary redundancy to limit the effects of breakdowns. The optimization process starts with an over estimated number of MEMS per cell (N). The optimal configuration can then be reached by removing the less effective switches, until the CRMSE overpasses a given threshold. be the number of remaining MEMS in the Let M cell after eliminating N-M MEMS. The most robust cell among M-MEMS cells is determined as the one with all possible best CMRSE. The process is repeated by decreasing M until the required robustness cannot be reached anymore. As a simple illustration, we have applied the optimization . The maximum reprocess to our test case cell where breakdowns quired CRMSE is arbitrary fixed to 50 for in the cell. As a first step, M is fixed to 9. By removing MEMS from the initial cell, 10 derived cells named (where k varies from 1 to 10) are produced with 512 combinations to tune the phase. For each DC, the CRMSE curve is calculated (P varies from 1 to 5) and presented in Fig. 11. The . most robust cell is the one having the least CRMSE, i.e.

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Moreover, we can deduce from Fig. 12 that the optimized cell MEMS behaves better than non optimized ones with and in Fig. 11. That means with 9 MEMS such as that, in MEMS based reconfigurable reflectarrays, the phaseshifting cell should be optimized by choosing the appropriate number and position of MEMS in the cell in order to minimize the complexity and the cost of the reflectarray while preserving the necessary redundancy to limit MEMS breakdowns effects. VI. CONCLUSION

Fig. 12. Optimized configurations (N

In this paper, the effect of MEMS breakdowns in reconfigurable reflectarrays has been studied. It has been shown that 1.5% MEMS breakdowns over the array can be responsible for a complete failure of the antenna. This is a major issue as MEMS reliability is still a concern. However, a correction procedure has been proposed that permits to increase the percentage of breakdowns up to 23%. A quantitative factor has also been defined to assess and compare the robustness of different cell topologies. Consequently, a derived methodology has been proposed to optimize the number and position of MEMS switches in the cell for both improved performance and reduced cost. As an illustration, an 8-MEMS cell has been obtained with better performance than its 9-MEMS counterpart. Future works will focus on the applicability of MEMS failure detection techniques (using both DC and RF approaches) in order to make the correction procedure feasible.

= 8 to 10, P = 1 to 5)

ACKNOWLEDGMENT The authors would like to thank reviewers of this paper for their comments and suggestions. Fig. 13. Linearization of the CC using robustness optimization (N M = 9).

= 10,

Moreover, the corresponding robustness curve still outperforms as the reached error is less than 40 (Fig. 12, ). This means another MEMS may be suppressed. A second step of optimization is then applied. At the second step we remove 2 MEMS from the initial cell. DC (with 128 Hence, M is fixed to 8, this produces combinations to tune the phase) for which we calculate again CRMSE. The most robust one is presented in Fig. 12 . Its CRMSE curve approaches the requirement and so the optimization process can be terminated. Furthermore, we have seen in Fig. 3 that redundancy in the initial 10 MEMS’ CC was not uniform. This means that the ability of this cell to correct phase errors was not equivalent for all phase values. Hence, the optimization process can be seen as a means of balancing the phase distribution all over the 360 range. By removing the less effective MEMS regarding robustness, it minimizes the high redundant areas in the initial CC and results in a more linear CC. For instance, let us come back to MEMS. Fig. 13 shows the optimization iteration where , and a comparison between the CC of the best derived cell, . We clearly see improves the linearity the worst one, of the CC.

REFERENCES [1] J. Huang and J. A. Encinar, Reflectarray Antennas, ser. Wiley-Interscience. New York: Wiley, 2007, pp. 34–35. [2] H. Rajagopalan, Y. Rahmat-Samii, and W. A. Imbriale, “Reconfigurable patch-slot reflectarray elements using RF MEMS switches: A subreflector wavefront controller,” in Proc. IEEE Antennas and Propagation Society Int. Symp., Jun. 9–15, 2007, pp. 5023–5206. [3] W. Hu, M. Y. Ismail, R. Cahill, H. S. Gamble, R. Dickie, V. F. Fusco, D. Linton, S. P. Rea, and N. Grant, “Tunable liquid crystal reflectarray patch element,” Electron. Lett., vol. 42, no. 9, pp. 509–511, Apr. 27, 2006. [4] J. Peruisseau-Carrier and A. K. Skrivervik, “Monolithic MEMS-based reflectarray cell digitally reconfigurable over a 360 phase range,” IEEE Antennas Wireless Propag. Lett., vol. 7, pp. 138–141, 2008. [5] H. Legay, G. Caille, P. Pons, E. Perret, H. Aubert, J. Pollizzi, A. Laisne, R. Gillard, and M. Van Der Worst, “MEMS controlled phase-shift elements for a linear polarized reflectarray,” in Proc. 28th ESA Antenna Technology Workshop on Space Antenna Systems Technologies, The Netherlands, May 20–31, 2005, pp. 443–448. [6] J. Papapolymerou, K. L. Lange, C. L. Goldsmith, A. Malczewski, and J. Kleber, “Reconfigurable double-stub tuners using MEMS switches for intelligent RF front-ends,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 1, pp. 271–278, 2003. [7] O. Vendier, Y. Cailloce, R. Barbaste, M. Paillard, C. Drevon, J. C. Cayrou, H. Legay, G. Caille, and J. L. Cazaux, “Need for robust RF MEMS in future space applications,” presented at the 4th MEMSWAVE, Toulouse, France, Jul. 2–4, 2003. [8] H. Legay et al., “Satellite antennas based on MEMS tunable reflectarrays,” in Eur. Conf. on Antennas and Propagation EuCAP 2007, Edinburgh, U.K., Nov. 11–16, 2007, pp. 1–6. [9] E. Perret, N. Raveu, H. Aubert, and H. Legay, “Scale changing technique for MEMS-controlled phase-shifters,” in Proc. 36th European Microwave Conf., Manchester, U.K., Sep. 2006, pp. 866–869.

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[10] N. Raveu, G. Prigent, H. Aubert, P. Pons, and H. Legay, “Scale changing technique design and optimization tool for active reflectarrays cell,” in Proc. 37th European Microwave Conf., Munich, Germany, Oct. 2007, pp. 983–986. [11] J. R. Reid, “Dielectric charging effects on capacitive MEMS actuators,” presented at the IEEE MTT-S Int. Microwave Symp. RF MEMS Workshop, Jun. 2002. [12] G. M. Rebeiz, RF MEMS Theory, Design, and Technology, ser. WileyInterscience. New York: Wiley, 2003, pp. 185–188. [13] H. Salti, E. Fourn, R. Gillard, E. Girard, and H. Legay, “Pharmacist cross phase-shifting cell loaded with MEMS switches for reconfigurable reflectarrays,” presented at the Eur. Conf. on Antennas and Propagation EuCAP 2010, Barcelona, Spain, Apr. 2010. [14] C. Goldsmith and J. Ehmke et al., “Lifetime characterization of capacitive RF MEMS switches,” in IEEE Int. Microwave Symp. Digest, Piscataway, NJ, 2001, pp. 227–230. [15] W. M. Van Spengen and R. Puers et al., “A low frequency electrical test set-up or the reliability assessment of capacitive RF MEMS switches,” J. Micromechan. Microeng., vol. 13, pp. 604–612, 2003. [16] S. Lee and R. Ramadoss et al., “Reliability testing of flexible printed circuit-based RF-MEMS capacitive switches,” Microelectron. Reliab., vol. 44, no. 2, pp. 245–250, 2004. [17] O. Vendier and M. Paillard et al., “Main achievements to date toward the use of RF MEMS into space satellite payloads,” in Proc. of the European Microwave Conf., 2005, pp. 285–288.

Hassan Salti was born in Tripoli, Lebanon, in December 1984. He received the Eng. Dipl. degree from the Lebanese University, Faculty of Engineering, Tripoli, Lebanon, in 2007. In 2007, he joined the Institut National des Sciences Appliquées, Rennes, France, as a Ph.D. student. His research activities concern the study analysis, the design and the optimization of reconfigurable reflectarray antennas based on MEMS switches for spatial communications. He also studies new conceptions of passive and active reflectarray cells.

Erwan Fourn was born in Brest, France, in April 1977. He received the Ph.D. degree in electronics from the Université de Bretagne Occidentale (UBO), Brest, France, in 2004. He was a Postdoctoral Fellow at the Laboratoire d’Analyse et d’Architecture des Systèmes (LAASCNRS), Toulouse, France, and is currently an Assistant Professor within the Institut National des Sciences Appliquées, Rennes, France. His research activities within the Institut d’Electronique et de Télécommunications de Rennes (IETR), are mainly fo-

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cused on the design of reconfigurable antennas and filters for microwave and millimeter waves applications.

Raphaël Gillard was born in July 1966. He received the Ph.D. degree in electronics from the National Institute of Applied Sciences (INSA), Rennes, France, in 1992. He first worked as a Research Engineer at IPSIS, France, developing a commercial MoM code for the simulation of microwave circuits and antennas. He joined INSA in 1993 as an Assistant Professor. Since 2001, he has been a Full Professor in the Antenna and Microwave Group of the Electronics and Telecommunications Institute of Rennes (IETR) where he was in charge of the EM Modeling and Optimization activity. Since 2006, he has been leading the Antenna and Microwave Group with Professor Himdi. At the moment, his main research interests are computational electromagnetics and reflectarrays. He is the coauthor of 130 conference papers, 44 journal papers and six patents. He also contributed to a book about active antenna modules. He has been involved in numerous research projects with industries (Thales Alenia Space, Orange Labs, Thales Airborne Systems, Nortel Communications, Thomson) and research centers (French and European Space Agencies, CNES and ESA). Prof. Gillard was a member of both the Executive and Governing Boards of the European Antenna Centre of Excellence (ACE), from 2004 to 2008. He was co-leader of its Antenna Software Activity (in charge of the software benchmarking work-package). He is a member of several Scientific Committees and Review Boards (EuCAP, EuMC, ...). He is also Chairman of the Antenna and Propagation sub-committee of the French National Microwave Conference (JNM) and Co-Chairman of the French URSI-B section.

Hervé Legay was born in 1965. He received the Electrical Engineering degree and the Ph.D. degree from the National Institute of Applied Sciences (INSA), Rennes, France, in 1988 and 1991, respectively. For two years, he was a Postdoctoral Fellow at the University of Manitoba,Winnipeg, Canada, where he developed innovating planar antennas. He joined Alcatel Space, Toulouse, France, in 1994, which is now Thales Alenia Space. He initially conducted studies in the areas of military telecommunication advanced antennas and antenna processing. He designed the architecture and the antijamming process of the Syracuse 3 antenna, He currently leads research projects in integrated front ends and reflectarray antennas and coordinates the collaborations with academic and research partners in the area of antennas. He is first author of 14 patents. Dr. Legay is a co-recipient of the 2007 Schelkunoffprize Paper Award. He received the Gold Thales Award in 2008, rewarding the best innovations in the Thales group.

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Band Rejection Methods for Planar Log-Periodic Antennas Joseph R. Mruk, Student Member, IEEE, W. Neill Kefauver, Senior Member, IEEE, and Dejan S. Filipovic, Senior Member, IEEE

Abstract—Full-wave modeling and measurements are utilized to propose three band rejection techniques integrated with a multioctave wideband planar log-periodic antenna. Antennas presented in this paper are designed to operate between 1.8 and 11 GHz with rejection at 6 GHz. Demonstrated band-rejection techniques include the removal of resonant teeth also referred to as aperture rejection, integration of a dual band filter, and combination of the two above techniques. Aperture rejection is shown to produce greater than 25 dB realized gain reduction. Integrated filter and combined methods achieve over 30 dB and 55 dB rejections, respectively. Antennas are fabricated on a 0.508 mm RT/Duroid 6002 substrate and excellent agreement between theory and measurements is obtained. Index Terms—Dual band, integrated filter, log periodic antenna, multiple band.

I. INTRODUCTION

O

VER THE past few years there has been a strong interest in antennas capable to reject narrow frequency bands within their nominally wideband instantaneous bandwidth. Particular emphasis is placed on a 3.1–10.6 GHz ultrawideband (UWB) systems where the suppression of IEEE802.11a WLAN band of 5.15–5.85 GHz is often desired. Several antenna examples that have their configuration modified for single or multiple band rejections are discussed in [1]–[4]. Band rejection is commonly achieved by adding (anti)resonant features to the antenna aperture and/or by integrating cavities. An increased VSWR with typical values of 6:1 to 10:1 are considered to be demonstrative of the desired effect. Desired band rejection has also been demonstrated by integrating various types of filters with an antenna [5]–[7]. Microstrip, coupled line, and waveguide filters are shown to produce band rejection of up to 20 dB. Planar log-periodic antennas were originally introduced by DuHamel and Isbell in 1957 [8]. It has been shown that these radiators have electrical properties that repeat logarithmically Manuscript received August 09, 2009; revised November 27, 2009; accepted January 15, 2010. Date of publication April 26, 2010; date of current version July 08, 2010. This work was sponsored by the Office of Naval Research under Grant #N00014-07-1-1161. J. R. Mruk and D. S. Filipovic are with the Department of Electrical, Computer, and Energy Engineering, University of Colorado, Boulder, CO 803090425 USA (e-mail: [email protected]; [email protected]). W. N. Kefauver is with the Department of Electrical, Computer, and Energy Engineering, University of Colorado, Boulder, CO 80309-0425 USA and also with Lockheed Martin Space Systems Company, Denver, CO 80201 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/TAP.2010.2048873

Fig. 1. Fabricated antennas with different band rejection implementations: aperture rejection (bottom left), integrated filter rejection (top left), and combined rejection (bottom right).

with frequency and are capable of achieving multiple octave bandwidths. The upper frequency limit is defined by the finite size of the feed region while the lower frequency cut-off is dependent on the length of the outermost teeth. They have been used in various communications and electronic warfare systems, and some researchers have recently considered them for UWB applications [9], [10]. In all these applications the band rejection remains important as the primary method for reducing the receiver saturation and interference from/with nearby antennas and systems. An aperture rejection approach based on a pair of metallic stubs embedded in the vertical slots of a UWB log-periodic antenna has been proposed in [10]. A VSWR of 3.5:1 and little discussion on far-field effects are reported. In this paper, we demonstrate several band rejection techniques integrated with 1.8–11 GHz wideband planar log-periodic antennas. Discussed methods include aperture rejection by removing resonant teeth, integrated filter rejection, and combined aperture/integrated filter rejection. Analysis and modeling are conducted with Ansoft’s HFSS [11], and all articles are fabricated on a 0.508 mm thick RT/Duroid 6002 substrate (see Figs. 1 and 2). Measurements are conducted in the far-field range at Lockheed Martin Space Systems Company in Waterton, CO. A log-periodic slot embodiment allows for a microstrip feed line to be integrated on the back side of the antenna aperture, thus enabling a single process antenna/feed-line/filter fabrication. Microstrip feeders include an impedance transformer that

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Fig. 2. Fabricated antennas featuring integrated filter rejection (left), aperture rejection (center), and combined rejection (right).

matches the nominal antenna impedance of 160 to 50 . Aperture rejection method results in simple implementation, reduced size, flexible single or multiple band rejection, and non-periodic nature of the rejection bands. It is done by removing a pair of resonant teeth from the antenna. VSWR greater than 13:1 and realized gain reduction greater than 25 dB are measured. Integration of a distributed element dual-band-pass filter is shown to provide a 50:1 VSWR and greater than 30 dB reduction in realized gain. Finally, these two techniques are combined to achieve greater than 55 dB rejection in measured realized gain at 6 GHz. This paper is organized as follows. • Aperture rejection method is introduced and discussed in Section II. Measurements and simulations are used to demonstrate important features of this method; • Integrated filter rejection approach is discussed in Section III. Filter design, integration, and different topologies are evaluated; • In Section IV, aperture and integrated filter approaches are combined to demonstrate very high co-polarized gain rejection; • Rejection method comparisons and additional application venues are discussed in Section V. II. APERTURE REJECTION Log-periodic antennas have multiple teeth which lengths directly determine corresponding, log-periodically distributed resonances [12]. This property is used to propose tooth removal as a band rejection method. A self-complementary planar log-periodic slot antenna with a backside integrated microstrip feed line and a pair of resonant teeth removed is shown in Fig. 3. A via is drilled through the substrate and is used to connect the feed line to the radiator. The gap located in the central feed region is 0.508 mm (20 mil) is shown in Fig. 3. This feed is used for all antennas discussed in this paper. The wide angle is chosen to allow for easier integration of a microstrip feed line. Booker’s extension of Babinet’s principle [13] predicts the nominal impedance of a free-standing structure to be about 188 . However, the finite size and metallization thickness, as well as the presence of the dielectric reduce this value to about 160 . Shown in Fig. 4 are computed and measured VSWR of the antenna from Fig. 3. As seen, the teeth removal results in a in the region where the measured peak teeth are resonant. At the same time, the antenna remains well

Fig. 3. Planar, slot log-periodic antenna with the 9th pair of teeth (from the center) removed. Geometry parameters used to describe the structure are: , : , ,R : ,r : .

45

= 0 828 = 135

= 53 2 mm

= 5 03 mm

Fig. 4. Measured and simulated VSWR (with respect to 50 shown in Fig. 3.

=

) of antenna

Fig. 5. The layout and dimensions (in mm) of a four step impedance transformer printed on the back side of the antenna shown in Fig. 3. The characteristic impedances from the left (antenna center) to the right (outside) are 126 , 104 , 86 , 61 , and 50 .











matched throughout the remaining operating bandwidth with . A four section impedance transformer with dimensions and impedances shown in Fig. 5 is printed on the back side of the antenna. It is designed to match a 160 nominal antenna impedance to the 50 . Circuit and full wave simulations have shown that the input VSWR for this microstrip realization is better than 1.9:1 over 1.8–11 GHz range. Notice that the impedance transformer does not increase the overall size of the antenna. The center frequency of the rejection band is directly related and to the log-periodic growth rate, . If the largest smallest dimensions of the antenna are held constant, the

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Fig. 6. Computed VSWR (to 50 ) for aperture rejection method with different teeth pairs removed.

Fig. 7. Far-field broadside gain of a simulated and measured antenna shown in Fig. 3.

growth rate can be used to set the number of resonant teeth used in the antenna aperture. Equation (1) shows how to compute when the number of desired teeth, , is odd and specified (1) The simulations have shown that rejection bandwidth obtained by removing different pairs of teeth from a radiator with a constant growth rate is essentially constant. As the growth rate increases, the number of teeth in the aperture for a given size increases and the percentage bandwidth related to each pair of resonant teeth is decreased. For sharp and narrowband rejection, a high growth rate is desirable. As the growth rate decreases, the sharpness of the rejection decreases. To demonstrate the way a specific rejection band can be targeted, different pairs of resonant teeth are removed from the an, 17, 13, 9, where tenna aperture. Specifically is the teeth pair in the antenna center, resonant pairs are removed and results are shown in Fig. 6. As seen, the rejection band changes as a function of the location of the resonant teeth. The closer the teeth are to the outside of the antenna aperture, the lower is the band rejection center frequency. As expected, due to the log-periodic nature of the antenna the rejection bands scale in a logarithmic fashion. Since the aperture is modified to not have a resonant tooth in the rejection band, the antenna impedance is increased in the rejection band thus causing high VSWR. It is important to note the performance of the antenna outside the rejection band is unaffected by the removed teeth. Computed and measured co- and cross- polarized realized gains at broadside for the antenna from Fig. 3 are shown in Fig. 7. As seen, the co-polarized gain rejection greater than 25 dB is achieved at 6 GHz. Also noticed is that the theory predicts this very well not only the band rejection phenomenon but also the overall antenna performance over a decade bandwidth. To demonstrate the effects of the aperture rejection method on pattern stability, four frequencies are chosen and results are shown in Fig. 8. Selected frequencies of 4.3, 8, and 10 GHz are in the pass band, and 6.1 GHz is within the rejection band of the antenna. As shown, the pass band patterns are quite stable. The full-wave simulations have shown that the aperture rejec-

Fig. 8. Computed and measured H-plane far-field gain patterns of antenna from Fig. 3. The same conclusions hold for E-plane patterns.

tion does not affect appreciably the patterns in the pass bands. It is also of interest to note that the rejection band performance is not just merely suppressing the broadside gain. The co-polarized gain is reduced in all directions, confirming that this method of rejection is an effective approach for spatial suppression of interference. To further illustrate the far-field effects of aperture rejection, the radiation characteristics are measured over the entire antenna upper hemisphere. Realized co- and cross- polarized gains in H-plane are shown in Fig. 9. A clear drop in realized gain at around 6 GHz for all elevation angles , and excellent pattern stability are observed. III. INTEGRATED FILTER REJECTION Filters are often used to tailor the shape of the spectral response of RF front end systems. They can be integrated with an

MRUK et al.: BAND REJECTION METHODS FOR PLANAR LOG-PERIODIC ANTENNAS

Fig. 9. Measured H-plane gains of antenna shown in Fig. 3. The same observations and trends hold for E-plane patterns.

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Fig. 11. Simulated performance of the filter shown in Fig. 10 using full-wave (HFSS) and circuit models (AWR). Both filter ports are matched to 50 .

Fig. 10. Dimensions (mm) of the fabricated microstrip filter connected to a four step impedance transformer to feed the antenna. The impedances, from left to right, are 40 , 29 , 29 , 40 , and 50 . The impedance of the stub is 50 .

antenna within a single process or in a hybrid fashion. Drawbacks include increased complexity and size, higher loss and noise figure. A single process to integrate filters on the aperture of an antenna could save space, improve repeatability, and reduce the cost of an RF system. In the integrated filter rejection method, a UWB microstrip filter design from [14] and short-circuited quarter-wavelength stub [15] are combined to achieve mid-band rejection. For the utilized filter, the quarter-wave series impedance transformers between the shunt stubs and the termination ports are used to increase bandwidth. The impedance of the stub can also be used to modify the bandwidth characteristics. Generally, increasing the stub impedance or adding additional impedance transformers increases the pass band of the filter. The designed filter has four series and one shunt section. The design center frequency is 3 GHz so that the even harmonics of the shorted shunt section represent the desired mismatch. Thus the first even harmonic results in a rejection at 6 GHz. The next pass-band is centered at 9 GHz with another even harmonic appearing at 12 GHz. Since the antenna is realized in the slot configuration, the metallization of the antenna is used as a ground plane as done for the impedance transformer discussed earlier. The shunt stub is realized by connecting a via from the stub, through the substrate, to the metallization of the antenna. The dimensions of the fabricated filter are shown in Fig. 10. Utilized filter is characterized using the full-wave and circuit modeling tools Ansoft’s HFSS and Applied Wave Research’s (AWR) Microwave Office [16], respectively. As seen in Fig. 11,

Fig. 12. Measured and simulated VSWR (with respect to 50 periodic antenna with integrated filter (top left in Fig. 1).

) of the log-

there is good correlation between these two models. The difference in the return loss in the pass bands is due to the typical modeling dissimilarity associated with the accurate prediction of electrical length of the stubs, via effects, and microstrip trace losses. Note that the actual electrical length of the shorted stub in these two models is somewhat different, causing a slight shift in pass-band nulls, while the losses account for the different levels. In both simulations, return loss is seen to be greater than 18 dB in the pass bands and the rejection is shown to be above 30 dB. The return loss of the filter can be improved by adjusting the shorted stub length and by including additional quarter-wave series transformers. Computed and measured VSWR of the filter integrated with a log-periodic slot antenna with all teeth and parameters as antenna shown in Fig. 3 are given in Fig. 12. The fabricated antenna is the top left article from Fig. 1. As seen, the simulated VSWR at the center of the rejection region approaches 70:1, while the measured result is close to 50:1. This difference corresponds to only a 0.1 dB variation in return loss, thus indicating an excellent agreement between the two. Due to the overall increase in the antenna size, the effects of the filter integration on the radiation pattern are the matter of concern. To address this issue, the broadside co- and cross-

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Fig. 13. Measured co- and cross-polarized broadside gain of antenna with integrated filter.

Fig. 14. Measured H-plane gains of antenna with integrated filter. The same observations and trends hold for E-plane patterns.

polarized gains for two configurations are shown in Fig. 13. Substrate configuration refers to the hemisphere above the antenna aperture. Superstrate configuration refers to the hemisphere above the filter/feeder aperture. As seen, in both cases the rejection is greater than 30 dB at the center frequency of 6 GHz. To further evaluate effects of integrated filter rejection method on antenna far-field, the hemispherical gain measurements are conducted and results for the H-plane are shown in Fig. 14. Clear rejection region at 6 GHz and the rejection associated with the higher order reentrant mode at 12 GHz are measured. Also noticeable is the reduction in the cross-polarization component. When compared with an antenna that features aperture rejection, the pass band characteristics for both polarizations are similar, confirming that the radiation pattern of the antenna is not altered by the integrated filter. To address the size increase associated with this implementation an approach tailored toward integrating the impedance transformer with filter is of interest. IV. COMBINED APERTURE AND INTEGRATED FILTER REJECTION The two band rejection methods discussed in Sections II and III have proved that band rejection is possible by modifying the

Fig. 15. Measured and simulated VSWR (with respect to 50 ) of the logperiodic antenna with removed teeth pair and integrated filter (bottom right in Fig. 1).

Fig. 16. Measured co- and cross-polarized broadside gains of antenna with removed teeth pair and integrated filter. Zoomed rejection region in the inset depicts the depth of the rejection.

log-periodic aperture and/or by integrating the filter onto the antenna. Realized gain rejection of 25 dB and 30 dB are measured. Also, inspection of the radiation patterns has shown that neither of the two methods affects the pass-bands. Thus, the question is if the two methods can be combined to achieve even larger rejection. A log-periodic antenna with a pair of resonant teeth removed is integrated with impedance transformer and filter and obtained computed and measured VSWR is shown in Fig. 15. As seen, the measured VSWR is less than that of the unmodified antenna and filter. The filter was designed such that the impedances at the input and output are 50 . When the filter is attached to the antenna with teeth removed the impedance of the antenna increases greatly in the rejection band, which alters the performance of the filter in this operation region. Measured realized co- and cross-polarized broadside gains for two topologies are shown in Fig. 16. As seen, the co-polarized rejection is greater than 55 dB indicating that the combining the two methods results in a strong rejection at the desired frequency band. Notice that the level of cross-polarization remains virtually unchanged and that the antenna cross-polarization component is much larger (albeit still small) than the co-polarization counterpart.

MRUK et al.: BAND REJECTION METHODS FOR PLANAR LOG-PERIODIC ANTENNAS

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REFERENCES

Fig. 17. Measured H-plane gains of antenna with removed teeth pair and integrated filter. The same observations hold true for E-plane patterns.

Measured hemispherical pattern is shown in Fig. 17. As seen, the rejection band at 6 GHz is wider when compared to other antennas. As expected, reentrant filter mode is present and the cross-polarized gain rejection is stronger. The pattern remains stable throughout the pass bands.

V. DISCUSSION AND CONCLUSION Due to the existence of reentrant modes, the aperture rejection is the favorable approach when band rejection is needed in the lower end of the multi-octave wideband system. This technique is flexible in terms of selecting multiple rejection bands, particularly if quasi log-periodic approach (variable growth rate ) is allowed for the antenna design. Aperture rejection is favorable to reconfiguration where integrated switches and control unit can be used to alter the location of the rejection band. Finally, the size of the antenna is smaller, though the future work in the design of combined filters/impedance transformers can remedy this issue. Filter integration and the combined rejection technique are shown to be capable of achieving stronger rejection at the expense of reentrant modes and increased length of the feeder line due to the addition of the band-pass filter. Extensive measurement and simulated data have shown that demonstrated rejection methods can be used without any adverse effects on the far-field performance of the pass bands. Finally, the recent advances in surface micromachining technologies [17] allow for easy scaling of the developed designs into millimeter waves. Specifically, a great interest exists for airborne radar warning antennas in 18–50 GHz and 75–110 GHz ranges. U-band systems are irrelevant due to the large atmospheric attenuation at these frequencies. Thus, the designs presented here scaled for a 10x factor apply perfectly. ACKNOWLEDGMENT The authors would like to thank Dr. P. Craig from the Office of Naval Research, M. Radway, and H. Zhou from the University of Colorado.

[1] Q.-X. Chu and Y.-Y. Yang, “A compact ultrawideband antenna with 3.4/5.5 GHz dual band-notched characteristics,” IEEE Trans. Antennas Propag., vol. 56, no. 12, pp. 3637–3644, Dec. 2008. [2] H.-J. Zhou, B.-H. Sun, Q.-Z. Liu, and J.-Y. Deng, “Implementation and investigation of U-shaped aperture UWB antenna with dual bandnotched characteristics,” Elect. Lett., vol. 44, no. 24, pp. 1387–1388, Nov. 2009. [3] D.-D. Yuan et al., “Development of ultrawideband antenna with multiple band-notched characteristics using half mode substrate integrated waveguide cavity technology,” IEEE Trans. Antennas Propag., vol. 56, no. 9, pp. 2894–2902, Sep. 2008. [4] D.-H. Bi and Z.-Y. Yu, “A CPW-fed staircase shape antenna with dual stopband characteristic for UWB communications,” in Proc. ISAPE, Nov. 2008, pp. 140–143. [5] J.-H. Lee, N. Kidera, S. Pinel, J. Laskar, and M. M. Tentzeris, “V-band integrated filter and antenna for LTCC front-end modules,” in Proc. IEEE MTT-S, Jun. 2006, pp. 978–981. [6] K. Sano and K. Ito, “Dielectric waveguide slot antenna with integrated filter for automotive UWB radar applications,” in Proc. IEEE MTT-S, Jun. 2008, pp. 113–116. [7] A. Saitou et al., “Ultra-wideband differential mode bandpass filters embedded in self-complementary antennas,” IEEE Trans. Microw. Theory Tech., pp. 1–4, Jun. 2005. [8] R. H. DuHamel and D. Isbell, “Broadband logarithmically periodic antenna structures,” IRE Int. Convention, vol. 5, pp. 119–129, Mar. 1957. [9] F. Dubrovka and S. Martynyuk, “Design and development of ultra wideband antennas for various applications,” in Proc. Int. Conf. on Mathematical Methods in Electromagnetics, 2006, pp. 95–98. [10] S.-Y. Chen, P.-H. Wang, and P. Hsu, “Uniplanar log-periodic slot antenna fed by a CPW for UWB applications,” IEEE Antennas Propag. Lett., vol. 5, pp. 256–259, 2006. [11] HFSS: High Frequency Structure Simulator Ansoft Corporation [Online]. Available: http://www.hfss.com [12] C. Balanis, Antenna Theory Analysis and Design, 3rd ed. Hoboken, NJ: Wiley, 2005. [13] H. G. Booker, “Slot aerials and their relation to complementary wire aerials (Babinet’s principle),” Proc. Inst. Elect. Eng., vol. 93, pp. 620–626, 1946. [14] M. Uhm, K. Kim, and D. S. Filipovic, “Ultra-wideband bandpass filters using quarter-wave short-circuited shunt stubs and quarter-wave series transformers,” IEEE Microw. Wireless Compon. Lett., vol. 18, no. 10, Oct. 2008. [15] D. Pozar, Microwave Engineering, 3rd ed. New York: Wiley, 1998. [16] AWR: Microwave Office Applied Wave Research [Online]. Available: http://web.awrcorp.com/Usa/Products/Microwave-Office [17] J. Mruk, H. Zhou, Y. Saito, and D. S. Filipovic, “Wideband mm-wave log-periodic antennas,” presented at the Eur. Conf. on Antennas Propag., Mar. 2009.

Joseph R. Mruk (S’09) was born in Springfield, MA, on July 24, 1984. He received the B.S. degree in electrical engineering from Northeastern University, Boston, MA, in 2007 and the M.Sc. degree in electrical engineering from the University of Colorado, at Boulder, in 2009. He held an internship with the Receiver Protector Group at Communications and Power Industries, Beverly, MA, from 2004 to 2007. He is currently a Research Assistant with the Department of Electrical, Computer, and Energy Engineering at the University of Colorado, at Boulder. His research interests include millimeter-wave antenna and filter design, broadband active components, and applied electromagnetics. Mr. Mruk was awarded the Graduate Assistance in Areas of National Need (GAANN) fellowship at the University of Colorado, at Boulder for the 20072008 academic year.

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W. Neill Kefauver (M’82–SM’08) received the B.S.E.E. and M.S.E.E. degrees from Virginia Polytechnic Institute and State, Blacksburg, in 1983 and 1984, respectively. He is currently working toward the Ph.D. degree in electrical engineering in the specialty of antenna design at the University of Colorado, at Boulder. He works professionally in the area of antenna measurement and design for Lockheed Martin Space Systems Company, Denver, CO, as a Senior Staff Engineer. Over the past 24 years he has supported numerous products including the Magellan, MGS, MRO interplanetary space probes, and the Kepler Observatory. In addition, he has provided results to be input into the Atlas, Orion, and Targets programs and full characterizations of antennas for GEOSAT GFO, Dawn, and New Skies, as well as several other military programs. He is the co-inventor of two patents. Mr. Kefauver received the NASA Bravery Award in 1986.

Dejan S. Filipovic (S’97–M’02–SM’08) received the Dipl. Eng. degree in electrical engineering from the University of Nis, Serbia, in 1994, and the M.S.E.E. and Ph.D. degrees from The University of Michigan at Ann Arbor, in 1999 and 2002, respectively. He is currently an Associate Professor with the University of Colorado at Boulder. His research interests are antenna theory and design, modeling and design of passive millimeter-wave components and systems, as well as computational and applied electromagnetics. Dr. Filipovic was the recipient of the Nikola Tesla Award and Provost’s Faculty Achievement Award. He and his students were co-recipients of the Best Paper Award presented at the IEEE Antennas and Propagation Society (AP-S)/ URSI and Antenna Application Symposium conferences.

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A New Method for Locating the Poles of Green’s Functions in a Lossless or Lossy Multilayered Medium Dao-Xiang Wang, Edward Kai-Ning Yung, Ru-Shan Chen, Member, IEEE, and Jian Bao

Abstract—A new method is presented to locate the poles of the Green’s functions for a general multilayered medium, whether lossy or lossless. The problem associated with the pole extraction is reduced to solve the contour integrals in the complex plane that are represented in terms of the spectral-domain transmission coefficients. With the help of Cauchy’s theorem, the proposed method can accurately and rapidly find all surface wave poles with a few contour integrals. The numerical examples are performed to show the efficiency of the method. Index Terms—General multilayered media, Green’s functions, surface wave poles.

I. INTRODUCTION NTEGRAL equations (IEs) have been widely employed for the modeling of microwave/millimeter-wave circuits and antennas based on multilayered media. Numerical solution of these IEs is usually achieved by using the spatial-domain method of moments (MoM). A critical requirement to apply the MoM is the evaluation of spatial-domain multilayered Green’s functions, which are customarily expressed in terms of the Sommerfeld integrals (SI) [1]. The computation of the SIs is quite time-consuming and dominates the performance of the MoM solution because the integrated functions are strongly singular, slowly decaying and highly oscillatory. A method to alleviate this difficulty is adopting the divide-and-conquer strategy. Simply put, the poles of the integrals and the corresponding residues are extracted beforehand. Their contributions to the integrals are calculated separately while the remaining parts could be handled easily by using the complex image

I

Manuscript received May 12, 2008; revised June 21, 2009; accepted August 14, 2009. Date of publication March 29, 2010; date of current version July 08, 2010. This work was supported in part by the Major State Basic Research Development Program of China (973 Program: 2009CB320201), in part by the Jiangsu Natural Science Foundation under Contract BK2008048, in part by the Natural Science Foundation under Contracts 60871013, 60701005, 60701003, 60701004, and in part by the China Postdoctoral Foundation under Contract 20090451215. D.-X. Wang is with the Department of Communication Engineering, Nanjing University of Science and Technology, Nanjing, China and also with Department of Electronic Engineering, City University of Hong Kong, Kowloon, Hong Kong, China (e-mail: [email protected]). R.-S. Chen is with the Department of Communication Engineering, Nanjing University of Science and Technology, Nanjing, China. E. K.-N. Yung, and J. Bao are with the Department of Electronic Engineering, City University of Hong Kong, Kowloon, Hong Kong, China. 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/TAP.2010.2046830

method (CIM) [2]. Therefore, the key point is finding the poles of the integrated functions, namely, surface wave poles for Green’s functions. Over the years, methods for locating the poles of Green’s functions have been advanced frequently [3]–[8]. In [3], a method based on the residue theorem was proposed for the lossless multilayered media. In this method, the concerned interval will be recursively split into a number of sub-intervals, over which contour integrals are performed to check whether or not there are poles inside. This method does offer a useful way to locate the poles of multilayered Green’s functions, but its accuracy heavily depends on the size of the smallest sub-interval. Although much smaller interval gives rise to higher accuracy, it will drastically increase the number of contour integrals and consequently becomes computationally expensive, particularly when the poles are in close proximity to the branch cuts. To reduce the number of contour integrals, another method was proposed in [4] by properly choosing a finite exponential series that is assumed to be a function of the poles and residues. Then, the poles are roughly approximated by using the generalized pencil-of-function (GPOF) method [5] and are further refined by applying a root-searching procedure such as the Newton-Raphson method. Unfortunately, the number of contour integrals is difficult to determine in advance and relies mostly on the experimental trials. Especially when there may exist two poles very adjacent to each other, this method will fail to pick up them. What’s more, a common deficiency of the above two methods is that they are not sufficiently efficient for lossy multilayered media, notwithstanding an example has been presented in [6] to show the potentials of the second method in handling a single-layer dielectric slab having a small loss permittivity. Recently, the other two methods for locating the surface wave poles of lossy layered media have been developed in [7] and [8]. They both exhibit high accuracy and speed, but they restrict themselves on the single-layer lossy slab with the grounded planes, which are only a small part of practical applications. The aim of this paper is to develop an accurate and fast method for locating the surface poles of Green’s functions in the general multilayered media, whether lossless or lossy. With the aid of the residue theorem, the problem is first transformed to solve the contour integrals in the complex -plane. In this way, the method will be not reliance on material properties and physical parameters of the media. For a given region that is assumed to be large enough to include all the poles, it is quite easy to check whether there are or not poles inside by

0018-926X/$26.00 © 2010 IEEE

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performing only a contour integral. If the region includes one pole, we observe that it needs two contour integrals to calculate the pole by directly applying Cauchy theorem, instead of successively performing the contour integrals over much smaller sub-regions [3]. If the region possibly includes many poles, we split it into some sub-regions so that each sub-region includes one pole at most. This will be achieved by the use of limitation conditions as described in the following section. The details of the method will be elaborated in Section II, and then followed by numerical examples to demonstrate its efficiency.

Fig. 1. Configuration of a general multilayered medium.

As shown in Fig. 1,

II. THEORY AND FORMULATION A. The Spectral-Domain Terms Including Poles The theory on the derivation of the multilayered Green’s functions has been well established in [1]. In common, the C Formulation is used more preferably since it eliminates extra line integrals in the spatial-domain MoM solution. Through a careful inspection, it will be found that the poles, either for the or for the scalar potential , are dyadic vector potential actually contained in some key terms, called spectral-domain transmission voltage and current coefficients, namely and (where or ) [9]. These spectral voltages and currents are complex rational functions whose denominators, for both TE and TM polarizations, are related to the dispersion equation of the multilayered structure. Thus, the problem is finding the poles of the voltage coefficients (or current coefficients ). Throughout this context, is used, and the spectral-domain voltage coefficients denoted as

(1) strands for TM or TE-type transmission line; is the wavenumber along z-axis and its sign is determined by to satisfy the radiation condition; is transverse propagation wave constant. where

(2) (3) (4) (5)

is the Fresnel reflection coefficient

looking from th to th layer; and are the generalized direction) reflection coefficients looking upward (i.e., in the is the TE and downward at the th interface, respectively; or TM characteristic impedance inside the th layer medium; is the position of the th interface and is the thickness of the th layer; and are source and observation positions, respectively. B. The Pole Extraction of Surface Waves Before extracting the poles of , we begin with a brief description of a lemma that forms the basis of the pole extraction in our method. having a simple pole Assuming that an analytic function within a simply connected domain bounded by a at Jordan curve , one may derive the following identity in terms of Cauchy’s integral theorem, (10) can be directly obtained by simple Obviously, the pole mathematic manipulation once two contour integrals in (10) are known. The pole obtained in such a manner will be highly accurate. It is because two contour integrals can be precisely calculated if an integration procedure is properly chosen. having more than one pole, However, for the function the formulation (10) will fail to give the correct pole and the pole obtained by using (10) may be a spurious solution. In this needs be recursively divided case, the integration domain into much smaller sub-domains as proposed in [3] until each sub-domain would contain at most one pole. To this end, the limitation conditions must be enforced in each sub-domain. is obtained by using (10) for a sub-domain If a solution bounded by , it will be considered as a possible candidate. Then, for a given tolerance , we shall have

(6) (11) (7)

(8)

(9)

where the closed contour is defined by a small circle . If expression (11) is true, will be regarded to needs to be further be one pole. Otherwise, the sub-domain divided into much smaller ones until (11) is satisfied. Therefore, the pole can always be found only if an appropriate tolerance is carefully chosen. Since the absolute tolerance used in (11) may

WANG et al.: A NEW METHOD FOR LOCATING THE POLES OF GREEN’S FUNCTIONS

increase the precision requirement of an integration routine, one by using the following conditions, alternatively can verify

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TABLE I TE AND TM WAVE POLES FOR A SINGLE-LAYER LOSSLESS AND LOSSY SUBSTRATE

(12) or equivalently,

(13) The above two inequalities are associated with each other and either one of them can be mathematically deduced from another while is unique pole in . However, thanks to the effects of numerical errors, they may sometimes not be satisfied simultaneously. For safety, these two conditions shall be used together more strictly. to examine In our experiments, we find that condition (11) are very sensitive to round-off errors and may miss the solution at a time while conditions (12) and (13) work well at all times. This is partly because the absolute errors used in (11) is more sensitive to the integration procedure than the relative errors used in (12) and (13). For ease of understanding, the algorithm is summarized as follows: Step 1: Calculate the contour integral . If its magnitude is smaller than the given tolerance, there is no pole within the enclosed domain and stop the searching procedure; and Step 2: Calculate the contour integral using (10); solve does not fall in the sub-domain , divide the Step 3: If sub-domain into much smaller ones and repeat from step 1. Otherwise, go to step 4; using the conditions of (11), or (12) and Step 4: Verify (13). Repeat from step 1 for other sub-domains. III. NUMERICAL RESULTS AND DISCUSSIONS In this section, numerical examples are presented to demonstrate the accuracy and rapidity of the proposed method for locating the surface wave poles of multilayered Green’s functions. All program codes according to the formulations in Section II are executed on a PC desktop computer with Intel Pentium® 4 CPU 1.86G. Since the integrated functions are usually not smooth, the adaptive Simpson quadrature method is adopted and a relative tolerance and an absolute tolerance are selected with and , respectively. of First example considers a single-layer medium with the di, the thickness mm and the operelectric constant GHz. This geometry is chosen because ated frequency the corresponding Green’s function includes a simple pole that ( is the free-space wave is close to its branch cut at number) and is not easy to extract [3]. To apply the proposed method, the integral domain should be defined beforehand. It can be proven that for a lossless layered medium, the surface along wave poles should locate in the range of

the real -axis (where is the maximum dielectric constant). For this geometry, the explicit expressions of can be derived analytically and the poles can be found using the Newton method. With our method, only three contour integrals are used to find all the poles for the given range and the overall CPU time is almost negligible. As listed in Table I. it is observed that the results obtained from our method are exactly identical with those from the Newton method. It is well known that the contribution of surface wave poles is dominant in the far-field region for a lossless medium while they are also main parts within a certain range for a lossy medium, and hence, must be carefully accounted for. For the first example, the dielectric slab is assumed to be lossy and . In this case, the real and imagine part of the and poles will be within the range of , respectively (where defines the complex wave number of the th layer medium). It is not difficult to prove that the results will be less significant in physics beyond this range. Finally, our method uses only three contour integrals to find all surface wave poles and the results are also well compared with those by the method [6] as listed in Table I. It is not surprising to see that the poles move away from the real axis into the fourth quadrant because they have to satisfy the radiation boundary condition. As the operated frequency is GHz, there are possibly more poles in the changed to be given range. Therefore, the limitation conditions of (11)–(13) need to be used simultaneously to guarantee that no pole is missed in the searching process. Finally, four poles are captured successfully with sixteen contour integrals totally and the CPU time is even less than 0.02 seconds. The results are as follows:

(14) (15) To further verify the poles obtained by our method, we plot bein the havior of the characteristic function complex -plane as shown in Figs. 2(a) and (b) where the value of the functions at the poles are usually corresponding to the position of the peak. It is clearly displayed that the poles for TE and TM waves are in good agreement with those by our method. To demonstrate the efficiency of the proposed method for the general multilayered media, a five-layer medium with a PEC ground plane is analyzed [6]. The geometrical dimension and dielectric parameters are shown in Fig. 3. As the operated freGHz, our method needs to calculate only sixteen quency

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Fig. 2. (a) Distribution of TM wave poles normalized by k for a two-layer loss medium with tan  = 0:02. The poles locate at (9:0012 j 0:1467) and (12:2040 j 0:1282). (b) Distribution of TE poles normalized by k for a two-layer loss medium with tan  = 0:02. The poles locate at (7:3966 j 0:1506) and (11:4078 j 0:1328).

0

0

0

0

Fig. 4. (a) Distribution of TM wave poles normalized by k for a five-layer loss medium with tan  = 0:02. (b) Distribution of TE wave poles normalized by k for a five-layer loss medium with tan  = 0:02.

TABLE II TE AND TM WAVE POLES FOR A FIVE-LAYER LOSSLESS AND LOSSY SUBSTRATE

Fig. 3. Configuration of a five-layer medium.

and twelve contour integrals for TM and TE wave poles, respectively and the whole CPU time is approximately 0.03 seconds. All the poles obtained by our method are listed in Table II, and are found to be well consistent with the existing data [6]. When or is specified for each bounded a loss tangent layer, all the poles are also captured successfully as given in Table II. To confirm that no pole is missed, the characteristic are plotted in Figs. 4(a) and (b). functions We can observe that all the poles corresponding to the peak of

the function are in good agreement to those by our method. Although a bit more contour integrals are calculated, the needed CPU time is less than 0.08 seconds. As a further check to the efficiency of our method, we also examine this example for the different frequencies. Table III summarizes the results, indicating that the proposed method needs

WANG et al.: A NEW METHOD FOR LOCATING THE POLES OF GREEN’S FUNCTIONS

TABLE III THE CPU TIMES VERSUS THE NUMBER OF POLES

less CPU time to find all the poles of the multilayered Green’s functions. For comparison, the distribution of the characteristic functions are also plotted to show the location of these poles and not shown here for the limited space.

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[7] S.-A. Teo, M.-S. Leong, S.-T. Chew, and B.-L. Ooi, “Complete location of poles for thick lossy grounded dielectric slab,” IEEE Trans. Microw. Theory Tech., vol. 50, no. 2, pp. 440–445, Feb. 2002. [8] M. J. Neve and R. Paknys, “A technique for approximating the location of surface- and leaky-wave poles for a lossy dielectric slab,” IEEE Trans. Antennas Propag., vol. 54, no. 1, pp. 115–120, Jan. 2006. [9] K. A. Michalski and J. R. Mosig, “Multilayered media Green’s functions in integral equation formulations,” IEEE Trans. Antennas Propag., vol. 45, no. 3, pp. 508–519, Mar. 1997.

Dao-Xiang Wang was born in Nanjing, China. He received the M.S. degree from Nanjing University of Science and Technology (NJUST) in 2004 and the Ph.D. degree from City University of Hong Kong (CityU) in 2007. Since 2007, he has been working as Research Fellow at CityU. His research interests include computational electromagnetics, electromagnetic scattering and propagation in complex media, and signal integrity.

IV. CONCLUSION A new method has been developed in this paper for automatic extraction of the surface wave poles of multilayered Green’s functions. Both lossless and lossy media have been considered. Pole solutions that are resulted from the spectral-domain transmission voltage/current coefficients can be easily accomplished in a few seconds by using the proposed method. Through the examples considered, the accuracy and rapidity of the method are demonstrated. Although the contour integral is required, the method is not reliance on the physical geometry, material properties or operated frequency, and therefore, is very useful for evaluating spatial-domain Green’s functions of a general multilayered medium. ACKNOWLEDGMENT The authors would like to express their thanks to the reviewers for their comments and suggestions. Thanks are also given to Prof. W. C. Chew with Department of Electronic Engineering, Hong Kong University, for his valuable discussions.

Edward Kai-Ning Yung was born in Hong Kong. He received the B.S. degree in 1972, the M.S. degree in 1974, and the Ph.D. degree in 1977, all from the University of Mississippi. After graduation, he worked briefly in the Electromagnetic Laboratory, University of Illinois at Urbana-Champaign. He returned to Hong Kong in 1978 and began his teaching career at the Hong Kong Polytechnic. He joined the newly established City University of Hong Kong in 1984 and was instrumental in setting up a new department. He was promoted to Full Professor in 1989, and in 1994, he was awarded one of the first two personal chairs in the University. He is the Founding Director of the Wireless Communications Research Center, formerly known as Telecommunications Research Center. Despite his heavy administrative load, he remains active in research in microwave devices and antenna designs for wireless communications. He is the principle investigator of many projects worth tens of million Hong Kong dollars. He is the author of over 450 papers, including 270 in refereed journals. He is also active in applied research, consultancy, and other technology transfers. Prof. Yung was the recipient of many awards in applied research, including the Grand Prize in the Texas Instrument Design Championship, and the Silver Medal in the Chinese International Invention Exposition. He is a fellow of the Chinese Institution of Electronics, the Institute of Electrical Engineers, and the Hong Kong Institution of Engineers. He is also a member of the Electromagnetics Academy. He is listed in Who’s Who in the World and Who’s Who in the Science and Engineering in the World.

REFERENCES [1] K. A. Michalski and D. Zheng, “Electromagnetic scattering and radiation by surfaces of arbitrary shape in layered media—Part I: Theory,” IEEE Trans. Antennas Propag., vol. 38, pp. 335–344, Mar. 1990. [2] Y. L. Chow, J. J. Yang, D. G. Fang, and G. E. Howard, “A closed-form spatial Green’s function for the thick microstrip substrate,” IEEE Trans. Microw. Theory Tech., vol. 39, no. 3, pp. 588–592, Mar. 1991. [3] F. Ling and J. M. Jin, “Discrete complex image method for Green’s functions of general multilayered media,” IEEE Trans. Microw. Guided Wave Lett., vol. 10, pp. 400–402, Oct. 2000. [4] S.-A. Teo, S.-T. Chew, and M.-S. Leong, “Error analysis of the discrete complex image method and pole extraction,” IEEE Trans. Microw. Theory Tech., vol. 513, pp. 406–41, Feb. 2003. [5] T. K. Sarkar and O. Pereira, “Using the matrix pencil method to estimate the parameters of a sum of complex exponentials,” IEEE Antennas Propag. Mag., vol. 37, pp. 48–55, Feb. 1995. [6] A. G. Polimeridis, T. V. Yioultsis, and T. D. Tsiboukis, “An efficient pole extraction technique for the computation of Green’s functions in stratified media using a sine transformation,” IEEE Trans. Antennas Propag., vol. 55, no. 1, pp. 227–229, Jan. 2007.

Ru-Shan Chen (M’01) was born in Jiangsu, China. He received the B.Sc. and M.Sc. degrees from Southeast University, in 1987 and in 1990, respectively, and the Ph.D. degree from City University of Hong Kong, in 2001. He joined the Department of Electrical Engineering, Nanjing University of Science and Technology (NUST), where he became a Teaching Assistant in 1990 and a Lecturer in 1992. Since September 1996, he has been a Visiting Scholar with Department of Electronic Engineering, City University of Hong Kong, first as Research Associate, then as a Senior Research Associate in July 1997, a Research Fellow in April 1998, and a Senior Research Fellow in 1999. From June to September 1999, he was also a Visiting Scholar at Montreal University, Canada. In September 1999, he was promoted to Full Professor and Associate Director of the Microwave & Communication Research Center in NUST and in 2007, he was appointed Head of the Department of Communication Engineering, Nanjing University of Science & Technology. His research interests mainly include microwave/millimeter-wave systems, measurements, antenna, RF-integrated circuits, and computational

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electromagnetics. He has authored or coauthored more than 200 papers, including over 140 papers in international journals. Prof. Chen is a Senior Member of the Chinese Institute of Electronics (CIE). He received the 1992 third-class science and technology advance prize given by the National Military Industry Department of China, the 1993 third class science and technology advance prize given by the National Education Committee of China, the 1996 second-class science and technology advance prize given by the National Education Committee of China, and the 1999 first-class science and technology advance prize given by JiangSu Province as well as the 2001 second-class science and technology advance prize. At NUST, he was awarded the Excellent Honor Prize for academic achievement in 1994, 1996, 1997, 1999, 2000, 2001, 2002, and 2003. He is the recipient of the Foundation for China Distinguished Young Investigators presented by the National Science Foundation (NSF) of China in 2003. In 2008, he became a Chang-Jiang Professor under the Cheung Kong Scholar Program awarded by the Ministry of Education, China.

Jian Bao was born in Zhejiang, China. He received the B.Sc. degree in electronic engineering from Zhejiang University, Hangzhou, China, in 2005 and the M.Phil. degree in electronic engineering from City University of Hong Kong, Hong Kong, in 2007. He is currently working toward the Ph.D. degree at City University of Hong Kong. His research interests include numerical method in electromagnetic, fast and efficient algorithms, electromagnetic scattering and propagation in complex media.

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Enhancement of Efficiency of Integral Equation Solutions of Antennas by Incorporation of Network Principles—Part I Adam W. Schreiber, Member, IEEE, and Chalmers M. Butler, Life Fellow, IEEE

Abstract—A method is presented for enhancing the efficiency of integral equation solutions for antennas by reducing the number of coupled integral equations to be solved in a method of moments analysis. This method is applied to the accurate modeling of the feed of a simple cylindrical monopole antenna. A microwave network is developed to replace the effects of coupled fields due to one of the unknowns. Computed reflection coefficient values are shown to agree well with values measured on laboratory models and a method of moments solution not incorporating network principles. Index Terms—Cylindrical antennas, method of moments, monopole antennas, two-port circuits, waveguides.

I. INTRODUCTION

M

ONOPOLE and dipole antennas have been of interest for many years [1]–[5]. More recently, attention has turned to accurate feed models for these antennas [6]. Modeling the feed more accurately leads to very useful practicable knowledge of the antenna’s input properties but incurs an increase in the overall costs of computing a solution: CPU time, processing power, and memory use. These costs result from the need to solve several coupled integral equations rather than a single integral equation. If the antenna were to be loaded, for instance with tuned cavities or ferrites, and optimized, the additional cost is compounded. Thus, an increase in the efficiency of the solution method is highly desirable. To enhance the efficiency of the solution method, the incorporation of network methods into a method of moments analysis, as in [7], is examined. If the end result of the coupling of the field in one region of a structure to that in another can be accomplished by a network, then the (coupled) integral equation associated with the coupling in the analysis can be eliminated. When a coupled integral equation is eliminated, there is a reduction in the memory required to store the system matrix, as well as in CPU time not expended to compute the additional coupling terms and to invert a larger matrix. II. ANALYSIS A coaxially-fed, cylindrical monopole antenna above an infinite ground plane is depicted in cross section in Fig. 1. In the Manuscript received August 13, 2009; revised October 12, 2009; accepted January 11, 2010. Date of publication April 26, 2010; date of current version July 08, 2010. The authors are with the Department of Electrical and Computer Engineering, Clemson University, Clemson, SC 29634-0915 USA (e-mail: [email protected]). Digital Object Identifier 10.1109/TAP.2010.2048875

Fig. 1. Cylindrical monopole antenna fed by coax.

monopole, the coaxial feed line couples to the excitation aperture via a parallel plate guide, which in the cylindrical structure is viewed as a radial waveguide. Given the input incident TEM field, one can determine the current on the surface of the antenna and the input reflection coefficient in the coaxial feed line at a measurement port by deriving and solving three coupled integral equations for and the two aperture electric fields and . It is proposed to model the junction of the coaxial and radial guides in the feed of the antenna by a 2-port network, eliminating one unknown and an equation, thereby reducing the complexity and resources needed for determining and . The coaxial-guide/radial-guide junction and the dimensions of the antenna are identified in Fig. 2. While coaxial and radial guides can be analyzed as wave guiding structures [8], [9] or alternately as uniform and non-uniform transmission lines [10], [9], respectively, the junction of the two guides results in a system that requires further analysis than what is required for characterizing either guide alone. In the literature, different models of the junction between a radial line and a coaxial line are proposed. Harrington uses variational methods to approximate the input impedance seen by the coaxial guide loaded with a matched radial guide [11]. Williamson develops lumped element equivalent (approximate) models for a number

0018-926X/$26.00 © 2010 IEEE

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Fig. 3. Coaxial-guide/radial-guide junction.

the total magnetic field in each guide are derived and an inteis obgral equation in terms of the aperture electric field tained. Scattering parameters are determined from the solution of the integral equation for . The incident TEM waves in the coaxial and radial guides are, respectively, Fig. 2. Cylindrical monopole fed by coaxial line with dimensions and the coaxial-guide/radial-guide junction identified.

(1) of structures involving different kinds of coaxial-guide/radialguide junctions [12], [13]. A modal-expansion method is used by Shen et al. to analyze a coaxial-guide/radial-guide junction loaded with a circular disk [14]. In this paper the authors outline the steps to integrate network principles into a MoM analysis. Scattering parameters are determined for the coaxial-guide/radial-guide junction from the solution of an integral equation for the aperture electric field where the guides intersect. The input reflection coefficient for a radial guide driven cylindrical monopole antenna is determined from the solution of a set of coupled integral equations. The coaxial-guide/radial-guide junction is loaded by the computed reflection coefficient to determine an overall reflection coefficient which is then compared to measured data and to data calculated from a set of coupled integral equations not incorporating network principles. It is important to note that the use of network analysis to increase the efficiency of integral equation solutions is not limited to coaxial-guide/radial-guide junctions or the feed region of the antenna specifically. Such efficiency gains can be realized wherever the effects of a coupled integral equation can be replaced by a network. The analysis presented herein is limited to the case that the structure is operated below the cutoff frequencies of the waveguides.

A. 2-Port Network for Coaxial-Guide/Radial-Guide Junction In this section, a 2-port network for the coaxial-guide/radialguide junction shown in Fig. 3 is developed. Expressions for

and (2)

in which , and . and are the magnitudes of the incident waves in each guide. 1) Magnetic Field in Coaxial Guide: The magnetic field in the coaxial guide can be written in terms of the incident TEM wave (1) and aperture field as [15] (3)

in which the short-circuit magnetic field is

(4) and where

(5) (6)

SCHREIBER AND BUTLER: ENHANCEMENT OF EFFICIENCY OF INTEGRAL EQUATION SOLUTIONS OF ANTENNAS

in which

, is the th root of

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The necessary homogeneous solution is found to be

(7) and (8) (13) 2) Magnetic Field in Radial Guide: The magnetic field in the radial guide can be written in terms of the incident TEM as wave (2) and the aperture electric field (9) where the short-circuit magnetic field is (10)

3) Integral Equation: In their respective regions, and of (9) and (3) satisfy all conditions of electromagnetics: Maxwell’s equations, boundary conditions, and the outward is formed wave condition. An integral equation in terms of by forcing the tangential field components in the aperture to be continuous. The electric field is continuous automatically due to the way and are computed from , which is common to the two regions. Continuity of the magnetic field in the aperture is enforced by the requirement that for , which leads to

and where the Green’s function in the radial guide is written (14) (11) in which and are the particular solutions of the scalar Helmholtz (Green’s function) equation in the radial guide and is the homogeneous solution that forces the Green’s function to satisfy the boundary condition that , at for on the conducting post in the radial guide, shown in Fig. 3. Expressions for the particular solutions are [16]

by typical numerical methods: Equation (14) is solved for is expanded in terms of piecewise constant the function pulses and the resulting equation is point matched. Acceleration of the series in (5), (12) and (13) is required to achieve sufficient numerical efficiency and accuracy. Numerical details for (5) and (12) can be found in [15] and [16], respectively, and, for (13), in the Appendix. From knowledge of , determined by solving (14), one can compute the electromagnetic field in both guides by standard techniques. 4) Network Equations: Since both guides support TEM fields, unique voltages can be identified so one can conveniently define scattering parameters in terms of traveling voltages in the two guides

(12a) (15)

and

(12b) where and

and denote reflected and incident voltages at port , and and are the locations of reference surfaces of port 1 in the coaxial guide and port 2 in the radial guide, respectively. From (1) and (2), one finds that and . In the above expressions, and . The scattering parameters (15) are (16) (17)

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Fig. 4. Radial guide driven monopole with shorted feed aperture and rings of magnetic current.

Fig. 5. Exterior region equivalent model.

1) Magnetic Field in Radial Guide: The magnetic field in the radial guide can be written in terms of the incident TEM as wave (20) and the magnetic surface current

(21) (18) and

in which the short-circuit magnetic field is (22) and the Green’s function is (23)

(19)

where is the same as in (12b). Equation (12a) is omitted because the magnetic field is computed only in the region . A homogeneous solution [different from of (13)] of the scalar Helmholtz equation is necessary to satisfy the boundary condition that , at for on the shorted aperture

B. Radial-Guide-Fed Cylindrical Monopole Antenna When the coupling of the field in the coaxial-guide/radialguide junction is accounted for by a 2-port network, one considers the cylindrical monopole antenna in Fig. 2 to be driven by a matched radial guide (Fig. 4). The aperture between the radial guide and the exterior region is shorted and a -directed band of unknown magnetic surface current is placed on either side of the short [17]–[19]. To complete the exterior equivalent model, a -directed equivalent electric current is placed on the surface of the monopole and image theory is employed to remove the ground plane as suggested in Fig. 5. The TEM wave incident on the shorted aperture in the radial guide is (20)

(24) 2) Coupled Integral Equations for Radial-Guide-Fed Cylindrical Monopole Antenna: Two coupled integral equations are formulated with and as the unknowns. The first equation forces the z-directed component of the electric field on the surface of the cylindrical surface of Fig. 5 to be zero (25)

SCHREIBER AND BUTLER: ENHANCEMENT OF EFFICIENCY OF INTEGRAL EQUATION SOLUTIONS OF ANTENNAS

where and are the electric field components due to and and their images, respectively. In the second equation, the -directed component of the magnetic field is made to be continuous through the now shorted aperture

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TABLE I SPECIFICATIONS OF A “THICK” CYLINDRICAL MONOPOLE ANTENNA

(26) where and and

is defined as in (21), and

,

are the magnetic field components due to and their images, respectively. Expressions for

and are given in [6]. The coupled equations (25) and (26) are solved for and by typical numerical methods in which and are expanded in piecewise linear functions and piecewise continuous pulses, respectively. The resulting equation corresponding to (25) is pulse tested and the equation associated with (26) is point matched. Details of accelerating the series contained in (12b) and (24) to achieve sufficient numerical efficiency and accuracy can be found in the Appendix. The reflection coefficient of the radial-guide-fed cylindrical monopole antenna, as seen from in the radial guide, is expressed in terms of as (27) where Fig. 6. Reflection coefficients for a “thick” cylindrical monopole antenna ( : m).

= 0 0650

(28) C. Network Analysis From signal flow analysis [10], the reflection coefficient at the measurement port of the cylindrical monopole antenna of Fig. 2 can be determined from the scattering parameters—(16), (17), (18), and (19)—and the reflection coefficient (27) of the radial-guide-fed cylindrical monopole antenna: (29) in which is the distance to the measurement port from port 1 of the coaxial-guide/radial-guide junction network. III. RESULTS Computed and measured results are presented to demonstrate the accuracy of the method discussed in this paper. Dimensions are given in Table I for a “thick” cylindrical monopole antenna whose feedline is a section of RG402 semi-rigid coaxial line. as a funcData for the input reflection coefficient at tion of frequency are plotted in Fig. 6, in which one observes excellent agreement among reflection coefficients determined from

Fig. 7. Reflection coefficients for a thinner cylindrical monopole antenna : cm). (

= 0 91

the method presented in this paper, from a full MoM solution not incorporating network principles, and from measurements. Data are printed also for the input reflection coefficient against frequency of a thinner cylindrical monopole (Table II) in Fig. 7, in which one observes excellent agreement again.

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Kummer’s method [21] is employed to accelerate the convergence of the infinite series in (30)

TABLE II SPECIFICATIONS OF THINNER CYLINDRICAL MONOPOLE ANTENNA

IV. CONCLUSION A method is presented that enhances the efficiency of integral equation solutions of antennas. There is excellent agreement among the data obtained from the method of this paper, an independent MoM solution not incorporating network principles, and measurements. The method and results herein are limited to the case in which the antenna the network is found in is operated at frequencies below the cutoff frequency of the first higher-order mode in both guides, but can be applied wherever a 2-port network is identified. This method can likely be extended to account for the coupling of higher-order modes by making use of the BLT equation [20]. The results validate a method for decreasing the number of coupled integral equations to be solved to accurately analyze an antenna, causing a speed up in the optimization of antennas. In part II of this paper, this method is applied to a novel structure for loading a cylindrical monopole antenna. Future work is planned to show the efficacy of this method in the optimization of a cylindrical monopole antenna. APPENDIX A ADMITTANCE MATRIX ENTRIES/SERIES ACCELERATION Acceleration techniques are required to ensure efficient and accurate numerical evaluation of the infinite series present in the admittance matrix entries obtained from the magnetic field expressions that make use of the Green’s functions (11) and (23). They are outlined in this Appendix.

(31) where

B. due to a Band of -Varying Magnetic Current in a Shorted Radial Guide The expression for the magnetic field due to a band of -varying magnetic current in a shorted radial guide becomes the admittance matrix entries

due to an Annulus of -Varying Magnetic Current in A. an Infinite Radial Guide The homogeneous portion of the expression for the magnetic field due to an annulus of -varying magnetic current in an infinite radial guide becomes the admittance matrix entries

(30)

(32)

SCHREIBER AND BUTLER: ENHANCEMENT OF EFFICIENCY OF INTEGRAL EQUATION SOLUTIONS OF ANTENNAS

Kummer’s method is employed to accelerate the convergence of the infinite series in (32) [22]

(33)

where

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[7] F. A. Pisano III, C. M. Butler, and J. P. Rudbeck, “Analysis of a tubular monopole loaded with a shielded helical coil,” IEEE Trans. Antennas Propag., no. 4, pp. 969–977, Apr. 2004. [8] M. G. Harrison and C. M. Butler, “An analytical and experimental investigation of planar discontinuities in coaxial waveguides,” Air Force Weapons Laboratory, Tech. Rep. AFWL-TR-79-187, 1981. [9] N. Marcuvitz, Waveguide Handbook. New York: McGraw-Hill, 1951. [10] R. E. Collin, Foundations for Microwave Engineering. New York: Wiley, 2001. [11] R. Harrington, Time-Harmonic Electromagnetic Fields. New York: McGraw-Hill, 1961. [12] A. Williamson, “Equivalent circuit for radial-line/coaxial-line junction,” Electron. Lett., vol. 17, no. 8, pp. 300–301, Apr. 1981. [13] A. Williamson, “Radial-line/coaxial-line junctions: Analysis and equivalent circuits,” Int. J. Electron., vol. 58, no. 1, pp. 91–104, Jan. 1985. [14] Z. Shen, J. L. Volakis, and R. H. MacPhie, “A coaxial-radial line junction with a top loading disk for broadband matchings,” Microw. Opt. Technol. Lett., vol. 22, no. 2, pp. 87–90, Jul. 1999. [15] C. Butler, K. Michalski, and S. Filipovic, “An analysis of the coax-fed monopole in a general medium,” Naval Ocean Systems Center, Tech. Rep. CR 220, 1983, NTIS Accession Number: AD-A137 981/7. [16] C. M. Butler and T. L. Keshavamurthy, “Investigation of a radial, parallel-plate waveguide with an annular slot,” Radio Sci., vol. 16, pp. 159–168, Apr. 1981. [17] C. M. Butler and K. R. Umashankar, “Electromagnetic excitation of a wire through an aperture-perforated conducting screen,” IEEE Trans. Antennas Propag., vol. 24, pp. 456–462, Jul. 1976. [18] C. M. Butler and K. R. Umashankar, “Electromagnetic penetration through an aperture in an infinite, planar screen separating two halfspaces of different electromagnetic properties,” Radio Sci., vol. 2, no. 7, pp. 611–619, Jul. 1976. [19] J. D. Shumpert and C. M. Butler, “Penetration through slots in conducting cylinders—Part 1: TE case, analysis of a strip in a waveguide,” IEEE Trans. Antennas Propag., vol. 46, no. 11, pp. 1612–1621, Nov. 1998. [20] C. Baum, T. Liu, and F. Tesche, “On the analysis of general multiconductor transmission-line networks,” Interaction Note, Nov. 1978. [21] K. Knopp, Theory and Application of Infinite Series Transl.: from the 2d German ed. and rev. in accordance with the 4th, R. C. H. Young, Ed. New York: Hafner Publishing, 1971. [22] V. Mangulis, Handbook of Series for Scientists and Engineers. New York: Academic Press, 1965.

(34) (35) (36)

(37)

REFERENCES [1] G. E. Albert and J. L. Synge, “The general problem of antenna radiation and the fundamental integral equation, with application to an antenna of revolution, pt. i,” Quart. Appl. Math., vol. 6, no. 1, pt. i, pp. 117–131, 1948. [2] R. H. Duncan and F. A. Hinchey, “Cylindrical antenna theory, pt. i,” Quart. Appl. Math., vol. 6, no. 1, pt. i, pp. 117–131, 1948. [3] T. T. Wu, “Input impedance of infinitely long dipole antennas driven from coaxial lines,” J. Math. Phys., pp. 1298–1301, 1962. [4] D. V. Otto, “The admittance of cylindrical antennas driven from a coaxial line,” Radio Sci., vol. 2, no. 9, pp. 1031–1042, Sep. 1967. [5] R. H. Duncan, “Theory of the infinite cylindrical antenna including the feed-point singularity in antenna current,” J. Res. NBS, vol. 66-D, no. 2, pp. 181–188, Mar.–Apr. 1962. [6] M. Lockard and C. Butler, “Feed models for coax-driven monopole and dipole antennas,” IEEE Trans. Antennas Propag., vol. 54, no. 3, pp. 867–877, Mar. 2006.

Adam W. Schreiber (S’01–M’09) received the B.S., M.S., and Ph.D. degrees in electrical engineering from Clemson University, Clemson, SC, in 2005, 2007, and 2009, respectively. His research interests include analytical Green’s functions, penetration of fields through apertures, broadband and low-profile antennas, and electromagnetic compatibility. He currently resides in Fredericksburg, VA. Dr. Schreiber is a member of Eta Kappa Nu, Tau Beta Pi, and the National Society of Collegiate Scholars, and is an associate member of Commission E of the International Union of Radio Science (URSI). He was a Science, Mathematics and Research for Transformation fellow from 2007 to 2009.

Chalmers M. Butler (S’61–M’63–SM’75–F’83 –LF’01) received the B.S. and M.S. degrees from Clemson University, Clemson, SC, and the Ph.D. degree from the University of Wisconsin, Madison. He has been a member of the faculty at Louisiana State University, the University of Houston, and the University of Mississippi where he was Chairman of Electrical Engineering (1965–74) and University Distinguished Professor (1976–83). Since 1985, he has been at Clemson University where he is presently Alumni Distinguished Professor and the Warren H. Owen Professor of Electrical and Computer Engineering. His research has focused primarily upon Green’s functions and integral equation techniques in

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electromagnetics and upon numerical methods for solving integral equations. His principal applications interests are in antennas and aperture penetration. Prof. Butler is a member of Sigma Xi, Tau Beta Pi, Phi Kappa Phi, and Eta Kappa Nu, and Commissions B and F of the International Union of Radio Science (URSI). He is a Life Fellow of the IEEE. He received the Western Electric Fund Award and numerous awards for excellence in teaching at the University of Mississippi and Clemson University. He has received two best paper awards: Best Basic EMP Non-Source Region Paper during 1975–78 from the SUMMA Foundation and the 1986 Oliver Lodge Premium Award from the Institute of Electrical Engineers of London. He received the 1990 and the 2003 Editor’s Citation for Excellence in Refereeing in Radio Science and several awards for excellence in research and scholarship at Clemson. From the University of Wisconsin he received the Centennial Medal for Contributions to Electrical and Computer Engineering. He is a recipient of the IEEE Millennium Medal and the 2003 recipient of the IEEE AP-S Chen-To Tai Distinguished Educator Award. In 2009 he was recognized by the National Academies of Science, Engineering, and Medicine for distinguished contributions to the field of radio science and outstanding service to both the USNC and the International Scientific Union. He has served as an Associate Editor of the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION (1972–77 and 1981–83) and of the IEEE TRANSACTIONS ON EDUCATION, as a member of the IEEE Antennas and Propagation Society Administrative Committee (1976–78 and 1988–90), as an IEEE Antennas and Propagation Society National Distinguished Lecturer (1977–79),

as Chairman of U. S. Commission B of URSI (1983–85), as International Commission B Editor of the Review of Radio Science (1978–80 and 1981–83), and as National President of Eta Kappa Nu. He has been a member of the Editorial Boards of Electromagnetics and of Computer Applications in Engineering Education, and has served as Guest Editor of two special issues of Radio Science. He served as Secretary (1985–87), Vice Chair (1987–90), and Chair (1990–93) of the U.S. National Committee for URSI. He has been Vice Chair (1994–96) and Chair (1997–99) of International Commission B of URSI. In 2008 he completed a six-year term as a Vice President of URSI. He was a U.S. delegate to the 18th–26th General Assemblies of URSI and Chaired the U.S. delegation for the 24th (Kyoto, 1993). He has served on a number of committees and panels including the IEEE Hertz Medal Committee (1996–97), the IEEE Awards Board, the National Academy of Sciences Panel for Evaluation of the Center for Electronics and Engineering of the National Bureau of Standards (now NIST) (1982–86), and the National Research Council’s Panel for the Evaluation of the U.S. Army’s Mine Detection Program (1985–90), which he chaired. He has been a member of numerous technical program committees of National Radio Science Meetings and IEEE AP-S International Symposia and served as General Chairman of the NIST Workshop on EMI/EMC Metrology Challenges for Industry. He was the Vice Chairman of the Technical Program Committee for the 1995 URSI Electromagnetic Theory Symposium in St. Petersburg, Russia, and chaired the same committee for the 1998 URSI Electromagnetic Theory Symposium held in Thessaloniki, Greece.

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Coupled Integral Equations for Microwave Induced Elastic Wave in Elastic Media Mei Song Tong, Senior Member, IEEE, and Weng Cho Chew, Fellow, IEEE

Abstract—The interaction of waves with materials could include multiple physics (multiphysics), depending on the properties of waves and materials. For microwave illumination on elastic media, the electromagnetic (EM) and mechanic processes exist simultaneously and are coupled together. To exactly describe the involved process with interaction of microwave and induced elastic wave, the coupled Maxwell’s equations and elastic wave equations should be solved. Although such coupled equations have been derived earlier but they are in partial differential equation (PDE) form. The solutions for the equations are then only based on finite difference method (FDM) or finite element method (FEM) in addition to analytical approaches. In this work, we first derive coupled integral equations for governing the process from its PDE counterpart. The derivation is based on the Huygens’ equivalence principle and extinction theorem by recognizing that the excitation of elastic wave is EM force and the induced elastic wave will be a new excitation source to affect the EM in return. The coupled integral equations is solved using Nyström method in first time and some basic results from numerical examples for microwave illumination on piezoelectric materials are presented. Index Terms—Coupled integral equations, elastic wave, microwave, multiphysics.

I. INTRODUCTION

W

AVE-TYPE energetic illumination on materials could cause multiple physical processes, depending on the properties of waves and materials. These processes could be electrodynamic, mechanical, thermodynamic, chemical or even quantum-mechanical. Although multiple physics (multiphysics) exist, one or more of those processes may be dominant and others are ignored in general, to facilitate the analysis for involved mechanism. In electromagnetic (EM) wave illumination on elastic media like piezoelectric material or biological tissues, the electrodynamic and mechanical processes are dominant when EM energy is limited and thermal effect can be ignored. The analysis for the processes is then based on the solution of corresponding governing equations which include the coupling of Maxwell’s equations and elastic wave equation. The study on the interaction of EM wave with piezoelectric materials started by Kyame [1], [2] in 1949. He first investigated

Manuscript received July 17, 2009; revised November 18, 2009; accepted January 11, 2010. Date of publication April 26, 2010; date of current version July 08, 2010. This work was supported in part by the Air Force Office of Scientific Research (AFOSR) under Grant F9550-04-1-0326. M. S. Tong is with the Center for Computational Electromagnetics and Electromagnetics Laboratory (CCEML), Department of Electrical and Computer Engineering (ECE), University of Illinois at Urbana-Champaign (UIUC), Urbana, 61801 IL USA (e-mail: [email protected]). W. C. Chew is with the Department of Electrical and Electronic Engineering, The University of Hong Kong, Pokfulam, Hong Kong. Digital Object Identifier 10.1109/TAP.2010.2048869

the propagation of EM plane wave in unbounded elastic media with an analytical approach. Later on, many other researchers also studied the interaction of EM wave with various elastic media [3]–[9]. For example, Tseng and White studied the surface waves in hexagonal crystals [4], while Spaight and Koerber analyzed surface waves in lithium niobate [5]. Mindlin first studied EM radiation from a vibrating quartz plate in 1972. Sedov and Schmerr derived some exact solutions for the propagation of transient electroacoustic waves in piezoelectric media. However, these early investigations mainly focused on solving some simple problems by using analytical approaches. Numerical methods were developed for solving more complicated problems since the 1970s [10]. For instance, Mindlin derived a variational principle for piezoelectromagnetism in a compound continuum representing a diatomic material [11]. Lee gave a variational formulation for the fields inside and outside a body with continuity conditions at the interface between the body and free space [12]. Yang first derived a generalized variational principle with all mechanical and electromagnetic fields as independent variables [13] and his group has conducted extensive studies for the interaction of EM wave with elastic wave in piezoelectric media [14]–[18]. In addition, the work in [19]–[21] was also very impressive. However, all solutions are based on the partial differential equation (PDE) form of the governing equations, i.e., the coupled Maxwell’s equations and elastic wave equations. Therefore, only PDE solvers like finite difference method (FDM) [22], [23] and finite element method (FEM) [24], [25] can be used to find the solutions. Although those differential equation solvers (DESs) may be robust in solving the problems, integral equation solver (IESs) may be preferred in some cases [26], [27]. IESs usually require a smaller number of unknowns and has a better scaling property for computational costs. This is because IESs solve source distribution on boundaries or within objects first, instead of solving field distribution at spatial points directly. Therefore, there is no need to implement absorbing boundary condition (ABC) for open field domains and the solution domain is much smaller in IESs. However, IESs are more complicated to implement in general due to the need of the Green’s function. The Green’s function in wave physics is singular and much effort is required generally to evaluate matrix elements with singular kernels. Also, the system matrix is inherently dense and accelerators are needed for solving large problems with a comparative costs to DESs. In contrast, DESs are simpler to implement and the system matrix is sparse. Moreover, DESs can easily account for the nonlinearity of transient state in time domain. Nevertheless, DESs usually entail worse cost scaling properties since the field solutions are sought directly and may involve ABC implementation for open field domains. In addition, the presence of

0018-926X/$26.00 © 2010 IEEE

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grid dispersion in DESs will further worsen their scaling properties for large-scale computations. Currently, both DESs and IESs are widely used in the community, so developing integral equations allowing the use of IESs for any wave problems is definitely desirable. In this work, we develop an integral equation method for the interaction of EM wave and elastic wave in piezoelectric-like elastic media with arbitrary three-dimensional (3D) shapes. The EM part of the integral equations is derived from the vector wave equation by using the equivalence principle and extinction theorem [28] and recognizing that the source current includes the contribution from the varying displacement vector through strain tensors in the Maxwell’s equations. The integral equations take the electric field integral equation (EFIE) form although other forms like magnetic field integral equation (MFIE) or Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) formulation [29] can be used. The elastic wave part of the integral equations is derived from the elastic wave equation in PDE form and the derivation also uses the equivalence principle and extinction theorem [31] with the recognition that the source (stress tensor) of elastic wave includes the contribution from electric field through the EM force. The two parts of integral equations are then fully coupled each other through the source. By the developed integral equations which take a boundary integral equation (BIE) or surface integral equation (SIE) form, all numerical methods for BIEs like the method of moments (MoM) [32], boundary element method (BEM) [33] or Nyström method [34] can be used, and the elegance of IESs can be exhibited. We use the Nyström method to solve the coupled BIEs for scattering by 3D piezoelectric objects and some numerical examples are presented to demonstrate the solutions.

Fig. 1. Scattering by a dielectric object. (a) Original problem. (b) Equivalent external problem. (c) Equivalent internal problem.

being the distance between a field point and a source point we can derive the electric field integral equation [28]

,

(3) and are the unknown where is the object surface, equivalent electric current and magnetic current on the surface, respectively, and (4)

II. EM WAVE INTEGRAL EQUATIONS The EM wave integral equations for scattering by a dielectric object, when ignoring the elasticity of the object and surrounding medium, can be derived from the vector wave equations

(1) and exterior of the object where we designate the interior as Region 1 and Region 2, respectively, and assume that there in Region 2 to excite the incident wave is a current source upon the object. Also, and are the permittivity is the electric and permeability of materials, and field in the corresponding region, respectively. By introducing the dyadic Green’s function (2) where is the wave number, is an identity dyad, and is the 3D scalar Green’s function with

is the incident field. Alternatively, the integral equations can be directly derived by the equivalent electric and magnetic current method with the help of vector and scalar potentials relating the fields to their sources. Consider the scattering by a 3D dielectric body as shown in Fig. 1(a). The original problem can be decomposed into an equivalent external problem shown in Fig. 1(b) and an equivalent internal problem shown in Fig. 1(c). In the equivalent external problem, the original electric and magnetic fields exist outside the object surface and no fields exist inside . To support such fields, there must exist equivalent electric and on the boundary , which magnetic surface currents and are unknowns to be solved. Since the tangential components of fields are continuous at the boundary, we can write the integral equation as follows

(5) where is the unit normal vector on the surface, and and are the electric and magnetic field, respectively. The subscript “inc” represents an incident field and the superscript “ ” denotes the interface where observation points are located. We use “ ” and “ ” on to indicate its interior side and exterior side of the surface , respectively. In the equivalent internal problem

TONG AND CHEW: COUPLED INTEGRAL EQUATIONS FOR MICROWAVE INDUCED ELASTIC WAVE IN ELASTIC MEDIA

described in Fig. 1(c), the original fields exist inside the object surface and none of fields exist outside the surface. Hence, there and magnetic curmust exist an equivalent electric current rent on the surface to produce the original fields inside the object. The boundary condition requires

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EM integral equations will be revised when considering the elasticity of the object and the surrounding medium. III. ELASTIC WAVE INTEGRAL EQUATIONS The elastic wave scattering from an elastic object is governed by the following PDE [35]

(6) which is another group of integral equations. The first two equations in (5) and (6) about electric field are known as electric field integral equation (EFIE) or E-field formulation, and the second two equations in (5) and (6) about magnetic field are known as magnetic field integral equation (MFIE) or H-field formulation. The electric field and magnetic field can be expressed in terms by recalling of the equivalent currents on the surface, and the vector and scalar potentials, i.e.,

(9) or (10) . These two equations are equivalent because . In the above, the elasticities of the elastic object and the surrounding medium are characand , respectively, where terized with and are Lamé constants and is the mass density of the object or medium. Also, stands for the displacement vector, denotes the body force per unit mass and is the angular frequency of a time-harmonic excitation. From the above PDE, and using equivalence principle and extinction theorem, we can derive corresponding integral equations. First, (9) can be solved using either Helmholtz decomposition or Fourier-Laplace transform [26] for a homogeneous medium as where

(11) where (12) (7) where and are magnetic and electric vector potential, and and are electric and magnetic scalar potential, respectively. Also, and are the wave impedance and wave number of the relevant medium, respectively. We have used and operators to represent the relationship between the fields and equivalent currents in the above. If we add the internal field equations to the external field equations by a weighted-sum method [26], then we can obtain PMCHWT equations or Müller formulations [30], but we only use the EFIE in this work, which takes the following specific form

are the scalar Green’s functions for shear wave with and compressional wave with , respectively. Here we usually have two kinds of wave in each elastic media, i.e., shear wave with a subscript and compressional wave with a subscript . We then identify that the dyadic Green’s function is (13) which satisfies

(14) , and left multiplying (14) by Right multiplying (10) by and subtracting the result, we have

(8) and are the 3D scalar Green’s function related to where the medium in Region 1 and Region 2, respectively. The above

(15)

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Using the vector identities

(16) we can integrate (15) over a volume

(21)

surrounded by S to get where we have used the identity and null quantity to the above [31]

. If we add the following

(22) (17) By changing the primed into the unprimed and the unprimed into the primed, we can rewrite the above equation as

and apply the identity

with have

(18) where

, where

(23) denotes a transpose, then we

(24) where

(19) represents the incident displacement field. Also, the extinction theorem is embedded in the above equation. The above equation includes , and as unknown functions but they are not solvable since the boundary conditions, i.e., the continuity of the displacement vector and traction vector across a boundary, cannot be applied to. The traction vector is related to the stress tensor or the displacement vector by Hooke’s law, i.e.,

(20)

(25) is a third-rank Green’s tensor and is the identity dyad. The above is for the exterior problem, namely, is the complementary space of the object. For the interior problem, namely, is the space occupied by the object, then (26) Substituting the above into (18), considering that the observation point is approaching the boundary from the interior of the object (exterior problem) and from the exterior of the object (interior problem), respectively, and taking a transpose on the resultant equations, we can obtain

To incorporate the boundary conditions, we must reformulate the integrals in (18), namely (we omit and for simplicity),

(27) , the subscript 1 or 2 is the region index, where and and are the total displacement and traction vectors at the object surface , which are the unknowns to be solved. Equation (27) is the BIE for elastic wave scattering by an object and we

TONG AND CHEW: COUPLED INTEGRAL EQUATIONS FOR MICROWAVE INDUCED ELASTIC WAVE IN ELASTIC MEDIA

have incorporated the boundary conditions in it, so it is solvable now. Note that the BIE is consistent with the one in publications [36], but our derivation here is new. IV. COUPLED INTEGRAL EQUATIONS When considering the interaction of EM wave with elastic wave in elastic media, the governing equations are the coupled electrodynamic and elastodynamic equations. In a PDE form, they are [10]

(28)

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To derive the coupled integral equations, we need to consider the EM wave part and elastic wave part separately. For elastic wave part, we recall the derivation of the elastic wave equation in the PDE form in (9), which is a force balance on the elastic body, namely [35] (33) where is an arbitrary volume in the object. The integrand on the left-hand side above is actually from the Newton’s second law of motion. Since (33) holds true for an arbitrary volume, we have (34)

which are the Maxwell’s equations and (29) which is the elastic wave equation equivalent to (9). Note that one uses instead of to denote a position vector in space in elastodynamics so that indicial notation can be used con, and correspond veniently (in the indicial notation, to , and , respectively, and the components of a vector or is the pertensor are denoted with indices). In the above, and are the components of the magnetic mutation tensor, induction (magnetic flux density) vector and electric displacement (electric flux density) vector , respectively, and are the components of stress tensor . A dot and two dots over a variable imply the first-order and second-order derivatives with respect to time, respectively, and a comma followed by an index denotes the partial differentiation with respect to the coordinate associated with the index. The coupling is reflected in the constitutive relations [10]

(30) are the components of the strain where is the elastic tensor is the permittivity, and is the stress constant. stiffness, If we consider the symmetries in the strain and stress tensors which usually hold, and re-order the indices 11, 22, 33, 23 or 32, 31 or 13, and 12 or 21 in and as 1, 2, 3, 4, 5, and 6 in and , respectively, then the components of those tensors can be re-indexed as

The divergence of stress tensor above can be found [37] (35) Substituting (35) into (34) in a time harmonic case, we can obtain (9). When EM wave is incident on the elastic body and there is no other external force, the force in the above equations is the EM force, i.e., (36) where the superscript implies that the variable is EM related. From the first equation in (32), it is clear that the EM force is generated by the second sum in the stress tensor expression which is contributed by electric field, i.e., (37) Therefore, the EM force can be found as

(38) By treating the EM force as the external force in the derivation of integral equation in the proceeding section, the integral equations for elastic wave are the same as (27), except that the incident displacement field in the first equation in (27) and the right-hand side in the second equation should be (39)

(31) With the new indices, the above constitutive relations can be written as

where is the volume of the object and is the EM force in . When the EM force exists outside the object, the excitation of elastic wave, namely, the right-hand side in the first equation in (27) is (40)

(32)

is the volume of surrounding medium which can be where is the EM force in . truncated in calculations and

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For the coupled integral equations for EM wave part, we can use the same strategy as for elastic wave part to derive. The integral equations are the same as (8) except that the excitation on the right-hand side should include the contribution of the source from strain tensor. From Maxwell’s equations, we have

values at the centers of cells in an average sense. Also, the surrounding medium needs to be truncated in terms of the attenuation of fields in the calculations of coupled excitations. The and stress constant needed in calculaelastic stiffness tions can be found from [10] for some typical elastic piezoelectric materials. For example, the langasite has

(41) We can treat the first term above as an effective current or new producing the incident excitation current and classify it into field in Region 2. The extra incident field by the effective current in Region 2 is

(45)

(42) (46) is the effective current in and the superscript where implies that it is related to the displacement field. From (32), the current has the following three components

and Lithium Niobate has

(43) (47) for time-harmonic fields and is determined by . In Region 1, there is no incident field and the excitation is only from the strain tensor, namely (48)

(44) is the effective current in . Using the excitation where in (42) and (44) as the right-hand side in the first and second equation in (8), respectively, we can solve it to obtain the extra electric fields in the two regions. These fields will create EM force by (38) and become the new excitations for the elastic wave integral equations in (27). V. SOLVING METHOD The developed integral equations can be solved by any IES, such as MoM, BEM, or Nyström method. We use the Nyström method with our local correction scheme to solve the equations [34], [38]. However, since the EM wave part and elastic wave part are coupled to each other by excitation, a special solving strategy is needed. One choice is to use an iterative method, namely, solving the EM wave integral equation first by assuming no contribution from elastic wave in the excitation, and substituting the obtained electric field to the elastic wave integral equation as an excitation so that the elastic wave integral equation can be solved. When the displacement field is obtained, we substitute it back to the EM wave integral equation as a new excitation or a perturbation and solve the resultant EM wave integral equation to obtain new electric field. This new electric field is a new excitation for the elastic wave integral equation and we go through this iterative process until the solutions converge. In the implementation, we use the central difference of electric field or displacement field to approximate the differential of the fields at a point because the partial derivatives of fields are required in calculating the coupled excitations. The medium bodies are discretized into small cubes or tetrahedrons in which the partial derivatives of fields are represented by the

where the unit is N/m for and C/m for use these parameters in the numerical examples.

. We will

VI. NUMERICAL EXAMPLES We use the Nyström method to solve the coupled integral equations for an elastic cube illuminated by a time-harmonic direction and in vertical polarization. EM plane wave along , where is the wavelength The cube has a side length in free space, and its elasticity is characterized by Lithium Nioand . Also, bate with and the cube has an isotropic relative permittivity . The surrounding medium is relative permeability the same as langasite in elasticity with and , and the same as free space in electric properties. We first ignore the elasticities of both the scatterer and surrounding medium and solve the EM wave part of the integral equations. Figs. 2 and 3 show the bistatic radar cross section (RCS) of the cube and a dielectric sphere with a radius and the same material as the cube. This is to verify the solutions of EM wave part of the integral equations by comparing with the MoM solutions or analytical solutions. We then ignore the electric properties of both the scatterer and surrounding medium and solve the elastic wave part of the integral equations. Fig. 4 sketches the normalized total displacement fields on the surface of an elastic sphere with a radius and the same material as the cube when an elastic plane wave illuminates in the elastic surrounding medium defined as before. The fields are observed along the principal cut and to 180 ) and compared with corresponding (

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Fig. 2. Bistatic radar cross section (RCS) for a dielectric cube with a side length s : .

