IEEE MTT-V053-I11 (2005-11) [53, 11 ed.]

Table of contents :
SPECIAL ISSUE ON 2005 INTERNATIONAL MICROWAVE SYMPOSIUM......Page 1
020 - [email protected] 2
2005 Symposium Issue......Page 3
Raytheon Company......Page 6
II. D ESIGN M ETHOD A......Page 7
III. D ESIGN M ETHOD B......Page 8
A. Test Filter 1......Page 9
B. Test Filter 2......Page 10
C. Comparisons Between the Two Design Methods......Page 11
VI. C ONCLUSION......Page 12
C. Quendo, E. Rius, and C. Person, Narrow bandpass filters using......Page 13
I. I NTRODUCTION......Page 14
Fig.€1. Coupled lines and reference system.......Page 15
Fig.€2. Decomposition of a set of $n$ -coupled lines in $n$ -unc......Page 17
III. S ENSITIVITY A NALYSIS......Page 18
Fig.€4. Assumed topology for the error network.......Page 19
Fig.€7. Comparison between theory and results from EmSight from......Page 20
Fig.€10. Coupled coaxial cables in lossy dielectric $(% \varepsilo......Page 21
J. C. Rautio, An ultrahigh precision benchmark for validation of......Page 22
II. T HEORY......Page 23
A. Fabrication and Measurement......Page 24
Fig.€4. Electrical pulses probed at 0.25, 1, 3, and 5 mm on two......Page 25
IV. F ULL -W AVE A NALYSIS......Page 26
V. R ESULTS AND D ISCUSSION......Page 27
F. Schnieder, T. Tischler, and W. Heinrich, Modeling dispersion......Page 28
T. Y. Hsiang, S. Alexandrou, and C. C. Wang, Terahertz dispersio......Page 29
II. S YNTHESIS OF THE P ROTOTYPE P OLYNOMIALS......Page 30
A. Example of Synthesis......Page 31
Fig.€3. 4 2 direct-coupled cul-de-sac BS filter. (a) Coupling an......Page 32
IV. T RANSFORMATION FOR D UAL -B AND F ILTERS......Page 33
Fig.€6. Coupling matrices for 8 4 dual-band filtering characteri......Page 34
Fig.€8. DBBS filter comparison of rejection characteristic with......Page 35
VI. H ARDWARE V ALIDATION......Page 36
Fig.€13. 4 2 direct-coupled cul-de-sac BS filter simulated and m......Page 37
G. Macchiarella and S. Tamiazzo, A design technique for symmetri......Page 38
II. E QUIVALENT -C IRCUIT M ODEL......Page 40
Fig.€3. Transverse slot loaded with a short-circuited waveguide......Page 41
Fig.€6. Insertion loss for a rectangular waveguide with and with......Page 42
Fig.€9. Effect of the waveguide height $b$ on the dispersion beh......Page 43
Fig.€11. Effect of the corrugations width-to-period ratio on the......Page 44
Advanced Design System 2003A, User's Guide, Agilent