Fig. 4. Normalized displacement field scattered by an elastic sphere with a radius a :  when an elastic plane wave illuminates.

Fig. 3. Bistatic radar cross section (RCS) for a dielectric sphere with a radius a : .

Fig. 5. Normalized displacement field inside an elastic cube illuminated by EM wave in free space.

analytical solutions. This is to verify the elastic wave part of the integral equations. For solving the coupled integral equations, we first consider a simplified case, i.e., the dielectric and elastic cube is put into a vacuum-like free space, so there is no excited elastic wave outside the cube. Fig. 5 plots the normalized displacement fields of the elastic wave inside the cube excited by the EM wave. The fields are observed along the central line from the center of direction. We the cube or the origin to the end facet in the then consider another simplified case which is opposite to the previous case, i.e., the cube is replaced by a traction-free and bubble-like cavity and the surrounding medium takes the material of the cube. There is no excited elastic wave inside the cubic cavity in this case and it only exists in the surrounding medium. Fig. 6 illustrates the normalized displacement field in the surrounding medium which is observed along the principal cut at s surface. Finally, we consider a generalized case, i.e., the both the object and surrounding medium are elastic. The properties of object and surrounding medium are those described in

the first paragraph. Fig. 7 depicts the normalized displacement field of the elastic wave in the surrounding medium which is obs surface. served along the principal cut at the Table I summarizes the computational costs, i.e., CPU time (Seconds) and memory usage (Megabytes) for all the cases above. The cube and sphere are discretized into 768 and 1520 triangular meshes, respectively, and all calculations are performed on a Dell Precision 690 workstation with a 3.0-GHz CPU and 16-GB RAM. Note that the used Nyström method in this work is slightly more efficient than the widely-used MoM because of its simpler mechanism of implementation. The results in Fig. 2 take 176 Seconds in CPU time and 116 MB in memory usage if the MoM is used. Since there exists a magnetic current in addition to the electric current on the object surface, we use the Rao-Wilton-Glisson (RWG) basis function [39] to expand the electric current and the dual basis function [40] to expand the magnetic current, respectively, in the MoM, because the system matrix will be very ill-conditioned if using the RWG basis function to represent both the electric and

= 02

= 02

=02

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sensors take this simple geometry. The developed approach is amenable to implementation as in other IESs because we only need to discretize the object surface or source region no matter how large the field space is. Usually the discretization for the source region is much easier than for the field space. The limitations of the approach could be the internal resonance problem as found in both EM and elastic wave integral equations, and the low-frequency breakdown problem as appearing in the EM integral equations. The relevant remedy techniques in the EM and elastodynamics can be incorporated in the future. VII. CONCLUSION

Fig. 6. Normalized displacement field from a traction-free cubic cavity illuminated by EM wave in elastic medium.

Fig. 7. Normalized displacement field from an elastic cube illuminated by EM wave in elastic medium.

TABLE I SUMMARY OF CPU TIME (T) AND MEMORY USAGE (M) FOR SOLVING ALL EXAMPLES

magnetic current. The dual basis function is complicated in construction and requires high costs in implementation. Also, the MoM is not suitable for solving the elastic wave part of the integral equations because the unknown and vectors on the object surface are 3D vectors instead of surface vectors and the Nyström method is more convenient in implementation. Although we only consider the simple geometry in the above, the coupled integral equations are developed based on 3D arbitrary shapes and they can be applied to more complicated objects with an increase of computational effort. Also, the simple cubic shape is not just for illustration and actually it can find many applications in practice because many piezoelectric

Wave interaction with materials may include multiple physics (multiphysics). EM wave illumination on elastic media includes electrodynamic and elastodynamic processes and coupled Maxwell’s equations and elastic wave equations should be solved to understand the involved physics. Although the coupled equations have been derived earlier, they were only in a PDE form and thus only PDE numerical solvers can be employed in seeking solutions. We first develop coupled BIEs for the problem in this work by using Huygens’ equivalence principle and extinction theorem. The coupling is reflected in the excitations or right-hand sides in both EM wave part and elastic wave parts of the integral equations. The EM force is the new excitation for elastic wave and the current due to the strain tensor is the new excitation for EM wave in the coupled BIEs. By the BIEs, the solution process can take all advantages of IESs like MoM, BEM and Nyström method. We use Nyström method with an iterative process to solve the coupled BIEs and some numerical results for the interaction of EM wave with piezoelectric materials are illustrated. The developed approach could also find applications in many other areas. For example, one has tried to use the illumination of microwave and measurement of induced elastic wave to reconstruct objects in geophysical exploration and medical imaging because the microwave illumination can result in a high contrast while the measurement of elastic wave can yield a high resolution in the imaging. Using the coupled integral equations could greatly facilitate the analysis for such problems. REFERENCES [1] J. J. Kyame, “Wave propagation in piezoelectric crystals,” J. Acoust. Soc. Amer., vol. 21, no. 3, pp. 159–167, 1949. [2] J. J. Kyame, “Conductivity and viscosity effects on wave propagation in piezoelectric crystals,” J. Acoust. Soc. Amer., vol. 26, no. 6, pp. 990–993, 1953. [3] H. Hruska, “The rate of propagation of ultrasonic waves in ADP and in Voigt’s theory,” Czech. J. Phys., vol. B16, pp. 446–453, 1966. [4] C. C. Tseng and P. M. White, “Propagation of piezoelectric and elastic surface waves on the basal plane of hexagonal piezoelectric crystals,” J. Appl. Phys., vol. 38, pp. 4274–4280, 1967. [5] R. N. Spaight and G. G. Koerber, “Piezoelectric surface waves on LiNbO ,” IEEE Trans. Sonics Ultrason., vol. 18, pp. 237–238, 1971. [6] R. D. Mindlin, “Electromagnetic radiation from a vibrating quartz plate,” Int. J. Solids Struct., vol. 9, pp. 697–702, 1972. [7] A. Sedov and L. W. Schmerr, Jr., “Some exact solutions for the propagation of transient electroacoustic waves I: Piezoelectric half-space,” Int. J. Eng. Sci., vol. 24, pp. 557–568, 1986. [8] L. W. Schmerr, Jr. and A. Sedov, “Some exact solutions for the propagation of transient electroacoustic waves II: Plane interface between two piezoelectric media,” Int. J. Eng. Sci., vol. 24, pp. 921–932, 1986. [9] P. C. Y. Lee, “Electromagnetic radiation from an AT-cut quartz plate under lateral-field excitation,” J. Appl. Phys., vol. 65, pp. 1395–1399, 1989.

TONG AND CHEW: COUPLED INTEGRAL EQUATIONS FOR MICROWAVE INDUCED ELASTIC WAVE IN ELASTIC MEDIA

[10] J. S. Yang, An Introduction to the Theory of Piezoelectricity. New York: Springer, 2005. [11] R. D. Mindlin, “A variational principle for the equations of piezoelectromagnetism in a compound medium,” in Complex Variable Analysis and Its Applications. USSR: Academy of Sciences, 1978, pp. 379–400. [12] P. C. Y. Lee, “A variational principle for the equations of piezoelectromagnetism in elastic dielectric crystals,” J. Appl. Phys., vol. 69, pp. 7470–7473, 1991. [13] J. S. Yang, “A generalized variational principle for piezoelectromagnetism in an elastic medium,” Arch. Mech., vol. 43, pp. 795–798, 1991. [14] J. S. Yang, “Variational principles for the vibration of an elastic dielectric,” Arch. Mech., vol. 45, pp. 279–284, 1993. [15] J. S. Yang and X. Y. Wu, “The vibration of an elastic dielectric with piezoelectromagnetism,” Q. Appl. Math., vol. 53, pp. 753–760, 1995. [16] J. S. Yang, “Bleustein-Gulyaev waves in piezoelectromagnetic materials,” Int. J. Appl. Electromagn. Mech., vol. 12, pp. 235–240, 2000. [17] J. S. Yang, “Piezoelectromagnetic waves in a ceramic plate,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 51, pp. 1035–1039, 2004. [18] X. F. Li and J. S. Yang, “Electromagnetoelastic behavior induced by a crack under antiplane mechanical and inplane electric imapcts,” Int. J. Fract., vol. 132, pp. 49–65, 2005. [19] P. C. Y. Lee, Y. G. Kim, and J. H. Prevost, “Electromagnetic radiation from doubly rotated piezoelectric crystal plates vibrating at thickness frequencies,” J. Appl. Phys., vol. 67, pp. 6633–6642, 1990. [20] C. F. Campbell and R. J. Weber, “Calculation of radiated electromagnetic power from bulk acoustic wave resonators,” in Proc. IEEE Int. Freq. Control Symp., Salt Lake City, UT, 1993, pp. 472–475. [21] S. Li, “The electromagneto-acoustic surface wave in piezoelectric medium: The Bleustein-Gulyaev mode,” J. Appl. Phys., vol. 80, pp. 5264–5269, 1996. [22] A. R. Mitchell and D. F. Griffiths, The Finite Difference Method in Partial Differential Equations. New York: Wiley, 1980. [23] A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. Norwood, MA: Artech House, 2005. [24] K. H. Huebner and E. A. Thornton, The Finite Element Method for Engineers, 2nd ed. New York: Wiley, 1982. [25] J. M. Jin, The Finite Element Method in Electromagnetics, 2nd ed. New York: Wiley, 2002. [26] W. C. Chew, M. S. Tong, and B. Hu, Integral Equation Methods for Electromagnetic and Elastic Waves. San Rafael, CA: Morgan & Claypool, 2008. [27] Fast and Efficient Algorithms in Computational Electromagnetics, W. C. Chew, J. M. Jin, E. Michielssen, and J. M. Song, Eds. Boston, MA: Artech House, 2001. [28] W. C. Chew, Waves and Fields in Inhomogeneous Media. New York: Van Nostrand Reinhold, 1990. [29] A. J. Poggio and E. K. Miller, “Integral equation solutions of three-dimensional scattering problems,” in Computer Techniques for Electromagnetics, R. Mittra, Ed. Oxford: Pergamon Press, 1973, ch. 4. [30] C. Müller, Foundations of the Mathematical Theory of Electromagnetic Waves. Berlin: Springer-Verlag, 1969. [31] Y. H. Pao and V. Varatharajulu, “Huygens’ principle, radiation conditions, and integral formulas for the scattering of elastic waves,” J. Acoust. Soc. Amer., vol. 59, no. 6, pp. 1361–1371, 1976. [32] R. F. Harrington, Field Computation by Moment Methods. Piscataway, NJ: IEEE Press, 1993. [33] M. H. Aliabadi, The Boundary Element Method. New York: Wiley, 2002, vol. 2. [34] M. S. Tong and W. C. Chew, “A higher-order Nyström scheme for electromagnetic scattering by arbitrarily shaped surfaces,” IEEE Antenna Wireless Propag. Lett., vol. 4, pp. 277–280, 2005. [35] J. A. Hudson, The Excitation and Propagation of Elastic Waves. Cambridge: Cambridge Univ. Press, 1980. [36] Y. H. Chen, W. C. Chew, and S. Zeroug, “Fast multipole method as an efficient solver for 2D elastic wave surface Integral equations,” Comput. Mech., vol. 20, pp. 495–506, 1997. [37] J. D. Achenbach, Wave Propagation in Elastic Solids. Amsterdam: North Holland, 1973. [38] M. S. Tong and W. C. Chew, “Super-hyper singularity treatment for solving 3D electric field integral equations,” Microw. Opt. Technol. Lett., vol. 49, pp. 1383–1388, 2007. [39] S. M. Rao, D. R. Wilton, and A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propag., vol. AP-30, pp. 409–418, 1982.

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[40] Q. L. Chen, “Electromagnetic modeling of three-dimensional piecewise homogeneous material bodies of arbitrary composition and geometry,” Ph.D. dissertation, Department of Electrical Engineering, University of Houston, Texas, 1990.

Mei Song Tong (S’01–M’04–SM’07) received the Ph.D. degree in electrical engineering from Arizona State University (ASU), Tempe, in 2004. Currently, he is a Visiting Research Scientist at the Center for Computational Electromagnetics and Electromagnetics Laboratory (CCEML), Department of Electrical and Computer Engineering (ECE), University of Illinois at Urbana-Champaign (UIUC). His research interests include numerical techniques in electromagnetics, acoustics and elastodynamics, simulation and design for RF/microwave circuits and systems, efficient solutions for antenna analysis, interconnect and packaging analysis, and inverse electromagnetic scattering. He has published more than 50 papers in refereed journals and conference proceedings, and coauthored a book. Dr. Tong is a fellow of the Electromagnetics Academy (EMA), a full member of USNC/URSI (Commission B), and a member of Applied Computational Electromagnetics Society (ACES) and Sigma Xi Honor Society. He has served as a technical reviewer for 14 international journals and conferences, served as an Associate Editor and editorial board member for Progress in Electromagnetics Research (PIER) and Journal of Electromagnetic Waves and Applications (JEMWA), and served as an Associate Editor and Guest Editor for a special issue for Waves in Random and Complex Media (WRCM). In addition, he has also served as a Session Organizer, Session Chair, and Technical Program Committee (TPC) Member for Progress in Electromagnetics Research Symposium (PIERS), the IEEE International Symposium on Antennas and Propagation (IEEE APS), and USNC/URSI National Radio Science Meeting. Weng Cho Chew (S’79–M’80–SM’86–F’93) received the B.S. degree in 1976, both the M.S. and Engineer’s degrees in 1978, and the Ph.D. degree in 1980, from the Massachusetts Institute of Technology, Cambridge, all in electrical engineering. He is serving as the Dean of Engineering, The University of Hong Kong. Previously, he was a Professor and the Director of the Center for Computational Electromagnetics and the Electromagnetics Laboratory at the University of Illinois. Before joining the University of Illinois, he was a Department Manager and a Program Leader at Schlumberger-Doll Research. His research interests are in the areas of waves in inhomogeneous media for various sensing applications, integrated circuits, microstrip antenna applications, and fast algorithms for solving wave scattering and radiation problems. He is the originator of several fast algorithms for solving electromagnetics scattering and inverse problems. He led a research group that developed parallel codes that solve dense matrix systems with tens of millions of unknowns for the first time for integral equations of scattering. He authored the book Waves and Fields in Inhomogeneous Media, coauthored the book Fast and Efficient Methods in Computational Electromagnetics, and authored and coauthored over 300 journal publications, over 400 conference publications, and over ten book chapters. Dr. Chew is an IEEE Fellow, an OSA Fellow, an IOP Fellow, and was an NSF Presidential Young Investigator (USA). He received the Schelkunoff Best Paper Award for a paper published in the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, the IEEE Graduate Teaching Award, UIUC Campus Wide Teaching Award, and IBM Faculty Awards. He was a Founder Professor of the College of Engineering, and currently, a Y. T. Lo Endowed Chair Professor in the Department of Electrical and Computer Engineering at the University of Illinois. From 2005 to 2007, he served as an IEEE Distinguished Lecturer. He served as the Cheng Tsang Man Visiting Professor at Nanyang Technological University in Singapore in 2006. In 2002, ISI Citation elected him to the category of Most-Highly Cited Authors (top 0.5%). In 2008, he was elected by IEEE AP Society to receive the Chen-To Tai Distinguished Educator Award. Previously, he served on the IEEE Adcom for Antennas and Propagation Society as well as Geoscience and Remote Sensing Society. He has been active with various journals and societies.

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Balanced Antipodal Vivaldi Antenna With Dielectric Director for Near-Field Microwave Imaging Jeremie Bourqui, Member, IEEE, Michal Okoniewski, Fellow, IEEE, and Elise C. Fear, Member, IEEE

Abstract—A balanced antipodal Vivaldi antenna is designed to be used as a sensor for a microwave breast cancer detection system. The antenna has the ability to send short electromagnetic pulses into the near-field, with low distortion, low loss and in a directional manner. The antenna directivity is further improved by the inclusion of a novel feature in the antenna aperture called a “director” which consists of a profiled piece of higher dielectric constant material. Several simulated results are successfully confirmed with measurements. Reflections of a tumor placed in a breast model are simulated for two cases, namely a balanced antipodal Vivaldi antenna with and without a director. Greater tumor responses are recorded with the director present, demonstrating the potential of this feature for microwave breast imaging. Index Terms—Antenna, microwave breast imaging, radar, ultrawideband (UWB).

I. INTRODUCTION

N

EAR-FIELD microwave imaging approaches for exploring interior structures of the body are a topic of growing interest. For example, assessment of bone, heart and breast health with microwave techniques has been proposed [1]–[3]. One approach to biological microwave imaging is radar-based, which operates by sending a short-time pulse of microwaves towards the object of interest using one or many antennas. The reflections are measured and used to create an image related to the differences in dielectric properties of the structure. For breast imaging, recent studies indicate a wide range in dielectric properties of healthy tissues, which appears to be related to the content of adipose tissues [4]. A second study showed contrast between healthy and malignant tissues ranging from 1:10 to 10:11, depending on the adipose content [5]. In order to reliably sense the reflections from tumors located in tissues ranging from adipose to glandular, a high quality antenna is required to send and receive short-time microwave pulses with low distortion and high efficiency. Selective illumination of the breast may assist in tumor localization. Additionally, the antenna has to be compact in order to ease its placement around the breast and to be compatible with prototype imaging systems. This type of sensor is not commercially available.

Manuscript received January 14, 2009; revised July 15, 2009; accepted January 25, 2010. Date of publication April 22, 2010; date of current version July 08, 2010. The authors are with the Department of Electrical and Computer Engineering, University of Calgary, Calgary, Alberta, AB T2N 1N4, 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/TAP.2010.2048844

Numerous antenna designs for radar-based ultrawideband (UWB) microwave breast imaging have been reported over the past decade. For example, stacked-patch [6] and wide slot [7] antennas have been developed at the University of Bristol. These antennas are mounted on a hemispherical surface and function as a multi-static system [8]. For monostatic data collection, a ridged pyramidal horn antenna [9] has been reported by the University of Wisconsin, and resistively loaded dipole, tapered slot, transverse electromagnetic horn, and balanced antipodal Vivaldi antennas have been presented by the University of Calgary (e.g., [10]). Our most recently developed antennas are designed to operate in an immersion medium of canola oil [11]. This immersion medium provides reduced antenna size and reflections from the skin when compared to free space, while providing reasonable imaging capabilities with an acceptable number of measurement locations. We further note that these antennas are designed to operate in, effectively, the radiative near-field. The balanced antipodal Vivaldi antenna (BAVA) is a compact and versatile design that was introduced in [12]. We have modified the design for our near-field imaging application, as reported in [13]. The BAVA provides a more compact profile and lower reflections from the feeding structure than the tapered slot antenna [10]. In this paper, we introduce a significant improvement to our design which consists of a profiled dielectric piece with higher permittivity that is placed in the antenna aperture. We refer to this new feature as a “director” as it focuses the energy in the endfire direction in the near-field. We note that there is a body of work describing the addition of dielectric layers or radomes to tapered slot antennas (e.g., [14], [15]). These layers typically improve matching of compact elements and can result in increased antenna gain. This is a different concept from the director, in which the dielectric piece is included inside the aperture and effects changes in the radiation behavior without significant changes to the impedance. We also note that inclusion of materials with different dielectric properties in and around the aperture of tapered slotline antennas has been previously reported. For example, dielectric material is removed from the aperture of the antenna in order to provide a better match to free space in [16]. In [17], a dielectric rod is placed around the aperture of a Vivaldi antenna, acting as a second traveling wave antenna and resulting in improved gain and phase center stability. In both of these examples, the permittivity of the inclusion is lower than that of the antenna substrate. The director that we explore in this paper has a higher permittivity than the antenna substrate, does not improve the impedance matching of the antenna and is part of the radiation mechanism of the antenna itself. Hence this novel feature functions in a different manner than

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Fig. 2. Geometry and parameters of the BAVA copper pattern. The origin used to generate the curves is labeled as . Fig. 1. Exploded view of the BAVA construction.

previously reported work. In the context of microwave imaging application, a more focused beam illuminates a smaller volume which leads to an increase in the tumor-to-clutter ratio. Section II introduces the BAVA design and the modified version including the dielectric director (BAVA-D). Section III presents the simulation and measurement methods used in this paper. Then, Section IV compares the BAVA and BAVA-D, with emphasis on the correlation between measured and simulated results and application to a breast model. The findings of the antenna studies are summarized in Section V. II. ANTENNA DESIGN This section presents the BAVA design, then introduces the director and BAVA-D. Details on implementation of both designs are also provided. A. BAVA Our BAVA design follows concepts described in [12]. It consists of three copper layers; the two external layers are the ground planes and the central layer is the conductor (Fig. 1). The copper layers are separated by two dielectric substrates (supportive substrates) and two additional dielectric layers are stacked on each side of the antenna (stacking substrates). This novel feature balances the dielectric loading between the conductor and ground planes. As a result, the usual beam squint observed in this type of antenna construction [18] is considerably reduced. Moreover, for this application, the efficiency is improved since contact between the lossy canola oil and the external copper layers is avoided. The antenna is fed through an SMA connector followed by a gradual transition from a stripline to a tri-strip transmission line (TL). Along the transition, the conductor width increases linearly while the ground width decreases exponentially to keep constant impedance. The tri-strip TL extends for a short distance before the grounds and conductor start to flare in opposite directions with exponential curvatures to create the antenna aperture. Fig. 2 presents the geometry and parameters values of the and follow the excopper pattern. The curvatures , ponential (1): (1)

TABLE I CURVATURES PARAMETERS AND RELATION TO THE OTHER ANTENNA DIMENSIONS DNDICATED IN FIG. 2

The curvatures parameters are listed in Table I. The overall , including the SMA attachment antenna size is elements length but excluding the SMA connector. We note that Fig. 2 does not include the SMA attachment elements length. The antenna is constructed using RT/duroid 6002 (Rogers Corporation, CT, USA) which has a relative permittivity of 2.94. A photolithography process is used to pattern the copper and the bonding of the different layers is achieved using a thermoplastic . Rogers 3001 bonding film B. BAVA With Dielectric Director (BAVA-D) The director consists of a shaped object of higher permittivity, placed in the aperture (Fig. 3). The director is expected to have two different effects. First, it should act as a waveguiding structure and direct most of the energy toward the aperture center. The second effect is related to the phase velocity, which will be lower in the director structure compared to the rest of the substrate. This produces differences in the propagation velocities in the director and the copper edges. As waves travel faster along the edges and the path length is physically longer, the overall effect is a more planar phase front near the aperture of the antenna (compared to the BAVA). The shape of the director is designed to avoid reflections from its extremities, i.e., the start and the end of the aperture, shown respectively as A and B in Fig. 3 a. The section A approximately follows the aperture curves while the section B has been limited to a simple triangle that reasonably avoids reflections from the aperture. Fig. 3 shows the dimensions. The substrate length is extended by 4 mm compared to the original design to accommodate the director placement. The BAVA-D is manufactured similarly to the BAVA. The opening in the substrate and the director are precisely machined using a milling machine and a water jet cutter respectively. The director is simply pressed into the opening and holds without

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smallest wavelength or smaller where refinements are needed due to geometrical features of the antenna. Perfectly matched layers (PML) are used for boundary conditions. Our microwave imaging system utilizes canola oil as an ambient immersion medium, so canola’s electrical properties are assigned to the background of each simulation. From 1 to 14 GHz, its permittivity and conductivity vary from approximately 2.55 to 2.35 and 0.01 to 0.04 S/m, respectively, [19]. For most simulations, it was found sufficient to consider an average and the maximum relative permittivity value of . However, in some cases, such conductivity of as comparing simulations with measurements, a single pole Debye model may be used to represent the property variations with frequency

(2) Fig. 3. BAVA including the higher dielectric permittivity director. (a) Top view and (b) 3D view with the director shown above its housing. For greater clarity the dielectric layers are shown as transparent in (a). All dimensions are in mm.

denotes where , is the complex relative permittivity, is the static relative the angular frequency, permittivity, is the relative permittivity at infinity, is the relaxation time and is the static conductivity. The performance of the antennas is evaluated in terms of: , , half energy beamwidth (HEBW), half energy beam and are simulated using the standard (HEB) and fidelity. broadband excitation implemented by SEMCAD X, however the simulations for the HEBW, HEB and fidelity are computed using a specific ultrawideband pulse [20] of the form:

(3) Fig. 4. The constructed BAVA (right) and BAVA-D (left).

any adhesive. The director is made of Eccostock HIK material (Emerson & Cuming Microwave Product, MA, USA) with relative permittivity of 6. This permittivity has been selected since it produces the expected effect, however other values may be utilized. The constructed antennas with and without the director are shown in Fig. 4. III. EVALUATION METHODS In order to test the BAVA and BAVA-D, full wave simulations are performed. In addition to reflection and transmission, several near-field parameters are introduced for antenna performance assessment. The manufactured antennas are immersed in oil, and measurements are collected in order to compare simulated and measured data. A. Simulation Simulated results are obtained using SEMCAD X (SPEAG, Zurich, Switzerland), which utilizes the finite-difference time-domain (FDTD) technique. To feed the antenna, a coaxial transmission line is connected to the stripline and represents the SMA-stripline transition used in practice. The coaxial line is excited using a waveguide source. The mesh size is 1/14 of the

where

is used to adjust the amplitude of the pulse, and . This pulse contains energy, above 10% of its maximum, from 20 MHz to 10 GHz in the frequency spectrum. The HEBW and HEB are based on the energy radiated by the antenna. The energy in and around the antenna structure is calculated by summing time samples of the instantaneous Poynting vector over the duration of the simulation time. We term this quantity the energy flux density (EFD). In the near-field, we define the HEBW on a plane orthogonal to the main radiation beam and situated at a given distance from the antenna aperture. The HEBW describes the region over which the energy is greater than half of the maximum value on the selected plane. For the example shown in Fig. 5(a), the antenna is aligned with the x-axis, so the HEBW is evaluated in the y- and z-directions. The HEB attempts to provide a more general representation of the radiation beam in the near-field. Fig. 5(b) shows the HEBW calculated along the x-axis instead of at a single point as shown by Fig. 5(a). To provide a more general representation of the radiation beam in the near-field, we model the conical shape with an equivalent angle in conjunction with a corresponding beam origin. As shown in Fig. 5(b), the HEB angle and origin are defined by fitting the half energy contour and maximum energy path recorded on a series of planes to linear functions. The HEB representation in the near-field

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Fig. 6. Measurement setup including the VNA, oil tank, positioning system, antenna and one of the objects used to record reflections.

Fig. 5. Half energy area on one plane (a) and HEB representation (b).

is powerful since, by including the beam origin information, it models the radiation behavior as function of the actual antenna structure and size. This makes radiation pattern comparison between antennas more straightforward and makes prediction of the radiation coverage of an object placed close to the antenna possible. The fidelity measures how faithfully the excitation pulse is transmitted or received by the antenna and therefore reflects the distortion due to the frequency band limitation and phase non-linearity [21]. Only the transmitting fidelity is of interest. It is calculated using the main polarization component ( component) of the electric field and the first derivative of the excitation pulse is used as a reference signal. The maximum value of fidelity is one.

Reflections are measured from objects consisting of cubes and spheres of dimensions varying from 13 mm to 3.2 mm. The objects are made out of Eccostock HIK and TMM6 (Rogers Corporation) materials with relative permittivities of 10 and 6, respectively. These objects are attached to a Plexiglas rod and positioned in front of the antenna using a manual linear stage as shown in Fig. 6. In order to extract the reflections from the objects, a reference measurement of the Plexiglas rod is subtracted from the total measurement. The resulting signal is reis measured using the ferred to as the calibrated response. same setup but with two antennas facing each other and separated by a known distance. The near-field radiation pattern is measured using a dosimetric assessment system (DASY 4 Professional, SPEAG). The antenna is placed in the same tank of oil as presented in Fig. 6. The radiated E-field is measured at 2.45, 4, 5.1, 5.9 GHz. Only relative radiation intensity is measured since the probes are not calibrated for canola oil. IV. RESULTS The director influence is assessed by comparing the BAVA-D performance to the original BAVA design with simulated and measured results. S-parameters, radiation fields, backscatter reflections and ability to sense a tumor in a breast model are presented. A. S-Parameters

B. Measurement All of the measurements are obtained with the antennas immersed in canola oil and data are recorded by an Agilent 8719ES Vector Network Analyzer (VNA) (Agilent, Palo Alto, CA). The time signals are synthetically created from the frequency domain S parameters. First, a Chirp-Z transform is used to find the frequency-domain representation of (3) at the measured frequencies. Next, the measured S-parameters are multiplied with the frequency-domain version of the excitation. Finally, the inverse Chirp-Z transform is used to obtain the time-domain signals [22].

The simulated reflection coefficients of the original BAVA and the BAVA-D are shown in Fig. 7. Both antennas operate over a 2.4 to 18 GHz band and no substantial difference is observed between the two versions besides slightly higher reflections at lower frequencies for the BAVA-D. of two constructed BAVA-Ds are In Fig. 8, the measured compared with the simulated data. The measurements match the main trends of the simulations. The main source of error comes from the thermoplastic used to bond the different layers together, since it does not match the substrate permittivity ( compared to 2.94 for the substrate). However, the measured

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Fig. 7. Simulated S

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 58, NO. 7, JULY 2010

for the BAVA and BAVA-D.

Fig. 8. Measured BAVA-Ds S

Fig. 9. Transmission coefficient (S ) obtained with two antennas facing each other with 100 mm separation (metalization end as reference).

compared to the simulation data.

results remain acceptable since the bandwidth is not significantly altered. Similar agreement is seen with the BAVA [13]. between two antennas Next, the transmission parameter assesses the improvements due to the director in the frequency domain. From a detection perspective, an antenna with higher will receive more reflected energy from an object placed in front of the antenna. Fig. 9 presents the simulated and measured for both antennas facing each other and separated by 100 mm (metalization end as reference). First, it is observed that magnitude between 2 to around the director increases the 12 GHz. Similar behavior has been observed at separation distances between 40 to 150 mm and therefore it is concluded that there is no direct dependence on the separation distance. Second, it is observed that the measured data does not match the magnitude of the simulated results for both antennas. This discrepancy mostly stems from the canola oil. When the same scenario is reproduced in the air, a good match is found between simulated and measured results. The reason for the disagreement, when the antennas are immersed in canola oil, is unknown measurements exand is being investigated. Nevertheless, hibit the same trends as the simulations and it can be observed

Fig. 10. Simulated total EFD on the Y plane @ y = 0 for the (a) BAVA and (b) BAVA-D. Data are normalized by the input energy. The EFD at each point is the sum of the sampled instantaneous Poynting vector over the duration of the simulation.

that the transmitted power is increased by approximately the same ratio when the director is present. B. Radiated Fields To define the beamwidth, the EFD is computed on Y and Z planes ranging from the antenna feed point to a distance of 70 mm away from the aperture. These data are shown for both antennas in Fig. 10 for the Y plane. The endfire radiation behavior is evident, while it can be noticed that the director significantly increases the near-field directivity of the BAVA. A slight increase in the back radiation is noticed when the director is present, however the front to back ratio is still 35% higher compared with the original BAVA. When the radiation behavior is analyzed in the frequency domain, it is observed that the director effect increases with frequency. This phenomenon is confirmed by the transmission coefficient in Fig. 9 while Fig. 11

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TABLE II SIMULATED BEAMWIDTH RESULTS FOR THE BAVA AND BAVA-D

Fig. 11. Simulated radiated E-field RMS modulus at 3, 6, 9 and 12 GHz on the Y plane @ y = 0 for the BAVA and BAVA-D. The fields are normalized in proportion to the energy accepted by each antenna at each frequency.

Fig. 12. Simulated HEB on the Z plane for the (a) BAVA and (b) BAVA-D. Dotted lines represent the half energy limits and the maximum energy path with the beam origin indicated by the circle.

illustrates this effect at selected frequencies. The HEB view in the Z plane (Fig. 12) shows that, when the director is present, the pulse energy stays concentrated inside the antenna structure while it starts to expand outside the substrate boundary around 15 mm before the end of the antenna for the original design. This illustrates the waveguide effect produced by the director. A quantitative comparison of the beamwidth is contained in Table II. As expected the effect of the director on the beamwidth is an overall narrowing on both axes as demonstrated by the HEBW values at 20 and 50 mm. It is observed that the director improvement to beamwidths in the Y and Z planes is not necessarily due to a smaller HEB angle as a shift of the beam origin towards the antenna aperture occurs. For example the HEB angle on the Y plane actually increases from 32 to 34 however the

HEBW measured at 20 and 50 mm are smaller with the director present. This occurs because the energy starts to expand further along the antenna in the X direction which is clearly exto pressed by the shift of the beam origin from with the director (Table II). On the Z plane, the director actually reduces the HEB angle from 60 to 51 while the to . beam origin is also moved from Therefore the HEBW on the Z plane is significantly reduced as indicated in Table II. For the BAVA and BAVA-D, beam deviations of 3 and 4 , respectively, appear on the Y plane while no deviation is observed on the Z plane. Thus the director slightly increases the beam deviation on the Y plane. Next, the measured radiation pattern in the near-field is compared with simulation. Very good agreement is found for both antennas at all tested frequencies. A typical result is shown in Fig. 13 for the BAVA-D at 5.1 GHz. The simulated fidelity is very close to 1 for both antennas, with values above 0.9 at the aperture and above 0.96 from 20 mm away, as shown by Fig. 14. For the original BAVA, the fidelity logically increases with the distance from the aperture, however the version with the director has a higher fidelity closer to the antenna which slightly decreases further away. This behavior is a direct effect of the director which evenly concentrates the radiated energy, across the frequency band, closer to the antenna aperture. The fidelity of the radiated pulse has not been measured because of equipment limitations. However the following section shows correlation between measured and simulated reflections from different objects, supporting the fidelity results. C. Backscatter Reflections Reflections from different objects placed 40 mm in front of the antenna aperture are measured and compared with simulated data. The dispersive behavior of the canola oil is included in simulations to closely reproduce the measurement environment. To calibrate the simulated data, the response computed without an object is subtracted from the total response received with the object present. To facilitate comparison between measured and simulated data, each signal is normalized to its maximum absolute value. Additionally the simulated signal is slightly shifted to be aligned with the measured data. Representative instances of the reflected signals are shown in Fig. 15 which illustrates cube made of Eccosthe reflections from a material . The shapes of measured tock backscatter signals are consistent with their simulated counterparts for both antennas. The good correlation between measured

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Fig. 15. Calibrated Backscatter time domain signature produced by a 6 2 6 2 6 mm cube made of Eccostock HIK = 10 material ( = 10). (a) Measured vs simulated time signature using the BAVA-D. (b) Measured reflected signal using the BAVA and BAVA-D.

to a large one. The measurements (Fig. 15(b)) confirm the increase in reflected energy observed with the director and its dependence on the object size. The BAVA-D tends to have slightly stronger late time ringing compared to the BAVA. This behavior is not surprising and improvement in this ringing may be expected with a modified director shape. Fig. 13. Simulated and measured radiation pattern at 5.1 GHz for the BAVA-D.

Fig. 14. Simulated fidelity along an X-directed line away from the antenna aperture. (x = 0 at the aperture as in Fig. 13).

and simulated signatures supports the simulated fidelity results presented earlier. Next, the intensity of the backscatter signal is explored. The simulated results obtained for the different objects demonstrate an increase in reflected intensity ranging from 2.6 to 3.6 when the director is used. It is also observed that smaller objects tend to increase this ratio, which makes sense since a narrower beam would increase the illumination of a small surface compared

D. Tumor Detection in Realistic Breast Model Since the ultimate purpose of these antennas is to sense breast tumors, simulations have been performed to assess the improvement induced by the director for this particular application. For this task, a breast model of realistic shape, derived from an MRI scan, is imported into SEMCAD X. The simulation model is presented in Fig. 16. A 40 mm thick object, that replicates the chest wall, is added on the upper part of the breast model. The breast interior is homogeneous and is simulated as adipose tissue. A 6 mm tumor is placed at a distance of 30 mm from the skin. The electric properties of breast tissues at microwave frequencies are modeled in SEMCAD X using single pole Debye models. The Debye parameters presented in [23] are used for the adipose tissue and tumor while the data measured in [24] are used to simulate dry skin. The chest wall, with a relative permittivity of 50 and electrical conductivity of 4 S/m, is not modeled as a dispersive material. The parameters for the different Debye models can be found in Table III. The antenna is aligned with the tumor and placed approximately 20 mm from the breast surface. The antenna scans the model in a circular pattern with 18 degree increments. The zero degree (reference) location is defined in Fig. 17. For each position, simulations are performed with and without the tumor present, such that the tumor reflections can be extracted from the overall signal by a simple subtraction. The energy contained in the tumor reflection at each antenna position is calculated and normalized to the maximum reflected energy sensed by the BAVA. Fig. 17 presents the EFD in the coronal plane of the breast models with the antennas at the reference location. It is observed

BOURQUI et al.: BAVA WITH DIELECTRIC DIRECTOR FOR NEAR-FIELD MICROWAVE IMAGING

Fig. 16. The breast model including the tumor and the antenna. The skin and the interior of the breast are transparent to show the tumor.

TABLE III DEBYE PARAMETERS USED TO MODEL THE PROPERTIES OF THE DIFFERENT BREAST TISSUES

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Fig. 18. Energy reflected by the tumor sensed with the BAVA and BAVA-D in function of azimuth position. The values are normalized to the maximum energy sensed by the BAVA. The delta values correspond to the difference between the BAVA-D and BAVA energies.

compensated for in practical terms by the increased tumor response. V. CONCLUSION

Fig. 17. Total EFD on the Y plane, radiated by (a) the BAVA and (b) BAVA-D inside the breast. The circle represents the tumor location. Data are normalized by the input energy.

In this paper the near-field directivity of a BAVA is improved by the inclusion of higher permittivity and specially shaped material in the aperture. This novel feature is called the director. The BAVA-D produces a narrower beamwidth and generally below between 2.4 higher fidelity while keeping to 18 GHz (SMA connector limit). The effect of this narrower beamwidth is also noticed in since the transmitted energy between two antennas is significantly higher when the director is present. Additionally, it is demonstrated that the BAVA-D increases the backscatter energy from an object placed in front of the antenna, such as a tumor contained in a breast. From a detection point of view, this is an advantage. Only basic explanations about the physical effect of the director are given in this paper. A deeper analysis of the director effect and the influence of its permittivity, shape and size is ongoing. Finally, we note that the director is expected to produce similar effect when applied to any type of aperture-based traveling wave antenna. ACKNOWLEDGMENT

that more energy penetrates into the breast when the director is used. Fig. 18 demonstrates that this increase is also noted as the antenna is scanned around the breast. Specifically the BAVA-D magnifies the tumor reflection by 3 to 4 dB for all positions. For this specific scenario, the reduced beamwidth does not reduce the number of locations at which the tumor is sensed. Practically, the number of locations at which the tumor response is received relates to the breast size, tumor location and glandular tissue distribution. The decrease in beamwidth may result in a small increase in the number of scan locations; however this is

The authors would like to acknowledge the technical support of F. Hickli, B. Isenor, C. Stern, R. Scorey, T. Williams and J. Shelley, all of the University of Calgary, Calgary, AB, Canada. REFERENCES [1] S. Semenov, V. Posukh, A. Bulyshev, and T. Williams, “Microwave tomographic imaging of the heart in intact swine,” J. Electromagn. Waves Applicat., vol. 20, no. 7, pp. 873–890, 2006. [2] S. Semenov et al., “Microwave tomography for functional imaging of extremity soft tissues: Feasibility assessment,” Phys. Med. Biol., vol. 52, no. 18, pp. 5705–5719, 2007.

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[3] T. Rubaek, P. Meincke, and O. Kim, “Three-dimensional microwave imaging for breast-cancer detection using the log-phase formulation,” in Proc. IEEE Antennas Propag. Soc. Int. Symp., 2007, pp. 2184–2187. [4] M. L. Lazebnik et al., “A large-scale study of the ultrawideband microwave dielectric properties of normal breast tissue obtained from reduction surgeries,” Phys. Med. Biol., vol. 52, no. 10, pp. 2637–2656, May 2007. [5] M. L. Lazebnik et al., “A large-scale study of the ultrawideband microwave dielectric properties of normal, benign and malignant breast tissues obtained from cancer surgeries,” Phys. Med. Biol., vol. 52, no. 20, pp. 6093–6115, Oct. 2007. [6] R. Nilavalan, I. Craddock, J. Leendertz, A. Preece, and R. Benjamin, “Wideband microstrip patch antenna design for breast cancer tumour detection,” IET Microwaves Antennas Propag., vol. 1, pp. 277–281, 2007. [7] D. R. Gibbins, M. Klemm, I. Craddock, G. Hilton, and D. Paul, “The design of a wide slot antenna for the transmission of UWB signals into the human body using FDTD simulation,” in Proc. 2nd Eur. Conf. Antennas Propag., Edinburgh, U.K., Nov. 11–16, 2007, vol. 1, 5 pages. [8] I. Craddock, M. Klemm, J. Leendertz, A. Preece, and R. Benjamin, “An improved hemispherical antenna array design for breast imaging,” in Proc. 2nd Eur. Conf. Antennas Propag., Edinburgh, U.K., Nov. 11–16, 2007, 5 pages. [9] X. Li, S. Hagness, M. Choi, and D. van der Weide, “Numerical and experimental investigation of an ultrawideband ridged pyramidal horn antenna with curved launching plane for pulse radiation,” IEEE Antennas Wireless Propag. Lett., vol. 2, pp. 259–262, 2003. [10] J. Bourqui, M. A. Campbell, J. Sill, M. Shenouda, and E. C. Fear, “Investigation of antenna performance for ultra-wideband microwave breast imaging,” in Proc. IEEE Radio Wireless Symp., San Diego, CA, 2009, pp. 522–525. [11] J. Sill and E. Fear, “Tissue sensing adaptive radar for breast cancer detection: Study of immersion liquids,” Electron. Lett., vol. 41, no. 3, pp. 113–115, 2005. [12] J. Langley, P. Hall, and P. Newham, “Novel ultrawide-bandwidth Vivaldi antenna with low crosspolarisation,” Electron. Lett., vol. 29, no. 23, pp. 2004–2005, 1993. [13] J. Bourqui, M. Okoniewski, and E. C. Fear, “Balanced antipodal Vivaldi antenna for breast cancer detection,” in Proc. 2nd Eur. Conf. Antennas Propag., Edinburgh, U.K., Nov. 11–16, 2007, 5 pages. [14] R. Simons and R. Lee, “Impedance matching of tapered slot antenna using a dielectric transformer,” Electron. Lett., vol. 34, no. 24, pp. 2287–2289, 1998. [15] D. Schaubert, S. Kasturi, A. Boryssenko, and W. Elsallal, “Vivaldi antenna arrays for wide bandwidth and electronic scanning,” in Proc. 2nd Eur. Conf. Antennas Propag., Edinburgh, U.K., Nov. 11–16, 2007, 6 pages. [16] N. Schuneman, J. Irion, and R. Hodges, “Decade bandwidth tapered notch antenna array element,” in Proc. Antenna Applicat. Symp., 2001, pp. 280–294. [17] A. Elsherbini, C. Zhang, S. Lin, M. Kuhn, A. Kamel, A. Fathy, and H. Elhennawy, “Uwb antipodal Vivaldi antennas with protruded dielectric rods for higher gain, symmetric patterns and minimal phase center variations,” in Proc. IEEE Antennas Propag. Soc. Int. Symp., 2007, pp. 1973–1976. [18] J. Langley, P. Hall, and P. Newham, “Balanced antipodal Vivaldi antenna for wide bandwidth phased arrays,” Proc. Inst. Elect. Eng. Microwaves Antennas Propagat., vol. 143, no. 2, pp. 97–102, 1996. [19] J. M. Sill, “Second generation experimental system for tissue sensing adaptive radar,” Master’s thesis, Dept. Elect. Comput. Eng., Schulich School of Engineering, University of Calgary, Calgary, AB, Canada, 2005.

[20] E. Fear, X. Li, S. Hagness, and M. Stuchly, “Confocal microwave imaging for breast cancer detection: Localization of tumors in three dimensions,” IEEE Trans. Biomed. Eng., vol. 49, pp. 812–822, 2002. [21] T. Montoya, T. Montoya, and G. Smith, “A study of pulse radiation from several broad-band loaded monopoles,” IEEE Trans. Antennas Propag., vol. 44, no. 8, pp. 1172–1182, 1996. [22] B. Ulriksson, “Conversion of frequency-domain data to the time domain,” Proc. IEEE, vol. 74, pp. 74–77, Jan. 1986. [23] M. Lazebnik, M. Okoniewski, J. Booske, and S. Hagness, “Highly accurate Debye models for normal and malignant breast tissue dielectric properties at microwave frequencies,” IEEE Microw. Wireless Compon. Lett., vol. 17, no. 12, pp. 822–824, 2007. [24] D. W. Winters, E. J. Bond, B. D. Van Veen, and S. C. Hagness, “Estimation of the frequency-dependent average dielectric properties of breast tissue using a time-domain inverse scattering technique,” IEEE Trans. Antennas Propag., vol. 54, no. 11, pp. 3517–3528, 2006.

Jeremie Bourqui was born in Switzerland in 1982. He received the Ing. HES (B.Sc.) degree in electrical engineering from the University of Applied Sciences, Fribourg, Switzerland, in 2004 and the M.Sc. degree from the University of Calgary, Calgary, AB, Canada, in 2008. He is currently a Research Engineer at the University of Calgary. His work involves the design, implementation and testing of a microwave breast imaging system. This includes UWB sensors, RF measurement and antenna positioning systems.

Michal Okoniewski (F’09) is a Professor in the Department of Electrical and Computer Engineering, University of Calgary, Calgary, AB, Canada, where he holds the Libin/Ingenuity Chair in biomedical-engineering and Canada Research Chair in Applied Electromagnetics. His interests range from computational electrodynamics, to tunable reflectarrays, RF MEMS and RF micro-machined devices, as well as hardware acceleration of computational methods. He is also involved in bio-electromagnetics, where he works on tissue spectroscopy and micro-imaging. In 2004 he cofounded Acceleware Corp.

Elise C. Fear (S’98–M’02) received the Ph.D. degree in electrical engineering from the University of Victoria, Victoria, BC, Canada, in 2001. She was an NSERC (Natural Sciences and Engineering Research Council of Canada) Postdoctoral Fellow in electrical engineering at the University of Calgary, Calgary, AB, Canada from 2001 to 2002, and is currently an Associate Professor in the same department. Her research interests include microwave breast cancer detection. Dr. Fear is currently serving as an Associate Editor for the IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, and was awarded the 2007 Outstanding Paper Award from the same journal.

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3D Nonlinear Super-Resolution Microwave Inversion Technique Using Time-Domain Data Maha A. Ali, Member, IEEE, and Mahta Moghaddam, Fellow, IEEE

Abstract—A nonlinear three-dimensional full-wave inverse scattering method using time-domain data and models is presented. It successfully reconstructs 3D images of various unknown objects using time-domain data. The method uses Born-type iterations and a constrained minimization to reconstruct successively improved images. The use of time-domain data allows very few transmitters and receivers to be used. It is shown that this technique achieves super-resolution, namely 0.1 wavelength. The method is able to recover contrasts of over 2:1. It can also recover objects with minute contrasts of as low as 10%, thus taking a step towards addressing recent findings in the breast cancer imaging community, for example, that some breast tumors have only a 10% contrast with respect to the glandular tissues. This method could present a promising tool for the early-stage breast cancer detection as well as other medical and subsurface imaging applications. Index Terms—3D inverse scattering, breast cancer imaging, medical imaging, subsurface imaging, super-resolution.

I. INTRODUCTION IGH-RESOLUTION imaging is a subject of high interest in medical imaging as well as applications related to subsurface target detection and characterization. For example, detection of tumors at an early stage, when they are very small, is key in increasing the survival rate of breast cancer patients. Detecting and correctly identifying such small masses requires a methodology with extremely high resolution and high specificity, and has been the subject of much recent work. For example, an ultrawideband (UWB) radar technique has been introduced [1] where miniature radars are used to detect malignant tumors in the breast. In this and other types of active microwave techniques, a low-power UWB microwave pulse is transmitted into the breast and the backscattered signal is recorded. This recorded signal is then used to form an image of the breast. The accuracy, quality, and resolution of the image depend largely on the technique used to form the image. Often, complex full tomographic image reconstruction is avoided by applying various signal processing techniques to the measured data. More specifically, in [1]–[6] confocal imaging is achieved by synthetically focusing reflections from the breast, which constructs a map of strong scatterers that might indicate tumors without quantifying the contrast. While very promising, this technique faces

H

Manuscript received February 21, 2009; revised October 16, 2009; accepted January 31, 2010. Date of publication April 22, 2010; date of current version July 08, 2010. This work was supported in part by the National Science Foundation. The authors are with the Radiation Laboratory, Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109 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/TAP.2010.2048848

some challenges. For example the mismatch of skin-breast interface generates a scattering response much greater than any known tumor response [1]. In addition, an error in skin thickness of 1 mm can move the reconstructed tumor location by 1 mm or more from the true location [3]. This could inhibit the detection of small tumors. Another potential challenge is that the tumor response is further masked by clutter generated by natural heterogeneity of normal breast due to lack of a sufficient interference-suppression capability. With optimized focusing in the post-processing step, this technique has been shown to recover a 5 mm mass. An improvement to this method is proposed in [7]–[10] by using data-adaptive methods in the post processing step. However, the improvement in resolution (down to 4 mm) is still not enough for very-early stage cancer detection. Also, the presence of skin is still not addressed. In [11], three-dimensional time-domain reconstruction is carried out using a forward-backward time-stepping algorithm (FBTS). This technique is reported to be numerically intensive (requiring on the order of 300 iterations). In [12], the same FBTS method is applied to breast cancer detection in 2D. The authors recover a 5 mm insertion in about 250 iterations using a-priori information about the breast, such as exact shape or exact location of skin of the acwith initial knowledge of properties equal to tual value [12]. In another set of works, quantitative frequency-domain solutions have been developed in 2D. In [13], the authors show the benefit of including multiple frequencies over a single frequency in the computation. More frequency data show improved image quality and the ability to recover higher contrast with ability to recover inclusions of 3.1 cm using data measured at 300, 500 and 900 MHz. In [14], where a two-stage Gauss-Newton reconstruction technique is used, full tomographic data acquisition is performed at seven different frequencies, resulting in multi-slice 2D images of the breast. Tumors of approximately 1.9 cm were recovered. Initial results for 3D extension of the same technique were presented in [15] with improvement in resolution to 1.5 cm. In [16], a full-wave 3D quantitative microwave inversion technique has been developed using a regularized Gauss-Newton method in the frequency domain. It is used for the 3D quantitative inversions of high-contrast or inhomogeneous objects. The authors use data at 2 and 4 GHz, and recover objects on the order of 4 cm. In [17], the distorted Born iterative method has been used in the frequency domain to reconstruct the breast image. To reduce computational cost, the authors have utilized a scalar approximation of the vector formulation. In addition, only six frequencies have been used leading to low resolution images. As in [16], difficulties in reconstructing low contrasted objects (10%) are reported. Combining contrast source inversion with the fast Fourier transform,

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image reconstruction is performed in 2D in [18] and in 3D in [19] with system prototype and experimental data in [20]. In this method, a large number of receiver points (105) are needed and only z-polarized field is collected. Insertions of the order of are recovered. 0.25 wavelengths In this paper, we solve a nonlinear vector inverse problem using a pulse waveform and time-domain data in order to accurately reconstruct the electrical properties of 3D inhomogeneous objects. There are a number of points of distinction between our method and the techniques discussed above: Our results show that very high resolutions, substantially beyond the standard diffraction limit, can be achieved. Furthermore, this can be done with only a few transmitters and receivers, making it of high practical value. As in the scalar 2D problem [21], the in the ab3D solution is shown to have a resolution of sence of noise. When applying this solution to the problem of breast cancer detection using a pulse waveform containing the ultra-wide frequency band of 0.3–3.7 GHz, and given the dielectric constant of around 9 of healthy breast tissue and of 18 translates into the to 50 of malignant tissue, a resolution of ability to detect tumors as small as 1 mm. In addition, the proposed reconstruction method is able to distinguish low contrasts, both positive and negative, thus taking a step towards addressing recent concerns that differences between tumors and fibro-glandular tissues are not as high as previously assumed [17].

Fig. 1. A model for full view data acquisition for the proposed inversion technique. Only a few transmitters (T) and receivers (R) are needed.

where is the total field at the receiver, is the incident field measured at the receiver without the object is the unknown total field inside the object, present, is the time domain dyadic Green’s function. The and is the unknown object function and is given by function (2)

II. 3D NONLINEAR TIME-DOMAIN INVERSE SCATTERING TECHNIQUE A. Formulation The 3D time-domain nonlinear inverse scattering algorithm investigated in this paper is based on the Born Iterative Method (BIM), which, for 2D problems, has been computationally [21] and experimentally [22] demonstrated to have a very high resolution in recovering simple 2D objects. One of the most important features of this inversion method is that it can generate accurate high-resolution results using spatially sparse data sets. In addition, the wide-band (time-domain) scattered field information provides for fast convergence of the iterative solution. Instrumentation can be relatively simple because of this sparsity, and the duration of the experiments (hence object exposure time) is minimal [21]. These advantages make this method attractive for practical medical imaging applications. Fig. 1 shows a simple configuration for retrieval of the unknown electrical properties of a general inhomogeneous unknown object in a 3D space. Microwave signals generated by a transmitting source (T) illuminate the object from different positions and the scattered signals are recorded in time by each receiver (R). The full-view geometry is shown in Fig. 1, but the technique applied equally to limited-angle geometries. The vector electric field at the receivers due to a general current source is given by the following time-domain volume integral equation [23]

(1)

where is the dielectric constant of the inhomogeneous is the dielectric constant of the background. In object and this work it is assumed that these quantities are independent of frequency (therefore time), in the bandwidth of the probing signal. The total field measured at the receivers is the sum of the incident and scattered fields (3) Thus, (1) can be written as

(4) Equation (4) is a nonlinear integral equation of both the object and the electric field inside the object , function whose direct solution is generally not possible. Thus the BIM is using time-domain used to solve for the object function data to retrieve the 3D map of electrical properties of the object. In BIM, the field inside the object is initially assumed to be equal to the incident field, which is the Born approximation. This is then used to solve for the first update to the object function using the integral equation in (4). Using an electromagnetic forward solver, in this case the finite-difference time-domain (FDTD) method with CPML radiative boundary conditions, the measured field at the receivers due to the estimated object function is calculated and compared to the actual measured field. Unless the difference is less than some prescribed tolerable error, the object function is updated using the newly calculated total field in the object region. This process is repeated until the measure of error is satisfactorily minimized and convergence is achieved. The details of this solution are further explained below.

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Equation (4) is a time-domain integral equation, which can be computationally expensive to evaluate even for spatially-small problems. To avoid the high computation costs, we start by transforming both sides of (4) into the frequency domain, realized through the fast Fourier transform

where is the total number of unknowns in the expansion. The and are assumed here functions are known basis functions to be constant pulse functions defined as

(5)

is the elemental voxel in the discretized computaIn (11), tional domain, with size no larger than 0.1 of the smallest wavelength. Substituting (10) and (11) in (9) and rewriting in matrix form we get

In the above equation, is the dyadic Green’s function in the frequency domain and is given by

if if

.

(12)

(6) where

is the 3D scalar Green’s function given by (7)

To be consistent with the coordinates of the FDTD, we choose to expand the dyadic Green’s function in the Cartesian coordinates as follows:

(11)

In (12), is a vector containing the unknowns, which is the same for each equation. The expressions for the elements of matrices , and are given in Appendix I. is the total number of frequencies, and and are If the number of transmitters and receivers, respectively, we can as the total number of measurement define points. With the number of unknowns, each of the vectors , and is of length Q and the matrices , , are of size Q by . Now let us define the composite matrix and composite vector as follows:

We can then rewrite (12) in a compact form as (8) Substituting the elements of the dyadic Green’s function into (5) and writing out each scattered field component we get (9) at the bottom of the page. In (9), with is receiver due to the transmitter at the scattered field at the frequency . The fields with are the fields inside the object at location due to transmitter t and frequency . We begin the solution by discretizing the object function using a set of basis functions (10)

(13) where now is a vector of size 3Q and is a 3Q by L matrix. Since the transmitted signal bandwidth, and hence the number of frequency points used, is large, the length of the data vector , which is 3Q, is much larger than the number of unknowns L. Therefore, the system of equations represented by (13) is and of vector over-determined. Since the elements of matrix depend on each other, the system is nonlinear as already mentioned. However, since we start by the Born approximation for the fields inside the object, and at each subsequent iteration calculate an approximate object field distribution with the latest object solution, we effectively solve a linear system of equations (13) at each iteration. In other words, we decouple the scattered field from the object field at each iteration.

(9)

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B. Solution of the Inverse Problem To solve for in (13) we choose to minimize a cost function norm . To mitigate the inherent defined by the ill conditioning of the resulting system matrix, it is necessary to employ a regularization technique. Here, Tikhonov regularization is used by minimizing a modified cost function as follows [18] (14) where is the identity matrix and is the regularization parameter. The regularization parameter implemented as such increases the eigenvalues of the resulting system matrix by the value so that the ratio of the largest and smallest eigenvalues is reduced, and hence the condition number of the matrix is improved. Thus at each iteration of the overall nonlinear problem, the unknown is obtained by solving the equation (15) Here, stands for conjugate transpose. Equation (15) is solved iteratively using the conjugate gradient method. The system in (15) must be solved at each iteration of the inverse problem. Although (15) represents a linear system of equations, by virtue of updating the object field and the object function at each iteration, ultimately the nonlinear problem represented by (13) is solved. Through the iterations, the vector remains fixed. All other quantities in (15) are updated at each iteration, including the regularization parameter . To choose the value of at each iteration, one could use the brute force approach of finding the eigenvalues of the matrix then assigning the value of such that when it is added to all eigenvalues, the ratio of the largest to smallest resulting eigenvalues [i.e., the condition number of the matrix of the left hand side of (15)] is smaller than a prescribed value, typically around 100. Although systematic, this approach is computationally expensive if done at every iteration. It is therefore more desirable to choose the value of based on one initial calculation of eigenvalues and setting gamma to a value needed to make the ratio of largest-to-smallest eigenvalues to be about 100. This is followed by a gradual decrease of gamma at subsequent iterations until convergence is achieved. The rate for decreasing was determined through our computational experiments to ensure accurate and convergent solutions with minimal artifacts. The physical impact of the regularization parameter at each iteration is that it imposes an effective spatial low-pass filter on the object function. Larger values of result in a larger number of high spatial frequencies to be eliminated from the object function, hence smoothing the results. This is why it is desirable to set the regularization parameter to a larger value initially so that a smooth approximation to the object function is first found. At further iterations, can be reduced to allow higher spatial frequencies for a higher-resolution object reconstruction, while reducing the probability of non-converging solutions or convergence to local minima. The solution steps are carried out as follows. 1. Calculate and store Green’s function for all receivers and each grid point in the discretized unknown object region;

2. Use CPML 3D FDTD without an object to calculate the incident field at each receiver and inside the object (in the Born approximation) due to each transmitter. Record for all time steps. In an actual experiment, this step would be replaced by an initial target-free measurement to measure the incident field at the receivers; 3. With the object present, calculate the total measured field at each receiver due to each transmitter and calculate the scattered field; 4. Perform FFT on the scattered field and store; 5. Start the solution by employing the Born approximation; 6. Use Tikhonov regularization and the conjugate gradient method to solve for the object function; 7. Use the CPML 3D FDTD with updated object function to update fields at receivers and the field inside the object in the time domain; 8. Compare with stored measured field in the time domain; 9. If error is acceptable, stop; 10. If error is not acceptable, go back to Step 6. III. RESULTS AND DISCUSSION Preliminary results have been successfully generated using the presented technique for 3D objects. Several cases have been simulated. Only lossless cases are considered here with the lossy case to be reported in a separate paper. In this work we assume that sources and receivers are confined to a single point in the computational grid. In other words, the antennas are assumed soft point sources. The source input pulse used has a frequency content ranging from 0.3–3.7 GHz which is the frequency range where the magnitude of the pulse spectrum reduces to 5% of its maximum. The transmitters and receivers generate and measure, respectively, the full vector wave fields. In practice, this would be accomplished by using dual-polarized antennas and then calculating the third component using Maxwell’s equations. The value of referred to in this work corresponds to the smallest wavelength contained in the signal spectrum in the highest dielectric constant in the solution domain. Although the dense sampling in time is required for FDTD stability—which depends on FDTD spatial grid size and therefore object material—it is not required for frequency domain representation of the signal. All we need is to ensure that the Nyquist criterion is met, which has been our guiding principle for choosing the number of inversion time samples and therefore frequency samples. We oversample by a small factor to make sure aliasing is avoided. But otherwise we keep all of the frequencies with non zero signal value that result from the FFT, since they all provide independent information. For the 0.3–3.7 GHz band used here, the number of frequency points kept for the computations were in the range of 23–45 depending on the object material and the grid size, which in turn determines how dense the sampling is. Most results were obtained with 6 transmitters and 18 receivers placed symmetrically around the unknown region cube for full-view geometries. For limited-angle geometries all transmitters and receivers above the object are removed. Slightly increasing the number of transmitters and receivers will likely produce better results, at the cost of increased computational time

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Fig. 2. z-plane slice of the reconstruction of a cube of dimension 0:1 of " = 1:5 in air background where X and Y show the number of grid points in each direction with dx = dy = dz = 6:2 mm < 0:1 (a) Original distribution, (b) recovered distribution, and (c) Comparison between recovered and original distribution in x-axis.

Fig. 3. A z-plane slice showing the resolving of two 0:1 cubes that are 0:1 apart and are in air background. (a) Original, (b) the 27th iteration using 25 frequency points, and (c) comparison between recovered and original distribution in x-axis where y and x show the number of grid points in each direction with dx = dy = dz = 6:5 mm < 0:1, (d) first iteration showing the Born approximation, (e) the recovered image using only 15 frequency points at the 27th iteration.

and memory, as well as experimental complexity later on. A typical run time for this algorithm is about 10 minutes per iteration on a 2-GHz processor with 4 G RAM, and it typically takes 35 iterations or fewer to converge. In Fig. 2, the 3D reconstruction of a point target, which is in each dimension, is shown. The a cube of 6.2 mm dielectric constant of the cube is 1.5 and the background is air. This example demonstrates the super resolution ability of this technique. The results were obtained here using 6 transmitters and 8 receivers. Fig. 3 shows the result of resolving two 6.5 mm cubes that are apart placed in the 3D slice shown in the figure. As can be observed, we are able to recover over 60% of the contrast of the dielectric constant of each object.

Fig. 3(d) shows the Born approximation where it is evident that the objects are not resolved where as Fig. 3(b) shows the convergent solution. The two objects are clearly resolved. Super-resolution is inherent in this technique and can be explained by noting that it takes into account multiple scattering effects in the reconstruction process, through its iterative approach. Indeed, all except the first iteration (which corresponds to Born approximation) represent nonlinear field dependencies on the object profile. Physically speaking, upon multiple scattering within and between targets located in adjacent grid points, mode conversions take place between evanescent and propagating modes. Therefore the higher spatial frequencies in the evanescent spectrum are converted to propagating modes, and therefore find representation in the measured signal at the

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Fig. 4. A z-plane slice showing the reconstruction of a 3 grid-point cube with a 10% contrast to the background. (a) Original, (b) recovered (c) Comparison between recovered and original distribution in x-axis. Y and X show the number of grid points in each direction dx = dy = dz = 2:8 mm = 0:1.

Fig. 5. A z-plane slice showing the reconstruction of a 3 grid-point cube with a 10% negative contrast to the background. (a) Original, (b) recovered (c) Comparison between recovered and original distribution in x-axis. Y and X show the number of grid points in each direction dx = dy = dz = 0:1 = 2:9 mm.

receivers. To show that super-resolution is achieved due to multiple scattering, one could look at the first iteration (Born approximation) and note that two closely spaced point targets cannot be resolved [Fig. 3(d)]. Whereas Fig. 3(b) show the 27th iteration where the two targets are clearly resolved. Fig. 3(e) shows the results at the 27th iteration with the frequency band sub-sampled by 40% (40% fewer frequencies) as opposed to using all of the frequencies in the band. Comparing Fig. 3(e) to (b) we can see that using the remaining frequencies in the band, even when the overall bandwidth is preserved, deteriorates the image, whereas using all of the frequency samples in the band does allow for better resolution. The sub-sampling factor was chosen arbitrarily here for illustration. Besides frequency samples, the factors that are expected to degrade the resolution are loss and noise, as shown in the much simpler 2D problem [24] as well as using realistic sources and receivers. Work on these points is ongoing and will be the subject of a future paper. Another factor that is relevant to note here is that to be conservative, we have used relatively low values for the permittivity of both the background and the inclusions. Some breast dielectric measurement studies have reported higher permittivity values, which if used here, would result in smaller effective wavelengths inside the target domain and therefore smaller detectable tumor size even if the resoluby, e.g., a factor of 2 to . tion is degraded from Figs. 4 and 5 demonstrate the ability of this method to re(8.4 cover contrasts as small as 10%. In Fig. 4, a cube of

in a background of is reconstructed to mm) of demonstrate the ability to recover a positive 10% contrast. Fig. 5 on the other hand demonstrates the ability to recover a nega(8.7 mm) of tive 10% contrast. Here, a cube of in a background of is reconstructed. In both examples, comparison of the recovered object to the original one shows very good agreement. Here, 18 receivers and 6 transmitters were used. Even though experimental noise is not considered here, the type of the problem determines the number of receivers needed. For example, in Fig. 2 only 8 receivers placed around the center plane were sufficient, since the inclusion is symmetric along the 3 axes and is exactly in the center (1 grid point). To recover a larger object or non-symmetric objects (whenever the scattered field could have nonsymmetric and highly varying spatial features), we need more receivers in different planes as to incorporate more information about the object for better recovery. Also, in the case of smaller contrasts, it is harder to recover the absolute value since the scattered fields could be very small. Using more receivers allows us to beat down the numerical noise (and eventually experimental noise). Also, since in general we do not have prior knowledge of the object, we need to err on the side of caution by including as many receivers as feasible but the limitation in this work is mainly imposed by the computational memory available. In the future enhancing the computational resources are expected to enhance the results. Fig. 6 shows the ability of the method to recover a cube of (2.8 mm) again with 10% conone grid point representing

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Fig. 6. A z-plane slice showing the reconstruction of a 1 grid-point cube with a 10% contrast to the background. (a) Original, (b) recovered, (c) comparison between recovered and original distribution in x-axis. Y and X show the number of grid points in each direction dx = dy = dz = 0:1 = 2:8 mm.

Fig. 7. Permittivity distribution of a 0:1 cube of " = 16 embedded in a homogeneous background of " = 8. (a) The original z-plane slice through center of tumor. (b) The recovered distribution. (c) Comparison between recovered and original distribution in y-axis. Y and X show the number of grid points in each direction. dx = dy = dz = 2 mm.

trast with respect to the background. Here again 18 receivers and 6 transmitters were used. The iterations produced a convergent solution that can indeed detect the object but recovers only 16% of the contrast. This is due to the regularization technique used in this method. As already mentioned, we are using Tikhonov regularization in finding the minimum value of the cost function in (14). This regularization technique forces the permittivity distribution to be smooth. With more iterations, the focus on the small object increases, thus improving the detected value of the object permittivity, but the background becomes less accurate as spurious spatial frequencies enter its solution. Therefore, to achieve convergence, the results are over-regularized. This is why the values of the recovered permittivity do not always reach the absolute original value but are very close to it. However the object is clearly visible. An improvement to the regularization technique is expected to preserve edges and improve the image. This is a subject of future research. In Fig. 7, the ability of this method to recover 2:1 contrast is demonstrated. We were able to recover, with high fidelity, and of size (2 mm), embedded in a a cube of . Here 18 receivers and 6 homogeneous background of transmitters were used. We are also able to recover objects embedded in multiple 3D in a background of layers. Consider the “sphere” of shown in Fig. 8. The sphere is simulated in the computational domain with a stair-case approximation. Embedded in the

(6 mm) dimensions with sphere’s center is a cube of . This could be a simplistic representation of breast tissue with an embedded tumor. Results in Fig. 8 show the successful reconstruction of the sphere and tumor. Here the z-plane cross section of the tumor is shown. Comparison between Fig. 8(a), which shows the original distribution, and Fig. 8(b), which shows the recovered distribution, demonstrates again the accuracy of this method. Fig. 8(c) presents a y-axis comparison between the recovered and original distributions, again showing that over 93% of the tumor dielectric constant was recovered. To investigate the results for a heterogeneous background, a is simsphere with a random distribution of (4 mm) ulated. Inside the sphere and off its center is a . This is intended as a rough representation of cube with heterogeneous breast tissue with an embedded tumor. The original distribution is shown in Fig. 9(a), which shows the z-plane cross section through the center of the tumor. Results in Fig. 9(b) show that this method is able to detect the tumor, even though the contrast to the background is small. This result is promising as recent data show that there might be only a small contrast between glandular and malignant tissue. Fig. 9(c) shows the y-axis distribution comparing recovered value of the permittivity with the original. As can be seen, the reconstructed results are in very good agreement with the original object. The previous results were obtained using full view as illustrated in Fig. 1. However, this work is intended to be applied

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Fig. 8. Permittivity distribution of a 6 mm (0:25) cube of " = 12 embedded in a homogeneous sphere of " = 9. Background is " = 8. Eighteen receivers and 6 transmitters were used in the reconstruction. (a) The original z-plane slice through center of tumor. (b) The recovered distribution. (c) Comparison between recovered and original distribution in y-axis. Y and X show the number of grid points in each direction dx = dy = dz = 2 mm.

6

Fig. 9. Permittivity distribution of a 4 mm (0:17) cube of " = 12 embedded in a heterogeneous sphere of a random distribution of " = 9 10%. Background is " = 8. Eighteen receivers and 6 transmitters were used. (a) original z-plane slice through center of tumor. (b) The recovered distribution. (c) Comparison between recovered and original distribution in y-axis. Y and X show the number of grid points in each direction. dx = dy = dz = 2 mm.

Fig. 10. Limited view recovery of the permittivity distribution of a 6 mm (0:25) cube of " = 12 embedded in a homogeneous sphere of " = 9. Background is " = 8. Eighteen receivers and 6 transmitters were used in the reconstruction. (a) The original z-plane slice through center of tumor. (b) The recovered distribution. (c) Comparison between recovered and original distribution in y-axis. Y and X show the number of grid points in each direction dx = dy = dz = 2 mm.

in the future to medical imaging in general and to breast cancer detection in particular. In these cases only a limited view of the unknown object is available. To test this method with limited view, another experiment is performed with the receivers and transmitters placed only around the 5 sides of the object instead of 6. In Fig. 1 this means eliminating all transmitters and receivers above the object. The same object of Fig. 8 is simulated. As expected, comparing the results shown in Fig. 10(b) with the image in Fig. 8(b), the image using limited view is somewhat degraded. However the object was indeed recovered.

IV. CONCLUSION A nonlinear three-dimensional inverse scattering method was investigated, and was used to successfully reconstruct accurate 3D images of various unknown objects using time-domain . data. It was shown that this technique has a resolution of This method could present a promising tool for the early-stage breast cancer detection as well as other medical and subsurface imaging applications. The results indicated that it is possible to in a random distribution of recover 4 mm inclusion of

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. The solution method used recovers over 90% of the absolute value of the inclusion. It is also able to recover positive and negative 10% contrasts. Future improvement to the regularization technique used here is expected to yield better edge preservation and more definition to the retrieved objects. Also increasing the number of receivers and transmitters is expected to yield further improvement of the results. These improvements together with using the true values and realistic models of the electrical properties of the healthy and malignant breast tissue, which are reported to have dielectric constants of several times higher than used in the examples shown above (therefore smaller wavelengths), are expected to enable the detection of tumors as small as 1-2 mm. This work has demonstrated the strong potential of the 3D time-domain technique for achieving high resolutions that can be of practical clinical use for early stage breast cancer detection. Towards meeting this goal, our future work will focus on implementing progressively more realistic target parameters and measurement scenarios. More specifically, our future work will include the following. • Simulating realistic numerical breast models, including conductivity of both the background and the tumorous material models; • adding the effect of noise; • using realistic sources and receivers; • improving the numerical efficiency of the algorithm so that larger objects can be simulated and larger number of transmitters and receivers can be included; • experimental demonstrations in the laboratory with a wide range of realistic phantoms. APPENDIX The detailed expressions for the elements of the matrix given in the equation at the top of the page, where

is

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REFERENCES [1] X. Li, E. J. Bond, B. D. Van Veen, and S. C. Hagness, “An overview of ultra-wideband microwave imaging via space-time beamforming for early-stage breast-cancer detection,” IEEE Antennas Propag. Mag., vol. 47, no. 1, pp. 19–34, Feb. 2005. [2] E. C. Fear and M. A. Stuchly, “Microwave detection of breast cancer,” IEEE Trans. Microw. Theory Tech., vol. 48, pp. 1854–1863, Nov. 2000. [3] T. C. Williams, E. C. Fear, and D. T. Westwick, “Tissue sensing adaptive radar for breast cancer detection—Investigations of an improved skin-sensing method,” IEEE Trans. Microw. Theory Tech., vol. 54, pp. 1308–1314, Apr. 2006. [4] S. C. Hagness, A. Taflove, and J. E. Bridges, “Three-dimensional FDTD analysis of a pulsed microwave confocal system for breast cancer detection: Design of an antenna array,” IEEE Trans. Antennas Propag., vol. 47, pp. 783–791, May 1999. [5] X. Yun, E. C. Fear, and R. H. Johnston, “Compact antenna for radarbased breast cancer detection,” IEEE Trans. Antennas Propag., vol. 53, pp. 2374–2380, Aug. 2005. [6] X. Li, S. K. Davis, S. C. Hagness, D. W. van der Weide, and B. D. Van Veen, “Microwave imaging via space-time beamforming: Experimental investigation of tumor detection in multilayer breast phantoms,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 8, pp. 1856–1865, Aug. 2004. [7] B. Guo, Y. Wang, J. Li, P. Stoica, and R. Wu, “Microwave imaging via adaptive beamforming methods for breast cancer detection,” in Proc. Prog. Electromagnetics Res. Symp., Hangzhou, China, Aug. 2005, pp. 350–353. [8] Y. Xie, B. Guo, J. Li, and P. Stoica, “Novel multistatic adaptive microwave imaging methods for early breast cancer detection,” Eurasip J. Appl. Signal Processing , vol. 2006, pp. 1–13, 2006, Article ID 91961. [9] Y. Xie, B. Guo, L. Xu, J. Li, and P. Stoica, “Multistatic adaptive microwave imaging for early breast cancer detection,” IEEE Trans Biomed. Eng, vol. 53, no. 8, pp. 1647–1657, Aug. 2006. [10] B. Guo, Y. Wang, J. Li, P. Stoica, and R. Wu, “Microwave imaging via adaptive beamforming methods for breast cancer detection,” J. Electromagn. Waves Applicat., vol. 20, no. 1, pp. 53–63, 2006. [11] T. Takenaka, H. Zhou, and T. Tanaka, “Inverse scattering for a threedimensional object in the time domain,” J. Opt. Society Amer., vol. 20, no. 10, pp. 1867–1874, Oct. 2003. [12] J. E. Johnson, T. Takenaka, and T. Tanaka, “Two-dimensional time-domain inverse scattering for quantitative analysis of breast composition,” IEEE Trans. Biomed. Eng., vol. 55, no. 8, pp. 1941–1945, Aug. 2008. [13] Q. Fang, P. M. Meaney, and K. D. Paulsen, “Microwave image reconstruction of tissue property dispersion characteristics utilizing multiple-frequency information,” IEEE Trans. Microw. Theory Tech., vol. 52, pp. 1866–1875, Aug. 2004. [14] P. M. Meaney, M. W. Fanning, D. Li, S. P. Poplack, and K. D. Paulsen, “A clinical prototype for active microwave imaging of the breast,” IEEE Trans. Microw. Theory Tech., vol. 48, pp. 1841–1853, Nov. 2000. [15] P. M. Meaney, Q. Fang, and K. D. Paulsen, “Data collection strategies and their impact on 3D microwave imaging of the breast,” in Proc. IEEE APS Int. Symp., 2005, vol. 1B, pp. 183–186. [16] J. De Zaeytijd, A. Franchois, C. Eyraud, and J.-M. Geffrin, “Full-wave 3-D microwave imaging with a regularized Gauss-Newton methodtheory and experiment,” IEEE Trans. Antennas Propag., vol. 55, pp. 3279–3292, Nov. 2007.

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[17] P. Kosmas, J. D. Shea, B. D. Van Veen, and S. C. Hagness, “Three-dimensional microwave imaging of realistic breast phantoms via inexact Gauss-Newton algorithm,” in Proc. IEEE APS Int. Symp., Jul. 2008, pp. 1–4. [18] Q. H. Liu, Z. Q. Zhang, T. Wang, G. Ybarra, L. W. Nolte, J. A. Bryan, and W. T. Joines, “Active microwave imaging I: 2-D forward and inverse scattering methods,” IEEE Trans. Microw. Theory Tech., vol. 50, pp. 123–133, Jan. 2002. [19] Z. Q. Zhang and Q. H. Liu, “3-D nonlinear image reconstruction for microwave biomedical imaging,” IEEE Trans. Biomed. Eng., vol. 51, pp. 544–548, 2004. [20] C. Yu, M. Yuan, J. Stang, E. Bresslour, R. T. George, G. A. Ybarra, W. T. Joines, and Q. H. Liu, “Active microwave imaging II: 3-D system prototype and image reconstruction from experimental data,” IEEE Trans. Microw. Theory Tech., vol. 56, pp. 991–1000, 2008. [21] M. Moghaddam and W. C. Chew, “Nonlinear two-Dimensional velocity profile inversion using time domain data,” IEEE Trans. Geosci. Remote Sensing, vol. 30, pp. 147–156, Jan. 1992. [22] F. C. Chen and W. C. Chew, “Experimental verification of super resolution in nonlinear inverse scattering,” Appl. Phys. Lett., vol. 72, no. 23, pp. 3080–3082, Jun. 1998. [23] W. C. Chew, Waves and Fields in Inhomogeneous Media. New York: Van Nostrand Reinhold, 1990. [24] M. Moghaddam and W. C. Chew, “Study of some practical issues in inversion with the born iterative method using time-domain data,” IEEE Trans. Antennas Propag., vol. 41, pp. 177–184, 1993.

Maha Ali (M’03) received the B.S. degree (with highest distinction) from Ain Shams University, Cairo, Egypt, in 1995 and the M.S. and Ph.D. degrees from the University of Central Florida, Orlando, in 1998 and 2004, respectively, all in electrical and computer engineering. She is currently a Research Fellow with the Radiation Lab, Electrical Engineering and Computer Science Department, University of Michigan, Ann Arbor, where she has been since 2006. Her research interests include microwave imaging for the detection and diagnosis of breast cancer as well as microwave hyperthermia for the treatment of cancer.

Mahta Moghaddam (S’86–M’87–SM’02–F’08) received the B.S. degree (with highest distinction) from the University of Kansas, Lawrence, in 1986, and the M.S. and Ph.D. degrees from the University of Illinois at Urbana-Champaign, in 1989 and 1991, respectively, all in electrical and computer engineering. From 1991 to 2003, she was with the Radar Science and Engineering Section, Jet Propulsion Laboratory (JPL), California Institute of Technology, Pasadena. At JPL, she introduced innovative approaches and algorithms for quantitative interpretation of multichannel SAR imagery based on analytical inverse scattering techniques applied to complex and random media. She also introduced a quantitative approach for data fusion by combining SAR and optical remote sensing data for nonlinear estimation of vegetation and surface parameters. She was a Systems Engineer for the Cassini Radar and Science Chair of the JPL Advanced Mission Studies Team (Team X). Currently, she is a Professor of electrical engineering and computer science at the University of Michigan, Ann Arbor, where she has been since 2003. Her research group is currently engaged in a variety of research topics related to applied electromagnetics, including the development of advanced radar systems for subsurface characterization, mixed-mode high resolution medical imaging techniques, and smart sensor webs for remote sensing data collection and validation. She is and has been the Principal and Co-Investigator on several research projects, and has authored or coauthored over 180 peer-reviewed journal and conference papers.

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Microwave Radar-Based Differential Breast Cancer Imaging: Imaging in Homogeneous Breast Phantoms and Low Contrast Scenarios Maciej Klemm, Jack. A. Leendertz, David Gibbins, Ian J. Craddock, Alan Preece, and Ralph Benjamin

Abstract—This paper presents an improved antenna array for radar-based breast cancer imaging. The improvement was achieved by increasing the number of antennas in the array to 31 elements, as well as by improving the antenna design itself. Using an experimental setup, with homogeneous curved breast phantoms, we have demonstrated substantial imaging improvement with the new antenna array. The new system is also able to detect 7 mm-diameter tumor phantoms in any location within the breast, even as close as 4 mm from the skin layer. Additionally, we have shown good imaging results in low-contrast scenarios, where the dielectric contrast between tumor and normal tissue was reduced to 2:1. Presented results clearly demonstrate the large impact of antenna’s characteristics on imaging performance. Index Terms—Antenna arrays, biomedical imaging, microwave imaging.

I. INTRODUCTION

T

HE application of microwaves to medical imaging, and specifically to breast cancer imaging, has attracted the interest of a number of research groups around the world. A review of this topic can be found in [1]. Currently there are two main approaches to microwave breast imaging: microwave tomography [2]–[4] and radar-based imaging [5]–[7]. Both approaches rely on a difference in the electrical properties of normal and malignant breast tissues. The early work on breast cancer detection was based on the assumption of high (about 5:1) dielectric contrast, as well as relatively homogeneous (electrically) internal breast structure [8]–[10]. The most recently published data on electromagnetic (EM) properties of breast tissues [11] suggest that the contrast might be significantly lower, and also that the breast interior is more inhomogeneous than previously assumed. This most recent report, disclosing a more challenging case for microwave breast imaging than previously thought, resulted in a development of realistic numerical breast phantoms, based on data from magnetic resonance imaging (MRI) [12], [13]. Before Lazebnik’s report it was not clear whether the relatively large complexity of breast interior, visible in MRI images, translates to a similar electrical complexity (variations in dielectric Manuscript received June 17, 2009; revised November 12, 2009; accepted January 10, 2010. Date of publication April 22, 2010; date of current version July 08, 2010. The authors are with the Centre for Communications Research, Department of Electrical and Electronic Engineering, University of Bristol, Bristol BS8 1UB, 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/TAP.2010.2048860

constant). But results shown in [11] give a basis to believe that indeed the breast electrical properties differ at the same level as pixel intensity of MRI images. It is therefore reasonable to use those MRI images in EM simulations of microwave imaging systems. From a technical point of view it is not a problem (it is lengthy though) to use MRI-based breast models in numerical EM solvers. First results of microwave radar-based imaging have been presented in [12], and for microwave tomography in [14]. Far more challenging is to build a real breast phantom with the same tissue complexity as in numerical MRI-based phantoms. Up until now there has only been limited experimental work on phantoms for microwave imaging [15]–[19], and more recently [20]–[25]. All experimental phantoms reported so far assume homogeneous breast tissue and only some include the very important skin layer. In this paper we present a new antenna array with 31 elements, designed for microwave radar-based breast imaging. Our system is based on multistatic radar operation, originally proposed for breast cancer and land mine detection by Benjamin [7]. In our previous prototype [26] we have used a 16-antenna array, formed on a section of a hemisphere to conform well to the breast shape. For better imaging performance of the system, we have decided to increase a number of antennas in the array. More antennas should provide more processing gain for our coherent ultrawideband (UWB) radar. To increase number of antennas, we had to redesign the array and also to design a new, smaller UWB antenna. Our new array has been experimentally tested first by comparing its performance with the previous 16-element system. Next, we have verified the capabilities of the new system by imaging our previously developed curved breast phantom [27]. The phantom represents homogeneous breast tissue and a large (5:1) dielectric contrast between a tumor phantom and normal tissue. Next, in the same homogeneous phantom, we imaged small tumors with low dielectric contrast (2:1). Our results demonstrate the effect of real antennas on system performance. To the best of our knowledge, the system presented in this research is the most advanced experimental system built for microwave breast imaging. Although our intent is to use it for radar imaging, this system could also be used in tomographic imaging. The performance of our system in more challenging cases of inhomogeneous breast tissue, with dielectric properties close to those reported in [11] will be presented in [28]. The paper is organized as follows. Section II briefly describes the new UWB antenna design and Section III presents details

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Fig. 2. (a) Schematic of the array modeled using CAD software. (b) Low loss ceramic matching shell and inserts (Eccostock HiK500F).

Fig. 1. Antenna arrays developed at the University of Bristol for microwave radar-based breast cancer imaging: (a) old prototype: 16-element array based on the stacked-patch antenna, (b) new prototype: 31-element array based on the wide-slot antenna.

of array construction. In Section IV the 3D imaging setup in presented, including breast phantom details. The final part of the paper, Section V, presents experimental results of phantom tumor detection. We provide here information about our focusing algorithm, compare imaging results of the previous and new systems, and present more demanding imaging results. II. UWB ANTENNA DESIGN The key to the new design of our imaging system was designing a new antenna. We have chosen a wide-slot UWB antenna as a good candidate. The main advantages of this antenna are its low-profile and excellent transient characteristics for a wide range of radiation angles [29]. A detailed design description of the new antenna is reported in [30]. The main advantages of the new design over the patch are a stable radiation pattern across the frequency band of interest, as well as extremely high % of radiated pulses for radiation angles even up fidelity from boresight. to III. ANTENNA ARRAY DESIGN As in the previous prototype (shown Fig. 1(a), further described in [22]), a new antenna array [Fig. 1(b)] is formed around the lower part of a 85 mm-radius sphere as presented in Fig. 2. The use of 3D CAD modeling was found to be vital, given very limited space. To provide the best radiation coverage

of a breast, all antennas were positioned to point towards a center of curvature, as depicted in Fig. 2(a). A plastic shell, with openings for the antennas, has been manufactured to assure the best possible accuracy of positioning antennas. IV. 3D RADAR IMAGING SETUP A. Measurement Setup In the measurement setup, the array is connected with coaxial cables to a custom-built network of electromechanical switches, previously developed for the planar antenna array [32]. The bank of switches selects all possible pairs of antennas within the array, and connects them in turn to a vector network analyzer (VNA; Rohde&Schwarz ZVB20), which performs the in this case); radar measurement in the frequency-domain ( is not recorded. In a post-reception step, monostatic data all measured data is transformed into the time-domain. With thirty one antenna elements in the array, four hundred and sixty five independent measurements (multistatic radar signals) are recorded. A computer controls both the VNA and the switch bank, and the measurement takes about 80 seconds to complete. The complete imaging system is presented in Fig. 3. B. 3D Breast Phantom For experimental testing we developed appropriate materials and a 3D breast phantom. It is the same phantom as presented in [25]. For completeness we will briefly describe the phantom. As shown in Fig. 2(a) during measurements the antennas are immersed in a matching liquid, to reduce reflections from the skin and for a more compact antenna design. We decided that the matching liquid would be the same as the material simulating the properties of normal breast-fat, mainly for practical reasons (only one liquid required). The matching and normal

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a background measurement, it could be used in realistic scenarios with breast cancer patients [22]. A modified delay and sum (DAS) algorithm ([25], [26]) is used to form 3D images of scattered energy. Essentially, the scattered energy at the given focal point, within the breast volume, can be expressed as

(1) Fig. 3. Experimental setup of our imaging system.

breast tissue equivalent liquid [33] has a relative dielectric constant of about 10 and an attenuation of 1.2 dB/cm at 6 GHz. This material is also dispersive, and its frequency-dependent characteristics have been presented in [34]. As an alternative to the lossy matching liquid, we have recently built a ceramic shell to fill the distance between antennas and a breast skin (a 1 mm thin layer of matching liquid still needs to be used between antennas and the ceramic shell). Also, to be able to accommodate breasts of different size, ceramic insert shells have been made. The ceramic matching shell and inserts were custom designed, using low loss material with controlled material Eccostock HiK500F from dielectric constant Emerson & Cuming. All ceramic parts are shown in Fig. 2(b). Next, a curved skin phantom was developed. The skin layer is 2 mm thick, it is a part of a 67 mm-radius hemisphere [shown in Fig. 2(a)]. When the skin phantom is fitted into the array it lies 20 mm above antenna elements. This distance between antennas and breast provides a full coverage of a breast by an antenna radiation pattern. The electrical parameters of the skin layer were chosen according to the previously published data. The material is dispersive and, at 6 GHz, it has a relative dielectric constant of 30 and attenuation of 16 dB/cm. Finally, a tumor phantom material with a relative dielectric constant close to 50 and conductivity 7 S/m (at 6 GHz) was developed. The contrast between dielectric properties of breast fat and tumor phantom materials is around 1:5. Recently published data on the electromagnetic (EM) properties of breast tissues [11] suggest that the contrast might be significantly lower, and also that the breast interior is more inhomogeneous than indicated in previously published reports [8]–[10]. These findings have serious implications on achievable performance of microwave imaging modalities (radar-based, as well as inverse scattering). C. Differential Imaging and Focusing Algorithm Before applying the focusing algorithm, the tumor response must be extracted from measured data. To do so we perform two measurements by rotating the array. This method provides a differential signal, which is used as an input into focusing algorithm. Detailed description of this method can be found in [27]. Because the differential imaging method does not require

where ( is the number of antennas in the array), is the location dependent weight calculated during is the measured radar signal and is the pre-processing, time-delay. is the length of the integration window. Constants and were introduced to account for real antennas’ effects and they are defined as (2) is a vector beginning at antenna location and where: ending at the center of curvature [ , see Fig. 2(a)], is a vector beginning at antenna location and ending at a focal point is the maximum assumed antenna beamwidth. Essentially, (2) checks whether for the th radar signal, focal lies within the aspoint sumed antenna beamwidth (Tx- or Rx-antenna). If so, then and the th signal for a given focal point is included in the DAS algorithm. Also note that since all antenna point towards center of curvature, vector shows the direction of a boresight radiation. V. 3D IMAGING RESULTS A. Comparison With Previous Antenna Array In this section we compare 3D imaging results obtained using our previous antenna array [shown in Fig. 1(a)] and the newly developed array [Fig. 1(b)]. Below we present results of imaging a 10 mm (diameter) tumor phantom, located at a position . In both cases we have used breast phantom as described in Section IV.B. The only difference between both breast phantoms used was their size. Phantom used with the 31-elements array had 9 mm bigger radius (skin had mm, as shown in Fig. 2(a)). For the 16-element array, mm. The phantom used the skin layer had a radius of with the 16-element array was slightly smaller due to the fact that the whole array was formed as a part of sphere with radius 78 mm, and the radius of the 31-element array was 85 mm. To quantitatively assess imaging results, we introduce a measure of detection quality: ratio of the clutter energy to the tumor . The clutter energy is energy, above a certain threshold calculated within the entire 3-D image (hemisphere with 67 mm radius), and is simply the sum of focused values (exceeding

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Fig. 4. Comparison of 3D imaging results: (a) 16-element array, 1:5 dB contour map for (1)=(2) = 25 , (b) 16-element array, 1:5 dB contour map for = 35 , (c) 16-element array, 7 dB contour map for (1)=(2) = 35 , (d) 31-element array, 1:5 dB contour map for (1)=(2) = 25 , (1)=(2) = 35 , (f) 31-element array, 7 dB contour map for (1)=(2) = 35 . (e) 31-element array, 1:5 dB contour map for (1)=(2)

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threshold ) in all pixels. The tumor energy is calculated as the sum of focused values above the threshold, for pixels located within a cube of 24 24 24 mm , with the maximum focused signal located in the center of the cube. It should be noted that the volume where we calculate the clutter is about forty five times larger than that of the tumor. Another measure for quantitative assessment of imaging results is a ratio of peak clutter energy to a peak tumor energy (peakC/T), calculated within a full 3D image volume. 3D and 2D imaging results are presented in Figs. 4 and 5, respectively. Looking at Fig. 4(a) for the 16-element array and Fig. 4(d) for the 31-elements array we can see that it both cases tumor has been detected. A single artifact is also visible for the 16-element array. 3D images are shown as contour plots dB cutoff (all values smaller than dB of a maxat imum value are not shown). For the same cutoff (threshold dB) value, for the 16-antenna array the [very little clutter, as seen in Fig. 4(a)], and for the 31-an(on clutter at all). The astenna array the sumed antenna beamwidth in the DAS algorithm was set to 50 , this means that, if for an th signal a given focal point lies more than 25 from a boresight (of Tx or Rx antenna), this signal will not be included in summation. The same results but in 2D are presented in Fig. 5(a) and Fig. 5(c). These 2D results show better images for the new array. The peak for the 16-antenna array, and 0.16 for the 31-antenna (almost five-fold improvement). A twin-target exists due to the differential imaging, as explained in [27]. A real difference in quality of focused images for both arrays emerges if we increase the assumed beamwidth to . From Fig. 4(b) we can see more artifacts (clutter) in the focused images for 16-antenna array and the . For the 31-antenna array however, focused

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Fig. 5. Comparison of 2D imaging results: (a) 16-elements array, = 25 , (b) 16-elements array, (1)=(2) = 35 , (c) 31-ele(1)=(2) = 25 , (d) 31-elements array, (1)=(2) = 35 . ments array, (1)=(2) 2D contour plots show signal energy on a linear scale, normalized to maximum in the 3D volume, values below 0.1 rendered as white.

image is still free of any scatterers other than tumor [Fig. 4(e)], . Comparing peak resulting therefore in values, they equal 1.05 and 0.17 for the 16- and 31-antenna arrays, respectively. A six-fold improvement in results for the new prototype has been achieved. The difference in focusing quality for both arrays is even more striking if one decreases the threshold in contour images. In Fig. 4(c), (f) we present the same results as in Fig. 4(b),

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For this reason we have investigated detection of tumor phantoms at several locations in the breast. Due to symmetry of our array, we have picked three positions located in one quadrant

Fig. 6. 2D imaging result for the 31-elements array, same as in Fig. 5(c), but when only 16 antennas are used for focusing. Sixteen antennas with positions closely resembling those for the old array were chosen here.

4(e), but with threshold lowered to dB. We can see that a 3D image for the 16-element array is unrecognizable , whereas the image for the new array still consists only of the tumor response, with no artifacts . The same results in 2D are presented in Fig. 5 and 5(d). For the 16-antenna array, we can see a clear increases, there is more and more clutter trend, when on the periphery of the images. The tumor is still visible, but image quality has significantly suffered. For the new 31-antenna array this effect is almost completely removed, and the are identical, as we can see when 2D images for different and Fig. 5(d) for comparing Fig. 5(c) for =35 . The key to obtaining these excellent results for our new array was the antenna design. The UWB wide-slot antenna, designed for this prototype, has excellent transient characteristic for a wide angular rage of radiation, compared to the previously used stacked-patch antenna. Also, this antenna is more compact allowing for more antennas to be used. To see how much improvement in imaging results comes from the improved antenna design and how much from the increased number of antennas, we decided to use only sixteen antenna for focusing with new array. We chose sixteen antennas with the positions closest to those from the old array. Results are presented in Fig. 6 and can be directly compared to those from Fig. 5(d), where all 31 antennas were used for focusing. As expected, there is more clutter in the image when using only 16 antennas. But these results are still significantly better than for the old array with the same number of antennas, shown in Fig. 5(b). The above results let us finally draw a conclusion that the superior imaging performance is due to the better antenna design, but also due to the larger number of antennas, which provides larger array aperture and higher diversity of the radar data. This is encouraging and suggest that an improvement could still be achieved by further working on the better antenna and by adding more antennas to the array. B. Location-Independent Imaging Using the New Antenna Array For a clinically viable imaging system one needs to assume that a malignant lump can be located anywhere within a breast.

. All three positions represent challenging cases of tumors in a close proximity of the skin layer. Any other locations further away from a skin are easier to detect. Imaging results in 3D and 2D are presented in Fig. 7. In has been used in DAS focusing, all cases which is necessary for locations very close to the skin. All focused images yield excellent detection with low levels of values clutter visible only in 2D images. Comparing peak and 0.4 for for different locations, peak locations P1, P2, and P3, respectively. These values are higher than for the location presented earlier in the paper, which can be expected for locations closer to skin. Imaging at several other locations within a quadrant has also been performed (results not shown herein), always providing the same clear images of tumors. Those results prove that, with our system, we have achieved virtually location-independent imaging capability. C. Low-Contrast Imaging Using New Antenna Array Recently in [11] it was reported that the dielectric contrast between normal and malignant tissues might be significantly lower than previously believed (see [8], [9]). To see how our system would cope with the potential low-contrast scenario, we have performed number of experimental tests. First, tumor-phantom materials with dielectric constants and 20 were made. We were therefore able to realize dielectric contrast of 5:1, 2.7:1, and 2:1, with our homogeneous normal-tissue liquid . with In Fig. 8 we present imaging results of a 7 mm (diameter) tumor phantom, in those different contrast scenarios. For variable contrasts the tumor was kept at the same location. In all cases the tumor was detected without any problem. However, as one would expect, as the dielectric contrast decreases, clutter for a 5:1 contrast, 0.54 for a 2.7:1 increases. Peak contrast, and 0.69 for a 2:1 contrast. This gives almost 100% value, when dielectric contrast decreases increase in peak from 5:1 to 2:1. This effect is well visible, when looking at 2D images in Fig. 8(d), (e) and (f), for contrast of 5:1, 2.7:1 and 2:1, respectively. These results confirm that the lower dielectric contrast imposes additional challenges for microwave imaging modalities. However, it does not prohibit successful detection. VI. CONCLUSION This paper presents the new improved antenna array for radarbased breast cancer imaging. Improvement was achieved by increasing the number of antennas in the array as well as by designing new UWB antenna. Comparing to the previously used stacked-patch antenna [31], which have a planar size of 18 23 mm , the new wide-slot antenna has a size 14 14 mm . The main advantages of the new design over the patch are stable radiation pattern across a frequency band of interest, as well as % of radiated pulses for radiation extremely high fidelity angles even up to 60 from boresight. We have demonstrated the significant imaging improvement of the new 31-antenna system

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Fig. 7. 3D imaging of a 7-mm tumor phantom ( = 50) at three positions: P1(x = 0; y = 50; z = 30); P2(x = 50; y = 0; z = 30); P3(x = 40; y = 40; z = 30). (a) 3D image for position P1, (b) 3D image for position P2, (c) 3D image for position P3, (d) 2D image for position P1, (e) 2D image for position = 45 has been used in DAS for all images. 3D images show 3 dB contour maps. 2D contour plots show signal P2, (f) 2D image for position P3. (1)=(2) energy on a linear scale, normalized to maximum in the 3D volume, values below 0.1 rendered as white.

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Fig. 8. 3D imaging of a 7-mm tumor phantoms with varying  (contrast). (a) 3D image for tumor with  = 50 (contrast 5:1), (b) 3D image for tumor with  = 27 (contrast 2.7:1), (c) 3D image for tumor with  = 20 (contrast 2:1), (d) 2D image for tumor with  = 50, (e) 2D image for tumor with  = 27, (f) 2D image for tumor with  = 20 1 (1)=(2) = 45 has been used in DAS for all images. 3D images show 03 dB contour maps. 2D contour plots show signal energy on a linear scale, normalized to maximum in the 3D volume, values below 0.1 rendered as white.

over the previous 16-element array. We have observed that with dB) in 3D images, the 16-element the low threshold level ( array provided a low quality images with high clutter. Targets were often unrecognizable in those images. For the new array, however, images consisted only of tumor response with no artifacts. The key to obtaining this excellent result for our new array was the antenna design. The effect of antenna’s character-

istics needs to be emphasized, as this issue is often ignored in microwave imaging, especially in tomographic approach. The new system is able to detect 7 mm-diameter tumor phantoms in any location within the breast, even as close as 4 mm from the skin layer. Additionally, we have shown good imaging results in low-contrast scenarios, where the dielectric contrast between tumor and normal tissue was reduced down to 2:1. These

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results confirm that the lower dielectric contrast imposes additional challenges for microwave imaging modalities. However, it does not prohibit successful detection. To the best of our knowledge, the system presented in this research is the most advanced experimental system built for microwave breast imaging. Although our intent is to use it for radar-based imaging, this system could potentially be used in tomographic imaging. REFERENCES [1] E. C. Fear, P. M. Meaney, and M. A. Stuchly, “Microwaves for breast cancer detection?,” IEEE Potentials, vol. 22, no. 1, pp. 12–18, Feb. –Mar. 2003. [2] P. M. Meaney, K. D. Paulsen, A. Hartov, and R. K. Crane, “Microwave imaging for tissue assessment: Initial evaluation in multitarget tissueequivalent phantoms,” IEEE Trans. Biomed. Eng., vol. 43, no. 9, pp. 878–890, Sept. 1996. [3] P. M. Meaney, M. W. Fanning, D. Li, S. P. Poplack, and K. D. Paulsen, “A clinical prototype for active microwave imaging of the breast,” IEEE Trans. Microw. Theory Tech., vol. 48, no. 11, pp. 1841–1853, Nov. 2000, Part 1. [4] P. M. Meaney, Q. Fang, Ch. A. Kogel, S. P. Poplack, P. A. Kaufman, and K. D. Paulsen, “Microwave imaging for neoadjuvant chemotherapy monitoring,” presented at the 1st Eur. Conf. on Antennas and Propagation: EuCAP 2006, Nice, France, Nov. 6–10, 2006. [5] S. C. Hagness, A. Taflove, and J. E. Bridges, “Two-dimensional FDTD analysis of a pulsed microwave confocal system for breast cancer detection: Fixed-focus and antenna-array sensors,” IEEE Trans. Biomed. Eng., vol. 45, no. 12, pp. 1470–1479, Dec. 1998. [6] R. Benjamin, “Synthetic, post-reception focusing in near-field radar,” in Proc. EUREL Int. Conf. The Detection of Abandoned Land Mines: A Humanitarian Imperative Seeking a Technical Solution, Oct. 7–9, 1996, pp. 133–137, Publ. No. 431. [7] R. Benjamin, “Detecting Reflective Object in Reflective Medium,” U.K. patent, GB2313969, Dec. 10, 1994. [8] A. J. Surowiec, S. S. Stuchly, J. B. Barr, and A. Swarup, “Dielectric properties of breast carcinoma and the surrounding tissues,” IEEE Trans. Biomed. Eng., vol. 35, pp. 257–263, 1988. [9] W. T. Joines, Y. Zhang, C. Li, and R. L. Jirtle, “The measured electrical properties of normal and malignant human tissues from 50 to 900 MHz,” Med. Phys., vol. 21, pp. 547–550, 1994. [10] A. M. Campbell and D. V. Land, “Dielectric properties of female human breast tissue measured in vitro at 3.2 GHz,” Phys. Med. Biol., vol. 37, pp. 193–210, 1992. [11] M. Lazebnik, L. McCartney, D. Popovic, C. B. Watkins, M. J. Lindstrom, J. Harter, S. Sewall, A. Magliocco, J. H. Booske, M. Okoniewski, and S. C. Hagness, “A large-scale study of the ultrawideband microwave dielectric properties of normal breast tissue obtained from reduction surgeries,” Phys. Med. Biol., vol. 52, pp. 2637–2656, 2007. [12] J. M. Sill, T. C. Williams, E. C. Fear, R. Frayne, and M. Okoniewski, “Realistic breast models for second generation tissue sensing adaptive radar system,” presented at the 2nd Eur. Conf. on Antennas and Propagation, Edinburgh, U.K., Nov. 2007. [13] E. Zastrow, S. K. Davis, M. Lazebnik, F. Kelcz, B. D. Van Veen, and S. C. Hagness, “Development of anatomically realistic numerical breast phantoms with accurate dielectric properties for modeling microwave interactions with the human breast,” IEEE Trans. Biomed. Eng., vol. 55, no. 12, pp. 2792–2800, Dec. 2008. [14] P. Kosmas, J. D. Shea, B. D. Van Veen, and S. C. Hagness, “Threedimensional microwave imaging of realistic breast phantoms via an inexact Gauss-Newton algorithm,” presented at the IEEE Antennas and Propagation Society Int. Symp., San Diego, CA, Jul. 5–11, 2008. [15] E. C. Fear, J. Sill, and M. A. Stuchly, “Experimental feasibility study of confocal microwave imaging for breast tumor detection,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 3, pp. 887–892, Mar. 2003. [16] L. Xu, S. K. Davis, S. C. Hagness, D. W. van der Weide, and B. D. Van Veen, “Microwave imaging via space-time beamforming: Experimental investigation of tumor detection in multilayer breast phantoms,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 8, pp. 1856–1865, Aug. 2004, Part 2.

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[17] I. J. Craddock, R. Nilavalan, J. Leendertz, A. Preece, and R. Benjamin, “Experimental investigation of real aperture synthetically organised radar for breast cancer detection,” in Proc. IEEE Antennas and Propagation Society Int. Symp., Jul. 3–8, 2005, vol. 1B, pp. 179–182. [18] S. Y. Semenov, A. E. Bulyshev, A. Abubakar, V. G. Posukh, Y. E. Sizov, A. E. Souvorov, P. M. van den Berg, and T. C. Williams, “Microwave-tomographic imaging of the high dielectric-contrast objects using different image-reconstruction approaches,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 7, pp. 2284–2294, July 2005. [19] J. M. Sill and E. C. Fear, “Tissue sensing adaptive radar for breast cancer detection—Experimental investigation of simple tumor models,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 11, pp. 3312–3319, Nov. 2005. [20] P. M. Meaney, M. W. Fanning, T. Raynolds, C. J. Fox, Q. Fang, S. P. Poplack, and K. D. Paulsen, “Initial clinical experience with microwave breast imaging in women with normal mammography,” Acad. Radiology, vol. 14, pp. 207–218, 2007. [21] C. Yu, M. Yuan, J. Stang, E. Bresslour, R. T. George, G. A. Ybarra, W. T. Joines, and Q. H. Liu, “Active microwave imaging II: 3-D system prototype and image reconstruction from experimental data,” IEEE Trans. Microw. Theory Tech., vol. 56, no. 4, pp. 991–1000, Apr. 2008. [22] M. Klemm, I. Craddock, J. Leendertz, A. Preece, and R. Benjamin, “Experimental and clinical results of breast cancer detection using UWB microwave radar,” presented at the IEEE Antennas and Propagation Society Int. Symp., San Diego, CA, Jul. 7–12, 2008. [23] Y. Lee, H. J. Kim, J. M. Lee, S. I. Jeon, T. M. Grzegorczyk, and P. M. Meaney, “Microwave tomography technology test-bed system for study breast cancer detection technology based on electromagnetic field,” presented at the IEEE Antennas and Propagation Society Int. Symp., San Diego, CA, Jul. 5–11, 2008. [24] S. Kubota, X. Xiao, N. Sasaki, K. Kimoto, W. Moriyama, and T. Kikkawa, “Experimental confocal imaging for breast cancer detection using silicon on-chip UWB microantenna array,” presented at the IEEE Antennas and Propagation Society Int. Symp., San Diego, CA, Jul. 5–11, 2008. [25] M. Klemm, I. J. Craddock, J. A. Leendertz, A. Preece, and R. Benjamin, “Radar-based breast cancer detection using a hemi-spherical antenna array—Experimental results,” IEEE Trans. Antennas Propag., vol. 57, pp. 1692–1704, Jun. 2009. [26] M. Klemm, I. J. Craddock, J. A. Leendertz, A. Preece, and R. Benjamin, “Improved delay-and-sum beamforming algorithm for breast cancer detection,” Int. J. Antennas Propag., vol. 2008, 2008, doi:10. 1155/2008/761402. [27] M. Klemm, I. J. Craddock, A. Preece, J. Leendertz, and R. Benjamin, “Evaluation of a hemi-spherical wideband antenna array for breast cancer imaging,” Radio Sci., vol. 43, 2008, doi:10.1029/2007RS003807, RS6S06. [28] M. Klemm, I. Craddock, J. Leendertz, A. Preece, and R. Benjamin, “31 elements antenna array for microwave radar-based differential breast cancer imaging: Imaging in inhomogeneous breast phantoms.,” IEEE Antennas Wireless Propag. Lett., to be published. [29] M. Klemm and G. Troester, “Characterization of small planar antennas for UWB mobile terminals,” Wireless Commun. Mobile Comput., Special Issue: Ultrawideband Wireless Commun., vol. 5, no. 5, pp. 525–536, Aug. 2005. [30] D. Gibbins, M. Klemm, I. Craddock, J. Leendertz, A. Preece, and R. Benjamin, “A comparison of a wide-slot and a stacked patch antenna for the purpose of breast cancer detection,” IEEE Trans. Antennas Propag., vol. 58, no. 3, pp. 665–674, Mar. 2009. [31] R. Nilavalan et al., “Wideband microstrip patch antenna design for breast cancer detection,” IET Microw. Propag., vol. 1, no. 2, pp. 277–281, 2007. [32] R. Nilavalan, J. Leendertz, I. J. Craddock, R. Benjamin, and A. Preece, “Breast tumour detection using a flat 16 element array,” in Proc. 16th Int. Zurich Symp. on Electromagnetic Compatibility-Topical Meeting on Biomedical EMC, Zurich, Switzerland, Feb. 2005, pp. 81–84. [33] J. Leendertz, A. Preece, R. Nilavalan, I. J. Craddock, and R. Benjamin, “A liquid phantom medium for microwave breast imaging,” presented at the 6th Int. Congress of the Eur. Bioelectromagnetics Association, Budapest, Hungary, Nov. 2003. [34] I. J. Craddock, R. Nilavalan, A. Preece, J. Leendertz, and R. Benjamin, “Experimental investigation of real aperture synthetically organised radar for breast cancer detection,” in Proc. IEEE Antennas and Propagation Society Int. Symp., 2005, vol. 1B, pp. 179–182, 1B.

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Maciej Klemm was born in 1978. He received the M.Sc. degree in microwave engineering from Gdansk University of Technology, Poland, in 2002 and the Ph.D. degree from the Swiss Federal Institute of Technology (ETH) Zurich, Switzerland, in 2006. In February 2003, he joined the Electronics Laboratory, Swiss Federal Institute of Technology (ETH) Zurich, Switzerland. At ETH his research interests included small UWB antennas and UWB communications, antenna interactions with a human body, electromagnetic simulations, microwave MCM technologies and millimeter-wave integrated passives (European IST LIPS project). In spring 2004, he was a Visiting Researcher at the Antennas and Propagation Laboratory, University of Aalborg, Denmark, where he was working on the new antennas for UWB radios. In February 2006, he joined the University of Bristol (UoB), Bristol, U.K., where he currently holds a position of Research Associate. At UoB he is working on the microwave breast cancer detection and UWB textile antennas. As the leading researcher on the breast cancer project, his work includes UWB antenna design, electromagnetic modeling, experimental testing as well as participating in clinical trial. He has several patents for his work on UWB and textile antennas, as well as microwave imaging. Dr. Klemm was awarded in the Young Scientists Content at the IEEE MIKON 2004 Conference for his paper about antennas for UWB wearable radios. For this paper on the novel directional UWB antennas he won the CST University Publication Award competition in 2006. In 2007 he won the “Set for Britain” competition for the top early-career research engineer and received a Gold Medal at the Hose of Commons.

Jack A. Leendertz received the B.Sc. degree in physics with mathematics. He is currently a Research Fellow at the University of Bristol, Bristol, U.K. His research interests include microwave engineering, coherent optics in engineering, instrumentation for medical research and microwave imaging. David Gibbins joined the University of Bristol in 2005 as a postgraduate research student. During his PhD, as a member of the Centre for Communications Research (CCR), he worked on the development and numerical simulation of complex UWB antenna. He became a member of Bristol’s breast cancer imaging team, developing a UWB antenna used in a prototype imaging system. He completed his doctorate at the beginning of 2010 and is currently working on the breast cancer detection as a research assistant in UWB imaging. His research interests in this project include UWB antenna design, numerical FDTD electromagnetic simulation, inverse scattering and the physical design of the imaging system. His other research areas include conformal FDTD meshing techniques and applications of UWB radar.

David Gibbons received the M.Eng. degree (first class honors) in aerospace engineering from Liverpool University, Liverpool, U.K., in 2004. He is currently working toward the Ph.D. degree at the University of Bristol, Bristol, U.K. He joined the University of Bristol, Bristol, U.K., in 2005 where he a Research Assistant in the Centre for Communications Research and a member of Bristol’s Breast Cancer Imaging Project. His involvement in this project includes UWB antenna design, FDTD electromagnetic simulation and inverse scattering. His other research interests include conformal FDTD meshing techniques and applications of UWB radar

Ian J. Craddock is a Reader in the CCR, University of Bristol, Bristol, U.K. His research interests include antenna design, electromagnetics, biomedical imaging and radar, funded by organizations such as EPSRC, QinetiQ, DSTL and Nortel. He leads Bristol’s breast cancer imaging project, this project winning the IET’s Innovation in Electronics prize in 2006. He has published over 100 papers in refereed journals and proceedings. He has led a workpackage on ground-penetrating radar in an EU Network of Excellence and has a related active research interest in antennas and propagation for instrumentation within the human body. He has delivered numerous invited papers to conferences in Europe, the US and Asia and chaired sessions at leading international conferences.

Alan Preece is a Clinical Scientist and Emeritus Professor of medical physics at the University of Bristol, Bristol, U.K., who previously researched biological effects of ionising and non-ionising radiation on humans. Current work is applied to practical equipment design and the clinical application of microwave imaging in human subjects for the purpose of identifying and evaluating the imaging possibilities of such microwaves in detection of breast cancer.

Ralph Benjamin received the B.Sc. degree (1st class honours) in electronic engineering from Imperial College, London, U.K. Currently, he is a Visiting Research Professor, University College, London, U.K., and Bristol University, Bristol, U.K. Until recently also a Visiting Professor at Imperial College, London, External Ph.D. supervisor, Open University, and external Post-Graduate Course Examiner, Military College of Science, Member of Court, Brunel University. After inventing the single-sideband mixer during his undergraduate course, he joined RN Scientific Service in 1944. He developed the first counter-measure resistant 3D radar, and first force-wide integrated CCIS (Command, Control, Communications and Intelligence System) from 1947–1957. In 1947, he patented the interlaced cursor, controlled by joy-stick or mouse, to link displays to stored digital information. He patented the world’s digital compression of video data, and first digital data link, 1947, still in use NATO-wide as “Link 11.” Following repeated “special merit” promotions, Head of Research and Deputy Director, Admiralty Surface Weapons Establishment from 1961–1964. (Evening/night work to lay the theoretical foundations for this field resulted in a Ph.D., then published as the textbook on Signal Processing.) In 1961, Acting International Chairman NATO “Von Karman” studies on “Man and Machine” and “Command and Control.” During 1950 through 1960s, leading member of DTI Advanced Computer Techniques Project. Chief Scientist Admiralty Underwater Weapons Establishment (AUWE), 1964–1971 combined with Director, AUWE, and MoD Director Underwater Weapons R&D (and member of Navy Weapons Department Board), 1965–1971. (Published personal contributions led to the London DSc.) Chief Scientist, Chief Engineer and Superintending Director, GCHQ 1971–1982. This entailed responsibility for fast-track research, development, procurement, and deployment and use of equipment and techniques for the collection interpretation evaluation and assessment of Electronic or Signals Intelligence information. (Most projects had to create urgent solutions to problems which the opposition’s leading experts thought they had made impossible.) From 1972–1982, his functions were combined with those of Chief Scientific Advisor to both the Security Service and SIS, and with acting as Cabinet Office Coordinator, Intelligence R&D. Also visiting Professor, University of Surrey for two 3-year terms, 1972–1978, during which time he helped to start the Surrey University mini-satellite programme. Then Head of Communications Techniques and Networks and semi-official Global Research Co-ordinator NATO (SHAPE Tech Centre) 1982–1987 and Graduate NATO Staff College, 1983. During all these appointments, he combined the administration of large scientific/engineering organizations and of their R&D programmes, with creative, innovative up-front leadership, as illustrated by numerous classified and learned-society publications and patents.

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On the Fundamental Limitations of Artificial Magnetic Materials Ali Kabiri, Leila Yousefi, and Omar M. Ramahi, Fellow, IEEE

Abstract—Fundamental limitations are presented on the performance of artificial magnetic materials based on the geometrical and physical characteristics of the inclusions comprising the medium. The permeability and magnetic susceptibility of the medium are formulated in terms of newly defined geometrical and physical parameters. Based on the Lorentzian form of the effective permeability function of the medium, it is shown that the flatness of the permeability function is limited by the desired operational bandwidth. Also, by applying a specific circuit-based model for inclusions, geometric invariant fundamental constraints are derived. It is shown that inclusions with larger surface area result in higher value of permeability. Next, the magnetic loss tangent in the medium is expressed as a function of the newly defined geometrical and physical parameters. It is found that there is a tradeoff between increasing the permeability and decreasing the loss on the one hand and reducing dispersion, on the other hand. Index Terms—Artificial magnetic material, electrically small resonators, magnetic loss tangent, magnetodielectric, metamaterial.

I. INTRODUCTION N MICROWAVE and sub-microwave frequencies, naturally-occurring materials are limited to certain levels of polarization and magnetization. Even if certain levels of magnetization and polarization are achievable, however, the materials suffer from high electric and magnetic loss. For example, ferrite composites are strongly magnetized yet they suffer from appreciable magnetic loss and high resistivity in the microwave frequency range [1], [2]. Due to these limitations, artificially engineered materials, also referred to as metamaterials, are designed to provide specific permeability and permittivity over microwave frequency ranges [3]–[6]. Artificial magnetic media (AMM), which are produced by an ensemble of small metallic looped inclusions organized periodically or aperiodically, exhibit magnetic behavior when exposed to an applied electromagnetic field. To obtain enhanced magnetic properties, different inclusions have been proposed having various geometrical configurations [4]–[6]. Each proposed structure provides its own advantages and disadvantages in terms of resultant permeability, dispersive

I

Manuscript received January 30, 2009; revised January 04, 2010; accepted January 23, 2010. Date of publication April 22, 2010; date of current version July 08, 2010. This work was supported in part by Research in Motion and in part by the National Science and Engineering Research Council Canada under the NSERC/RIM Industrial Research Chair Program. The authors are with the Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON N2L 3G1, Canada (e-mail: oramahi@ece. uwaterloo.ca). 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/TAP.2010.2048845

characteristics and dissipation factor. The single and coupled split-ring resonators (SRR), the modified split-ring resonators (MSRR), and the “Swiss Roll” resonators (SR-R) are among popular configurations. In [5], a new configuration named metasolenoid was proposed with the potential to provide higher permeability compared to SRR and MSRR configurations. In [7], the n-turn spiral resonator (n-SR) configuration was introduced, and in [8] new inclusions based on fractal Hilbert curves were proposed to reduce the size of inclusions. A number of analytical models were developed to explicate the physics behind the peculiar characteristics of AMMs [4], [6], [9], [10]. When the periodicity and the size of the inclusions are small compared to the wavelength, electromagnetic mixing formulas such effective medium theory (EMT) and homogenization theories (HT) can be used to derive the effective permeability and permittivity for composite media [11]. Using the EMT technique, Pendry et al. calculated the effective permeability of a medium containing looped metallic inclusions such as metal cylinders, Swiss Rolls, and SRRs and showed that negative permeability can be obtained in microwave frequencies [4]. EMT allows identifying the average field propagating inside a composite medium with respect to the field propagating inside a homogeneous medium with the same effective electrical characteristic [12]. The circuit-based models of metamaterials, especially artificial magnetic materials, have been developed to capture either the behavior of the entire composite medium or the behavior of the separate inclusions [5]. These models, which depend on the geometry and dimension of the inclusions, have been proposed to describe the magnetic behavior of the inclusions rather than the electric behavior. Different shapes of inclusions have been studied in the literature. The SRR consists of two concentric metallic broken rings printed on a dielectric circuit board. Marques et al. presented a quasi-static study of the SRR by proposing a circuit model for the capacitive behavior of the inclusions [6]. Sauviac et al. and Shamonin et al. proposed more accurate models for SRR inclusions [9], [13]. Sauviac et al. used a detailed circuit-based model to extract the magnetic and electric polarization of the SRR [9]. Shamonin et al. expanded a set of differential equations describing the current and voltage distribution in SRRs [13]. Most recently, Ikonen et al. offered a generalized equivalent-circuit model which mimics the experimental permeability function [14]. The unique properties of metamaterials have encouraged researchers to use metamaterial slabs in various microwave applications including using metamaterials as a substrate or a superstrate for enhancing low-profile antenna performance [15], [16], as a probe for the near-field imaging [17], or for shielding

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applications and microwave absorbers [18]–[20]. In [15], extensive research was done on the performance of developed engineered magnetic materials when used for antenna miniaturization. It was shown in [8] that new inclusions can provide lower dispersion, nevertheless, high magnetic losses persist. In [21], the effective properties of the medium are expressed in terms of the Q-factor. It was claimed that by measuring the Q-factor of a single fabricated SRR, the effective permeability and permittivity of an AMM can be estimated to better than 20% accuracy. In addition, in [21], a lower limit for the magnetic loss tangent was proposed for frequencies up to about 1 GHz. This work aims to establish a relationship between the design specification of inclusions and the performance features of artificially engineered magnetic materials. The parameters that play a role in the effective permeability and its variation with respect to frequency are classified into physical and geometrical variables. Physical variables are parameters which are restricted to (a) fabrication techniques such as the width and height of the printed conductor on the board (i.e., trace), (b) structural characteristics such as space between parallel printed lines, the entire size of structure and its unit cells, and (c) electrical or material characteristics such as conductivity of the conductor and the permittivity of the host medium. Geometrical parameters, on the other hand, include the inclusion’s shape and a contour’s perimeter, area and curvature. In this work, we derive a general relationship which relates the effective permeability of the structure to the physical and geometrical variables of the inclusion. Moreover, we study the sensitivity of an AMM’s magnetic properties such as the permeability function, the magnetic loss tangent (MLT) and dispersion with respect to variation of the geometrical and physical parameters. In this work, a circuit-based model is used for calculating the magnetic behavior of inclusions and the slab itself. The circuit model developed considers the capacitance between the pairs, ohmic resistance of the inclusions and the inductance created due to the circulating current excited on the inclusions. Although more elaborate models proposed in literature [9], [14] consider more circuit components such as the capacitance of the inclusions gap, inductance of the metallic routes and mutual induction between adjacent inclusions, it has been shown that the general functionality of the effective magnetic behavior of inclusions will not change [4], [5]. Thus, our derivations and conclusions, in essence, are general, and they can be applied for any application and design. It is worth noting that in this work, we only considered the magnetic loss, however, the total loss in the medium can be comprised of electric and magnetic losses. This paper is organized as follows: In Section II, a general circuit-based model is developed to calculate the effective permeability of inclusions. In Section III, an explicit relationship is derived to connect the deviation in the relative permeability to the relative bandwidth of the artificial magnetic medium, thus predicting a fundamental restriction on the operational bandwidth based on the permissible variation in the permeability. It is shown that the achieved restriction is general and does not depend on the shape of the metallic inclusions. In Section IV, the effect of the geometrical and physical parameters on the permeability and its variation with respect to frequency is studied. Section V provides concluding remarks.

Fig. 1. A metamaterial slab (an artificial composite of metallic inclusions).

II. PROBLEM FORMULATION Various geometrical patterns have been proposed to develop artificial magnetic materials [4]–[6]. The key idea to produce magnetic properties is to generate a circulating electric current that mimics a magnetic dipole. The current circulation occurs in a metallic contour leading to increased magnetic flux. To generate a capacitive property, another metallic contour is positioned adjacent to the first contour. The coupling between the two contours creates capacitance between them leading to a net effective increase in the permeability. The resultant capacitance and inductance create the potential for resonance at a certain frequency, henceforth referred to as the resonance frequency. Fig. 1 shows an artificial magnetic medium composed of periodic unit cells of generic rings. The ring resonator in a unit cell can be an n-turn spiral or multiple split rings. The rings provide different coupling schemes, namely edge-coupled if the rings are concentric in a plane, and broadside-coupled if the rings are parallel along their axes. Fig. 2(a) shows a two-turn spiral ring resonator, Fig. 2(b) shows split ring resonators which are edge-coupled, and Fig. 2(c) shows split ring resonators which are broadside-coupled. Fig. 2(e) and Fig. 2(f) show a cross section of edge-coupled and broadside-coupled ring resonators, respectively. The artificial magnetic medium is then created by reproducing the contour in a periodic fashion, infinitely spread along the x, y, and z axes. width of The unit samples in Fig. 2 have the height of and depth of . The area of each cell is , and its . The area and circumference of volume is the contours are denoted by and , respectively. The conductor material used in printed inclusions is assumed to have electric conductivity of , width of , and height of . Without loss of generality, we assume the other (twin) conductor is positioned either to the inside and follow the shape of the outer conductor with the uniform gap (see Fig. 2(e)) or parallel to the former and separated by a distance of (see Fig. 2(f)). is apWhen an external monochromatic magnetic field plied, it induces a circulating current on the metallic inclusion. develops. As a consequence, an induced magnetic field Based on Faraday’s law an electromotive force, , develops on the metallic rings given by (1) (2)

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sions. Accordingly, the induced dropped over any inclusion can be expressed by the impedance of the rings and the induced current on the inclusion as [5] (5) where the effective impedance of the loops has been modeled with a resistor, , in series with a capacitor, . The skin depth of the conductor determines the relationship between the resistance and the frequency. Therefore, is given by: (6)

Fig. 2. Configuration of a unit cell of an artificial magnetic material with arbitrary shape of the inclusion. The inclusions’ contour, area and perimeter are denoted by 0; s, and l , respectively. However, V and A represent the volume and surface area of the unit cell. (a) Two-turn spiral inclusion, (b) edge-coupled double split ring resonator, (c) broadside-coupled double modified split ring resonator, (d) a cross section of an edge-coupled inclusion, (e) a cross section of a broadside-coupled inclusion.

where and are the magnitude of the vectors and , respectively, is the induced current, is the number of wire turns that carries the induced current ( for Fig. 2(a) for Figs. 2(b) and (c)) [5], is the frequency [16], and is the permeability of air. of the applied external field, and The inclusions are also distributed in the y-direction (along their axis), and, thus, the produced magnetic field in each column passes through the other inclusions of the same stack. For evaluis considered to be smaller than the ating the magnetic field, largest dimension of the inclusion. Therefore, each column of inclusions in the y-direction can properly be modeled as a solenoid with the magnetic field given by (2). In an artificial medium, the effective magnetic susceptibility, the degree of magnetization of the medium in response to an applied magnetic field is defined as

where is the number of wire turns which contribute to ohmic for case (a), (b) and (c)], and is losses [

The relative permeability of the conductor in (6) was considered to be 1. Also, is given by (7) , and are defined as the per-unit-length resistance and the per-unit-length capacitance of the inclusion. The per-unitlength capacitance, for the edge-coupled inclusion can be expressed as [22] (8) and for the broadside-coupled inclusion as [5] (9) where

is the relative permittivity of the host substrate, and is the elliptical integral of the first kind

(3)

(10)

where is the magnitude of , the magnetization vector of the medium. Magnetization is defined as the magnetic moment per unit volume. In this case, the magnetic dipole moments are in phase with the external magnetic field yielding a magnetized medium where the effective magnetic susceptibility is larger than zero (or the effective permeability is larger than unity). The magnetic dipole moment of inclusions can be simply derived as1

It is worth noticing that in the case of metasolenoid [5] the gap, , between the parallel inclusions is equal to the unit cell height, . Equating (1) and (5), and using (3) and (4), the effective magnetic susceptibility can be expressed as

(4)

(11)

To derive an explicit relation for the magnetic susceptibility based on physical and geometrical characteristics of the inclusion-filled medium, we propose a circuit model for the inclu1In previous works [5], [8] the magnetic dipole moment was incorrectly expressed as m =  nI s.

where the inductance, , is defined as (12) and

is the per-unit-area inductance of the inclusion.

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Substituting the resistance, inductance and capacitance from (6), (7) and (12) in (11) results in an expression for the net magnetic susceptibility as a function of the geometrical and physical properties of the contour (13) As observed in (13), the susceptibility is related to the perimeter and area of the contour. Thus, inclusions with different topologies but having the same perimeter and area, result in the same values for the magnetic susceptibility and permeability (assuming all other physical parameters remain constant). Equation (13) can be rewritten as

In (19), depends on the resonance frequency , as well as the physical properties of the design such as the permittivity of the host substrate, , width of the metal strips, , and space between the strips, , (in edge-coupled inclusions) or gap, , between parallel contours in a unit cell (in broadside-coupled inclusion) and the resistance. By factoring the frequency-related parts, the physical parameter can be expressed as (21) where is related only to the physical parameters (conductivity of inclusion, width and height of route of an inclusion, and permittivity of host medium), and is expressed as

(22) (14)

where

are defined as

The circumference and area of the contour, however, are not independent parameters. They are related according to the following relation: (15)

III. FUNDAMENTAL LIMITATIONS ON FREQUENCY DISPERSION

Hence (16) where the frequency is considered as the resonance frequency of the artificial magnetic medium. Considering (16), grouping all the physical parameters into one parameter , and defining as the normalized frequency ) (14) can be (with respect to the resonance frequency rewritten as (17) and is the fractional area of the cell occuwhere pied by the interior of the inclusion given by (18) and

Note that is expressed as the multiplication of a freand a simple function of the quency-invariant coefficient, resonance frequency which is typically specified in a given design problem. As a summary, we have derived generalized expressions for the permeability and susceptibility governing the behavior of composite engineered magnetic materials with any arbitrary shape of inclusion. To generalize the expression for use in any frequency range, it is expressed in terms of the normalized angular frequency . Therefore, for any structure, calculations and are sufficient to obtain the effective magnetic of behavior.

is defined as

Artificial magnetic materials are designed to provide enhanced positive permeability over a specific range of frequencies. For most of applications, it is desirable to have a uniform permeability over the range of frequencies of interest, however, due to the resonating nature of inclusions, the permeability resulting from engineered magnetic materials changes rapidly with frequency [4], [5]. The variation with frequency will result in dispersion leading to limited if not poor performance in many applications related to antenna miniaturization and gain enhancement [15]. In this section, the fundamental limitations on frequency dispersion reduction in the design of artificial magnetic materials are investigated for the lossless case where the conductivity of the conductor is assumed infinite and for the case where Ohmic losses are present. A. Lossless Case A typical response of an artificial magnetic medium is shown in Fig. 3. By assuming zero resistance in the metallic inclusions, the resultant susceptibility of the lossless case, from (14) and (16) will be a real number and is equal to

(19) (23) Using (17), the effective permeability can be written as

(20)

and as the lowest and highest operational Assuming , and as the resultant permeability frequencies at these frequencies respectively, we are seeking a general rela, and, . (Since tionship between,

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or equivalently (28) Since the ratio of is always less than one, the limit achieved in (28) is even stronger than that of (26). Therefore, the change of susceptibility with frequency is even more rapid than the square of frequency. By defining mean permeability and central frequency , respectively, as

Fig. 3. A typical response of an artificial magnetic medium showing the effective permeability as a function of normalized frequency.

the engineered magnetic materials are designed to provide perare chosen meability higher than one, the frequencies and to be less than the resonance frequency .) and we have Enforcing (23) at

and and as the deviation of susceptibility and permeability, respectively, (28) can be rewritten as (29) In many application and . Using these conditions, (29) can be simplified using first-order binomial expansions as

(24) (30) Solving the system of equations (24) for

yields (25)

Recall that since is the fractional area occupied by the interior of the inclusion in the unit cell, is bound by unity. Satleads to restrictions on the isfying the conditions of susceptibilities at two selected frequencies. For the first condition , it is clear that the permeability is larger than one and therefore the susceptibility is positive for all frequencies less and ). Consequently, since than , (i.e., , we have (26) The above equation shows an interesting constraint which limits the ratio of the susceptibility at any two arbitrary frequencies to the square of the ratio of those frequencies. Another interesting observation is that the relationship given in (26) is independent of both physical and geometrical characteristics of the designed inclusion. Any effort to improve the frequency bandwidth of the resultant permeability is strictly confined to , then this limitation. As an example, suppose cannot be less than 9. , we consider (25) For the second condition, namely, and after some algebraic manipulations, we have

(27)

Substituting (30) in (28) results in (31) The condition in (31) relates the deviation in the relative permeability to the relative bandwidth. Since the bandwidth BW is inversely proportional to the mean permeability , there is a tradeoff between maximizing the effective permeability and broadening the frequency range in which the smooth deviation of permeability is obtainable. In fact, for two different designs with the same relative permeability deviation, wider bandwidth can be achieved in the design with lower permeability. Fig. 4 illustrates (31) graphically. For any design, the resultant bandwidth lies in the gray area shown in Fig. 4. As an exequal to 5, requiring the relative permeability deample, for viation to be less than 1 percent bounds the relative frequency bandwidth to 0.125%, and say, for a central frequency of 200 MHz the bandwidths would theoretically be less than 250 kHz. , having 1% deviation in the As a second example, if permeability leads to a maximum of 0.5% relative bandwidth. Although first-order terms were used in the Taylor’s expansion in (31), it can be shown that making the approximation more accurate by including second-order terms in the expansion gives identical conclusions. B. Lossy Case By considering loss, the resultant permeability in (20) or the resultant susceptibility in (17) will have real and imaginary parts. Since only the real part affects the permeability in the

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has a second-order simple singularity at The function the normalized resonance frequency (i.e., ), thus approaches infinity as approaches one. The factor in (34) is and all its derivaa parameter that scales the magnitude of tives. Differentiation of with respect to gives (35)

Fig. 4. The relative frequency bandwidth is depicted versus the relative permeability deviation. The gray area determines the possible interval for the bandwidth. Notice that the slope is inversely proportional to the central susceptibility.

artificial magnetic medium and the imaginary part appears only when introducing loss in the medium, the deviation with frequency is mostly important for the real part. In this section we study the frequency deviation of the real part only, and in the next section the magnitude of the imaginary part and methods and limitations to decrease it will be discussed. As shown in Section I, the resultant permeability can be modeled as the response of an RLC circuit. It is expected that adding resistance or loss to the system (inclusions) leads to a smoother frequency response. Therefore, it is expected that the fundamental limits achieved for the frequency response of the permeability in Subsection III.A for the lossless case to be sufficient for the lossy case. To show this, we consider the real part of (17) as the resultant magnetic susceptibility of the medium. The real part of the magnetic susceptibility is given by

In the range , (35) is always positive, therefore, the function increases monotonically with respect to . So, for , we have (36) Using (36), (33) leads to (37) Simplification of (37) results in (38) The inequality in (38) states that the ratio of the magnetic susceptibility at two different frequencies for the lossless case is larger than that of the lossy case. This indicates that the magnetic susceptibility function is flatter for the lossy case than for the lossless case. Note that the limit achieved in (31) is independent of the topology of the inclusion. IV. THE EFFECT OF PHYSICAL AND GEOMETRICAL PARAMETERS ON DISPERSION AND LOSS

(32) Using (23), the real part can be expressed in term of the susas ceptibility of the lossless case,

(33)

As shown in Section II, all physical properties can be summarized in one parameter, , and all geometrical properties can be summarized in one parameter . Equation (33) gives the magnetic susceptibility and consequently the permeability in terms of these two parameters, and . Therefore, the study of the effect of physical and geometrical parameters on the resultant permeability and its frequency domain behavior will be confined to and . A. Real Part of Permeability Differentiation of (36) with respect to

where

gives

is defined as (34)

and . The factor determines the level of loss in the medium and therefore we call it the dissipation factor. Since frequencies below the resonance frequency result in permeability higher is considered to be than one, the frequency range the only frequency range of relevance when designing artificial magnetic permeability that achieves enhanced positive permeability. Therefore, in the context of this work, we focus our attention on this range only.

(39) In the frequency range of interest,

, we have (40)

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Fig. 5. Real part of the permeability as a function of the normalized frequency,

, for different values of F . The inclusion trace is made of copper and the dimensions are similar to those reported in [8]: g = b = 0:127 mm, " = 3:38; y = 3:028 mm, x = z = 20 mm.

Therefore, the larger , the higher the permeability. Since is defined as the ratio of the surface enclosed by the inclusion to the total surface of the unit cell, the contours which provide higher enclosed surface lead to higher permeability. On the other hand, the surface of the inclusion and its length are related to each other through the resonance frequency in (15). Indeed, they are inversely proportional at a fixed resonance frequency. Therefore, for all inclusions designed to operate at the same resonance frequencies, the ones that provide larger enclosed surface (or larger ) and shorter total length (i.e., perimeter) will result in higher value for permeability. Fig. 5 shows the real part of the permeability as a function of for different values of . Furthermore, Fig. 5 shows that an increase in leads to a larger value of the permeability which is expected from (40). Using (32), the real part of the permeability can be written as (41) In (41), is a function of with respect to gives

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Fig. 6. The real part of permeability for different values of P , the geometrical parameter F is assumed to be 0.8. Notice that all curves are almost overlapping.

the upper frequency of interest is not close to the resonance frequency. As the resonance frequency is approached, the curves is no longer much smaller in Fig. 7 start to diverge and than one.) Table I shows three values for designs proposed earlier in the literature. In all cases, the factor was small, even in some cases smaller than the numbers we considered for the graph in Fig. 6. B. Magnetic Loss Tangent An important parameter in designing artificial magnetic materials is the Magnetic Loss Tangent, , which represents the magnetic loss in the medium. In most applications, it is desirable as small as possible. In this section, the behavior to have of with respect to the geometrical and physical parameters, and , is investigated. The magnetic loss tangent is defined as (43)

. Taking the derivative of (41) Using (20),

can be rewritten as (44)

Differentiating (44) with respect to

, we obtain

(42) (45) . Therefore, Notice that (42) is always negative for by increasing , we expect the permeability to decrease. However, what is interesting is that for practical considerations, is highly insensitive to changes in . Fig. 6 shows a plot of vs. , for the case of (this case was simply selected as an example). We observe that as changes by one order of magnitude, the resultant permeability remains practically constant. Notice that the curves in Fig. 6 are indistinguishable. This is due to the fact that in (41), the only part that is a function of is which is much smaller than 1. (Since , and from (34), it can be shown that for practical geometries such as those con. Notice that we are assuming that sidered in Table I,

, are positive for all values In (45), all terms except is inversely related to [see (34)], of and . Since has a local maximum at a specific value of denoted as . is plotted as a function of for different values In Fig. 7, , the value of corresponding to of and . Notice that, , is relatively small compared to unity, meaning maximum that reaches a maximum when the area of the inclusions is small in comparison to the area of the unit cell. Since the permeability approaches unity for small values of , it is most desirable to achieve the highest permeability, hence, is chosen to be greater than .

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TABLE I PARAMETERS OF SOME PREVIOUSLY DESIGNED INCLUSIONS

Fig. 7. The magnetic loss tangent, tan  , as a function of the geometrical parameter, F , for different values of P and .

Fig. 9. The magnetic loss tangent tan  as a function of the physical parameter, P for different values of F and .

35 when is 0.8 and is 0.1). In addition, it can be observed decreases. that as approaches unity To study the effect of physical parameters on loss, we need to with respect to consider the derivative of

(47)

Fig. 8. The magnetic loss tangent, tan  , as a function of and F , for P = 0:05.

For designs with larger than , as shown in Fig. 7, increasing leads to a smaller value of . Consequently, an optimal design is a design with inclusions whose area is close which leads to a lower magnetic to the unit cell’s area , achieved at , is loss. Hence, the minimum value of (46) Fig. 8 shows a three dimensional presentation of as a function of and . As shown in this figure, the maximum occurs at the lower value of . For instance, for an value of inclusion with a physical factor less than 0.002, the maximum at any frequency occurs at less than 0.2. Moreover, of as increases, i.e., the inclusion occupies more area of the unit cell, the maximum moves to larger and also becomes larger (from about 10 when and are close to zero, and more than

, the term For a specific value of , denoted as vanishes, and reaches a maximum for a certain value of and . (It is a simple exercise to show has only one maximum within the range of . In that is plotted as a function of for different values Fig. 9, of and . As shown in Fig. 9, the maximum of function occurs for values of much higher than those used in practical structures. V. CONCLUSION In this work, we presented fundamental limitations on the performance of artificial magnetic materials. The formulation is based on a circuit model that incorporates the physical behavior of the inclusion. The permeability and magnetic susceptibility of the media were formulated in terms of a geometrical parameter, , that represents the geometrical characteristics of the inclusions such as area, perimeter and curvature, and a physical parameters, , that represents the physical, structural and fabrication characteristics of the medium. Fundamental constraints expressing the effect of the relative permeability on the relative bandwidth were derived for the lossless and lossy structures. It is shown that the achieved restriction is general and does not depend on the shape of the metallic inclusions comprising the artificial magnetic medium.

KABIRI et al.: ON THE FUNDAMENTAL LIMITATIONS OF ARTIFICIAL MAGNETIC MATERIALS

The effect of the physical and geometrical parameters, and , respectively, on the effective permeability of the medium and the magnetic loss tangent were studied. It was found that increasing increases the effective permeability of the medium, however, it also leads to increased dispersion. Increasing the geometrical factor was found to decrease the loss. It was also found that the physical parameter, has very little impact on the effective permeability and dispersion; however, it affects the loss more pronouncedly. Therefore, there is a tradeoff between increasing the permeability and decreasing the loss on the one hand, which results from increasing , and reducing dispersion, on the other hand by decreasing . In other words, designing inclusions with larger surface area (i.e., increasing ) results in lower loss and higher value for permeability; however, this leads to an increase in the rate of change of permeability with frequency, thus higher dispersion. The constraints and relations derived in this work can be used to methodically design artificial magnetic material meeting specific operational requirements. REFERENCES [1] S. B. Narang and I. S. Hudiara, “Microwave dielectric properties of m type barium, calcium and strontium hexaferrite substituted with co and ti,” J. Ceramic Processing Res., vol. 7, no. 2, pp. 113–116, 2006. [2] W. D. Callister, Materials Science and Engineering, an Introduction. New York: Wiley, 2000. [3] M. V. Kostin and V. V. Shevchenko, “Artificial magnetics based on double circular elements,” in Proc. Bian-Isotropics’94, Perigueux, France, May 1994, pp. 49–56. [4] J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech., vol. 47, no. 11, pp. 2075–2084, Nov. 1999. [5] S. Maslovski, P. Ikonen, I. Kolmakov, and S. Tretyakov, “Artificial magnetic materials based on the new magnetic particle: Metasolenoid,” Progr. Electromagn. Res. (PIER), vol. 54, no. 9, pp. 61–81, Sept. 2005. [6] R. Marques, F. Medina, and R. Rafii-El-Idrissi, “Role of bianisotropy in negative permeability and left-handed metamaterials,” Phys. Rev. B, vol. 65, no. 14, pp. 44 401–44 404, Nov. 2002. [7] J. D. Baena, R. Marques, and F. Medina, “Artificial magnetic metamaterial design by using spiral resonators,” Phys. Rev. B, vol. 69, pp. 144 021–144 025, Jan. 2004. [8] L. Yousefi and O. M. Ramahi, “New artificial magnetic materials based on fractal Hilbert curves,” in Proc. IWAT07, 2007, pp. 237–240. [9] B. Sauviac, C. R. Siovski, and S. A. Tretyakov, “Double split-ring resonators: Analytical modeling and numerical simulation,” Electromagnetics, vol. 24, no. 5, pp. 317–338, 2004. [10] A. Ishimaru, S. Lee, Y. Kuga, and V. Jandhyala, “Generalized constitutive relations for metamaterials based on the quasi-static lorentz theory,” IEEE Trans. Antennas Propag., vol. 51, no. 10, pp. 2550–2557, Oct. 2003. [11] D. R. Smith and J. B. Pendry, “Homogenization of metamaterials by field averaging,” J. Opt. Soc. Am. B, vol. 23, no. 3, pp. 391–403, Mar. 2006. [12] M. G. Silveirinha, “Metamaterial homogenization approach with application to the characterization of microstructured composites with negative parameters,” Phys. Rev. B, vol. 75, pp. 1–15, 2007, 115104. [13] M. Shamonin, E. Shamonina, V. Kalinin, and L. Solymar, “Properties of a metamaterial element: Analytical solutions and numerical simulations for a singly split double ring,” J. Appl. Phys., vol. 95, no. 57, pp. 3778–3784, 2004. [14] P. Ikonen and S. A. Tretyakov, “Determination of generalized permeability function and field energy density in artificial magnetics using the equivalent-circuit method,” IEEE Trans. Antennas Propag., vol. 55, no. 1, pp. 92–99, 2007. [15] P. Ikonen, S. I. Maslovski, C. R. Simovski, and S. A. Tretyakov, “On artificial magnetodielectric loading for improving the impedance bandwidth properties of microstrip antennas,” IEEE Trans. Antennas Propag., vol. 54, no. 6, pp. 1654–1662, Jun. 2006. [16] K. Buell, H. Mosallaei, and K. Sarabandi, “A substrate for small patch antennas providing tunable miniaturization factors,” IEEE Trans. Microw. Theory Tech., vol. 54, pp. 135–146, Jan. 2006.

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[17] M. Boybay and O. M. Ramahi, “Near-field probes using double and single negative media,” in Proc. NATO Advanced Res. Workshop: Metamaterials for Secure Information and Communication Technologies, May 2008, vol. 1B, pp. 725–731. [18] G. Lovat and P. Burghignoli, “Shielding effectiveness of a metamaterial slab,” in Proc. IEEE Int. Symp. of Electromagnetic Compatibility, Jul. 2007, vol. 1B, pp. 1–5. [19] N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padillal, “Perfect metamaterial absorber,” Phys. Rev. Lett., vol. 100, no. 20, pp. 207–402, May 2008. [20] F. Bilotti, A. Alu’, N. Engheta, and L. Vegni, “Features of a metamaterial based microwave absorber,” in Proc. the Workshop on Metamaterials and Special Materials for Electromagnetic Applications and TLC, Rome, Italy, Mar. 2006, vol. 1B, pp. 11–14. [21] S. A. Cummer, B.-I. Popa, and T. H. Hand, “Q-based design equations and loss limits for resonant metamaterials and experimental validation,” IEEE Trans. Antennas Propag., vol. 56, no. 1, pp. 127–132, Jan. 2008. [22] R. Schinzinger and P. Laura, Conformal Mapping: Methods and Applications. The Netherlands: Elsevier, 1991. Ali Kabiri was born in Tehran, Iran, in 1978. He received the B.Sc. degree in electrical engineering from Sharif University of Technology, Tehran, Iran, in 2000 and the M.Sc. degree in theoretical physics and elementary particles (highest honors) from the University of Tehran, Tehran, in 2002. From 2002 to 2006, He was a Manager at SAM Electronics (subsidiary of Samsung), Tehran. Currently, he is working toward the Ph.D. degree at the University of Waterloo, Waterloo, ON, Canada. His research interests include metamaterials, artificial magnetic materials, nano-plasmonics, and optical magnetism.

Leila Yousefi was born in Isfahan, Iran, in 1978. She received the B.Sc. and M.Sc. degrees in electrical engineering from Sharif University of Technology, Tehran, Iran, in 2000, and 2003, respectively, and the Ph.D. degree in electrical engineering from the University of Waterloo, Waterloo, ON, Canada, in 2009. Currently, she is working as a Postdoctoral Fellow at the University of Waterloo. Her research interests include metamaterials, miniaturized antennas, electromagnetic bandgap structures, and MIMO systems.

Omar M. Ramahi (F’09) received dual B.S. degrees in mathematics and electrical and computer engineering (summa cum laude) from Oregon State University, Corvallis, in 1984, and the M.S. and Ph.D. degrees in electrical and computer engineering from the University of Illinois at Urbana-Champaign, in 1986 and 1990, respectively. From 1990 to 1993, he held a visiting fellowship position at the University of Illinois at Urbana-Champaign. From 1993 to 2000, he worked at Digital Equipment Corporation (presently, HP), where he was a member of the Alpha Server Product Development Group. In 2000, he joined the faculty of the James Clark School of Engineering, University of Maryland at College Park, as an Assistant Professor and later as a tenured Associate Professor. At the University of Maryland, he was also a faculty member of the CALCE Electronic Products and Systems Center. Presently, he is a Professor in the Electrical and Computer Engineering Department and holds the NSERC/RIM Industrial Research Associate Chair, University of Waterloo, Ontario, Canada. He also holds cross appointments with the Department of Mechanical and Mechatronics Engineering and the Department of Physics and Astronomy. He served as a consultant to several companies and was a co-founder of EMS-PLUS, LLC and Applied Electromagnetic Technology, LLC. He has authored and coauthored over 230 journal and conference papers. He is an coauthor of the book EMI/EMC Computational Modeling Handbook (Springer-Verlag, 2001). Dr. Ramahi serves as an Associate Editor for the IEEE TRANSACTIONS ON ADVANCED PACKAGING and as an IEEE EMC Society Distinguished Lecturer.

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A Compact Printed Antenna With an Embedded Double-Tuned Metamaterial Matching Network Michael Selvanayagam, Graduate Student Member, IEEE, and George V. Eleftheriades, Fellow, IEEE

Abstract—A compact antenna intended for use in a laptop computer is proposed with the antenna consisting of a simple radiating strip and a matching network based on a metamaterial particle. The matching network is used to increase the 10 dB bandwidth of the antenna. Double-tuned matching network theory is used to increase the bandwidth of the antenna by forming a loop on the Smith Chart inside a given VSWR circle. The matching network is implemented using a complementary-split-ring-resonator (CSRR) microstrip network to act as a shunt LC network. This is confirmed by means of a circuit model to model the CSRR-microstrip network. Finally the antenna is fabricated and tested with the measured and simulated results showing good agreement. The measured antenna has 560 MHz of bandwidth centered at 2.54 GHz with an efficiency of 89%. Index Terms—Laptop antennas, matching networks, metamaterials.

I. INTRODUCTION

T

HE use of double tuned matching networks to increase the bandwidth of a frequency dependant load, such as an antenna, is a useful technique. Double tuned matching networks have been presented in [1]–[3]. Their application to antennas has also been shown. For example, a disk-loaded monopole antenna using a double-tuned matching network is described in [4]. Double-tuned matching has also been applied to patch antennas in the form of stacked patches [5]. In the design of compact antennas such techniques can be useful provided that the matching network can be made to fit into a compact area. In this paper we present a compact planar antenna with an embedded double-tuned matching network. A metamaterial unit cell is used for the matching network to fit the entire antenna into a compact area. The antenna is designed with an application for laptop computers in mind. Hence its geometry is such that the entire antenna, including the ground plane, fits onto the frame of a laptop monitor. In Section II, the concept of double-tuned matching is reviewed. Section III describes the antenna to be matched. Sections IV and V describe the design of the matching network as well as a the circuit model for the matching network. Finally Section VI describes a fabricated prototype of the antenna and its experimental results.

Manuscript received August 14, 2009; revised November 23, 2009; accepted January 13, 2010. Date of publication April 26, 2010; date of current version July 08, 2010. This work was supported by INTEL Corporation. The authors are with the Edward S. Rogers Department of Electrical and Computer Engineering, University of Toronto, Toronto, ON M5S 1A1, 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/TAP.2010.2048876

II. THEORY The design of double-tuned matching networks is well known and the following explanation draws from [1]–[3]. The goal of the double-tuned matching network is to match an impedance locus below a given VSWR level over a range of frequencies ). The impedance locus (in this paper, a VSWR of 2:1, or examined in this paper is any part of a series RLC load (i.e. a resistance R, a series RC, a series RL, or a series RLC, circuit). Note that the same treatment can be extended for a parallel RLC load. The double-tuned matching network then consists of two stages. The first stage sets up the impedance locus for the second stage by meeting a specific set of constraints, while the second stage of the matching network brings the impedance locus below the given VSWR level. This paper is concerned primarily with the design of the second stage of the double-tuned matching network, specifically for cases where the first stage does not meet all the constraints.

A. First Stage The first stage of the double-tuned matching network sets up the impedance locus to meet three constraints. The first constraint is that at a frequency , the impedance locus intersects the negative imaginary axis of on the Smith Chart, where is the reflection coefficient. The second constraint is that at a fre, intersects the positive imaginary quency , where axis of on the Smith Chart. The last constraint is that at a fre, where , the load at be purely real quency circle. and that it lies on the edge of the The first two constraints can be met by adding series reactive components, depending on the load. If the load is purely resistive adding a series inductor and a capacitor can meet the first two constraints. For a series RC or a series RL circuit, adding an appropriately valued series inductor or capacitor respectively would also meet the first two constraints. The values of the reare at the active components can be adjusted so that and desired frequencies. For a series RLC load, no extra reactive components are needed as the first two constraints are already met. where the The third constraint occurs at the frequency load is purely real. This is because the reactive components of the load and the first stage cancel out. An ideal impedance transformer can then be used to adjust the impedance locus such that lies on the edge of the circle. the load at Thus, the input impedance looking into the first stage of the matching network is a series RLC load whose impedance locus circle through has been adjusted to lie on the edge of

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SELVANAYAGAM AND ELEFTHERIADES: A COMPACT PRINTED ANTENNA WITH AN EMBEDDED DOUBLE-TUNED METAMATERIAL

Fig. 1. The input impedance looking into the first stage on the Smith Chart with circle and the vertical all three constraints met. The dashed circle is the S line is the imaginary axis of .

0

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=2

Fig. 3. The input impedance looking into the second stage on the Smith Chart. circle. The input impedance is now contained in The dashed circle is the S the S circle.

=2

=2

Fig. 2. A schematic of the matching network after the first stage. The R,L,C elements can be part of the load or 1st stage depending on the load. The impedance transformer bring the impedance locus to the edge of the S circle.

=2

Fig. 4. A schematic of the matching network after the second stage.

an impedance transformer. This is shown in Fig. 1 on the Smith Chart along with a schematic of the load and first stage in Fig. 2. B. Second Stage The second stage of the double-tuned matching network brings the impedance locus inside the circle. This . To bring the happens in the frequency range circle, a shunt inductor, , and impedance inside the , are added in the second stage. The a shunt capacitance, values of and can be found by looking at the input impedance at the first stage. Looking at the frequency on the Smith Chart in Fig. 1 the load is capacitive with a susceptance . At the frequency , the load is inductive with a susceptance . Using and the susceptance at both these frequencies can be canceled out. This is expressed as (1) (2) where for both

and and

. Solving (1) and (2) together gives the following expressions: (3) (4)

and from (3) and (4), the By using the values of impedance locus is brought onto the real axis of the Smith Chart at the frequencies and . This forms a loop as shown

in Fig. 3 that lies within the circle. The entire matching network can be seen in Fig. 4. The importance of the second stage of the double tuned matching network is that it can simultaneously cancel out the inductive and capacitive components of a frequency dependant load (in this case an RLC circuit), to form a loop on the Smith circle because Chart. This loop is contained within the the first stage of the matching network sets up the load to meet the constraints listed in the previous section. However, a more general interpretation of the second stage of the matching network can be understood separately from the first stage. Equations (1) and (2), show that any frequency dependant load, that is capacitive at a frequency and inductive at a frequency , can have its susceptance canceled out at both these frequencies by a shunt inductance and capacitance without having to meet the constraints for the first stage. A loop will still be formed on the Smith Chart, except that it will not be contained circle. This is demonstrated in Fig. 5 where within the , a series RLC load is shown on the Smith Chart ( , ). This load can be transformed into various loops on the Smith Chart using a shunt inductance and capacitance, whose values are found using (1)–(4). Note that circle showing that part of the loop still falls into the partial matching can still be achieved. This is the tradeoff between a complete two stage matching network that matches the impedance locus over a maximal range of frequencies versus the second stage only where only a partial improvement of the bandwidth can be achieved by forming a loop on the Smith Chart. By using the second stage

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Fig. 5. Matching a series RLC load using only the second stage of a double tuned matching network. The solid curve is the series RLC load (R = 15 , L = 2:65 nH, C = 1:5 pF). The dashed and dotted curves are different 2nd stage matching networks found using Equations (3) and (4). Notice that a loop is still formed even though f and f did not lie on the imaginary 0 axis. Also, part of the load is still brought into the S = 2 circle (dashed circle), showing that an improvement in matching can be achieved for a certain frequency range.

Fig. 7. Simulated jS j and input impedance of the reference antenna with some of the microstrip transmission line de-embedded. (a) jS j, (b) Input Impedance on the Smith Chart. Notice that the input impedance somewhat resembles a series RLC circuit, despite the real part of the input impedance varying with frequency. Because of the resemblance, the reference antenna is a good candidate for matching using the second stage of a double-tuned matching network to increase its 010 dB bandwidth. Fig. 6. Schematic of the reference antenna that will be matched using the second stage of a double tuned matching network. The antenna sits on an FR-4 substrate that is 0.4 mm thick.

only, the matching network itself is much simpler, requiring only a shunt LC network, avoiding the implementation of an impedance transformer and other series components. Thus the second stage of a double-tuned matching network can still be used to broaden the bandwidth of a load. This is done by forming a loop on the Smith Chart for a frequency dependant load without using the first stage of the double-tuned matching network. III. PROPOSED ANTENNA We start with the antenna being matched, which will be referred to as the reference antenna. The reference antenna consists of a microstrip feed-line over a ground plane on an FR-4 substrate that is 0.4 mm thick. The microstrip line is extended from the feed-line in the form of a strip as shown in Fig. 6. This ‘strip’ is the radiating element of our antenna and is 21 mm long. It should be noted that we do not refer to this antenna as a planar monopole because the ground plane is very narrow with a width of 6 mm. These dimensions have been chosen with

a specific application in mind, namely a WiMax antenna on a laptop computer, hence the narrow width, to allow the antenna and its ground plane to fit on the frame of a laptop monitor. The antenna will be matched to the 2.3–2.7 GHz WiMax band. The reference antenna is simulated using Ansoft’s High Frequency Structure Simulator (HFSS) which uses the finite eleand input impedance of the ment method. The simulated reference antenna can be seen in Fig. 7. The input impedance is shown on the Smith Chart with part of the microstrip feedline de-embedded to show where the matching network will it can be seen that be approximately placed. From the the antenna is never matched below 10 dB. From the input impedance of the antenna it can be seen that the antenna crudely resembles a series RLC circuit. It is capacitive at low frequencies and inductive at high frequencies. It should be noted however that the load does not maintain a completely constant real part, a deviation from the ideal case that can be tolerated because it is the susceptance that will be canceled out by the matching network. Using the theory discussed in Section II we can use the second stage of a double tuned matching network to increase the 10 dB bandwidth of the antenna. This will bring part of the circle. Intuitively, this matching network load within the must resemble a shunt LC circuit.

SELVANAYAGAM AND ELEFTHERIADES: A COMPACT PRINTED ANTENNA WITH AN EMBEDDED DOUBLE-TUNED METAMATERIAL

Fig. 8. Schematic of the reference antenna with a CSRR-microstrip matching network with dimensions (a) Top view with coordinate system, (b) Bottom view.

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Fig. 9. Simulated jS j and input impedance of the reference antenna with the CSRR-microstrip matching network. (a) jS j, (b) Input impedance on the Smith Chart. Notice that a loop has formed in the input impedance. This is due to the effective shunt inductance and capacitance of the CSRR.

A. Implementation of the Embedded Matching Network The matching network can be implemented in a number of ways. Chip components could be used though these are difficult to place in shunt with microstrip lines and cannot scale to higher frequencies. Printed components are another option. In our design we will use a microstrip line with a complementary-split-ring-resonator (CSRR) embedded in the ground plane below. CSRR’s are metamaterial elements that are used to realize ‘resonant’ left-handed transmission lines [6]–[8]. Integrating a microstrip network with a CSRR, loads the shunt capacitance of the transmission line with an LC resonator. The CSRR-microstrip networks have been used in various metamaterial networks and in various filter designs [9], [10]. We will use the CSRR below the microstrip line to implement the shunt LC network needed to match the antenna. Because the CSRR-microstrip network is compact it also fits very easily within the geometry of the antenna. IV. DESIGN OF THE MATCHING NETWORK The matching network is placed on the microstrip feed line of the reference antenna as shown in Fig. 8. The matching network and antenna are simulated together using HFSS. As stated previously we have chosen to design the matching network to match the reference antenna to the WiMax band of 2.3–2.7 GHz. To design the matching network the geometrical parameters of the CSRR-microstrip network are tuned in HFSS to meet this specification. Using full-wave simulations to design the CSRR

network, one must keep in mind the equivalent circuit of the matching network to design the geometry of the CSRR. The relevant geometrical parameters of the CSRR include the size of the CSRR, the flare in the microstrip line over the CSRR and the location of the CSRR relative to the edge of the ground plane. The correspondence between the geometry and the equivalent circuit are as follows: the size of the CSRR is proportional to the total shunt inductance and capacitance, and the flare of the microstrip line is also proportional to the shunt capacitance. The position of the CSRR relative to the edge of the ground plane adjusts the amount of transmission line between the strip and the CSRR, which affects the frequency that the antenna is matched at. By tuning the size of the CSRR and the microstrip flare in HFSS, the CSRR can be used to cancel out the appropriate amount of susceptance to form the desired loop on the Smith Chart. By adjusting the location of the CSRR the desired frequency band can be matched. Thus by using an iterative process of varying the geometry of the CSRR and its location an appropriate design can be quickly found using HFSS. It will also be shown in Section V that the values of the shunt inductance and capacitance can be extracted in a circuit model. The final dimensions of the matching network are also shown in Fig. 8 and are as follows: the CSRR has a length of 12.2 mm, and is placed 1 mm away from the edge of the ground plane, the flare of the microstrip line over the CSRR has a width of 3.5 mm and a length of 6.1 mm.

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Fig. 11. The circuit model of the CSRR matching network with the extracted values.

Fig. 10. The imaginary component of Z tion of the CSRR-microstrip network.

from a two-port full-wave simula-

We can see in Fig. 9 the and input impedance from the full-wave simulation of the antenna and its matching network. we No transmission line has been de-embedded. From the can see a band from 2.25–2.93 GHz below 10 dB which aligns with the WiMax band from 2.3–2.7 GHz. On the Smith chart we can see that a loop forms that is partially contained within circle. This indicates that the CSRR-microstrip netthe work is acting like the second stage of a double-tuned matching network.

Fig. 12. A plot of the Im(Z ) from the full-wave simulation versus the circuit model.

From Fig. 10 we can take , where . From these values an approximate value for C is found . To find the inductance L, the resonant freto be quency is used and L is given by

V. CIRCUIT MODEL OF THE MATCHING NETWORK To demonstrate that the CSRR-microstrip particle is acting as a shunt LC network, we need to extract the values of the shunt inductance and capacitance from the CSRR-microstrip network. There have been various circuit models for a CSRR coupled to a microstrip line proposed in [6], [10]. These circuit models model the two-port S-parameters of the CSRR-microstrip line. In our case when using the CSRR-microstrip particle as a matching network we only want to model the shunt LC behaviour of the CSRR to capture its behaviour as a matching network. To model the CSRR-microstrip matching network we first extract the two-port S-parameters from an HFSS simulation of the matching network only. The ports are de-embedded right to the edge of the flare in the microstrip transmission line. From this two-port simulation we can extract the Z-parameters. It is known that for a shunt network, the impedance of the shunt network of the T-netcan be extracted using a T-model and that work gives the impedance of the shunt elements [11]. Thereis plotted in Fig. 10 to model fore the imaginary part of the shunt reactance of the CSRR-microstrip network. From the we can see that the CSRR-microstrip particle resembles of 3.34 a shunt LC circuit. There is a resonant frequency GHz with the load being inductive below the resonant frequency and capacitive above. We can extract approximate values for L, C by making the following approximations. At a frequency we can assume that the load is mostly capacitive and . Therefore the capacitance is given by (5)

(6) The value of L is then found to be . From this extraction we have approximate values for a shunt LC circuit model of the CSRR-microstrip particle. A schematic of the circuit model is shown in Fig. 11. In Fig. 12 the imaginary part of the full-wave simulation of the two-port CSRR-miof crostrip network and the circuit model are plotted. From Fig. 12 it can be seen that the shunt LC circuit approximates the shunt reactance of the CSRR-microstrip network well. We can further demonstrate the validity of this model by using the reference antenna in Fig. 6 as a load and placing the cirin a circuit cuit model in series with it and finding the simulator (Agilent’s Advanced Design System). This setup is seen in Fig. 13. A 50 transmission line of an electrical length at 2.54 GHz is added after the matching network. The transmission line is needed because physically there is a length of transmission line between the microstrip-CSRR network and the base of the antenna where the input impedance is measured. The electrical length is then used as a fitting parameter to rotate the impedance on the Smith Chart and was found to be at 2.54 GHz. In Fig. 14(a) we can see the from the circuit simulation compared to the full-wave simulation of the antenna with the CSRR matching network. They both show good agreement with a band below 10 dB at similar frequencies. In Fig. 14(b) there is a plot of the input impedance on the Smith chart for the full-wave simulation and the circuit simulation. There is a good agreement between the full-wave simulation and the circuit model with a loop also forming on the Smith chart in the

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Fig. 13. Schematic of the reference antenna combined with the circuit model of the matching network.

Fig. 15. Fabricated antenna and matching network. (a) Top view. (b) Bottom view.

Fig. 14. jS j and input impedance of the reference antenna with the circuit model matching network compared to the full-wave simulation. (a) jS j. (b) Input Impedance on the Smith Chart. The solid curve is the full-wave simulation of the reference antenna and CSRR matching network and the dashed curve is the circuit model with the reference antenna. The dashed circle circle. is the S

=2

circuit model. The electrical length of the transmission line was used to rotate the loop on the Smith Chart until it aligned with the full-wave results. VI. EXPERIMENTAL RESULTS The antenna was built on a 0.4 mm thick FR-4 substrate using an LPKF ProtoMat H100 milling machine and the fabricated prototype can be seen in Fig. 15. The antenna was then measured on an Agilent E8364B Vector Network Analyzer (VNA). Fig. 16 compared to the simulated as shows the measured well as the input impedance on the Smith chart for both the measured and simulated cases. As shown, there is good agreement and input impedance. between the measured and simulated The measured 10 dB bandwidth is from 2.18 GHz to 2.74 GHz for a total bandwidth of 560 MHz and is centered at 2.54 GHz,

giving a 22% measured bandwidth. On the Smith Chart we can see the loop that has been formed due to the matching network. The loop in the measured input impedance is slightly rotated clockwise compared to the simulated results. The measured radiation patterns along with the simulated radiation patterns are shown for two different cuts in Fig. 17 and Fig. 18 respectively at 2.54 GHz, which corresponds to the minimum in both the mea. It is important to note that because the sured and simulated antenna has a small ground plane, the coaxial cable connected to the antenna during measurement is prone to radiation due to the coaxial-to-microstrip transition. To make sure that the cable does not radiate in the measurement setup, ferrite beads were used to prevent any currents on the cable from radiating. Both the simulated and measured patterns show a dipole-like radiation pattern, which arises from the current distribution on the strip. The efficiency was also measured using a modified Wheeler-cap method [12] at 2.54 GHz. The efficiency was also calculated in HFSS at the same frequency. The measured efficiency was 89% while the simulated efficiency was 97%, showing good agreement between the measurement and simulated results. It can also be seen that this antenna is very efficient as it is a simple radiating strip with the only losses resulting from the copper on the CSRR element and the substrate. VII. CONCLUSION An antenna with a double tuned metamaterial matching network has been built to increase the bandwidth. The reference antenna resembled the load of a series RLC circuit and the matching network was based on the second stage of a double tuned matching network. The matching network

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Fig. 18. Measured radiation patterns. The co-polarization is the solid line and the cross-polarization is the dashed line. The coordinate system can be seen in Fig. 8(a). (a) Measured xz cut, (b) Measured xz cut. Fig. 16. Measured jS j and input impedance of the antenna with the CSRR matching network. (a) jS j, (b) Input Impedance on the Smith Chart. The dashed curve is the measured input impedance and the solid curve is the simulated. The dashed circle is the S circle.

=2

matching network is done by controlling the geometry of the CSRR and microstrip network. The CSRR-microstrip network itself can be successfully modeled as a shunt- LC circuit. The antenna was built and measured and showed good agreement with the simulated results. This measured antenna exhibits a wide 560 MHz bandwidth centered at 2.54 GHz and along with its compact geometry is well suited for applications such as a WiMax antenna on a laptop computer. ACKNOWLEDGMENT Useful conversations with Dr. D. Choudhury are gratefully acknowledged REFERENCES

Fig. 17. Simulated radiation patterns. The co-polarization is the solid line and the cross-polarization is the dashed line. The coordinate system can be seen in Fig. 8(a). The xz cut is the E-plane of the antenna and the yz cut is the H-plane. (a) xz cut, (b) yz cut.

is implemented using a CSRR-microstrip network to create a compact fully printed shunt LC circuit. The design of the CSRR

[1] H. A. Wheeler, “Wideband Impedance Matching,” Wheeler Laboratories Inc, Great Neck, NY, 1950, Tech. Rep.. [2] H. Wheeler, “The wide-band matching area for a small antenna,” IEEE Trans. Antennas Propag., vol. 31, no. 2, pp. 364–367, Mar. 1983. [3] Antenna Engineering Handbook, J. Volakis, Ed., 4th ed. New York: McGraw Hill, 2007. [4] C. Friedman, “Wide-band matching of a small disk-loaded monopole,” IEEE Trans. Antennas Propag., vol. 33, no. 10, pp. 1142–1148, Oct. 1985. [5] D. Pozar, “Microstrip antennas,” Proc. IEEE, vol. 80, no. 1, pp. 79–91, Jan. 1992. [6] J. Baena, J. Bonache, F. Martin, R. Sillero, F. Falcone, T. Lopetegi, M. Laso, J. Garcia-Garcia, I. Gil, M. Portillo, and M. Sorolla, “Equivalentcircuit models for split-ring resonators and complementary split-ring resonators coupled to planar transmission lines,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 4, pp. 1451–1461, Apr. 2005. [7] F. Falcone, T. Lopetegi, M. A. G. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marqués, F. Martín, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett., vol. 93, no. 19, p. 197401, Nov. 2004. [8] J. Bonache, M. Gil, I. Gil, J. Garcia-Garcia, and F. Martin, “On the electrical characteristics of complementary metamaterial resonators,” IEEE Microw. Wireless Compon. Lett., vol. 16, no. 10, pp. 543–545, Oct. 2006.

SELVANAYAGAM AND ELEFTHERIADES: A COMPACT PRINTED ANTENNA WITH AN EMBEDDED DOUBLE-TUNED METAMATERIAL

[9] M. Gil, J. Bonache, and F. Martín, “Metamaterial filters with attenuation poles in the pass band for ultra wide band applications,” Microw. Opt. Technol. Lett., vol. 49, no. 12, pp. 2909–2913, 2007. [10] C. Li and F. Li, “Characterization and modelling of a microstrip line loaded with complementary split-ring resonators (csrrs) and its application to highpass filters,” J. Phys. D: Appl. Phys., vol. 40, no. 12, pp. 3780–3787, 2007. [11] D. Pozar, Microwave Engineering. Hoboken, NJ: Wiley, 2005. [12] W. McKinzie, “A modified wheeler cap method for measuring antenna efficiency,” in IEEE Antennas and Propagation Society Int. Symp. Digest, Jul. 1997, vol. 1, pp. 542–545.

Michael Selvanayagam (GS’09) received the B.A.Sc. degree (with honors) in electrical and computer engineering from the University of Toronto, Toronto, ON, Canada, in 2007, where he is currently working toward the M.A.Sc degree. His research interests include metamaterials and antenna design.

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George V. Eleftheriades (F’06) received the Diploma in Electrical Engineering from the National Technical University of Athens, Greece, in 1988, and the M.S.E.E. and Ph.D. degrees in electrical engineering from the University of Michigan, Ann Arbor, in 1989 and 1993, respectively. From 1994 to 1997, he was with the Swiss Federal Institute of Technology, Lausanne. Currently, he is a Professor in the Department of Electrical and Computer Engineering, University of Toronto, Toronto, ON, Canada, where he holds the Canada Research Chair/Velma M. Rogers Graham Chair in Engineering. Prof. Eleftheriades received the Ontario Premier’s Research Excellence Award in 2001 and an E.W.R. Steacie Fellowship from the Natural Sciences and Engineering Research Council of Canada in 2004. He served as an IEEE AP-S Distinguished Lecturer during the period 2004–2009. Amongst his other scholarly achievements he is the recipient of the 2008 IEEE Kiyo Tomiyasu Technical Field Award “for pioneering contributions to the science and technological applications of negative-refraction electromagnetic materials.” He is an IEEE Fellow and was elected a Fellow of the Royal Society of Canada in 2009. He serves as an elected member of the IEEE AP-S AdCom and as an Associate Editor of the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION. He is a member of the Technical Coordination Committee MTT-15 (Microwave Field Theory). He was the General Chair of the IEEE AP-S/URSI 2010 Int. Symposium, Toronto, in July 2010.

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EFIE Modeling of High-Definition Multiscale Structures Francesca Vipiana, Member, IEEE, Matteo Alessandro Francavilla, and Giuseppe Vecchi, Fellow, IEEE

Abstract—We propose a method to significantly improve the spectral properties of the EFIE MoM matrix for broad-band analysis of structures with fine details, non-uniform meshes, and large overall sizes. A multilevel approach allows to overlay fine meshes and quasi-Nyquist sampled meshes; the fine-mesh conditioning is solved via hierarchical basis functions, and the quasi-Nyquist sampled part is treated by an algebraic incomplete LU preconditioner. Numerical results show the effectiveness of the approach for several realistic structures with overall sizes of ten/twenty wavelengths and levels of detail from very moderate to extending over the whole structure. Index Terms—Antennas, fast solvers, method of moments (MoM), multilevel systems, multiresolution techniques.

I. INTRODUCTION AND STATEMENT OF WORK HE electric field integral equation (EFIE) is a very versatile approach to the full-wave analysis of complex electromagnetic problems. The method of moments (MoM) discretization of the EFIE integro-differential operator is conveniently done via conventional mixed-order elements like the Rao-Wilton-Glisson (RWG) basis functions [1] that can suitably conform to all real-life geometries. The spectrum of the MoM matrix plays an obviously pivotal role in large problems, whose solution requires the use of iterative solvers associated to fast matrix-vector products, like the fast multipole method [2]. When the body is largely smooth and the mesh size is close to the “Nyquist sampling” limit (about 5 points per wavelength), the condition number increases with the number of unknowns moderately, and typically with a linear trend [3]. Typical scattering problems fall into this category; they are “pure high frequency” problems, with very large electrical sizes, but with comparatively few geometrical asperities (edges, corners, etc.) and nearly-Nyquist mesh size. The condition number issue is however relevant because of the inherently very large computational scale. At the opposite end, the MoM system is ill-conditioned for very low frequencies and/or fine meshes; the condition

T

Manuscript received April 28, 2009; revised December 23, 2009; accepted January 26, 2010. Date of publication April 22, 2010; date of current version July 08, 2010. This work was supported by the European Community’s Seventh Framework Programme FP7/2007-2013, under Grant 205294, HIRF SE project. F. Vipiana is with the Antenna and EMC Lab (LACE), Istituto Superiore Mario Boella, 10138 Torino, Italy (e-mail: [email protected]). M. A. Francavilla and G. Vecchi are with the Antenna and EMC Lab (LACE), Politecnico di Torino, 10129 Torino, Italy (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/TAP.2010.2048855

number—and more generally the matrix spectrum—also suffers from non-uniform meshes with disparate sizes, and in general in the presence of multiple scales in the geometry and in the solution. This is the typical situation in realistic antennas, EMC, packaging and similar applications, that always imply fine discretizations and a large number of unknowns. Conditioning of the EFIE is obviously attacked in very different ways for these two opposite classes of problems. For “pure” high frequency problems as in scattering, the condition number problem is attacked by algebraic preconditioners, typically of the incomplete LU (ILU) type (e.g., [4]–[8]). However, algebraic preconditioners are unreliable when geometrical details appear, and they may converge (fast) to a wrong solution. In “low-frequency” problems the classical countermeasure to the ill-posedness is a Helmholtz decomposition of the system of basis functions (e.g., [9]–[13]). The solenoidal basis functions are loops, the remainder non-solenoidal basis functions are known as trees or stars, hence the loop-tree (LT) and loop-star (LS) denomination of the approaches. However, the loop-tree/ star performances are poor for beyond-resonant-length overall sizes, and for markedly non-uniform meshes. More recent works have improved the Helmholtz decomposition by re-arranging the non-solenoidal part [14], [15], or both [16], [17], extending its applicability and efficiency. In this paper, we address the challenging issue of “mixed-frequency” problems, in which the overall size of the structure is large, but the geometry also possesses fine and very fine details. This is the typical situation encountered in the analysis of complex antennas, and antennas mounted on platforms like satellites, cars, and -especially- ships. Moreover, we are interested in broad-band analysis. Indeed, we aim at the user-friendly analysis of antenna placement on a realistic platform, where one would like to import and directly use the CAD description of the platform, which includes many details that are foreign to electromagnetic (EM) considerations and analysis. In these “high-fidelity” CAD models the details not only drastically increase the number of unknowns, but also make the MoM matrix conditioning problematic. On the other hand, obtaining EM-friendly, “low fidelity” CAD models may require days of person-time. As apparent from the previous discussion, the class of problems of present interest cannot be attacked by the preconditioning techniques discussed above, and tailored for either “high-frequency” or “low-frequency” problems. The performances of ILU-based and other algebraic preconditioners quickly deteriorate in the presence of geometrical details; when the level of detail is relevant, convergence simply disappears for reasonable costs of the preconditioning. Methods like those in

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[15]–[17] are robust against structural complexities, but loose steam as the overall size of the problem increases above a few wavelengths. This motivates our present introduction of a method to improve the spectral properties of the MoM matrix in structures with fine details and possibly large smooth sections, non-uniform meshes, and large overall sizes. Our approach will be shown to have a complexity scaling that is fully compatible with fast factorizations. Our scope is similar to that of a recent work [18], that addressed problems featuring at the same time electrically small, geometrically complex regions, and regions that are smooth and electrically large. That work proposed a hybrid static/full-wave method where quasi-static equations are used for the electrically small parts. There are two significant differences between the present work and that in [18], whose discussion also helps in highlighting our scope. First, we do not assume that the different scales appearing in the solution be spatially separated; our method is applicable to structures that possess multiple scales superimposed in the same spatial region. For example, the proposed method is applicable to large structures that are geometrically complex everywhere. Second, we apply the full-wave approach to the entire structure without any quasi-static assumption. In this work, we employ a multiscale representation of the solution to deal differently with different scales. We systematically hybridize a set of basis functions that solves the fine-mesh conditioning problems, and an algebraic ILU-based preconditioner on larger scales. Thanks to the systematic approach taken, the algorithm does not require any user intervention on the geometry. The adopted multiscale representation is applicable to any mesh, and exploits a hierarchical basis [15]–[17], whose multilevel nature allows to separate detail levels from levels where basis functions have quasi-Nyquist size. As mentioned above, on detail levels, the dense-mesh approach of [15] to conditioning is very efficient; on the quasi-Nyquist level the algebraic ILU is safe and performing. The result is a hybrid scheme that is robust throughout. Finally, we observe that despite the very similar names, our multilevel-based hybrid preconditioner is completely different from the preconditioners called “ILU multilevel” in the literature (e.g., [19]–[21]). These latter combine the ILU factorization with an algebraic multilevel recursive reduction. In [21], and in its block versions [19], [20], the original system is permuted using an independent set reordering, and an ILU factorization of the reordered matrix is performed. Then the reordering and the ILU factorization is applied again to the reduced system, that is the approximate Schur complement associated with the previous partitioning. The process is repeated recursively until the reduced system is small enough (or dense enough) to be solved with a Gaussian elimination. Instead, here the multilevel characteristics of the proposed preconditioner are not inside the ILU algorithm, but in the organization of the mesh/unknowns before the application of the ILU on a part of the resulting system.

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The outline of the present paper is as follows. In Section II we briefly report the formulation and the implemented MoM-based fast solver. Then Section III illustrates the incomplete LU, the Multi-Resolution approach, and the proposed hybrid hierarchicalgebraic multilevel approach. Several realistic test structures are studied in Section IV. Finally, Section V contains the conclusions. II. BACKGROUND: EFIE FORMULATION AND FAST ITERATIVE SOLVER We are concerned with the EFIE for PEC objects in free space, whose surface is denoted by . The surface is discretized by a mesh with triangular cells, over which a usual is defined. The unknown surface system of RWG functions current is approximated by the above set of RWG basis functions

(1) A Galerkin testing is used to convert the EFIE into the MoM linear system; hence we obtain the matrix equation

(2) where a generic element of the scalar potential and of the vector and respectively, is expressed as potential matrix,

(3)

(4) where , and is the definition domain of the function . The coefficients in (1) are collected in the vector , and the th is equal to element of

(5) is the impressed field in absence of bodies. where In order to make explicit examples, we apply the proposed method to a specific fast factorization approach; however we underline that the proposed hybrid preconditioner (Section III.C) is completely independent from the specifically employed fast MoM-based solver, and it can be easily interfaced with other solvers such as the fast multipole method (FMM) or the multilevel fast multipole algorithm (MLFMA) [2] (Section III.D).

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Without going into the details (which can be found in [22]–[24]), the MoM matrix can be factorized as follows:

(7) where and , with , collect the projections of the divergences of the basis functions, and of the vector components, onto the interpolating polynomials, respectively. becomes a poor approximation of the In (7) the matrix when the interpolation (6) is near to original MoM matrix the singularity of the Green’s function. Hence we add to the a sparse correction matrix , whose elements matrix are equal to if the two considered funcand are defined in the same grid cell or in two adtions jacent ones (Fig. 1), and zero elsewhere. Finally the original MoM system (2) is approximated by the following linear system

(8)

Fig. 1. Example of a 3D structure discretized with triangular cells in the 3D Cartesian grid. (a) 3D view, (b) 2D view.

The specific fast factorization approach employed here can be classified into the grid-based approaches, where the Green’s function is mapped onto a regular Cartesian grid, as the one shown in Fig. 1, and the fast Fourier transform (FFT) is applied to efficiently perform convolution products. The implemented fast solver is based on the Green’s function Interpolation with FFT (GIFFT) presented in [22], [23] for planar arrays, and its extension to 3D PEC objects [24]. Here the free space Green’s function is expanded in terms of Lagrange polynomials, defined over a regular Cartesian grid

(6) where is the total number of interpoequal to the number of nodes along the lating nodes with corresponding axis of the Cartesian grid is the usual Lagrange interpolating polynomial, and is the Green’s function value due to a source in the th node and an observer in the th node.

To solve the system in (8) we use the biconjugate gradients stabilized (BiCGStab) iterative solver [25]. At each iteration the is performed with low complexity since the product is sparse. The remaining product can matrix be quickly performed by exploiting the properties of the faccan be indeed suitably reorganized torization. The matrix as a Toeplitz matrix. Therefore the matrix-vector multiplication can be sped up by applying the 3D FFT algorithm [26], [27, p. 170–175]. III. HYBRID HIERARCHIC-ALGEBRAIC MULTILEVEL APPROACH A. Incomplete-LU Preconditioners The ILU preconditioners were originally developed for positive-definite matrices arising from the discretization of partial differential equations. In recent years, they have been also successfully applied to large dense systems arising from the discretization of EFIE in the case of scattering problems. The incomplete LU decomposition is constructed using the near field (strong interaction) part of the MoM matrix, which needs to be computed and stored anyway in fast methods. This strong macontains only the entries corresponding to test and basis trix functions with a distance not exceeding a threshold distance . A huge literature about the ILU-class preconditioners is available, and many extensions of ILU, to increase its accuracy and robustness, have been designed. Here we refer to [28], [29], and references therein, for a partial account of the literature. In our work, we apply the preconditioner with partial pivoting incomplete LU factorization with dual threshold strategy [28, p. 312–314], indicated with “ILUTP” in the following, and simply with “ILU” when there is no risk of ambiguity. In the ILUTP

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scheme, an incomplete LU factorization is applied to the strong , interaction MoM matrix

(9) and only the entries with magnitude and in the matrices larger than a chosen threshold are kept. In addition, in order to know a priori the size of the incomplete factors, no more than elements are allowed for each row of and , where is the row average number of non-zero elements in . The combination of the threshold parameter and of the fill-in parameter is called “dual threshold strategy”. Moreover, to avoid small pivots that cause instability in the decomposition, a partial pivoting is applied. Hence a column partial pivoting is performed in the incomplete row-wise factorization. The tolerance ratio used to determine whether or not to permute two columns is indicated in the following with . Finally a strong indicator of the quality of the performed ILU , called “condest” preconditioner is an estimate of [29]. This condition estimate is defined as

(10) and it can be easily computed before solving the system, by using a forward substitution followed by a backward substitution. B. Multiresolution Preconditioners Multiresolution (MR) [15]–[17], [30], [31] preconditioners are made out of two components. The first is a MR set of basis functions for the MoM, the second is a diagonal precondtioner applied to the MoM matrix in the MR basis. The MR basis, in fact, allows a simple diagonal preconditioner to improve the spectrum of the MoM matrix. The first step of the MR algorithm is the generation of a set of meshes with different cell sizes, which starts from the input stanand called level-0 mesh. dard triangular mesh, denoted with All other meshes of the following levels will be composed of groups of adjacent cells of the level-0 mesh, called “macro-cells”, as shown in Fig. 2 (details in [16]). The , contains a single macro-cell covering the last level mesh, entire structure [Fig. 2(f)]. Then, on each level mesh, a generalized version of the RWG functions (gRWG) is defined on each pair of adjacent macro-cells. The generalized RWG are built enforcing a charge proportional to the cell area, positive on one cell and a negative on the other one, and, since the charge-to-current mapping is obviously non-unique [10], we add the condition that solenoidal currents do not contribute to the generated gRWG. Each gRWG function of a generic level is described as a linear combination of the gRWG functions of the previous level mesh; applying this relation recursively, a generic gRWG function can be written as a linear combination of the standard RWG [15]. After having defined the functions of the initial mesh

Fig. 2. Cell grouping algorithm. (a) level-1 mesh, (b) level-2 mesh, (c) level-3 mesh, (d) level-4 mesh, (e) level-5 mesh, (f) level-6 mesh (last level). The initial level-0 mesh is not reported.

multilevel set of meshes with the corresponding gRWG functions, the multiresolution functions are generated at each level, splitting the unknown current into solenoidal and non-solenoidal parts (details in [15], [17]). Each MR function

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defined on the quasi-Nyquist mesh. Note that . The construction of the hybrid preconditioner needs only the , which is the usual application for the MoM strong matrix ILU. The MR conditioning effect comes from the diagonal preconditioning of the MoM matrix in the MR basis; because of the intrinsic near-field nature of the operator to be (approximately) inverted to achieve preconditioning, it is enough to employ the of the MoM matrix to build the MR diagonal strong part that will then effect the preconditioning. Therefore, the first step in the process is obtaining the MoM in the new multilevel basis, that has gRWG strong matrix on the coarse mesh, and MR functions on the remaining detail levels; this is achieved by applying the basis-change matrix in (11) to the strong matrix for the (standard) underlying RWG : basis,

Fig. 3. Example of a coarse level mesh with quasi-Nyquist cell size (a) whole mesh; (b) a detail.

1

(12)

.

is described as a linear combination of the gRWG functions of the same level mesh, and consequently as a linear combination of the standard RWG functions of the level-0 mesh. C. Hybrid Preconditioner Here we employ the multilevel nature of the hierarchical basis, described in Section III.B, in order to separate detail levels from levels where the mesh cells are quasi-Nyquist. First we stop the cell aggregation process when the macro-cells ; so we obtain a set of detail are of the quasi-Nyquist size level meshes, with cell size increasing with the level, and a coarse level mesh (the last is the level- mesh), where all the macro-cells are of the quasi-Nyquist size. Fig. 3(a) reports an example of coarse level mesh, with an enlargement in Fig. 3(b) to better show how the originally non-uniform mesh is converted in a uniform quasi-Nyquist generalized mesh. On the detail level meshes, we employ the MR functions (of Section III.B). The macro-cells of the last, coarse level are obtained by grouping those of the finer levels; therefore, the support of any MR function extends at most over one macro-cell of . This the coarse level, whose size in our case limited by is important, because MR functions are very efficient in inducing preconditioning for dense-mesh problems [15] with limited overall size, which is precisely the present situation. Opposite to that, on the quasi-Nyquist mesh we use the associated gRWG functions as one would do in a scattering problem with (standard) RWG of quasi-Nyquist size. So the change-ofis divided in two parts: basis matrix

where the subscript “MR” indicates the interactions between only MR functions, the subscript “gRWG” the interactions between only gRWG functions, and the double subscript the interactions between a MR function and a gRWG function. The is highly sparse; more important yet, basis change matrix the employed multilevel basis is localized and hierarchic in nature; “localized” means that the functions have a maximum spa(the two cells that constitute a gRWG of the tial extension coarse level), and “hierarchic” implies that MR functions with larger spatial support are less in number than those with smaller is still sparse, as dissize. As a result, the obtained matrix cussed later on in this section. Next, one proceeds separately on the two different sets of basis functions (and of geometrical details). For further use, we that effects the diagonal precondefine the diagonal matrix ditioning (DP), with entries

(13) This diagonal preconditioning is applied to the whole basis; it is enough to obtain the preconditioning for the part represented by MR functions, while it has only a balancing effect on the gRWG the portion of part; with transparent notation, we call that pertains to the gRWG of the coarse level. The gRWG block then undergoes the approximate LU factorization through the ILUTP algorithm: (14)

(11) where collects the set of detail level meshes, and

functions defined on the the set of functions

To

increase

the

sparsity pattern of the matrix , all its elements lower are dropped; this will go implied, than a chosen threshold and we will not indicate it with a different notation. We

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underline that the ILU decomposition is applied only to a portion of the MoM system (the one relative to the gRWG part); with respect to the standard ILU scheme, one now requires a lower memory occupation and a faster time generation of the and factors. Inserting the proposed hybrid preconditioner into the MoM system (8), the resulting system can be algebraically written as (15) with

(16) Fig. 4. CPU time to generate the matrix [Z ] versus the number of unknowns N . Inset: test case with radius = 1:26 m, discretized with N = 81 522.

(17) (18) (19) is an identity matrix, and is a zero matrix. As where described in Section II, the system in (15) is solved with the BiCGStab iterative solver, where at each iteration all the reported products are performed from right to left. We observe that in (16) and in (19) obviously multiplications times the term are instead implemented by a forward written as substitution followed by a backward substitution. Moreover these forward and backward substitutions are applied only to the gRWG portion, with a reduced per-iteration cost with respect to the standard ILU scheme. We now discuss the complexity cost of the proposed hybrid preconditioner. Taken in isolation, the ILUTP application is standard, and we will not discuss its complexity (see [4]); the only observation that is relevant to our approach is that this complexity of course depends on the size of the strong matrix, , and the fill-in strategy (i.e., on the parameters and ). As far as the MR part is concerned, instead, one has to assess the computational complexity of the products in (12) that and the MoM are necessary to compute the diagonal matrix (starting from the strong matrix in the strong matrix ). The discussion below will show that this cost RWG basis : we can expect this complexity observing that the mais represents the interactions between localized functions, trix solely. obtained through the RWG strong matrix We analyze this complexity for an increasing electrical size of the object as usual, i.e., increasing the number of unknowns with constant mesh density. We begin by observing that the number of non-zero elements in each row (or in each column) is constant with respect to , and can be bounded with of a constant value . and , respectively, the maximum number Next, we call of non-zero elements in each column and each row of represents the maximum number of RWG functions that form

the same MR/gRWG function, and is the maximum number of MR/gRWG functions that include the same RWG function. Considering the generation process of the MR basis on the detail level meshes and of the gRWG functions on the coarse mesh, it appears that and are independent of . Because of these bounds, the product between one column of and the whole matrix has a constant complexity equal and is also the maximum number of non-zero to elements in the resulting vector. Then the product between the and this vector has again a constant comwhole matrix plexity equal to , and is also the maximum number of non-zero elements for each row or column of the re. Repeating this operation for all the sulting strong matrix column vectors of , we obtain that the whole complexity is , hence the complexity is linear. The predicted behavior is verified in Fig. 4, for a sphere with increasing radius, con, and for a multilevel basis with stant average mesh size of ; the figure reports the CPU time to evaluate the ma, performing the products in (12), versus the number of trix unknowns : it is evident that the computational complexity is . We conclude this section by emphasizing the advantages of the described hybrid preconditioner over the stand-alone MR and ILU preconditioners for non-uniform meshes with large overall sizes; specific examples of these properties will be discussed in Section IV. 1) The instability due to the dense meshes is fixed by the employed (localized) MR basis; this instability would prevent the direct (standard) application of an ILU preconditioner. 2) The algorithm allows isolating a set of basis functions of quasi-Nyquist size, on which an effective preconditioning is effected by the ILU; the MR basis would have a limited effect on these scales. and matrices and their ap3) The generation of the plication in the iterative solution process is much less time consuming, because the ILU factorization is only applied to the quasi-Nyquist mesh.

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4) The memory occupation of the generated and matrices is minimized, most of the times resulting much lower than the storage of the corresponding MoM strong matrix . 5) In a broad-band analysis the proposed preconditioner allows the use of the highest frequency mesh in all the frequency sweep, with two different and complementary actions. On the one hand, it prevents condition number explosion due to small details at all frequencies. On the other hand, it adds efficiency also on mostly-smooth structures at lower frequencies, where the mesh results in oversampling; the scheme aggregates standard RWG into larger gRWG functions that are thus always close to quasi-Nyquist dimensions, thus improving ILU performances. D. Insertion of the Hybrid Preconditioner Into Fast MoM Solvers As alluded in the previous sections, the proposed hybrid preconditioner can be easily combined with preexisting MoM-based fast solvers, such as the MLFMA, that has a lower computational complexity than the GIFFT algorithm. In a fast solver the original MoM matrix is rewritten as the sum of a strong (sparse) matrix , that collects the interactions be, expressed tween close basis functions, and a weak matrix as the product of several sparse matrices, able to describe the interactions between far basis functions. Then an iterative solver is applied where at each iteration the matrix-vector products are performed with low complexity (e.g., for the MLFMA) exploiting the properties of the employed factorization. Hence the total solution time is equal to the computational time for the matrix-vector products at each iteration by the total number of iterations, that is not improved by the used fast solver. The proposed hybrid preconditioner can be inserted to reduce the required number of iterations, with a low computational cost for its construction and application. Apart from the chosen fast solver, the hybrid preconditioner is applied in the solution procecorresponds to , dure as reported in (15)–(19), where and to . The only inputs required for the generation of the preconditioner are the mesh of the structure, to build the MR to genand gRWG basis functions, and the strong matrix erate the diagonal preconditioner and the LU factorization of the gRWG portion of the MoM matrix. Hence all the required data are available in the chosen fast solver scheme. IV. NUMERICAL RESULTS To demonstrate the effectiveness of the proposed approach, indicated in the following “MR-ILU”, we analyze three realistic 3-D structures. All considered structures are electrically large (from 8 to 20 ) and exhibit mesh non-uniformity due to geometrical details. Since we expect standard ILU to work well with smooth structures, in order to test the proposed method we will analyze cases with a very limited degree of details in an otherwise smooth structure, as well as structures where details are present almost everywhere. The chosen examples well represent different classes of practical problems with different levels of details.

The proposed MR-ILU approach is compared, in terms of computational time and memory requirements, to the standard ILUTP preconditioning [28] applied to the whole MoM matrix in the RWG basis, indicated in the following simply with “ILU”, and to the MR preconditioning [16]. The threshold parameters relative to the ILU factorization, employed in all the following simulations, are , and ; we recall that is the dropping and is the tolthreshold relative to the matrices is erance ratio for the pivoting column permutation, and the dropping threshold relative to the MoM strong matrix . For all the reported examples, in the new basis the polynomial order in the Green’s function interpolation is , the requested BiCGStab solver accuracy is , and . The condest the quasi-Nyquist (macro)cell size parameter described in Section III.A is reported for all the simulations, and the diagonal preconditioning (DP) is always applied. The numerical simulations were performed on an Intel Core 2 Duo E4700 (2.6 GHz) 32-bit workstation with 2 GB of RAM (Section IV.B), and on an Intel Core 2 Duo E4400 (2 GHz) 64-bit workstation with 8 GB of RAM (Section IV.B and IV.C); double precision implementation was always used.

A. UAV The UAV (Unmanned Aerial Vehicle) model depicted in Fig. 3(a) is discretized with an average mesh size around (at the frequency of 1 GHz). A monopole is attached to the UAV, with a finer discretization [mesh size around 0.01 , as shown in Fig. 3(b)]. The length of the UAV is 3.6 m (about 12 at the considered frequency). The total number of unknowns is 29 582. Table I summarizes the results of the simulations with different preconditioning methods. The threshold distance to genis , and the step in the sampling grid of erate . The columns of the table refer the Green’s function to, from left to right: preconditioning method, parameter of and ILU routines, condest, time for generating the matrices , number of iterations of the BiCGStab solver, total simuand . lation time, memory occupation of the matrices and , The total simulation time includes the generation of the DP generation, and the time to obtain the solution with the BiCGStab solver. As one could expect for this case, the conventional ILU preconditioning applied to the RWG basis performs well, since only one detail (the antenna) is present in an otherwise uniform mesh. To investigate more the behavior of the iterative solver, Fig. 5 reports the distribution of the singular values, comparing the unpreconditioned, MR-ILU, and ILU preconditioned MoM systems, for the case reported in Table I. In [32] the convergence of the conjugate gradient (CG) solver has been related to the spectra of the MoM matrix, and in particular the error functional, minimized at each step, is expressed in terms of the residual polynomial. It is derived there that the convergence is reached when the iterative algorithm has placed a zero of the residual polynomial at each eigenvalue of the MoM matrix. Here we are using a BiCGStab solver and not a plain CG

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Fig. 5. UAV: sorted singular values, comparison among different preconditioners (frequency = 1 GHz).

as in [32], hence the previous analysis can be applied only partially. In Fig. 5, we can verify that for the preconditioned systems the singular values are more clustered, allowing the iterative algorithm to place less zeros in the cluster to significantly reduce the error functional, improving the convergence. We remark that in this specific case the ILU precodnitioner performs better than the MR-ILU in terms of convergence. Finally to check the correct convergence of the iterative solver, Fig. 6 compares the surface current density obtained with the MR-ILU preconditioning [Fig. 6(a)] with the one obtained for the unpreconditioned system [Fig. 6(b)] both systems converge to the same with a relative tolsolution (the relative difference is ). erance equal to on the proThe effects of reducing the dimension of posed preconditioner is then investigated. Table II summarizes the comparison between the MR-ILU and the ILU precondi(first column), consequently decreasing tioning, reducing (second column), and keeping the memory occupation of the other parameters as reported in Table I. We can see that, by , the performance of reducing the amount of information in the ILU preconditioner quickly deteriorates, and convergence is lost in practice. Conversely, the MR-ILU approach appears significantly less sensitive to the size of the strong region and, while the convergence rate worsens as memory occupation for the strong matrix is reduced, a significant robustness is added. B. Airbus A320 A 3-D model of a commercial airplane has been discretized with 58 380 unknowns, as shown in Fig. 7. A blade antenna is placed on the topside of the fuselage toward aft (as highlighted with an arrow in Fig. 8), fed by a voltage gap. Numerical simulations are performed in the frequency range 20–50 MHz. The aircraft is about 120 m long, that correspond to about 8 at the lowest frequency, and 20 at the highest frequency. The mesh is not changed during the frequency sweep (as typically desirable for ease of use), and therefore cell size is determined by the highest frequency; it ranges from 0.8 cm to 1 m, that correat 20 MHz, and the largest cell size sponds to at 50 MHz. The strong matrix range is set to is about

Fig. 6. UAV: surface current density [dBA/m] at 1 GHz; (a) obtained with MR-ILU, (b) obtained without preconditioner.

, leading to a memory occupation around 2 GB for at . 20 MHz, and Table III compares in detail the different preconditioners at the frequency of 20 MHz. The standard ILU preconditioner (fourth row) converges in 23 iterations, but the gain in terms of number of iterations is obtained at a high computational cost, in terms of both time and memory requirements for the generand factors (fourth and seventh columns). ation of the Instead the MR-ILU approach performs the ILU decomposition of only a part of the system matrix, and in this case (lowest frequency in range) there are significantly less gRWG on the ) than standard coarse level (with macro-cell size of about RWG (with average size of ) on the original mesh. As a and matrices is result the memory occupation of the around 30 times lower, and the time required for generating these matrices is about 6 times lower. The total simulation time of the ILU scheme is in fact completely dominated by the ILU decomposition itself. Consequently, although the number of iterations for the ILU approach is lower with respect to the MR-ILU approach, the total simulation time of the MR-ILU approach is around 3.5 times lower. The interesting observation that emerges is that this hybrid scheme not only protects from convergence difficulties associated to fine levels, but also adds

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TABLE I UAV: COMPARISON OF PRECONDITIONING SCHEMES AT 1 GHz (1 =

=4; [Z

] RAM = 51 MB)

TABLE II UAV: COMPARISON BETWEEN MR-ILU AND ILU PRECONDITIONERS WITH DIFFERENT DIMENSIONS OF [Z ] AT 1 GHZ; (*) CONVERGENCE NOT REACHED IN 4000 ITERATIONS

Fig. 7. Airbus A320: mesh.

Fig. 8. Airbus A320: surface current density [dBA/m] obtained with MR-ILU at 50 MHz; the excited antenna is highlighted with an arrow.

efficiency by “absorbing” the over-sampling on the smooth part of the structure when present. Table IV summarizes the performances of both schemes, ILU and MR-ILU, in the frequency range 20–50 MHz. Increasing the frequency, the convergence is reached only with the MR-ILU scheme, keeping the number of iterations pretty stable. As one (second can see, the memory occupation of the matrix column) decreases with the frequency, since the threshold is fixed with respect to the wavelength. The RAM requested by the proposed approach (last column) instead increases with frequency. The reason for this behavior is in the generation of the multilevel set of meshes, which is stopped when the macro-cells . This reach a dimension approximately equal to means that at higher frequencies the macro-cells of the last level are smaller, and thus higher in number. Therefore ILU factorization has to be applied to a larger part of the MoM matrix, requiring more memory. Finally the surface current density at 50 MHz is shown in Fig. 8. C. Ship Finally we address an example that well represents in practice the issue of high-fidelity vs. low-fidelity modelling alluded in the Introduction. To show this feature, we report the analysis of two models of the same ship, placed over an infinite ground plane to represent the presence of the sea. One model, indicated with “low fidelity” model, is cleaned from the most part of small and geometrically complex details; the second, instead, is called “high fidelity” model, and the mesh is generated on the original CAD geometry without any “handmade” cleaning; this would obviously save significant person-time effort. The present MR-ILU approach allows for simulating the original geometry, with a complexity comparable to that of the low-fidelity model. 1) Low Fidelity Model: A 3-D model of a ship has been discretized with 47 163 unknowns [see Fig. 9(a)]. Many critical details have been removed from the original CAD of the ship (available in [33]), in order to obtain a structurally simpler model. The structure has been simulated at the frequency of 50 MHz, with a voltage gap at the base of the monopole antenna [a detail of the antenna is shown in Fig. 9(b)]. The ship is about

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TABLE III AIRBUS A320: COMPARISON OF PRECONDITIONING SCHEMES AT 20 MHz ( = ITERATIONS

1 = 3; [Z ] RAM = 2 GB); (*) CONVERGENCE NOT REACHED IN 2000

TABLE IV AIRBUS A320: PERFORMANCES IN THE FREQUENCY BAND 20–50 MHz, COMPARISON BETWEEN THE ILU AND THE MR-ILU PRECONDITIONERS; (*) CONVERGENCE NOT REACHED IN 2000 ITERATIONS

Fig. 10. Ship—Low fidelity model: convergence of the relative residual with the BiCGStab solver; comparison among different preconditioners MHz). (

frequency = 50

Fig. 9. Ship—Low fidelity model. (a) whole mesh; (b) detail of the monopole antenna.

60 m long, corresponding to 10 . Different preconditioning methods have been tested, and the behavior of the residual of the BiCGStab is shown in Fig. 10. The threshold distance for generating is , and . Table V summarizes the comparison between MR-ILU preconditioning and ILU preconditioning: the gain of the MR-ILU approach (fourth row) is about 8 in terms of iterations, about 30 in terms of memory ocand matrices, with respect to the stancupation for the

Fig. 11. Ship—Low Fidelity Model: surface current density [dBA/m] obtained with MR-ILU at 50 MHz.

dard ILU preconditioning (third row). Finally the surface current density is shown in Fig. 11.

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TABLE V SHIP—LOW FIDELITY MODEL: COMPARISON OF PRECONDITIONING SCHEMES AT 50 MHz ( NOT REACHED IN 4000 ITERATIONS

1 = =4; [Z ] RAM = 805 MB); (*) CONVERGENCE

Fig. 12. Ship—high fidelity model: mesh.

Fig. 14. Ship—high fidelity model: convergence of the relative residual with the BiCGStab solver; comparison among different preconditioners MHz). (

frequency = 50

Fig. 15. Ship—high fidelity model: surface current density [dBA/m] obtained with MR-ILU at 50 MHz.

Fig. 13. Ship—high fidelity model: mesh details.

2) High Fidelity Model: The same ship has been simulated without removing any detail from the original CAD model [33]. The structure, with the same overall electrical dimensions as the low-fidelity model, has been discretized with 113 556 un, knowns (see Fig. 12). The average edge length is around while details have required a much finer mesh, with edges as (see Fig. 13). We would like to remark that this short as

example also exhibit multiple scales superimposed in the same spatial region; in fact, this is a large structure that is geometrically complex everywhere. is , and . In this case The threshold the usual ILU preconditioning method does not converge to a solution, and Table VI summarizes the trials. Table VII shows the comparison with the proposed MR-ILU preconditioning method, which leads the BiCGStab to a solution in 516 iterations, with a negligible request of memory for the factorization and . The corresponding convergence of the matrices relative residual is reported in Fig. 14. Finally the surface current density obtained with MR-ILU is shown in Fig. 15.

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TABLE VII SHIP—HIGH FIDELITY MODEL: COMPARISON OF PRECONDITIONING SCHEMES AT 50 MHz ( REACHED IN 10000 ITERATIONS

1 = =4; [Z ] RAM = 1863 MB); (*) CONVERGENCE NOT

TABLE VI SHIP—HIGH FIDELITY MODEL: ILU PRECONDITIONING (OUT OF MEMORY REFERS TO A 8 GB RAM WORKSTATION)

V. CONCLUSION We have presented an approach to analyze EFIE problems with electrically large overall sizes, and the presence of geometrical details that require fine or very fine meshes in parts of the structure, or even on all of it. The problems of interest are therefore of the “mixed-frequency” type, and of critical importance in “high-fidelity” EM modelling of real-life structures, i.e., in which the CAD is imported, meshed and EM analyzed without the need of human intervention to simplify the model. The method employs a systematic multiscale representation of the solution and the geometry, allowing to use different preconditioning schemes on different scales. The scheme hybridizes the preconditioning induced by hierarchic basis functions on fine levels, and the algebraic ILU on the coarse level. Numerical examples have shown that the method allows single-frequency and broad-band analysis of large and very complex structures that are definitely challenging. For low levels of complexity (and especially when the fine details reside in limited regions) ILU can sometime work; in these cases, the proposed scheme adds considerable robustness, and affords a significant reduction of the memory necessary to store the information needed for the ILU. A further advantage in this milder cases emerges for broad-band analysis; the scheme allows to do wide frequency sweeps without changing the mesh: in addition to protecting from conditioning blowup, it also allows to regain efficiency by aggregating the triangles of the smooth sections into larger quasi-Nyquist macro-cells. ACKNOWLEDGMENT The authors would like to acknowledge the valuable help of E. Porcu in the early implementation and testing of this scheme. REFERENCES [1] S. M. Rao, D. R. Wilton, and A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propag., vol. 30, pp. 409–418, May 1982. [2] W. C. Chew, J. M. Jin, E. Michielssen, and J. M. Song, Fast and Efficient Algorithms in Computational Electromagnetics. Boston, MA: Artech House, 2001. [3] K. F. Warnick and W. C. Chew, “Error analysis of the moment method,” IEEE Antennas Propag. Mag., vol. 52, pp. 38–53, Dec. 2004.

[4] T. Malas and L. Gurel, “Incomplete LU preconditioning with the multilevel fast multipole algorithm for electromagnetic scattering,” SIAM J. Sci. Comput., vol. 29, pp. 1476–1494, June 2007. [5] P. L. Rui, R. S. Chen, Z. H. Fan, J. Hu, and Z. P. Nie, “Perturbed incomplete ILU preconditioner for efficient solution of electric field integral equations,” IET Microw. Antennas Propag., vol. 1, no. 5, pp. 1059–1063, 2007. [6] J. Lee, J. Zang, and C. C. Lu, “Incomplete LU preconditioning for large scale dense complex linear systems from electromagnetic wave scattering problems,” J. Comput. Phys., vol. 185, pp. 158–175, Feb. 2003. [7] A. Heldring, J. M. Rius, and L. Ligthart, “New block ILU preconditioner scheme for numerical analysis of very large electromagnetic problems,” IEEE Trans. Magn., vol. 38, no. 2, pp. 337–340, 2002. [8] K. Sertel and J. L. Volakis, “Incomplete LU preconditioner for FMM implementation,” Microw. Opt. Technol. Lett., vol. 26, no. 7, pp. 265–267, 2000. [9] T. F. Eibert, “Iterative-solver convergence for loop-star and loop-tree decomposition in method-of-moments solutions of the electric-field integral equation,” IEEE Antennas Propag. Mag., vol. 46, pp. 80–85, Jun. 2004. [10] G. Vecchi, “Loop-star decomposition of basis functions in the discretization of EFIE,” IEEE Trans. Antennas Propag., vol. 47, pp. 339–346, Feb. 1999. [11] M. Burton and S. Kashyap, “A study of a recent moment-method algorithm that is accurate to very low frequencies,” Appl. Computat. Electromagn. Soc. J., vol. 10, pp. 58–68, Nov. 1995. [12] W. Wu, A. W. Glisson, and D. Kajfez, “A study of two numerical solution procedures for the electric field integral equation at low frequency,” Appl. Computat. Electromagn. Soc. J., vol. 10, pp. 69–80, Nov. 1995. [13] D. R. Wilton, “Topological consideration in surface patch and volume cell modeling of electromagnetic scatterers,” in Proc. URSI Int. Symp. Electromagn. Theory, Santiago de Compostela, Spain, Aug. 1983, pp. 65–68. [14] J. S. Zhao and W. C. Chew, “Integral equation solution of maxwell’s equations from zero frequency to microwave frequency,” IEEE Trans. Antennas Propag., vol. 48, pp. 1635–1645, Oct. 2000. [15] F. P. Andriulli, F. Vipiana, and G. Vecchi, “Hierarchical bases for nonhierarchic 3D triangular meshes,” IEEE Trans. Antennas Propag., vol. 56, pp. 2288–2297, Aug. 2008. [16] F. Vipiana, F. P. Andriulli, and G. Vecchi, “Two-tier non-simplex grid hierarchic basis for general 3D meshes,” Waves in Random and Complex Media, vol. 19, pp. 126–146, Feb. 2009. [17] F. Vipiana and G. Vecchi, “A novel, symmetrical solenoidal basis for the MoM analysis of closed surfaces,” IEEE Trans. Antennas Propag., vol. 57, pp. 1294–1299, Apr. 2009. [18] B. D. Braaten, R. M. Nelson, and M. A. Mohammed, “Electric field integral equations for electromagnetic scattering problems with electrically small and electrically large regions,” IEEE Trans. Antennas Propag., vol. 56, pp. 142–150, Jan. 2008. [19] Y. Saad and J. Zhang, “BILUTM: A domain-based multilevel block ILUT preconditioner for general sparse matrices,” SIAM J. Matrix Anal. Appl., vol. 21, no. 1, pp. 279–299, 1999. [20] Y. Saad and J. Zhang, “BILUM: Block versions of multielimination and multilevel ILU preconditioner for general sparse linear systems,” SIAM J. Sci. Comput., vol. 20, no. 6, pp. 2103–2121, 1999. [21] Y. Saad, “ILUM: A multi-elimination ILU preconditioner for general sparse matrices,” SIAM J. Sci. Comput., vol. 17, pp. 830–847, Jul. 1996. [22] B. J. Fasenfest, F. Capolino, D. R. Wilton, D. R. Jackson, and N. J. Champagne, “A fast MoM solution for large arrays: Green’s function interpolation with FFT,” IEEE Antennas Wireless Propag. Lett., vol. 3, pp. 161–164, 2004. [23] B. J. Fasenfest, F. Capolino, and D. R. Wilton, “Preconditioned GIFFT: A fast MoM solver for large arrays of printed antennas,” ACES J., vol. 21, pp. 276–283, Nov. 2006.

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[24] S. Seo and J. Lee, “A fast IE-FFT algorithm for solving PEC scattering problems,” IEEE Trans. Magn., vol. 41, pp. 1476–1479, May 2005. [25] H. A. Van der Vorst, “Bi-CGStab: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems,” SIAM J. Sci. Stat. Comput., vol. 13, pp. 631–644, 1992. [26] J. R. Phillips and J. K. White, “A precorrected-FFT method for electrostatic analysis of complicated 3-D structures,” IEEE Trans. Computer-Aided Design of Integrated Circuits and Systems, vol. 16, no. 10, pp. 1059–1072, 1997. [27] A. Peterson, S. Ray, and R. Mittra, Computational Methods for Electromagnetics. New York: IEEE Press, 1998. [28] Y. Saad, Iterative Methods for Sparse Linear System. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM), 2003. [29] E. Chow and Y. Saad, “Experimental study of ILU preconditioners for indefinite matrices,” J. Comput. Appl. Math., vol. 86, pp. 387–414, Dec. 1997. [30] H. Chen, D. Z. Ding, R. S. Chen, D. X. Wang, and E. K. Yung, “Application of multiresolution preconditioner technique for scattering problem in a half space,” in Proc. Int. Conf. on Microwave and Millimeter Wave Technology, Apr. 2008, vol. 2, pp. 975–977. [31] J. J. Ding, J. Zhu, D. Z. Ding, R. S. Chen, D. X. Wang, and E. K. N. Yung, “Application of perturbed multiresolution preconditioner technique combined with MLFMA for scattering problem,” in Proc. Int. Conf. on Microwave and Millimeter Wave Technology, Apr. 2008, vol. 2, pp. 978–981. [32] A. F. Peterson, C. F. Smith, and R. Mittra, “Eigenvalues of the moment-method matrix and thier effect on the convergence of the conjugate gradient algorithm,” IEEE Trans. Antennas Propag., vol. 36, pp. 1177–1179, Aug. 1988. [33] [Online]. Available: http://www-c.inria.fr/gamma/download/download.php Francesca Vipiana (M’07) received the Laurea and Ph.D. (Dottorato di Ricerca) degrees in electronic engineering from the Politecnico di Torino, Torino, Italy, in 2000 and 2004, respectively, with doctoral research carried out partly at the European Space Research Technology Centre (ESTEC, Noordwijk, The Netherlands). From 2005 to 2008, she was with the Electronics Department, Politecnico di Torino, as a Research Fellow. She was a Visiting Scientist at the University of Houston, Houston, TX, in 2008 and 2009. Since

2009, she has been with the Antenna and EMC Lab (LACE), Istituto Superiore Mario Boella, Torino, Italy. Her main research activities concern numerical techniques based on the Integral-equation, with focus on multi-resolution and hierarchical schemes, domain-decomposition, preconditioning, fast solution methods, and Green’s function regularization. She is also involved in the analysis, synthesis and optimization of contour-beam antennas, periodic structures and large arrays. Dr. Vipiana received the Young Scientist Award at the Union of Radio Science (URSI) General Assembly in 2005, and the first prize in the poster competition at the First IEEE Women in Electromagnetics Workshop in 2009.

Matteo Alessandro Francavilla received the Laurea degree in telecommunication engineering from the Politecnico di Torino, Italy, in 2007. During 2007, he spent six months with the Defence, Security and Safety Institute, Netherlands Organization for Applied Scientific Research, The Hague, The Netherlands. Since 2008 he is working toward the Ph.D. degree at the Politecnico di Torino. His scientific interests include numerical techniques for antennas, periodic structures analysis and GPU programming.

Giuseppe Vecchi (M’90–SM’07–F’10) received the Laurea and Ph.D. (Dottorato di Ricerca) degrees in electronic engineering from the Politecnico di Torino, Torino, Italy, in 1985 and 1989, respectively, with doctoral research carried out partly at Polytechnic University (Farmingdale, NY). He was a Visiting Scientist with Polytechnic University in 1989–1990. In 1990, he joined the Department of Electronics, Politecnico di Torino, as an Assistant Professor (Ricercatore) where, from 1992 to 2000, he was an Associate Professor and, since 2000, he has been a Professor. He was a Visiting Scientist at the University of Helsinki, Finland, in 1992, and has been an Adjunct Faculty in the Department of Electrical and Computer Engineering, University of Illinois at Chicago, since 1997. His current research activities concern analytical and numerical techniques for analysis, design and diagnostics of antennas and devices, RF plasma heating, electromagnetic compatibility, and imaging.

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A Comparative Study of Calderón Preconditioners for PMCHWT Equations Su Yan, Student Member, IEEE, Jian-Ming Jin, Fellow, IEEE, and Zaiping Nie, Senior Member, IEEE

Abstract—The Calderón identities are used to precondition the Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) equations for wave scattering by dielectric objects. Based on the Calderón identities, several versions of preconditioners are presented and studied. The memory requirements and computational costs of different preconditioners are analyzed and discussed. The convergence properties of the iterative solutions and the solution accuracy of the Calderón preconditioned PMCHWT equations are also investigated and compared theoretically and numerically at different frequencies. With the help of the Calderón preconditioners, the convergence rate of the iterative solutions of the PMCHWT equations is significantly improved. Several numerical examples are given to show the performance of the Calderón preconditioners and to draw some conclusions. Index Terms—Calderón preconditioner, electromagnetic scattering, method of moments (MoM), numerical analysis, Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) equations.

I. INTRODUCTION

A

NALYSIS of scattering properties of dielectric objects under the excitation of electromagnetic waves attracts special interest in the computational electromagnetics (CEM) community. Based on integral equations, the method of moments (MoM) [1] is one of the most popular methods among a variety of analysis methods, because of its good accuracy and flexibility. In the MoM analysis, surface integral equations (SIEs) [2]–[7] based on the surface equivalence principle [8] and volume integral equations (VIEs) based on the volume equivalence principle [8] are commonly used. The VIEs can model arbitrary inhomogeneity and have an excellent spectrum property [9], [10], but they require a large number of unknowns due to the three-dimensional discretization of the object.

Manuscript received November 01, 2009; revised January 18, 2010; accepted January 31, 2010. Date of publication April 26, 2010; date of current version July 08, 2010. This work was supported in part by the China Scholarship Council (CSC), the National Science Foundation of China (NSFC) under Contract No. 60728101, and in part by the 111 Project under Contract No. B07046. S. Yan is with the Department of Microwave Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, China and also with the Center for Computational Electromagnetics, Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801-2991 USA (e-mail: [email protected]). J. Jin is with the Center for Computational Electromagnetics, Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801-2991 USA (e-mail: [email protected]). Z. Nie is with the Department of Microwave Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, China (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/TAP.2010.2048881

The SIEs, on the other hand, yield a much smaller number of unknowns because they deal with the unknown surface current densities on the surface of the object. However, the SIEs are only capable of modeling homogeneous or piecewise homogeneous dielectric objects and their spectrum properties depend very much on the formulation. Although the N-Müller formulation [11], [12] has a very good spectrum property, many other SIEs suffer from the poor spectrum property owing to the electric-field integral equation (EFIE) operator involved in the equations [13]. As a matter of fact, the spectrum of the EFIE operator clusters at zero and infinity when the discretization becomes finer and finer, which leads to a dramatic increase in the condition number of the discretized impedance matrix and hence the iteration counts needed to solve the matrix equation. To improve the spectrum property of the EFIE operator, a Calderón preconditioner is introduced based on the Calderón relation and Calderón identities [13]–[17] for scattering by perfect electric conductor (PEC) objects. According to the Calderón identity, the EFIE operator is a very good preconditioner to itself, which transfers the first-kind EFIE operator to a secondkind Fredholm integral operator and shifts the spectrum of the preconditioned EFIE operator far away from both zero and infinity. As a result, the matrix equation resulting from the preconditioned operator converges rapidly and independently with respect to mesh configurations. Different from the EFIE for PEC cases which has only one operator, the PMCHWT equations [2]–[4], which are known to be accurate and free of interior resonance corruption [18], [19], have two different kinds of operators which make it much more complicated to be preconditioned. The direct use of the EFIE operator as a preconditioner is less effective than in the PEC cases due to the existence of the magnetic-field integral equation (MFIE) operator. In [20], an operator matrix instead of a single EFIE operator is used as a preconditioner for the PMCHWT equations. However, the use of the unbalanced form of the PMCHWT equations deteriorates its convergence property in an iterative solution. In this paper, different Calderón preconditioners are used to accelerate the convergence rate of the PMCHWT equations. The effectiveness and the resource consumption of these preconditioners are thoroughly studied and compared. Several numerical examples are given to demonstrate the performance of the preconditioners.

II. FORMULATION In this section, the PMCHWT equations are first reviewed briefly, and then the Calderón identities are derived. After that, three different preconditioners are presented to improve the spectrum property of the PMCHWT equations. The memory

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requirements and computational costs of these preconditioners are discussed and compared at the end of this section. A. PMCHWT Equations Consider a scattering problem with an incident plane wave illuminating a homogeneous dielectric obstruction (region 2) having a permittivity and permeability and immersed in an infinite homogeneous background medium (region 1) with a permittivity and permeability . According to Love’s equivalence principle [8], the solution can be formulated in terms of an equivalent surface electric current and an equivalent surface magnetic current defined on the surface of the obstruction. Here, and stand for the total electric field and total magnetic field on , and stands for the outward pointing unit normal vector. The equivalent surface currents satisfy the PMCHWT equations [2]–[4] given by (1)

and In (8), by discretizing

are the impedance matrices obtained and using CRWG basis functions, and are the and are the excitation vectors vectors of unknowns, using and as the testing functions. Since the , it is clear from (8) that the memory number of unknowns is requirement for storing the matrix equation using MoM is , and when an iterative solver is used to solve this matrix equation, the computational requirement for each matrix-vector . It is well known that is a first-kind product (MVP) is is a compact operator. Therefore, Fredholm operator and the operator matrix in (5) can be considered as a first-kind operator, and its spectrum property is similar to that of the operator, which has the eigenvalues clustered around zero and at infinity with an increase of the discretization density. When an iterative solver is employed to solve (8), the iteration counts will increase dramatically as the number of unknowns increases. In this paper, the Calderón identities are employed to accelerate the convergence rate of the iterative solution of (8). B. Calderón Relation and Calderón Identities

(2) where stands for the intrinsic impedance in region , and the operators and are defined as (3) (4) In (3) and (4), stands for the wavenumber in region , stands for the Green’s function in an infinite homogeneous medium with the wavenumber , and stands for the stands for the Cauchy principal identity operator. In (4), value integration. In (1) and (2), instead of is treated as is multiplied on (2) in order to the unknown function and balance the magnitude of each operator and make the whole system better conditioned. Equations (1) and (2) can also be written in a more compact matrix form as (5) To solve (5) using MoM, two sets of basis functions are used to discretize the surface electric current and surface magnetic current, respectively (6) (7)

In the scattering problem, the equivalent currents can be decomposed into an incident part associated with the incident fields, and a scattering part associated with the scattered fields, i.e., , . The relation and in region 2 and the between the scattered fields and of the dielectric equivalent scattered currents scattering problem is governed by the following:

(9)

(10) or compactly [13]

(11) Equation (11) is called the Calderón relation and the matrix operator in (11) is actually an oblique projection operator. From , the Calderón the property of this projection operator identities can be obtained and expressed as [13]–[17]

(12) (13)

where and denote curvilinear Rao-Wilton-Glisson (CRWG) basis functions [21], [22]. Equation (5) can be transformed into a matrix equation using and as testing functions (8)

where the subscript 2 is omitted since these identities are true in any homogeneous media. It is suggested from (12) that is actually a second-kind integral operator with the spectrum clustered at . Therefore, the operator can be used as a very effective preconditioner for itself, and this is called the “self-regularizing property” of the operator.

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C. Calderón Preconditioner: Version 1

D. Calderón Preconditioner: Version 2

From (12), it is straightforward that the solution of (5) can be obtained more efficiently by solving the preconditioned system

Another way to precondition (5) is to use an operator matrix which is very similar to the PMCHWT operator in (5)

(14) (18) We call (14) Calderón preconditioned PMCHWT version one (CP-PMCHWT-v1). In order to avoid the internal resonance problem, a small imaginary part is introduced into the wavenumber in the preconditioner . Unless otherwise menin tioned, the wavenumber in is set to be this paper. The preconditioned operator matrix can be expressed as (15) Apparently, the diagonal blocks are the second-kind integral operators which are the compact perturbations of an identity op, where erator since, for example, is compact [11] and is a second-kind integral operator according to (12). Theoretically, the off-diagonal blocks are also compact because they are given by a compact operator times a non-compact operator, which produces a compact operator according to [10]. Following the same procedure as in [17], [23], the CRWG basis functions can be used to discretize the PMCHWT operator and the Buffa-Christiansen (BC) basis functions [24] can be used to discretize the preconditioner, then a Gram matrix can be used to link the range of the inner PMCHWT matrix and the domain of the outer preconditioner matrix. Therefore, the CP-PMCHWT-v1 can be discretized as

Equation (18) is called Calderón preconditioned PMCHWT version two (CP-PMCHWT-v2). The inner PMCHWT operator and the outer Calderón preconditioner operator can be discretized by using CRWG basis functions and testing functions, and BC basis functions and testing , again, is used to functions, respectively. The Gram matrix connect the range of the inner operator and the domain of the outer operator and thus makes them multiplicative. Hence, the CP-PMCHWT-v2 can be discretized as

(19) and are the impedance matrices obtained by In (19), and using BC functions. The Gram matrix discretizing is the same as (17) and can be solved in a constant iteration count. When MoM is used, the memory consumption in storing , and the computational cost per MVP is . (19) is In order to analyze the spectrum property of (18), the preconditioned operator matrix can be further expanded as

(16) In (16), is the impedance matrix obtained by discretizing using BC basis functions. The element of the Gram matrix is defined as the inner product of the basis function and the testing function

(20) By noting (12) and (13), (20) could be simplified as

(21) (17) The memory consumption in storing (16) is when MoM is used. In order to compute the matrix-vector product in an needs to be iterative solver, the Gram matrix equation is very well conditioned, the solved twice per MVP. Since Gram matrix equation can be solved in a small iteration count. Thus, the computational cost in solving the Gram matrix is only , and the computational cost for one MVP is .

In (21), the diagonal blocks of the second and the third terms are the compact perturbations of the identity operators, and the off-diagonal blocks of these two terms are also compact due to the same reasons stated in the preceding subsection. However, it should be pointed out that, although the off-diagonal terms in CP-PMCHWT-v1 and CP-PMCHWT-v2 are compact mathematically, they will suffer from the low-frequency breakdown

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as the frequency decreases, due to the numerical errors in discretizing the operators in these two versions. In order to improve the performance of CP-PMCHWT-v2 at lower frequencies, another version is presented in the next subsection. E. Calderón Preconditioner: Version 3 in the same medium, As shown in (13), since the off-diagonal blocks of the CP-PMCHWT-v2 can be modified into a better form as suggested in [20]. In this paper, however, a slightly different way of modification is used to cancel the hyper-singular term in the operator. Take the off-diagonal block of the third term in (21) for example

(22) is compact and has no low-frequency The operator breakdown problem because of the cancellation of the hypersingular part [11]. Following the same procedure, (21) can be modified as (23). See (23) and (24) at the bottom of the page. Equation (23) can now be considered as a compact perturbation of an identity operator which has the spectrum fixed at a non-zero point in the complex plane. Unfortunately, due to the introduction of the extra terms in the off-diagonal blocks, (23) cannot be expressed in a multiplicative way as in (14) and (18). Instead, it can only be written in a summation form as (24). Equation (24) is called Calderón preconditioned PMCHWT version three (CP-PMCHWT-v3), which can be discretized into a matrix equation following the same strategy used in CP-PMCHWT-v1 and CP-PMCHWT-v2. The memory requirement for directly storing the matrices in (24) is , which is rather large. Therefore, instead of storing their combinations, we store

and separately, which needs memory. Under this storage strategy, the computational cost per MVP is . It should be mentioned that, mathematically, the first term (diagonal blocks) of (24) has no low-frequency breakdown problem according to the Calderón identity (12), and the second term (off-diagonal blocks) of (24) has no low-frequency breakdown problem either. This is because the hyper-singular part has a frequency dependence of [11], of which is the same as the singular part. As a result, the overall CP-PMCHWT-v3 should be immune from the low-frequency breakdown problem theoretically. Table I compares the memory and computational requirements of the original PMCHWT, CP-PMCHWT-v1, CP-PMCHWT-v2, and CP-PMCHWT-v3. It should be pointed out that, when the symmetric properties of the operators are utilized, all the memory requirements shown in Table I can be reduced by half. The computational cost listed is the cost for each MVP. The final total cost would depend on the number of iterations, which is investigated in the next section. III. NUMERICAL EXAMPLES In this section, the performance of all the four PMCHWT versions discussed in this paper is compared in terms of the convergence rates, the accuracy, and the immunity from the internal resonance corruption. A more complicated example is also given to show the application of the PMCHWT versions discussed in this paper. A. Convergence Rate and Accuracy The first example considered here is scattering from a dielectric sphere with a radius of 1.0 m. The relative permittivity and , and permeability of the sphere are respectively. A 100-MHz plane wave illuminates the sphere.

(23)

(24)

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TABLE I COMPARISON OF THE MEMORY AND COMPUTATIONAL REQUIREMENTS USING MOM

=4

=1

Fig. 1. Performance comparison of different PMCHWT formulations for scattering analysis from a dielectric sphere with " . The radius of the and  sphere is 1.0 m and the frequency of the incident wave is 100 MHz. (a) Computational costs required versus the number of unknowns to achieve a relative residual . (b) Relative RMS error in the bistatic RCS versus the number of unknowns. The Mie series solution is used as reference data. error of

10

Fig. 1(a) displays the computational costs required by the BiCGstab(1) [25], [26] iterative solution in order to achieve a , with respect to different relative residual error (RSS) of numbers of unknowns. In order to make a fair comparison, all . From the computational costs are measured in terms of Fig. 1(a), it can be seen that the computational costs of the CP-PMCHWT-v1, CP-PMCHWT-v2, and CP-PMCHWT-v3 remain almost the same for different numbers of unknowns, while the computational cost needed by the un-preconditioned PMCHWT increases rapidly as the number of unknowns increases. Among the three preconditioned versions, CP-PMCHWT-v2 has the lowest computational cost for all mesh configurations. Fig. 1(b) compares the relative RMS error of the bistatic RCS obtained by different versions using different numbers of unknowns. It can be seen that CP-PMCHWT-v1 and CP-PMCHWT-v2 have the same error as PMCHWT, while CP-PMCHWT-v3 gives an error which is slightly larger than the other three versions. The extra error comes from the different way in the implementation of CP-PMCHWT-v3 compared with CP-PMCHWT-v1 and CP-PMCHWT-v2. In the implementation of CP-PMCHWT-v3, the preconditioner is not matrix multiplicative, but in a summation form as (24). Furthermore, the storage strategy of the impedance matrices also increases the error accumulation slightly. To summarize, in the mid-frequency range, all the three preconditioned versions can converge independently with respect to the number of unknowns, while the CP-PMCHWT-v2 has the best performance in terms of the computational cost and accuracy. A lower frequency, which is 1.5 MHz, is then considered for the same problem. The comparison illustrated in Fig. 1 is performed again to show the performance of the four formulations at this frequency. The results are given in Fig. 2. At this frequency, the PMCHWT cannot converge, even with the

lowest number of unknowns. Hence, the results obtained by the PMCHWT are not shown in Fig. 2. From Fig. 2(a), it is clear that the computational cost of CP-PMCHWT-v3 almost stays constant as the number of unknowns changes. The computational costs of CP-PMCHWT-v1 and CP-PMCHWT-v2, however, increase significantly as the number of unknowns increases, and they eventually diverge at the number of unknowns of 7056 and 3600, respectively. The increases of the computational costs in CP-PMCHWT-v1 and CP-PMCHWT-v2 are caused by the operators in the off-diagonal blocks in (15) and (21), which begin to suffer from the low-frequency breakdown problem at a lower frequency. From Fig. 2(b), we can see that CP-PMCHWT-v3 gives much more accurate results than the other two versions. The high accuracy indicates the good stability of CP-PMCHWT-v3 in the low frequency range. In order to investigate the performance of the four PMCHWT formulations in a wide frequency band, comparisons are made at different frequencies, where the number of unknowns is fixed at 2304, and the operating frequency varies from 100 MHz to 0.4 MHz. Fig. 3(a) and (b) shows the computational costs needed and the relative RMS error in the bistatic RCS at different frequencies, respectively. From Fig. 3(a), the computational cost of PMCHWT increases dramatically when the frequency decreases and it diverges at the frequency of 1.5 MHz, because of the low-frequency breakdown of the operators in (5). The CP-PMCHWT-v1 can reach a lower frequency of 0.8 MHz, because after preconditioning, mathematically, the diagonal blocks of (15) have no low-frequency breakdown anymore. However, CP-PMCHWT-v1 still diverges at 0.6 MHz, because of the numerical discretization error of the diagonal blocks [27], [28] and also because of the low-frequency breakdown of the off-diagonal blocks in (15). Although it can converge from 100 MHz to 1.5 MHz, CP-PMCHWT-v2 diverges at 1.0 MHz. The

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=4

=1

=4

=1

Fig. 2. Performance comparison of different PMCHWT formulations for scattering analysis from a dielectric sphere with " . The radius of the and  sphere is 1.0 m and the frequency of the incident wave is 1.5 MHz. (a) Computational costs required versus the number of unknowns to achieve a relative residual . (b) Relative RMS error in the bistatic RCS versus the number of unknowns. The Mie series solution is used as reference data. error of

10

Fig. 3. Performance comparison of different PMCHWT formulations for scattering analysis from a dielectric sphere with " and  . The radius of the sphere is 1.0 m and the frequency of the incident wave varies from 0.4 MHz to 100 MHz. (a) Computational costs required at different frequencies to achieve a relative residual error of . (b) Relative RMS error in the bistatic RCS at different frequencies. The Mie series solution is used as reference data.

10

reason that CP-PMCHWT-v2 diverges at a higher frequency operators than CP-PMCHWT-v1 is because there are more in the off-diagonal blocks in (21) than in (15), which exhibit a more serious low-frequency breakdown problem, and the accumulation of the numerical discretization error of the diagonal blocks of (21) is also more serious than (15). Among all these versions, CP-PMCHWT-v3 exhibits the best performance as it can converge at the lowest frequency, which is 0.4 MHz. This is because both the diagonal blocks and off-diagonal blocks in (24) have no low-frequency breakdown problem as stated in the previous section. However, it still diverges at the frequencies below 0.4 MHz because of the numerical discretization error that exists in the cancellation of the hyper-singular terms in both the diagonal and off-diagonal blocks in (24). This problem can be alleviated through a more accurate calculation and a matrix. However, this will direct storage of the lead to an increase of the memory consumption. From Fig. 3(b), we can also see that CP-PMCHWT-v3 has the best accuracy in the wide frequency band.

According to the three tests presented in this subsection, it can be concluded that, at mid-frequencies, all the three preconditioned versions can converge independently with respect to the number of unknowns (mesh density), while CP-PMCHWT-v2 has the best performance in terms of computational cost and solution accuracy. At lower frequencies, however, only CP-PMCHWT-v3 can converge independently as the number of unknowns increases. Moreover, CP-PMCHWT-v3 has the most stable performance in a broad frequency band, which suggests that CP-PMCHWT-v3 is the most reliable formulation. B. Internal Resonance An example is designed to test the immunity from the internal resonance corruption for the four different PMCHWT formulations presented. The model used here is a dielectric sphere with a radius of 0.444 m and the relative permittivity and , respectively. The and permeability of frequency is 300 MHz, which corresponds to the first resonant frequency of a spherical cavity filled with air. The five

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=4

=1

Fig. 4. Internal resonance test of different PMCHWT formulations for scattering analysis from a dielectric sphere with " . The radius of the and  sphere is 0.444 m and the frequency of the incident wave is 300 MHz. (a) Convergence histories of different formulations to achieve a relative residual error of . (b) HH-polarized bistatic RCS.

10

= 3+0 01

=1

Fig. 5. Scattering analysis for the NASA almond with " : i and  . A 150-MHz, H-polarized incident wave is incident from the tip of the almond. . (a) Problem description and mesh configuration. (b) Convergence histories of different PMCHWT formulations to achieve a relative residual error of

versions tested here are the original PMCHWT, CP-v1-realK in the preconditioner which uses the real wavenumber in (14), CP-v1-compK which uses in , CP-PMCHWT-v2, and CP-PMCHWT-v3. From Fig. 4(a), all the formulations except for CP-v1-realK can converge to a , which suggests that by desired relative residual error of using the real wavenumber, the internal resonance problem may be introduced in CP-PMCHWT-v1 by the preconditioner , and this problem can be avoided if a small imaginary part is added to the wavenumber in . The other three formulations, PMCHWT, CP-PMCHWT-v2, and CP-PMCHWT-v3, can all avoid the internal resonance problem effectively. All the RCS data from the four converged solutions agree very well with the Mie series solution as shown in Fig. 4(b). C. NASA Dielectric Almond The NASA almond is considered as the last example. The total length of the dielectric almond is 2.524 m, and the dielecand . A 150-MHz, tric parameters are H-polarized plane wave is incident from the tip of the almond.

10

Fig. 5(a) shows the mesh configuration of this problem. The convergence histories of different formulations are given in Fig. 5(b). It is clear that only CP-PMCHWT-v1 and CP-PMCHWT-v3 can converge to a desired relative residual error of , while CP-PMCHWT-v3 has a much faster convergence rate. IV. CONCLUSION AND DISCUSSIONS Three preconditioners based on the Calderón identities to accelerate the iterative solution of the PMCHWT equations are presented and investigated in this paper. The memory requirements, computational costs, convergence rates, and solution accuracy are compared and discussed in detail. From the theoretical analysis and the numerical simulations, it can be concluded that all the three preconditioners can converge independently with respect to the number of unknowns at mid-frequencies, while the second preconditioner has the best performance. At lower frequencies, only the third preconditioner can converge in constant computational costs when the number of unknowns is increased. The third preconditioner

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also performs better in a broad frequency band because of its immunity from the low-frequency breakdown problem, and therefore is the most reliable one among the three. Furthermore, all the three preconditioners have the capability to avoid the internal resonance corruption.

REFERENCES [1] R. F. Harrington, Field Computation by Moment Methods. New York: Macmillan, 1968. [2] A. J. Poggio and E. K. Miller, “Integral equation solutions of three dimensional scattering problems,” in Computer Techniques for Electromagnetics, R. Mittra, Ed. Elmsford, NY: Permagon, 1973. [3] Y. Chang and R. Harrington, “A surface formulation for characteristic modes of material bodies,” IEEE Trans. Antennas Propag., vol. 25, pp. 789–795, Jun. 1977. [4] T.-K. Wu and L. L. Tsai, “Scattering from arbitrarily-shaped lossy dielectric bodies of revolution,” Radio Sci., vol. 12, no. 5, pp. 709–718, 1977. [5] C. Müller, Foundations of the Mathematical Theory of Electromagnetic Waves. Berlin, Germany: Springer, 1969. [6] M. S. Yeung, “Single integral equation for electromagnetic scattering by three-dimensional homogeneous dielectric objects,” IEEE Trans. Antennas Propag., vol. 47, pp. 1615–1622, Oct. 1999. [7] P. Yla-Oijala and M. Taskinen, “A novel combined field integral equation formulation for solving electromagnetic scattering by dielectric and composite objects,” in Proc. IEEE Antennas Propag. Symp., Jul. 2005, vol. 4B, pp. 297–300. [8] C. A. Balanis, Advanced Engineering Eelectromagnetics. New York: Wiley, 1989. [9] J. Rahola, “On the eigenvalues of the volume integral operator of electromagnetic scattering,” SIAM J. Sci. Comput., vol. 21, no. 5, pp. 1740–1754, 2000. [10] N. V. Budko and A. B. Samokhin, “Spectrum of the volume integral operator of electromagnetic scattering,” SIAM J. Sci. Comput., vol. 28, no. 2, pp. 682–700, 2006. [11] P. Ylä-Oijala and M. Taskinen, “Well-conditioned Müller formulation for electromagnetic scattering by dielectric objects,” IEEE Trans. Antennas Propag., vol. 53, pp. 3316–3323, Oct. 2005. [12] S. Yan, J.-M. Jin, and Z. Nie, “Calderón preconditioner: From EFIE and MFIE to N-Müller equations,” IEEE Trans. Antennas Propag., accepted for publication. [13] G. C. Hsiao and R. E. Kleinman, “Mathematical foundations for error estimation in numerical solutions of integral equations in electromagnetics,” IEEE Trans. Antennas Propag., vol. 45, pp. 316–328, Mar. 1997. [14] S. H. Christiansen and J. C. Nedelec, “A preconditioner for the electric field integral equation based on Calderón formulas,” SIAM J. Numer. Anal., vol. 40, no. 3, pp. 1100–1135, Aug. 2002. [15] R. J. Adams, “Physical and analytical properties of a stabilized electric field integral equation,” IEEE Trans. Antennas Propag., vol. 52, pp. 362–372, Feb. 2004. [16] R. J. Adams and N. J. Champagne, “A numerical implementation of a modified form of the electric field integral equation,” IEEE Trans. Antennas Propag., vol. 52, pp. 2262–2266, Sep. 2004. [17] F. P. Andriulli, K. Cools, H. Bagci, F. Olyslager, A. Buffa, S. Christiansen, and E. Michielssen, “A multiplicative Calderón preconditioner for the electric field integral equation,” IEEE Trans. Antennas Propag., vol. 56, pp. 2398–2412, Aug. 2008. [18] A. F. Peterson, “The interior resonance problem associated with surface integral-equations of electromagnetics—numerical consequences and a survey of remedies,” Electromagnetics, vol. 10, no. 3, pp. 293–312, 1990. [19] K. C. Donepudi, J.-M. Jin, and W. C. Chew, “A higher order multilevel fast multipole algorithm for scattering from mixed conducting/dielectric bodies,” IEEE Trans. Antennas Propag., vol. 51, pp. 2814–2821, Oct. 2003. [20] F. Olyslager, K. Cools, J. Peeters, F. P. Andriulli, and E. Michielssen, “A Calderón multiplicative preconditioner for the PMCHWT integral equation,” in Proc. IEEE Antennas Propag. Symp., North Charleston, SC, Jun. 2009.

[21] S. M. Rao, D. R. Wilton, and A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propag., vol. 30, pp. 409–418, May 1982. [22] R. D. Graglia, D. R. Wilton, and A. F. Peterson, “Higher order interpolatory vector bases for computational electromagnetics,” IEEE Trans. Antennas Propag., vol. 45, pp. 329–342, Mar. 1997. [23] S. Yan, J.-M. Jin, and Z. Nie, “Implementation of the Calderón multiplicative preconditioner for the EFIE solution with curvilinear triangular patches,” in Proc. IEEE Antennas Propag. Symp., North Charleston, SC, Jun. 2009. [24] A. Buffa and S. H. Christiansen, “A dual finite element complex on the barycentric refinement,” Mathematics of Computation, vol. 76, no. 260, pp. 1743–1769, Oct. 2007. [25] G. L. G. Sleijpen and D. R. Fokkema, “BiCGstab(l) for linear equations involving unsymmetric matrices with complex spectrum,” Electronic Trans. Numer. Anal., vol. 1, pp. 11–32, Sep. 1993. [26] R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. M. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, and H. V. der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods. Philadelphia: SIAM, 1994. [27] M. B. Stephanson and J. F. Lee, “Preconditioned electric field integral equation using Calderón identities and dual loop/star basis functions,” IEEE Trans. Antennas Propag., vol. 57, pp. 1274–1279, Apr. 2009. [28] S. Yan, J.-M. Jin, and Z. Nie, “EFIE analysis of low-frequency problems with loop-star decomposition and Calderón multiplicative preconditioner,” IEEE Trans. Antennas Propag., vol. 58, no. 3, pp. 857–867, Mar. 2010.

Su Yan (S’08) was born in Chengdu, China, in 1983. He received the B.S. degree in electromagnetics and microwave technology from the University of Electronic Science and Technology of China, Chengdu, China, in 2005, where he is currently working toward his Ph.D. degree. Since September 2008, he has been a Visiting Researcher in the Center for Computational Electromagnetics, Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, under the financial support from the China Scholarship Council. His research interests include numerical methods in computational electromagnetics, especially integral equation based methods and fast algorithms.

Jian-Ming Jin (S’87–M’89–SM’94–F’01) received the B.S. and M.S. degrees in applied physics from Nanjing University, Nanjing, China, in 1982 and 1984, respectively, and the Ph.D. degree in electrical engineering from The University of Michigan at Ann Arbor, in 1989. He is currently the Y. T. Lo Endowed Chair Professor of electrical and computer engineering and Director of the Electromagnetics Laboratory and Center for Computational Electromagnetics with the University of Illinois at Urbana-Champaign. He was appointed as the first Henry Magnuski Outstanding Young Scholar in the Department of Electrical and Computer Engineering in 1998 and later as a Sony Scholar in 2005. He was appointed as a Distinguished Visiting Professor in the Air Force Research Laboratory in 1999 and was an Adjunct, Visiting, or Guest Professor with the City University of Hong Kong, University of Hong Kong, Anhui University, Beijing Institute of Technology, Peking University, Southeast University, Nanjing University, and Shanghai Jiao Tong University. His name often appears in the University of Illinois at Urbana-Champaign’s List of Excellent Instructors. He was elected by ISI as one of the world’s most cited authors in 2002. He has authored or coauthored over 200 papers in refereed journals and 20 book chapters. He has also authored The Finite Element Method in Electromagnetics (Wiley, 1st ed, 1993, 2nd ed, 2002) and Electromagnetic Analysis and Design in Magnetic Resonance Imaging (CRC, 1998), coauthored Computation of Special Functions (Wiley, 1996) and Finite

YAN et al.: A COMPARATIVE STUDY OF CALDERÓN PRECONDITIONERS FOR PMCHWT EQUATIONS

Element Analysis of Antennas and Arrays (Wiley, 2008), and coedited Fast and Efficient Algorithms in Computational Electromagnetics (Artech, 2001). He was an Associate Editor for Radio Science and is also on the Editorial Board for Electromagnetics and Microwave and Optical Technology Letters. His current research interests include computational electromagnetics, scattering and antenna analysis, electromagnetic compatibility, high-frequency circuit modeling and analysis, bioelectromagnetics, and magnetic resonance imaging. Dr. Jin is a member of Commission B of USNC/URSI and Tau Beta Pi. He was an Associate Editor of the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION. He was a recipient of the 1994 National Science Foundation Young Investigator Award, the 1995 Office of Naval Research Young Investigator Award, and the 1999 Applied Computational Electromagnetics Society Valued Service Award. He was also the recipient of the 1997 Xerox Junior Research Award and the 2000 Xerox Senior Research Award presented by the College of Engineering, University of Illinois at Urbana-Champaign. He was the Co-Chairman and Technical Program Chairman of the Annual Review of Progress in Applied Computational Electromagnetics Symposium, in 1997 and 1998, respectively.

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Zaiping Nie (SM’96) was born in Xi’an, China, in 1946. He received the B.S. degree in radio engineering and the M.S. degree in electromagnetic field and microwave technology from the Chengdu Institute of Radio Engineering (now UESTC: University of Electronic Science and Technology of China), Chengdu, China, in 1968 and 1981, respectively. From 1987 to 1989, he was a Visiting Scholar with the Electromagnetics Laboratory, University of Illinois, Urbana. Currently, he is a Professor with the Department of Microwave Engineering, University of Electronic Science and Technology of China, Chengdu, China. He has published more than 300 journal papers. His research interests include antenna theory and techniques, fields and waves in inhomogeneous media, computational electromagnetics, electromagnetic scattering and inverse scattering, new techniques for antenna in mobile communications, transient electromagnetic theory and applications.

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An Efficient Method to Reduce the Numerical Dispersion in the LOD-FDTD Method Based on the (2, 4) Stencil Qi-Feng Liu, Wen-Yan Yin, Senior Member, IEEE, Zhizhang (David) Chen, Fellow, IEEE, and Pei-Guo Liu

Abstract—A parameter-optimized (2, 4) stencil based locally-one-dimensional (LOD) finite-difference time-domain (FDTD) is presented with much reduced numerical dispersion errors. The method is first proved to be unconditionally stable. Then by using different optimization schemes, the method is optimized to satisfy different accuracy requirements, such as minimum dispersion errors in the axial directions, in the diagonal direction, and in the specified angles. Performances of the parameter-optimized LOD-FDTD with different time steps and frequencies are also studied. It is found that the parameter optimization can significantly reduce numerical dispersion errors, bringing them down to the level of the conventional FDTD but with the time step exceeding the CFL limit and without much additional computational cost. In addition, the optimized parameters are not sensitive to frequencies; in particular, the optimized parameters obtained at a higher frequency still present low numerical dispersion errors at a lower frequency. Index Terms—Alternating direction implicit (ADI), CourantFriedrich-Levy (CFL) limit, finite-difference time-domain (FDTD) method, locally one-dimensional, numerical dispersion, phase velocity error, unconditionally stability.

I. INTRODUCTION HE finite-difference time domain (FDTD) has found wide applications due to its simplicity and flexibility. However, for electrically large and high-Q structures, the FDTD computational expenditure is still high due to the Courant-Friedrich-Levy (CFL) stability condition that limits the size of time step. To alleviate this problem, the unconditionally stable alternating direction implicit finite-difference time-domain (ADI-FDTD) was presented in [1] and [2]. In it, the CFL limit is removed and the computations involve solution of a tri-diagonal matrix at each time step. More recently, other unconditionally stable methods such as the split-step [3], [4] and the locally one-dimensional (LOD) FDTD methods [5]–[7] have been proposed. The LOD approach, often termed as the LOD-FDTD method, applied local splitting of the operators and was claimed to be more CPU time

T

Manuscript received May 21, 2009; revised January 18, 2010; accepted January 23, 2010. Date of publication April 22, 2010; date of current version July 08, 2010. This work was supported by the National Science Fund of China under Grant 60831002. Q.-F. Liu and W.-Y. Yin are with the Center for Microwave and RF Technologies, School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai, China (e-mail: [email protected]). Z. Chen is with the Microwave and Wireless Research Laboratory, Department of Electrical and Computer Engineering, Dalhousie University, Halifax B3J 2X4, Nova Scotia, Canada (email: [email protected]). P. G. Liu is with the Department of No. 4, National University of Defense Technology, Changsha 410073, Hunan, China. Digital Object Identifier 10.1109/TAP.2010.2048857

efficient than the ADI-FDTD method. To account for open-region problems, the LOD-FDTD method has also been incorporated with the split-field and the convolution PML [8] and [9], respectively. The LOD FDTD has been mostly implemented in two dimensions except that in [10] and [11] where the three-dimensional LOD-FDTD method was shown; however, it requires input processing for every simulation and output processing at every time step for every field component at each time step. In our previous work, we proposed an arbitrary-order LOD-FDTD algorithm with its stability and numerical dispersion analyses [12]. It is found that the second-order LOD-FDTD has the same level of numerical dispersion error as that of the unconditionally stable alternating direction implicit finite-difference time-domain (ADI-FDTD) method but with higher computational efficiency. On the other hand, all the above implicit methods, either LOD-FDTD or ADI-FDTD, suffer from the large numerical dispersion errors when time steps increase. To further reduce the dispersion errors, a parameter optimized method has been proposed for the ADI-FDTD method based on the (2, 2) stencil [13] (the method is then termed as (2, 2) PO-ADI-FDTD). It minimized the dispersion errors of the ADI-FDTD methods for different incident angles and different time step sizes. Along the same line, [14] applied the similar approach to the LOD-FDTD, and implemented a parameter optimized method to reduce the numerical dispersion errors of the conventional (2, 2) stencil-based LOD-FDTD (note that there exist some errors in [14] including (4) and (5) therein). Reference [16] is an extension of the work in [13], [15] and applied the optimized method to the ADI-FDTD method and further reduce the dispersion errors by using the (2, 4) stencil approach (the method is then termed as (2, 4) PO-ADI-FDTD). In [17], artificial anisotropy was introduced to reduce the numerical dispersion in the traditional FDTD method, and the similar approach was then applied to ADI-FDTD method [18]. This paper proposes and applies the parameter optimized method to the fourth-order LOD-FDTD to further reduce the dispersion errors of LOD-FDTD based on the (2, 4) stencil. In addition, unlike the two-dimensional cases considered in [14]–[16], the proposed approach in this paper is in three dimensions. In the following sections, we will first present in details a threedimensional parameter optimized LOD FDTD method based on the (2, 4) stencil together with its stability and dispersion analysis. Then we will show the results that minimize dispersion errors based on different requirements. Finally, we will present the parameter optimization with different time steps and frequencies.

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II. THE PARAMETER-OPTIMIZED THREE-DIMENSIONAL LOD-FDTD BASED ON (2, 4) STENCIL Let us consider the wave propagating in a lossless homogeand permeability . The nous medium with permittivity second-order finite-difference is applied to approximate the time derivative while the central finite difference scheme with four stencils is used to replace the spatial differential operators in Maxwell’s equations. This forms the three-dimensional (2, 4) stencil-based LOD-FDTD method. The updating procedure of the three-dimensional (2, 4)-stencil LOD-FDTD method is then performed in two sub-procedures. The first sub-procedure is represented by . The second (1a)–(1c) for time marching form to sub-procedure is represented by (2a)–(2c) for time marching to . They are formulated as follows. form Sub-step #1: advancement form to time step:

(4b)

(4c) Here, is the approximation of a spatial differential operator with a fourth-order central finite-difference in the direction. For example, can be the difference operator defined as

(5a)

(5b)

(1a)

(1b)

(1c)

(2a)

(2b)

(2c) Sub-step #2: advancement from

to

time step

(3a)

(3b)

(3c)

(5c) where , or and are the parameters to be optimized. With (5a)–(5c), (1a)–(4c) represent the finite difference approximations to the first-order spatial derivative of electric and magnetic fields. By applying the Taylor series approximation and the central finite difference, it is found that their accuracies are generally of the 2nd order, but become of the 4th order when , as explained in [19], [20]. and can be chosen and optimized in such In general, a way that they improve the accuracy of the numerical method or achieve other accuracy-related objectives. There can be many accuracy-related objectives. In this paper, we choose the minimization of the numerical dispersion as the objective. Therefore, we need to perform the stability and dispersion analysis as described in the following sections. III. STABILITY AND DISPERSION ANALYSIS The von Neumann method has been used as a standard approach to stability analysis of an unconditionally stable FDTD method where eigenvalues of the amplification matrix in spectral domain are evaluated [1], [2]; if all the eigenvalues are not larger than unity in magnitudes, the method is stable. In this section, we will use the method to prove the unconditional stability of the (2, 4) LOD method described in this paper. and are the spatial frequencies along Assume that the , and directions, respectively. The field components in the spectral domain at the th time step are then (6)

(4a)

Here of the field components with

is the magnitude being the spectral-domain

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at the th time step and being the magnitude of the at the th time step. and . spectral-domain By substituting (6) into (1a)–(4c), the following equations can be obtained:

with

(7) where (8) is the amplification matrix with (9a)–(10d), shown at the bottom and . of the page. Here, With the help of MAPLE, the eigenvalues of can be found as

(11)

Since are real, and are both positive , the magnitudes of all the eigenvalues and expressed by (11) are then unity. Therefore, the (2, 4)-stencil based LOD-FDTD method presented in Section II is unconditionally stable. The numerical dispersion of the proposed method can be found by following the procedure described in [21]. For a time-harmonic signal,

(12)

(13)

where

(9a)

(9b)

(9c)

(9d)

(10a) (10b) (10c) (10d)

LIU et al.: AN EFFICIENT METHOD TO REDUCE THE NUMERICAL DISPERSION IN THE LOD-FDTD

Then (7) becomes (14) To ensure a non-trivial solution, the determinant of (14) should be zero, which leads to the numerical dispersion relationship

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Numerical phase velocity error With the above definitions, the phase velocity error, denoted at a propagation angle can be defined as as % % %

(19)

(15) After some manipulations, (15) can be simplified as (16) Equation (16) is the numerical dispersion relationship of the (2.4) stencil-based LOD FDTD method. Now suppose that a plane wave propagates in the directions of and in the spher. Then, ical coordinates and the numerical wave number is

(17) and are the numerical spatial frequencies along where , and directions, respectively. By substituting (17) into the , one (16) with a known propagation direction defined by can solve for numerical wave number . By comparing with the analytical wave number , numerical dispersion error is taken, the dispersion is can be found. Note that if reduced to the one for the two dimensional parameter-optimized LOD-FDTD.

Note that is the speed of light with being the analytical wave number. Furthermore, (19) is related to and through (17), (16), (12) and (10). The averaged phase velocity error over pre-selected is then angles (20) The averaged phase velocity function (20) can be used for forming different optimization objectives, such as minimization of dispersion errors in the axial directions, in the diagonal direction, and in a range of specified angles. They lead to different parameter values for minimization of the numerical dispersion errors as described below. A. Minimization of Dispersion Errors in the Axial Directions In some applications, minimization of the dispersion errors along three axial directions is desired. In other words, by using (20), the following objective function can be set up for the minimization:

(21) IV. PARAMETER OPTIMIZATIONS In this section, several optimization criteria are described and , and . Before the descriptions, used to find parameters several notations are introduced for clarity. The CFL Number (CFLN) CFLN is introduced as the ratio of the time step to the , i.e., CFL limit (18) Normalized numerical phase velocity From electromagnetic theory, the numerical phase velocity in is equal to , where propagation angle being the angular frequency and being the frequency. As a result, the numerical phase velocity normalized to speed of light in free space, can be expressed as

Suppose that and with being the wavelength associated with [i.e., ]. By applying the well-known conjugate gradient technique to minimize (21), the following optimized parameters are obtained: (22) Substitution of (22) into (16) finds the numerical wave number which in turn presents the numerical phase velocity error as defined by (19). Fig. 1 shows the phase velocity error with and without the above parameter optimization. Without the optimization, the maximum phase velocity error is about 1%. After the optimization, it is reduced to 0.1%, more than 10 times smaller. The dispersion error curves of the conventional explicit FDTD based are also plotted in Fig. 1 on the (2, 4) stencil with for comparison. The parameter-optimized implicit LOD-FDTD method is shown to have even smaller dispersion errors than the conventional FDTD.

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TABLE I PARAMETERS OPTIMIZED FOR THREE SETS OF PROPAGATION ANGLES

Fig. 1. Phase velocity errors of the (2, 4) stencil LOD-FDTD with and without and 90 . the parameter optimization along the axial directions.  and x y z  = .

CFLN = 2

1 = 1 = 1 = = 20

= 0

Fig. 3. Phase velocity errors of the (2, 4) stencil LOD-FDTD with and without the parameter optimization at the 1st set of the propagation angles. (the elevation angle at which ; x y z  = , and  the phase velocity errors are minimized).

2 1 = 1 = 1 = = 20

= 15

CFLN =

C. Minimization of Dispersion Errors in Specified Angles Fig. 2. Phase velocity errors of the (2, 4) stencil LOD-FDTD with and without ; CF LN the parameter optimization along the diagonal direction.  and x y z  = .

1 = 1 = 1 = = 20

= 45

=2

B. Minimization of Dispersion Error in the Diagonal Direction The minimization of the dispersion error can also be set along . That is, the objective the diagonal direction function below is minimized again with the conjugate gradient technique: (23) The minimization leads to

The numerical phase velocity errors can also be minimized in other specified propagation angles. Table I shows the optimized parameters when the objective function (20) is minimized for three sets of specified propagation angles, respectively. Figs. 3, 4 and 5 show the phase velocity errors with and without the parameter optimizations at the three sets of propagation angles. After the optimization, the phase velocity errors of the (2.4)-stencil LOD-FDTD are reduced to almost zeros, even smaller those of the conventional FDTD with . This is an indication of the effectiveness of the parameter optimization. D. Minimization of Dispersion Errors in an Array of Angles To reduce the overall dispersion errors of the method within a specified sector of propagation angles, we can set up the objective function (20) to be minimized over a pre-selected array of angles. To illustrate the process, let’s take the array to be (24)

The numerical dispersion errors with and without the parameter optimization are shown in Fig. 2. Without the parameter optimization, the phase velocity error is about 0.6%; with the optimization, it is reduced to about 0.01%, 60 times smaller. In other words, the error reduction is quite significant. The dispersion curves of the conventional (2, 4) FDTD with are also plotted in Fig. 2 for comparison. As can be seen, the LOD-FDTD with the parameter optimization has smaller errors that the conventional FDTD method around the intended diagonal directions.

After the minimization of (20) with the conjugate gradient technique, we obtain the optimized parameters as , and under the condi. The phase dispersion tion that error with and without the optimization is shown in Fig. 6. As seen, the dispersion errors are reduced quite significantly. To check the effects of the parameter optimization on difand be , and , ferent mesh sizes, let respectively, while the time step size remains to be the default

LIU et al.: AN EFFICIENT METHOD TO REDUCE THE NUMERICAL DISPERSION IN THE LOD-FDTD

Fig. 4. Phase velocity errors of the (2, 4) stencil LOD-FDTD with and without the parameter optimization at the 2nd set of the propagation angles. CFLN = 2; 1x = 1y = 1z =  = =20 and  = 30 (the elevation angle at which the phase velocity errors are minimized).

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Fig. 7. Phase velocity errors of the (2, 4) stencil LOD-FDTD with and without the parameter optimization along a planar range propagation angles. Note: the figure is very close to Fig. 6.

TABLE II OPTIMIZED PARAMETERS WITH DIFFERENT CFLNs

V. PARAMETER OPTIMIZATION VERSUS TIME STEP Fig. 5. Phase velocity errors of the (2, 4) stencil LOD-FDTD with and without the parameter optimization at the 3rd set of the propagation angles. CFLN = 2; 1x = 1y = 1z =  = =20 and  = 45 (the elevation angle at which the phase velocity errors are minimized).

Fig. 6. Phase velocity errors of the (2, 4) stencil LOD-FDTD with and without the parameter optimization along an array of propagation angles.

value of . Again we can set up the same objective function (20) to be minimized over a pre-selected array of angles determined by (24). Upon carrying out the optimization, we obtain the optimized parameter . Fig. 7 shows the phase dispersion error with and without the optimization. Again, the dispersion errors can be seen significantly reduced.

One advantage of using the unconditionally stable LOD-FDTD method is that its time-step size is not constrained by the stability but numerical errors. Therefore, it is useful and meaningful to see whether the optimized parameter values are affected by different time steps (or CFLNs) and what the implications are. Again, minimization of the dispersion errors along the three axial directions was carried out. Table II shows the optimized parameters with different CFLNs, while Figs. 8 and 9 show the dispersion errors with the optimized parameters; for the comparison purpose, the dispersion errors of the conventional (2, 4) explicit FDTD is also plotted. As can be seen from Figs. 8 and 9, it is found that when the time step increases, the phase velocity error increase correspondingly. However, with the optimized parameters, the dispersion errors of the (2, 4) LOD-FDTD are reduced significantly to a level comparable to that of the conventional ex. For inplicit FDTD but the LOD-FDTD is with , the maximum dispersion errors of the stance, with LOD-FDTD are reduced from 2.0% without the optimization to 0.01% with the optimized parameters of Table II; 0.01% is very close to the dispersion errors of the conventional (2.4) FDTD . with To further illustrate the case with different time steps in an array of angles, let CFLN be 1, 2, and 4 respectively. In other words, (20) was minimized with different CFLNs respectively were selected to be an array of but the incident angles angles specified by (24). Table III presents the optimized parameters with different CFLNs and array of specified angles.

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Fig. 8. Phase velocity errors of the (2, 4) stencil LOD-FDTD with the parameter optimization along the axial directions and with CFLN = 1; 2, and 4.  = 0 , and 1x = 1y = 1z =  = =30.

Fig. 9. Phase velocity errors of the (2, 4) stencil LOD-FDTD with the parameter optimization along the axial directions and with CFLN = 1; 2, and 4.  = 90 , and 1x = 1y = 1z =  = =30. TABLE III OPTIMIZED PARAMETERS WITH DIFFERENT CFLNs

Figs. 10 and 11 show the numerical phase velocity errors with and without the optimized parameters. For comparison purpose, the dispersion errors of the conventional (2, 4) FDTD are also plotted. Again, as can be seen, the dispersion errors are reduced significantly to the level comparable to those of the conventional FDTD. Without the optimization, the phase velocity errors are and 90 with . After about 1.2% and 1.7% at the optimization, the phase velocity errors are about 0.12% and 0.14%, almost 10 times smaller. Based on Fig. 8–11, we can conclude that by applying the parameter optimization, numerical dispersion errors of the LODFDTD can be reduced to the level of that of the conventional . In other FDTD method but with larger time step words, the parameter-optimized LOD-FDTD may require less simulation time without scarifying the accuracy.

Fig. 10. Phase velocity errors of the (2, 4) stencil LOD-FDTD with and without the parameter optimization along an array of propagation angles and with CFLN = 1; 2, and 4, when  = 45 , and 1x = 1y = 1z =  = =30.

Fig. 11. Phase velocity errors of the (2, 4) stencil LOD-FDTD with and without the parameter optimization along an array of propagation angles and with CFLN = 1; 2, and 4, when  = 90 , and 1x = 1y = 1z =  = =30. TABLE IV OPTIMIZED PARAMETERS WITH DIFFERENT VALUES OF w

VI. PARAMETER OPTIMIZATION VERSUS FREQUENCY Numerical dispersion or phase velocity errors also change with the frequency. Normally, the errors increase with the increase of frequency (or decrease of wavelength ). To study this rad/s, effect, let’s consider and . Minimization of (20) is done with different values of , and the objective function is selected as the same as (21) for minimization of the dispersion errors along the three axial directions. Table IV gives the optimized parameters obtained with the application of the conjugate gradient technique.

LIU et al.: AN EFFICIENT METHOD TO REDUCE THE NUMERICAL DISPERSION IN THE LOD-FDTD

Fig. 12. Phase velocity errors of the (2, 4) stencil LOD-FDTD with the parameter optimization along the axial directions and with w ; y : w ; : w ; : w , and : w .  , and x z  = .

01 10 15 1 = = 60

30

= 90 CFLN = 3

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= the parameter optimization along the axial directions and with w = 1 = 1 = 0:1w ; 1:0w ; 1:5w , and 3:0w .  = 90 , and 1x = 1y = 1z =  = =60. Fig. 14. Phase velocity errors of the (2, 4) stencil LOD-FDTD with

TABLE V OPTIMIZED PARAMETERS WITH DIFFERENT VALUES OF w

Fig. 13. Phase velocity errors of the (2, 4) stencil LOD-FDTD with the parameter optimization along the axial directions and with w , and x y z  : w ; : w ; : w , and : w .  = .

01 10 60

15

30

= 45

= 1 =1 =1 = =

Fig. 12 shows that the numerical phase velocity errors with and without the optimized parameters of Table IV and with different , respectively. As can be seen from Fig. 12, when the frequency increases, the phase velocity error increase correspondingly. However, with the parameter optimization, the impact of the frequency increase is substantially minimized. To further illustrate the case with different frequency, the optimization is applied for an array of propagation angles with , 1.0 , 1.5 , and 3.0 , varied frequencies of 0.1 respectively. Minimization of (20) was carried out over the pre-selected array of incident angles defined by (24). Table V presents the optimized parameters with different values of . Figs. 13 and 14 show the numerical phase velocity errors with and without the optimized parameters. For comparisons, the dispersion errors of the conventional FDTD are also plotted. As can be seen from Figs. 13 and 14, when the frequency increases, the phase velocity error increase correspondingly. However, the parameter optimization again minimizes the impact of the frequency increase. For instance, without the

optimization, the phase velocity errors are about 1.2% and and 90 at . After the optimization, 2.1% for the average phase velocity errors are about 0.2% and 0.13%, which are the error level of the conventional FDTD. Therefore, numerical dispersion error is reduced significantly. To assess the sensitivity of the optimized parameters to frequency, numerical dispersions were computed with varying frequencies but fixed parameters. Figs. 15 and 16 show the numerical phase velocity errors with different frequencies with which were obtained after minimization of numerical phase velocity errors along the three axial . For comparison, numerical phase three directions at velocity errors of the conventional FDTD with CFLN=1 and are also plotted in Figs. 15 and 16. As can be seen from Figs. 15 and 16, the parameter optimization is not sensitive to frequency variations. This is reflected by Table IV where the optimized parameters at different frequencies are little different from each other. Therefore, the parameters obtained at a frequency are also good at other frequencies. In particular, the parameters obtained at a higher frequency even present lower phase velocity errors at lower frequencies. In other words, the parameter optimization is preferred to be carried out at a higher frequency than at a lower frequency. In addition, like what was discussed previously, the parameter optimization does bring the numerical phase velocity errors down to the level of the conventional FDTD.

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= 0:1w ; 1:0w ; 1:5w , and 3:0w , = 1 8787; = 45 ; 1x = 1y = 1z =

Fig. 15. Phase velocity errors with w respectively. c c c : = ; .

= 60 CFLN = 3

=

= 0:1w ; 1:0w ; 1:5w , and 3:0w , = 1 8787; = 90 ; 1x = 1y = 1z =

Fig. 16. Phase velocity errors with w c c : respectively. c = ; .

= 60 CFLN = 3

=

VII. CONCLUSION This paper has presented a parameter optimized LOD-FDTD method based on the (2, 4) stencil to achieve better dispersion performance. The method has been proved to be unconditionally stable for any real parameters. By setting different optimization criteria, the proposed method can satisfy different accuracy requirements, such as minimum dispersion error in the axial directions, minimum dispersion error in the diagonal direction, and minimum dispersion error for a few arbitrary angles. The performance variations of the performance of the (2, 4) parameter-optimized LOD-FDTD method with different frequencies and time steps have also been studied. Our results show that the parameter optimization proposed in this paper can dramatically bring the dispersion errors down to the level of the conventional (2, 4) stencil FDTD but with larger time steps and without introducing additional computational cost. In addition, the optimized parameters are not very sensitive to the frequencies. The optimization is then recommended to be carried out at a high frequency point. REFERENCES [1] F. Zheng, Z. Chen, and J. Zhang, “A finite-difference time-domainmethod without the Courant stability conditions,” IEEE Microw. Guided Wave Lett., vol. 9, no. 11, pp. 441–443, Nov. 1999.

[2] 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. [3] J. Lee and B. Fornberg, “A split step approaches for the 3-D Maxwell’s equations,” J. Comput. Appl., vol. 158, pp. 485–505, 2003. [4] J. Lee and B. Fornberg, “Some unconditionally stable time stepping methods for the 3D Maxwell’s equations,” J. Comput. Appl., vol. 166, pp. 497–523, 2004. [5] J. Shibayama and M. Muraki, “Efficient implicit FDTD algorithm based on locally one-dimensional scheme,” Electron. Lett., vol. 41, no. 19, Sep. 2005. [6] J. Shibayama, M. Muraki, J. Yamauchi, and H. Nakano, “Efficient implicit FDTD algorithm based on locally one-dimensional scheme,” Electron. Lett., vol. 41, no. 19, pp. 1046–1047, Sep. 2005. [7] J. Shibayama, M. Muraki, R. Takahashi, J. Yamauchi, and H. Nakano, “Performance evaluation of several implicit FDTD methods for optical waveguide analyses,” J. Lightw. Technol., vol. 24, no. 6, pp. 2465–2472, June 2006. [8] V. E. do Nascimento, B. H. V. Borges, and F. L. Teixeira, “Split field PML implementations for the unconditionally stable LOD-FDTD method,” IEEE Microw. Wireless Compon. Lett., vol. 16, no. 7, pp. 398–400, Jul. 2006. [9] I. Ahmed, E. P. Li, and K. Krohne, “Convolutional perfectly matched layer for an unconditionally stable LOD-FDTD method,” IEEE Microw. Wireless Compon. Lett., accepted for publication. [10] E. L. Tan, “Unconditionally stable LOD-FDTD method for 3-D Maxwell’s equations,” IEEE, Microw. Wireless Compon. Lett., vol. 17, no. 2, Feb. 2007. [11] I. Ahmed, E. K. Chua, E. P. Li, and Z. Chen, “Development of the three-dimensional unconditionally stable LOD-FDTD method,” IEEE Trans. Antenna Propag., vol. 56, no. 11, pp. 3596–3600, Nov. 2008. [12] Q. F. Liu, Z. Chen, and W. Y. Yin, “An arbitrary-order LOD-FDTD method and its stability and numerical dispersion,” IEEE Trans. Antennas Propag., vol. 57, no. 8, pp. 2409–1417, Aug. 2009. [13] M. Wang, Z. Wang, and J. Chen, “A parameter optimized ADI-FDTD method,” IEEE Antennas Wireless Propag. Lett., vol. 2, pp. 118–121, Sep. 2003. [14] E. Li, I. Ahmed, and R. Vahldieck, “Numerical dispersion analysis with an improved LOD-FDTD method,” IEEE Microw. Wireless Compon. Lett., vol. 17, no. 5, pp. 319–321, May 2007. [15] G. Sun and C. W. Trueman, “Optimized finite-difference time-domain methods based on the (2, 4) stencil,” IEEE Trans. Microw. Theory Tech., vol. 53, pp. 832–841, Mar. 2005. [16] W. Fu and E. L. Tan, “A parameter optimized ADI-FDTD method based on the (2, 4) stencil,” IEEE Trans. Antennas Propag., vol. 54, no. 6, pp. 1836–1842, Jun. 2006. [17] J. S. Juntunen and T. D. Tsiboukis, “Reduction of numerical dispersion in FDTD method through artificial anisotropy,” IEEE Trans. Microw. Theory Tech., vol. 48, no. 4, pp. 582–588, Apr. 2000. [18] A. P. Zhao, “Improvement on the numerical dispersion of 2D ADIFDTD with artificial anisotropy,” IEEE, Microw. Wireless Compon. Lett., vol. 14, no. 6, pp. 292–294, Jun. 2004. [19] J. Fang, “Time domain finite difference computation for Maxwell’s equations,” Ph.D. dissertation, Univ. California, Berkeley, CA, 1989. [20] K. Lan, Y. Liu, and W. Lin, “A high order (2, 4) scheme for reducing dispersion in FDTD algorithm,” IEEE Trans. Electromagn. Compat., vol. 41, no. 2, pp. 160–165, May 1999. [21] F. H. Zheng and Z. Z. Chen, “Numerical dispersion analysis of the unconditionally stable 3-D ADI-FDTD method,” IEEE Trans. Microw. Theory Tech., vol. 49, no. 5, pp. 1006–1009, May 2001.

Qi-Feng Liu was born in Anhui province, China, in 1981. He received the B.S. degree in electrical engineering from the Anhui Normal University, China, in 2003, the M.S. degree from Anhui University, Hefei, China, in 2006, and is currently working toward the Ph.D. degree at Shanghai Jiao Tong University, Shanghai, China. His current research interests include computational electromagnetics and electrical-thermal analysis of semiconductor devices.

LIU et al.: AN EFFICIENT METHOD TO REDUCE THE NUMERICAL DISPERSION IN THE LOD-FDTD

Wen-Yan Yin (M’99–SM’01) received the M.Sc. degree in electromagnetic field and microwave technique from Xidian University (XU), China, in 1989 and the Ph.D. degree in electrical engineering from Xi’an Jiaotong University (XJU), Xi’an, China, in 1994. He worked in the Department of Electronic Engineering, Northwestern Polytechnic University (NPU), as an Associate Professor from 1993 to 1996. He was a Research Fellow with the Department of Electrical Engineering, Duisburg University, granted by the Alexander von Humblodt-Stiftung of Germany from 1996 to 1998. In December 1998, he joined the MMIC Modeling and Packing Lab, Department of Electrical Engineering, National University of Singapore (NUS), as a Research Fellow. In March 2002, he joined the Temasek Laboratories of NUS, as a Research Scientist and Project Leader of high-power microwave and ultrawideband EMC/EMI. In April 2005, he joined the School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University (SJTU), Shanghai, China, as a Professor in electromagnetic fields and microwave techniques. He is also the Director of Center for Microwave and RF Technologies, SJTU. His main research interests are in EMC, EMI and EM protection, on-chip passive and active MM(RF)IC device testing, modeling, and packaging, ultra-wide band interconnects and signal integrity, and nanoelectronics. He is a reviewer of some international journals, including five IEEE TRANSACTIONS, Radio Science, IEE Proc-H, Microwave, Antennas, and Propagation. He is listed as an the editorial board member and reviewer of the Journal of Electromagnetic Waves and Applications. As a leading author, he has published more than 130 international journal articles including 15 book chapters. One chapter, “Complex Media” is included in the Encyclopedia of RF and Microwave Engineering (Wiley, 2005). Dr. Yin is the Technical Chair of Electrical Design of Advanced Packaging and Systems-2006 (EDAPS’06), technically sponsored by IEEE CPMT Subcommittee.

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Zhizhang (David) Chen (S’92–M’92–SM’96–F’10) received the Ph.D. degree from the University of Ottawa, Ottawa, ON, Canada, in 1992. From January to August of 1993, he was an NSERC Postdoctoral Fellow with the ECE Department, McGill University, Montreal, Canada. In 1993, he joined Dalhousie University, Halifax, Canada, where he is presently a full Professor and holds the Killam Chair in Wireless Technology. He has authored and coauthored over 140 journal and conference papers in computational electromagnetics and RF/microwave electronics. He was one of the originators in developing new numerical algorithms (including ADI-FDTD method) and in designing new classes of compact RF front-end circuits for wireless communications. His current research interests include numerical modeling and simulation, RF/microwave electronics, smart antennas, and wireless transceiving technology and applications. Dr. Chen received the 2005 Nova Scotia Engineering Award, a 2006 Dalhousie Graduate Teaching Award, 2006 Dalhousie ECE Professor of the Year Award, and the 2007 Dalhousie Faculty of Engineering Research Award.

Peiguo Liu received the B.S. and M.S. degrees in electromagnetic field and microwave technologies and the Ph.D. degree in communication and information system, all from National University of Defense Technology (NUDT), Changsha, China, in 1990, 1994, and 2000, respectively. From 2004 to 2005, he was a Visiting Scholar an the University of Calgary, Canada. He is currently an NUDT professor, and his research interests are in electromagnetic radiation, scattering, and electromagnetic compatibility.

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Implementation of Collocated Surface Impedance Boundary Conditions in FDTD Gregory Kobidze, Senior Member, IEEE

Abstract—Surface impedance boundary conditions (SIBCs) for finite-difference time-domain (FDTD) are implemented with collocated H and E components in which first-order spatial finite difference have been used for the spatial derivatives. Transient error analysis is done for the reflected field for the whole possible range of modeled material conductivity. Magnitude and phase error analysis of the calculated reflection coefficients for wideband pulses is presented as well. The resulting numerical errors are compared with the errors of traditional SIBCs implementation when the tangential magnetic fields on the boundary are approximated with the neighboring FDTD magnetic field component located at half-cell size distance in space and half time step behind in time. It is shown that the collocated fields approach is considerably more accurate for both constant real resistive and dispersive complex lossy dielectric SIBCs, in both magnitude and especially phase. Unlike the traditional approach, it is stable for all values of modeled material conductivity. The collocated fields approach is also applied to SIBCs with coating, and the transient and reflection coefficient errors are studied. It is shown that in contrast to the traditional implementation, it is stable for arbitrarily thin coating and for any substrate conductivity, and requires storage only half of the auxiliary coefficients when computing the convolution integrals. Index Terms—Error analysis, finite-difference time-domain (FDTD) method, surface impedance boundary conditions (SIBCs).

bodies. SIBCs relate the electric and magnetic field components outside of the body right at the surface. In the case of staggered mesh such as in FDTD-type solvers, the electric and magnetic field components are not collocated in space and the marching on in time is done with leap-frog arrangement. To alleviate the contradiction of having collocated SIBCs and non-collocated mesh the majority of methods employ a quasi plane-wave assumption stating that the (magnetic) field at spatial half-step distance in the propagation direction is delayed by a temporal half-step. That is, say, if the field propagates in the positive x-direction, then , where

is an FDTD magnetic field y-component in a magnetic field node at a magnetic field time instance, and

I. INTRODUCTION LECTROMAGNETIC simulation solvers with volumetric discretization such as finite element method (FEM), FVM, method of moments (MoM), finite-difference time-domain (FDTD), etc., in most of the cases limit the characteristic dimensions of their mesh elements by a fraction of the wavelength of the modeled medium. For high dielectric contrasts or high material conductivity the effective wavelength is considerably shorter than that of surrounding space. The mesh for bodies made of materials of extremely short wavelength becomes prohibitively dense, especially taking into account the CFL time step limitations in explicit time-domain differential-equation-based solvers. To make the problem computationally tractable by a chosen solver, a number of approximation models in the form of special surface impedance boundary conditions (SIBCs) have been designed ([1]–[8], [10]–[12] and references therein to mention a few) to avoid expensive computation of the fields inside the high contrast

E

Manuscript received June 13, 2009, revised December 02, 2009; accepted January 26, 2010. Date of publication April 22, 2010; date of current version July 08, 2010. The author is with EM Performance, Austin, TX 78749 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/TAP.2010.2048859

is a magnetic field y-component in an electric field node at an electric field instance. In other words, the neighboring to surface boundary H-node is shifted half-step in space to the boundary and half-step forward in time. This practically never happens exactly except in a very special 1-D case at CFL limit , being the speed of light, in the absence of reflection at perfectly matching SIBCs. In many cases the difference is small enough to result in just a few percents of error for the reflection coefficient. In other cases it may result in higher errors and for a wide range of SBC parameters often lead to instabilities. The purpose of this paper is to show how SIBCs implemented without such a strong assumption for H-node shift can bring three big advantages: i) be up to orders of magnitude more accurate, ii) lead to unconditional with respect to SIBCs parameters stability, and iii) be of the same level of complexity and compared to some implementations may in fact even be faster and require storage of twice as fewer variables. Thorough error analysis of all possible cases is used throughout the paper to compare different methods. The paper first considers the implementation of perfect magnetic conductor (PMC) SIBCs and takes a close look at how the FDTD equations are coupled with PMC condition to ensure the collocation of the fields at the boundary. Next, a simple constant (resistive) relation between E and H tangential field components is integrated into FDTD scheme to achieve algorithm

0018-926X/$26.00 © 2010 IEEE

KOBIDZE: IMPLEMENTATION OF COLLOCATED SURFACE IMPEDANCE BOUNDARY CONDITIONS IN FDTD

H

Fig. 1. Magnetic field at adjacent face is used when electric field boundary surface edge is updated.

E

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stability and machine-precision accuracy for the reflection coefficient for all possible values of surface resistivity. Implementations of surface impedance boundary conditions with lossy dielectric are examined next and it is shown that alternative to H-node shifting implementation is of the same complexity and always more (up to orders of magnitude) accurate. At last, implementations of SIBCs with coating layers are analyzed. It is observed that H-node shift may lead to numerical instabilities for thin coatings and that regular stabilization technique can be successfully applied when integrating collocated SIBCs into FDTD codes. It is also shown that only half of the auxiliary coefficients are stored for the proposed algorithm. It should be noted that for commercial 3D implementations of SIBCs in FDTD codes one needs to take into consideration the arguments and technique described in [2].

Fig. 2. For resistive surface BC b) coaxial cable example.

E =  J =  n^ 2 H: a) half-space and

III. RESISTIVE SIBCs Let the tangential electric field at the boundary surface be proportional to displacement current density (2) or (3) is the SIBCs resistivity, the SIBCs conwhere ductivity, as shown in Fig. 2. This, e.g., can be a case of (may be mismatching) coaxial cable junction. In general electrically lossy medium the FDTD electric field update at the BC becomes

II. PERFECT MAGNETIC CONDUCTOR The perfect magnetic conductor (PMC) boundary condition is enforced by setting the tangential magnetic field to zero. Often in Yee FDTD mesh the boundary surface is defined along the electric field components and the tangent discretized magnetic field elements are not available. As an alternative to artificial spatial shifting one can utilize modification of the updating scheme for the discretized electric field elements at the boundary. Tangential electric field at the PMC boundary surface is computed with the assumption that the tangential on the boundary is zero. component of the magnetic field In terms of 3D programming, the tangential component of the is used, where is the unit magnetic field vector normal to the boundary surface. Its spatial derivative in the direction of at the position of an E edge on the boundary surface is taken from one side and is approximated as shown in Fig. 1. via If in 1D problem the electric field is polarized in the z-direction and the magnetic field is oriented in the y-direction, the fields can vary in the x-direction, and a general 1D FDTD upat the boundary with normal is date expression for written as (1) with , , being the permittivity, relative permeability and conductivity of the medium outside of the body modeled by SIBCs. For any PMC 1D code implementation it means that one when computing . can simply double the residual

(4) For

,

, or (5)

Equations (4) and (5) combined give

(6) Setting (7) gives the following update equation for (8) The algorithm is stable for any positive and as long as CFL condition is met. Notice that the equation is valid for not only very large but also for very small conductivity. A simplified version (9)

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Fig. 3.

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L

error

%, with: a) shifting H in space and time (diverges for small conductivity), and b) proposed solution (machine precision accurate).

is fairly accurate for surface resistivity lower than , but is unstable for higher resistivity, as explained in the following error analysis. A. Error Analysis in 1D Experimental error and stability analysis is possible since the 1-D analytical solution is known for the reflection coefficient . A 5-period ramp tapered sinusoidal signal of carrier frequency was launched from the right side of a free-space computational domain with 100 FDTD grid points and resistive boundary conditions on the left side. The density of about 20 points per wavelength (2 mm) are chosen with the and the “magic” time step of number of time steps small enough to avoid the reflection from the right boundary. The resulting FDTD transient total electric and magnetic field components in the wavelength vicinity at the boundary have been compared to exact analytical solution. percentage error versus conductivity Fig. 3(a) shows for traditional approach with H-node shifts Figs. 3(b) and (9) percentage error for the solution obtained using shows (8) for the whole possible conductivity range. Here is the standard measure notation for maximum error, defined as for and all spatial coordinates in the computational domain for all time steps . It is seen that unlike the method with time and space shift for the magnetic component, the collocated approach is indeed always stable and is in fact machine-precision accurate.

Fig. 4. Lossy dielectric body with permittivity " , permeability  and conductivity  is surrounded by a medium with corresponding ",  and  .

with inverse Laplace transform in the time domain as

(11) , and are the modified Bessel funcwhere tions of the first kind of order zero and one, is the Heaviis the Dirac delta function. The side unit step function, and electric field is a convolution

(12) and the discrete sum is (13)

IV. BC FOR LOSSY DIELECTRIC Resistive BC has been considered as an illustrative example that allows performing thorough error analysis of the BC methods. Conductors and lossy dielectrics on the other hand exhibit dispersive nature. Fig. 4 shows a sketch of such a boundary with corresponding electromagnetic parameters. With certain approximations the surface impedance for conductors is assumed to be in the frequency domain as [1] (10)

(14) Performing change of variables, integration by parts and using the identity

KOBIDZE: IMPLEMENTATION OF COLLOCATED SURFACE IMPEDANCE BOUNDARY CONDITIONS IN FDTD

(15a) (15b) , being Kummer conwith fluent hypergeometric function. As compared to the original discrete integral form (14), it contains only order zero modified Bessel function and it can be computed more efficiently. Using the Maloney-Smith method with Prony’s complex harmonic decomposition [8] of the resulting convolution integrals

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, ; 1. Initialize for every and for every of 2. Update FDTD grid except on the surface boundary; ; 3. Update 4. Update from (21); and go to step 2 if . 5. Increment Following, however, the outlined in Section III procedure com, bining (20) and (7) into and bringing it to (4) and collecting together the factors at factors at , yield

(22) (16) with updating formula for SIBCs E node makes the final representation as (23)

(17) (18)

The proposed procedure changes steps 3 and 4 as follows: , and update 1 Find

2 Update

from (23).

A. Error Analysis for Reflection From Lossy Dielectric

and

gives (19)

(20) Traditional approach is to shift H in space and E in time assigning

(21) in which case the following procedure can be implemented for N step FDTD with shifted H-node SIBCs.

A numerical experiment, similar to the one for real resistivity was done to validate the approach. Analytical solutions for a sinusoidal incident waveform modulated by the Heaviside unit step function and for a ramp-sinusoidal incident waveform are given in the Appendix for reference. The normalized relative error for both excitation cases have been computed for the new approach and for the simplified H-node shifted implementation. Fig. 5(a) shows the relative for computed for the boundary vicinity, and error Fig. 5(b) shows it in the log scale. It is clearly seen that the simplified implementation with shifting the H-node in space and time is giving from several times to several orders higher errors as compared to the error with proposed implementation. When the errors decrease a little; and the proposed scheme are is always many times more accurate. Errors for shown in Fig. 6. Next, a Gaussian-modulated pulse incident waveform was used to generate a wideband response of a SIBCs with and . The central frequency of the signal and ensure coverage of the entire spectrum in the bandwidth from DC to the wavelength down , with to 20 spatial step sizes, . The time and the 1D computational domain size delay are large enough to eliminate the aliasing and overlapping of the incident and the reflected field at the central , which serves as a control point and point where the fields were recorded, and their Fourier transforms

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Fig. 5. "

= 1:0, SIBCs error % for L

Fig. 6. "

= 4:2, SIBCs error %, for (a) magnitude and (b) L

, (a) linear and (b) log scale, with shifting H in space and time and with proposed solution.

, with shifting H in space and time and with proposed solution.

have been known in the literature [3]–[7], [10]–[12]. Surface impedance of a coated substrate for a normally incident wave is (24)

Fig. 7. Lossy dielectric body with permittivity " , permeability  and conductivity  , coated with a d-thick layer with permittivity " , permeability  and conductivity  is surrounded by a medium with corresponding parameters ",  and  .

taken to calculate the resulting reflection coefficient . Fig. 8(a)–(d) show the magnitude, phase and corresponding using the two methods. It is clearly errors of the calculated seen that the proposed solution is considerably more accurate as compared to the traditional with H-node shifts, drastically . improving the calculated phase of V. SIBCs WITH COATING Models of various levels of complexity for SIBCs with thin and thick lossy dielectric coatings on conducting substrates

where is the coating thickness, is the waveand length in the coating material, are the coating and substrate materials intrinsic impedances respectively. A sketch with a coated boundary surface and notation for the main electromagnetic properties of the materials is shown in Fig. 7. A thin layer approximation [10] (25) leads to

(26)

KOBIDZE: IMPLEMENTATION OF COLLOCATED SURFACE IMPEDANCE BOUNDARY CONDITIONS IN FDTD

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Fig. 8. Reflection coefficient 0(f) in the wide band calculated for lossy dielectric SIBCs with " = 4:2,  = 0:2 S=m using H-node shift and with proposed collocation: comparison of magnitude with exact solution (a), comparison of phase with exact solution (b), magnitude errors (c), and phase errors (d).

where

,

so that using the transform parameter becomes (27), shown at the bottom of the page. The inverse Laplace transform

(28)

gives the time-domain relationship of the tangent fields as Notice that when

the last equation leads to (12).

(27)

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The finite-difference representations, H-node shift assumpand Prony’s expansion (16) result in a retion cursive convolution algorithm as shown in [10]. In the algorithm and , two arrays of auxiliary coefficients are updated before solving for from , , , , , and . As an alternative and to H-node shift, one can use (4) and collocated values at the boundary. Following the outlined in Section III procedure utilize (1D) FDTD expression of the Faraday’s law (4)

(29)

and now only one array of auxiliary coefficients is used to recursively compute the convolution integrals as

(32) The resulting algorithm becomes as follows. 1. Initialize 2. Find intermediate quantity

The finite difference representation of the SIBCs fields and their derivatives at can be 3. Update

where a choice of guarantees the stability of secondorder in time marching scheme. The SIBCs differential equation is now discretized as

(30) where

(31a) (31b)

(31c)

(31d)

(31e)

(31f)

from

4. Update H at E-node 5. Update from (32). that is, in terms of arithmetic operations the complexity is similar to the “traditional” with space and time shifts, but in terms of memory the “traditional” method requires storage of twice as many auxiliary coefficients as compared to the proposed method. A. Error Analysis in 1D Again, the numerical experiments with chosen computational domain and 1D FDTD grid have been done to analyze the transient response of SIBCs on incident waves. First, the same as in the previous section tapered sinusoidal incident waveform has been used and the total fields in the wavelength vicinity of the boundary have been compared with the exact solution. The following parameters were used for the coating: , , , , and for , and a wide the underlying substrate at . Fig. 9 range of substrate conductivity compares the E and H errors for the “traditional” implementation with shifting H in space and in time against the errors with the proposed collocated approach. At this coating thickness there is no overwhelming advantage of any of the two methods if the whole range of substrate conductivity is considered. Fig. 10(a) shows the same errors with thinner coating ; the advantage of the collocated method becomes obvious for thinner coatings. The traditional algorithm becomes unstable if the coating is even thinner, e.g., it , as shown in Fig. 10(b). diverges when As the coating becomes thinner, the errors of the proposed solution with collocation become closer to the errors found in the previous section for the case with no coating. Fig. 10(b) in part

KOBIDZE: IMPLEMENTATION OF COLLOCATED SURFACE IMPEDANCE BOUNDARY CONDITIONS IN FDTD

=42

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= 0 01 S=m, d = 1x = 2 mm coating BC (a) magnitude and (b) L % errors for f = 7:5 GHz with H-node time and space shift

Fig. 9. " : , : and with proposed solution.

= 4:2,  = 0:01 S=m, coating BC L % errors with H time and space shift and with collocated solution: (a) d = 0:21x = 0:4 mm, (b) = 0 11 = 0:2 mm.

Fig. 10. " d : x

representing the errors for the collocated implemented soluerrors shown in Fig. 5(b). The thinner tions is very close to is the coating the higher is the minimal substrate conductivity that can be modeled with the traditional implementation. The reflection of the Gaussian modulated pulse from , , , the coated substrate and has also been studied. The same waveform parameters of the incident wave and the same computational domain as in the previous section were used to extract the FFT of the incident and reflected fields at the center of the domain. An auxiliary was also calculated with tangent raanalytical tional expression (25) to isolate the errors due to tangent’s approximation. Fig. 11(a)–(d) show the magnitude, phase and using FFT, the corresponding errors of the calculated way it was discussed in Section IV. It is seen that for this case the proposed solution is more accurate as compared to the traditional with H-node shifts VI. CONCLUSION Surface Impedance Boundary Conditions for FDTD have been implemented with collocated H and E components. Thorough transient error analysis has been done for the reflected

field in 1D when the exact solution is available for the whole possible range of modeled material conductivity. Error analysis using FFT for the magnitude and phase of the calculated reflection coefficient for the wideband pulse has presented as well. The resulting numerical errors have been compared with the errors of traditional SIBCs implementation when the tangential magnetic fields on the boundary are approximated by shifting the neighboring FDTD magnetic field component in space and time. It was shown that the approach with collocated fields is considerably more accurate for both resistive and dispersive lossy dielectric SIBCs, in both magnitude and phase. Unlike the traditional approach, it is stable for all values of modeled material conductivity. The collocated fields approach was also applied to SIBCs with coating, and the transient and reflection coefficient errors have been studied. It was shown that in contrast to the traditional implementation, it is stable for arbitrarily thin coating and for any substrate conductivity, and is more computationally effective since it requires storage of only half of the auxiliary coefficients when computing the convolution integrals. An expression for efficient implementation of the inverse Laplace transform discrete convolution integrals for the lossy surface impedance via Kummer confluent hypergeometric function is derived.

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 58, NO. 7, JULY 2010

0(f ) for coating on  = 0:2 S=m using H shifts and with collocation: (a) magnitude, (b) phase, (c) magnitude errors and (d) phase error.

APPENDIX EXACT EXPRESSIONS FOR THE REFLECTED FIELDS GENERATED BY INCIDENT SINUSOIDAL WAVEFORMS: I) MODULATED BY HEAVISIDE STEP FUNCTION AND II) RAMP TAPERED Let a TEM plane wave propagate in the negative x-direction and the incident electric field waveform at the boundary be

For example, when

and the inverse Laplace transform gives

(33) is the Heaviside unit step function. The reflected where field is shown in (34) at the bottom of the page, where is the inverse Laplace transform of the reflection coefficient

resulting in

(35)

(34)

KOBIDZE: IMPLEMENTATION OF COLLOCATED SURFACE IMPEDANCE BOUNDARY CONDITIONS IN FDTD

(36) For the time

-period ramp tapered sinusoidal excitation (ramp ) (37) otherwise.

(38)

The reflected field is shown as

(39) REFERENCES [1] J. G. Maloney and G. S. Smith, “The use of surface impedance concepts in the finite-difference time-domain method,” IEEE Trans. Antennas Propag., vol. 40, pp. 38–48, Jan. 1992. [2] S. Kellali, B. Jecko, and A. Reineix, “Implementation of a surface impedance formalism at oblique incidence in FDTD method,” IEEE Trans. Electrom. Compat., vol. 35, no. 3, pp. 347–356, Aug. 1993. [3] K. S. Oh and J. E. Schutt-Aine, “An efficient implementation of surface impedance boundary conditions for the finite-difference time-domain method,” IEEE Trans. Antennas Propag., vol. 43, pp. 660–666, Jul. 1995.

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[4] C. F. Lee, R. T. Shin, and J. A. Kong, “Time domain modeling of the impedance boundary conditions,” IEEE Trans. Microw. Theory Tech., vol. 40, pp. 1847–1850, Sep. 1992. [5] B. Z. Wang, “Time-domain modeling of the impedance boundary condition for an oblique incident parallel-polarization plane wave,” Microw. Opt. Technol. Lett., vol. 7, pp. 19–22, 1994. [6] B. Z. Wang, “Time-domain modeling of the impedance boundary condition for an oblique incident perpendicular-polarization plane wave,” Microw. Opt. Technol. Lett., vol. 7, pp. 355–359, 1994. [7] C. W. Penney, R. J. Luebbers, and J. W. Schuster, “Scattering from coated targets using a frequency-dependent, surface impedance boundary condition in FDTD,” IEEE Trans. Antennas Propag., vol. 44, pp. 343–443, Apr. 1996. [8] A. Taflove and S. Hagness, Computational Electrodynamics, the FiniteDifference Time-Domain Method, New York: Artech House M. Young, the Techincal Writers Handbook. Mill Valley, CA: University Science, 1989. [9] F. B. Hildebrand, Introduction to Numerical Analysis. New York: McGraw-Hill, 1956. [10] M. K. Kärkkäinen, “FDTD surface impedance model for coated conductors,” IEEE Trans. Electrom. Compat., vol. 46, no. 2, pp. 222–233, May 2004. [11] M. K. Kärkkäinen, “FDTD surface impedance models for electrically thick dispersive material coatings,” Radio Sci., vol. 38, no. 3, pp. 16–1, Jun. 2003. [12] M. K. Kärkkäinen, “FDTD model of electrically thick frequency-dispersive coatings on metals and semiconductors based on surface impedance boundary conditions,” IEEE Trans. Antennas Propag., vol. 53, pp. 1174–1186, Mar. 2005. Gregory Kobidze (SM’04) received the Ph.D. degree in technical sciences from Moscow Bauman State Technical University, Moscow, Russia, in 1992, and the M.S. degree in applied math and the Ph.D. degree in electrical engineering from Iowa State University, Ames Iowa, in 1998. From 1998 to 2001, he worked as a Visiting Research Scientist with the High-Frequency Electromagnetics Group at the Advanced Technology R&D Center, Mitsubishi Electric Corporation, Japan. In August 2001, he was a Research Associate with the Electromagnetics Group in the Department of Electrical and Computer Engineering, Iowa State University, and in August 2002, he moved to the Department of Electrical and Computer Engineering at Michigan State University. He was a Sr. Development Engineer with ANSYS, and a Developer at EM Performance. His research interests are in theoretical and computational electromagnetics.

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A Reconfigurable PIFA Using a Switchable PIN-Diode and a Fine-Tuning Varactor for USPCS/WCDMA/m-WiMAX/WLAN Jong-Hyuk Lim, Gyu-Tae Back, Young-Il Ko, Chang-Wook Song, and Tae-Yeoul Yun, Member, IEEE

Abstract—A reconfigurable planar inverted-F antenna using a switchable PIN-diode and a fine-tuning varactor is presented for mobile communication applications. Selection of operating modes is achieved by switching the PIN-diode between radiators and tuning the varactor on an antenna’s shorting line. Mode I, with the PIN-diode off and tuning the varactor, operates for USPCS (1.85–1.99 GHz), WCDMA (1.92–2.18 GHz), and WLAN (5.15–5.825 GHz). As a result, the varactor used to achieve frequency fine-tuning does not need a DC bias circuit and can expand the bandwidth without increasing the physical size. Mode II, with the PIN diode on and the fixed 0-V varactor, operates for USPCS and m-WiMAX (3.4–3.6 GHz). To optimize the antenna structure, a parametric analysis is performed by sweeping the length and width of the radiators. Furthermore, equivalent models of a PIN diode and a varactor are presented for accurate prediction of antenna performances which are also analyzed by varying diode parameters. All simulated results are confirmed with measured data. The peak gains show 2.84, 2.81, 1.25, and 1.49 dBi at USPCS, WCDMA, m-WiMAX, and WLAN, respectively. Index Terms—Planar inverted-F antenna (PIFA), PIN-diode, reconfigurable, switching, tuning, varactor.

I. INTRODUCTION UE to rapid growth in mobile handset markets and customers’ needs, it is necessary to merge diverse wireless communication systems such as United States personal communications services (USPCS), wideband code division multiple access (WCDMA), mobile worldwide interoperability for microwave access (m-WiMAX), and wireless local area network (WLAN). In order to merge these service bands, the design of an antenna is needed and must be either of the multiband or frequency reconfigurable type. The frequency reconfigurable antenna offers many advantages such as compact size, similar radiation pattern, and proper gain for all desired frequency-bands, compared to the multiband antenna. For this reason, many antenna types have recently been developed in reconfigurable systems [1]–[5]. Design of internal antennas is very important for the miniaturization and aesthetical appearance of the mobile handset. Currently, the planar inverted-F antenna (PIFA) is generally used for internal antennas because of its easy fabrication, low profile, low

D

Manuscript received March 16, 2009; revised December 14, 2009; accepted January 31, 2010. Date of publication April 22, 2010; date of current version July 08, 2010. This work was supported by the Technology Innovation Program (or Industrial Strategic technology development program, 00007812) funded by the Ministry of Knowledge Economy (MKE, Korea). The authors are with the Department of Electrical and Computer Engineering, Hanyang University, Seoul 133-791, Korea (e-mail: [email protected]). Digital Object Identifier 10.1109/TAP.2010.2048849

cost, and reduction of special absorption rate (SAR) [6]. In addition, the PIFA offers small size and easy multiband operations by inserting the slot and slit on the radiator [6], [7]. However, the PIFA has a narrow bandwidth. To overcome this drawback, a reconfigurable PIFA was presented in [8] using a PIN-diode and discrete passive components. However, this antenna resulted in a size increase due to an added radiating element with a tuning circuit. In this paper, we propose a reconfigurable PIFA using a varactor and a PIN-diode. By varying capacitance of the varactor on an impedance matching short-line, frequency fine-tuning is easily achieved without increase of the antenna size or the addition of a bias circuit. Also, based on the PIN-diode on and off status between radiating elements, the antenna is able to select a very separate frequency band. The proposed antenna covers four service bands: USPCS (1.85–1.99 GHz), WCDMA (1.92–2.18 GHz), m-WiMAX (3.4–3.6 GHz), and WLAN (5.15–5.825 GHz). In Section II, a new reconfigurable PIFA design is presented with a parametric analysis and surface current distributions. Section III shows equivalent circuit models for a PIN-diode and a varactor. Section IV describes simulated and measured impedance characteristics, gains, efficiencies, and radiation patterns. Finally, a conclusion is given in Section V. II. DESIGN OF RECONFIGURABLE PIFA A. Antenna Design As shown in Fig. 1, the proposed reconfigurable PIFA consists of main and additional radiating elements on an FR4 substrate with a relative permittivity of 4.4, a feeding conductor, a folded part, a short line, a PIN-diode [9], and a varactor [10]. The size of the ground plane has the dimension of 30 70 mm for a typical mobile handset. A top view of the proposed antenna is shown in Fig. 1(b). The switching PIN-diode is located between the main and additional radiators as a conducting bridge. Fig. 1(c) shows the right side view including the of the main radiator for the antenna size defolded part crease and the short line for the impedance matching. The tunable varactor is placed on the short line. Fig. 1(d) depicts the front view of the proposed antenna. When the PIN-diode is off (0 V), the antenna operates at the USPCS and WLAN bands. On the contrary, when the PIN-diode is on (1 V), the antenna operates in the USPCS and m-WiMAX bands because the surface current path of the antenna is lengthened into the additional radiating element

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Fig. 1. Geometry of a proposed PIFA of unit in mm: (a) 3-dimensional view, (b) top view, (c) side view, and (d) front view.

through the PIN-diode. The varactor, which operates between approximately 5 pF at 4 V and 52 pF at 0 V, is used for fine frequency tuning between USPCS and WCDMA because the inductance of the shorting line is reduced by the capacitance of the varactor. Thus, frequency tuning can be obtained without change of antenna structure. To design and optimize the proposed antenna, many parameters were considered. First, it is important to determine the overall size of the antenna at a resonant frequency, which is dependent on the width and length of the radiator. As a result, quarter-wavelengths of the proposed PIFA are chosen as approximately 39, 21.4, and 13.6 mm at USPCS (1.92 GHz), m-WiMAX (3.5 GHz), and WLAN (5.5 GHz), respectively. In such a quarter-wavelength structure, 50 impedance matching of the antenna can easily be obtained by a proper choice of the and location of the short line. The antenna was feed spacing simulated with Microwave Studio of the CST [11]. B. Parametric Analysis of Radiating Elements In order to optimize the physical parameters of the antenna, the parametric analysis was performed, as shown in Fig. 2. First, at the lowest frequency band (USPCS), parameters , and are analyzed. According to an increase in , the resonant frequency shifts downward without change of the highest band (WLAN), as shown in Fig. 2(a). It can be seen that the optimized is 12.5 mm in the USPCS band. By increasing not value of

but also , the resonant frequency moves downward, only and are 5 as shown in Fig. 2(b). The optimized values of and 5.5 mm, respectively. Thus, the overall size can be reduced by the folded radiating element, . Next, at the highest frequency band (WLAN), parameters of and are analyzed. By increasing of the radiating element, the resonant frequency shifts downward, as shown in is 2 Fig. 2(c). It can be seen that the optimized value of mm for WLAN. By increasing , the resonant frequency shifts downward for the lower frequency, as shown Fig. 2(d). It is is 4.5 mm. shown that the optimized value of Other parameters were similarly optimized. As a result, the optimized values for the PIFA design are described in Table I. C. Surface Current Distributions To explain operations of the reconfigurable PIFA, the excited surface current distributions on the radiating elements were studied. Fig. 3 shows CST simulation results of the PIFA surface current distributions at 1.9/2.0, 3.5, and 5.5 GHz, respectively. As shown in Fig. 3(a), the surface current flows from the feed conductor to the end of the folded patch, in which the path length is close to the quarter-wavelength of 1.92 and 2.0 GHz for the USPCS and WCDMA bands. The path length, in this paper, was chosen as the inside surface current path. Fig. 3(b) shows that the surface current distributions for a PIN-diode on-status flow from the feed

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Fig. 2. Parametric analysis of radiating elements varying: (a)

W , (b) L

and

L , (c) W , and (d) L .

TABLE I OPTIMIZED PARAMETER VALUES FOR THE PIFA DESIGN

conductor to the end of the additional radiator, in which the path length is close to the quarter-wavelength of 3.5 GHz for the m-WiMAX band. Finally, Fig. 3(c) shows the surface current distributions for a PIN-diode off-status. Then the antenna operates at the highest frequency band around 5.5 GHz for the WLAN band. It can be observed that the surface current path in this case is close to the quarter-wavelength at 5.5 GHz.

Fig. 3. Simulated PIFA surface current distributions at (a) 1.9 GHz (USPCS) and 2.0 GHz (WCDMA) (b) 3.5 GHz (m-WiMAX), and (c) 5.5 GHz (WLAN).

Fig. 4. Equivalent circuit for a PIN-diode.

III. EQUIVALENT CIRCUIT MODELING OF DIODES In order to accurately predict the reconfigurability of the proposed antenna, it is essential to extract the diode’s characteristics. Therefore, we performed an equivalent-circuit modeling of

the diodes based on the through-delay-line de-embedding to obtain accurate measurement data. As shown in Fig. 4, we adopted a simplified RLC equivalent circuit for a PIN-diode without the

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Fig. 5. Simulated and measured S-parameters for the PIN-diode at: (a) 0 V (off), (b) 1 V (on).

Fig. 6. Equivalent circuit for a varactor.

surface mounting effect because the CST simulation tool can’t apply a complex RLC model. It consists of a series parasitic inand an intrinsic capacitance in parallel with an ductance . Parameter values of the equivalent-cirintrinsic resistance cuit model are calculated by Agilent Advanced Design System (ADS). As a result, when the PIN-diode is off (0 V), the values , and are 3 k , 0.45 nH, and 0.08 pF, respectively. of On the contrary, when the PIN-diode is on (1 V), the values of , and are 3.5 , 0.45 nH, respectively. Fig. 5 shows simulated and measured S-parameters for a micro- semi MPP4203 PIN-diode [9] from 1 to 6 GHz. When the PIN-diode is off (0 V), it has an isolation of 11.32 dB at 5.5 GHz due to the small total capacitance (0.08 pF). On the contrary, when the PIN-diode is on (1 V), it has an insertion loss of 0.66 dB at 3.5 GHz due to the small resistance (3.5 ). The insertion loss caused by intrinsic resistance diminished an antenna gain. Fig. 6 shows an adopted equivalent circuit for the varactor, which omits a surface mounting effect for the same reason as in ,a the PIN-diode case. It consists of a parasitic inductance , and a variable capacitance in series. variable resistance

Fig. 7. Simulated and measured S-parameters for the varactor biased at: (a) 0 V, (b) 2 V, and (c) 4 V. TABLE II PARAMETER VALUES OF EQUIVALENT CIRCUITS FOR DIODES

Fig. 7 validates the equivalent-circuit model for an Infineon BBY59 varactor [10] with measured data from 1 to 6 GHz.

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Fig. 8. Configuration of measurement.

Fig. 10. Simulated gain and efficiency variations depending on the PIN-diode capacitance for the mode I; (a) gain, (b) efficiency.

When the varactor reverse voltage is 0 V, the maximum capacitance is 52.15 pF. On the contrary, when the varactor is biased at 2 and 4 V, the capacitances are 14.96 and 5.37 pF, respectively. These capacitances will compensate the inductance of the short line and change an operating frequency. changes from 0 to 4 V, it has an insertion When the varactor loss of 0.18 dB around 2 GHz. As shown in Figs. 5 and 7, the simulated and measured results for both diodes agree well. Finally, the parameter values of the equivalent circuits for the PIN-diode and the varactor are listed in Table II. The simulated and measured results for the proposed antenna using PIN- and varactor- diodes will be presented in the following sections.

Fig. 9. Simulated and measured S for the proposed PIFA when: (a) PIN is off, (b) PIN is on, and (c) PIN is off and a varactor with 0 and 4 V.

IV. ANTENNA SIMULATION AND MEASUREMENT Fig. 8 shows the DC bias setup of the proposed antenna with PIN- and varactor- diodes. The antenna is fed through the bias tee which supplies the RF signal and the DC bias for the varactor. For DC biasing the PIN-diode without leakage of RF signal to the DC bias line, the RF choke inductor (12 nH), which has a self-resonant frequency around 3.5 GHz and a peak impedance at that frequency, was attached on the additional of the PIN-diode for radiator. The forward bias voltage frequency switching was controlled by the DC bias between 0 and 1 V. The PIN-diode maximally consumes a forward bias current of 16 mA at 1 V. The varactor for the frequency fine-tuning was controlled by the DC bias between 0 and 4 V. of the proFig. 9 shows the simulated and measured posed PIFA for the different band operation depending on the

LIM et al.: A RECONFIGURABLE PIFA USING A SWITCHABLE PIN-DIODE AND A FINE-TUNING VARACTOR

Fig. 11. Simulated gain and efficiency variations depending on the varactor capacitance for the mode I; (a) gain, and (b) efficiency.

DC biases of the PIN-diode and varactor. Both the simulated and measured data satisfy the return loss of more than 6 dB for all bands. As shown in Fig. 9(a), when the PIN-diode is off, the antenna operates at the USPCS and WLAN. On the contrary, when the PIN-diode is on, the antenna operation shifts from WLAN to m-WiMAX without a change of the lower frequency band of the USPCS, as shown in Fig. 9(b). The simulated and measured with varying varactor bias conditions are shown in Fig. 9(c). When the varactor is biased at 4 V, the lower band just moves toward WCDMA slightly. As a result, the proposed PIFA can cover four bands: USPCS (1.85–1.99 GHz), WCDMA (1.92–2.18 GHz), m-WiMAX (3.4–3.6 GHz), and WLAN (5.15–5.35 GHz and 5.725–5.825 GHz). The simulation and measurement results for input impedance matching showed good agreement. Fig. 10 shows simulated antenna gains and efficiencies by varying the PIN-diode capacitance when the antenna operates in mode I (PIN-diode off). When the capacitance parameter of the PIN-diode increases from 0.08 to 0.3 pF, the peak frequencies of the gain and efficiency decrease from 5.5 to 4.5 GHz. For the lower bands (USPCS and WCDMA) near 2 GHz, we had similar results. This means that the off-state capacitance affects antenna performances very much and should be small. In addition, when the varactor capacitance decreases, controlled by the bias from 0 to 4 V for fine tuning of the operating

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Fig. 12. Simulated gain and efficiency variations depending on the PIN-diode intrinsic resistance for the mode II; (a) gain, (b) efficiency.

Fig. 13. Simulated and measured radiation efficiencies for each band.

band, the peak frequencies of the gain and efficiency are shifted from USPCS to WCDMA band, as shown in Fig. 11(a) and (b). On the contrary, when the antenna operates in mode II (PINdiode on), the antenna gain and efficiency are also simulated with variations of the PIN-diode’s resistance in Fig. 12. The antenna gains and efficiencies decreases when the resistance of the PIN-diode increases from 0 (ideal) to 3.5 . It should be noted that variations of the parasitic inductance of both diodes didn’t affect antenna performances.

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Fig. 14. Simulated (dotted line) and measured (solid line) co-polarization radiation patterns in the xz-, xy-, and yz-planes, respectively at: (a) 1.95 GHz (USPCS, WCDMA), (b) 3.5 GHz (m-WiMAX), and (c) 5.5 GHz (WLAN).

Fig. 13 shows simulated and measured radiation efficiencies for the mode I and II. When the PIN-diode is off, the radiation efficiencies have near 90%. On the other hand, when the PIN-diode is on, the radiation efficiency abruptly decreases to 63% for the m-WiMAX (3.35–3.69 GHz) band due to the resistance effect of the PIN-diode but remains 93% for the USPCS (1.85–1.99 GHz) band due to no radiation through the Pin-diode for this band. The simulated and measured co-polarization radiation patterns of the proposed PIFA are plotted at 1.95, 3.5, and 5.5 GHz according to the cutting plane in Fig. 14. The radiation patterns of the proposed PIFA were measured in an anechoic shielded chamber. As shown in Fig. 14(a), the radiation pattern in the xy-plane for the lower frequency band showed dipole-like characteristics and the radiation pattern in the yz-plane has an omni-directional characteristic because the surface current excited in the x-direction is dominant, as shown in Fig. 3(a). As shown in Fig. 14(b) and (c), however, the radiation patterns in the xy-plane for higher frequencies have nulls in several directions since the antenna has a dominant operating current to the y-direction and undesired weak surface currents to other

directions, as shown in Fig. 3(b) and (c). The measured radiation antenna peak gains are 2.84 and 2.81 dBi at the USPCS and WCDMA bands, respectively. In the diode-on case for the m-WiMAX, the peak gain is 1.49 dBi. On the contrary, when the diode is off for the WLAN, the peak gain is 1.25 dBi. The antenna gains for the m-WiMAX and WLAN bands are lower than the lowest bands because the weak surface currents of other directions contribute to additional radiation in cross-polarized directions. All the calculated and measured gain radiation patterns showed good agreement. Finally, the measured results are summarized in Table III. V. CONCLUSION The reconfigurable PIFA design with a PIN-diode and a tunable varactor covering the USPCS, WCDMA, m-WiMAX, and WLAN bands has been demonstrated with analysis and measurement. This paper also presented equivalent-circuit models of the PIN-diode and varactor. The proposed antenna was able to select a very separate frequency band and also achieved fine-frequency tuning without increasing the physical size. Overall, the

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TABLE III PERFORMANCE SUMMARY OF THE PROPOSED RECONFIGURABLE PIFA

simulated and measured results showed good agreement. Therefore, the proposed reconfigurable PIFA can be useful for an upcoming generation of mobile systems. REFERENCES [1] J. T. Aberle, S. H. Oh, D. T. Auckland, and S. D. Rogers, “Reconfigurable antennas for portable wireless devices,” IEEE Antennas Propag. Mag., vol. 45, no. 6, pp. 148–154, Dec. 2003. [2] G. H. Huff, J. Feng, S. Zhang, and J. T. Bernhard, “A novel radiation pattern and frequency reconfigurable single turn square spiral microstrip antenna,” IEEE Microw. Wireless Compon. Lett., vol. 13, no. 2, pp. 54–57, Feb. 2003. [3] C. J. Panagamuwa, A. Chauraya, and J. C. Vardaxoglou, “Frequency and beam reconfigurable antenna using photoconducting switches,” IEEE Trans. Antennas Propag., vol. 54, no. 2, pp. 449–454, Feb. 2006. [4] A. C. K. Mak, C. R. Rowell, R. D. Murch, and C. L. Mak, “Reconfigurable multiband antenna designs for wireless communication devices,” IEEE Antennas Propag. Mag., vol. 55, no. 7, pp. 1919–1928, July 2007. [5] N. Behdad and K. Sarabandi, “Dual-band reconfigurable antenna with a very wide tunability range,” IEEE Trans. Antennas Propag., vol. 54, no. 2, pp. 409–416, Feb. 2006. [6] Y. J. Cho, S. H. Hwang, and S. O. Park, “A dual-band internal antenna with a parasitic patch for mobile handsets and the consideration of the handset case and battery,” IEEE Antennas Wireless Propag. Lett., vol. 4, pp. 429–432, 2005. [7] P. Ciais, R. Staraj, G. Kossiavas, and C. Luxey, “Design of an internal quad-band antenna for mobile phones,” IEEE Microw. Wireless Compon. Lett., vol. 14, no. 4, pp. 148–150, Apr. 2004. [8] M. Komulainen, M. Berg, H. Jantunen, E. T. Salonen, and C. Free, “A frequency tuning method for a planar inverted-F antenna,” IEEE Trans. Antennas Propag., vol. 56, no. 4, pp. 944–955, Apr. 2008. [9] Data Sheet of MPP4203 PIN Diodes, Microsemi, Application Note [Online]. Available: http://www.microsemi.com [10] Data Sheet of BBY59, Infineon Technologies, Application Note [Online]. Available: http://www.infineon.com [11] CST Corporation, CST Microwave Studio (MWS) ver.2007 [Online]. Available: http://www.cst.com

Jong-Hyuk Lim received the B.S. degree from Hongik University, Korea, in 2004 and the M.S. degree from Hanyang University, Seoul, Korea, in 2006, where he is currently working toward the Ph.D. degree. His research interests include antenna design, microwave circuit design, and wireless communication systems.

Gyu-Tae Back received the B.Sc. degree in electrical engineering from Gyeongju University, Korea, in February 2004. He is currently working toward the M.S. degree at University of Hanyang, Seoul, Korea. His research interests include reconfigurable/multi input multi output (MIMO) antennas and the design of RF integrated circuits (RFICs).

Young-Il Ko received the B.Sc. degree in communication engineering from Daejin University, Korea, in 2008. He is currently working toward M.S. degree at the University of Hanyang, Seoul, Korea. His current research interests include microstrip and reconfigurable antenna design.

Chang-Wook Song received the B.Sc. degree in information and communication engineering from Dongeui University, Busan, Korea, in February 2007. He is currently working toward the M.S. degree at the University of Hanyang, Seoul, Korea. His research interests are reconfigurable/multi input multi output (MIMO) antennas and the design of RF integrated circuits (RFICs).

Tae-Yeoul Yun received the B.S.E.E. degree from the Kyungpook National University, Korea, in 1987, the M.S.E.E. degree from KAIST, Korea, in 1989, and the Ph.D. degree from Texas A&M University, College Station, in May 2001. From 1989 to 1996, he worked for an optical telecommunication system group, ETRI, Korea, where he developed 2.5-Gb/s and 10-Gb/s systems. From 2001 to 2003, he was an MMIC Designer at Triquint Semiconductor, Dallas, TX. Since March 2003, he has been a Professor at Hanyang University, Korea. He has published more than 100 technical papers. His research interests are RFICs, MMICs, antennas, and wireless communication systems.

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High-Gain Dual-Loop Antennas for MIMO Access Points in the 2.4/5.2/5.8 GHz Bands Saou-Wen Su, Member, IEEE

Abstract—A high-gain, three-antenna system suitable to be concealed inside wireless access points for multiple-input multiple-output (MIMO) applications in the WLAN 2.4/5.2/5.8 GHz bands is presented. The MIMO antenna system is composed of three dual-loop antennas occupying a moderate size of 10 20 40 mm3 . Each dual-loop antenna further comprises a large outer loop and a small inner loop, both operating at 1.0-wavelength resonant mode and sharing common antenna feeding and grounding portions. In addition, the antennas are placed in a sequential, rotating arrangement on a ground plane with an equal inclination angle of 120 to form a symmetrical multiple-antenna structure. Good impedance matching for outer and inner loops over the 2.4 and 5.2/5.8 GHz bands can easily be achieved by tuning the widths of feeding and grounding portions and a small gap therein between. The results show that well port isolation can be obtained together with high-gain, directional radiation characteristics. Calculated envelope correlation is less than 0.007 within the bands of interest. Details of a design prototype are described and discussed in the paper. Index Terms—Antennas, internal access-point (AP) antennas, loop antennas, multiple-input multiple-output (MIMO) antennas, WLAN antennas.

I. INTRODUCTION ANY “11n” or “pre-n” [1] wireless applications are readily accessible on the open market. Most of the 11n products have adopted multiple-input multiple-output (MIMO) technology, in which multiple transmit and/or receive antennas are used in mobile devices [2]–[9] to increase data throughput without additional spectrum and at the same time, to make use of multi-path propagation to improve signal quality and reliability. For access-point (AP) or router applications, external dipole and monopole antennas are widely used, especially high-gain, omnidirectional dipole arrays [10], [11] and collinear antennas [12]–[16] are the most popular. However, there has been strong demand for internal AP antennas [17], [18] simply from an esthetic point of view that external antennas are not very pleasing to the end user. A three-antenna system with a wide operating bandwidth of 2400–5850 MHz is demonstrated in [17] as internal AP antennas. In [18], a low-profile, six-antenna system is proposed to provide concurrent WLAN operation in the 2.4 and 5 GHz bands. These

M

Manuscript received July 23, 2009; revised November 20, 2009; accepted January 23, 2010. Date of publication April 26, 2010; date of current version July 08, 2010. The author is with the Network Access Strategic Business Unit, Lite-On Technology Corp., Taipei County 23585, Taiwan (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/TAP.2010.2048871

designs mainly utilize monopole antennas mounted above an antenna ground such that conical radiation patterns are obtained. If high-gain and directional radiation are required for AP applications, patch or microstrip antennas are usually employed [19]–[21]. This kind of antenna is known to operate as a half-wavelength, resonant structure [22]. Despite the fact that some size reduction techniques for antennas have been reported [23], [24], the patch antenna can generate fringing fields at the edges (see [22, Figs. 9–21]). The fringing fields of the patch antenna have a devastating effect on the mutual coupling between antennas when multiple patch antennas are closely placed on a ground plane in MIMO devices. Due to the constraints of the conventional patch/microstrip-antenna size and fringing fields thereof, this kind of antenna may not easily meet the requirements for internal AP antennas with high-gain directional radiation properties. To mitigate large coupling between antennas that operate in the same frequency band and also achieve high-gain and directional radiation patterns, a loop antenna can be of a very promising solution and embedded within the casing of an AP as internal MIMO antennas. A self-balanced, one-wavelength loop antenna is particularly suited because it is capable of exciting less surface currents on the system or antenna ground plane [25]. In this case, the ground plane behaves more like a reflector than a part of the radiator, and accordingly, directional radiation with enhanced antenna gain in the axial direction is achieved. Furthermore, the isolation characteristics between multiple antennas are learnt to be largely related to the surface-current distributions as have been analyzed in [4], [26]. Thus, it can be expected that the multiple loop antennas are able to obtain less isolation between antennas. In addition, the structure of the loop antenna are more likely to provide a closed signal-to-ground form of excited surface currents on the antenna, which may leads to smaller fringing fields around the loop. In this paper, a novel, high-gain, dual-loop antenna design applied to a three-antenna system for MIMO AP applications is presented. The metal shape of the dual-loop antenna is configured to be affixed to the surfaces of a foam base occupying , which allows the ana moderate size of tenna to be surface-mountable on the ground plane and to be concealed in the casing of the AP at the height of 10 mm. The proposed design comprises two loop antennas of uniform width, namely a large 2.4-GHz outer loop and a small 5-GHz inner loop, both attached onto the rectangular foam base and operating at 1.0-wavelength resonant mode. Both loops also share common antenna feeding and grounding portions. The three antennas are put in a sequential, rotating arrangement on the ground plane with an equal inclination angle of 120 to form a symmetrical MIMO-antenna structure. This configuration is

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Fig. 2. Detailed dimensions of the dual-loop antenna unbent into a planar structure.

Fig. 1. (a) Configuration of the proposed, high-gain, dual-loop antennas for MIMO access-point applications. (b) Top view of the proposed, three-antenna MIMO system. (c) Photograph of a design prototype.

not only for ease of studying and analysis but also allows each dual-loop antenna to have equal, 3-D space coverage. Furthermore, using three MIMO antennas for configuration up to 3 3 ) are more cost effective and practical (representing than the four-MIMO-antenna system reaching up to 3 4 configuration (see [27, Fig. 7]). By adjusting proper dimensions of the two loop antennas, especially the widths of feeding and grounding portions and a small gap therein between, good excitation of the three resonant modes (two 1.0-wavelength loop modes and one 1.5-wavelength loop mode) to cover the 2.4 GHz (2400–2484 MHz) and 5.2 GHz (5150–5350 MHz)/5.8 GHz (5725–5825 MHz) WLAN bands can be attained. The proposed three-MIMO-antenna system can easily be constructed from stamping flat metal plates at low cost with two sets of molds for tooling. A design example for applications in MIMO APs is demonstrated. Details of the design consideration are described and discussed. Radiation characteristics and surface current distributions of the antenna are also analyzed. II. ANTENNA DESIGN CONSIDERATION Fig. 1(a) shows the configuration of the three dual-loop antennas mounted on an antenna ground plane in the shape of a regular dodecagon (polygon with 12 sides) for MIMO AP applications. Although the ground plane is dodecagonal in the design prototype, regular polygonal or circular ground planes

are feasible too as long as the multiple antennas can be set on the ground symmetrically. Each of the three antennas (denoted as antenna 1, 2, and 3) occupies a space with the dimensions and is equally spaced along the perimeter of the ground plane. The antenna is situated next to another with the feeding portion facing the grounding portion of the folaway from lowing one. All the antennas are located 15 mm the vertex of the ground with equal inclination angles (formed by two adjacent vertices and the center) of 120 , and the center to the vertex is 60 mm long. In this case, the diagonal length of the ground plane studied here is 120 mm long, about one wavelength of the central frequency in the 2.4 GHz band at 2442 MHz. The separation distance between two adjacent antennas is 43 mm, which is only about half a distance of 80 mm between two parallel to achieve port isolation below 2.4-GHz dipole antennas (minimal space of 0.65-wavelength required between two parallel dipoles [28]). Also for high- gain dipole arrays [10], [11], the antenna height is much larger than 100 mm, which is 10 times more than that of the proposed antenna. These characteristics show that the proposed design is a better candidate for AP applications, compared to external dipole (or monopole) antennas. A comprehensible drawing of the design described above is given in Fig. 1(b). Clearly, the antennas are in a sequential, rotating arrangement and of a symmetrical structure. A photograph of the prototype, made of a 0.3-mm-thick copper-nickel-zinc alloy, is shown in Fig. 1(c), too, for better understanding. In general, the prototype can easily be constructed from stamping flat metal plates at low cost with two sets of molds for tooling. The proposed dual-band antenna further comprises two loop antennas: a large 2.4-GHz outer loop and a small 5-GHz inner loop. The near optimal dimensions for both loop antennas are detailed in Fig. 2. The outer loop, which dominates the overall size of the antenna, has width 20 mm and length 45 mm and encompasses the inner loop of size 15 . Both loops are of uniform width of 1 mm and share common and feeding and ground portions, which are of width 5 mm of 1 mm therein between. The length of have a small gap the grounding portion is chosen to be 10 mm; that’s, the antenna height above the ground plane is fixed at 10 mm, which is a fair limit defined for practical applications to internal AP antennas. The total length of the outer loop excluding the feeding and ground portions is close to 1 wavelength of the frequency at 2442 MHz, and that of the inner loop is about 1 wavelength, too,

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Fig. 3. Measured S-parameters for the antennas of a constructed prototype: (a) reflection coefficients (S , S , S for antenna 1, 2, 3); (b) isolation (S , S , S ) between two antennas.

at 5490 MHz. Following the bending lines shown in Fig. 2, the proposed antenna is bent into a compact structure and attached onto a foam base of a moderate size [also see Fig. 1(c)]. The bending can also slightly increase the separation distance between two adjacent antennas, which has a beneficial effect on reducing the isolation between the antennas. To feed the dual-loop antennas, three 50- mini-coaxial cables with I-PEX connectors are utilized. The inner conductor of the coaxial cable is connected to point A on the feeding portion; the outer braided shielding is soldered to the area opposite to point A on the antenna ground plane. The preferred dimensions of the dual-loop antenna were attained by means of parametric studies with the aid of the simulation program, Ansoft HFSS [29], and the task was long and laborious before reaching the near optimal antenna size. For simplicity, the 2.4 GHz outer loop was first designed; then the 5 GHz inner loop was added later. Through the process of simulation studies (not shown for brevity), few things are noted here. First, the occurrence of the 2.4 GHz band is mainly controlled by the 1.0-wavelength mode of the outer loop. With an increase in the length , both 1.0- and 2.0-wavelength modes are decreased, and the input matching for the 1.0-wavelength mode is affected more. On the other hand, the 5 GHz operation is deterhas more effects on mined by the inner loop, whose length the matching than operating frequencies, which remain nearly unchanged in this case. Notice that the 0.5-wavelength mode of the inner loop is found to affect the 2.4 GHz impedance bandwidth more whereas the 2.0-wavelength mode of the outer loop influences the 5.2 GHz band less. Second, the width of the

Fig. 4. Simulated S-parameters for the antennas of a constructed prototype: (a) reflection coefficients (S , S , S for antenna 1, 2, 3); (b) isolation (S , S , S ) between two antennas. (c) Calculated envelope correlation for the three antennas.

Fig. 5. Simulated S-parameters for the dual-loop antenna (antenna 1), the 2.4 GHz outer loop only and the 5 GHz inner loop only.

grounding portion plays an important role in fine-tuning the frequencies of the resonant modes in the antenna lower and upper

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Fig. 6. Measured 3-D radiation patterns at 2442 MHz for antenna 1 studied in Fig. 3.

bands. Further increases in width can lead to two nearby resonance, for instance the 1.0-wavelength mode of the 2.4 GHz loop and the 0.5-wavelength mode of the 5 GHz loop, merged into one. For the gap between the feeding and grounding portions, although it has little impacts on the impedance bandwidth for 2.4 GHz operation, the gap balances the two resonant modes in the 5 GHz band. As for the small gap (1 mm in this study) between the outer and the inner loops, it produces more effects on the resonant modes of the inner loop, especially in the 5.7 GHz band. III. REFLECTION COEFFICIENTS, ISOLATION, AND ENVELOPE CORRELATION The proposed three-antenna system was constructed and tested based upon the design and the dimensions thereof described in Figs. 1 and 2. Fig. 3(a) and (b) shows the measured reflection coefficients and isolation between antennas, whose simulated counterparts are given in Fig. 4(a) and (b). The reflec, , for tion coefficients are plotted by the curves of the three antennas. The isolation between any two of the three antennas is only presented by the curves of , , due to the symmetrical structure of the proposed MIMO antenna system. It is first noticed that on average, the experimental data compare favorably with the simulation results, which are based on the finite element method (FEM). All measured impedance bandwidth of the three antennas meets the required bandwidth specification for 2.4 and 5.2/5.8 GHz WLAN operation with (about VSWR of 2). reflection coefficient below Second, for the isolation between any two antennas, it is found

and over the 2.4 and 5.2/5.8 GHz to be below , , are bands respectively. In general, the parameters about the same to each other, and the variation between and (or between and ) is small because of the symmetry of the three-antenna design. However, some discrepancies are found due largely to manufacture tolerance and effects of coaxial cable in the experiments. Notice that the isolation can be improved further by moving the three antennas toward the ground edge (that’s to decrease the value of ) without affecting the characteristics of the reflection coefficients. The only drawback in this case is that the antenna gain can be reduced a little. If the antenna is further set on the ground edge, the peak gain in the axial direction here will be tilted toward the horizontal plane away from the loop, as can be learnt in [30]. Fig. 4(c) presents the envelope correlation among the three antennas operating in the 2.4 and 5.2/5.8 GHz bands. The envelope correlation here is determined by the use of parameters in (1) as described in [31] for sufficiently accurate results in many practical cases [31], [32]

(1) where the magnitude and phase of parameters are first required and obtained from the simulation in this study. Then the , complex conjugate denoted by an asterisk of the parameters

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Fig. 7. Measured 3-D radiation patterns at 5250 MHz for antenna 1 studied in Fig. 3.

, is given by multiplying the phase part by . Finally, the real and imaginary parts from the product of the parameters on the numerator are calculated to gain the sum and the absolute value thereof. As for the value of the denominator, it would be easier to obtain because no imaginary part is involved. From the results, the envelope correlation values remain under 0.007 within the bands of interest, which is much better than the value of 0.3 demanded widely by industry specification and the value of 0.7 at the base station as suggested in [33]. However, it should be noted that this method of gaining the envelope correlation can not tell other figures of merit in a MIMO environment. In addition, the evaluation of the envelope correlation can also be carried out as described in [33] or measured in a reverberation chamber [34]. To understand the wavelength state of each loop, the antenna is also separated into two loops, and the corresponding results on the reflection coefficients are shown in Fig. 5 for comparison. In the case of the 2.4-GHz outer loop only, 1.0-, 1.5-, and 2.0-wavelength resonant modes at about 2.5, 3.7, and 5.1 GHz can be spotted. As for the 5-GHz inner loop only, 0.5and 1.0-wavelength loop modes at about 2.4 and above 6 GHz are seen. As described in Section II that although the 2.4 GHz band is largely controlled by the outer loop and the 5 GHz band by the inner loop from the viewpoint of the parametric analysis on the reflection coefficients, the radiation properties and surface-current behavior are also needed examining in order to verify the findings.

IV. RADIATION PERFORMANCE AND CURRENT DISTRIBUTION ANALYSIS Radiation characteristics of the proposed antenna were also studied. For brevity the radiation patterns are given at the central operating frequencies of the operating bands. Also, due to the symmetrical arrangement of the three antennas, only results of one dual-loop antenna are necessarily presented. Thus, antenna 1 is chosen to suit the convenience of defining the antenna coordinates [see Fig. 1(b)]. Figs. 6–8 plot the measured radiation patterns at 2442, 5250, and 5775 MHz, the central frequencies of the 2.4, 5.2, and 5.8 GHz bands, respectively; the antenna parameters are the same as studied in Fig. 3. Other frequencies within the bands of interest were also measured, and no inconsistency on the patterns was found. The 3-D, far-field measurement in this study was made by the ETS-Lindgren OTA test system using the great-circle method in a CTIA authorized test laboratory [35]. It can first be seen that maximum field strength is generally in the direction away from the antenna ground plane, and near broadside radiation patterns at 2442 and 5775 MHz are observed too. This behavior is expected simply because the 1.0-wavelength loop antenna is a self- balanced structure, which can suppress a lot of excited surface currents on the antenna ground plane, and in turn, more directional radiation patterns are formed with the ground plane acting like a reflector [25]. Second, for the radiation at 5250 MHz, conical-patterns are noticeable with comparatively less field strength around the

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Fig. 8. Measured 3-D radiation patterns at 5775 MHz for antenna 1 studied in Fig. 3.

axis. This phenomenon is probably because the 2.0-wavelength mode of the outer loop, the 2.4 GHz antenna, effects the radiation caused by the 1.0-wavelength inner loop of the 5 GHz antenna. Fig. 9 presents the measured peak antenna gain and radiation efficiency against frequency. The peak gain over the 2.4 GHz band varies from 5.1 to 6.9 dBi with radiation efficiency exceeding 86%. For the 5.2/5.8 GHz bands, the peak gain is seen at a constant level of about 7 dBi; the radiation efficiency exceeds 80%. This good radiation efficiency is due to the use of the low-loss, low-permittivity foam base for the antenna. Notice that the gain measurement here takes account of the mismatch of the antenna. The radiation efficiency is obtained by calculating the total radiated power (TRP) of the antenna under test (AUT) over the 3-D spherical radiation first and then dividing that total amount by the input power of 0 dBm given to the AUT. Finally, the studies on replacing the dodecagonal ground with a circular ground of the same size were also conducted. The results (not shown for brevity) indicate that both reflection coefficients and isolation are almost the same, and the peak antenna gain is slightly increased. Fig. 10 shows the simulated, excited, surface-current distributions at the central frequencies of the 2.4, 5.2, and 5.8 GHz bands for antenna 1 with the antenna ground plane. The currents are plotted in the form of the magnitude scale. As expected, the surface currents for the three resonant frequencies are less on the ground plane and mainly distributed on the dual-loop antenna and ground-plane area around the feeding and grounding portions. Notice that even though there may be some currents

Fig. 9. Measured peak antenna gain and radiation efficiency against frequency.

excited by the 1.0-wavelength mode of the 2.4 GHz loop over 5.2 GHz operation, the current distributions on the ground are still small [36]. The surface currents on the dual-loop antenna only are given in Fig. 11; the currents are presented in the form of vectors in order to identify the nulls. It can be seen that the surface currents at 2442 MHz show two current nulls on the outer loop on both sides of the short edges, which confirms again the outer loop to be of 1.0-wavelength loop mode (scale index at bottom-left corner). For the inner loop operating in the 5.2/5.8 GHz bands, similar characteristics of a 1.0-wavelength loop antenna are also obtained with two current nulls on both sides (scale index at bottom-right corner). However, with the presence of the outer loop resonant path, the 2.0-wavelength loop mode of the 2.4 GHz antenna, known for four current nulls (denoted as crosses here in the figure), also occurs in the lower 5.2 GHz band as seen in the reflection-coefficient curve of the

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Fig. 10. Simulated surface-current distributions for antenna 1 excited at 2442, 5250, and 5775 MHz with the antenna ground plane.

Fig. 11. Simulated excited surface currents on the dual-loop antenna of antenna 1 excited at 2442, 5250, and 5775 MHz.

outer loop only in Fig. 5. This also helps explain the cause of effected radiation patterns at 5250 MHz in Fig. 7. As operating frequencies increase, more current nulls are spotted too. At 5775 MHz, the state of the current distributions on the outer loop are changing from the 2.0- to 2.5-wavelegth mode (notice six nulls are formed), but the dominant resonant mode is still by the 1.0-wavelength inner loop of the 5 GHz antenna. For the loop antenna in an odd-number wavelength mode, the currents on the feeding and grounding portions are out of the phase, while those are in phase for an even-number wavelength loop. In this case, the currents on the outer loop in the transition state has a less impact on the radiation patterns of the 5 GHz loop antenna compared to the case for the dual-loop antenna at 5250 MHz. Also notice that the out-of-phase currents are usually identified as current nulls on the antenna, and those crosses in the figure

represent nulls from the viewpoint of the 2.4-GHz outer-loop antenna. V. CONCLUSION A novel three-antenna system aimed at operating in the 2.4 and 5.2/5.8 GHz bands as internal MIMO AP antennas has been demonstrated. The design prototype of the antenna has been successfully constructed and tested. The antenna comprises an outer loop and an inner loop, which are configured to be affixed to the surfaces of a rectangular foam base of a moderate size. By carefully choosing proper dimensions of the loop feeding and grounding portions and the gap therein between, the 10-dB return-loss bandwidth for 2.4 and 5.2/5.8 GHz WLAN operation can be attained. Low mutual coupling with port isolation and between any two antennas has of less than

SU: HIGH-GAIN DUAL-LOOP ANTENNAS FOR MIMO ACCESS POINTS IN THE 2.4/5.2/5.8 GHz BANDS

been obtained over the 2.4 and 5.2/5.8 GHz bands respectively. The antenna also shows good radiation characteristics with peak gain of about 7 dBi for the three operating bands, and directional radiation patterns in the elevation planes have been observed too. The proposed multiple antennas are well suited for internal MIMO antennas embedded in a wireless AP for WLAN operation as a promising alternative to conventional, high-gain patch or microstrip antennas.

REFERENCES [1] 11n, Wikipedia, the Free Encyclopedia [Online]. Available: http://en. wiki-pedia.org/wiki/11n [2] C. C. Chiau, X. Chen, and C. G. Parini, “A compact four-element diversity- antenna array for PDA terminals in a MIMO system,” Microw. Opt. Technol. Lett., vol. 44, pp. 408–412, Mar. 2005. [3] S. B. Yeap, X. Chen, J. A. Dupuy, C. C. Chiau, and C. G. Parini, “Lowprofile diversity antenna for MIMO applications,” Electron. Lett., vol. 42, pp. 69–71, Jan. 2006. [4] K. L. Wong, C. H. Chang, B. Chen, and S. Yang, “Three-antenna MIMO system for WLAN operation in a PDA phone,” Microw. Opt. Technol. Lett., vol. 48, pp. 1238–1242, Jul. 2006. [5] D. W. Browne, M. Manteghi, M. P. Fitz, and Y. Rahmat-Samii, “Experiments with compact antenna arrays for MIMO radio communications,” IEEE Trans. Antennas Propag., vol. 54, pp. 3239–3250, Nov. 2006. [6] M. Manteghi and Y. Rahmat-Samii, “A novel miniaturized triband PIFA for MIMO applications,” Microw. Opt. Technol. Lett., vol. 49, pp. 724–731, Mar. 2007. [7] S. W. Su, J. H. Chou, and Y. T. Liu, “Printed coplanar two-antenna element for 2.4/5 GHz WLAN operation in a MIMO system,” Microw. Opt. Technol. Lett., vol. 50, pp. 1635–1638, Jun. 2008. [8] R. A. Bhatti, J. H. Choi, and S. O. Park, “Quad-band MIMO antenna array for portable wireless communications terminals,” IEEE Antennas Wireless Propag. Lett., vol. 8, pp. 129–132, 2009. [9] J. H. Choi, Y. S. Shin, and S. O. Park, “Performance evaluation of 2 2 MIMO handset antenna arrays for mobile WiMAX applications,” Microw. Opt. Technol. Lett., vol. 51, pp. 1558–1561, Jun. 2009. [10] K. L. Wong, J. W. Lai, and F. R. Hsiao, “Omnidirectional planar dipolearray antenna for 2.4/5.2-GHz WLAN access points,” Microw. Opt. Technol. Lett., vol. 39, pp. 33–36, Oct. 2003. [11] K. L. Wong, F. R. Hsiao, and T. W. Chiou, “Omnidirectional planar dipole array antenna,” IEEE Trans. Antennas Propag., vol. 52, pp. 624–627, Feb. 2004. [12] R. Bancroft and B. Bateman, “An omnidirectional planar microstrip antenna,” IEEE Trans. Antennas Propag., vol. 52, pp. 3151–3153, Nov. 2004. [13] K. M. Luk and S. H. Wong, “A printed high-gain monopole antenna for indoor wireless LANs,” Microw. Opt. Technol. Lett., vol. 41, pp. 177–180, May 2004. [14] R. Bancroft and B. Bateman, “An omnidirectional planar microstrip antenna with low sidelobes,” Microw. Opt. Technol. Lett., vol. 42, pp. 68–69, Jul. 2004. [15] R. Bancroft, “Design parameters of an omnidirectional planar microstrip antenna,” Microw. Opt. Technol. Lett., vol. 47, pp. 414–418, Dec. 2005. [16] S. W. Su and J. H. Chou, “Printed omnidirectional access-point antenna for 2.4/5-GHz WLAN operation,” Microw. Opt. Technol. Lett., vol. 50, pp. 2403–2407, Sep. 2008. [17] J. H. Chou and S. W. Su, “Internal wideband monopole antenna for MIMO access-point applications in the WLAN/WiMAX bands,” Microw. Opt. Technol. Lett., vol. 50, pp. 1146–1148, May 2008. [18] S. W. Su, “Very-low-profile monopole antennas for concurrent 2.4- and 5-GHz WLAN access-point applications,” Microw. Opt. Technol. Lett., vol. 51, 2010. [19] S. W. Su, K. L. Wong, Y. T. Cheng, and W. S. Chen, “High-gain broadband patch antenna with cavity ground for 5-GHz WLAN operation,” Microw. Opt. Technol. Lett., vol. 41, pp. 397–399, Jun. 2004.

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[20] F. S. Chang, K. C. Chao, C. H. Lu, and S. W. Su, “Compact vertical patch antenna for dual-band WLAN operation,” Electron. Lett., vol. 44, pp. 612–613, May 2008. [21] F. S. Chang, Y. T. Liu, and S. W. Su, “A probe-fed patch antenna with a step-shaped ground plane for 2.4 GHz access point,” Microw. Opt. Technol. Lett., vol. 51, pp. 139–141, Jan. 2009. [22] J. D. Kraus and R. J. Marhefka, Antennas: For All Applications, 3rd ed. New York: McGraw-Hill, 2003, ch. 9, pp. 322–329. [23] A. A. Kishk, K. F. Lee, W. C. Mok, and K. M. Luk, “A wide-band small size microstrip antenna proximately coupled to a hook shape probe,” IEEE Trans. Antennas Propag., vol. 52, pp. 59–65, Jan. 2004. [24] R. Chair, C. L. Mark, K. F. Lee, K. M. Luk, and A. A. Kishk, “Miniature wide-band half U-slot and half E-shaped patch antennas,” IEEE Trans. Antennas Propag., vol. 53, pp. 2645–2652, Aug. 2005. [25] H. Morishita, Y. Kim, and K. Fujimoto, “Design concept of antennas for small mobile terminals and the future perspective,” IEEE Antennas Propag. Mag., vol. 44, pp. 30–34, 2002. [26] K. L. Wong, J. H. Chou, S. W. Su, and C. M. Su, “Isolation between GSM/DCS and WLAN antennas in a PDA phone,” Microw. Opt. Technol. Lett., vol. 45, pp. 347–352, May 2005. [27] “MIMO Architecture: The Power of 3, White Papers,” Atheors Communications, Inc. [Online]. Available: http://www.atheros.com/pt/papers.html [28] S. W. Su, J. H. Chou, and Y. T. Liu, “Realization of dual-dipole-antenna system for concurrent dual-radio operation using polarization diversity,” Microw. Opt. Technol. Lett., vol. 51, pp. 1725–1729, Jul. 2009. [29] Ansoft Corp. HFSS [Online]. Available: http://www.ansoft.com/products/hf/hfss [30] C. C. Lin, G. Y. Lee, and K. L. Wong, “Surface-mount dual-loop antenna for 2.4/5 GHz WLAN operation,” Electron. Lett., vol. 39, pp. 1302–1304, Sep. 2003. ) [31] J. Thaysen and K. B. Jakobsen, “Envelope correlation in ( MIMO antenna array from scattering parameters,” Microw. Opt. Technol. Lett., vol. 48, pp. 832–834, May 2006. [32] V. Plicanic, Z. Ying, T. Bolin, G. Kristensson, and A. Derneryd, “Antenna diversity evaluation for mobile terminals,” in Proc. Eur. Conf. Antennas Propag., Nice, France, 2006, pp. 1–3. [33] R. G. Vaughan and J. B. Andersen, “Antenna diversity in mobile communications,” IEEE Trans. Veh. Technol., vol. 36, pp. 149–172, Nov. 1987. [34] P.-S. Kidal and K. Rosengren, “Correlation and capacity of MIMO systems and mutual coupling, radiation efficiency and diversity gain of their antennas: Simulations and measurements in a reverberation chamber,” IEEE Commun. Mag., vol. 42, pp. 104–112, Dec. 2004. [35] CTIA Authorized Test Laboratory, CTIA, the Wireless Association [Online]. Available: http://www.ctia.org/business_resources/certification/test_labs/ [36] Y. W. Chi and K. L. Wong, “Internal compact dual-band printed loop antenna for mobile phone application,” IEEE Trans. Antennas Propag., vol. 55, pp. 1457–1462, May 2007.

N; N

Saou-Wen Su (S’05–M’08) was born in Kaohsiung, Taiwan, in 1977. He received the B.S., M.S., and Ph.D. degrees in electrical engineering from National Sun Yat-Sen University, Kaohsiung, Taiwan, in 2001, 2003, and 2006, respectively. Since 2007, he has worked at the Technology Research and Development Center (TRDC), Lite-On Technology Corporation, Taipei, Taiwan, and is currently working at the Network Access Strategic Business Unit at the same company. Many antennas designed are successfully mass produced there. Currently, he has published more than 65 refereed SCI journal papers and numerous international conference articles. He has 16 U.S. and 14 Taiwan patents granted, and many patents pending. His main research interests are in industrial antenna designs for wireless communications, especially planar antennas for access-point, WLAN, and MIMO applications, and also in microwave and some RF circuit design. Dr. Su won a one-year full-time School Study Exchange Program Scholarship to The University of Auckland, New Zealand, from the Asian 2000 Foundation in 1998. He was awarded the Best Student Paper Award at the 2004 International Conference on Electromagnetic Applications and Compatibility, in Taipei, Taiwan.

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Miniaturization of Planar Monopole Antenna for Ultrawideband Radios Mei Sun, Member, IEEE, Yue Ping Zhang, Fellow, IEEE, and Yilong Lu, Member, IEEE

Abstract—The miniaturization is described of a beveled planar monopole antenna in low temperature cofired ceramic technology for integration with ultrawideband radios. We demonstrate through simulations that a 40% reduction in size can be realized by simply exploiting its structural symmetry. We find that the miniaturized beveled planar monopole antenna exhibits wider impedance bandwidth, higher cross-polar radiation, and slightly lower gain at higher frequencies as compared with its un-miniaturized counterpart. We confirm the miniaturization with the measurements of both un-miniaturized and miniaturized beveled monopole antennas. The miniaturized beveled monopole antenna of size 17 10 1 mm3 has achieved impedance bandwidth of 8.25 GHz from 2.85 to 11.1 GHz, gain from 5.6 to 2.3 dBi, and broad patterns. Both frequency domain and time domain characteristics of the beveled monopole antennas are also carefully investigated with a normalized measured transfer function. Index Terms—Planar monopole antennas low temperature cofired ceramic (LTCC) technology, ultrawideband (UWB) antennas, wireless communications.

I. INTRODUCTION

U

ULTRAWIDEBAND (UWB) radio has drawn considerable attention recently. Significant progress has been made in its implementation and application. Two distinct schemes are currently under development. One features orthogonal frequency division multiplexing (OFDM) and the other direct sequence (DS) technique. In the OFDM-UWB scheme, a sub-band with 128 OFDM carriers occupies 528 MHz band, and different sub-bands are selected from time to time to achieve the frequency hopping [1]; while in the DS-UWB scheme, only two sub-bands are used to avoid IEEE 802.11a, i.e., the mandatory low band with 2.05 GHz bandwidth and the optional high band with 4.775 GHz bandwidth [2]. Most UWB radio devices today are implemented in silicon germanium (SiGe) technology. A single-chip solution of UWB radio has also been successfully demonstrated in complementary metal oxide semiconductor (CMOS) technology [3]. With the characteristics of low power, low cost, and very high rates at limited range, UWB radio is positioned to address the applications for wireless personal area networks [4].

Manuscript received March 26, 2009; revised December 23, 2009; accepted January 15, 2010. Date of publication April 22, 2010; date of current version July 07, 2010. M. Sun is with the RF and Optical Department, Institute for Infocomm Research, Singapore 138623, Singapore (e-mail: [email protected]). Y. P. Zhang, and Y. L. Lu are with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798, Singapore (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/TAP.2010.2048851

Driven by the development of UWB radios, many antennas for UWB applications have been designed to cover the single band or multi-band of 3.1–10.6 GHz frequency range. Among them, the planar monopole antenna has become the choice of antennas for UWB radios due to its attractive merits, such as the ultra wideband characteristic, near omnidirectional radiation patterns, simple structure and low cost [5]. The planar monopole antenna in low temperature cofired ceramic (LTCC) is particularly interesting because it offers the possibility of the singlepackage solution of UWB radios [6]–[13]. The existing planar monopole antenna in LTCC with the integration capability of UWB radios measures 30 25 1.2 mm [6]. In this paper, we report the miniaturization of a beveled planar monopole antenna in LTCC for integration with UWB radios. The designed antenna is targeted to cover the part or even the whole of the UWB frequency band of 3.1–10.6 GHz with available gain, and radiation patterns. In Section II we demonstrate through simulation that a 40% reduction in size can be realized for the beveled planar monopole antenna. The performances of both un-miniaturized and miniaturized beveled planar monopole antennas are compared to evaluate the miniaturization effects in impedance matching, radiation patterns, and gain. A physical insight into the operating mechanism behind the miniaturization is also illustrated. In Section III, we validate the miniaturization with the measurement. Finally, we summarize the conclusions in Section V. II. MINIATURIZATION SIMULATION STUDIES The existing planar monopoles for UWB applications are mostly in symmetrical structures. For example [13] shows a 47 40 1.6 mm circular disc symmetrical antenna in PCB and [5] shows a 47 40 1.6 mm beveled symmetrical antenna in FR4 PCB. These symmetrical structures lead to the large antenna footprint. According to the operation principle of these UWB antennas [12], it is known that the small feature dimension contributes to the high resonant frequency, whereas the large dimension contributes to the low resonant frequency. For these symmetrical structures their half formats have all the necessary dimension features for the resonant frequencies. Thus, it is expected that the miniaturized half structures of these symmetrical planar monopoles can achieve similar bandwidth as the un-miniaturized full structures. This technique, if feasible, will greatly miniaturize the antenna to its half dimensions, which will have great advantage to be further integrated. The feasibility of this miniaturization will be simulated in this section, taking the beveled planar monopole antenna in LTCC as an example. Fig. 1(a) shows an un-miniaturized beveled shape. The antenna and its feeding network are formed by the 10- m thick

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Fig. 1. Planar monopole antenna in LTCC for UWB applications: (a) a unminiaturized beveled antenna and (b) a miniaturized beveled antenna.

Ag metallization on a 17 17 1 mm LTCC substrate. The LTCC material used is Dupont 951 with a relative permittivity and loss tangent of 7.8 and 0.0015, respectively. The CPW line is designed to be 50 . The antenna shape is optimized to obtain the best impedance matching for a 50 source with CPW length fixed at 3 mm. As shown in Fig. 1(b) a 40% reduction in size is realized by simply exploiting the un-miniaturized antenna structure symmetry. The miniaturized antenna on an LTCC substrate only has small dimensions of 17 10 1 mm . The effect of the miniaturization on the electrical current distribution across the surface of the antenna is first examined. This will help us to acquire a clear physical insight into the operating mechanism behind the miniaturization. Fig. 2 shows the current distributions of both miniaturized and un-miniaturized structures with the same current scale at frequencies of 3.5, 6.85, and 10 GHz. As shown, the current distribution on the miniaturized structure is similar to that on the right half of the un-miniaturized structure at the same frequency. This is because the CPW feed imposes an even mode excitation on the un-miniaturized structure where the mirror symmetry Y-Z plane (as shown in Fig. 1) acts as an open circuit (or as a magnetic wall). Hence, the removal of the left half of the un-miniaturized structure would not affect too much on the current distribution on its right half, the miniaturized structure. It is also interesting to note from Fig. 2 that the surface current distributions strongly depend on the operating frequency. At the low frequency 3.5 GHz, the currents on the radiating elements mainly flow along the Y direction for the two structures, which favors the radiation. At the middle frequency 6.85 GHz, a current null occurs on the radiating element for the either structure. At the high frequency 10 GHz, the current null moves down to the junction area of the radiating element and the signal line. Further, it is more important to note that the X-directed current component on the radiating element of the un-miniaturized structure cancels; while the X-directed current component on the radiating element of the miniaturized structure does not. The X-directed current components on the radiating elements of the two structures get stronger as the frequency becomes higher. Hence, the cross-polar radiation will be stronger at a higher frequency and the cross-polar radiation of the miniaturized structure will be stronger than that of the un-miniaturized structure. Finally, it should be noted that the bevel forces the current to flow vertically and therefore leads to an improvement in both impedance bandwidth and matching.

Fig. 2. Effect of miniaturization on electric current distribution across the surface of the antennas: (a) at 3.5 GHz, (b) at 6.85 GHz, and (c) at 10 GHz.

Fig. 3. Effect of miniaturization on impedance matching.

The miniaturization technique proves to be successful for impedance matching as shown in Fig. 3, which compares the of the miniaturized and un-miniaturized UWB antennas. Table I also clearly lists the impedance bandwidth comparison. The impedance bandwidth is defined as the frequency bandvalue is equal to or smaller than dB. width where the As shown, the impedance bandwidth is 7.4 GHz from 3.4 to 10.8 GHz for the miniaturized structure as compared to 5.9 GHz from 4.2 to 10.1 GHz for the un-miniaturized structure. The

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TABLE I COMPARISION OF BANDWIDTH, GAIN FOR UN-MINIATURIZED AND MINIATURIZED ANTENNAS

Fig. 5. Fabricated beveled monopole antennas for UWB radio: (a) un-miniaturized and (b) miniaturized.

Fig. 4. Effect of miniaturization on radiation patterns at 6.85 GHz with solid lines for co-polarization components, short dash lines for cross-polarization components, normal lines for un-miniaturized antenna, and thicker lines for miniaturized antenna: (a) H plane and (b) E plane.

miniaturized antennas exhibit the better and wider impedance matching as compared with its un-miniaturized counterpart. The effect of the miniaturization on the radiation patterns is then examined by comparing the radiation patterns for the un-miniaturized and miniaturized antennas. The radiation patterns at 3.5, 6.85, and 10 GHz show the similar characteristics. For brevity only the radiation patterns at 6.85 GHz are presented in Fig. 4. According to the figure all the radiation patterns show the common characteristics for the un-miniaturized and miniaturized antennas. The H plane (XZ plane) patterns are rather uniform whereas the E plane (YZ plane) patterns exhibit dual-polarized properties. However, compared to the un-miniaturized antennas the miniaturized antennas have the more significant cross-polarization components in radiation patterns whatever in the E and H planes as clearly observed in Fig. 4. This agrees with our mechanism analysis. Table I also compares the gain for the un-miniaturized and miniaturized antennas. It is found that the miniaturized antenna exhibits the lower gain at higher frequencies compared with that of its un-miniaturized counterpart. III. MINIATURIZATION EXPERIMENTAL RESULTS The slots on the antennas can successfully combat the warpage or fracture in LTCC fabrication. As shown in Fig. 1(b) the finalized footprint of the miniaturized beveled antenna only has small dimensions of 8 15 mm . The final designed dimensions are, mm, mm, mm, mm, mm, mm, mm, mm, mm, mm, mm. Fig. 5 shows the fabricated beveled monopole antennas for UWB radios in the un-miniaturized and miniaturized formats. Each antenna was fed by a PSF-S01 SMA connector in our measurement. For the miniaturized antenna the asymmetry of the structure was enhanced by the feeding SMA connector, which would make the cross-polar radiation more significant.

Fig. 6. Measured jS

j

of beveled monopole antennas.

A. Impedance Bandwidth and Radiation Patterns The S-parameter was measured with the N5230A network result. For the analyzer. Fig. 6 shows the measured un-miniaturized antenna the measured impedance bandwidth is 7.55 GHz from 3.5 to 11.05 GHz; while for the miniaturized antenna the measured impedance bandwidth is 8.25 GHz from 2.85 to 11.1 GHz. Both un-miniaturized and miniaturized antennas have wider measured bandwidths than simulated ones. The discrepancy is caused by the extended ground effect due to the cable and SMA connectors. They were not included in the simulation. Furthermore, it should be noted that the extension is not as large of the upper frequency edge in the measured , which is due to the frequency as that in the simulated limitation of the SMA connectors used in the measurement. Nevertheless, as simulated, the miniaturized antenna has indeed values above a wider impedance bandwidth and smaller the upper frequency edge. Fig. 7 shows the measured radiation patterns in both E and H planes at 3.5, 6.85, and 10 GHz, respectively. The miniaturized and un-miniaturized antennas show the similar co-polar radiation patterns. However, the miniaturized antenna has higher cross-polar radiation as compared with its un-miniaturized counterpart. This agrees with our simulation results and mechanism analysis. B. Transfer Functions and Gain To compare the transmission performance of miniaturized and un-miniaturized UWB antennas (AUT) the measurement

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Fig. 8. Measured transmission scattering parameters of beveled monopole antennas.

Fig. 9. Normalized transfer functions of beveled monopole antennas. Fig. 7. Measured radiation patterns of beveled monopole antennas with solid lines for co-polarization components, short dash lines for cross-polarization components, normal lines for un-miniaturized antennas, and thicker lines for miniaturized antennas: (a) H plane at 3.5 GHz, (b) E plane at 3.5 GHz, (c) H plane at 6.85 GHz, (d) E plane at 6.85 GHz, (e) H plane at 10 GHz, and (f) E plane at 10 GH.

was conducted in an anechoic chamber. During the measurement the transmitting antenna was fixed while the AUT or the standard antenna was mounted as the receiving antenna. The transmitting and receiving antenna pair was placed in an on-axis orientation with a separation distance of 1.6 m. In our measurement the WJ-48430 dual-polarized quad-ridged horn antenna was chosen to be both the transmitting and standard receiving antenna. This antenna has proved to be well matched to the measurement system from 3 to 18 GHz. The transmission scattering and were then measured by parameters the N5230A network analyzer. It should be mentioned that the system was calibrated to the antenna terminals in advance. magnitude and group Fig. 8 shows the measured S delay. As seen the miniaturized and un-miniaturized antennas show the similar characteristic. The magnitudes of the transmission scattering parameters are relatively flat and the group delays are relatively constant over the whole UWB frequency range. The normalized antenna transfer function of the AUT

is further defined as [12, Eq. (5)] to calibrate the range related effects. Fig. 9 shows its magnitude and group delay. It is observed that the miniaturized and un-miniaturized beveled antennas show the similar characteristic. The magnitudes of the normalized transfer functions are rather flat and the group delays are nearly constant over the frequency band of interest. As a consequence, the miniaturized and un-miniaturized beveled antennas have proved to be very suitable for UWB radios. This also demonstrates the feasibility of miniaturization. In addition, it is observed from Fig. 9 that the magnitude of the normalized transfer function of the miniaturized antenna is almost the same as that of the un-miniaturized structure below 6 GHz, while it is smaller than that of its un-miniaturized counterpart above 6 GHz. This is due to the stronger cross-polar radiation at higher frequencies for the miniaturized antenna according to our mechanism analysis. It should be emphasized that the magnitude in decibels of the normalized transfer function is exactly the antenna absolute gain to 2.3 [12]. As seen from Fig. 9 that the gain varies from dBi for the miniaturized beveled antenna and from to 3 dBi for the un-miniaturized beveled antenna over the whole UWB frequency range of 3.1–10.6 GHz. As simulated, the miniaturized antenna exhibits a slightly lower gain at higher frequencies.

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beveled antennas do not distort the incident pulse significantly. It also proves their applicability in UWB radios. The feasibility of miniaturization is therefore fully confirmed. IV. CONCLUSION A significant 40% reduction in size has been realized for LTCC based planar monopole antennas for UWB applications by simply exploiting their structural symmetry, taking a beveled planar monopole antenna as an example. The miniaturized antenna exhibit wider impedance bandwidth, higher cross-polar radiation, and slightly lower gain at higher frequencies as compared with their un-miniaturized counterparts. The physical insight into the operating mechanism behind the miniaturization was also illustrated. We confirmed these effects of miniaturization with the measurements of both un-miniaturized and miniaturized beveled monopole antennas. The final miniaturized beveled monopole antenna of size 17 10 1 mm achieved impedance bandwidth of 8.25 GHz from 2.85 to 11.1 to 2.3 dBi, and broad patterns. In addition, GHz, gain from both frequency domain and time domain characteristics of the beveled monopole antennas were also carefully investigated with a normalized measured transfer function. They all proved the feasibility of the miniaturization and applicability of this miniaturized beveled monopole antenna in UWB radios. ACKNOWLEDGMENT The authors would like to thank K. M. Chua of the Singapore Institute of Manufacturing Technology for his help in fabricating the antennas and their colleague S. H. Wi for his help in measuring the antennas.

Fig. 10. Waveforms of the incident pulses and received pulses.

REFERENCES C. Time-Domain Characteristics Two kinds of incident pulse are selected in this study. One is the fourth derivative of a Gaussian function pulse expressed as [12, Eq. (7)] with the parameters of and ps. The other is the modulated pulse expressed with carrier frequency GHz and ps as (1) The waveforms of these two kinds of incident pulse are illustrated in Fig. 10. It should be mentioned that their power spectrum density (PSD) comply with the required FCC indoor emission mask. The output waveform at the receiving antenna terminal can be expressed by an inverse Fourier transform as follows [12], (2) where represents an ideal bandpass filter from 2 to 12 GHz. Fig. 10 also illustrates the received pulses by beveled monopole antennas. A well-defined parameter named Fidelity is used to evaluate the capability of pulse distortion of the antennas [12, Eq. (9)]. It reaches the maximum unity as the two pulses are exactly the same in shape. As shown in Fig. 10 the well-behaved received pulses are demonstrated with values of Fidelity better than 0.97 and the late time ringing is almost negligible. This validates that the miniaturized and un-miniaturized

[1] “Multiband OFDM Physical Layer Proposal for IEEE 802.15Task Group 3a (Doc. Number P802.15-03/268r3),” Mar. 2004, IEEE P802.15. [2] R. Fisher, R. Kohno, M. McLaughlin, and M. Welbourn, “DS-UWB Physical Layer Submission to IEEE 802.15 Task Group 3a (Doc.Number P802.15-04/0137r4),” Jan. 2005, IEEE P802.15. [3] [Online]. Available: http://artimi.com/news/archive/press_releases/31 _may_05 [4] [Online]. Available: http://ieee802.org/15/pub/TG3a.html [5] H. Schantz, The Art and Science of Ultrawideband Antennas. Boston: Artech House, 2005. [6] G. Brzezina, L. Roy, and L. MacEchern, “Planar antennas in LTCC technology with transceiver integration capability for ultra-wideband applications,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 6, pp. 2830–2839, 2006. [7] G. Brzezina, L. Roy, and L. MacEchern, “LTCC ultra-wideband antenna with transceiver integration capability,” in Proc. 35th Eur. Microwave Conf., Oct. 2005, p. 2011. [8] C. Ying and Y. P. Zhang, “A planar antenna in LTCC for single-package ultrawideband radio,” IEEE Trans. Antennas Propag., vol. 53, no. 9, pp. 3089–3093, 2005. [9] Y. Chen, G. Y. Li, and Y. P. Zhang, “An LTCC planar ultra-wideband antenna,” Microw. Opt. Technol. Lett., vol. 42, no. 3, pp. 220–222, Aug. 14, 2004. [10] Y. Chen and Y. P. Zhang, “Integration of ultra-wideband slot antenna on LTCC substrate,” Electron. Lett., vol. 40, pp. 645–646, 2004. [11] Taiyo Yuden Co., LTD, “Ultrawideband antenna and filter design,” presented at the Ansoft Workshop, Sep. 2005. [12] T. G. Ma and S. K. Jeng, “Planar miniature tapered-slot-fed annular slot antennas for ultrawideband radios,” IEEE Trans. Antennas Propag., vol. 53, no. 3, pp. 1194–1202, 2005. [13] J. Liang, L. Guo, C. C. Chiau, and X. Chen, “CPW-fed circular disc monopole antenna for UWB applications,” presented at the Proc. IEEE Int. Workshop on Antenna Technology: Small Antennas and Novel Metamaterials, Singapore, Mar. 7–9, 2005.

SUN et al.: MINIATURIZATION OF PLANAR MONOPOLE ANTENNA FOR ULTRAWIDEBAND RADIOS

Mei Sun (M’09) received the B.E. degree from Hunan University, China, in 2000, the M.E. degree from the Beijing Institute of Technology, China, in 2003, and the Ph.D. degree from Nanyang Technological University (NTU), Singapore, in 2007, all in electronic engineering. She became a Research Associate at NTU in 2006 and subsequently progressed to Research Fellow in 2007. In September 2009, she joined the Institute for Infocomm Research, Singapore, as a Research Fellow. Her research interests include intra- and inter-chip RF wireless communication system simulation and implementation, and integrated antenna design for wireless communication. Dr. Sun was the recipient of a Best Paper Prize from the Third IEEE International Workshop on Antenna Technology, March 2007, Cambridge, UK.

Yue Ping Zhang (M’03–SM’07–F’10) received the B.E. and M.E. degrees from Taiyuan Polytechnic Institute and Shanxi Mining Institute of Taiyuan University of Technology, Shanxi, China, in 1982 and 1987, respectively, and the Ph.D. degree from the Chinese University of Hong Kong, Hong Kong, in 1995, all in electronic engineering. From 1982 to 1984, he worked at Shanxi Electronic Industry Bureau, from 1990 to 1992, the University of Liverpool, Liverpool, U.K., and from 1996 to 1997, City University of Hong Kong. From 1987 to 1990, he taught at Shanxi Mining Institute and from 1997 to 1998, the University of Hong Kong. He was promoted to a Full Professor at Taiyuan University of Technology in 1996. He is now an Associate Professor and the Deputy Supervisor of Integrated Circuits and Systems Laboratories with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore. He has broad interests in radio science and technology and published widely across seven IEEE societies. He has delivered scores of invited papers/keynote address at international scientific conferences. He has organized/chaired dozens of technical sessions of international symposia. Prof. Zhang received the Sino-British Technical Collaboration Award in 1990 for his contribution to the advancement of subsurface radio science and technology. He received the Best Paper Award from the Second International Symposium on Communication Systems, Networks and Digital Signal Processing, July 2000, Bournemouth, U.K., and the Best Paper Prize from the Third IEEE International Workshop on Antenna Technology, March 2007, Cambridge, U.K. He was awarded a William Mong Visiting Fellowship from the University of Hong Kong in 2005. He was a Guest Editor of the International Journal of RF and Microwave Computer-Aided Engineering and an Associate Editor of the International Journal of Microwave Science and Technology. He serves as an Editor of the ETRI Journal and an Associate Editor of the International Journal of Electromagnetic Waves and Applications. He also serves on the Editorial Boards of a large number of international journals including the IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES and IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS.

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Yilong Lu (S’90–M’92) received the B.Eng. degree from Harbin Institute of Technology, China, in January 1982, the M.Eng. degree from Tsinghua University, China, in November 1984, and the Ph.D. degree from University College London, in November 1991, all in electronic engineering. From November 1984 to September 1988, he was with the Department of Electromagnetic Fields Engineering, University of Electronic Science and Technology of China, Chengdu, as a lecturer in the Antenna Division. In December 1991, he joined the School of Electrical and Electronic Engineering, Nanyang Technological University (NTU), where he is currently a full Professor in the Communication Engineering Division. He was a Visiting Academic at University of California–Los Angeles, from October 1998 to June 1999. His research interests include antennas, array based signal processing, radar systems, computational electromagnetics, and evolutionary computation for optimization of complex problems. He is the leader of the Radar Research Group, the Coordinator of the Microwave Circuits, Antennas and Propagation Research Group, and Deputy Director of Centre for Modeling and Control of Complex Systems, in NTU. He is a member of the Editorial Board for IET Radar, Sonar & Navigation.

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Magnetic Induction Communications for Wireless Underground Sensor Networks Zhi Sun, Student Member, IEEE, and Ian F. Akyildiz, Fellow, IEEE

Abstract—The main difference between the wireless underground sensor networks (WUSNs) and the terrestrial wireless sensor networks is the signal propagation medium. The underground is a challenging environment for wireless communications since the propagation medium is no longer air but soil, rock and water. The well established wireless signal propagation techniques using electromagnetic (EM) waves do not work well in this environment due to three problems: high path loss, dynamic channel condition and large antenna size. New techniques using magnetic induction (MI) create constant channel condition and can accomplish the communication with small size coils. In this paper, detailed analysis on the path loss and the bandwidth of the MI system in underground soil medium is provided. Based on the channel analysis, the MI waveguide technique for communication is developed in order to reduce the high path loss of the traditional EM wave system and the ordinary MI system. The performance of the EM wave system, the ordinary MI system and our improved MI waveguide system are quantitatively compared. The results reveal that the transmission range of the MI waveguide system is dramatically increased. Index Terms—Channel modeling, magnetic induction (MI), MI waveguide technique, underground communication, wireless sensor networks.

I. INTRODUCTION

W

IRELESS underground sensor networks (WUSNs) enable a wide variety of novel applications [1], [2], including soil condition monitoring, earthquake and landslide prediction, underground infrastructure monitoring, sports-field turf management, landscape management, border patrol and security, and etc. However, underground is a challenging environment for wireless communication [3]. The propagation medium is no longer air but soil, rock and water, where the well established wireless propagation techniques for terrestrial wireless sensor networks do not work well. Traditional wireless communication techniques using electromagnetic (EM) waves encounter three major problems in underground environments: the high path loss, the dynamic channel condition and the large antenna size [3]. In particular, first, EM waves experience high levels of attenuation due to absorption by soil, rock, and water in the underground. Since the WUSN devices have very limited radio power due to the energy

Manuscript received May 20, 2009; revised January 06, 2010; accepted January 28, 2010. Date of publication April 22, 2010; date of current version July 08, 2010. This work was supported by the US National Science Foundation (NSF) under Grant CCF-0728889. The authors are with the Broadband Wireless Networking Laboratory, School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332 USA (e-mail: [email protected]; [email protected]). Digital Object Identifier 10.1109/TAP.2010.2048858

constraint, the transmission range between two sensor nodes using EM waves is very small (no more than 4 m). Second, the path loss is highly dependent on numerous soil properties such as water content, soil makeup (sand, silt, or clay) and density, and can change dramatically with time (e.g., increased soil water content after a rainfall) and location (soil properties change dramatically over short distances). Consequently, the bit error rate (BER) of the communication system also varies dramatically in different times or positions. The unreliable channel brings design challenges for the sensor devices and networks to achieve both satisfying connectivity and energy efficiency. Third, large size antenna is necessary for the efficient propagation of EM waves. Path loss can be reduced if lower operating frequencies are used. The lower the frequency is, the larger the antenna must be to efficiently transmit and receive EM waves [4], which obvious conflicts with the necessity that underground sensors remain small. If the sensors of WUSNs are buried in the shallow depth, sensor can communicate with the aboveground data sinks directly using EM waves. This is because the underground path is short in this case. Hence the impacts of the additional path loss and the dynamic channel caused by the soil medium are much smaller. However, many WUSN applications, such as underground structure monitoring, require the sensors buried deep underground, where only underground-to-underground channel is available. Magnetic induction (MI) is a promising alternative physical layer technique for WUSNs in deep burial depth. It can address the problems on the dynamic channel condition and the large antenna size of the EM waves techniques. Specifically, the underground medium such as soil and water cause little variation in the attenuation rate of magnetic fields from that of air, since the magnetic permeabilities of each of these materials are similar [2], [5], [6]. This fact guarantees that the MI channel conditions remain constant for a certain path in different times. Moreover, in the MI communication, the transmission and reception are accomplished with the use of a small size coil of wire. In addition, since the radiation resistance of coil is much smaller than electric dipole, very small portion of energy is radiated to the far field by the coil. Hence, the multi-path fading is not an issue for MI communication. However, MI is generally unfavorable for terrestrial wireless communication. As the transmission distance increases, magnetic field strength falls off much faster than the EM waves in terrestrial environments. In underground environments, although it is known that the soil absorption causes high signal attenuation in the EM wave systems but does not affect the MI systems, it is not clear whether the total path loss of the MI system is lower than the EM wave

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system or not. Additionally, since the MI communication involves reactance coils as antenna, the system bandwidth needs to be analyzed. In this paper, we first provide a detailed analysis on the path loss and the bandwidth of the MI communication channel in underground environments. Then based on the analysis, we develop the MI waveguide technique for WUSNs, which can significantly reduce the path loss, enlarge the transmission range and achieve practical bandwidth for MI communication in underground environments. In particular, the MI transmitter and receiver are modeled as the primary coil and secondary coil of a transformer. Multiple factors are considered in the analysis, including the soil properties, coil size, the number of turns in the coil loop, coil resistance, operating frequency. The analysis shows that the ordinary MI systems have larger transmission range but lower bandwidth than the EM wave systems. However, neither the ordinary MI system nor the EM wave system is able to provide enough communication range for practical WUSNs applications. Motivated by this fact, we develop the MI waveguide technique [7] to enlarge the communication range. In this case, some small coils are deployed between the transmitter and the receiver as relay points, which form a discontinuous waveguide. The remainder of this paper is organized as follows. In Section II, the related work is introduced. Then in Section III, the path loss and the bandwidth of the underground MI communication system is analyzed. In Section IV, the MI waveguide technique for underground wireless communication is developed. Finally, the paper is concluded in Section V.

munication applications (such as the link between a cell phone or an MP3 player and a headset), the rapid fall off of the MI signal strength is exploited to provide each user with his own private bubble, without having to worry about mutual interference among multiple users, and permitting bandwidth reuse. However, in the underground communication applications, the high path loss is obviously not an advantage. In [5], the MI is first introduced to the field of wireless underground communication. It shows that the MI transmission is not affected by soil type, composition, compaction, or moisture content, and requires less power and lower operating frequencies than RF transmission. However, the theoretical/experimental results show that the communication range is no more than 30 inches (0.76 m). Moreover, the bandwidth of the MI system is not considered in the paper. Besides underground, the MI communication can also be used in other RF-impenetrable environments, such as human body. In [12], a body network is built to collect data from, and transport information to, implanted miniature devices at multiple sites within the human body. The MI technique is employed to link information between a pair of implants, and to provide electric power to these implants. In [13], a new magnetic material is analyzed to guide magnetic information to the receiver coil, permitting a clear image deep within the body. In [7], [14], [15], the MI waveguide is investigated. It is shown that an array of loops can act as a waveguide, propagating a new form of wave known as a MI wave. Up to now, the MI waveguide has been designed and used as artificial delay lines and filters, dielectric mirrors, distributed Bragg reflectors, slow-wave structures in microwave tubes, coupled cavities in accelerators, modulators, etc. However, there is no attempt to utilize the MI waveguide in the wireless communication field. The theoretical analysis of the MI waveguide in [14] is validated by experiments in [16]. Note that we adopt similar theoretical analysis method as [14] in this paper. Currently, there is no solution to address the low communication range problem of both the EM wave technique and the MI technique in underground environments. Also no theoretical analysis on underground MI communications is provided. In this paper, we provide a detailed analysis on the path loss and bandwidth of the underground MI communications. Based on the analysis, we develop the MI waveguide communication technique to enlarge the transmission range of the MI systems in underground environments.

II. RELATED WORK The propagation characteristics of EM waves in underground environments (soil, water and rock) have been presented in [3]. The analysis shows that the path loss is much higher than the terrestrial case due to the material absorption. The communication success significantly depends on the composition of the soil and the operating frequency. Since lower operating frequency achieves lower path loss but requires larger antenna size, a middle course solution is proposed, where the 0.3 m long antenna is used to transmit and receive signals at 300 MHz. The transmission range is around 4 m, which is still too short for efficient deployment of WUSNs. The theoretical analysis of [3] has been validated by the testbed developed in [8]. Recently, the magnetic induction has been introduced as a new physical layer technique for wireless communication. However it suffers from the high path loss and low bandwidth problems. In [6], MI communication is employed in the mine warfare (MIW) operations to provide a more reliable wireless command, control and navigation channel. The EM channel is qualitatively analyzed and the low data rates of 100 to 300 bit/s are achieved in various MI communication experiments carried out in coastal areas. The authors notice that the high path loss limits the transmission range. They suggest to place more MI transceivers to mitigate the high path loss, which is not feasible for underground wireless networks due to cost/energy constraint and deployment difficulty. In [9]–[11], the MI is utilized as an alternative personal communication technique to the Bluetooth. In the near-field com-

III. MI CHANNEL CHARACTERISTICS A. System Modeling In MI communications, the transmission and reception are accomplished with the use of a coil of wire, as shown in the first are the radii of the transmission row in Fig. 1, where and coil and receiving coil, respectively; is the distance between the transmitter and the receiver. Suppose the signal in the transmitter coil is a sinusoidal cur, where is the angle frequency of the rent, i.e., and is the system operating fretransmitting signal. quency. This current can induce another sinusoidal current in the receiver then accomplish the communication. The interaction

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According to the transmission line theory, the reflections take place unless the line is terminated by its matched impedance. In the equivalent circuit described in Fig. 1, to maximize the received power, the load impedance is designed to be equal to the complex conjugate of the output impedance of the secondary loop, i.e., (3) The following task is to find the analytical expression for the resistance, self and mutual induction of the transmitter and receiver coils. The resistance is determined by the material, the size and the number of turns of the coil

(4)

Fig. 1. MI communication channel model.

between the two coupled coils is represented by the mutual induction. Therefore, the MI transmitter and receiver can be modeled as the primary coil and the secondary coil of a transformer, is respectively, as shown in the second row in Fig. 1, where the mutual induction of the transmitter coil and receiver coil; is the voltage of the transmitter’s battery; and are the and are the resistances of the coil; is self inductions; the load impedance of the receiver. We use its equivalent circuit to analyze the transformer, as shown in the third row in Fig. 1, where

where, and are the number of turns of the transmitter coil is the resistance of a unit and receiving coil, respectively; length of the loop. According to American Wire Gauge (AWG) can be a value from to 3 with standard, different wire diameter [17]. Since the coil is modeled as a magnetic dipole, the self induction and mutual induction can be deduced by the magnetic potential of the magnetic dipole, which is provided in polar coordinate system by [18] (5) where is the permeability of the transmission medium; is the wavelength of the signal. By using Stokes’ theorem [18], the mutual induction of the two coils can be calculated (6) The self induction can be derived in the same way

(7) (1) and are the self impedances of the transmitter coil where is the influence of the reand the receiver coil, respectively; ceiver on the transmitter while is the influence of the transis the induced voltage on the receiver mitter on the receiver; coil. In the equivalent circuit, the transmitting power is equal to the power consumed in the primary loop. The receiving power is equal to the power consumed in the load impedance . Both received power and transmitting power are functions of the transmission range

(2)

Consequently, by substituting (1), (3), (4), (6) and (7) into (2), the received power and the transmitting power can be calculated. It should be noted that, the underground transmission medium contains different type of soil, water, rocks and etc. It is necessary to analyze the differences between the permeabilities of these materials. According to [19], the substances of the underground medium can be categorized into four main groups including organic materials, inorganic materials, air, and water, where organic materials come from plants and animals; inorganic materials include sand, silt and clay. The relative permeabilities of the plants, animals, air and water are very close to 1. If the sand, silt, and clay do not consist of magnetite, their permeabilities are also close to 1. An example is that the average value for sedimentary rocks is given in [19] as 1.0009. Since most soil in the nature does not contain magnetite, we can assume that the permeability of the underground transmission medium is a constant based on the above discussion.

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B. Path Loss For wireless communication using EM waves, the Friis transmission equation [20] gives the power received by one antenna, given another antenna some distance away transmitting a known amount of power. Since the radiation power is the major consumption of the EM wave transmitter, the transmitting power of the EM wave system is a constant and not influenced by the is a function of position of the receiver, i.e. for EM waves, distance while is a constant. Hence the path loss is measured by the ratio of the received power to the radiation power. of the EM wave propagation in soil medium The path loss is given by [3] Fig. 2. Path loss of the EM wave system and the MI system with different soil water content.

(8) where the transmission distance is given in meters; the attenuation constant is in 1/m and the phase shifting constant is in radian/m. The values of and depend on the dielectric properties of soil, and is derived in [3, (8)–(14)] using the Peplinski principle [21]. Note that the reflection from the air-ground interface is neglected since the burial depth is large, which has been explained in [3]. Unlike the EM wave transmitter, the radiation power of the MI communication system can be neglected since the radiation resistance is very small. Meanwhile, the induced power consumed at the MI receiver is the major power consumption since the MI communication is achieved by coupling in the non-propagating near-field. The transmitting power of the MI system consists of the induced power consumed at the MI receiver and the power consumed in the coil resistance. If the coil resistance is small, the ratio of the received power to the transmitting power will be close to 1 since the receiving power and transmission power decrease simultaneously as the transmission distance increases. The advantage of this feature is that the limited transmission power won’t be wasted on radiation to the surrounding space. Most power is transmitted to the receiver, which is favorable to the energy constrained WUSNs. However, as the transmission distance increases, less and less power is transmitted to the receiver. Hence there still exists a so called Path loss. It should be noted that the power is not really lost but in fact not transmitted. To fairly compare the performance of the EM wave system and MI system, the path loss of the MI system with transmission distance is defined as , where is the received power at the receiver that is meters away from the transmitter; is the reference transmitting power when the transmission distance is a very small value . We can consider that if is small enough. In case of low coil resis, the path loss tances and high operating frequency of the MI communication system can be simplified as

(9)

We compare (8) with (9) to analyze the path loss of MI and EM wave systems in underground environments. In (8), there are two terms in the path loss that are determined by the disis due to the space spread and tance , where the term the term is due to the material absorption. The transmission medium has significant influence in the path loss since it determines the propagation constants and . In (9), only is determined by the distance , which is due one term to the spread of the magnetic field. The transmission medium has no obvious influence on the MI path loss since we assume that the permeability of the medium is a constant as discussed in in MI case the beginning. Although the path loss term is much higher than the term in EM waves case, it is not clear whether the total path loss of MI system is larger than that of the EM wave system or not, since the material absorpin EM wave path loss varies a lot in different tion term transmission medium. C. Numerical Analysis 1) Path Loss: The path losses of the MI system and the EM wave system shown in (8) and (9) are evaluated using MATLAB. The results are shown in Fig. 2. According to [3], the propagation of the EM waves in soil medium is severely affected by the soil properties, especially, the volumetric water content (VWC) of soil. Hence in the evaluations, we set the VWC of the soil medium as 1%, 5% and 25% The permittivity and conductivity of soil medium is calculated by the Peplinski principle [3, (8)–(12)], which are functions of VWC and soil composition. In our simulations, besides VWC, the soil composition is set as follows, the sand particle percent is 50%, the clay percent , and the solid soil is 15%, the bulk density is 1.5 particle density is 2.66 , which are typical values in nature. As discussed in the beginning, the permeability of the underground transmission medium is a constant and is the same . Other simulation paas that in the air, which is rameters are set as follows: for EM wave system, the operating frequency is set to 300 MHz. The reason for this choice is as follows: on the one hand, lower frequency bands are necessary for acceptable path loss. On the other hand, decreasing operating frequency below 300 MHz increases the antenna size, which

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Fig. 3. Bit error rate of the EM wave system and the MI system with different soil water content and noise level. Fig. 4. Frequency response of the MI system with different transmission range.

can also prevent practical implementation of WUSNs. For MI system, the transmitter and the receiver coil have the same radius of 0.15 m and the number of turns is 5. The coil is made of copper wire with a 1.45 mm diameter. Hence the resistance of can be looked up in AWG standard [17] as 0.01 unit length . The operating frequency is set to 10 MHz. This low operating frequency together with the small number of turns can effectively mitigate the influence of the parasitic capacitance [22]. In Fig. 2, the path losses of the MI system and EM wave system are shown in dB versus the transmission distance with different soil VWC. As expected, the path loss of the MI system is not affected by the environment since the permeability remains the same. On the other hand, the path loss of the EM wave system dramatically increases as the VWC increases. When the , the path loss of the EM waves soil is very dry is smaller than that of the MI system. When the soil is very wet , the path loss of the EM waves is significant , the path larger than that of the MI system. When losses of these two systems are similar. It can be seen that the path loss of the MI system is a lg function of the distance while the path loss of the EM wave system is an approximately linear function of the distance . This is because that the path loss caused by material absorption is the major part in the EM , in the near region bewaves’ propagation. When tween 0.5 m and 3 m, the EM wave system has smaller path , the MI system has loss; in the relatively far region smaller path loss than the EM wave system. Even in the very dry , the MI system can achieve smaller soil medium path loss than the EM wave system after a sufficient long transmission distance. 2) Bit Error Rate: Furthermore, we investigate the bit error rate (BER) characteristics of the two propagation techniques. The results are shown in Fig. 3. The BER characteristic depends mainly on three factors: 1). the path loss, 2). the noise level and 3). the modulation scheme used by the system. The path loss of the MI system and the EM wave system has been given in (8) and (9). The noise power in soil is measured using the BVS YellowJacket wireless spectrum analyzer [23] in [3]. The average is found to be 103 dBm. Besides the experiment noise level measurement, we also assume a high noise scenario where the is set to be 83 dBm. Then the signal to average noise level

, noise ratio (SNR) can be calculated by is the transmitting power and is the path loss given where as 10 dBm in the simulation. Conin (8) and (9). We set sidering the modulation scheme as the simple but widely used , the BER can be derived as a function of SNR: , where is the error function [24]. In Fig. 3, the BERs of the MI system and EM wave system are shown as a function of the transmission distance with different soil VWC. In low noise scenario, the transmission range of the MI system is larger than the EM wave system no matter what VWC is, which can be explained by the following reasons: 1) path loss below 100 dB cannot influence the BER performance when the noise is low. 2) The MI system has higher path loss than the EM wave system at the near region where the path losses of both systems are below 100 dB; while in the far region where the path losses are higher than 100 dB, the MI system has lower path loss. 3) It is the path loss in the far region that determines the transmission range. In the high noise scenario, the transmission range of MI system is between the range of EM wave system in dry soil and the system in wet soil, since this time the path loss above 80 dB can influence the BER performance. 3) Bandwidth: It should be noted that, the path loss of the MI system derived above is based on the assumption that the load impedance is designed to be equal to the complex conjugate of the output impedance of the secondary loop. However, since the output impedance of the secondary loop consists of not only resistance but also reactance, only one central frequency can realize this load matching. Any deviation from the central frequency will cause the power reflections and increase the path loss. Hence it is necessary to analyze the bandwidth of the MI system. In Fig. 4, the frequency response of the MI system described above is shown with different transmission distance. It indicates that the 3-dB bandwidth of the MI system is around 2 KHz when the operating frequency is 10 MHz. The bandwidth is not affected by the transmission distance. Although the 2 KHz bandwidth is much smaller than the EM wave system, it should be enough for the WUSNs considering that the underground sensing and monitoring applications do not require very high data rate [2].

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how close the coils are to each other. In underground communication, we set the distance between two relay coils to 5 m, which is larger than the maximum communication range of the EM wave system. Hence the MI waveguide system do not cost more on deploying the underground device than the traditional EM wave system. A lot of money can be saved by replacing the expensive relay sensor devices using EM waves by the relay coils that have very low cost. In the later part of this section, we vary the relay distance of the MI waveguide to analyze the influence. We assume that the radius of the relay coil is around 0.15 m. Comparing to the coil radius, the relay distance is large enough to validate the fact that the coils are sufficiently far from each other and only interact with the nearest neighbors. Hence, only the mutual induction between the adjacent coils needs to be taken into account in this paper. A. System Modeling

Fig. 5. MI waveguide communication channel model.

To sum up, the MI system provides larger transmission range (around 10 m) than that of the EM wave system (around 4 m). The MI system also has the advantage that its performance is not influenced by the soil medium properties, especially the water content. Although the bandwidth of the MI system is smaller than that of the EM wave system, it should to a large extent fulfill the requirements of the WUSNs applications. However, the transmission ranges of both systems are still too short for a practical applications in underground medium.

Similar to the strategy in Section III, the MI waveguide is modeled as a multi-stage transformer, where only adjacent coils are coupled, as shown in the second row in Fig. 5. Since in practical applications, the transceivers and the relay points usually use the same type of coils, we assume that all the coils have the same parameters (resistance, self and mutual inductions). is the mutual induction between the adjacent coils; is the voltage of the transmitter’s battery; is the coil self induction; is the resistances of the coil; is the capacitor loaded in each is the load impedance of the receiver. The equivalent coil; circuits of the multi-stage transformer is shown in the third row in Fig. 5, where

IV. MI WAVEGUIDE FOR UNDERGROUND COMMUNICATION Although the ordinary MI system has constant channel condition and relatively longer transmission range than that of the EM wave system, its transmission range is still too short for practical applications. One solution is to employ some relay points between the transmitter and the receiver. Different from the relay points using the EM wave technique, the MI relay point is just a simple coil without any energy source or processing device. The sinusoidal current in the transmitter coil induces a sinusoidal current in the first relay point. This sinusoidal current in the relay coil then induces another sinusoidal current in the second relay point, and so on and so forth. Those relay coils form an MI waveguide in underground environments, which act as a waveguide that guides the so-called MI waves. A typical MI waveguide structure is shown in the first row relay coils equally spaced along one in Fig. 5, where axis between the transmitter and the receiver, hence the total number of coils is ; is the distance between the neighbor coils; is the distance between the transmitter and the receiver ; is the radius of the coils. Each relay coil and (including the transmitter coil and the receiver coil) is loaded with a capacitor . By appropriately designing the capacitor value, resonant coils can be formed to effectively transmit the magnetic signals. There exists mutual induction between any pair of the coils. The value of the mutual induction depends on

(10) is the influence of the coil on the where coil and vice versa; is the induced voltage on the coil. Then the received power at the receiver can be calculated as (11)

B. System Optimization To maximize the received power is equal to maximize the induced voltage at the receiver coil. According to (10), if the coils are resonant, then the impedance of each coil consists of only resistance and the absolute value becomes much smaller. , Hence we design the capacitor to fulfill

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then using the expression of the self induction in (7), the value of the capacitors should be (12) In case that the coils are resonant, the expression of the received power in (10) can be developed as

(13) where

Basing on the above equations, it can be shown that the multipliis in fact an order polynomial cation of , which is denoted as and

(14) are the coefficients of the where polynomial, which is fixed for a certain and not affected by other parameters. Since the coils are all resonant, the matched load impedance . Finally, in the is pure resistance, which is MI waveguide system, if the receiver is m away from the transmitter and there are relay coils between them, the received power can be expressed as (15) . where is the total transmission range and The same as the ordinary MI system, the transmission power and the receiving power of the MI waveguide system decrease simultaneously as the transmission distance increases. Hence, is defined in the same the path loss of the MI waveguide way

(16)

is defined as the transmission power when the where transmitter is very close to the receiver and no relay coil exists. According to (16), the path loss of the MI waveguide . It is the polynomial system is actually a function of that has the major influence on the path loss. Therefore the path loss is a monotone increasing function . Consequently, to minimize the path of the variable loss is equal to minimize the variable . By using the expressions of the wire resistance and the mutual induction in (4) and (6) respectively, the variable can be expressed as (17) of the total Note that here the relay distance is only transmission range . By this means the influence of the cubic function of the distance on the path loss can be significantly mitigated. Using this scheme, we can reduce the path loss by: — reducing the ratio of the relay distance to the coil radius ; — increasing the operating frequency and the number of turns of the coils ; — reducing the wire resistance . However, there are other factors that constrain the path loss minimization. • To ease the device deployment, the ratio of the relay distance to the coil radius is expected to be as large as possible, which conflicts with the requirements of the low total path loss. In this paper, to keep the incontrovertible advantage over the underground EM wave system, the relay distance is set to at least the maximum transmission range of EM wave system, which is 4 m. Considering the coil radius is 0.15 m, the ratio of the relay distance to the coil radius is over 27 in this paper. • It is also impossible to unlimitedly increase the operating frequency and the number of turns of the coils, since these two parameters are constraint by (12). The loaded capacitors in each resonant coil should be larger than 10 pF, otherwise it is comparable to the coil parasitic capacitance. To achieve a practical value of the loaded cannot be capacitors in each resonant coil, the and too large. Moreover, extreme high operating frequency and large number of turns may induce severe performance deterioration caused by the parasitic capacitance [22]. In this paper, we use 10 MHz operating frequency and the each coil contains 5 loops of wire. The loaded capacitor is around 35 pF in this case. • Although reducing the wire resistance can reduce the total path loss, it may cause two problems: 1) lower wire resistance require larger wire diameter, which cost more and cause the coils heavier; 2) low wire resistance can also cause dramatical in-band signal fluctuation, which may create difficulties on equalization of the received signal. In this paper, the coil is made of copper wire with a 1.45 mm diameter. According to AWG standard [17], the resistance is 0.01 . The influence of different of unit length wire resistances will be analyzed in the later part of this section.

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Fig. 6. Path loss of the MI waveguide system with different wire resistance and relay distance.

Fig. 7. Bit error rate of the MI waveguide system with different wire resistance, relay distance and noise level.

C. Numerical Analysis 1) Path Loss: The path losses of MI waveguide system shown in (16) are evaluated using MATLAB. The results are shown in Fig. 6. For better comparison, the path loss of the 300 MHz EM wave system in 5% VWC soil and the path loss of the 10 MHz ordinary MI system are also plotted. According to the discuss in Section III, the performance of the MI system is not affected by the soil properties and the soil medium has the . same permeability as that in the air, which is Hence in the evaluation of the MI waveguide, we do not need to consider the environment parameters. Except studying the effects of certain parameters, the default values are set as follows: all the coils including the transmitter, receiver and relay and the number of points have the same radius of . The resistance of unit length is turns is for normal coil and for low resistance coil. The operating frequency is set to 10 MHz. The relay distance is 5 m. The total number of coils is determined by the . In Fig. 6, the transmission distance , where path losses of the MI waveguide system are shown in dB versus the transmission distance with different relay distances and different wire resistances . It can be found that the MI waveguide can greatly reduce the signal path loss comparing with the EM wave system and the ordinary MI system. The path loss of the MI waveguide is less than 100 dB even after 250 m transmission distance, while the path loss of the EM wave system and the ordinary MI system becomes larger than 100 dB when the transmission distance is larger than 5 m. In addition, the path loss can be further reduced by reducing the relay distance and the wire resistance. 2) Bit Error Rate: In Fig. 7, we investigate the bit error rate (BER) characteristics of the MI waveguide. The same as the is selected as the modulation analysis in Section III, scheme. Two noise level are considered, where the average noise in low noise scenario is 103 dBm while in high level is set noise scenario is 83 dBm. The transmission power to 10 dBm. In Fig. 7, the BER of the MI waveguide system are shown as a function of the transmission distance with different relay distances and different wire resistances . The BER of the EM wave system and the ordinary MI system are also plotted for comparison. Comparing with the small transmission range

Fig. 8. Frequency response of the MI waveguide system with different wire resistance and relay distance.

of the other two techniques (less than 10 m), the transmission range of the waveguide system is above 250 meters even in the high noise scenario. It means that the transmission range of the MI waveguide system is increased for more than 25 times compared with the other two systems. In accord with the analysis on the path loss, the transmission range of the MI waveguide can be extended by reducing the relay distance and the wire resistance. 3) Bandwidth: The above path loss and the transmission range of the MI waveguide system is calculated under the assumption that the transmitted signal has only one frequency. Under this central frequency, all the coils can achieve the resonant status. However, if there is any deviation from the central frequency, the resonant status of each coil will disappear and the load at the receiver also becomes unmatched with the system. Hence we need to analyze the bandwidth of the MI waveguide system. In Fig. 8, the frequency response of the MI waveguide system is shown with different relay distances and different wire resistances . The number of relay coils are fixed to 7. The results indicate that, when the operating frequency is 10 MHz, the 3-dB bandwidth of the MI waveguide system is in the same range with the ordinary MI system, which is 1 KHz to 2 KHz. Although lower wire resistance can reduce the path loss in the central frequency, the fluctuation of the in-band frequency response becomes so serious that may cause difficulties in the equalization at the receiver. The bandwidth can be enlarged by

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Fig. 10. Frequency response of the MI waveguide system with different deviation from the designed relay distance.

We assume that the relay coils are not deployed at the exact relay planed positions but may not deviate a lot. There are coils deployed between the transceivers and the transmission. . Their designed positions are of relay coil is a Gaussian random variable The position and standard deviation . Then with mean value intervals with the transmission distance is divided into length: , where . and are the positions of the transmitter and the receiver, respectively. We assume that the standard deviation are either 5%, 10% or 20% of the designed relay distance. Other simulation parameters are set to the default value. The results are the average of 100 iterations. Both mean value and the standard deviation of the results are plotted. It is shown that there exists additional path loss in practical deployment. Moreover, the bandwidth decreases dramatically when the standard deviation is 20%. The level of the additional path loss and the bandwidth decrease are determined by the standard deviation. Higher standard deviation can cause larger performance deterioration. Moreover, the additional path loss also increases as the transmission distance increase, which is because that more relay coils are deployed with longer transmission distance hence more deployment deviation may occur. The standard deviation of the path loss and the bandwidth also increases dramatically as the deployment deviation increases, which indicates that the reliability of the MI waveguide system also decreases if deployment deviation occurs. It should be noted that the influence of the deployment deviation on the performance of the MI waveguide system can be neglected if the standard deviation is less than 10%.

reducing the relay distance. However, for a certain transmission range, reducing the relay distance means that more relay coils needs to be deployed hence more effort is cost in the deployment. Two practical parameter sets maybe: 1) the relay distance and the unit length resistance . In this case, the 10 MHz operating MI waveguide system can accomplish the communications within 250 m range and achieve and the 1 KHz bandwidth. And 2) the relay distance . In this case, the 10 MHz unit length resistance operating MI waveguide system has 400 m transmission range and 2 KHz bandwidth. 4) Influence of Position Deviation: It should be noted that the above performance of MI waveguide system is derived in the ideal deployment case, where all the relay coils are accurately deployed so that the relay coils are uniformly distributed between the transceivers. The transmission range is divided into exactly equal intervals hence the mutual inductions between each relay coil are the same. However, in the practical applications, this requirements may not be precisely satisfied due to the following two reasons: on the one hand, in the initial deployment stage, the relay coils can not be set in the exact position as planned because of deployment constraints, such as rocks or pipes in the soil; on the other hand, the positions of the coils may change while the network is operating due to the above ground pressure or the movement of the soil. Hence, in Fig. 9 and Fig. 10, the influence of the non-ideal deployment is analyzed.

In wireless underground communications, traditional techniques using EM waves encounter three major problems: high path loss due to material absorption, dynamic channel condition due to various soil properties, and too large antenna size. MI is an alternative technique that has constant channel condition and can accomplish the communication with small size coils. However currently there is no detailed analysis on the path loss and the bandwidth of the MI system in underground soil medium. In this paper, we provide an analytical model to characterize the underground MI communication channel. Based on the channel analysis, we develop the MI waveguide technique to significantly enlarge the transmission range in underground environments. Our analysis shows the following. • The MI technique has constant channel condition because its path loss only depends on the permeability of the propagation medium, which remains the same if the medium is air, water and most kinds of soil and rock. However, the material absorption is the major part of the path loss of EM wave system, which may change a lot in different soil conditions. • In underground environments, the path loss of the MI system is slightly smaller than the EM wave system in normal and wet soil medium; while in very dry soil, the EM wave system has smaller path loss. However, due to the high path loss, both the systems can not provide a transmission range that is more than 10 m, which prevent

Fig. 9. Path loss of the MI waveguide system with different deviation from the designed relay distance.

V. CONCLUSION

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them from practical applications. Although the bandwidth of the MI system and the MI waveguide system is only 1 to 2 KHz, which is much smaller than the EM wave system, it is enough for the low data rate monitoring applications of WUSNs. Another advantage of the MI and MI waveguide system is that, as the transmission range increases, the transmission power decreases simultaneously with the received power, which is favorable for the energy-constrained WUSNs. • The MI waveguide technique can greatly reduce the path loss, which is attributed to the relay coils deployed between the transceivers. It should be noted that the relay coils do not consume any energy and the cost is very low. The relay distance is also larger than the maximum transmission range of the EM wave system. The bandwidth of the MI waveguide system is in the same range as the ordinary MI system. The transmission range of the MI waveguide system is increased dramatically compared with that of the ordinary MI system and the EM wave system.

[17] Standard Specification for Standard Nominal Diameters and CrossSectional Areas of AWG Sizes of Solid Round Wires Used as Electrical Conductors, ASTM Standard B 258-02, ASTM International, 2002. [18] D. R. Frankl, Electromagnetic Theory. Englewood Cliffs, NJ: Prentice-Hall, 1986. [19] W. M. Telford, L. P. Geldart, and R. E. Sheriff, Applied Geophysics, 2nd ed. New York: Cambridge Univ. Press, 1990. [20] J. D. Kraus and D. A. Fleisch, Electromagnetics, 5th ed. New York: McGraw-Hill, 1999. [21] N. Peplinski, F. Ulaby, and M. Dobson, “Dielectric properties of soils in the 0.3–1.3-GHz range,” IEEE Trans. Geosci. Remote Sensing, vol. 33, no. 3, pp. 803–807, May 1995. [22] L. A. Charles and W. A. Kenneth, Electronic Engineering, 3rd ed. New York: Wiley, 1973. [23] “YellowJacket Wireless Spectrum Analyzer,” Berkeley Varionics Systems, Inc. [Online]. Available: www.bvsystems.com [24] J. G. Proakis, Digital Communications, 4th ed. New York: McGrawHill, 1995.

REFERENCES [1] I. F. Akyildiz, W. Su, Y. Sankarasubramaniam, and E. Cayirci, “Wireless sensor networks: A survey,” Comput. Netw. J., vol. 38, no. 4, pp. 393–422, March 2002. [2] I. F. Akyildiz and E. P. Stuntebeck, “Wireless underground sensor networks: Research challenges,” Ad Hoc Netw. J., vol. 4, pp. 669–686, Jul. 2006. [3] L. Li, M. C. Vuran, and I. F. Akyildiz, “Characteristics of underground channel for wireless underground sensor networks,” presented at the Med-Hoc-Net’07, Corfu, Greece, Jun. 2007. [4] T. A. Milligan, Modern Antenna Design, 2nd ed. Piscataway, NJ: IEEE Press, 2005. [5] N. Jack and K. Shenai, “Magnetic induction IC for wireless communication in RF-impenetrable media,” presented at the IEEE Workshop on Microelectronics and Electron Devices (WMED 2007), Apr. 2007. [6] J. J. Sojdehei, P. N. Wrathall, and D. F. Dinn, “Magneto-inductive (MI) communications,” presented at the MTS/IEEE Conf. and Exhibition (OCEANS 2001), Nov. 2001. [7] R. R. A. Syms, I. R. Young, and L. Solymar, “Low-loss magneto-inductive waveguides,” J. Phys. D: Appl. Phys., vol. 39, pp. 3945–3951, 2006. [8] A. R. Silva and M. C. Vuran, “Development of a testbed for wireless underground sensor networks,” EURASIP J. Wireless Commun. Netw. (JWCN) [Online]. Available: http://cse.unl.edu/~mcvuran/ ugTestbed.pdf [9] V. Palermo, “Near-field magnetic comms emerges,” Electron. Eng. Times, Nov. 2003. [10] R. Bansal, “Near-field magnetic communication,” IEEE Antennas Propag. Mag., vol. 46, pp. 114–115, Apr. 2004. [11] C. Bunszel, “Magnetic induction: A low-power wireless alternative,” RF Design, vol. 24, no. 11, pp. 78–80, Nov. 2001. [12] M. Sun, S. A. Hackworth, Z. Tang, G. Gilbert, S. Cardin, and R. J. Sclabassi, “How to pass information and deliver energy to a network of implantable devices within the human body,” in Proc. IEEE Conf. on Engineering in Medicine and Biology Society (EMBS 2007), Aug. 2007, pp. 5286–5289. [13] M. C. K. Wiltshire, J. B. Pendry, I. R. Young, D. J. Larkman, D. J. Gilderdale, and J. V. Hajnal, “Microstructured magnetic materials for RF flux guides in magnetic resonance imaging,” Science, vol. 291, no. 5505, pp. 849–851, Feb. 2001. [14] V. A. Kalinin, K. H. Ringhofer, and L. Solymar, “Magneto-inductive waves in one, two, and three dimensions,” J. Appl. Phys., vol. 92, no. 10, pp. 6252–6261, 2002. [15] R. R. A. Syms, E. Shamonina, and L. Solymar, “Magneto-inductive waveguide devices,” Proc. IEE Microw. Antennas Propag., vol. 153, no. 2, pp. 111–121, 2006. [16] M. C. K. Wiltshire, E. Shamonina, I. R. Young, and L. Solymar, “Dispersion characteristics of magneto-inductive waves: Comparison between theory and experiment,” Electron. Lett., vol. 39, no. 2, pp. 215–217, 2003.

Zhi Sun (S’06) received the B.S. degree from Beijing University of Posts and Telecommunications (BUPT), Beijing, China and the M.S. degree from Tsinghua University, Beijing, in 2004 and 2007, respectively. He is working toward the Ph.D. degree at the Georgia Institute of Technology, Atlanta, under the supervision of Prof. Ian F. Akyildiz. Currently, he is a Graduate Research Assistant in the Broadband and Wireless Networking Laboratory (BWN Lab), School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta. His current research interests are in wireless underground communication networks and wireless sensor networks.

Ian F. Akyildiz (M’86–SM’89–F’96) received the B.S., M.S., and Ph.D. degrees in computer engineering from the University of Erlangen-Nurnberg, Germany, in 1978, 1981, and 1984, respectively. Currently, he is the Ken Byers Distinguished Chair Professor with the School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, the Director of Broadband Wireless Networking Laboratory and Chair of the Telecommunication Group at Georgia Tech. In June 2008, he became an Honorary Professor with the School of Electrical Engineering, Universitat Politecnica de Catalunya (UPC), Barcelona, Spain. He is also the Director of the newly founded NaNoNetworking Center (N3Cat), Catalunya. He is the Editor in Chief of Computer Networks Journal, and the founding Editor-in-Chief of the Ad Hoc Networks Journal and the Physical Communication Journal. His current research interests are in nano-networks, cognitive radio networks and wireless sensor networks. Dr. Akyildiz received the “Don Federico Santa Maria Medal” for his services to the Universidad of Federico Santa Maria, in 1986. From 1989 to 1998, he served as a National Lecturer for ACM and received the ACM Outstanding Distinguished Lecturer Award in 1994. He received the 1997 IEEE Leonard G. Abraham Prize Award (IEEE Communications Society) for his paper entitled “Multimedia Group Synchronization Protocols for Integrated Services Architectures” published in the IEEE JOURNAL OF SELECTED AREAS IN COMMUNICATIONS (JSAC) in January 1996. He received the 2002 IEEE Harry M. Goode Memorial Award (IEEE Computer Society) with the citation “for significant and pioneering contributions to advanced architectures and protocols for wireless and satellite networking.” He received the 2003 IEEE Best Tutorial Award (IEEE Communication Society) for his paper entitled “A Survey on Sensor Networks,” published in IEEE COMMUNICATIONS MAGAZINE, in August 2002. He also received the 2003 ACM Sigmobile Outstanding Contribution Award with the citation “for pioneering contributions in the area of mobility and resource management for wireless communication networks.” He received the 2004 Georgia Tech Faculty Research Author Award for his “outstanding record of publications of papers between 1999 and 2003.” He also received the 2005 Distinguished Faculty Achievement Award from School of ECE, Georgia Tech. He has been a Fellow of the Association for Computing Machinery (ACM) since 1996.

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Communications Planar-Monopole-Fed, Surface-Mounted Quasi-TEM Horn Antenna for UWB Systems Y. Ranga, A. K. Verma, and Karu P. Esselle

Abstract—A compact, quasi-TEM horn antenna is presented. This planar-monopole-fed, surface-mounted, UWB antenna has nearly con0 65 dBi from 2.75–12 GHz. It is 4 (45 mm) long stant gain of 4 8 at the lowest operating frequency. It also has nearly linear phase response in this ultrawideband. The radiation pattern in the azimuth plane is broad and the pattern in the elevation plane is relatively narrow. Index Terms—Planar monopole, printed monopole, pulse, quasi-TEM, short horn, surface mounted horn, TEM horn, ultrawideband (UWB).

I. INTRODUCTION TEM horn antennas, developed for ground penetrating radar (GPR) and other such applications [1]–[7], have ultra wide bandwidths and high, nearly constant gain over the operating bandwidth. However, these antennas are  to 10 long and in addition an UWB balun is usually required to feed the balanced TEM horn from a coaxial cable. These antennas are too bulky and inconvenient for compact UWB impulse radar and wireless communication systems. On other fronts, novel feeding methods have been reported for metallic horn antennas, including a Yagi antenna feeding a long metallic horn and a microstrip patch feeding a compact, surface-mounted, =4-horn [8], [9]. However, the metallic horn itself is not an UWB radiator. Also, the microstrip patch is not an ideal UWB feeding element because of its relatively narrow impedance bandwidth. Several planar monopole UWB antennas have been investigated [10]–[12] for FCC-based UWB systems operating from 3.1–10.6 GHz. Most of these antennas have very wide impedance bandwidths and nearly omnidirectional radiation patterns in the azimuth plane. These antennas have low gains and their gain increases with frequency at lower frequencies in the UWB band. On the other hand, the transmission transfer function of an ideal UWB antenna should have a flat gain response and a linear phase response for faithful radiation of short UWB pulses [13], [14]. The objective of this communication is to report a new, compact, surface-mounted, =4-long, quasi-TEM horn antenna that is fed by an UWB, printed, circular monopole antenna (PCMA) [10]. The new Manuscript received December 16, 2008; revised June 30, 2009; accepted July 05, 2009. Date of publication April 22, 2010; date of current version July 08, 2010. Y. Ranga is with the Center for Microwave and Wireless Applications, Electronics Engineering, Macquarie University, NSW 2109, Australia and also with the CSIRO ICT Centre, Epping, NSW 1710, Australia (e-mail: [email protected]. edu.au). A. K. Verma is with the Department of Electronic Science, University of Delhi, Delhi, India and also with the Center for Microwave and Wireless Applications, Electronics Engineering, Macquarie University, NSW 2109, Australia (e-mail: [email protected]; [email protected]). K. P. Esselle is with the Center for Microwave and Wireless Applications, Electronics Engineering, Macquarie University, NSW 2109, Australia (e-mail: [email protected]). Color versions of one or more of the figures in this communication are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2010.2048843

Fig. 1. PCMA fed compact surface mount TEM Horn: W = 70 L = 42 L2 = 40 L1 = 20 h = 0 36 D = 1 575 W1 = 2 78 W2 = 10 W3 = 40 S = 45 H1 = 100 G = 15 r = 10, and = 65 ;

;

;

;

;

;

;

:

;

;

:

;

;

:

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(dimensions in mm).

antenna has nearly constant gain (4:8 6 0:65 dBi) over an ultrawide bandwidth from 2.75 GHz to 12 GHz. To the best of our knowledge, such a short, UWB, quasi-TEM horn antenna has not been reported previously. It may be suitable for compact UWB and multiband systems, including multisignal, satellite-based, precision positioning and navigation systems, UWB communication systems and some radar systems. II. THE NEW ANTENNA The new antenna configuration is shown in Fig. 1. The printed circular monopole is made on a FR-4 ("r = 4:4; D = 1:575 mm) substrate, which is separated from a second FR-4 substrate, by a uniform air-gap, maintained using Teflon spacers. Two slots (W2 = 10 mm, L2 = 40 mm) have been cut in the top FR-4 sheet on both sides of the monopole. The second FR-4 sheet is just a plain dielectric layer; there is no copper on either side. A standard TEM-horn antenna, usually made out of two relatively long metallic plates and fed by a coaxial line through a UWB balun, supports a TEM mode [1], [2]. The field in the compact antenna employed here is quasi-TEM due to extreme shortening of the horn; this was confirmed by simulations conducted using CST Microwave Studio [15]. The transverse field distribution inside the horn changes in the z-direction as well as with frequency. Fig. 2(a) shows the total transverse electric field (i.e., Ex and Ey combined) in the transverse plane at a height (z) of 10 mm, at 3 GHz. One may note that the presence of both Ex and Ey field components can contribute to some cross polarization. Fig. 2(b) shows that for sufficiently large values of z, Ez monotonically decreases with z for each of the three frequencies considered (3, 6.5, and 9 GHz). Thus this hybrid wave gradually becomes a TEM wave. Hence this antenna can be treated as a quasi-TEM horn antenna, despite its extremely short dimension in z-direction. Our simulation study further indicated that the performance of the structure is satisfactory when there are no substrates. In that case, the field distribution is closer to the TEM mode. When the quasi-TEM

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Fig. 3. Antenna prototype.

Fig. 4. Simulated and measured input reflection coefficient magnitude of the new antenna. Fig. 2. Electric field distribution. (a) Transverse electric field on the x-y plane inside the horn at z = 10 mm, (b) variation of E component in z-direction.

III. EXPERIMENTAL RESULTS horn is mounted on a FR-4 substrate, the field distribution changes and performance degrades. Hence, to approximate an air medium at mm, 2 mm) the base of the TEM horn, two slots ( 2 were created in the top FR-4 sheet and an air gap is established between the two FR-4 sheets using Teflon spacers, as indicated in Fig. 1. It was noted that even the PCMA (without horn) made on this composite substrate has 1 dB higher gain between 8–11 GHz. [See Fig. 5(a)]. Conventional TEM horn antennas can be designed by altering the slant length s, conducting plate apex angle and horn internal apex angle  between two conducting planes, following design charts of Lee and Smith for s  to  [2]. In Fig. 1, the angle of the con ducting plate with respect to the horizontal axis is  0 = . We conducted a numerical analysis of a truncated quasi-TEM horn with = slant length and optimized the dimensions W, L and slant angle  to achieve nearly constant gain and good matching from 2.57 GHz to 10.42 GHz. The final dimensions are in Fig. 1. According to Fig. 6 in [2], for s= , the theoretical gain increase linearly from 0 : dBi   at  to 4.8 dBi at  . A TEM horn with s= and   has an estimated gain of 6.4 dBi and the gain of the very short s= = quasi-TEM horn could have an estimated gain of 2.1 dBi, according to Fig. 6 of [2]. In contrast, the simulation results from CST Microwave Studio indicate that this = -quasi-TEM horn integrated to a PCMA feed have a higher and consistent gain over a wide bandwidth. The new antenna provides broad beam coverage in the azimuth plane and a relatively narrow pattern in the elevation plane, with only a small change of beam direction over its ultrawide operating bandwidth. The fabricated antenna is shown in Fig. 3. The experimental results given in the next section confirms the simulation predictions.

W = 10

=

7

4

=1 = 10 = 50 ( = 1 4) 4

= 35

L = 40

= 90

2

0 97 =1

4

The slant length chosen for the example design is 4.5 cm, which is equal to = at 1.7 GHz. Fig. 4 indicates that at 1.7 GHz the predicted and measured j 11 j of the antenna is about 0 dB. The predicted j 11j becomes 0 dB at 2.42 GHz; in measurements, 0 dB j 11j occurs at 2.75 GHz. The predicted j 11 j is less than 0 dB from 10–11.7 GHz, whereas the experiments indicate a j 11 j less than 0 dB from 2.67 GHz to 18.8 GHz. Measured j 11 j is less than 0 dB from 2.75–10.14 GHz (covering most of the FCC approved UWB bandwidth). Fig. 5 shows the measured gain and phase response of the antenna. Fig. 5(a) also shows the measured gain of a comparable printed circular monopole antenna (PCMA) on a standard FR-4 substrate and also on the composite substrate of the present antenna. The PCMA on the composite substrate shows about 1 dB gain improvement for a range of frequencies. Otherwise the gain variation is similar in both the cases—linear increase with frequency up to 6 GHz and then nearly constant gain up to 12 GHz. The incorporation of the quasi-TEM horn improves the gain at the lower frequencies up to 6 GHz. The new antenna has nearly constant gain within : 6 : dBi up to 12 GHz. Fig. 5(b) shows that the transmitting transfer function of the new antenna has almost linear phase response. This phase response should help to maintain the integrity of a transmitted short pulse in a pulse-based UWB system [13], [14]. Fig. 6(a)–(c) shows measured radiation patterns of the new antenna  ) at 3.0, 6.5, and 9.0 on the azimuth (Y-Z) plane (  for  GHz, respectively. These extremely wide radiation patterns highlight the dominance of printed monopole radiation on this plane. The presence of nulls in some directions at 9 GHz would distort the radiated pulse in those directions. The quasi-TEM horn narrows the beam in the elevation (X-Y) plane, as shown in Fig. 6(d)–(f) for 3.0, 6.5, and

s

s 10

3

s

9 10

s

4 8 0 65

E

= 90

s

10 s 8

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Fig. 5. Gain and phase response of the new antenna. (a) Measured gain of a standard PCMA, a PCMA on a composite substrate and the new antenna with quasi-TEM horn, (b) phase response of the new antenna.

9.0 GHz, respectively. The narrowing of the beam results in an increase of the directivity and gain. Even in the elevation plane, the impact of the printed monopole is evident from the null along the axis of the monopole at lower frequencies. At 9 GHz this null disappears and the beam has a small asymmetry. This beam changes its direction only slightly when frequency changes over its ultrawide bandwidth. IV. CONCLUSION A short, surface-mounted, quasi-TEM horn can be used with a printed monopole antenna to achieve nearly constant gain over an ultrawide bandwidth. A prototype antenna designed to demonstrate this concept has measured gains in the range of 4:8 dBi 6 0:65 dBi from 3–12 GHz. The radiation pattern in the azimuth plane is wide, the pattern in the elevation plane is narrower and the beam direction changes only slightly with frequency. The concept of enhancing and flattening the gain with a short, quasi-TEM horn has been validated with a circular monopole antenna. This method can be applied to other types of printed monopole antennas to further improve the performance of UWB antennas. ACKNOWLEDGMENT The uthors would like to thank Dr. A. R. Weily of CSIRO ICT Center for helping the pattern measurements at the Australian Antennas Measurement Facility (AusAMF). The second author acknowledges the financial support of UGC, India and thanks Prof. E.K. Sharma for useful

Fig. 6. Radiation pattern at 3 GHz, 6.5 GHz, 9.0 GHz: (a)–(c) azimuth plane, (d)–(f) elevation plane.

discussion on pulse distortion. The authors also express their appreciation to reviewers for their constructive suggestions.

REFERENCES [1] Li-Chung, T. Chang, and W. D. Burnside, “An ultra wide-bandwidth tapered resistive TEM horn antenna,” IEEE Trans. Antennas Propag., vol. 48, no. 12, pp. 1848–1857, Dec. 2000. [2] R. T. Lee and G. S. Smith, “A design study for the basic TEM horn antenna,” IEEE Antennas Propag. Mag., vol. 46, no. 1, pp. 86–92, Feb. 2004. [3] A. S. Turk, “Ultra-wideband TEM horn design for ground penetrating impulse radar systems,” Microw. Opt. Tech. Lett., vol. 41, no. 5, pp. 333–336, Jun. 2004. [4] A. S. Turk and H. Nazli, “Hyper-wide band TEM horn array design for multiband ground penetrating impulse radar,” Microw. Opt. Tech. Lett., vol. 50, no. 1, pp. 76–81, Jan. 2008. [5] J. A. G. Malherbe and N. Barnes, “TEM horn antenna with an elliptic profile,” Microw. Opt. Tech. Lett., vol. 49, no. 7, pp. 1548–1551, Jul. 2007. [6] J. A. G. Malherbe, “Extreme performance TEM horn,” Microw. Opt. Tech. Lett., vol. 50, no. 8, pp. 2121–2125, Aug. 2008. [7] A. K. Y. Lai, A. L. Sinopoli, and W. D. Burnside, “A novel antenna for ultrawideband applications,” IEEE Trans Antennas Propag., vol. 40, no. 7, pp. 755–760, Jul. 1992. [8] M. Sironen, Y. Qian, and T. Itoh, “A 60 GHz conical horn antenna excited with quasi-Yagi antenna,” in IEEE MTT-S Int. Symp. Digest, 2001, vol. 1, pp. 547–550. [9] A. A. Rahman, A. K. Verma, and A. S. Omar, “High gain wideband compact microstrip antenna with quasi-planner surface mount horn,” in IEEE MTT-S Int. Microwave Symp. Digest, 2003, vol. 1, pp. 571–574.

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[10] L. Jianxin, C. C. Chiau, C. Xiaodong, and C. G. Parini, “Study of a printed circular disc monopole antenna for UWB systems,” IEEE Trans. Antennas Propag., vol. 53, no. 11, pp. 3500–3504, 2005. [11] K. P. Ray and Y. Ranga, “Ultrawideband printed elliptical monopole antennas,” IEEE Trans Antennas Propag., vol. 55, no. 4, pp. 1189–1192, 2007. [12] X. L. Bao and M. J. Ammann, “Investigation on UWB printed monopole antenna with rectangular slitted ground plane,” Microw. Optical Tech. Lett., vol. 49, no. 7, pp. 1585–1587, Jul. 2007. [13] X. Qing, Z. N. Chen, and Chia, “Network approach to UWB antenna transfer functions characterization,” in Proc. Eur. Conf. Wireless Technology, Oct. 2005, pp. 293–296. [14] X. Qing and Z. Chen, “Transfer functions for UWB antenna,” in Proc. IEEE AP-S Int. Symp. Antennas and Propagation, Jun. 2004, vol. 3, pp. 2532–2535. [15] CST Microwave Studio 2009 [Online]. Available: www.cst.com Fig. 1. Sketch of the differential UWB antenna: disc monopoles and microstrip lines (black), structured ground plane (dark gray) and the basic element of the array (light gray square) are depicted. The dimensions are in millimeters.

A Planar, Differential, and Directive Ultrawideband Antenna Andrea Locatelli, Daniele Modotto, Filippo Maria Pigozzo, Stefano Boscolo, Costantino De Angelis, Antonio-Daniele Capobianco, and Michele Midrio

Abstract—A novel planar differential ultrawideband antenna is described and both numerically and experimentally characterized. The proposed antenna is formed by two disc monopoles fed by 50-Ohm microstrip lines with a structured ground plane. Simulations and measurements demonstrate that it is possible to achieve a huge increase in directionality with respect to conventional monopoles by carefully engineering the ground plane and by exploiting the array effect. Index Terms—Antenna arrays, antenna theory, directive antennas, microstrip antennas, monopole antennas.

I. INTRODUCTION Ultrawideband (UWB) antennas have been thoroughly studied since the regulation of UWB technology in the USA [1]. Planar antennas have a low-profile structure and are an excellent solution in terms of ease of manufacturing and integration with the electronic parts of UWB devices. Several planar structures suitable for UWB applications have been reported in the literature (e.g., monopole antennas [2]–[5]), and most of these are characterized by an omnidirectional radiation pattern. This feature is desirable for broadcast communication systems, whereas strongly directive radiators are required both when it is necessary to mitigate the effects of multipath in the indoor UWB channel, and for usage in radar systems or specific applications such as wireless body-area networks (WBAN) [6]. Manuscript received July 21, 2009; revised November 19, 2009; accepted January 29, 2010. Date of publication April 26, 2010; date of current version July 08, 2010. This work was supported by the Ministero dell’Istruzione, dell’Università e della Ricerca, PRIN 2007 programme, project 2006093373. A. Locatelli, D. Modotto, and C. De Angelis are with the Dipartimento di Ingegneria dell’Informazione, Università degli Studi di Brescia, Brescia 25123, Italy (e-mail: [email protected]). F. M. Pigozzo and A.-D. Capobianco are with the Dipartimento di Ingegneria dell’Informazione, Università degli Studi di Padova, Padova 35131, Italy. S. Boscolo, and M. Midrio are with the Dipartimento di Ingegneria Elettrica, Gestionale e Meccanica, Università degli Studi di Udine, Udine 33100, Italy. Digital Object Identifier 10.1109/TAP.2010.2048870

Few attempts have been made in order to increase directionality of printed UWB antennas. To reach this goal, a flat reflector has been introduced at a certain distance from the board [6], [7], or a monopole with L-shaped ground plane has been used [8], [9]. All the previously cited structures are single-ended, but differential antennas are preferable for systems that contain single-chip UWB transceivers, which typically have a differential input/output structure, since direct connection between chip and antenna would be possible, without resorting to baluns [10], [11]. An example of differential UWB antenna with omnidirectional radiation pattern was reported in [12]. In this work we describe a novel planar differential UWB antenna characterized by high directivity. The proposed structure is composed of two disc monopoles with L-shaped ground plane [8], [9], fed by 50-Ohm microstrip lines (100-Ohm differential input). The introduction of a structured ground plane and the array effect permit to achieve a measured gain exceeding 11 dB even on a low-cost substrate, maintaining at the same time a reasonable size of the board. As reference application, the antenna has been optimized to work between 6 and 8 GHz in combination with a single-chip radar transceiver [13]. II. ANTENNA STRUCTURE AND DESIGN A sketch of the novel differential UWB antenna is reported in Fig. 1. The structure is formed by two disc monopoles with L-shaped ground plane, fed by 50-Ohm microstrip lines (width equal to 3 mm), on a low-cost FR4 substrate. We assumed that the FR4 dielectric constant is 4.5, and the declared board thickness is equal to 1.6 mm. Optimization of the antenna was performed through CST Microwave Studio simulations [14], and the reported results correspond to the device with the geometric parameters that guarantee the best theoretical performance. In Fig. 1 we show the size of the board, and the position of the centers of the two disc monopoles, whose radius is 9 mm. The basic element of the proposed differential antenna is a single disc monopole, with the related 50-Ohm microstrip feeding line and the L-shaped ground plane. In Fig. 2 we show a schematic view of the initial structure, along with its in-plane radiation pattern [9]. The structured ground plane behaves as a corner reflector, which partially suppresses one of the two main lobes of radiation; as a result, it has been demonstrated that directivity can almost be doubled [8], [9]. The distance between the edge of the disc and the horizontal and vertical metal strips that compose the L-shaped ground plane is 1 and 2 mm, respectively. It is worth noting that we have also smoothed the sharp corner of the ground plane in order to get a larger bandwidth [8]. This building

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Fig. 2. Schematic view of a planar disc monopole with L-shaped ground plane, overlapped with the radiation pattern in the same plane [9].

Fig. 3. Measured differential (solid line) and common-mode (dashed-dotted line) reflection coefficients jS j and jS j, and measured single-port reflection coefficient jS j (dotted line) between 4 and 9 GHz.

block (50 2 50 mm2 ) is then rotated by 40 degrees in the xy -plane (see the light gray square in Fig. 1), in order to align the main lobe of radiation with the y -axis. The second element of the array is obtained by mirroring the first one with respect to the x = 0 plane. The region between the two elements on the ground side is filled with metal, so that this large common ground plane can be exploited for a straightforward placement of the single-chip transceiver and its circuitry. As reported in Fig. 1 the distance between the two disc monopoles is about 70 mm, which is larger than the maximum signal wavelength. III. NUMERICAL AND EXPERIMENTAL RESULTS

Differential and common-mode reflection coefficients (jSdd j and jSccj) have been measured by using a 4-port vector network analyzer Anritsu MS4624D, whereas the single-port reflection coefficient at port 1 (jS11 j) has been measured through a 2-port Agilent N5230A PNA-L network analyzer. In Fig. 3 we report results obtained from measurements between 4 and 9 GHz; it is worth noting that the three curves are almost overlapped and this implies that, as desired, coupling between the two antenna elements is very weak. The differential

Fig. 4. Measured group delay curve between 5.5 and 8.5 GHz.

Fig. 5. Measured (solid line) and simulated (dashed-dotted line) normalized radiation pattern in the xy -plane for co-polarization at 7 GHz. Only port 1 was excited, maximum gain is 8.6 dB. The results are reported in logarithmic scale, and the display scale is 10 dB per division.

reflection coefficient is below 010 dB in the frequency range between 5.3 and 9 GHz, thus the differential UWB antenna exhibits a good behavior in terms of impedance matching over a bandwidth larger than 4 GHz. Also the group delay has been measured in anechoic chamber, by using the same setup we have used for measurements of gain and radiation patterns (see below for the setup description). The results are reported in Fig. 4: it is fundamental to note that the maximum group delay variation is equal to fractions of one nanosecond (which is approximately the pulse duration for a 2-GHz bandwidth [13]), therefore the antenna guarantees low pulse distortion. The radiative properties of the differential UWB antenna have been characterized in anechoic chamber by utilizing a 2-port Agilent N5230A PNA-L network analyzer, two 180-degree hybrid couplers, a Satimo SGH-820 ridged horn wideband probe antenna, and a remotely controlled turntable. Here we report the results for co-polarization at 7 GHz; we emphasize the fact that the shape of the radiation patterns is rather uniform over the entire bandwidth, and the level of cross-polarization is quite low. In Fig. 5 we show measured and simulated normalized radiation pattern in the xy -plane when only port 1 is excited, whereas port 2 is terminated in a 50-Ohm load. The results show the typical behavior of a disc monopole with L-shaped ground

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Fig. 6. Measured (solid line) and simulated (dashed-dotted line) normalized radiation pattern in the xy -plane for co-polarization at 7 GHz. Port 1 and port 2 are excited with opposite polarity (differential excitation), maximum gain is 11.6 dB. The results are reported in logarithmic scale, and the display scale is 10 dB per division.

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Fig. 8. Measured (solid line) and simulated (dashed-dotted line) normalized radiation pattern in the xy -plane for co-polarization at 7 GHz. Port 1 and port 2 are excited with the same polarity, maximum gain is 9.1 dB. The results are reported in logarithmic scale, and the display scale is 10 dB per division.

Fig. 9. Snapshot of the y -component of the surface currents at 7 GHz, white (black) represents positive (negative) values. The two ports are excited with opposite polarity.

Fig. 7. Measured (solid line) and simulated (dashed-dotted line) normalized radiation pattern in the yz -plane for co-polarization at 7 GHz. Port 1 and port 2 are excited with opposite polarity (differential excitation). The results are reported in logarithmic scale, and the display scale is 10 dB per division.

plane (see Fig. 2), with a single lobe of radiation oriented along the y -axis, and the maximum gain is equal to 8.6 dB. In Figs. 6 and 7 we report measured and simulated radiation patterns in the xy - and yz -plane respectively, when the two input ports are excited with signals with opposite polarity. The increase of directionality is clearly visible even from a simple analysis of the shape of the patterns: indeed, the maximum gain is equal to 11.6 dB. In Fig. 8 we report, for the sake of comparison, measured and simulated radiation pattern in the xy -plane for in-phase excitation of the two ports. It is possible to note the birth of two lobes, with a maximum gain equal to 9.1 dB. In all the cases, it is worth noting the excellent agreement between numerical and experimental data. These results clearly demonstrate that the proposed differential UWB antenna is a good candidate to be used whenever a highly directional differential radiator with planar profile is required. We have numerically investigated the pattern of the surface currents on the UWB differential antenna, in order to identify the reasons for such a huge increase of directionality. The usage of a disc monopole with L-shaped ground plane guarantees the suppression of one lobe of radiation with respect to conventional monopoles, and this corresponds to an increase in gain of about 3 dB [8], [9]. The two disc monopoles that compose the differential antenna can be considered as an array of

two elements, wherein each element radiates with only one main lobe of radiation along the y -direction. The structure should ideally behave as a broad-side array, with maximum value of the array factor in normal direction with respect to the alignment direction (i.e. x-axis) [15]. From theory of antenna arrays, it is well known that we get a broad-side array when the current distribution on each antenna element is in phase. In Fig. 9 we plot a snapshot of the y -component of the surface currents at 7 GHz for differential input (the two ports have opposite polarity). It is straightforward to see that the currents on the microstrips have opposite polarity, whereas on the radiating elements they are predominantly distributed on the edge of the discs and are in phase due to the mirror symmetry between the two elements. As a consequence, in this case the differential antenna behaves as a broad-side array, as shown by the radiation pattern in Fig. 6. Viceversa, when the two input ports are fed in phase the currents on the two microstrips are obviously in phase, whereas on the radiating elements they are out of phase. Indeed, the radiation pattern in Fig. 8 exhibits two radiation lobes and no enhancement of directivity, in perfect agreement with the calculation of the array factor. Notice that the increase in gain in the case of differential input, with respect to excitation of a single port, is about 3 dB, which is exactly the value predicted by theory of antenna arrays for a two-element array. In Fig. 10 we report measured and simulated gain in the band of interest for the case of differential excitation. The two curves exhibit good agreement, in spite of the high degree of uncertainty associated with the electromagnetic parameters of the FR4 substrate. In particular, in all the simulations we took a dielectric loss tangent equal to 0.02, which seems to be a reasonable value according to what is commonly reported in the literature. It is worth noting that the gain curves are quite

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Fig. 10. Measured (solid line) and simulated (dotted line) gain of the fabricated antenna with differential excitation, and simulated gain of the same structure by considering negligible losses in the dielectric substrate (dashed-dotted line).

flat, with values between 10 and 12 dB over the entire bandwidth. In the same figure we also report simulations that show the gain that could be achieved with the same structure by considering negligible losses in the dielectric substrate. We have found that the maximum gain would be between 11.5 and 13.5 dB: it is worth noting that these are huge values for a structure with planar profile.

[7] M. Ameya, M. Yamamoto, T. Nojima, and K. Itoh, “Leaf-shaped element bowtie antenna with flat reflector for UWB applications,” IEICE Trans. Commun., vol. E90-B, pp. 2230–2238, Sept. 2007. [8] A. Locatelli, D. Modotto, F. M. Pigozzo, S. Boscolo, E. Autizi, C. De Angelis, A.-D. Capobianco, and M. Midrio, “Highly directional planar ultra wide band antenna for radar applications,” in Proc. 37th Eur. Microwave Conf., 2007, pp. 1421–1424. [9] A. Locatelli, D. Modotto, F. M. Pigozzo, S. Boscolo, E. Autizi, C. De Angelis, A.-D. Capobianco, and M. Midrio, “Increasing directionality of planar ultra-wideband antennas,” Microw. Opt. Tech. Lett., vol. 52, pp. 78–82, Jan. 2010. [10] S. Bagga, A. V. Vorobyov, S. A. P. Haddad, A. G. Yarovoy, W. A. Serdijn, and J. R. Long, “Codesign of an impulse generator and miniaturized antennas for IR-UWB,” IEEE Trans. Microw. Theory Tech., vol. 54, pp. 1656–1666, April 2006. [11] P. K. Datta, X. Fan, and G. Fischer, “A transceiver front-end for ultrawide-band applications,” IEEE Trans. Circuits Syst. II, vol. 54, pp. 362–366, April 2007. [12] N. Telzhensky and Y. Leviatan, “Planar differential elliptical UWB antenna optimization,” IEEE Trans. Antennas Propag., vol. 54, pp. 3400–3406, Nov. 2006. [13] A. Cacciatori, L. Lorenzi, and L. Colalongo, “A power efficient HBT pulse generator for UWB radars,” in Proc. of ISCAS, 2007, pp. 3916–3919. [14] CST Microwave Studio 2009. Darmstadt, Germany. [15] C. G. Someda, Electromagnetic Waves, 2nd ed. London, U.K.: CRC Press, 2006.

Bandwidth Enhancement Method for Low Profile E-Shaped Microstrip Patch Antennas Yikai Chen, Shiwen Yang, and Zaiping Nie

IV. CONCLUSION We have presented a differential planar ultrawideband antenna characterized by higher gain (more than 11 dB around 7 GHz) with respect to conventional printed radiators. The presence of a large common ground plane is a key feature in order to simplify placement of singlechip UWB transceivers, which typically have a differential input/output structure: as a consequence, direct connection between chip and antenna would be possible, without resorting to baluns. The antenna has been fabricated on a low-cost FR4 substrate and has been completely characterized: both simulations and measurements performed in anechoic chamber have demonstrated that the strong increase in directionality is mainly due to the presence of a carefully structured ground plane and to the array effect. In particular, we have found a good agreement between measured radiation patterns and predictions based on theory of antenna arrays.

REFERENCES [1] Federal Communications Commission (FCC), “Revision of Part 15 of the Commission’s Rules Regarding Ultra-Wideband Transmission Systems,” First Report and Order, FCC 02-48, 2002. [2] N. P. Agrawall, G. Kumar, and K. P. Ray, “Wide-band planar monopole antennas,” IEEE Trans. Antennas Propag., vol. 46, pp. 294–295, Feb. 1998. [3] H. G. Schantz, “Planar elliptical element ultra-wideband dipole antennas,” in Proc. of the IEEE Antennas and Propagation Society Int. Symp., June 2002, vol. 3, pp. 44–47. [4] S. Y. Suh, W. L. Stutzman, and W. A. Davis, “A new ultrawideband printed monopole antenna: The planar inverted cone antenna (PICA),” IEEE Trans. Antennas Propag., vol. 52, pp. 1361–1365, May 2004. [5] J. X. Liang, C. C. Chian, X. D. Chen, and C. G. Parini, “Study of a printed circular disc monopole antenna for UWB systems,” IEEE Trans. Antennas Propag., vol. 53, pp. 3500–3504, Nov. 2005. [6] M. Klemm, I. Z. Kovacs, G. F. Pedersen, and G. Troster, “Novel smallsize directional antenna for UWB WBAN/WPAN applications,” IEEE Trans. Antennas Propag., vol. 53, pp. 3884–3896, Dec. 2005.

Abstract—A simple bandwidth enhancement method for low profile E-shaped patch antennas is presented. By introducing a distributed LC circuit to the E-shaped patch antenna, a new resonant frequency close to that of the E-shaped patch is obtained, thus the bandwidth is widened. Moreover, the air thickness of the E-shaped patch antennas is reduced to only 0 0344 . A prototype antenna operated at AMPS band (824–894 MHz) was fabricated and measured. Measured results show that the designed low profile antenna has an impedance bandwidth over 9% for VSWR 2, with a satisfactory radiation performance within the bandwidth. The proposed method is also applicable to the design of other types of low profile slot-loaded patch antennas. Index Terms—Low profile, microstrip antennas, wideband antennas.

I. INTRODUCTION It is well known that a narrow impedance bandwidth (typically a few percent) is the most serious disadvantage of microstrip patch antennas. In modern wireless communication systems, the typically required operating bandwidths for antennas are about 8.1% for an advanced mobile phone system (AMPS; 824–894 MHz), 7.6% for a global system for mobile communication (GSM; 890–960 MHz), and 9.5% for a digital Manuscript received March 21, 2009; revised May 22, 2009; accepted January 28, 2010. Date of publication April 22, 2010; date of current version July 08, 2010. This work was supported in part by the Natural Science Foundation of China under Grant (60971030), the New Century Excellent Talent Program in China under Grant (NCET-06-0809), and in part by the 111 Project of China under Grant (B07046). The authors are with the School of Electronic Engineering, University of Electronic Science and Technology of China (UESTC), Chengdu 611731, China (e-mail: [email protected]). Digital Object Identifier 10.1109/TAP.2010.2048850

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communication system (DCS; 1710–1880 MHz). On the other hand, compact microstrip antennas are essential in personal mobile communication and other miniaturized communication systems for low-cost manufacturing and high integration with other electronic devices. However, in the low microwave frequency range such as AMPS, GSM, and DCS band, the sizes of microstrip antennas are usually too large to be installed into a mini-system. Thus, the problem of achieving a wide impedance bandwidth for a compact microstrip antenna is becoming an important topic in modern microstrip antenna design. Recently, several techniques have been proposed to reduce the size of wideband microstrip antennas [1]–[21]. In [1]–[10], various compact wideband microstrip antenna designs with slot cutting in the radiating patch are described. However, most of the slot-loading techniques, such as U-slot patch antennas [1]–[5], V-slot loaded rectangular patch antenna [6] and E-shaped patch antennas [4], [7]–[10], require a large antenna thickness over 0:060 . The large thickness of these slot-loaded patch antennas is mainly due to their thick air substrate. As another type of wideband single-layer single-patch antenna, the L-probe fed patch antenna proposed in [11], [12] exhibits a wide impedance bandwidth over 30%. However, as mentioned in [4], substrate thickness of the L-probe fed patch antenna will always be larger than 0:080 . The miniaturization of wideband patch antennas has also been accomplished by using shorting posts or shorting walls [13]–[16]. However, these shorted patch antennas usually suffer from the disadvantage of poor gain and degradation in the radiation patterns. The stacking of multiple resonators on different layers of dielectric substrates is also a practical approach for broadband operation, but the total antenna height will be very large for lower operating frequencies [17]–[19]. The chip-resistor loading technique is another promising technique to achieve wide impedance bandwidth and small antenna size [20]–[23]. However, due to the introduced ohmic loss of the chip-resistor loading, the antenna gain will be decreased significantly. With the development of modern communication systems, low profile configuration, wide impedance bandwidth, and high gain are becoming important design considerations for practical applications of microstrip antennas. Apparently, the techniques presented in [1]–[23] are not suitable if low profile configuration, wide bandwidth, and high gain are required simultaneously. To our knowledge, little study has been carried out to enhance the bandwidth of a low profile patch antenna without shorting or chip-resistor loading techniques to avoid the gain reduction. In this paper, we propose a low profile wideband patch antenna with simple coaxial feed configuration based on the conventional E-shaped patch, with a thickness of only 0:0430 . A simple distributed LC circuit connected to the E-shaped patch via the feed probe is introduced. In the low profile patch antenna, the low inductance resulted from the probe is compensated by the distributed LC circuit, thus the thickness of the air substrate in the conventional E-shaped patch antenna can be reduced. Meanwhile, the new resonant frequency obtained from the LC circuit is near from that of the E-shaped patch, thus the impedance bandwidth is widened. No additional shorting or chip-resistor loading techniques is applied, thus there is no reductions in the gain. The patch antenna was designed using the commercial software Ansoft HFSS, and was fabricated and measured. Measured results of the VSWR and far-field E and H-plane radiation patterns of the designed antenna over the frequency band are in good agreement with those simulated. II. ANTENNA DESIGN A. Review on the Conventional E-Shaped Patch Antenna Various types of slot-loaded patch antennas have been proposed for size reduction and wideband operation, such as the U-slot loaded [1]–[5], V-slot loaded [6], E-shaped patch [7]–[10], C-shaped patch

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Fig. 1. Configuration of the conventional E-shaped patch antenna. (a) Side view of the antenna; (b) dimensions of the E-shaped patch.

Fig. 2. Simulated VSWRs for conventional E-shaped patch antennas with

2 cm and 1 = 1 2 cm. :

1=

[24], and H-shaped patch [25], etc. The antenna used in this study employs an E-shaped patch operated at AMPS band. Fig. 1 shows the configuration of the E-shaped patch antenna presented in [7], which is composed of an E-shaped patch fabricated on glass epoxy substrate ("r = 4:3, h = 0:16 cm, and tan  = 0:02), a probe feed and an air-filled substrate with a thickness of 1 = 2 cm. With the optimized slot dimensions and feed locations, the simulated VSWR plot is shown in Fig. 2. As can be seen, a broadband impedance bandwidth of 164 MHz is obtained. Fig. 3 shows the E- and H-plane radiation patterns at 870 MHz. An ultra low cross-polarization is observed in the E-plane, and the maximum cross-polarization level in the H-plane (016:5 dB) is much higher than that in the E-plane. On the other hand, if the air thickness is reduced from 2 cm to 1.2 cm and the patch size is reduced to 12:7 cm 2 14:5 cm for low profile and compactness purpose, only a narrow bandwidth of 40 MHz is obtained with its optimized slot dimensions, slot locations, and feed locations. The simulated VSWR of the E-shaped patch with 1.2 cm air thickness is also presented in Fig. 2. The configuration of this narrowband E-shaped patch antenna is shown in Fig. 4, where the side walls built up from the ground plane are intended to improve the front-to-back (F/B) ratio of the far-field radiation pattern. In Fig. 5, the input impedance of the E-shaped patch antennas with 1 = 2 cm is plotted in the Smith Chart, in comparison with that of the antenna with 1 = 1:2 cm. As can be seen, the resonant locus for 1 = 2 cm is located very close to the center, therefore, a wide impedance bandwidth is obtained. However, the resonant locus for 1 = 1:2 cm is too capacitive to provide a satisfactory input impedance matching, thus the impedance bandwidth is rather limited. The capacitive input impedance of the narrowband antenna with 1 = 1:2 cm can be explained from the following aspects. Firstly, the probe is shorted as the air thickness between the patch and ground plane is reduced, thus the inductance contributed by the probe is very low. Secondly, also due to the reduction of the air thickness, the capacitance introduced by the radiating patch and ground plane becomes very large, which in turn over compensates the low probe

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Fig. 5. Comparison of the input impedance for the two conventional E-shaped and : patch antennas with .

1 = 2 cm

1 = 1 2 cm

loop will move to the upper part of the Smith Chart, thus a low profile wideband patch antenna can be readily obtained. B. Geometry of the Low Profile Wideband E-Shaped Patch Antenna

Fig. 3. Radiation patterns of the antenna with (a) E-plane; (b) H-plane.

1 = 2 cm at 870 MHz.

Fig. 4. The optimized geometry of the E-shaped patch antenna with

1 2 cm. :

1=

inductance, thus the input impedance becomes too capacitive. Thirdly, it can be observed from Fig. 4 that the side walls and radiating patch are closely spaced, and this will also contribute a large capacitance in the antenna. It is obvious to note that if the low probe inductance was increased and simultaneously compensated by a suitable capacitance, in the case that the air thickness has not been increased, the resonant

The proposed antenna is designed with the center frequency chosen at 860 MHz. The radiating patch of the low profile wideband E-shaped patch antenna is kept the same as that illustrated in Fig. 4, and a distributed LC circuit is fabricated on the back side of the FR4 epoxy substrate ("r = 4:5, h = 0:16 cm, and tan  = 0:02). The substrate is suspended over the ground plane over an air gap of 1.2 cm, which corresponds to an electric thickness of 0:03440 . Side walls are also included in this design for high F/B ratio, the total height of the antenna is 1.5 cm (only 0:0430 ). Detailed dimensions of the distributed LC circuit and side view of the antenna geometry are depicted in Figs. 6(a) and 6(b), respectively. In Fig. 6(b), the LC circuit is in series of the feed, where the circular plate in the distributed LC circuit is integrated with spiral inductor, and both of them are connected to the radiating patch through the feeding probe of a 50 SMA launcher [see Fig. 6(b)]. The simple spiral inductor is employed to increase the inductance component of the input impedance. Meanwhile, a series of capacitor is introduced by the circular plate, E-shaped radiating patch and the ground plane, this new capacitor can well compensate the inductance produced by the probe and spiral inductor, thus a new resonant frequency is expected to be formed. By properly selecting the dimensions of the distributed LC circuit, the newly formed resonant frequency can be very close to the resonant frequency of the E-shaped patch, thus leading to a widened impedance bandwidth. In the distributed LC circuit design, one thing should be kept in mind is that the number of winding turns and the width of the spiral inductor should be adjusted according to the locus of the normalized input impedance in the Smith Chart. Specifically, if the input impedance is too capacitive, the number of winding turns should be increased, and the width should be reduced. Meanwhile, the size of the circular plate should also be adjusted to provide a sufficient capacitance to match the inductance. Similarly, if the input impedance is too inductive, size of the circular plate should be adjusted accordingly to match a low inductance. Nevertheless, the low-profile microstrip antenna will always exhibit as a capacitive circuit, since the closely spaced patch and ground lead to a large equivalent capacitance.

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Fig. 6. Configuration of the E-shaped patch antenna with a distributed LC circuit. (a) Geometry of the distributed LC circuit; (b) side view of the antenna.

III. EXPERIMENTAL RESULTS To validate the design principle, a prototype antenna was fabricated and measured. The simulated and measured VSWRs of the low profile E-shaped patch antenna are presented in Fig. 7(a). The measurement results agree well with the simulation results, and it is observed that the proposed antenna has a wide impedance bandwidth over 9%, ranging from below 820 MHz to above 900 MHz for VSWR < 2. Fig. 7(b) shows the simulated impedance locus versus the frequency. As compared to the impedance locus of the antenna without distributed LC circuit (Fig. 5, dotted line), the impedance locus was indeed shifted to the upper part of the Smith Chart, thus the bandwidth is doubled from 40–80 MHz. This impedance locus shift is due to the additional inductance introduced by the spiral inductor. To explicitly demonstrate the mechanism of the bandwidth enhancement method, the equivalent circuit of the antenna is modeled. Let’s begin by considering the equivalent circuit of the conventional E-shaped patch antenna (with large air thickness 0:080 at 2.4 GHz) in [10]. It is not difficult to note that the inductance L in Fig. 2(b) of [10] is resulted from the probe. However, as the air thickness is reduced, the inductance L will be very small. Therefore, the first resonant frequency is failed to be created, and there will be only one resonant frequency, where the inductance (L + 1Ls) is mainly due to L. the slots cut in the patch, i.e., 1Ls Based on the analysis for the equivalent circuit of conventional E-shaped patch antenna, the equivalent circuit of the present antenna is modeled in an explicit way. L1, L2, and L3 are the inductances produced by the patch slots, feed probe, and spiral inductor, respectively, while C1 is the capacitance between the patch and ground (with side walls), C2 is the capacitance between the circular plate and the ground, and C3 represents the capacitance between the circular



Fig. 7. VSWR, input impedance, and the equivalent circuit model of the low profile E-shaped patch antenna. (a) Simulated and measured VSWRs; (b) input impedance in the Smith Chart; (c) the equivalent circuit model.

plate and patch. The first equivalence circuit in Fig. 7(c) shows the formation of the first resonant frequency f1 , which is produced by L1, L2 and C1. When the parasitic LC circuit is introduced on the back side of the substrate, a new resonant frequency f2 is created. As shown in the second LC circuit of Fig. 7(c), the new resonant frequency f2 is created by L2, L3, C2, and C3, where the probe inductance L2 is very small in the low-profile patch antennas, and the spiral inductor will dominate the inductance component in the circuit. Thus, the new resonant frequency f2 will differ from that arising in the E-shaped patch. Therefore, it is reasonable to think that the antenna consists of two LC resonant circuits with different resonant frequencies, and when the two resonant circuits couple together, a wide bandwidth is obtained.

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creation of an equivalent LC circuit. As can be seen, the concept of LC circuit is very useful for microstrip antenna designs, and with this concept in mind, antenna designers can develop various novel methods for their particular aims. With the design method we have developed, a prototype antenna with a wide impedance bandwidth of 9% (VSWR < 2) has been fabricated. The total height of the proposed antenna is only 0:0430 , which outperforms all the other kinds of slot loaded patch antennas in [1]–[23]. Although only E-shaped patch antenna is discussed in this paper, the design method is also applicable to other kinds of slot loaded patch antennas. The proposed antenna is expected to have great potential usage in modern communication systems. ACKNOWLEDGMENT The authors would like to express their sincere thanks to the anonymous reviewers of this paper, whose constructive comments and suggestions have greatly improved the quality of this paper.

REFERENCES

Fig. 8. Simulated and measured radiation patterns at the center frequency 860 MHz. (a) E-plane; (b) H-plane.

Simulated and measured radiation patterns of the proposed antenna in both E-plane and H-plane at 860 MHz are illustrated in Fig. 8. Also, good agreement is obtained between the simulation and measurement results. Obviously, due to the side walls built from the ground, a good F/B ratio of 12 dB is obtained, which offers benefits to many wireless communication systems. In addition, both simulated and measured radiation patterns demonstrate that the antenna has a maximum gain of 7 dBi within the operating bandwidth. Since there is no additional shorting or chip-resistor loading techniques applied in our design, the gain of this antenna is larger than those presented in [13]–[16] and [20]–[23]. Simulation results demonstrate that the maximum cross-polarization appears in the H-plane and has a relatively low value of 022 dB, thus the high gain is also owing to the high polarization purity. IV. CONCLUSION A low profile and compact wideband E-shaped patch antenna is proposed. By introducing a distributed LC circuit on the backside of the conventional E-shaped patch antenna, the small probe inductance of the low profile antenna is increased, and a new resonant frequency close to that of a conventional E-shaped patch is obtained to produce a wideband frequency response. Other novel design methods based on the concept of equivalent LC resonator circuit can also be found in [26], [27]. In [26], a parallel LC resonator is introduced in the feed structure, and the input impedance bandwidth of a microstrip patch antenna has been improved from 3.2% to 6.9%. For the enhancement of the radiation efficiency, a defected ground structure is developed in [27] for the

[1] S. Weigand, G. H. Huff, K. H. Pan, and J. T. Bernhard, “Analysis and design of broadband single-layer rectangular U-slot microstrip patch antennas,” IEEE Trans. Antennas Propag., vol. 51, pp. 457–468, Mar. 2003. [2] A. A. Deshmukh and G. Kumar, “Compact broadband U-slot loaded rectangular microstrip antennas,” Microw. Opt. Technol. Lett., vol. 46, no. 6, pp. 556–559, Sep. 2005. [3] T. Huynh and K. F. Lee, “Single-layer single-patch wideband microstrip antenna,” Electron. Lett., vol. 31, no. 6, pp. 1310–1312, Aug. 1995. [4] R. Chair, C. Mak, K. Lee, K. Luk, and A. A. Kishk, “Miniature wideband half U-slot and half E-shaped patch antennas,” IEEE Trans. Antennas Propag., vol. 53, pp. 2645–2652, Aug. 2005. [5] B. Ooi, “A double-II stub proximity feed U-slot patch antenna,” IEEE Trans. Antennas Propag., vol. 52, pp. 2491–2496, Sep. 2004. [6] A. A. Deshmukh and G. Kumar, “Broadband compact V-slot loaded RMSAs,” Electron. Lett., vol. 42, no. 17, pp. 951–952, Aug. 2006. [7] A. A. Deshmukh and G. Kumar, “Compact broadband E-shaped microstrip antennas,” Electron. Lett., vol. 41, no. 18, pp. 989–990, Sep. 2005. [8] Y. Ge, K. P. Esselle, and T. S. Bird, “E-shaped patch antennas for highspeed wireless networks,” IEEE Trans. Antennas Propag., vol. 52, pp. 3213–3219, Dec. 2004. [9] B. Ooi and M. Leong, “Novel design of broad-band stacked patch antenna,” IEEE Trans. Antennas Propag., vol. 50, pp. 1391–1395, Oct. 2002. [10] F. Yang, X. Zhang, X. Ye, and Y. Rahmat-Samii, “Wide-band E-shaped patch antennas for wireless communications,” IEEE Trans. Antennas Propag., vol. 49, pp. 1094–1100, Jul. 2001. [11] C. L. Mak, K. M. Luk, and K. F. Lee, “Microstrip line-fed L-strip patch antenna,” Proc. Inst. Elect. Eng. Microw. Antennas Propag., vol. 146, no. 4, pp. 282–284, Aug. 1999. [12] Y. X. Guo, K. M. Luk, and K. F. Lee, “L-probe proximity-fed annular ring microstrip antennas,” IEEE Trans. Antennas Propag., vol. 49, pp. 19–21, Jan. 2001. [13] A. A. Deshmukh and G. Kumar, “Compact broadband gap-coupled shorted square microstrip antennas,” Microw. Opt. Technol. Lett., vol. 48, no. 7, pp. 1261–1265, Jul. 2006. [14] Y. J. Wang, C. K. Lee, and W. J. Koh, “Single-patch and single-layer square microstrip antenna with 67.5% bandwidth,” IEE, Proc. Microw. Antennas Propag., vol. 148, no. 6, pp. 418–422, Dec. 2001. [15] D. M. Kokotoff, R. B. Waterhouse, and J. T. Aberle, “An annular ring coupled to shorted patch,” IEEE Trans. Antennas Propag., vol. 45, pp. 913–914, May 1997. [16] R. B. Waterhouse, “Broadband stacked shorted patch,” Electron. Lett., vol. 35, no. 2, pp. 98–99, Jan. 1999. [17] Z. Liu, P. Kooi, L. Li, M. Leong, and T. Yeo, “A method for designing broad-band microstrip antennas in multilayered planar structures,” IEEE Trans. Antennas Propag., vol. 47, pp. 1416–1420, Sep. 1999. [18] A. A. Deshmukh and G. Kumar, “Compact broadband stacked microstrip antennas,” Microw. Opt. Technol. Lett., vol. 48, no. 1, pp. 93–96, Jan. 2006.

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[19] M. A. Matin, B. S. Sharif, and C. C. Tsimenidis, “Probe fed stacked patch antenna for wideband applications,” IEEE Trans. Antennas Propag., vol. 55, pp. 2385–2388, Aug. 2007. [20] K. L. Wong and Y. F. Lin, “Microstrip-line-fed compact broadband circular microstrip antenna with chip-resistor loading,” Microw. Opt. Technol. Lett., vol. 17, no. 1, pp. 53–55, Jan. 1998. [21] K. L. Wong and Y. F. Lin, “Small broadband rectangular microstrip antenna with chip-resistor loading,” Electron. Lett., vol. 33, no. 19, pp. 1593–1594, Sep. 1997. [22] K. L. Wong and J. Y. Wu, “Bandwidth enhancement of circularly polarized microstrip antenna using chip resistor loading,” Electron. Lett., vol. 33, no. 21, pp. 1749–1751, Oct. 1997. [23] C. Y. Huang, J. Y. Wu, and K. L. Wong, “Broadband circularly polarized square microstrip antenna using chip-resistor loading,” Proc. Inst. Elect. Eng. Microw. Antennas Propag., vol. 146, no. 1, pp. 94–96, Feb. 1999. [24] G. Kossiavas, A. Papiernik, J. P. Boisset, and M. Sauvan, “The C-patch: A small microstrip element,” Electron. Lett., vol. 25, no. 4, pp. 253–254, Feb. 1989. [25] V. Palanisamy and R. Garg, “Rectangular ring and H-shaped microstrip antennas-alternative approach to rectangular microstrip antenna,” Electron. Lett., vol. 21, no. 19, pp. 874–876, Sep. 1985. [26] D. De Haaij, J. W. Odendaal, and J. Joubert, “Increasing the bandwidth of a microstrip patch antenna with a single parallel resonant circuit,” in Proc. IEEE AFRICON Conf., Oct. 2002, vol. 2, pp. 527–529. [27] A. K. Arya, M. V. Kartikeyan, and A. Patnaik, “Efficiency enhancement of microstrip patch antenna with defected ground structure,” in Proc. Int. Conf. Recent Adv. Microw. Theory Appl., Nov. 2008, pp. 729–731.

Frequency-Scaled UWB Inverted-Hat Antenna Jing Zhao, Chi-Chih Chen, and John L. Volakis

Abstract—A novel ultrawideband (UWB) antenna referred to as the inverted-hat antenna (IHA) is described. Specifically, the paper provides a systematic approach to generate a frequency-scaled IHA structure subject to aperture width and height constraints. An experimental verification is also given. The proposed compact wideband antenna exhibits frequency-independent behavior by introducing a moderate number of appropriately scaled elliptical segments and by controlling the outer surface growth profile. A modified seven-ellipse IHA is demonstrated in this paper to provide a 10:1 impedance bandwidth with satisfactory radiation properties. The simulation and measurement results are in reasonably good agreement. Index Terms—Frequency independent antennas, ultrawideband (UWB) antennas.

I. INTRODUCTION Low-profile ultrawideband (UWB) monopole antennas are attractive for aircraft and ground vehicle voice communication systems. The volcano smoke structure [1], conical [2], and Vivaldi antenna are wellknown broadband radiators sharing the feature of tapering their surface away from the feed to maintain nearly constant impedance over a large bandwidth. Their pattern is also of the dipole-type. However, they are protruding and non-conformal for low frequency operation. Manuscript received July 09, 2009; revised December 20, 2009; accepted January 23, 2010. Date of publication April 26, 2010; date of current version July 08, 2010. The authors are with the ElectroScience Laboratory, Department of Electrical and Computer Engineering, The Ohio State University, Columbus, OH 43212 USA (e-mail: [email protected]). Color versions of one or more of the figures in this communication are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2010.2048866

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Broadband planar monopoles were also considered in recent years for portable wireless devices where low-profile radiators are typically required. Among them, planar circular and elliptical discs [3], invertedcones [4] and staircase printed monopoles [5] were shown to achieve large impedance bandwidth and stable patterns in the vertical plane. But, their patterns were not omindirectional in the horizontal plane. Three-dimensional (3-D) antenna structures (constructed of planar elements) were also reported in [6], [7]. However, the latter were not low-profile as their height was more than =6 at the lowest frequency of operation. Parasitic elements were introduced to the body-of-revolution structure in [8] and [9] to increase the impedance bandwidth while maintaining low-profile. Nevertheless, the resulting azimuth plane pattern was not omnidirectional at high frequencies. Being low profile, spiral antennas have been extensively studied as alternative frequencyindependent radiators [10], [11]. But spirals radiate a patch-like pattern, not desirable for over the horizon low frequency operation. A compact frequency-scaled monopole antenna for UWB operation is therefore desirable. In [12], we presented a compact low-profile inverted-hat antenna (IHA) operating from low VHF frequencies up to 2 GHz with excellent vertical polarization (VP) radiation near grazing incidences (over the horizon). By properly controlling the diffracted fields at each local elliptical segment forming the IHA, the proposed [12] double-ellipse and triple-ellipse IHA was shown to achieve good performance at both low and high frequencies. However, the presented design was not optimal as its impedance exhibited large variations. In this communication, we provide a systematic approach to design the outer profile of the IHA subject to aperture size and height. The goal is to achieve controllable input impedance and uniform radiation pattern. Specifically, a seven-ellipse IHA prototype is designed and fabricated, showing good agreement between measurements and calculations. The proposed UWB configuration is targeted for Single-Chanel Ground-Air Radio System (SINGARS) as well as VHF and UHF band. II. ANTENNA PROFILE The geometry of the proposed IHA is shown in Fig. 1. Its feed generates outward travelling waves giving vertically polarized radiation over the horizon. Referring to [13], an UWB antenna can be formed by assembling structures with similar geometry scaled with distance from a reference feed point. To achieve a nearly invariant radiation over a large bandwidth, the IHA’s surface was constructed by many elliptically contoured (concave and convex) surfaces as depicted in Fig. 1(b). The arrangement of theses elliptical surfaces was inspired by the exponential spiral’s growth. Specifically, the major radii of the ellipses forming the IHA were chosen to related with the  = 0 spiral crossing points. Referring to Fig. 1(a), we chose

Xn = ea

(1)

where Xn are the x-axis crossings of the spiral, n = ; 3; 5; 7; . . ., and a is the spiral growth rate. We can surmise that if the IHA’s outer surface consists of N ellipses, then

Xn = ea(2n01)

for n = 1; 2; . . . ; N:

(2)

As dictated, the frequency-scaled operation requires that the radiating structure sections be similar, but scaled proportionally to the wavelength. Different frequencies are designed to diffract at appropriately scaled local elliptical segments. The major radius ratio between adjacent ellipses is therefore a constant, implying

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Xn+1 = ea : Xn

(3)

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Fig. 2. IHA (15” wide and 6” tall) geometry for several multi-ellipse outer surfaces.

2

3

M

h M +1 01 :

1 1 ln (w=2) 1 = 1 e (w=2) =

(7)

is a parameter used to adjust the curvature of the convex or Also, concave curve to improve impedance matching. For our design, = 0 5 is found to be a good choice. We remark that the major and minor 2 and , respectively, for the uppermost ellipse. These radius reach values do, of course, control the lowest frequency of operation. This is true for all types of IHA antennas (linear, convex, and concave) as depicted in Fig. 4(a). As seen from Fig. 1(b), the n and n values must be scaled down to satisfy the pre-specified aperture size and height . Doing so, the revised n and n become

:

M

w=

h

X

x

Fig. 1. (a) Spiral pattern for the determination of the major radius of each elliptical segment. (b) Configuration (side view) of a triple-ellipse inverted-hat antenna (IHA) having an aperture size of w and height of h; for each elliptical segment, x is the major radius and y is the minor radius. (c) 3-D view of a triple-ellipse linear IHA.

Y

y

w

h

xn = fx 1 Xn yn = fy 1 Yn : (8) The scaling parameters fx and fy are appropriately given by fx = (Nw=2)X n n h fy = N : (9) n Yn For the linear profile multi-ellipse IHA, fx and fy are identical. An =1

N

Since the antenna is fed from the high frequencies region, the th ellipse (uppermost one) corresponds to the lowest frequency. From 2 to acFig. 1(b), if the total IHA width is , we chose N to be count for the travelling distance of the lowest frequency before diffraction, viz

w

XN = ea

N01) =

(2

X

w=

w:

(4)

2

=1

explicit illustration of the linear triple-ellipse IHA geometry is shown in Fig. 1(b), accompanied by a 3-D view in Fig. 1(c). III. ANTENNA PERFORMANCE A. Multi-Ellipse IHA for Frequency-Independent Operation

Thus,

a = (2N 10 1) ln w2 :

(5)

X n

Consequently, the major radius of other elliptical segments n ( = 1 2 . . . 0 1)) can be determined by inserting (5) into (2). As seen later, the outer surface growth profile of the IHA provides input impedance control. This is achieved by adjusting the ratio of major radius n to minor radius n of the elliptical segments. Specifically, we set [see Fig. 4(a)]

; ; N

X

Y

1 Xn Yn = M 1 e X 0 1 M 1 ln( 1 Xn + 1) The indicated i factors are given by

= (w=h 2) 1

1

3

1

linear convex concave:

(6)

Following the geometrical prescription given above, we now consider several different IHA outer surfaces (up to eleven ellipses). In all cases, the IHA is 15” (381 mm) wide and 6” (152 mm) tall. Full-wave simulations were carried out using commercial computational electromagnetics software FEKO. The geometry and corresponding electrical performance for various multi-ellipse IHA are given in Figs. 2 and 3, respectively. (The double-ellipse IHA is referred to [12]). In particular, an infinite ground plane was assumed for all calculations below. As seen, when the number of ellipses describing the outer surface increases, the resistance approaches 50 and the reactance levels-off at 0 , indicating a very desirable matching condition. Furthermore, we observed that the realized gain over horizon achieves a fairly constant level of about 5 dB at high frequencies. This is a result of the multiple diffraction points forming the outer surface of the multi-ellipse IHA design. Indeed, smooth transitions between each segment allow for continuous diffraction along the whole curved antenna profile, resulting in UWB performance.

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Fig. 3. Electrical performances of IHA (15” wide and 6” tall) for several multiellipse outer surfaces: (a) realized gain in the horizontal plane ( = 90 ), (b) input resistance, and (c) input reactance.

B. Outer Surface Growth Profile for Flexible Impedance Control

Fig. 4. Impedance calculation for different outer surface profiles of the elevenellipse design using 15” wide and 6” tall IHA: (a) geometry, (b) resistance, and (c) reactance.

As can be seen from Fig. 2, the points interconnecting the ellipses lie on a linear curve. However, for better impedance control, we may consider designs where these points lie on a non-linear curve (say, convex or concave). Indeed, Fig. 4 shows that the concave profile exhibits higher resistance than the linear one, whereas the convex profile gives lower input resistance value. This observation is similar to that for the conical antenna. To better illustrate impedance flexibility, we also investigated a 24” (610 mm) wide and 6” (152 mm) tall IHA with different outer surface profiles. Enlargement of the aperture size is, of course, needed to achieve lower operational frequency. However, a larger aperture size

leads to lower input resistances, causing mismatch and gain reduction. In particular, calculations were carried out for a conical antenna, single-ellipse IHA and eleven-ellipse concave IHA. As shown in Fig. 5, the input resistance of the conical antenna is roughly 40 for this specific width/height ratio. We observed that the single-ellipse IHA exhibited high impedance, and only the eleven-ellipse concave IHA achieved 50 , with relatively low oscillations, necessary for UWB operation. That is, for a given aperture size and height, the multi-ellipse IHA is capable of achieving a desired input impedance.

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Fig. 5. Impedance performance for two IHA designs versus a conical antenna all being 24” wide and 6” tall: (a) geometry, (b) resistance, and (c) reactance.

C. Measurements and Validation In this section, we present measurements to validate our multi-ellipse IHA design. However, for practical purposes (manufacturing difficulties), we replaced the IHA tip near the feed with a tapered concave profile as depicted in Fig. 6(a). This resulted in a modified seven-ellipse 15” (381 mm) 2 6” (152 mm) IHA that was enclosed in a 16” (406 mm) radome having a dielectric constant of r = 2:2 [see Fig. 6(b)]. As seen, a reasonably good agreement is observed between measurements and calculations. The reflection coefficient and realized gain in the horizontal plane ( = 90 ) are depicted in Fig. 6(c)–(d). Fed by a 50 coaxial cable, the modified seven-ellipse IHA prototype provided a 10 dB return loss from 0.2–2 GHz, indicating a 10:1 impedance bandwidth. Satisfactory radiation was also achieved. We note that one of the reference horn antennas had a lowest operational frequency of 1 GHz. As a result, some gain inconsistencies can occur at this frequency. Due to the 17” (432 mm) finite ground plane, both measured and simulated gain over horizon are lower than that of the infinite ground plane case. Use of ferrite material on the ground plane is likely to recover some of this gain reduction [14]. Fig. 7 shows the calculated and measured normalized gain patterns in the elevation plane for different frequencies. Clearly, the IHA exhibits

Fig. 6. Measurements versus calculation for a modified seven-ellipse IHA: (a) geometry, (b) fabricated prototype with randome, (c) reflection coefficient, and (d) realized gain in the horizontal plane ( = 90 ).

the desired monopole-like patterns at all frequencies. This performance demonstrates the effectiveness of the diffraction points at the junctions of the adjoining ellipses forming the IHA outer surface. IV. CONCLUSION We presented an inverted-hat antenna (IHA) design whose outer surface is composed of multiple ellipses that followed the growth rate of an exponential spiral. The communication provided the mathematical details for constructing the outer IHA surface aimed at providing UWB performance. We observed a nearly frequency-independent behavior for a moderate number of elliptical segments used to construct the IHA. Impedance control can also be achieved by employing different outer surface profiles. Due to fabrication difficulties in realizing the eleven-ellipse IHA, a modified seven-ellipse design was tested to validate the concept. This approach manages to maintain a similar scattering geometry in terms of wavelength, providing controllable input impedance and uniform radiation patterns, important in guiding the disign of future low-profile UWB antennas. In particular, the proposed

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[13] C.-C. Chen, “Ultrawide bandwidth antenna design,” in Antenna Engineering Handbook, J. L. Volakis, Ed., 4th ed. New York: McGrawHill, 2007. [14] F. Erkmen, C.-C. Chen, and J. L. Volakis, “UWB magneto-dielectric ground plane for low-profile antenna applications,” IEEE Antennas Propag. Mag., vol. 50, no. 4, pp. 211–216, Aug. 2008.

Reinforced Continuous Carbon-Fiber Composites Using Multi-Wall Carbon Nanotubes for Wideband Antenna Applications Aidin Mehdipour, Abdel-Razik Sebak, Christopher W. Trueman, Iosif D. Rosca, and Suong. V. Hoa

Fig. 7. Measured and calculated normalized gain patterns for a modified sevenellipse IHA (in the elevation plane).

compact wideband antenna can be applied across a variety of vehicular platforms.

Abstract—We explore using reinforced continuous carbon fiber (RCCF) composite for wideband antennas in wireless applications. We use composite material as the radiating element for a monopole antenna. An electromagnetic (EM) model of the composite antenna is developed using Microwave Studio for numerical analysis. An RCCF composite sample is prepared including up to 2% multiwall carbon nanotube (MWCNT) to enhance the conductivity. The anisotropic conductivity of the resulting material is determined by measurement using standard waveguide setups. The reflection coefficient, radiation pattern and gain of the composite antenna are investigated. The frequency- and time-domain dispersions are found for the composite antenna to show its suitability for ultrawideband (UWB) communication systems. It is observed that RCCF/MWCNT composite is an effectively alternative to metal for the antenna structure. Index Terms—Antenna, radiating element, reinforced carbon-fiber composites, wideband antennas.

REFERENCES [1] J. D. Kraus, Antennas, 2nd ed. NewYork: McGraw-Hill, 1988, pp. 692–694. [2] S. S. Sandler and R. W. P. King, “Compact conical antenna for wideband coverage,” IEEE Trans. Antennas Propag., vol. 42, no. 3, pp. 436–439, Mar. 1994. [3] N. P. Agrawall, G. Kumar, and K. P. Ray, “Wide-band planar monopole antennas,” IEEE Trans. Antennas Propag., vol. 46, no. 2, pp. 294–295, Feb. 1992. [4] S. Suh, W. L. Stutzman, and W. A. Davis, “A new ultrawideband printed monopole antenna: The planar inverted cone antenna (PICA),” IEEE Trans. Antennas Propag., vol. 52, no. 5, pp. 1361–1364, May 2004. [5] D. Valderas, R. Alvarez, J. Melendez, I. Gurutzeaga, J. Legarda, and J. I. Sancho, “UWB staircase-profile printed monopole design,” IEEE Antennas Wireless Propag. Lett., vol. 7, pp. 255–259, 2008. [6] Z. N. Chen, “Broadband roll monopole,” IEEE Trans. Antennas Propag., vol. 51, no. 11, pp. 3175–3177, Nov. 2003. [7] B. Heydari, A. Afzali, and H. R. Goodarzi, “A new ultrawideband omnidirectional antenna [antenna designer’s handbook],” IEEE Antennas Propag. Mag., vol. 51, no. 4, pp. 124–130, Aug. 2009. [8] S. Palud, F. Colombel, M. Himdi, and C. L. Meins, “A novel broadband eighth-wave conical antenna,” IEEE Trans. Antennas Propag., vol. 56, no. 7, pp. 2112–2116, Jul. 2008. [9] H. Nakano, H. Iwaoka, K. Morishita, and J. Yamauchi, “A wideband low-profile antenna composed of a conducting body of revolution and a shorted parasitic ring,” IEEE Trans. Antennas Propag., vol. 56, no. 4, pp. 1187–1192, Apr. 2008. [10] P. E. Mayes, “Frequency-independent antennas and broadband derivatives thereof,” Proc. IEEE, vol. 80, no. 1, pp. 103–112, Jan. 1992. [11] B. A. Kramer, C.-C. Chen, and J. L. Volakis, “Size reduction of a low-profile spiral antenna using inductive and dielectric loading,” IEEE Antennas Wireless Propag. Lett., vol. 7, pp. 22–25, 2008. [12] J. Zhao, C.-C. Chen, and J. L. Volakis, “Low-profile ultra-wideband inverted-hat monopole antenna for 50 MHz–2 GHz operation,” Electron Lett., vol. 45, no. 3, pp. 142–144, Jan. 2009.

I. INTRODUCTION Metals such as copper or aluminum are commonly used for the radiating element of an RFID tag. In harsh environments corrosion resistance and the adhesion between radiating element and the substrate supporting it are major issues. Some recent studies have used various composite materials as replacements for metals [1]–[6]. In [1], a conducting-polymer patch antenna is proposed. In [2], a conductive textile coated with carbon nanotubes (CNTs) and gold is used to fabricate a patch antenna. Silver nanoparticle ink [3], [4] and metallo-organic conductive ink [5] have been used to prepare a highly-conductive material as a replacement for metal for RFID tag antennas. In [6], metalized foam is used to make microstrip-patch antenna. Advanced carbon-fiber composite (CFC) materials are being used in the aerospace industry as a good replacement for metal because of Manuscript received June 25, 2009; revised September 25, 2009; accepted November 08, 2009. Date of publication April 26, 2010; date of current version July 08, 2010. This work was supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC), Bell Helicopter Textron Canada Ltd., Delastek Ltd., and in part by the Consortium for Research and Innovation in Aerospace in Quebec (CRIAQ). A. Mehdipour, A. R. Sebak, and C. W. Trueman are with the Department of Electrical and Computer Engineering, Concordia University, Montreal, QC H3G 2W1, Canada (e-mail: [email protected]; [email protected]; [email protected]). I. D. Rosca and S. V. Hoa are with the Department of Mechanical and Industrial Engineering, Concordia University, Montreal, QC H3G 2W1, Canada (e-mail: [email protected]; [email protected]). Color versions of one or more of the figures in this communication are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2010.2048862

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Fig. 2. Fabrication procedure for RCCF/MWCNT composite material.

Fig. 1. (a) RCCF composite, (b) cross-sectional view, (c) optical micrograph of RCCF composite (scale bar 50  ).

m

their outstanding mechanical properties [7]–[10]. Higher strength and lower cost and weight make CFC materials very good candidates to replace metals. However, CFCs have lower electrical than metals, and so shielding effectiveness is of concern for electromagnetic compatibility (EMC) applications [8], [9]. Reinforced continuous carbon-fiber (RCCF) composite is used extensively due to its low cost and ease of fabrication [9], [10]. The high oxidation stability recommends RCCF composites for applications where metals cannot be used because of corrosion. The density of RCCF composites is around 1.5 g=cm3 , half that of aluminum and more than five times lower than copper. This material has a higher conductivity than many other kinds of composites. It is an effective replacement for metal when high shielding is required. Because the carbon fibers run in one direction only, the conductivity is anisotropic, being high along the direction of fibers, but low in the perpendicular direction. The effective anisotropic conductivity of one-layer composite depends on the thickness of layer, the fiber diameter, the separation distance between fibers and the conductivity of the fibers [9]. In [11], using numerical modeling, we investigated RCCF and braided-tissue carbon-fiber materials for the radiating element of an RFID antenna. It was observed that RCCF composite can be efficiently used in such a resonant antenna. In this work, we explore using reinforced carbon fiber composites for wireless and ultrawideband (UWB) antenna applications. The allocated frequency spectrum for wireless local area networks (WLANs) is 5.15–5.875 GHz [12] and for UWB systems is 3.1–10.6 GHz [13]. The metal radiating element of a wideband monopole antenna is replaced with composite material, and the performance is investigated by measurement and by numerical simulation. II. CARBON-FIBER COMPOSITE MATERIAL The structure of RCCF composite material and the method of fabrication are explained in this section. The composite samples are produced by the Concordia Center for Composites (CONCOM) [14]. Standard waveguide setups are used to measure the scattering parameters of the sample with the fibers oriented parallel to and also perpendicular to the narrow side of the guide. Then the waveguide setup is modeled with CST-Microwave Studio (CST MWS) [15]. By minimizing the difference between the simulated and measured scattering parameters over a frequency range, the complex permittivity can be extracted [16]. A. Single-Layer RCCF Composite Fig. 1 shows a typical RCCF composite material. The carbon fibers are embedded in epoxy resin and are oriented in a specific direction. The effective complex permittivity of one-layer composite depends on the thickness of layer (t), the fiber diameter (D), the separation distance (s) and the complex permittivity of fibers and the host medium

("f ; "m ). The effective complex permittivity of the homogenized model of RCCF is given by [9] 1 01 01 "0 z = (1 0 g)"m + g"f "x = "y = (1 0 g)"m + g"f

(1) (2)

where g is a coefficient which depends on the volume fraction of the fibers inside the host medium (g = D2 =4st). In reality, the average diameter of fibers (D) is 4:9860:36 m and the separation distance between the fibers is typically 1 m. The conductivity of RCCF is anisotropic, being high along the direction of fibers, but low in the perpendicular direction. B. Composite Sample Preparation and Characterization In order to enhance the conductivity of RCCF composite, we add a small volume fraction of multiwall carbon nanotubes (MWCNTs) to the RCCF material. High electrical conductivity and high aspect ratio make carbon nanotubes (CNTs) one of the most promising filler materials for increasing the conductivity of polymer composites [7], [8], [16]. The aspect ratio of a carbon nanotube is the ratio of the length to the diameter. Higher aspect ratio leads to higher conductivity. MWCNTs are about 1000 times smaller than the fibers in RCCFs. The method of preparation of an RCCF sample loaded with MWCNTs is illustrated in Fig. 2. MWCNTs synthesized by catalytic vapor deposition are produced by NanoLab. The epoxy resin Epon 862 and the curing agent Epikure W are produced by Hexion Specialty Chemicals [17]. The unidirectional carbon cloth is purchased from MF Composites [18]. The resin, the curing agent (26.4 wt%) and a measured quantity of MWCNTs are weighed and three-roll-milled on a laboratory scale three roll mill (EXAKT 80E, EXAKT Technologies, Inc.). The mixture is degassed in a vacuum oven at 90 C for 30 min. Next, one ply of unidirectional carbon cloth is impregnated with the mixture and placed between two aluminum plates coated with demolding agent. Finally, the plates are tightened together by bolt joints, and the composite is cured at 120 C for 6 hours. An MWCNT loading of 2% is used for this antenna study. In order to characterize the composite sample, we use standard G-band (3.95–5.85 GHz) and X-band (8.2–12.4 GHz) rectangular waveguides with cross-section dimension of 47.548 2 22.148 mm2 and 22.86 2 10.16 mm2 , respectively. The thickness of the composite is 0.6 mm. The scattering parameters are measured with the fibers both parallel to and perpendicular to the T E10 electric field vector, to obtain the magnitude of S21 reported in Fig. 3. The figure shows that by adding 2% wt of MWCNT, the magnitude of S21 decreases by about 20 dB with the fibers parallel to the electric field (z -directed), and by about 8 dB with the fibers perpendicular. Comparing computations with MWS for various conductivity values with the waveguide measurements of the scattering parameters shows that the effective conductivity of the RCCF/MWCNT composite over the desired frequency range is 4000 S/m along fiber direction and 150 S/m perpendicular to the fibers. As expected, the conductivity of RCCF

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Fig. 3. Measured S parameter using standard waveguides. (a) Magnitude of S parameter over G-band, (b) magnitude of S parameter over X-band.

Fig. 5. Simulated reflection coefficient of the monopole antenna with metal and composite radiating element.

Fig. 4. Monopole antenna, (a) schematic front view, and (b) EM model in CST MWS.

is not significantly frequency dependant [9]. The effective permittivity of around 5 is obtained for both directions, showing that the permittivity is not anisotropic whereas the conductivity is highly anisotropic. III. MONOPOLE COMPOSITE ANTENNA Fig. 4 shows the EM model of the monopole antenna developed in MWS. The antenna is fed through a 50-ohm SMA connector at the bottom of the radiating element. The antenna geometrical parameters are G1 = G2 = 200 mm, L1 = 65 mm, L2 = 66 mm, g = 1:5 mm and d = 1 mm. The monopole antenna thickness is t = 0:6 mm. In simulations, we consider composite material as a homogeneous anisotropic medium as characterized in Section II. As a result, the composite antenna performance depends on the direction of fibers inside the radiating element. In order to address this issue, we study two different configurations: fibers along the x-axis and along the z -axis. A. Fiber Orientation The calculated reflection coefficient of the monopole composite antenna is shown in Fig. 5 for different fiber orientations. When the direction of the carbon fibers is along x-axis, parallel to the ground plane, the composite antenna’s reflection coefficient is very similar to that of the metal antenna. However, when the fibers are parallel to z -axis, the reflection coefficient of the composite antenna is quite different for x = 10 S=m than for 150 S/m. With the low value, the reflection coefficient is almost constant with frequency. With the high value, the reflection coefficient is somewhat similar to that of the metal antenna. This phenomenon can be understood by graphing the current distribution on the radiating element, as shown in Fig. 6. With the fibers horizontal or parallel to the ground plane, part (b) of the figure shows that the current on the horizontal edges is similar to that on the metal antenna in part (a). Note that there is more current on the vertical edges of the metal antenna, particularly at 900 MHz. But with the fibers oriented vertically and low conductivity in the horizontal direction, part

Fig. 6. The current distribution on monopole antenna at different frequencies, (a) Metal antenna, (b) composite antenna with x-directed fibers, (c) composite antenna with z -directed fibers ( = 10 S=m), and (d) composite antenna with z -directed fibers ( = 150 S=m).

(c) shows that the current distribution is reminiscent of a monopole antenna and quite unlike that of the metal antenna. When the horizontal conductivity is increased to 150 S/m, the current distribution in part (d) resembles that of the metal antenna of part (a), including the currents on the vertical edges. Note that the frequencies in Fig. 6 of 2, 6, and 9 GHz were chosen near the minima in the reflection coefficient curves of Fig. 5. However, for the top row the frequencies of 900, 800, 750, and 560 MHz were chosen to be the lowest frequency where the reflection coefficient in Fig. 5 is 010 dB. Orienting the fibers in the horizontal direction (x-directed) supports current flow along the bottom edge of the patch, making the current in Fig. 6(a) and (b) similar, especially at 2, 6, and 9 GHz. Current in the vertical direction is suppressed. When the fibers are vertical with a low conductivity of 10 S/m in the horizontal direction, Fig. 6(c), the current is forced to flow in the center of the radiating element, and is effectively suppressed in the horizontal edges. As a result, the resonant modes are then quite different than those of the metal antenna. The current of Fig. 6(c) is like a monopole at its fundamental resonance, at 560 MHz. The second and third resonances might be expected at 1680 and 2800 MHz, but the reflection coefficient of Fig. 5 shows no resonant

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Fig. 8. (a) Reflection coefficient of monopole RCCF/MWCNT composite antenna, (b) Measured input impedance.

Fig. 7. The efficiency and peak gain of composite antenna versus: (a) Thickness for a horizontal conductivity of 4000 S/m and a vertical conductivity of 10 S/m, (b) conductivity in the horizontal direction for a thickness of 0.6 mm and a vertical conductivity of 150 S/m.

behavior at these frequencies. Fig. 6(d) shows that increasing the horizontal conductivity to 150 S/m restores the behavior to be similar to that of the metal antenna. B. Ohmic Loss Due to the much lower conductivity of composites compared to metals, the ohmic loss (RLoss ) of the composite radiating element is higher. Therefore, the gain and radiation efficiency ( ) of composite antenna are lower than of a metal antenna. The ohmic loss of a conductive box with effective conductivity of e can be expressed as

Rloss =  LA e e

(3)

where Ae is the effective area along a current path of length L. For a composite antenna the current flows inside the volume of radiating element, Ae can be controlled by changing the conductivity itself and hence the skin depth, and the thickness t. Hence the gain of the composite antenna can be adjusted by changing both t and e . Fig. 7 shows a computational study, using the MWS model, of the effect of the sample thickness and the conductivity on the composite antenna performance. No data is provided in the frequency range from 2 to 5 GHz, where the reflection coefficient, see Fig. 5, is between 010 and 04 dB, and the antenna is not useful. In Fig. 7(a), the conductivity in the x- or horizontal direction is 4000 S/m and in the z - or vertical direction is 10 S/m. Fig. 7(a) shows that the radiation efficiency can be improved 20 to 30% by increasing t, but increasing the thickness beyond the skin depth does not much increase the efficiency. Fig. 7(a) also shows that the gain of the composite antenna is about 4 dB lower than that of the metal antenna for the thickest composite. Fig. 7(b), for a thickness of 0.6 mm and a vertical conductivity of 150 S/m, shows that if the horizontal conductivity can be increased, then the gain and efficiency also increase. By adding MWCNTs to the RCCF composite, we can increase the conductivity of composite along both fiber directions, leading to enhance the gain and radiation efficiency.

Fig. 9. Normalized radiation pattern of composite antenna at (a) and (b) -plane ( ).

E

yz

H -plane (xy),

IV. EXPERIMENTAL RESULTS In order to investigate the composite antenna performance experimentally and to verify the simulation results, the composite monopole antenna of Fig. 4 is fabricated using the composite material described in Section II. The composite antenna is installed such that the direction of fibers is parallel to x- or horizontal axis. The antenna geometrical parameters are G1 = G2 = 200 mm, L1 = 65 mm, L2 = 66 mm, t = 0:6 mm, g = 1:5 mm and d = 1 mm. A thin aluminum sheet is used as a ground plane and the composite antenna is fed through a 50-ohm SMA connector. Using HP8720 network analyzer, the reflection coefficient of fabricated RCCF/MWCNT monopole antenna is measured as displayed in Fig. 8(a). Good agreement is observed between simulated and measured results. The reflection coefficient is better than 10 dB from 4.9–10 GHz, which includes the WLAN frequency range of 5.15–5.825 GHz. The input impedance of the composite antenna is displayed in Fig. 8(b). The normalized radiation patterns in the E - and H -planes were measured using a standard ridged horn antenna (ETS-3115) as a receiver. Fig. 9 shows the radiation patterns at 5.5, 7 and 8.5 GHz. Due to the symmetry, only one-quarter of H - plane and half of E -plane is considered. The polarization of the composite antenna at boresight angle  ( = ' = 90 ) is also evaluated. The ratio of antenna gain for  -polarization to '-polarization, namely G =G' , is displayed in Fig. 10(a). It can be seen that G is 5 dB greater than G' in the measurement over almost the entire frequency range. We also investigated the polarization for ' = 0 , 30 , 45 , and 60 , not shown here, and we found that the antenna shows almost G =G' > 5 dB at these angles.

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G =G

 '

Fig. 10. (a) at boresight angle ( = = 90 ), and (b) boresight and peak gain of the monopole composite antenna.

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Fig. 11. Composite antenna Tx/Rx setup transfer function, (a) magnitude, (b) group delay.

According to Fig. 7(b), the largest gain over the wireless frequency band of the composite antenna in the MWS simulation varies between 4.7 dB and 5.2 dB. In order to validate the simulation results, the boresight gain of the composite antenna is measured. The IEEE standard antenna gain can be obtained by means of the antenna transfer function. Two identical composite antennas are considered in a Tx/Rx setup in front of each other, so that the S21 (f ) of two antennas can be written as

S21 (f ) = HT x (f )HCH (f )HRX (f )

(4)

where HT X (f ) and HRX (f ) are the Tx and Rx antenna transfer functions, respectively. Furthermore, HCH (f ) is the channel transfer function in free space defined as =4R where R is the separation distance between the antennas. The antenna gain can be calculated from

G(f ) = HT X (f )HRX (f )

2

1

0 jS11 (f )j2 1 1 0 jS22 (f )j2 0(1=2)

(5)

where S11 (f ) and S22 (f ) are the input reflection coefficient of the Tx and Rx antennas, respectively. By using (4), (5) can be written as

G(f ) = S21 (f ) (HCH (f ))01 2 1 0 jS11 (f )j2

1 1 0 jS22 (f )j2 0(1=2)

Fig. 12. The single-band scheme, (a) pulse signal, (b) normalized spectrum.

performed to calculate the fidelity factor between transmitted and received UWB pulses in Tx/Rx setups [19]. A UWB pulse source is designed using the derivatives of a Gaussian pulse [20], to cover the desired frequency range. To cover 4.9 to 10 GHz, the eighth derivative of the Gaussian pulse function was used, so the pulse source is given by

s(t) = Amax

105

0 420

t 

(6)

which gives the measured boresight gain of the antenna. Fig. 10(b) shows the measured boresight gain, using two identical composite antennas separated by R = 25 cm. The figure shows good agreement between the MWS simulation and the measurement. V. ULTRAWIDEBAND APPLICATION Since the composite antenna has a wide impedance bandwidth of 4.9 to 10 GHz, it could be used in ultrawideband (UWB) communication systems in the 3.1 to 10.6 GHz band. The dispersive behavior of an ultrawideband antenna should be considered [13], in both the frequency domain and the time domain. The frequency domain antenna dispersion characteristics can be defined by the magnitude of Tx/Rx transfer function jS21 j and the group delay 0d'=df , where ' is the angle of S21 . The Tx/Rx transfer function of the composite antennas in the front of each other ( = 90 , ' = 90 ) is displayed in Fig. 11. A fairly constant group delay shows that the antenna has low dispersion. When the group delay of antennas shows a highly frequency dependant behavior, the time domain pulse is considerably distorted due to the nonlinearity of phase. Specifically for UWB pulse signals, the group delay variations may lead to high level of error in wireless/UWB communication systems. It is very desirable to have an almost constant group delay over the frequency range of interest. To investigate the dispersion characteristics of an UWB antenna in more detail, time domain analysis is

038

2

+ 260

t 

6

+

t  t 

4

8

2 1 exp 02t2

(7)

where Amax is the peak power spectral density that FCC allows for UWB applications. The parameter  can be selected in order to satisfy the FCC spectral mask. With Amax = 3:2 mV=m and  = 60 ps, the pulse signal and its normalized Fourier transform are shown in Fig. 12. For wireless systems using UWB antennas, it is critical to evaluate the dispersive behavior for different angles between Tx and Rx antennas. This is due to the fact that the antenna could have low dispersion in some limited angular ranges, but have high dispersion for other angles. Using MWS, we simulated a transceiver setup consisting of the composite antenna as the transmitter and nine virtual probes (co-pol) as receivers. The virtual probes are located in both the xy - or H - plane at ' = 0 , 30 , 45 , 60 and 90 and in the yz - or E -plane at  = 30 , 45 , and 60 . Note that the probe located at  = 90 is identical for the H - and E -planes and also the transmission/reception at  = 0 of E -Plane would be very poor because it is a null in the radiation pattern. The received probe signals are illustrated in Fig. 13. The fidelity factor between virtual probe signals and the transmitted pulse is derived from the response in Fig. 13, and is reported in Table I. It is observed that the fidelity factor for the composite antenna is 0.83 or greater showing that the antenna does not impose significant distortion on the transmitted UWB pulse.

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of the conductivity of RCCF composites can be used to control the direction of current flow, and this suggests many possibilities for new antenna configurations.

REFERENCES

Fig. 13. Virtual probes signals: (a)

H -plane, (b) E -plane.

TABLE I FIDELITY FACTOR BETWEEN TRANSMITTED PULSE AND VIRTUAL PROBES SIGNAL

TABLE II FIDELITY FACTOR OF TX/RX SETUPS

To verify the calculations for Table I, the fidelity factor was computed using the frequency domain transfer function S21 as follows. Consider a transceiver setup composed of two identical composite antennas, and transmit the pulse of (7) with spectrum St (f ) shown in Fig. 12(b). The received signal in the time domain is given by the inverse Fourier transform as

sr (t) = =01 [St (f ) 1 S21 (f )]:

(8)

This relation was used to find the pulse response for both face-to-face ' = 90 ) antennas and side-to-side ( = 90 , ' = 0 ) antennas, and the fidelity factor was calculated as in Table II. The calculation was done using the transfer function calculated with MWS, and using the measured transfer function, and Table II shows reasonable agreement. Also, the values in Table II agree reasonably with the direct calculation of Table I.

( =

VI. CONCLUSION We use RCCF composite material to build a wideband antenna. Low cost, low weight and high corrosion resistance make RCCF composites a very good replacement for metals and other kinds of composites. A small percentage by weight of carbon nanotubes is mixed with the RCCF sample to improve the conductivity of the composite material. The composite antenna performance is evaluated both numerically and experimentally, and good agreement is found between the simulations and the measurements. The RCCF composite antenna is shown to have suitable properties for an UWB antenna, and may have advantages over an antenna made of metal. Moreover, extending this work may lead to new antenna designs using RCCF composites. The anisotropic nature

[1] H. Rmili, J. -L. Miane, H. Zangar, and T. Olinga, “Design of microstrip-fed proximity-coupled conducting polymer patch antenna,” Microw. Opt. Technol. Lett., vol. 48, pp. 655–660, 2006. [2] Y. Bayram, Y. Zhou, J. L. Volakis, B.-S. Shim, and N. A. Kotov, “Conductive textiles and polymer-ceramic composites for novel load bearing antennas,” presented at the IEEE Antenna and Propagation Symp. (APS 2008), Jul. 2008. [3] P. V. Nikitin, S. Lam, and K. V. S. Rao, “Low cost silver ink RFID tag antennas,” in Proc. IEEE Antennas Propag. Society Int. Symp., 2005, pp. 353–356. [4] 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, pp. 2894–2901, 2007. [5] S. Ludmerer, “Conductive Inks for RFID Antenna: The Low Cost High Speed Route to RFID Labels,” Parelec. Inc. [Online]. Available: www. parelec.com [6] J. Anguera, J.-P. Daniel, C. Borja, J. Mumbru, C. Puente, T. Leduc, N. Laeveren, and P. Van Roy, “Metallized foams for fractal-shaped microstrip antennas,” IEEE Antennas Propag. Mag., vol. 50, pp. 20–38, 2008. [7] M. H. Choi, B. H. Jeon, and I. J. Chung, “The effect of coupling agent on electrical and mechanical properties of carbon fiber/phenolic resin composites,” Polymer, vol. 41, pp. 3243–3252, 2000. [8] I. M. De Rosa, F. Sarasini, M. S. Sarto, and A. Tamburrano, “EMC impact of advanced carbon fiber/carbon nanotube reinforced composites for next-generation aerospace applications,” IEEE Trans. Electromagn. Compat., vol. 50, pp. 556–563, 2008. [9] C. L. Holloway, M. S. Sarto, and M. Johansson, “Analyzing carbonfiber composite materials with equivalent-layer models,” IEEE Trans. Electromagn. Compat., vol. 47, no. 4, pp. 833–844, 2005. [10] C. Buccella, “Quasi-Stationary analysis of the electric field in anisotropic laminated composites,” IEEE Trans. Industry App., vol. 35, pp. 1296–1305, 1999. [11] A. Mehdipour, A. -R. Sebak, C. W. Trueman, and S. V. Hoa, “Carbonfiber composite T-match folded bow-tie antenna for RFID applications,” presented at the IEEE Antenna and Propagation Symp. (APS 2009), Charleston, SC, Jun. 1–5, 2009. [12] R. Li, B. Pan, J. Laskar, and M. M. Tentzeris, “A novel low-profile broadband dual-frequency planar antenna for wireless handsets,” IEEE Trans. Antennas Propag., vol. 56, pp. 1155–1162, 2008. [13] A. Mehdipour, K. Mohammadpour-Aghdam, R. Faraji-Dana, and M. R. Kashani-Khatib, “A novel coplanar waveguide-fed slot antenna for ultrawideband applications,” IEEE Trans. Antennas Propag., vol. 56, no. 12, pp. 3857–3862, 2008. [14] “Concordia Center for Composites (CONCOM),” Concordia University, QC, Canada, 1979 [Online]. Available: http://concom.encs.concordia.ca [15] CST—Microwave Studio Computer Simulation Technology, 2009. [16] R. K. Challa, D. Kajfez, V. Demir, J. R. Gladden, and A. Z. Elsherbeni, “Characterization of multiwalled carbon nanotube (MWCNT) composites in a waveguide of square cross section,” IEEE Microw. Wireless Compon. Lett., vol. 18, no. 3, pp. 161–163, 2008. [17] Hexion Specially Chemicals Inc.. Columbus, OH, 2006. [18] Freeman Mfg. & Supply Co. Columbus, OH, 2001. [19] T. P. Montoya and G. S. Smith, “A study of pulse radiation from several broadband loaded monopole,” IEEE Trans. Antennas Propag., vol. 44, pp. 1172–1182, 1996. [20] Z. N. Chen, X. H. Wu, H. F. Li, N. Yang, and M. Y. W. Chia, “Considerations for source pulses and antennas in UWB radio systems,” IEEE Trans. Antennas Propag., vol. 52, pp. 1739–1748, 2004.

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325 GHz Single Layer Sub-Millimeter Wave FSS Based Split Slot Ring Linear to Circular Polarization Convertor M. Euler, V. Fusco, R. Cahill, and R. Dickie

Abstract—A single layer, frequency selective surface based, sub-millimeter wave transmission polarizer is presented that converts incident slant linear 45 polarization into circular polarization upon transmission. The polarization convertor consists of a 30 mm diameter 10 thick silicon reinforced metalized screen containing 2700 resonator cells and perforated with nested split ring slot apertures. The screen was designed and optimized using CST Microwave Studio and predictions were validated experimentally by transmission measurements over the 250–365 GHz frequency range. This frequency range is used for remote environmental monitoring and 325 GHz represents a molecular emission line . The results obtained show good agreement between measured for and modeled predictions. The measured 3 dB axial ratio bandwidth was 11.75%, measured minimum Axial Ratio was 0.19 dB and the measured insertion loss of the single layer screen was 3.38 dB.

m

HO

Index Terms—Circular-polarization, frequency selective surfaces, polarization conversion, split ring resonator.

I. INTRODUCTION Polarization converters are key elements in sensor applications and coherent optical systems. [1], [2] Polarization converter types include; single and multilayer meander-line polarizer technology [2], [3], dipole arrays [4], alternating dielectric plates [5], and lattice structures [6]. However, most of these concepts cannot be readily implemented in the sub-mm wave range, where dimensional tolerances are critical and accurate repeatable manufacturing is needed. In this paper, we show the design, manufacturing, and characterization of a new type of single layer FSS based polarization converter. This polarizer sits at 45 with respect to an incident 45 slant linear polarized (LP) plane wave and converts it to a circularly polarized signal. Due to reciprocity and incident circularly polarized signal is converted to a slant linear 45 signal upon exit from the polarizer. II. PRINCIPLE OF OPERATION The split slot ring geometry shown in Fig. 1 is used to obtain a CP exit wave from an LP input wave. The polarizer is designed to be orientated at 45 relative to an incident slant 45 LP signal in order to minimize reflections within the quasi-optical network in a future radiometer. The incident LP signal resolves into two equal components, aligned along the vertical and horizontal directions. If the FSS is made to phase advance one component by +45 and at the same time phase retard the other component by 045 while at the same time producing equiamplitude outputs then an exit CP signal will occur. Thus 1) the exit wave components must be equal EH = EV at the output of the polarizer and 2) there must be a 90 phase difference between the two components 8V 0 8H = 90 . Both criteria can be enforced by using two split-ring slots in a nested configuration, Fig. 1. The dimensions of these rings are selected such Manuscript received August 16, 2009; revised November 18, 2009; accepted January 11, 2010. Date of publication April 26, 2010; date of current version July 08, 2010. This work was supported in part by the U.K. Engineering and Physical Science Research Council under Grant EP/E01707X/1 and in part by the Northern Ireland Department of Education Strengthening all Island Mobile Wireless Futures Project. The authors are with The Institute of Electronics, Communications and Information Technology, Queen’s University Belfast, Queen’s Island, Belfast BT3 9DT, Northern Ireland, U.K. (e-mail: [email protected]). Digital Object Identifier 10.1109/TAP.2010.2048874

Fig. 1. Geometry of single layer ring slot polarization converter design: dx = 475 m, dy = 540 m, R1 = 135:6 m, R2 = 160:6 m, R3 = 191:5 m, R4 = 216:5 m, 1 = 21:7 , 2 = 60:6 .

that the incident TE (Y directed) wave component causes the longer outer slot to resonant slightly below the centre specified operating frequency of the polarizer while the TM (X directed) wave component causes the inner slot to resonate at a frequency slightly above the centre specified operating frequency. At the centre operating frequency the length of both slots is one wavelength. Therefore the width length and relative spacing dimensions of the inner and outer slots control the amplitude and phase of the exit signals. Since the elements are arranged periodically the bandpass filtering characteristics associated with slot frequency selective surfaces are preserved. [7] Meanderline structures have been traditionally used to convert linearly polarized radiation into circularly polarized radiation. In order to benchmark the split slot loop design presented in this paper we used the meander line arrangement in [3] to design a single layer polarization converter operating at the same center frequency as the split slot ring, 325 GHz. The 3 dB Axial Ratio Bandwidth of the transmitted CP signal, as well as the stability to varying angles of incidence were found to be inferior to the performance of the design presented in this paper. For example at normal incidence the 3 dB AR bandwidth for the split slot ring polarizer is 21%, as compared to 6.4% for the meander line. The other popular polarizer arrangement a cross slot when oriented at 45 to the incident wave when simulated generated a passband response in the TE plane which is much narrower compared to the passband generated in the TM band, leading to an unsymmetrical and narrow 3 dB AR bandwidth of 10%. Alternative approaches including alternating dielectric plates [5] and lattice structures [6] were not further investigated, since they require significantly more complex precision silicon micromachining technique than is required to produce the freestanding split slot loop FSS polarizer now discussed. III. DESIGN, MANUFACTURING, AND MEASUREMENT CST Microwave Studio was used to design and optimize the structures consisting of nested annular slot elements. Periodic boundary conditions were implemented in order to reduce the computational volume to that of a single unit cell. [8] The screen metallization selected was high conductivity silver, 61.7 2106 S=m of 1 m thickness. The structure in Fig. 1 was fabricated on a 400 m thick low resistivity silicon wafer using a precision silicon micromachining technique developed to produce freestanding FSS structures, as depicted in Fig. 2. [9] This method

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Fig. 2. Main fabrication steps: (a) Array slot pattern etched into the silicon. (b) Removal of the 400  thick substrate. (c) High conductivity metallization stage.

m

uses “Silicon on Insulator” (SOI) wafers to form the structural core of the device. Slots are micromachined into the silicon to fashion the array. Substrate material from below the array is removed in order to form a thin perforated diaphragm. The remaining silicon is then encased by sputtered metal in order to eliminate the influence of the dielectric material losses on electrical performance. [10] Fig. 2 depicts the three major fabrication steps. (1) The 10  SOI wafer has the slot array etched by Deep Re). This is the active Ion Etching (DRIE) (etch rate 3.5  = blanket etch process for formation of the slots with a thin photoresist masking layer providing the slot patterns. (2) The 30 mm diameter, 400  thick substrate is removed by ) in order to release the FSS DRIE etching (etch rate 8  = structure. (3) In the final stage of the process the array is sputter coated with a 0.25  copper seed layer and electrodeposited with 1  silver on both sides of the mesh and also onto the slot walls, a 30 nm gold flash prevents oxidization. The finished FSS accommodates 2700 unit cells on the 30 mm diameter screen; Fig. 3 shows eight of the unit cells. The FSS sits within an un-etched annular frame which is 413  thick in order to give mechanical stability to the structure. The total diameter of the surface is 50 mm. The surface has excellent planarity, computer modeling using Coventorware software [11], shows residual compressive stress would displacement of the elements which is practicable generate a < negligible at the 325 GHz operating frequency of the polarizer. The electromagnetic performance of the screen was measured using a two-port vector network analyzer in conjunction with an AB quasi optical test system. [12] Here sub-millimeter signals were generated by a harmonically multiplied swept 8–18 GHz wave source radiated into free space by a wideband corrugated horn antenna. The radiated beam is then focused by ellipsoidal mirrors which produce a Gaussian beam waist of 4 mm at the position of the polarizer in the sample holder which

m

Fig. 3. Screen accommodating 30 mm 2700 unit cell polarizer: (a) Array element microphotograph. (b) The array is supported by an un-etched annular frame.

TABLE I FINAL POLARIZER DIMENSIONS AFTER FABRICATION

m min

m m min

m

m

m

57 nm

is orientated at 45 relative to the incident signal. The exit signal from the polarization converter is mixed down to 8-18 GHz and fed back to the vector network analyzer, VNA. The co- and cross-polar spectral responses of the FSS were measured by obtaining the transmission spectra through the polarizer first without it in the sample holder, free space calibration, then with it in each of the two orthogonal positions, i.e., TE, TM positions. In order to eliminate the effect of any residual standing waves in the quasi optical feed train, the raw 21 data was time-gated within MATLAB. The gated amplitude and phase data for each of the orthogonal positions was then post-processed to find the axial ratio of the exit CP signal using the formulae in [13].

S

IV. EXPERIMENTS AND RESULTS The equi-amplitude point of the measured structure is shifted away /325 GHz to a from the predicted operational frequency 0 : / 320.8 GHz, this was due to mask lower frequency point at 0 : quantization arc to rectangular approximation errors. With reference to Fig. 1 the measured final unit cell dimensions are given in Table I.

3 38 dB

3 25 dB

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The analysis shows that a decrease in metallization layer conductivity of 1 2107 S=m from the expected high conductivity silver value hardly affects the polarizer’s insertion loss or the AR of the transmitted CP signal. V. CONCLUSION A new concept for a silicon micromachined FSS based sub-mm wave transmission polarization convertor has been demonstrated. A 3 dB AR Bandwidth of the transmitted circularly polarized signal of 11.75% with 3.38 dB insertion loss can be achieved with the design. The structure reported should find application in next generation radiometer applications where polarization analysis is required.

REFERENCES

Fig. 4. Post manufacture simulated and measured results: (a) Amplitude, (b) Phase, and (c) AR of transmitted CP signal.

Fig. 5. Conductivity study: f

= 325 GHz.

Fig. 4 compares the simulated results from the CST model, after the mask approximation and fabrication errors have been taken into account, with the measured results of the micromachined screen. The phase difference at 320.8 GHz was measured to be 88 . Hence, the point where the minimum axial ratio occurs moved from 325 GHz (original design) to 320.8 GHz (measured). The 3 dB AR bandwidth was calculated to be 11.75% remaining close to its predicted value of 12%. The measured insertion loss was 03:38 dB which is very close to the simulated insertion loss of 03:25 dB. Analysis for the variation of the 3 dB axial-ratio bandwidth of the transmitted circular polarized signal and the polarizers insertion loss as a function of screen metallization conductivity was made. The conductivity of the polarizer’s metallization layer (high conductivity silver, 6.1 2107 S=m) was decreased and the performance of the screen re-simulated. The results of these simulations are summarized in Fig. 5. The line with the triangular symbols denotes the deviation of the minimum axial ratio in decibels and the line with the round symbols shows how insertion loss is increasing with decreasing conductivity of the metallization layer, due to increasing ohmic losses.

[1] K. Mertens, B. Scholl, and H. J. Schmitt, “Strong polarization conversion in periodically loaded strip waveguides,” IEEE Photon. Opt. Lett., vol. 10, no. 8, pp. 1133–1135, 1998. [2] L. Young, L. A. Robinson, and C. A. Hacking, “Meander-line polarizer,” IEEE Trans. Antennas Propag., vol. 21, pp. 376–378, 1973. [3] J. S. Tharp, B. A. Lail, B. A. Munk, and G. D. Boreman, “Design and demonstration of an infrared meanderline phase retarder,” IEEE Trans. Antennas Propag., vol. 55, pp. 2983–2988, 2007. [4] R. W. Jackson, “Printed dipoles electromagnetically coupled to coplanar waveguide for linear or circular polarization,” Electron.Lett., vol. 22, no. 6, pp. 324–325, 1986. [5] J. Bornemann, “Computer-aided design of multilayered dielectric frequency-selective surfaces for circularly polarized millimeter-wave applications,” IEEE Trans. Antennas Propag., vol. 41, pp. 1588–1591, 1993. [6] D. S. Lerner, “A wave polarization converter for circular polarization,” IEEE Trans. Antennas Propag., vol. 13, pp. 3–7, 1965. [7] R. Dickie, R. Cahill, H. Gamble, V. Fusco, B. Moyna, P. Huggard, N. Grant, and C. Philpot, “A micromachined 300 GHz high Q resonant slot frequency selective surface filter,” Proc. IEEE Microw. Antennas Propag., vol. 151, no. 1, pp. 31–36, 2004. [8] CST Studio Suite 2006 Advanced Topics CST-Comp. Simulation Technology, 2005. [9] R. Dickie, R. Cahill, H. Gamble, V. Fusco, M. Henry, M. Oldfield, M. Huggard, P. Howard, N. Grant, Y. Munro, and P. de Maagt, “Submillimeter wave frequency selective surface with polarization independent spectral responses,” IEEE Trans. Antennas Propag., vol. 57, pp. 1985–1994, 2009. [10] R. Dickie, R. Cahill, H. Gamble, V. Fusco, N. Grant, and S. P. Rea, “Dual polarised sub-mm wave frequency selective beamsplitter,” presented at the 1st Eur. Conf. on Antennas Propag., EUCAP, Nice, 2006. [11] Analyzer Data Sheet. Cary, NC, Conventor Inc., 2005. [12] R. Dickie, R. Cahill, H. Gamble, V. Fusco, A. Schuchinsky, and N. Grant, “Spatial demultiplexing in the sub-mm wave band using multilayer free-standing frequency selective surfaces,” IEEE Trans. Antennas Propag., vol. 53, pp. 1903–1911, 2005. [13] C. A. Balanis, Antenna Theory: Analysis and Design. , NY: John Wiley & Sons, 2005.

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A Generalized Synthesis Procedure for Low-Profile, Frequency Selective Surfaces With Odd-Order Bandpass Responses Nader Behdad and Mudar A. Al-Joumayly

Abstract—We present a generalized synthesis procedure for designing low-profile frequency selective surfaces (FSS) with bandpass responses of = 3 5 7 . . .). The FSSs designed using this technique odd-order ( use a combination of resonant and non-resonant sub-wavelength constituting unit cells with unit cell dimensions and periodicities in the order is the free space wavelength. The main advantage of 0 15 , where of using this technique, compared to traditional FSS design techniques, is that it allows for the design of low-profile and ultrathin FSSs that can proth order FSS designed using this vide sharp frequency selectivity. An ( technique typically has an electrical thickness in the order of 1) 50 which is significantly smaller than the overall thickness of a tra( 1) 4). The proposed ditionally designed th order FSS ( synthesis procedure is validated for two FSS prototypes having third- and fifth-order bandpass responses. Principles of operation, detailed synthesis procedure, and implementation guidelines for this type of FSS are presented and discussed in this communication. Index Terms—Bandpass filters, frequency selective surfaces (FSSs), periodic structures, radomes, spatial filters.

I. INTRODUCTION Frequency selective surfaces (FSSs) are widely used as spatial filters for electromagnetic (EM) waves in a variety of applications. Classic examples of these applications include design of radar domes (radomes), radar cross section (RCS) reduction of military targets, and design of dichroic feeds for reflector antennas [1], [2]. In this regards, an FSS can be considered to be analogous to a microwave filter, albeit, one that filters electromagnetic waves propagating in space rather than electric signals flowing in transmission lines. Generally these structures are designed using two-dimensional periodic structures where resonant metallic elements (dipole or patch type) or their complementary topologies (resonant slots or apertures) are arranged in a two-dimensional periodic lattice. In the vicinity of the resonant frequency of the constituting elements, these structures will either completely reflect an incident EM wave (dipole or patch resonance) or will be transparent (slot or aperture resonance). In this manner, a single layer metallic structure composed of periodic arrangement of dipole or slot type resonators acts as a first-order band-stop or bandpass FSS, respectively. In many applications, however, a single first-order FSS does not provide enough out-of-band rejection. To circumvent this problem, FSSs with higher-order responses are used. Traditionally, higher-order bandpass or band-stop FSSs are designed by cascading multiple first-order FSS panels a quarter wavelength apart from each other (e.g., see [1, pp. 253–255 ]). This approach, however, results in relatively thick structures that are heavy and bulky, especially at low frequencies (e.g., see [1, Ch. 7]). Recently, the application of non-resonant periodic structures in the design of frequency selective surfaces has received significant attention [3]–[11]. Using such techniques, new FSS topologies are presented that allow for the design of low-profile frequency selective surfaces with Manuscript received December 01, 2009; accepted January 31, 2010. Date of publication April 26, 2010; date of current version July 08, 2010. The authors are with the Department of Electrical and Computer Engineering, University of Wisconsin-Madison, Madison, WI 53706 USA (e-mail: [email protected]). Digital Object Identifier 10.1109/TAP.2010.2048882

Fig. 1. (a) 3-D topology a frequency selective surface composed of successive arrays of sub-wavelength capacitive patches and miniaturized slot resonators. (b) Side view of the FSS and the top views of a constituting unit cell of the structure.

higher-order bandpass responses [8]–[11]. In particular, recently, we reported a technique for designing a low-profile, third-order bandpass FSS using a combination of resonant and non-resonant elements [11]. The FSS consists of three metal layers and two dielectric substrates where the first and the third metal layers are in the form of two-dimensional (2-D) periodic arrangement of sub-wavelength capacitive patches, while the middle metal layer is a periodic structure composed of miniaturized slot resonators. The main advantage of this structure over traditional third-order bandpass FSSs is its extremely thin overall thickness (0:040 in [11] compared to at least 0:50 in traditional designs, where 0 is the free space wavelength). In [11], a qualitative explanation was provided describing why this particular structure operates as a third-order bandpass FSS. However, a quantitative procedure for synthesis of the FSS had not yet been developed and was absent in [11]. In this communication, we extend our previous work and generalize that FSS topology to allow for the design of low-profile FSSs with any higher-order bandpass responses of odd-order (N = 3; 5; 7; . . .). Furthermore, we provide a procedure for synthesizing the proposed general, odd-order bandpass FSSs. This procedure is based on a generalized equivalent circuit model of the structure that allows for synthesizing the FSS from system level performance indicators such as center frequency of operation (f0 ), fractional bandwidth ( = BW=f0 ), response type (e.g., Chebyshev, Butterworth, etc.), and response order (N = 3; 5; . . .). In what follows, the design procedure and the generalized synthesis procedure of the proposed structures are presented. The proposed synthesis procedure is validated with two design examples of FSSs having third- and fifth-order bandpass responses. II. GENERALIZED FSS TOPOLOGY A. Topology and Equivalent Circuit Model Fig. 1(a) shows the three-dimensional (3-D) topology of the proposed FSS. The structure is composed of several metal layers separated from one another by very thin dielectric substrates. Each metallic layer is either in the form of 2-D periodic arrangement of sub-wavelength capacitive patches or a two-dimensional periodic arrangement of miniaturized slot resonators. Fig. 1(b) (top portion) shows the side view of the structure; as can be seen, the first and last layer of the structure are always composed of sub-wavelength capacitive patches, while the layers in between are composed of miniaturized slot resonators and capacitive patches repeated sequentially. Fig. 1(b) (bottom portion) depicts the top view of one unit cell of the sub-wavelength capacitive

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capacitor. Our synthesis procedure is based on the fact that the circuit model shown in Fig. 2(b) is a special case of the coupled resonator filter shown in Fig. 2(c), where the inductors of resonators with odd-order, = 1 3 5 . . ., are infinite (i.e., 1 3 . . . N ! 1). However, this can only be done for symmetric coupled resonator networks (i.e., networks with symmetric LC values with respect to the center resonator). Consequently, FSSs of the type shown in Fig. 1 can only be used to synthesize symmetric response types (such as a Chebyshev or a Butterworth response), whereas the coupled resonator filter topology shown in Fig. 2(c) can be used to synthesize filters with non-symmetric response types (e.g., maximally flat group delay) as well as symmetric ones. In the coupled resonator filter topology shown in Fig. 2(c), the shunt blocks in the circuit model represent parallel LC resonators, while the series blocks represent the coupling networks, where series inductors are used to couple the resonators to each other. The order of the filter is determined by the number of the shunt resonators ( ) and the response type of the filter is determined by the normalized quality factor of the first and th resonators ( 1 and N ), the normalized load and source impedances ( 1 and N ),1 and the normalized coupling coefficients between the resonators ( 1;2 2;3 . . . N 01;N ) [13]. Therefore, by , and specifying the frequency of operation, 0 , FSS bandwidth, the response type and order, all of the element values of the equivalent circuit shown in Fig. 2(c) can be determined. The synthesis procedure presented in this paper, however, ensures that, for symmetric networks, the inductance values of 1 3 5 . . . N [in Fig. 2(c)] will become infinite. This will automatically convert the equivalent circuit model shown in Fig. 2(c) to that of our proposed FSS [shown in Fig. 2(b) and Fig. 2(a)]. Once the parameter values of the equivalent circuit model shown in Fig. 2(a) are obtained, they can be mapped to the geometrical parameters of the proposed FSS shown in Fig. 1. The generalized synthesis procedure developed for this type of FSS results in slightly different formulae for FSSs with third-order bandpass response and any higher-order bandpass responses other than the third order ( = 5 7 . . .). Therefore, first in Section II-B, the design procedure of the third order FSS is presented and the general design pro3 is presented in Section II-C. cedure for FSSs with orders of

N

; ; ;

L ;L ; ;L

N

N

Fig. 2. (a) Equivalent circuit model of the general FSS shown in Fig. 1(a) for normal angle of incidence. (b) Transmission lines which represent the dielectric substrates in the equivalent circuit model of Fig. 2(a) can be represented by their simple LC equivalent network. The replacements are shown in dark gray. (c) The general circuit model representing an th order, bandpass coupled resonator filter. The equivalent circuit model shown in Fig. 2(b) can be obtained ... can be designed to have infinite from that shown in Fig. 2(c) if inductance values.

N

L ;L ; ;L

patches and the miniaturized slot resonators. The different capacitive patch layers (or different miniaturized slot layers) are not necessarily identical to one another. Additionally, the structure is always composed of an odd number of metal layers and an even number of dielectric substrates that separate them from each other. An FSS of this topology, metallic layer acts a th order bandpass which is composed of is always an odd number (i.e., = 3 5 7 . . .). In FSS, where this particular th order bandpass FSS, ( 0 1) 2 of the metallic layers are composed of miniaturized resonators and ( + 1) 2 of the layers are composed of sub-wavelength capacitive patches. To understand the principles of operation of this general odd-order bandpass FSS, we use a simple equivalent circuit model of the FSS as shown in Fig. 2(a). Here, the sub-wavelength capacitive patches are modeled by parallel capacitors ( L1 L3 . . . LN ) in a transmission line circuit. The miniaturized slot resonators are modeled using parallel LC resonators ( 2 L2 4 L4 . . . N 01 L(N 01) ) and the ultrathin dielectric substrates separating the metallic layers from one another are modeled by transmission lines with lengths of 1;2 2;3 . . . N 01;N and characteristic impedances of 1;2 2;3 . . . N 01;N . Free space on each side of the FSS is modeled with two semi-infinite transmission lines with the characteristics impedances of 0 = 377 . This equivalent circuit [Fig. 2(a)] can be converted to the one shown in Fig. 2(b) by converting the transmission lines to their equivalent LC network using the Telegrapher’s equations [12]. With the assumption 12 that the electrical length of a transmission line is small (i.e., or 30 ), a short piece of a transmission line with a length 1 can be modeled with a series inductor and a parallel capacitor with inductance and capacitance values of 1 and 1 , where (H/m) and (F/m) are inductance and capacitance per unit length of the line, respectively. Based on this, i;i+1 = 0 r;i;i+1 i;i+1 , where r;i;i+1 and i;i+1 are the relative permeability and the thickness of the substrate which separates the th and ( +1)th metallic layers from one another. Similarly, i;i+1 = 0 r;i;i+1 i;i+1 2, where r;i;i+1 is the relative permittivity of the same substrate. In this equivalent circuit, all the parallel capacitors at each node can be combined and lumped into a single

N

N

N

N

N N

; ; ; = N =

C ;C ; ;C L C ;L C ; ;L C

h ;h ; ;h Z ;Z ; ;Z Z

` < = z

`


B. Synthesis Procedure for Third-Order FSSs A third-order bandpass FSS of the topology shown in Fig. 1(a) is composed of three metallic layers (two capacitor layers and one resonator layer) separated from one anther by two very thin dielectric substrates [11]. The operation of this FSS can be described using the = 3. For this cirequivalent circuit model shown in Fig. 2(c) with cuit, the capacitors of the first and the third resonators ( 1 and 3 ) are determined from

N

C3 = !0qZ30 

C1 = !0qZ10 

Z

 BW=f

C

C

(1)

q

where 0 = 377 , = 0 is the fractional bandwidth, and 1 and 3 are the normalized quality factor of the first and third resonators. Values of 1 and 3 can be found from filter synthesis handbooks and are provided in Table I for third-order coupled resonator filters with various response types. Since 1 = 3 (due to symmetry of the network), 1 and 3 are equal to one another. The capacitance values of the resonator in the middle layer can then be calculated from (2)

q

q

C

q

q

C

q

C2 = k2C12 = k2C32





q q k ;k ; ;k f

k

k

1;2

2;3

(2)

where 1;2 and 2;3 are the normalized coupling coefficients between the first and second, and second and third resonators, respectively 1For

odd-order bandpass filters,

r

=

r

= 1

.

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5) For N = 5; 9; 13; . . ., calculate the value of the remaining capacitor from

TABLE I NORMALIZED QUALITY FACTORS AND COUPLING COEFFICIENTS FOR THIRD-ORDER COUPLED RESONATOR FILTERS WITH DIFFERENT FILTER RESPONSES

= 2

C

k

+k

C

;

N

and their values are provided in Table I. For symmetric networks, k1;2 = k2;3 . These particular choices of capacitor values C1 , C2 , and C3 causes the inductance of the first and third resonators (L1 and L3 ) of Fig. 2(c) to become infinite. This transforms the equivalent circuit of Fig. 2(c) to that of Fig. 2(b) (for N = 3). By determining the value of C2 , L2 can be determined from

L2

= !2(C 0 k  pC 1C 0 k pC C ) : 2 12 1 2 2 3 23 ;

(3)

;

L1;2

= !2 k

0 1;2

L2;3

1 2

= !2 k

0 2;3

1p  C C

(4)

2 3

Because of symmetry, L1;2 = L2;3 . Synthesis formulae provided in (1)–(4) can be used to synthesize a third-order bandpass FSS of the type shown in Fig. 1(a) (for N = 3). C. Synthesis Procedure for Higher-Order Band-Pass FSSs (N > 3)

For bandpass FSSs with higher-order responses (i.e., N = 5; 7; . . .), a similar approach is followed to obtain the equivalent circuit model parameters. First, all the capacitor values are determined. From the calculated capacitance values, the values of the coupling inductors and the inductances of the resonators are calculated. Since conversion of the circuit shown in Fig. 2(c) to that of Fig. 2(b) is only possible for symmetric networks, symmetry is used to greatly simplify the calculation of the equivalent circuit values. To ensure that this communication remains concise, details of the derivation procedure are not presented and only the main design equations are given. For the generalized filter topology of Fig. 2(c), the procedure given below can be used to determine the values of all capacitors 1) Calculate the capacitance values of the first and the second layers using (5)

C1

= !0qZ10 

C2

= k2C12

(5)

1;2

2) Choose Ci (for i = 3; 5; . . .) according to the following condition:

Ci
f0 , which is not predicted by the equivalent circuit model. This out of band null happens at 5.27 GHz for the third-order FSS and at 5.22 GHz for the fifth-order one. The specific physical mechanisms that give rise to this null are comprehensively studied in [11, Sect. II]. In [11], it is demonstrated that this null is caused by the particular method used to implement the miniaturized slot resonators and can be predicted in the equivalent circuit model of Fig. 2(a) by considering the equivalent circuit model of the miniaturized slot resonators to have an inductor in series with the parallel LC resonator as shown in [11, Fig. 3]. This model, however, is not used in the current manuscript for two main reasons: 1) Using this model significantly complicates the proposed synthesis procedure to the point where derivation of closed form synthesis formulae is not possible, and 2) For a given miniaturized slot resonator and periodicity, the location of that transmission null is uniquely determined and cannot be changed as a design parameter. In spite of this discrepancy, the proposed synthesis procedure does a very good job of predicting the actual response of the FSS in its passband.

[1] B. A. Munk, Frequency Selective Surfaces: Theory and Design. New York: Wiley-Interscience, 2000. [2] G. T. Ruck, Radar Cross Section Handbook. New York: Plenum, 2000, vol. 1. [3] K. Sarabandi and N. Behdad, “A frequency selective surface with miniaturized elements,” IEEE Trans. Antennas Propag., vol. 55, no. 5, pp. 1239–1245, May 2007. [4] R. J. Langley, L. L. Hui, and K. L. Ford, “Design methodology for a miniaturized frequency selective surface using lumped reactive components,” IEEE Trans. Antennas Propag., vol. 57, no. 9, pp. 2732–2738, Sep. 2009. [5] C.-N. Chiu and K.-P. Chang, “A novel miniaturized-element frequency selective surface having a stable resonance,” IEEE Antennas Wireless Propag. Lett., vol. 8, pp. 1175–1177, 2009. [6] S. Barbagallo, A. Monorchio, and G. N. Manara, “Small periodicity FSS screens with enhanced bandwidth performance,” IET Electron. Lett., vol. 42, no. 7, pp. 382–384, Mar. 2006. [7] F. Bayatpur and K. Sarabandi, “Single-layer high-order miniaturizedelement frequency-selective surfaces,” IEEE Trans. Microw. Theory Tech., vol. 56, no. 4, pp. 774–781, Apr. 2008. [8] N. Behdad, “A second-order band-pass frequency selective surface using nonresonant subwavelength periodic structures,” Microw. Opt. Technol. Lett., vol. 50, no. 6, pp. 1639–1643. [9] M. Al-Joumayly and N. Behdad, “A new technique for design of low-profile, second-order, bandpass frequency selective surfaces,” IEEE Trans. Antennas Propag., vol. 57, no. 2, pp. 452–459, Feb. 2009. [10] M. Salehi and N. Behdad, “A second-order dual X-/Ka-band frequency selective surface,” IEEE Microw. Wireless Compon. Lett., vol. 18, no. 12, pp. 785–787, Dec. 2008. [11] N. Behdad, M. Al-Joumayly, and M. Salehi, “A low-profile third-order bandpass frequency selective surface,” IEEE Trans. Antennas Propag., vol. 57, no. 2, pp. 452–459, Feb. 2009. [12] D. M. Pozar, Microwave Engineering. New York: Wiley, Dec. 2008, vol. 18, pp. 785–787, no. 12. [13] A. I. Zverev, Handbook of Filter Synthesis. New York: Wiley, 1967. [14] 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. 1623–1632, Jun. 2008. [15] RF-35 High-Performance Laminates Taconic Corporation, datasheet available [Online]. Available: http://www.taconic-add.com/pdf/ rf35.pdf

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Numerical Analysis of Propagating and Radiating Properties of Hollow Core Photonic Band Gap Fibres for THz Applications Luca Vincetti and Alessia Polemi

Abstract—Hollow core photonic bandgap fibres (HC-PBGFs) are numerically investigated in order to obtain low loss wave-guiding and good aperture field distribution in the terahertz region (0.1–10 THz) of the electromagnetic spectrum. The purity of the aperture field distribution at the HC-PBGF section combined with low loss propagation and high coupling efficiency with free-space propagating Gaussian beams suggest a possible employment of such a structure as aperture antennas, for possible feed systems in THz applications and in THz wireless sensing. Index Terms—Aperture coupling, optical fibers, photonic bandgap materials, Terahertz radiation.

I. INTRODUCTION In recent years the terahertz region of the electromagnetic spectrum (from 0.1 to 10 THz) has attracted growing interest because of its significant scientific and technological potential in many fields, including sensing, imaging, spectroscopy, radio astronomy, and wireless communications [1]–[4]. In the past, THz technological applications were limited by the lack of low cost, high power and high sensitivity sources and detectors. Rapid progress in laser and electronic technologies allowed for different techniques in the generation and detection of THz radiations, enabling turnkey systems. However, progress is limited by the overwhelming reliance on free-space transport of the THz beam due to the lack of low loss waveguide. In many applications the line-of-sight condition is not readily accessible and, however, an efficient coupling between freely propagating waves and source or detector is a desirable feature. Further, in high directivity applications, such as in radio astronomy or high resolution imaging, feeders must be realized for coupling in and out subwavelength transmitter or detector with radiating aperture which are sized in hundreds to thousands of wavelengths. In THz region, the development of low loss waveguides with high free space coupling efficiency is a tough feature [5]–[13]. Hollow core photonic bandgap fibres (HC-PBGFs) are a promising solution to the problem. So far, they have been proposed and developed for applications in visible and near infrared (NIR) spectrum and they consist of a hollow core surrounded by a dielectric cladding having a lattice of air holes running along the whole fibre length [14]–[16]. Electromagnetic field is confined inside the core through photonic bandgap of the cladding structure. In this way the fraction of power propagating in the dielectric is very low, and losses due to material absorption are drastically reduced. However, in visible and NIR regions, HC-PBGFs suffer from high leakage and scattering loss [17], [18]. However all these losses are inversely proportional to the wavelength, thus at THz frequencies their values do not significantly affect the overall loss mechanism. Manuscript received April 23, 2009; revised December 16, 2009; accepted January 10, 2010. Date of publication April 22, 2010; date of current version July 08, 2010. The authors are with the Department of Information Engineering, University of Modena and Reggio Emilia, Modena, Modena 41100, Italy, (e-mail: luca. [email protected]; [email protected]). Color versions of one or more of the figures in this communication are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2010.2048854

Fig. 1. Cross sections of the analyzed HC-PBGFs. The fibre on the left (7c) is obtained by removing seven unit cells. The fibre on the right (3c) is obtained by removing three unit cells. Gray regions represents dielectric material and white region represents air. The inset shows details of the holes.

This work is focused on the numerical analysis of guided-wave propagation characteristics of a HC-PBGF made of Teflon, with particular care to the coupling efficiency with freely propagating waves and to the radiating properties. Numerical results show that losses lower than some dB/m (over hundreds of GHz centered at 1 THz) and high quality output beams can be obtained. The purity of the aperture field distribution at HC-PBGF section leads to a 90% coupling efficiency and to a highly collimated output beam, which can be possibly exploited for the design of feeds, even in array configuration, coupled to optical or electronic devices and for wireless sensing at THz. The possible employment of such a structure as an aperture antenna has not been investigated, yet. The numerical analysis has been performed by using a complex modal solver based on the finite element method (FEM) [19], already applied in the past for losses analysis in several kinds of photonic bandgap fibres [13], [20]. II. HOLLOW CORE FIBRE The cross sections of the fibres here investigated are reported in Fig. 1. They consist of a dielectric material with a triangular lattice of air holes. As shown in the inset of Fig. 1, the air holes are hexagonal with rounded corners in order to better approximate cross sections of fibres manufactured by the stack-and-draw method. 3 is the hole-to-hole distance (pitch) d is the edge-to-edge distance and dc is the rounded corner curvature. Details of this representation can be found in [22]. The hollow core is usually obtained by removing some air holes at the center of the lattice. In the present work two different cores have been considered: in the fibre hereinafter called 7c, the core is constructed by removing seven air holes; in the fibre called 3c the air holes removed are three. In both cases, the core is surrounded by a dielectric boundary with thickness t. The fibre 7c exhibits a six-fold symmetry and its core diameter is about 3 3. Due to the core shape, the 3c fibre has a mirror symmetry along y axis, and core dimensions are about 1.8 3 both along x and y . In the present analysis, the real and imaginary parts of the dielectric refractive index have been assumed to be nr = 1:44 and ni = 1:2 2 1003 corresponding to Teflon refractive index at 1 THz. III. ANALYSIS AND RESULTS A. 7c-Fibre Firstly, let us consider the 7c-fibre with the following geometrical parameters: 3 = 900 m, d=3 = 0:98, dc =3 = 0:44, t=3 = 9 1 1003 corresponding to a core diameter of 3 mm. If the number of hole rings is equal or greater than two, leakage loss is negligible compared to absorption loss over a band of 300 GHz centered at 1 THz [13], [21]. The fundamental mode (FM) consists of two degenerate hybrid mode HE11 -like with orthogonal polarization as in conventional optical fibres. The normalized magnetic field profile at 1 THz is reported in the

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Fig. 4. Propagation properties (effective index and propagation loss) comparison between the fundamental mode and the second order mode of the hollow core 7c-fibre with one ring.

Fig. 2. Normalized radiation intensity generated by the fundamental mode (inset) for the 7c-fibre. Both principal planes are shown. The radiation intensity is compared with the one produces by assuming a Gaussian profile on the fibre aperture. The Gaussian profile is chosen as the one that better approximates our far-field pattern. In particular, the Gaussian spot size is set to 510  . Inset: Mode field profile along both x (dashed line) and y (dotted line) axes.

m

( is the phase constant and k0 the vacuum wave number) is significantly lower than the FM one, the difference is about 0.006 at 1 THz. This aspect, combined with the extremely low overlap of the modes, makes the coupling coefficient due to the fibre imperfections very low. SOM propagation loss is higher than the FM one, because of the higher leakage loss and higher overlap with absorbing material. The extinction ratio between FM and SOM, that is the difference between the propagation loss in dB/m, is about 3.7 dB/m at 1 THz. By reducing the number of hole rings to one, the extinction ratio can be increased at the expense of higher propagation loss. As the low loss band shifts towards higher  in order frequencies, the pitch has been increased to to set the minimum loss at 1 THz. This pitch corresponds to a 3.4 mm core diameter. Fig. 4 shows propagation properties of FM and SOM in the case of fibre 7c with one ring. The bigger core causes a slight reduction of the effective index difference, nevertheless it still guarantees a low coupling between the modes. On the other hand, the extinction ratio is increased up to 15 dB/m, though propagation loss is as high as 7.3 dB/m at 1 THz. Since the field distribution does not depends on the number of rings, the mode field profile is the same of Fig. 2, but because of a larger core, it now extends over a wider area. However, in both cases, by a proper design of the excitation condition, the fibre can be effectively single mode. In fact, the coupling coefficient A between a freely propagating beam with a transverse electric field et , and the  th mode of the fiber with a transverse magnetic field Ht is [24]

3 = 1130 m

Fig. 3. Propagation properties (effective index and propagation loss) comparison between the fundamental mode and the second order mode of a hollow core 7c-fibre with two rings.

inset of Fig. 2. It is worth noting how the field is well confined inside the hollow core along both the x and y planes. This property can be exploited in antenna applications, for the design of feeds coupled to optical or electronic devices, because the good field confinement results in a high collimated beam. This kind of feeds have the advantage of being extremely light, easy to package and to bend. The far field pattern for the 7c fibre is shown in Fig. 2, generated by the fundamental mode whose distribution is reported in the inset. The normalized radiation intensity in both principal planes (zx and zy ) is compared with that generated by a Gaussian profile on the aperture with spot size set to 510  . The Gaussian profile is chosen as the one which better approximates the modal far-field pattern. The Gaussian field is the same in both planes, while the asymmetry of the aperture profiles (see inset of Fig. 2) produces slightly different patterns, but still highly collimated. The half power beamwidth is also shown in the Fig. 2. In Fig. 3 the dispersion and losses for the FM and for the second order modes (SOMs) are compared, in case of two air hole rings. The minimum of FM propagation loss is 1.2 dB/m at 1.05 THz, and it is about two decades lower than the bulk Teflon absorption loss, which is about 220 dB/m [23], over a band of 175 GHz. The SOMs consist of quasi-degenerate four modes: two HE21 -like modes with orthogonal polarization, a T E01 -like mode, and a T M01 -like mode. As SOMs propagation characteristics are very similar, here, for sake of simplicity, only =k0 the HE21 -like are reported. The SOM effective index neff

m

=

A

=

A

( )

 t3 1 z^ et 2 H p 2 Pb P





(1)

where A1 is the infinite x; y plane (transverse to the fiber axis z ), and Pb and P are the beam power and the mode power, respectively. Fig. 5 shows the coupling efficiency jA j2 in case of a Gaussian beam, with spot size W0 , linearly polarized along the x axis, and with a planar phase front

et (x; y) = E0 ex

+y =W

^i:

(2)

On top of Fig. 5 a possible coupling mechanism between a freely propagating beam and the mode of the fiber is also depicted. FM coupling reaches its maximum, i.e., 93%, with a spot size of about 810  ,  and 950  . The and it remains above 90% between W0  is shown in the inset of far field Gaussian beam with W0 Fig. 5, compared with FM-based pattern. It is worth noting that the Gaussian beam achieving the maximum coupling is narrower with respect to both the zx and zy modal field patterns, as expected, because the coupling is the result of an integration process over the complete beam span. Despite the field is non-azimuthally symmetric, the coupling efficiency does not change by changing et polarization with respect to the two polarizations of the fundamental mode HE11 . A small percentage of coupling with the higher order mode HE12 occurs, with

= 695 m = 810 m



m

m

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 58, NO. 7, JULY 2010

W

Fig. 5. Coupling efficiency between the modes of the hollow core 7c-fibre . A possible coupling with two rings and a Gaussian beam with spot size system between a freely propagating beam and the mode of the fiber is depicted on top. In the inset, the normalized radiation intensity generated by the fundamental mode compared with the far-field pattern produced by assuming an aperture Gaussian distribution which maximizes the coupling with the funda. mental mode. The Gaussian profile has a spot set to 520

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Fig. 7. Normalized radiation intensity generated by the fundamental mode (inset) for the 3c-fibre. Both principal planes are shown. The radiation intensity is compared with the one produces by assuming a Gaussian profile on the fibre aperture. The Gaussian profile is chosen as the one that better approximates our far-field pattern. In particular, the Gaussian spot size is set to 250 . Inset: Mode field profile along both (dashed line) and (dotted line) axes.

x

m

m

y

Fig. 6. HC-PBGF 3c loss versus frequency without (“x”) and with (stars) dielectric absorption for three air hole rings around the hollow core.

W

a small spot size; however, it vanishes approaching 0 values corresponding to maximum coupling efficiency with FM, and moreover its propagation loss is greater than 100 dB/m and 30 dB/m in case of one and two rings respectively. SOM coupling coefficients are constantly zero due to their odd symmetry with respect to the fibre axis. They can be nonzero only in a off-axis coupling.

W

Fig. 8. Coupling efficiency between the FM of the hollow core fibre 3c with . A possible coupling system three rings and a Gaussian beam with spot size between a freely propagating beam and the mode of the fiber is depicted on top. In the inset, the normalized radiation intensity generated by the fundamental mode compared with the far-field pattern produced by assuming an aperture Gaussian distribution which maximizes the coupling with the fundamental mode in the fibre. The Gaussian profile has a spot set to 810 .

m

B. 3c-Fibre When excitation conditions are not under control and a single mode propagation is mandatory, the fibre must be strictly single mode. In order to have a strictly single mode fibre, the core diameter should be lower than the pitch 3 of the cladding. This is the case of 3 -fibre, recently proposed and realized for NIR applications [25]. Geometrical parameters are the same of 7c fibre, with more than one ring (3 = 900 m, 3 = 0 98 and 3 = 9 1 1003 ). Fig. 6 shows FM loss in the case of three surrounding rings. Confinement loss are negligible compared with absorption loss; however, due to the smaller core size, the effect of material is stronger and this loss is significantly higher than in the 7c-fibre. The core size reduction also affects the FM field distribution, reported in the inset of Fig. 7. Here, the unique symmetry is with respect to the axis. Now, a no negligible fraction of the field extends into the first ring hole, especially in the plane (dashed line in Fig. 7). Nevertheless, the output beam still results to be highly collimated for both principal planes, as shown in Fig. 7; in fact, the half power beamwidth along the principal planes only differs for  1 . As

c

 d=

:

t=

y

x

expected, the 3c-fibre half power beamwidth is higher than the 7c-fibre one, due to a reduction of the effective area. As done for 7c-fibre, the comparison with the equivalent far field characteristic generated by a Gaussian profile is also shown. The Gaussian distribution is chosen as the one which better approximates the modal far-field pattern. In particular, the Gaussian spot size is set to 250 m. As for the 7c-fibre, the Gaussian field is the same in both planes, while the asymmetry of the aperture profiles (see inset of Fig. 7) produces slightly different patterns. Due to the lower quality of the FM field profile, the coupling efficiency with the Gaussian beam, shown in Fig. 8, is lower than that of 7 -fiber, even if it reaches the maximum of 83% at 0 = 520 m and is higher than 80% between 440 m and 610 m. On top of Fig. 8 a possible coupling mechanism is depicted again. The far field Gaussian beam with 0 = 520 m is shown in the inset, compared with FM-based pattern. Even in this case, the far field due to the Gaussian beam is narrower than the modal far field, as explained for the 7c-fibre.





c

W







W

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IV. CONCLUSION In this communication we presented an interesting employment of a hollow core photonic bandgap fibre in the terahertz region. The structure has been numerically investigated in order to obtain low loss wave guiding, which is a major challenge for THz signals, due to the high conductivity losses of metals and high absorption of dielectrics. Numerical results have shown the possibility to reach propagation loss two decades lower than the bulk absorption losses of the material used to fabricate the fibre, over a wide range of wavelength. In addiction, the purity of the aperture field distribution suggests the employment of this fibres as aperture antennas. It has been shown how they guarantee a highly efficient coupling with freely propagating Gaussian beams, which can be exploited in optical or electro-optical systems, and how the output beam is highly collimated.

[20] L. Vincetti, F. Poli, and S. Selleri, “Confinement loss and nonlinearity analysis of air-guiding modified honeycomb photonic bandgap fibers,” IEEE Photon. Tech. Lett., vol. 18, pp. 508–510, 2006. [21] L. Vincetti and A. Polemi, “Hollow core fibre for THz applications,” presented at the IEEE Int. Symp. on Antennas and Propag. and USNC/ URSI National Radio Science Meeting, Charleston, SC, Jun. 2009. [22] N. A. Mortensen and M. D. Nielsen, “Modeling of realistic cladding structures in air-core photonic band-gap fibres,” Opt. Lett., vol. 29, pp. 349–351, 2004. [23] C. Winnewisser, F. Lewen, and H. Helm, “Transmission characteristics of dichroic filters measured by THz time-domain spetroscopy,” Appl. Phys. A, Mater. Sci. Processing, vol. 66, pp. 593–598, 1998. [24] A. W. Snyder and J. D. Love, Optical Waveguide Theory. London, U.K.: Chapman and Hall, 1983. [25] M. N. Petrovich, F. Poletti, A. van Brakel, and D. J. Richardson, “Robustly single mode hollow core photonic bandgap fiber,” Opt. Express, 2008.

REFERENCES [1] J. Xu, K. W. Plaxo, and S. J. Allen, “Probing the collective vibrational dynamics of a protein in liquid water by terahertz absorption spectroscopy,” Protein Sci., vol. 15, pp. 1175–1181, 2004. [2] D. J. Cook, B. K. Decker, and M. G. Allen, “Quantitative THz spectroscopy of explosive materials,” in Proc. Optical Terahertz Science and Technology, 2005, pp. SI–SR. [3] M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photon., vol. 1, pp. 97–105, 2007. [4] R. Piesiewicz, M. Jacob, M. Koch, J. Schoebel, and T. Kürner, “Performance analysis of future multigigabit wireless communication systems at THz frequencies with highly directive antennas in realistic indoor environments,” IEEE J. Sel. Top. Quantum Electron., vol. 14, no. 2, Mar./Apr. 2008. [5] G. Gallot, S. P. Jamison, R. W. McGowan, and D. Grischkowsky, “Terahertz waveguides,” J. Opt. Soc. Am. B, vol. 17, no. 5, pp. 851–863, May 2000. [6] K. Wang and D. M. Mittleman, “Metal wires for terahertz wave guiding,” Nature, vol. 432, pp. 6092–6094, Nov. 2004. [7] T. Ito, Y. Matsuura, M. Miyagi, H. Minamide, and H. Ito, “Flexible terahertz fiber optics with low bend-induced losses,” J. Opt. Soc. Am., vol. 24, pp. 1230–1235, May 2007. [8] R. Mendis, “THz transmission characteristics of dielectric-filled parallel-plate waveguides,” J. Appl. Phys., vol. 101, pp. 83115–83115, 2007. [9] R. Mendis and D. Grischkowsky, “Plastic ribbon THz waveguides,” J. Appl. Phys., vol. 88, no. 7, pp. 4449–4451, Oct. 2000. [10] C. Themistos and B. M. A. Rahman, “Characterization of silver/polystyrene (PS)-Coated hollow glass waveguides at THz frequency,” J. Lightwave Technol., vol. 25, pp. 2456–2462, Sep. 2007. [11] A. Hassani, A. Dupuis, and M. Skorobogatiy, “Porous polymer fiber for low-loss terahertz guiding,” Opt. Expr., vol. 16, no. 9, pp. 6340–6351, Apr. 2008. [12] Y. F. Geng, X. L. Tan, P. Wang, and J. Q. Yao, “Transmission loss and dispersion in plastic terahertz photonic band-gap fibers,” Appl. Phys. B, vol. 91, pp. 333–336, 2008. [13] L. Vincetti, “Hollow core photonic band gap fibre for THz applications,” Micro. Technol. Lett., vol. 51, no. 7, pp. 1711–1714, 2009. [14] F. Benabid, “Hollow-core photonic bandgap fibre: New light guidance for new science and technology,” Phil. Trans. R. Soc. A, vol. 364, no. 364, pp. 3439–3462, Dec. 2006. [15] R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, D. Allen, and P. J. Roberts, “Single-mode photonic band gap guidance of light in air,” Science, vol. 285, pp. 1537–1539, 1999. [16] J. C. Knight and P. St. J. Russell, “New ways to guide light,” Science, vol. 296, pp. 276–277, 2002. [17] C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Mller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature, vol. 424, pp. 657–659, 2003. [18] P. J. Roberts, F. Couny, H. Sabert, B. J. Mangan, D. P. Williams, L. Farr, M. W. Mason, A. Tomlinson, T. A. Birks, J. C. Knight, and P. St. J. Russell, “Ultimate low loss of hollow-core photonic crystal fibres,” Opt. Express, vol. 13, pp. 9115–9124, 2005. [19] S. Selleri, L. Vincetti, A. Cucinotta, and M. Zoboli, “Complex FEM modal solver of optical waveguides with PML boundary conditions,” Opt. Quantum Electron., vol. 33, pp. 359–371, 2001.

Analysis of Electromagnetic Scattering and Radiation From Finite Microstrip Structures Using an EFIE-PMCHWT Formulation Wei-Jiang Zhao, Le-Wei Li, and Ke Xiao

Abstract—An EFIE-PMCHWT formulation is obtained in an easy manner for finite microstrip structures when they are regarded as separate conducting and dielectric bodies. By simply eliminating equivalent magnetic surface currents on the dielectric interface where the conductor is attached to, the formulation is reduced to a formulation which is identical to that originally proposed for conductors with partial dielectric coatings. Using the resulting EFIE-PMCHWT formulation, electromagnetic radiation from a patch antenna due to a localized voltage source on the conducting patch is computed. Good agreement is observed between the calculated and measured radiation patterns. Index Terms—Antenna radiation patterns, electromagnetic scattering, microstrip antennas, moment methods.

I. INTRODUCTION The basic structure of patch antennas is a metallic patch printed on a finite grounded dielectric substrate. The patch antennas can therefore be modeled by combined conducting and dielectric structures where conducting and dielectric surfaces touch each other. One of the popular Manuscript received July 17, 2009; revised December 16, 2009; accepted January 13, 2010. Date of publication April 26, 2010; date of current version July 08, 2010. This work was supported in part by the Defence Science and Technology Agency of Singapore via a Defence Innovative Program Project: DSTA-NUS DIRP/2007/02 and in part by the US Air Force AOARD/AFOSR Projects: AOARD-07-4024 and AOARD-09-4069. W.-J. Zhao was with the Department of Electrical and Computer Engineering, National University of Singapore, Kent Ridge, Singapore 119260, Singapore. He is now with the Department of Computational Electronics and Photonics, Institute of High Performance Computing, Agency for Science Technology and Research (A*STAR), Singapore 138632, Singapore. L. W. Li is with the Institute of Electromagnetics, University of Electronic Science and Technology of China, Chengdu 611731, China and also the Department of Electrical and Computer Engineering, National University of Singapore, Kent Ridge, Singapore 119260, Singapore (e-mail: [email protected]; http://www.ece.nus.edu.sg/lwli). K. Xiao is with the School of Electronic Science and Engineering, National University of Defense Technology, Hunan, China. Color versions of one or more of the figures in this communication are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2010.2048867

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numerical methods for the analysis of such structures is the surface integral equation (SIE) solved using the method of moments (MoM) [1]. Analysis of finite microstrip structures by modeling these structures with composite conducting and dielectric bodies which are separated by a layer of zero-thickness free space and using the SIE has been reported in [2], [3], where the electric field integral equation (EFIE) was used for both conducting and dielectric surfaces. The method in [2], [3] adopted mutually orthogonal sets of basis functions for electric and magnetic currents to handle the hybrid where the conducting surfaces are infinitesimally close to the dielectric surface. The method has some disadvantages although it works well for finite microstrip structures. The use of Rao-Wilton-Glisson (RWG) basis functions [4] for electric currents and another set of basis functions for magnetic currents does not allow one to exploit the duality properties of the integro-differential operators for the dielectric body, and the application of EFIE for closed dielectric surface limits the method to thin substrate where the resonance problem may not be significant. The resonance problem for closed dielectric bodies can be avoided by using the PMCHWT formulation [5], [6]. By combing with EFIE, the PMCHWT has been used for handing composite conducting and dielectric bodies [7]. Analysis of electromagnetic (EM) scattering and radiation from finite microstrip structures has been reported using the EFIE-PMCHWT formulation and the precorrected-FFT method [8]. However, the methods in [7], [8] may not work accurately when the conducting and dielectric bodies are infinitesimally close to each other [3]. The above methods model microstrip structures with separate conducting and dielectric bodies [2], [3], [7], [8], resulting in two unknown electric currents and one unknown magnetic currents in the overlapped region, and the singularities due to the overlapping needs to be evaluated very carefully. On the other hand, an EFIE-PMCHWT formulation for conductors with partial dielectric coatings was proposed in [9] and it has been successfully applied to the analysis of EM radiation from microstrip antennas excited by a dipole source [10], [11] and EM scattering by a dielectric circular cylinder capped with a conducting disk [12]. When conducting and dielectric bodies are infinitesimally close to each other but non-touching, one has to compute the principal value of electric field from an element of magnetic current [3]. Hence the EFIE-PMCHWT fails to handle accurately such problem because the principal value has been canceled out when the integral equations corresponding to the external and internal regions are combined. When conducting and dielectric bodies touch each other which is the situation for microstrip structures, it is not necessary to compute such principal value because the magnetic currents on the dielectric interface where the conductors are attached to just vanish. In this communication, we derived an EFIE-PWCHWT formulation from that given in [7] by simply eliminating the equivalent magnetic surface currents on the dielectric interface where a conductor is attached to. The obtained formulation has been found to be consistent with that given in [9] which is originally derived for conductors with partial dielectric coatings. The relationship between the two EFIE-PMCHWT formulations [7], [9] is hence clearly seen. A brief discussion on the resonance problem associated with finite microstrip structures is presented. As a dipole source is difficult to be used as the excitation for the microstrip array where the conducting patches share one same dielectric substrate, analysis of EM radiation from a patch antenna due to a localized voltage source on the conducting patch is investigated. II. INTEGRAL EQUATIONS The geometry considered is a hybrid structure comprising of both conducting and dielectric bodies as shown in Fig. 1(a). The PEC, referring to perfect electric conductor, consists of two sub-surfaces for metallic patch and ground plane for the problem of microstrip structures. "1 and 1 denote, respectively, the permittivity and permeability

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Fig. 1. Problem representation and its equivalence. (a) Original problem; (b) external equivalence; (c) internal equivalence.

of the free space. The dielectric body has permittivity of "2 and permeability of 2 . The hybrid conducting and dielectric surfaces can be of arbitrary shape and they touch each other. The excitation is due to a plane wave for scattering problems or a localized voltage source on the PEC structure for radiation problems. The sources of the excitation are resulted respectively from impressed electric and magnetic currents, J i1 and M i1 in the free space and J i2 and M i2 inside the dielectric body. The surfaces Sc1 , Sc2 and Sd represent, respectively, the interfaces between PEC and the free space, the PEC and the dielectric body, and the dielectric body and free space. The conducting and dielectric bodies are first treated as disconnect objects. According to the equivalent principle [13], the problem shown in Fig. 1(a) can be solved by considering its two equivalent problems, i.e., external and internal equivalence which are shown in Fig. 1(b) and Fig. 1(c). Let SD denote the outer surface of the dielectric body composed of Sd and Sc1 , the inner surface of the dielectric body can hence be represented by 0SD which consists of 0Sd and Sc2 . Let J c1 denote the equivalent electric surface currents on Sc1 ; and assume that J d and M represent the equivalent electric and magnetic currents on SD , respectively. Since tangential components of electric and magnetic fields across a dielectric interface are continuous, the electric and magnetic currents on 0SD are hence known as 0J d and 0M , respectively. By applying the boundary conditions on conducting and dielectric surfaces, a set of electric and magnetic field integral equations involving the above three unknown currents can be obtained as follows

0 E 1 (J 1 ; M 1 ) tan ; E 1 (J 1 ; J ; M ) tan = 0 E 1 (J 1 ; M 1 ) ; tan H 1 (J 1 ; J ; M ) tan = 0 H 1 (J 1 ; M 1 ) ; tan E 2 (0J ; 0M ) tan = 0 E 2 (J 2 ; M 2 ) ; tan 2 H (0J ; 0M ) tan = 0; outside S E s1 (J c1 ; J d ; M ) tan = s

s

s

s

c

d

c

d

d

d

i

i

i

on Sc1

(1a)

i

i

i

inside SD

(1b)

inside SD

(1c)

outside SD

(1d)

i

i

i

i

i

i

D

(1e)

where the subscript “tan” stands for the tangential component. The terms on the right hand side of the above equations are the incident electric and magnetic fields produced by the impressed source. The terms on the left hand side of the above equations denote the scattered

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electric and magnetic fields yielded by the equivalent surface currents.

M ) represents the scattered electric field produced by E s1 (J c1 ; J d ;M the currents J c1 , J d and M when they radiate into the unbounded medium ("1 ; 1 ), while H s2 (0J d ; 0M ) denotes the scattered magnetic field due to the currents 0J d and 0M when they radiated into the unbounded medium ("2 ; 2 ). Other terms in the above equations are defined similarly. The scattered electric field E s and magnetic field H s due to the electric current J and magnetic current M are given respectively by [14]

E s (r ) = 0 j!AA(r ) 0 r8(r ) 0 r 2 F (r ) H s (r ) = 0 j!FF (r ) 0 r9(r ) + r 2 A(r ) :

(2a) (2b)

Combining (1b) with (1d) and (1c) with (1e), we establish the following two new equations

E s1 (J c1 ; J d ; M ) + E s2 (J d ; M ) tan i1 i1 i1 = 0 E (J ; M ) 0 E i2 (J i2 ; M i2 ) tan ; tan H s1 (J c1 ; J d ; M ) + H s2 (J d ; M ) tan i1 i1 i1 ; on SD : = 0 H (J ; M ) tan

on

SD (3a) (3b)

Equations (3a) and (3b) form the PMCHWT formulation for the dielectric surface. Equation (1a) denotes the electric field integral equation (EFIE) for conducting surfaces. These three equations form an EFIE-PMCHWT formulation which is identical to that given in [7] as a scattering problem is under consideration. Then the conductors are allowed to touch dielectric interface, hence it is necessary for the magnetic currents on Sc1 to be eliminated. Since the tangential electric field is continuous across the dielectric interface, the magnetic current on Sc2 is removed accordingly. J d on Sc1 is combined into J c1 because both of them represent the equivalent electric surface current on the identical fictitious mathematic surface Sc1 . Let J c2 represent the equivalent electric surface current on Sc2 , and let J d and M , respectively, denote the electric and magnetic currents on Sd only. Rewrite (3a) and (3b) on Sd , we obtain

0

E s1 (J c1 ; J d ; M ) + E s2 (J c2 ; J d ; M ) tan i1 i1 i1 = 0 E (J ; M ) ; on Sd ; tan s1 s2 H (J c1 ; J d ; M ) + H (J c2 ; J d ; M ) tan i1 i1 i1 = 0 H (J ; M ) ; on Sd : tan

(4a)

(4b)

Since a localized source on the conducting patch is used here, the incident fields due to this source vanish on the dielectric interface Sd in the above two equations. Rewrite (3a) on Sc2 and remove the fields corresponding to the external region which has been considered already in (1a), we have

E s2 (0J c2 ; 0J d ; 0M ) tan = 0 E i2 (J i2 ; M i2 ) tan ;

on

Sc2 ;

(5)

As a result, the integral equations of (1a), (4a), (4b) and (5) form a formulation for solving the four unknown currents J c1 , J c2 , J d and M . The formulation is consistent with the EFIE-PMCHWT formulation given in [9] as a scattering problem is considered. The EFIE-PMCHWT formulation presented in [9] is a reduced one of the EFIE-PMCHWT formulation presented in [7] when the condition that conductors touch dielectric interface is considered, this is the reason why the former is more accurate for microstrip structures than the latter. The presented formulation is a little different from that presented in [10], [11]. The incident fields in the formulation given in [10], [11] are due to a dipole source existing only inside the dielectric

Fig. 2. Bistatic RCS for the structure of a dielectric cone capped by a conducting disk, at  polarization.

body, but the incident fields in the presented formulation are due to a localized voltage source on the conducting patch and the source exists both outside and inside the dielectric body. In the overlapped region of the conducting and dielectric surfaces, with the magnetic surface current being eliminated and only two electric surface currents being used, the presented formulation saves the computational resources drastically compared to the formulation given in [2], [3], [7], [8], because the size of the overlapped region is usually comparable to that of the remaining part. In addition, evaluating the singularities due to the overlapping is avoided in the presented method. The integral equations are solved via the MoM in a standard fashion where the Galerkin MoM procedure is employed and the RWG basis functions are used for expanding both the electric current and the magnetic current. The internal resonance problem is relevant to the structures which involve two regions, with one of which is finite. This problem has been studied abundantly for dielectric bodies, and the studies can be extended to the finite microstrip structures directly. The conductors in the microstrip structures are assumed as zero-thickness conducting layers which touch dielectric interface directly, hence the EFIE on the conducting surface can also be regarded as an EFIE on the outer surface of the dielectric body where the conducting and dielectric surfaces are mathematically identical. Just like that in the problem of a closed dielectric body, in the problem of a finite microstrip structure, a cavity solution of the finite dielectric region bounded by a perfect conductor and filled with free space plus the true solution of the problem still satisfies the integral equations corresponding to the external region, but the sum of the cavity solution and the true solution of the problem fails to satisfy the integral equations corresponding to the internal region on the non-closed dielectric interface, thus leading to a spurious solution. The internal resonance problem can be avoided by using the EFIE-PMCHWT formulation. III. NUMERICAL RESULTS Six examples are considered in this Section to demonstrate the efficiency and accuracy of the proposed method. In the first example, a test case which was used in [3] is re-considered. The geometry considered is a PEC disk placed on the top of a dielectric cone. The dielectric cone has a radius of 0.3  and a height of 0.6 , where  is the wavelength in free space. The relative permittivity of the dielectric cone is assumed to be 2. The structure is illuminated by a normally incident plane wave with the incident electric field along the +x-axis direction. The bistatic RCS in the XOZ plane for  polarization versus the polar angle  is calculated using the presented method and shown in Fig. 2.

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Fig. 3. Bistatic RCS for the structure of a dielectric cylinder capped by a conducting disk, at  polarization.

The disk and cone without its top face are modeled by 126 and 164 triangular patches, respectively. The result calculated by a body of revolution code [3] is also presented in the figure for comparison. A good agreement is observed, except for a slight difference around  = 0 and  = 180 . In the second example, the electromagnetic scattering by a dielectric cylinder capped by a conducting disk is considered. The dielectric cylinder is of a radius of 0.3  and a height of 0.6 , where  is the wavelength in free space. The material has a relative permittivity of "r = 2. The structure is illuminated by a normally incident plane wave with the incident electric field along the +x-axis direction. The bistatic RCS in the XOZ plane for  polarization versus the polar angle  is calculated using the presented method and the other method introduced in [7]. The disk is modeled by 126 triangular patches. In the presented method, the cylinder without its top face is used and modeled by 308 triangular patches. For the method in [7], the complete cylinder is used and modeled by 376 triangular patches. The results are shown in Fig. 3. Three sets of results using the existing method in [7] are presented in the figure for three different cases where the gap distances between the conducting disk and top of the dielectric cylinder are taken as 0.005 , 0.0003  and 0, respectively. It can be seen that only the result in the 0.005  gap case is close to that calculated by the presented method. It indicates that the method in [7] may lead to inaccurate solutions when it is used to handle hybrid conducting and dielectric bodies whose surfaces are infinitesimally close to each other. Although the existing method for the gap distance of 0.005  gap gives a close solution to the problem, it is not accurate at all when the gap distance is set to be small enough or zero. This structure was also previously considered in [12] and [8], and it is noted from the Fig. 3 of the [8] that the technique introduced in [7] achieved a result which agrees well with the reference solution given in [12]. By choosing a proper non-zero value for the gap distance between the conducting and dielectric surfaces, e.g., around 0.005  in this example, it is really possible for the EFIE-PMCHWT formulation introduced in [7] to yield an accurate solution. However, if a problem does not have an available solution for reference, it is unknown what the appropriate gap value is, with which the technique introduced in [7] just yields an accurate solution, and one possible way is to choose a gap value which has been proven appropriate in other examples. Unfortunately, the optimal gap value is on a case-by-case basis, using a inappropriate gap value the technique given in [7], [8] will lead to an inaccurate solution for microstrip structures. To further demonstrate the different solution accuracy of the above two different EFIE-PMCHWT formulas, an example considered previously in the Fig. 4 of the [8] is re-considered in the next example.

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Fig. 4. Bistatic RCS for the structure of a dielectric cone capped by a conducting disk, at  polarization.

Fig. 5. Geometry and dimension of the patch antenna.

In the third example, the biststic RCS is calculated using the presented method for a dielectric cone capped by a PEC disk. The dielectric cone has a radius of 1.2  and a height of 0.6 , where  is the wavelength in free space. The relative permittivity of the dielectric cone is assumed to be 2. The structure is illuminated by a normally incident plane wave with the incident electric field along the +x-axis direction as shown in Fig. 2. Fig. 4 shows a comparison of the calculated bistatic RCS with that presented in [8] in the XOZ plane for  polarization versus the polar angle  . Obvious difference between the two results can be seen at the angles around  = 30 ,  = 60 ,  = 114 and  = 150 . In the fourth example, the EM scattering by a patch antenna is considered. The geometry and dimension of the antenna system are shown in Fig. 5. A plane wave is incident on the antenna along the 0z -axis direction. The bistatic RCS values in the XOZ and Y OZ planes for different polarizations are calculated as a function of the polar angle  . The patch and ground plane are modeled by 405 triangular patches, and the surface of the dielectric substrate without the parts in contact with the PEC surface is modeled by 412 triangular patches. The results for the XOZ plane are shown in Fig. 6, and those for the Y OZ plane are shown in Fig. 7. In the example, the presented technique uses 558 unknowns respectively for equivalent electric and magnetic currents on the dielectric surface and 569 unknowns respectively for equivalent electric currents on the conducting surfaces Sc1 and Sc2 , and hence the total number of unknowns used is 2254. If the technique introduced in [2], [3] is used, for the same triangular discretization, it will use more than 1127 unknowns respectively for equivalent electric and magnetic

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Fig. 6. Bistatic RCS for the patch antenna in the

XOZ plane.

Fig. 8. Radiation pattern of the patch antenna in the

H -plane.

Fig. 7. Bistatic RCS for the patch antenna in the

Y OZ plane.

Fig. 9. Radiation pattern of the patch antenna in the

E -plane.

currents on the dielectric surface and 569 unknowns for equivalent electric current on the conducting surface, and hence the total number of the unknowns used is more than 2823, about a quarter larger than the number of unknowns used by the presented technique. In the fifth example, the EM radiation from a patch antenna shown in Fig. 5 is considered. The patch is excited by a 1 V source placed across a delta gap in the feed edge. The -plane and -plane patterns at 1.875 GHz near the patch resonance are shown in Fig. 8 and Fig. 9, respectively. The calculated results are compared with the measured results provided in [15]. For the measurement, a signal source was applied to the microstrip patch through a coaxial feed, and a metal block was used to secure coaxial connector under the ground plane which may affect the measured radiation pattern in the backside radiation. In the -plane, only the comparison for varying from 090 to 90 is given because the measured sidelobe levels are very sensitive to alignment of the antenna and horn used in measurement [15]. From the figures, it can be seen that the agreement between the calculated and measured patterns is good for -plane, and it is also good for the frontside radiation in the -plane; but the agreement is not so good for the backside radiation in the -plane. The calculated and measured patterns have the same null locations but different sidelobe levels. The last example considered is the EM scattering by a structure with two PEC square plates attached to the top and bottom surfaces of a dielectric cube as shown in Fig. 10. The cube has a relative permittivity so that the size corr = 4 and its side length is chosen as 1.125 responds to a resonant frequency of the air-filled cubical cavity, where is the wavelength in free space. As discussed in Section II, a cavity solution of the finite dielectric region bounded by a perfect conductor

H



H

E

" 

E

H

E



Fig. 10. Comparison of two different solutions for the bistatic RCS for the structure of a dielectric cube capped by conducting square plate on its top and bottom surfaces, at polarization.



and filled with free space may enter into the solutions of the integral equations corresponding to the external region and lead to a spurious solution. The side lengths of the two PEC square plates are same and they are identical to that of the cube. Two sets of formulations are used to calculate the bistatic RCS of the structure with the results shown in Fig. 10. One is the EFIE-PMCHWT formulation presented in the communication, and the other is formed by four integral equations, i.e., (1a), (5) and two equations of (4a) and (4b) but with the fields corresponding

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to the internal region in these two equations removed. Of these two formulations, the former is free of resonance problem, and the latter may yield spurious solutions near or at resonance frequencies of the interior plane for body. Shown in Fig. 10 is the bistatic RCS in the polarization as a function of the polar angle , for an incident plane wave with the electric field along the + -axis. Significant difference between the two solutions is clearly observed in the figure.

x



XOZ



IV. CONCLUSION The direct application of the EFIE-PMCHWT formulation proposed for separate conducting and dielectric bodies to a finite microstrip structure may result in an inaccurate solution, but by further applying the condition that conductors touch dielectric interface, the formulation can be reduced to the EFIE-PMCHWT formulation which is originally proposed for conductors with partial dielectric coatings and has been proved very useful for finite microstrip structures. Electromagnetic scattering by, and radiation from, patch antennas are successfully analyzed by using the EFIE-PWCHWT formulation. The method yields resonance-free solutions, needs a less number of unknowns and avoids the evaluation of singularities due to overlapping of the conducting and dielectric surfaces, compared to other existing methods for modeling the microstrip structures by composite conducting and dielectric bodies separated with a layer of zero-thickness free space. The same RWG basis functions are used for electric and magnetic currents, which allows ease of its future implementation into fast integral algorithms.

REFERENCES [1] R. F. Harrington, Field Computation by Moment Methods. New York: Macmillan, 1968. [2] T. K. Sarkar, S. M. Rao, and A. R. Djordjevic, “Electromagnetic scattering and radiation from finite microstrip structures,” IEEE Trans. Microw. Theory Tech., vol. 38, no. 11, pp. 1568–1575, Nov. 1990. [3] S. M. Rao, T. K. Sarkar, P. Mydia, and A. R. Djordjevic, “Electromagnetic radiation and scattering from finite conducting dielectric structures: Surface/surface formulation,” IEEE Trans. Antennas Propag., vol. AP-39, pp. 1034–1037, Jul. 1991. [4] S. M. Rao, D. R. Wilton, and A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propag., vol. AP-30, pp. 409–418, May 1982. [5] J. R. Mautz and R. F. Harrington, “Electromagnetic scattering from a homogeneous material body of revolution,” Arch Elek Übertragung, vol. 33, pp. 71–80, 1979. [6] K. Umashankar, A. Taflove, and S. A. Rao, “Electromagnetic scattering by arbitrary shaped three-dimensional homogeneous lossy dielectric objects,” IEEE Trans. Antennas Propag., vol. AP-34, pp. 758–766, Jun. 1986. [7] E. Arvas, A. Rahhal-Arabi, A. Sadigh, and S. M. Rao, “Scattering from multiple conducting and dielectric bodies of arbitrary shape,” IEEE Antennas Propag. Mag., vol. 33, no. 2, pp. 29–36, 1991. [8] N. Yuan, T. S. Yeo, X. C. Nie, L. W. Li, and Y. B. Gan, “Efficient analysis of electromagnetic scattering and radiation from patches on finite, arbitrarily curved, grounded substrates,” Radio Sci., vol. 39, pp. 1–13, May 2004. [9] J. R. Mautz and R. F. Harrington, “Boundary formulation for aperture coupling problems,” Arch. Elek. Ubertragung, vol. 34, pp. 377–384, 1980. [10] A. A. Kishk and L. Shafal, “Different formulations for numerical solution of single or multibodies of revolution with mixed boundary conditions,” IEEE Trans. Antennas Propag., vol. AP-34, pp. 666–673, May 1986. [11] A. A. Kishk and L. Shafal, “The effect of various parameters of circular microstrip antennas on their radiation efficiency and the mode excitation,” IEEE Trans. Antennas Propag., vol. AP-34, pp. 969–976, Aug. 1986.

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[12] J. Shin, A. W. Glisson, and A. A. Kishk, “Analysis of combined conducting and dielectric structures of arbitrary shapes using an E-PMCHW integral equation formulation,” in IEEE AP-S Int. Symp., 2000, vol. 4, pp. 2282–2285. [13] R. F. Harrington, Time-Harmonic Electromagnetic Fields. New York: McGraw-Hill, 1961. [14] W. J. Zhao, L. W. Li, and Y. B. Gan, “Efficient analysis of antenna radiation in the presence of airborne dielectric radomes of arbitrary shape,” IEEE Trans Antennas Propag., vol. AP-53, pp. 442–449, Jan. 2005. [15] R. A. York, R. C. Compton, and B. J. Rubin, “Experimental verification of the 2-D rooftop approach for modeling microstrip patch antennas,” IEEE Trans Antennas Propag., vol. AP-39, pp. 690–694, May 1991.

UHF RFID Systems; Their Susceptibility to Backscattered Signals Induced by Electronic Ballast Driven Fluorescent Lamps Ghassan Ibrahim and Albert Plytage

Abstract—It was demonstrated that high speed switching of electronic ballast driven fluorescent lamp (EBFL) reflects and modulates the incident UHF RFID forward link reader- tag signal in a manner similar to that of modulated reverse link backscattered tag-reader signal. Qualitative analysis of EBFL’s backscattered radiation properties indicated it has a half dipole pattern similar to that of the UHF RFID tag. Its backscatter signal spectrum falls within the spectral band of the tag signal with power levels exceeding that of a tag-reader signal power when located at distances over 5 meters from the reader antenna. Performance analyses results of an operating UHF RFID system, in close proximity to a set of active EBFLs, indicated without any doubt that the EBFL’s modulated backscattered signal is a source of strong interference. It can compromise the reverse link and significantly affect the reception of modulated backscattered UHF RFID tag signals. The effects of this interference must be taken into consideration when developing an RFID system operating in an environment abundant with EBFLs. Index Terms—Backscattered radio frequency identification (RFID), electronic fluorescent lamps, radio frequency communication, spectral analysis, UHF.

I. INTRODUCTION Radio frequency identification (RFID) has gained significant attention in the technology and business arenas. The two main system components are the RFID reader, and RFID tags which are attached to items to be identified (merchandise, people, pets, furniture, instruments, etc.). Today there is a considerable interest in UHF passive RFID technology, but insufficient understanding of its capabilities and limitations [1]. We have identified and bring to the attention of the RFID systems designers and developers an overlooked source of interference that can, if ignored, limit the capabilities and considerably reduce the reliability of the UHF passive RFID system, namely the backscatter reflection of UHF RFID signals by electronic ballast driven fluorescent lamps (EBFLs). Manuscript received June 29, 2008; revised November 02, 2009; accepted January 15, 2010. Date of publication April 22, 2010; date of current version July 08, 2010. The authors are with Department of Physics and Engineering Technology, Bloomsburg University of Pennsylvania, Bloomsburg, PA 17815 USA (e-mail: [email protected]; [email protected]). Digital Object Identifier 10.1109/TAP.2010.2048841

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It is well known that fluorescent lamps can introduce significant effects on various transmitted wireless signals. It was shown that fluorescent lights driven by conventional power line ballasts absorb and reflect RF signals in the range 700–1800 MHz causing significant attenuation in personal communication wireless signals [2]. This effect was verified on WLAN utilizing MIMO/OFDM [3] and is attributed to the fact that RF signals encounter variable media characteristics due to changing dielectric characteristics of the fluorescent plasma medium between the on and off states of the lamp. The cyclic ionization and deionization of the gaseous medium introduces another form of interference. When the fluorescent tube is in the off state, it is transparent to the RF signal and the reflection will be generated by the tube metal fixture. In its on state the gas is ionized and acts as a medium with lossy dielectric; the tube absorbs and reflects incident RF signals [4]. It was also demonstrated that high speed switching of a fluorescent light by the electronic ballast voltage reflects and modulates the incident RF signal in a manner similar to that of a modulated backscattered RFID transponder (tag) signal [5]. The reflected backscattered RF wave from the fluorescent lamp is amplitude modulated with sidebands located at multiples of electronic ballast frequency components, extending to hundreds of kilohertz with significant power levels spread within this range. Analysis of the measured sidebands spectra indicated that the sidebands themselves are modulated at multiples of twice the power line frequency. Fluorescent lamps driven by different types of electronic ballasts operating at different unsynchronized frequencies exhibited different power levels at different frequencies. The reverse link from the RFID tag to the interrogator receiver will be compromised when the EBFL generates sidebands of the same order of magnitude as those generated by the tag. Consequently in an environment abundant with active EBFLs, the reflected RF signals can significantly affect the reception of modulated backscattered tag RFID signals at UHF and higher bands. However, it is almost impossible to state whether or not the lamps will have significant effects until simulations, real-time tests, and analysis are done with an operating RFID system. In this paper the effect of the EBFLs in proximity of an operating passive UHF RFID system is investigated. The RFID system and the EBFLs are set apart at different distances and oriented at different locations with respect to each other. The operation of the RFID system, using EPC Class 1 Gen 2 high speed long range and high sensitivity tags [6], is analyzed at different reader power levels using a number of EBFL fixtures. In the following sections the experimental procedures, their results, and their analysis are presented. II. ANALYSIS OF THE EBFL BACKSCATTERED SPECTRUM A. Modeling the EBFL’s Backscattering The fluorescent gases ionize every half cycle of the switching signal creating high dielectric plasma medium. The medium thus acts as a high speed switch varying the gaseous medium resistance at twice the ballast switching frequency, which is measured to be a 42 KHz triangular waveform. The EBFL set consisting of fluorescent tubes with metallic background, thereby acting as a target with variable radar cross section, will reflect and pulse modulate the incident RF signal at a rate of 2 !1 . This backscattered modulated signal is mathematically modeled by

gbs = gf 1 2 gi gi = D cos !i t: where

gf 1

Fig. 1. Modeling the modulated backscattered waveform, notice the resemblance to the recorded backscatter signal spectra in Fig. 2.

Fig. 2. The recorded backscatter signal spectra.

modulates the incident signal gi creating the modulated backscattered signal. Representing the modulating signal gf 1 by its Fourier series then gbs is modeled by

gbs = 8CD 22

1 1

1 (2n 0 1) [cos(!i 0 (2n 0 1)2!1)t + cos(!i + (2n 0 1)2!1)t]:

(3)

The MATLAB simulation of the backscattered carrier signal is shown in Fig. 1 using arbitrary values for D, the amplitude of gi , and C the amplitude of the modulating signal gf 1 . Notice the similarity to the experimental plot of the spectrum shown in Fig. 2. The above model clearly verifies the source of the modulation and backscattering of the incident RF signal. B. EBFL Backscatter Modulation Depth As stated earlier the incident RF wave is backscattered and modulated by the EBFL set. To better understand this phenomenon a qualitative analysis is presented. With the EBFL set directly in the LOS of the reader antenna it will act as target with variable radar cross section (RCS) when switching between the on and off states. In the de-ionized off state the tubes are transparent to the incident RF wave which encounters the EBFL metallic fixture with an approximate flat plane area A1 = 0:2 m2 . The RCA can be then calculated using the RCA equation for rectangular flat plate [8]

(1)

2 1 1 = 4A 2 

(2)

is the fluorescent gas ionization signal with frequency of

2!1 , in tens of KHz, and gi is the incident RFID carrier signal with fre- 1 = plate RCA; A1 = area of the plate,  = wavelength of the quency !i in hundreds of MHz. The lower frequency signal amplitude

RF signal.

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The backscattered signal power density from the target PBS1 , ignoring the multipath propagation effects, is determined by the classical radar equation

2 PBS1 = Pt G3t  4 1 (4) R

Pt = transmitter in watts, Gt = Reader antenna gain,  = wavelength in meters, R = LOS distance between reader antenna and EBFL metal fixture, 1 = Metallic xture RCA. In the ionized on state it is assumed that the tubes plasma will absorb and attenuate the RF wave. The reflecting flat metallic area will then be reduced by the total flat area obstructed by the six T8 17 w tubes (each 55 cm 2 2.54 cm) used in the experiment to an area A2 = 0:116 m2 . The RCA will then be

2 2 = 4A2 2 : 

Fig. 3. Backscattered signal with 3 EBFL fixtures on at 2 m.

The backscatter signal power density from the target PBS2

2 PBS2 = Pt G3t  4 2 : (4) R

The reduction in the backscattered signal power level between the on and off states

2

2 = 05 dB 10Log10 PPBS21 = 10 log A A2 BS

1

The corresponding change is backscattered signal level

V1 = 1000:25 = 0:56: V2

Fig. 4. Backscattered signal 2nd sideband with one fixture on.

This value is an estimate of the modulation level not taking into consideration the multipath reflection effects, and assuming that the gaseous plasma absorbs the RF wave completely. However the qualitative analysis supports our findings that the EBFL modulates as it reflects the incident RF signal. III. EXPERIMENTAL REALIZATION Having shown that the EBFL can significantly interfere with the RFID tag-reader reverse link it is important to determine the effect of this interference on the RFID system operation and its reliability to retrieve tag information. An RFID system was set up in a laboratory environment together with a set of EBFLs. The set consists of 3 fixtures; each fixture consists of two T8 17 W lamps driven by “Advanced” electronic ballast model Centinum ICM-4P32-SC. The test and spectral analysis system consisted of a 6 dBi MACOM/MAANAT0123 dual element RFID circularly polarized test reader antenna (TRA) connected to a function generator and a spectrum analyzer. The lab environment was tested to ensure non-existence of extraneous electromagnetic or RF interference prior to conducting the experiments. The experimental analyses consisted of the following multiple phases. — Analysis of the backscatter spectrum of the EBFL set at a typical UHF RFID frequency; — Determination and analysis of the EBFL set backscatter signal spectra in proximity of an operating UHF RFID system; — Analysis of the EBFL backscattered RF signal radiation properties; — Performance analysis of the operating UHF RFID system in proximity to the EBFL set. IV. ANALYSIS OF THE EBFL BACKSCATTERED SPECTRUM The EBFL set was located at a distance of 2 meters facing the TRA and aligned with its maximum directional gain. The function generator

Fig. 5. Backscattered signal 2nd sideband with 3 fixtures on.

was set at 915.0 MHz and 20 dBm giving an EIRP of 26 dBi, ignoring cable losses. The spectrum of the modulated backscattered signal from the “3 fixture” EBFL is shown in Fig. 3. It is evident that the bandwidth of the modulated backscattered signal is greater than 830 KHz, with a lowest sideband power of 086 dBm. This is well over the 500 kHz reverse link tag signal bandwidth, specified by EPCglobal specifications [9], and well within its operating power level. The effective sidebands of the modulated backscattered signal are located at multiples of the EBFL’s switching frequency 2nd harmonics (83 kHz), which is equally true when only one fixture is on. In both cases the first prominent sideband spectrum is located at 915.083 MHz and shows the multiple peaks spaced by 120 Hz, the main’s second harmonics (Figs. 4 and 5). These results supports the previous findings [5] indicating that the EBFL, under certain circumstances and RFID system configuration, may effectively interfere with the tag’s reverse link signal.

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Fig. 6. Reader-to-tag forward link signal spectrum.

Fig. 8. Backscatter signal spectrum with the EBFL replacing the tag.

With the “3 fixture” EBFL replacing the tag, the backscattered signal spectrum from the EBFLs together with the reader-tag signal spectrum are shown in Fig. 8. The EBFL backscattered signal occupies approximately 560 kHz bandwidth at a level of 070 dB. It is clearly evident that the EBFL backscatter signal spectrum falls within the spectral band of the tag signal and at a comparable level. However, the effect of these findings on the operation of the RFID system and its reliability to identify tag information required further experimental investigation and analysis. VI. EBFL BACKSCATTERED SIGNAL RADIATION FIELD

Fig. 7. Tag-to-reader spectrum.

V. EBFL BACKSCATTER SIGNAL SPECTRA IN PROXIMITY OF AN ACTIVE UHF RFID SYSTEM To practically determine the existence of the EBFL’s backscattered signal spectrum within the UHF RFID reader-tag and tag-reader signals spectra, a passive UHF RFID system was operated using EPC Class 1 Gen 2 tag [9]. The operating RFID system of choice was the ALIEN 9900 system, together with ALN-9540 tag [6]. The spectrum of reader-to-tag link signal, the tag-to-reader reverse link signal, and the EBFL backscattered signal, using ‘3 fixture” EBFL set, were recorded and analyzed. In real-life the reader-tag signal is higher by orders of magnitude than the tag-reader signal which renders the simultaneous detection of tag-reader signal spectrum impossible. To ensure the simultaneous detection and identification of the reader high signal level and the relatively very low level tag signal, the TRA was located such that it is far from the reader antenna but in close proximity to the tag. At the same time the tag was in the reader signal range; activated and communicating with the reader. The TRA was located at a distance of 3 meters from the reader antenna and 50 cms from the tag. The spectrum of the reader-to-tag signal (Fig. 6) clearly shows the carrier frequency with amplitude modulated forward reader spectrum having a bandwidth of 300 kHz. The tag-reader signal spectrum together with reader-tag signal spectrum are shown in Fig. 7; it indicates a tag-toreader signal bandwidth of 500 kHz at signal levels of 050 to 070 dBm, see EPC specifications [9].

As demonstrated the EBFL acts in a similar manner to an RFID tag; modulating and transmitting backscattered RF signal whose spectrum falls within the tag-reader signal bandwidth. Its ability to radiate and transmit RF signals can be better understood through the measurement and analysis of its RF radiation pattern and signal strength attenuation with distance. The following measurements were done in a lab environment, which lacked the precision of the anechoic chamber environment, but it gave a real-life qualitative analysis of the EBFL’s RF radiation properties. A. The EBFL Radiation Pattern The TRA was fixed at a distance of 1 meter from the EBFL set. The EBFL set was rotated horizontally around its axes through 360 at increments of 22.5 and the reflected 1st sideband signal level was recorded and plotted, see Fig. 9. Two radiation field patterns were determined, one with all three fluorescent lamp fixtures on and the other for one fixture on. The patterns show that the backscatter signal response of the EBFL resembles that of an RFID tag, see Fig. 10, with significant backscaterred 1st sideband power refelected back to the reader antenna. Depending on the orientation of the EBFL with respect to the reader antenna the backscattered 1st sideband power varies between 050 dBm to 0100 dBm, which is within the received reverse link tag-reader signal level. Using one EBFL fixture a similar pattern is measured with slight reduction in power and narrower radiation bandwidth. The experiment was repeated with the TRA located at a distance of 2m. The 1st sideband backscattered signal radiation patterns, at 1 m and 2 m, are shown in Fig. 11. Next, with the EBFL fixture aligned with the maximum directional TRA gain, the 1st sideband backscattered signal attenuation vs. distance is plotted (Fig. 12). From Figs. 11 and 12 it can be seen that significant backscattered signal level is radiated over a very wide angular orientation, 315 and over a long range, between the EBFL and

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Fig. 12. EBFL 1st sideband backscattered signal’s power is attenuated by approximately 9 dB/meter.

Fig. 9. 1st sideband backscattered radiation patten using one and three EBFL fixtures.

Fig. 10. Alien Technology ALN-9540 tag radiation pattern provided by the manufacturer [6].

Fig. 11. 1st sideband backscattered radiation pattern of EBFL, with TRA at 1 m and 2 m distance.

VII. SUSCEPTIBILITY OF AN OPERATING UHF RFID SYSTEM TO EBFL’S BACKSCATTER SIGNALS From the preceding analysis, since the RFID system is designed to detect backscattered tag signals as low as the 0100 dBm range [10], the effects of the EBFLs on the system performance became a very strong possibility. The significance of these effects required further analyses using an operating RFID system. A testing environment was setup by placing the “3 fixture” EBFL set at 0.5, 1, 2, and 3 meters from the reader and at about 45 off the maximum directional gain position of the reader antenna. The ALN 9540 and ALN-9529 tags used are of the latest generation EPC-Class 1 Gen 2. In real world the reader, tags, and EBFLs are oriented and located at different distances from each other. The aim was to verify our findings and show that it is possible with a certain reader, tag, and EBFLs configurations the reliability of the RFID system can be compromised. The performance of the ALIEN 9900 RFID system was analyzed using the ALN-9540 squiggle tag, which is one of the most versatile tags, characterized by high speed read capability at very long range. The following reader-tag-EBFL configurations were implemented and results are shown in Figs. 13 and 14. — Tag at 0.5, 1 m, 2 m, and 3 m from the reader and aligned with the maximum directional gain of the reader antenna; — “3 fixture” EBFL located 2 m away from the reader and aligned at 45 to the reader antenna maximum directional gain; — With the reader power level set at 1 watt, the reader reliability was analyzed. The system average number of read/sec was taken as an indicator of the performance criteria; — Performance analysis was repeated with reader power set at 0.5 Watts and 0.1 Watts. The experiment was repeated using ALN-9529, a widely used but less sensitive tag, and the results are shown in Fig. 15. A realistic real world experiment was performed with RFID system set in a laboratory environment with large number EBFL lightings. The reader antenna was placed on a bench below the EBFL fixtures located in the lab ceiling at a distance of 1.5 meters. Two different tags were used, the ALN-9540, and the ALN-9554 located at distance of 0.7, 1.5 and 2 meters from and pointing directly to the reader antenna. Fig. 16 clearly indicates the performance degradation of the RFID system when the EBFLs are switched on. VIII. SUMMARY OF RESULTS

the TRA. The maximum backscattered signal strength is comparable to that of the tag-reader signal level at distances exceeding 5 meters.

Figs. 13–15 clearly indicate the effect of the EBFL backscattering on the RFID system performance. For two different tags, the ALN-9540 and 9529, with the EBFL at 2 m from the reader antenna the backscatter

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Fig. 13. RFID system performance with the EBFL set switched off using the ALN-9540 tag located at different distances and aligned with the maximum reader antenna directional gain. With the EBFL switched on at a distance of 2 m the backscattered EBFL signal introduced considerable degradation in system performance, especially at 1 and 0.5 watt reader transmit power. At a low power of 0.1 watt, the EBFL backscatter had no effect.

Fig. 16. RFID system performance in laboratory environment. The RFID system was set below a row of 4 EBFLs with reader antenna.

at tag distances of over 1 meter. Using ALN-9529, a less sensitive tag, the system was much more susceptible to EBFL backscatter effects. The in lab real world simulation, Fig. 16, confirmed that the EBFL can interfere and degrade the RFID system reliability. The experimental results indicate without any doubt that the EBFL backscattering phenomenon is a source of strong interference that cannot be ignored and must be taken into consideration when developing an RFID system operating in an environment abundant with EBFLs. The orientation and location of the reader antennas with respect to the EBFL lighting within the environment need to be carefully considered to avoid the backscatter effects of the EBFLs, which particularly important when the reader is operating at its high power level settings.

REFERENCES Fig. 14. RFID system using ALN-9540, with the EBFL located at a distance of 1 meter from the reader antenna causing higher degradation in performance especially at high reader transmit power of 0.5 and 1 w. Some degradation is noticeable at 0.1 w reader power level.

Fig. 15. The RFID system performance using the ALN-9529. With the EBFL switched on and at a distance of 2 meters, communication between the tag and the reader was completely disabled when the tag and the reader were set at more than 1 meter apart. Signs of degradation in performance are noticeable at all power levels when the tag is within 0.5 meter.

affect is more prominent at reader powers of 1 watt and 0.5 watts. The higher the reader power the higher the power of the EBFL backscattered signal thereby causing a higher degradation in system performance. Using ALN-9540, with the EBFL at 1 m from the reader and the reader at 1 W, the RFID system was rendered completely inoperable

[1] D. M. Dobkin and T. Wandinger, “A radio-oriented introduction to radio frequency identification,” High Frequency Electron., pp. 46–54, Jun. 2005. [2] W. J. Vogel, H. Ling, and G. W. Torrence, “Fluorescent light interaction with personal communication signals,” IEEE Trans. Commun., vol. 43, no. 234, pp. 194–197, Feb./Mar./Apr. 1995. [3] H. Suzuki, M. Hedley, G. Daniels, and C. Jacka, “Spatial distribution of temporal variation caused by active fluorescent lights in office environment,” in Proc. URSI Commission F Triennium Open Symp., Cairns, Australia, Jun. 2004, pp. 181–186. [4] P. Melancon and J. Lebel, “Effects of fluorescent lights on signal fading characteristics for indoor radio channels,” IEE Electron. Lett., vol. 28, Aug. 1992. [5] G. Ibrahim and T. Al-Mahdawi, “Jeremy sensening; Dynamic reflection of RF signals from fluorescent lights: Their spectral analysis and effects on backscattered RFID tag signals,” presented at the SARNOFF Symp., Apr. 2007. [6] “Alien Technology Corporation ALN-9540 and 9529 Product Overview,” Sep. 2007 [Online]. Available: www.alientechnology.com [7] “Electronic Ballasts Using the Cost-Saving IR215X Drivers,” Application Note AN-995A, International Rectifier Control Integrated Circuit Designers’ Manual. [8] M. I. Skolnik, Radar Handbook, 3rd ed. Englewood Cliffs, NJ: McGraw-Hill, 2008, ch. 14, Radar Cross Section. [9] “EPC Radio Frequency Identity Protocol Class-1 Generation 2 UHF RFID Protocols for Communication at 860–960 MHz,” 2005, version 1.1, Annex G, EPCglobal Inc. [10] K. Finkenzeller, RFID Handbook, 2nd ed. New York: Wiley, 2003, pp. 145–148.

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 58, NO. 7, JULY 2010

Planar Monopole With a Coupling Feed and an Inductive Shorting Strip for LTE/GSM/UMTS Operation in the Mobile Phone Cheng-Tse Lee and Kin-Lu Wong

Abstract—A planar monopole having a small size yet providing two wide bands for covering the eight-band LTE/GSM/UMTS operation in the mobile phone is presented. The small-size yet wideband operation is achieved by exciting the antenna’s wide radiating plate using a coupling feed and short-circuiting it to the system ground plane of the mobile phone through a long meandered strip as an inductive shorting strip. The coupling feed leads to a wide operating band to cover the frequency range of 1710–2690 MHz for the GSM1800/1900/UMTS/LTE2300/2500 operation. The inductive shorting strip results in the generation of a wide operating band to cover the frequency range of 698–960 MHz for the LTE700/GSM850/900 operation. The planar monopole can be directly printed on the no-ground portion of the system circuit board of the mobile phone and is promising to be integrated with a practical loudspeaker. The antenna’s radiating plate can also be folded into a thin structure (3 mm only) to occupy a small volume of 3 6 40 mm (0.72 cm ) for the eight-band LTE/GSM/UMTS operation; in this case, including the 8-mm feed gap, the antenna shows a low profile of 14 mm to the ground plane of the mobile phone. The proposed antenna, including its planar and folded structures, are suitable for slim mobile phone applications. Index Terms—Coupling feed, handset antennas, inductive shorting strip, mobile antennas, planar monopole.

I. INTRODUCTION Planar monopoles with a wide radiating plate are simple in configuration and have been shown to generate wideband operation to cover the multiband WWAN (wireless wide area network) communications [1], [2] for mobile phone applications. However, in order to cover the GSM operation in the 900-MHz band, the wide radiating plate in the planar monopole usually occupies a large volume and is required to be in the folded structure to achieve a reduced size for internal mobile phone antenna applications. In the reported designs, this kind of planar monopole for covering the 900-MHz band operation requires the use of a folded radiating plate of size 10 2 10 2 70 mm3 (7.0 cm3 ) [1] or 10 2 15 2 35 mm3 (5.25 cm3 ) [2]. In addition to the large volume occupied, the thickness of the folded radiating plate is as large as 10 mm, which is not promising for applications in the modern slim mobile phone which generally requires its internal antenna to have a thin profile of 4 mm or less [3]–[8]. When a planar radiating plate is used, it is reported that a planar monopole with a size of 30 2 50 mm2 (1500 mm2 ) can have a wide operating band of 870–2450 MHz for the mobile phone [9]. However, the large size of 1500 mm2 will greatly limit its applications in the internal mobile phone antennas. In this communication, we present a novel planar monopole design having a small size yet capable of generating two wide operating bands to cover the eight-band LTE/GSM/UMTS operation in the mobile phone, which includes the LTE700 (698–787 MHz), GSM850 Manuscript received September 17, 2009; revised December 04, 2009; accepted December 16, 2009. Date of publication April 26, 2010; date of current version July 08, 2010. The authors are with the Department of Electrical Engineering, National Sun Yat-sen University, Kaohsiung 80424, Taiwan (e-mail: [email protected]. edu.tw). Color versions of one or more of the figures in this communication are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2010.2048878

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(824–894 MHz), GSM900 (880–960 MHz), GSM1800 (1710–1880 MHz), GSM1900 (1850–1990 MHz), UMTS (1920–2170 MHz), LTE2300 (2305–2400 MHz) and LTE2500 (2500–2690 MHz) bands. Notice that the LTE (long term evolution) operation [10] can provide better mobile broadband and multimedia services than the existing GSM and UMTS mobile networks [11] and is expected to become attractive for the mobile users. The lower band of the proposed planar monopole can have a large bandwidth to cover the frequency range of 698–960 MHz for the LTE700/GSM850/900 operation. The upper band can have an even larger bandwidth (>1 GHz) to cover the frequency range of 1710–2690 MHz for the GSM1800/1900/UMTS/LTE2300/2500 operation. The proposed planar monopole is suitable to be directly printed on the no-ground portion of the system circuit board of the mobile phone, making it easy to fabricate at low cost. The size of the wide radiating plate of the planar monopole is 12 2 40 mm2 or 480 mm2 only, which is much smaller than those in [1], [2] (both at least 1400 mm2 ). When including the 8-mm feed gap, the no-ground portion required in the proposed design is 20 2 40 mm2 (800 mm2 ), which is much less than that (1500 mm2 ) in [9]. The antenna can also be integrated with a nearby loudspeaker in a compact configuration. To achieve small size yet wideband operation, the proposed planar monopole is excited using a coupling feed and short-circuited to the system ground plane of the mobile phone through a long meandered strip as an inductive shorting strip. Detailed effects of the coupling feed and the inductive shorting strip are discussed in the communication. Further, the radiating plate of the proposed antenna can be folded into a thin structure (3 mm only) to occupy a small volume of 3 2 6 2 40 mm3 (0.72 cm3 only) for the eight-band LTE/GSM/UMTS operation. The 3 mm in thickness is promising for applications in the modern slim mobile phone. In this case, by including the 8-mm feed gap between the radiating plate and the system ground plane of the mobile phone, the antenna also shows a low profile of 14 mm to the top edge of the ground plane. Details of the proposed antenna are presented. II. PROPOSED ANTENNA Fig. 1(a) shows the geometry of the proposed planar monopole with a coupling feed and an inductive shorting strip for the eight-band LTE/ GSM/UMTS operation in the mobile phone. Dimensions of the metal pattern of the antenna are given in Fig. 1(b). A 0.8-mm thick FR4 substrate is used as the system circuit board of the mobile phone. The 1-mm thick plastic casing (relative permittivity 3.0 and conductivity 0.02 S/m) enclosing the circuit board as the casing of a slim mobile phone has a thin profile of 9.8 mm. On the circuit board there is a printed system ground plane of size 40 2 100 mm2 and a no-ground portion of size 40 2 20 mm2 . The planar monopole is printed on the no-ground portion and comprises a wide radiating plate of size 12 2 40 mm2 flushed to the top edge of the circuit board. Between the radiating plate and the ground plane, there is a feed gap of length 8 mm. A simple coupling strip of length (t) 12.5 mm, which is connected to the 50- microstrip feedline printed on the circuit board through a 8-mm long metal strip across the feed gap, capacitively excites the radiating plate. Across the feed gap, there is also a long meandered metal strip to short circuit the radiating plate to the ground plane. The meandered metal strip has a length of about 31 mm and a narrow width of 0.3 mm and behaves like a simple shorting strip loaded with a chip inductor (see Ref3 in the inset of Fig. 11; detailed discussion will be given in Section IV). The meandered metal strip is hence considered as an inductive shorting strip here.

0018-926X/$26.00 © 2010 IEEE

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Fig. 2. Measured and simulated return loss of the proposed antenna.

are large effects of the inductive shorting strip on the antenna’s lower band, the impedance matching for frequencies over the desired upper band of 1710–2690 MHz is relatively slightly affected. This makes it easy to fine-tune the desired lower and upper bands for the antenna to cover the eight-band LTE/GSM/UMTS operation. The proposed antenna can also be in other possible embodiments for practical applications. The first one is to use a chip-inductor-loaded shorting strip replacing the inductive shorting strip and is shown in Ref3 in the inset of Fig. 11. The second one is to have its wide radiating plate folded into a thin structure (3 mm in thickness) such that the folded radiating plate occupies a small volume of 3 2 6 2 40 mm3 or 0.72 cm3 only (see Ref4 in the inset of Fig. 12). The third one is to integrate with a nearby loudspeaker [19]–[21] such that a compact integration of the proposed antenna in the mobile phone is achieved. For these possible embodiments, the eight-band LTE/GSM/UMTS operation can also be obtained. Detailed results will be discussed in Section IV. Fig. 1. (a) Geometry of the proposed planar monopole with a coupling feed and an inductive shorting strip for the eight-band LTE/GSM/UMTS operation in the mobile phone. (b) Dimensions of the metal pattern of the antenna.

The coupling feed applied in this study effectively compensates for the large inductive reactance over a wide frequency range, especially over the desired upper band of 1710–2690 MHz. This leads to a very wide operating band obtained for the antenna’s upper band to cover the GSM1800/1900/UMTS/LTE2300/LTE2500 operation. This coupling-feed effect is different from that applied for the internal WWAN antennas for mobile phone or laptop computer applications [12]–[18], in which the coupling feed mainly leads to enhanced bandwidth for the antenna’s lower band at about 900 MHz [12]–[16] or causes the excitation of the one-eighth-wavelength resonant mode as the antenna’s lowest mode for the 900-MHz band operation [17], [18]. The different coupling-feed effect obtained here is related to the use of the wide radiating plate in the proposed design, which is different from the long, narrow radiating strips used in [12]–[16]. The coupling-feed effect in the proposed design is also different from the use of a long (26 mm) coupling T-strip protruded from the ground plane, which is mainly for decreasing the lowest resonant frequency of the antenna [9]. By incorporating the use of the inductive shorting strip, a wide operating band to cover the frequency range of 698–960 MHz for the LTE700/GSM850/900 operation can be generated. Detailed effects of the inductive shorting strip on the generation of the antenna’s wide lower band are discussed with the aid of Fig. 3 in Section III. Also note that without the use of the wide radiating plate, that is, when the width w of the radiating plate is decreased (the preferred width w is 12 mm in this design), good impedance matching over the desired wide frequency range of 698–960 MHz cannot be achieved (see the results shown in Fig. 5; detailed discussion will be given in Section III). Although there

III. RESULTS AND DISCUSSION Fig. 2 shows the measured and simulated return loss of the proposed antenna. The measured data agree with the simulated results obtained using Ansoft simulation software HFSS version 11.2 [22]. With the 3:1 VSWR bandwidth definition, which is widely used as the design specification of the internal mobile phone antenna for WWAN communications [3]–[5], [9], two wide operating bands are obtained. The lower band shows a wide bandwidth of 490 MHz (690–1180 MHz), while the upper band has an even wider bandwidth of 1220 MHz (1670–2890 MHz). The wide lower and upper bands cover the LTE700/ GSM850/900 and GSM1800/1900/UMTS/LTE2300/2500 operation, respectively. Fig. 3 shows the comparison of the simulated return loss for the proposed antenna, the case with a direct feed and a simple shorting strip (Ref1) and the case with a coupling feed and a simple shorting strip (Ref2). The corresponding dimensions for the three studied antennas in the figure are the same. Ref2 applies a coupling feed to replace the conventional direct feed used in Ref1. From the results of Ref1 and Ref2, a much wider bandwidth for Ref2 than for Ref1 is seen. The obtained bandwidth for Ref2 reaches about 1.7 GHz, from about 1.1 to 2.8 GHz; while the bandwidth for Ref1 is less than 300 MHz. From the comparison of Ref2 and proposed antenna in Fig. 3, a wide lower band centered at about 900 MHz is generated, which is owing to the use of the inductive shorting strip replacing the simple shorting strip in Ref2. There are two resonant modes, the first one at about 700 and the second one at about 1000 MHz, contributed to the obtained wide lower band. The first one is owing to the presence of the inductive shorting strip, while the second one is related to the resonant mode at about 1.5 GHz for Ref2. This is mainly because the inductive shorting strip causes the lengthening of the effective resonant path of the antenna, which not only generates a new additional resonant mode but also shifts

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Fig. 5. Simulated return loss as a function of the width w of the radiating plate. Other dimensions are the same as in Fig. 1.

Fig. 3. Simulated return loss for the proposed antenna, the corresponding antenna with a direct feed and a simple shorting strip (Ref1) and the corresponding antenna with a coupling feed and a simple shorting strip (Ref2).

Fig. 6. Simulated surface current distributions at 750, 1000, 2000, and 2650 MHz.

Fig. 4. Simulated return loss as a function of the length t of the coupling strip. Other dimensions are the same as in Fig. 1.

the 1.5 GHz resonant mode of Ref2 to lower frequencies. It is also seen that the input impedance for higher frequencies larger than about 1.7 GHz is very slightly varied for Ref2 and proposed antenna. A wide upper band covering the desired frequency range of 1710–2690 MHz is thus maintained. Effects of varying the length t of the coupling strip are also studied. The simulated return loss for the length t varied from 9.5 to 15.5 mm is shown in Fig. 4. Small effects on the antenna’s lower band are seen. The bandwidth of the upper band, however, can be controlled by the length t. By increasing the length t, the upper band is shifted to lower frequencies. That is, by selecting a proper length t (12.5 mm in this study), the upper band can be adjusted to cover the desired frequency range of 1710–2690 MHz. The simulated return loss for the width w of the radiating plate varied from 2 to 12 mm is presented in Fig. 5. Large effects of the width w on the antenna’s lower band are seen. When the width w decreases, the obtained bandwidth of the antenna’s lower band is quickly decreased and becomes unable to cover the desired frequency range of 698–960 MHz. Some effects on the upper band are also seen, which are, however, small compared to those on the lower band. The simulated surface current distributions at typical frequencies are shown in Fig. 6. At 750 and 1000 MHz, relatively strong excited surface current distributions are seen in the system ground plane, compared to those at higher frequencies. An additional current null is also seen at

Fig. 7. Simulated return loss as a function of the length of the system ground plane. Other dimensions are the same as in Fig. 1.

about the center of the system ground plane; this is owing to the shorter wavelength at higher frequencies. On the other hand, relatively strong surface current distributions in the radiating plate are seen at 2000 and 2650 MHz than at lower frequencies. These results indicate that the system ground plane is an important radiating part, especially at lower frequencies. Effects of the length of the system ground plane on the antenna performances are studied in Fig. 7. Results of the simulated return loss for the length L varied from 80 to 100 mm are shown. Large effects on the obtained 3:1 VSWR bandwidth for the lower band are seen. When the length L is decreased, the impedance matching for frequencies between the two resonant modes in the lower band is degraded. For the upper band, however, the effects are relatively small and the obtained bandwidth is generally about the same.

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Fig. 10. SAR simulation model and the simulated SAR values for 1-g and 10-g head tissues for the proposed antenna placed at the bottom of the mobile phone. The return loss indicates the impedance matching level at the testing frequency. Fig. 8. Measured radiation patterns at 830 and 2200 MHz for the proposed antenna.

Fig. 11. Comparison of the simulated return loss for the proposed antenna and the corresponding antenna with a coupling feed and a chip-inductor-loaded shorting strip (Ref3).

Fig. 9. Measured antenna gain and simulated radiation efficiency of the proposed antenna. (a) The lower band. (b) The upper band.

Fig. 8 plots the measured radiation patterns at 830 and 2200 MHz (about central frequencies of the desired lower and upper bands). At 830 MHz, dipole-like radiation patterns with omnidirectional radiation in the azimuthal plane (x-y plane) are observed. While at 2200 MHz, more variations in the patterns are seen. Also note that measured radiation patterns at other frequencies in the lower and upper bands showed similar results as those plotted in Fig. 8. The obtained radiation patterns also show no special distinctions to those of the printed internal WWAN mobile phone antennas [16]–[18]. Fig. 9

shows the measured antenna gain and simulated radiation efficiency. Over the 698–960 MHz band shown in Fig. 9(a), the antenna gain is about 00:8–0:9 dBi radiation and the radiation efficiency ranges from about 52% to 78%. Over the 1710–2690 MHz band in Fig. 9(b), the antenna gain is about 1.9–3.8 dBi, and the radiation efficiency ranges from about 68% to 92%. The SAR (specific absorption rate) values of the proposed antenna are also tested using the simulation software SEMCAD [23]. Since it is known that this kind of printed antenna with no ground plane on back is suitable to be placed at the bottom of the mobile phone to obtain decreased SAR values [24], [25], only the proposed antenna at the bottom of the mobile phone as shown in the simulation model in Fig. 10 is tested. The obtained SAR values are given in the figure, which are all below the SAR limit of 1.6 W/kg for the 1.0-g head tissue and 2.0 W/kg for the 10-g head tissue [26]. The results suggest that the proposed antenna is promising for practical mobile phone applications. IV. OTHER EMBODIMENTS OF THE PROPOSED ANTENNA The inductive shorting strip in the proposed antenna can be replaced by a simple shorting strip loaded with a chip inductor. Fig. 11 shows the comparison of the simulated return loss for the proposed antenna and the corresponding antenna with a coupling feed and a chip-inductor-loaded shorting strip (Ref3). The chip inductor has an inductance of 8 nH (selected from the aid of Ansoft HFSS simulation) and is not necessarily to be placed in the middle of the shorting

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Fig. 12. Comparison of the simulated return loss for the proposed antenna and the case with a folded radiating plate (Ref4). Both cases have the same groundplane dimensions.

strip. There are almost no differences in the simulated return loss for the proposed antenna and Ref3. This also confirms that the long meandered shorting metal strip can be treated as an inductive shorting strip. The antenna structure of Ref4 in the inset of Fig. 12 shows that the wide radiating plate of the proposed antenna can be in the folded structure with a thin thickness of 3 mm and a small volume of 3 2 6 2 40 mm3 (0.72 cm3 ). Notice that the total length of the folded radiating plate of Ref4 is 15 mm, longer than that (12 mm) of the printed structure shown in Fig. 1. In this case, as shown in Fig. 12, the obtained return loss of Ref4 is about the same as that of the proposed antenna. Ref4 also shows a low profile of 14 mm to the system ground plane of the mobile phone, which is smaller compared to that (20 mm) of the proposed antenna in Fig. 1. The proposed antenna can also be in compact integration with a practical loudspeaker [19]–[21]. The measured return loss for the cases with and without the loudspeaker is about the same (measured data not shown for brevity), indicating that such a compact integration is promising for practical applications. Also note that, by using the loudspeaker simulation model in [21], [27], the simulated results indicate that the radiation efficiency will be decreased by about 5% in the lower band and about 10% in the upper band, which may be owing to some lossy materials contained in the loudspeaker. V. CONCLUSION A planar monopole with a wide radiating plate excited by a coupling feed and short-circuited by an inductive metal strip has been shown to achieve small size yet wideband operation for applications in the mobile phone to cover the eight-band LTE/GSM/UMTS operation. The proposed antenna can be in an all-printing structure or folded thin structure; both structures can provide two wide operating bands to cover the desired frequency ranges of 698–960 and 1710–2690 MHz. The antenna can also be in compact integration with a practical loudspeaker. The obtained results indicate that the proposed antenna is suitable to be applied in the modern slim mobile phone for the eight-band LTE/GSM/UMTS operation.

REFERENCES [1] C. C. Lin, H. C. Tung, H. T. Chen, and K. L. Wong, “A folded metalplate monopole antenna for multi-band operation of a PDA phone,” Microw. Opt. Technol. Lett., vol. 39, pp. 135–138, Oct. 20, 2003. [2] S. Y. Lin, “Multiband folded planar monopole antenna for mobile handset,” IEEE Trans. Antennas Propag., vol. 52, pp. 1790–1794, Jul. 2004. [3] R. A. Bhatti and S. O. Park, “Octa-band internal monopole antenna for mobile phone applications,” Electron. Lett., vol. 44, pp. 1447–1448, Dec. 4, 2008.

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[4] R. A. Bhatti, Y. T. Im, J. H. Choi, T. D. Manh, and S. O. Park, “Ultrathin planar inveretd-F antenna for multistandard handsets,” Microw. Opt. Technol. Lett., vol. 50, pp. 2894–2897, Nov. 2008. [5] J. Villanen, C. Icheln, and P. Vainikainen, “A coupling element-based quad-band antenna structure for mobile handsets,” Microw. Opt. Technol. Lett., vol. 49, pp. 1277–1282, Jun. 2007. [6] K. L. Wong, Y. C. Lin, and B. Chen, “Internal patch antenna with a thin air-layer substrate for GSM/DCS operation in a PDA phone,” IEEE Trans. Antennas Propag., vol. 55, pp. 1165–1172, Apr. 2007. [7] K. L. Wong, Y. C. Lin, and T. C. Tseng, “Thin internal GSM/DCS patch antenna for a portable mobile terminal,” IEEE Trans. Antennas Propag., vol. 54, pp. 238–242, Jan. 2006. [8] M. F. Abedin and M. Ali, “Modifying the ground plane and its effect on planar inverted-F antennas (PIFAs) for mobile phone handsets,” IEEE Antennas Wireless Propag. Lett., vol. 2, pp. 226–229, 2003. [9] Z. Du, K. Gong, and J. S. Fu, “A novel compact wide-band planar antenna for mobile handsets,” IEEE Trans. Antennas Propag., vol. 54, pp. 613–619, Feb. 2006. [10] , S. Sesia, I. Toufik, and M. Baker, Eds., LTE, The UMTS Long Term Evolution: From Theory to Practice. New York: Wiley, 2009. [11] K. L. Wong, Planar Antennas for Wireless Communications. New York: Wiley, 2003. [12] K. L. Wong and C. H. Huang, “Bandwidth-enhanced internal PIFA with a coupling feed for quad-band operation in the mobile phone,” Microw. Opt. Technol. Lett., vol. 50, pp. 683–687, Mar. 2008. [13] C. H. Chang and K. L. Wong, “Internal coupled-fed shorted monopole antenna for GSM850/900/1800/1900/UMTS operation in the laptop computer,” IEEE Trans. Antennas Propag., vol. 56, pp. 3600–3604, Dec. 2008. [14] K. L. Wong and C. H. Huang, “Printed PIFA with a coplanar coupling feed for penta-band operation in the mobile phone,” Microw. Opt. Technol. Lett., vol. 50, pp. 3181–3186, Dec. 2008. [15] K. L. Wong and S. J. Liao, “Uniplanar coupled-fed printed PIFA for WWAN operation in the laptop computer,” Microw. Opt. Technol. Lett., vol. 51, pp. 549–554, Feb. 2009. [16] C. T. Lee and K. L. Wong, “Uniplanar coupled-fed printed PIFA for WWAN/WLAN operation in the mobile phone,” Microw. Opt. Technol. Lett., vol. 51, pp. 1250–1257, May 2009. [17] K. L. Wong and C. H. Huang, “Compact multiband PIFA with a coupling feed for internal mobile phone antenna,” Microw. Opt. Technol. Lett., vol. 50, pp. 2487–2491, Oct. 2008. [18] C. H. Chang and K. L. Wong, “Printed =8-PIFA for penta-band WWAN operation in the mobile phone,” IEEE Trans. Antennas Propagat., vol. 57, pp. 1373–1381, May 2009. [19] C. H. Wu and K. L. Wong, “Internal hybrid loop/monopole slot antenna for quad-band operation in the mobile phone,” Microw. Opt. Technol. Lett., vol. 50, pp. 795–801, Mar. 2008. [20] Y. W. Chi and K. L. Wong, “Half-wavelength loop strip fed by a printed monopole for penta-band mobile phone antenna,” Microw. Opt. Technol. Lett., vol. 50, pp. 2549–2554, Oct. 2008. [21] M. R. Hsu and K. L. Wong, “WWAN ceramic chip antenna for mobile phone application,” Microw. Opt. Technol. Lett., vol. 51, pp. 103–110, Jan. 2009. [22] Ansoft Corporation HFSS [Online]. Available: http://www.ansoft.com/ products/hf/hfss/ [23] SEMCAD, Schmid & Partner Engineering AG (SPEAG) [Online]. Available: http://www.semcad.com [24] Y. W. Chi and K. L. Wong, “Quarter-wavelength printed loop antenna with an internal printed matching circuit for GSM/DCS/PCS/UMTS operation in the mobile phone,” IEEE Trans. Antennas Propa., vol. 57, pp. 2541–2547, Sept. 2009. [25] Y. W. Chi and K. L. Wong, “Compact multiband folded loop chip antenna for small-size mobile phone,” IEEE Trans. Antennas Propag., vol. 56, pp. 3797–3803, Dec. 2008. [26] “Safety levels with respect to human exposure to radio-frequency electromagnetic field, 3 kHz to 300 GHz,” Apr. 1999, American National Standards Institute (ANSI), ANSI/IEEE standard C95.1. [27] C. H. Wu and K. L. Wong, “Internal shorted planar monopole antenna embedded with a resonant spiral slot for penta-band mobile phone application,” Microw. Opt. Technol. Lett., vol. 50, pp. 529–536, Feb. 2008.

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Preconditioning Matrix Interpolation Technique for Fast Analysis of Scattering Over Broad Frequency Band Z. H. Fan, Z. W. Liu, D. Z. Ding, and R. S. Chen

Abstract—A hybrid interpolation method is proposed for the fast analysis of the radar cross-section (RCS) over a broad frequency band by use of the matrix interpolation method. In order to efficiently compute electromagnetic scattering, the general minimal residual (GMRES) iterative solver is applied to compute the coefficients of Rao-Wilton-Glisson (RWG) basis functions and the sparse approximate inversion (SAI) preconditioning technique is used to accelerate the iterative solver. Moreover, both the near field impedance and SAI preconditioning matrices are interpolated at intermediate frequencies over a relatively large frequency band with rational function interpolation technique. Therefore, a lot of time can be saved for the calculation of both the near field impedance and preconditioning matrices. Numerical results demonstrate that this hybrid method is efficient for wideband RCS calculation with high accuracy. Index Terms—Electromagnetic scattering, fast frequency sweep, impedance matrix interpolation, preconditioning matrix interpolation, sparse approximate inversion (SAI).

I. INTRODUCTION Electromagnetic wave scattering problems address the physical issue of detecting the diffraction pattern of the electromagnetic radiation scattered from a large and complex body when illuminated by an incident incoming wave. A good understanding of these phenomena is crucial to radar cross section (RCS) calculation, antenna design, electromagnetic compatibility, and so on. All these simulations are very demanding in terms of computer resources, and require efficient numerical methods to compute an approximate solution of Maxwell’s equations. Using the equivalence principle, Maxwell’s equations can be recast in the form of integral equations that relate the electric and magnetic fields to the equivalent electric and magnetic currents on the surface of the object. Amongst integral formulations, the electric field integral equation (EFIE) is widely used for electromagnetic wave scattering problems as it can handle the most general geometries. The matrix associated with the resulting linear systems is large, dense, complex and non-Hermitian [1]. It is basically impractical to solve EFIE matrix equations using direct methods because they have a memory requirement of O(N 2 ), where N refers to the number of unknowns. This difficulty can be circumvented by use of iterative methods, and the required matrix-vector product operation can be efficiently evaluated by multilevel fast multipole algorithm (MLFMA) [2], [3]. The use of MLFMA reduces the memory requirement to O(N log N ) and the computational complexity of per-iteration to O(N log N ). It is well-known that EFIE provides a first-kind integral equation, which is ill-conditioned and gives rise to linear systems that are challenging to solve by iterative methods. Although using CFIE can Manuscript received February 16, 2009; manuscript revised July 13, 2009; accepted September 05, 2009. Date of publication March 29, 2010; date of current version July 08, 2010. This work was supported in part by the Major State Basic Research Development Program of China (973 Program: 2009CB320201); in part by the Natural Science Foundation under Grants 60701003, 60701005, 60871013, and in part by the State Key Laboratory of Millimeter Waves under Grant K200810. The authors are with the Department of Communication Engineering, Nanjing University of Science and Technology, Nanjing, 210094, China (e-mail: [email protected]). Color versions of one or more of the figures in this communication are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2010.2046841

alleviate this difficulty [4], it is not suitable for object with opened structure. Therefore, it is natural to use preconditioning techniques to improve the condition number of the system and accelerate the convergence rate of iterative solvers. Sparse approximate inverse (SAI) methods are generally less prone to instabilities on indefinite systems [5]. It has been shown in [6] that this technique outperforms more classical approaches like incomplete factorizations. To obtain the RCS over a band of frequencies using MoM, one has to repeat the calculations at each frequency over the band of interest. This can be computationally prohibitive despite the increased power of the present generation of computers. In [10], the model-based parameter estimation (MBPE) is used to obtain the wide-band data from frequency and frequency-derivative data. In [11]–[13], a similar technique called asymptotic waveform evaluation (AWE) technique has been applied to frequency-domain electromagnetic analysis. Both MBPE and AWE interpolate the coefficients of RWG which can avoid repeated construction and solution. Other current-based methods, such as Cauchy-method and spline-method, are applied in fast frequencyand angular- sweep as well [14], [15]. However, coefficients of RWG are not a linear function of frequency so that great many samples are required for frequency swap. There are some attempts to obtain the wide-band data by interpolating the impedance matrix [7]–[9]. This method saves much time for constructing impedance matrix but can do nothing for iterative solution repeatedly. SAI preconditioning method can accelerate iterative solution but increases large time for constructing SAI matrices. Thus, new method is required to circumvent this difficulty. Due to SAI matrix is an approximate inverse of impedance matrix, it is still a continuous function of frequency. Moreover, inaccurate preconditioning matrix can not impact the precise of linear system. Consequently, using interpolation technique is a good way to accelerate the construction of SAI matrices. In this communication, the combination of the impedance matrix interpolation and the preconditioning matrix interpolation is proposed to efficient computation of RCS over broad frequency band. The numerical simulations demonstrate that the hybrid interpolation technique can reduce the computation time significantly. The remainder of this communication is organized as follows. Section II demonstrates the basic theory of SAI preconditioning matrix interpolation method. Numerical experiments of three geometries are presented to demonstrate the efficiency of this proposed method in Section III. Conclusions are provided in Section IV. II. SAI PRECONDITIONING MATRIX INTERPOLATION METHOD The methodology on how to efficient calculation of scattering over a broad-band is discussed in this section. First of all, the impedance matrix interpolation method is introduced. Then SAI preconditioning matrix interpolation method is proposed. Finally, a hybrid method combines both of the two interpolation methods is discussed, which make a good way to the efficient analysis of wide-band scattering. The EFIE formulation of electromagnetic wave scattering problems using planar Rao-Wilton-Glisson (RWG) basis functions for surface modeling is presented in [1], [16]. The resulting linear systems from EFIE formulation after Galerkin’s testing are briefly outlined as follows:

ZJ = V (1) where Z is the impedance matrix, J is the complex coefficient vector of RWG basis and V is the right hand side generated by incident wave. Using the FMM, the matrix-vector product ZJ can be written as ZJ = Z nearJ + Z farJ (2)

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where Z near is the near field impedance matrix and Z far is the far field part of Z . When FMM is implemented in multilevel, the total cost at each iteration step can be reduced further to O(N log N ). Theoretically, the combination of MoM and MLFMA is able to accurately analyze the scattering of any geometry. However, in order to obtain the RCS over a band of frequencies, one has to repeat the calculations at each frequency over the band of interest. This process can be computationally prohibitive for computation of wideband RCS of electrically large object. Impedance matrix interpolation method [7]–[9] can alleviate this difficulty by interpolating the impedance matrix Z in (1) instead of construction repeatedly. Only a few samples of Z at several frequency points are required to be computed by MoM, since the impedance matrix elements are relative smooth over certain frequency range. It is obviously that this impedance matrix interpolation method can easily applied in MLFMA to interpolating the near field impedance matrix Z near . Although the impedance matrix interpolation method can avoid repeatedly constructing impedance matrix, iterative solution of matrix equations is still required at each frequency point. Thus, computational efficiency has been challenged by ill-conditioned linear equations. Preconditioning technique, such as sparse approximate inversion (SAI), can greatly improve the condition number of system to accelerate the convergence of iterative solver [6]. The basic formulation of preconditioning technique can be described by

MZJ = MV

(3)

where M is the SAI preconditioning matrix in this communication. However, it is still time-consuming to construct SAI preconditioning matrix repeatedly at each frequency point. According to the theory of SAI, preconditioning matrix is a sparse matrix and explicitly computed and stored, which makes interpolation method easily to be implemented. Accordingly, matrix interpolation method can be transplanted to interpolating SAI preconditioning matrix. Assume matrices M 1 ; M 2 ; . . . ; M p+q+1 are p + q + 1 samples at frequency f1 ; f2 ; . . . ; fp+q+1 , respectively. As same as impedance matrix interpolation method, the SAI preconditioning matrix M at frequency f can be computed by p M ij (f ) = c10++dc1ff ++ 111111 ++ dcpffq

1

III. NUMERICAL RESULTS

where M denotes the element of M , i and j is the serial number of row and column. c0 ; . . . ; cp and d1 ; . . . ; dq are coefficients determined by solving linear equations, as shown in (5) at the bottom of the page. A hybrid interpolation method is proposed to fast calculate scattering from electrically object over wideband. In MLFMA implementation, both the near field impedance matrices and SAI preconditioning matrices are interpolated at intermediate frequencies over a relatively large frequency band with rational function interpolation technique. Therefore, this hybrid method includes two parts: (1) interpolating the impedance matrices to decrease the construction time of impedance

.. . 1 1

.. . 1

f1 fp+1 fp+2 fp+q+1

111

f1p

M1ij f1

0

111

fpp+1 fpp+2 .. .

111

fpp+q+1

In this section, a number of numerical results are presented to demonstrate the accuracy and efficiency of the preconditioning matrix interpolation method for fast calculation of RCS over wide band. The restarted version of GMRES(m) [17] algorithm is applied to solve linear systems, where m is the dimension size of Krylov subspace for GMRES. “m” is set to be 30 in this communication. All experiments are conducted on an Intel Core II 8300 with 1.96 GB local memory and run at 2.66 GHz in single precision. The iteration process is terminated when the 2-norm residual error is reduced by 1003 , and the limit of the maximum number of iterations is set as 1000.

M1ij f1q

c0

Mpij+1 fpq+1 ij q 0Mp+2 fp+2

cp d1

Mpij+q+1 fpq+q+1

dq

111

0

.. .

.. .

.. .

111

matrices; (2) interpolating the SAI preconditioning matrices to decrease the construction time of SAI preconditioner. Large time reduction can be achievable by this novel method.

(4)

q

ij

1

Fig. 1. Calculation results for metallic Missile: (a) RCS for horizontal polarization; (b) Number of matrix vector products.

Mpij+1 fp+1 ij 0Mp+2 fp+2 0

111 111

.. .

.. .

Mpij+q+1 fp+q+1

0

0

111

0

M1ij .. .

.. .

.. .

=

Mpij+1 Mpij+2 .. .

Mpij+q+1

:

(5)

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Fig. 2. Calculation results for PEC Plate: (a) RCS; (b) Number of matrix vector products.

As well known, interpolating current coefficients J is a good way to accelerate frequency swap. However, in most of the cases, the RCS curve versus broadband frequency becomes complex for electrically large objects and plenty of sampling nodes are required for current approximation. Since the elements of impedance matrix and the elements of SAI preconditioning matrix are relative smooth over certain frequency range, the hybrid interpolation method requires only a few samples and becomes efficient over wide band. Three geometries are applied to illustrate the performance of our proposed hybrid method. They consist of a metallic missile with 7818 unknowns, a PEC plate (1 m 2 1 m) with 34165 unknowns, and a metallic cube (1 m 2 1 m 2 1 m) with 121854 unknowns. The direction of incident wave is  = 90 , ' = 45 for the first example, and  = 0 , ' = 45 for last two examples. In our simulations, 6 uniform samples are required in the impedance matrix interpolation method for these three examples. When applying current interpolation method, 61 frequency points are required for the first example, 41 points for the second example and 51 points for the last example. As shown in Figs. 1(a), 2(a) and 3(a), it can be seen that the impedance matrix interpolation method is more accurate than the current interpolation method. Therefore, the impedance matrix interpolation method is more efficient than the current interpolation method. As shown in Figs. 1(b), 2(b) and 3(b), it can be observed that there is no difference for the number of the matrix-vector production when the SAI matrices are interpolated. It can be concluded that almost the same convergence can be obtained whether the SAI preconditioning matrix is constructed by interpolation method or not.

Fig. 3. Calculation results for PEC Cube: (a) RCS; (b) Number of matrix vector products.

As shown in Table I, the construction time of SAI matrices are compared between traditional method and interpolation method for these three examples. It can be found that the computational cost of the interpolation method is much less. The main cost of SAI interpolation method is the construction time and memory requirement for those frequency sampling points. The memory requirement to save samples of near-field impedance matrices and preconditioning matrices is 128 MB for the first example, 526 MB for the second example and 1.5 GB for the last example. As shown in Table II, the total computation time is compared for the frequency sweep. “Without Interpolation” means impedance matrix constructed directly and SAI preconditioner constructed directly. “Current Interpolation” means the current interpolation technique combined with cubic spline method. “Hybrid Interpolation” means impedance matrix interpolation and SAI preconditioning method interpolation with the rational interpolation method. It can be also found by comparison that the large calculation time can be saved when the hybrid interpolation technique is used. IV. CONCLUSION In this communication, the hybrid interpolation technique is proposed for efficient analysis of the scattering from electrically large objects over a wide frequency band. The MLFMA and Krylov subspace iterative solver are used and the SAI preconditioning technique is used to accelerate the convergence. This hybrid interpolation technique is combined with both the impedance matrix interpolation method and SAI preconditioning matrix interpolation method.

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TABLE I CONSTRUCTION TIME FOR SAI PRECONDITIONING MATRIX (TIME: SECOND)

TABLE II TOTAL SOLUTION TIME FOR FAST FREQUENCY SWEEP (TIME: SECOND)

Numerical experiments demonstrate that our proposed hybrid interpolation method is more efficient when compared with the current interpolation method for electromagnetic scattering from the electrically large objects.

REFERENCES [1] R. F. Harrington, Field Computation by Moment Methods. Malabar, FL: Krieger, 1968. [2] W. C. Chew, J. M. Jin, E. Michielssen, and J. M. Song, Fast and Efficient Algorithms in Computational Electromagnetics. Boston, MA: Artech House, 2001. [3] J. M. Song, C. C. Lu, and W. C. Chew, “Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects,” IEEE Trans. Antennas Propag., vol. 45, pp. 1488–1493, 1997. [4] J. R. Mautz and R. F. Harrington, “H-field, E-field, and combined field solution for conducting bodies of revolution,” Arch. Elecktron. Übertragungstech (AEÜ), vol. 32, pp. 157–164, 1978. [5] M. Benzi and M. Tuma, “A sparse approximate inverse preconditioner for nonsymmetric linear systems,” SIAM J. Sci. Comput., vol. 19, pp. 968–994, 1998. [6] P. L. Rui and R. S. Chen, “An efficient sparse approximate inverse preconditioning for FMM implementation,” Micro. Opt. Tech. Lett., vol. 49, no. 7, pp. 1746–1750, 2007. [7] E. H. Newman, “Generation of wide-band data from the method of moments by interpolating the impedance matrix,” IEEE Trans. Antennas Propag., vol. 36, pp. 1820–1824, 1988. [8] K. L. Virga and Y. R. Samii, “Efficient wide-band evaluation of mobile communications antennas using Z or Y matrix interpolation with the method of moments,” IEEE Trans. Antennas Propag., vol. 47, pp. 65–76, 1999.

[9] X. C. Wei and E. P. Li, “Wide-band EMC analysis of on-platform antennas using impedance-matrix interpolation with the moment of method-physical optics method,” IEEE Trans. Electromagn. Compat., vol. 45, no. 3, pp. 552–556, 2003. [10] G. J. Burke, E. K. Miller, S. Chakrabarthi, and K. Demarest, “Using model-based parameter estimation to increase the efficiency of computing electromagnetic transfer functions,” IEEE Trans. Magn., vol. 25, pp. 2807–2809, Jul. 1989. [11] C. J. Reddy, M. D. Deshpande, C. R. Cockresll, and F. B. Beck, “Fast RCS computation over a frequency band using method of moments in conjunction with asymptotic waveform evaluation technique,” IEEE Trans. Antennas Propag., vol. 46, pp. 1229–1233, Aug. 1998. [12] Y. E. Erdemli, J. Gong, C. J. Reddy, and J. L. Volakis, “Fast RCS pattern fill using AWE technique,” IEEE Trans. Antennas Propag., vol. 46, pp. 1752–1753, Nov. 1998. [13] R. D. Slong, R. Lee, and J. F. Lee, “Multipoint Galerkin asymptotic waveform evaluation for model order reduction of frequency domain FEM electromagnetic radiation problems,” IEEE Trans. Antennas Propag., vol. 49, pp. 1504–1513, Oct. 2001. [14] M. S. Chen, X. L. Wu, W. Sha, and Z. X. Huang, “Fast and accurate radar cross-section computation over a broad frequency band using the best uniform rational approximation,” IET Micro. Antennas Propag., vol. 2, no. 2, pp. 200–204, 2008. [15] Z. W. Liu, D. Z. Ding, Z. H. Fan, and R. S. Chen, “Adaptive sampling bicubic spline interpolation method for fast computation of monstatic RCS,” Micro. Opt. Tech. Lett., vol. 50, no. 7, pp. 1851–1857, Jul. 2008. [16] S. M. Rao, D. R. Wilton, and A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propag., vol. 30, pp. 409–418, 1982. [17] Y. Saad and M. Schultz, “GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems,” SIAM J. Sci. Stat. Comput., vol. 7, no. 3, pp. 856–869, 1986.

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Corrections Corrections to, “Radiation Characteristics of Ingestible Wireless Devices in Human Intestine Following Radio Frequency Exposure at 430, 800, 1200, and 2400 MHz” Lisheng Xu, Max Q.-H. Meng, Yawen Chan, and Hongliang Ren I. INTRODUCTION In [1], the biography of Yawen Chan contained incorrect information. The corrected biography now follows. Manuscript received November 24, 2009; revised November 29, 2009; accepted December 02, 2009. Date of publication March 29, 2010; date of current version July 08, 2010. L. Xu is with the Sino-Dutch Biomedical and Information Engineering School, Northeastern University, Shenyang 110004, China (e-mail: [email protected]). M. Q.-H. Meng and H. Ren are with the Department of Electronic Engineering, The Chinese University of Hong Kong, Shatin, Hong Kong (e-mail: [email protected]; [email protected]). Y. Chan is with the Department of Medicine and Therapeutics, The Chinese University of Hong Kong, Shatin, Hong Kong (e-mail: [email protected]. hk). Digital Object Identifier 10.1109/TAP.2010.2046873

Yawen Chan received the Bachelor of Applied Science degree in electrical engineering from the University of Waterloo, Waterloo, ON, Canada, in 2003, and the Master of Philosophy degree in biomedical engineering from The Chinese University of Hong Kong, Hong Kong, in 2005. In summer 2003, she was with the Thermodynamic Laboratory, Institute of Biomaterials and Biomedical Engineering, University of Toronto, Toronto, ON, Canada. Since 2005, she has been working with the Faculty of Medicine, The Chinese University of Hong Kong, where she is currently a Research Associate. She is heavily involved in clinical research work in the area of endoscopy and gastroenterology. Her current research interests include diagnostic technique of clinical medicine, health-related quality of life of patients suffering from gastrointestinal diseases, as well as the pathophysiological mechanism of related diseases.

REFERENCES [1] L. Xu, M. Q.-H. Meng, H. Ren, and Y. Chan, “Radiation characteristics of ingestible wireless devices in human intestine following radio frequency exposure at 430, 800, 1200 and 2400 MHz,” IEEE Trans. Antennas Propag., vol. 57, no. 8, pp. 2418–28, Aug. 2009.

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Digital Object Identifier 10.1109/TAP.2010.2056572

INSTITUTIONAL LISTINGS The IEEE Antennas and Propagation Society is grateful for the support given by the organizations listed below and invites applications for Institutional Listings from other firms interested in the field of Antennas and Propagation.

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Digital Object Identifier 10.1109/TAP.2010.2056573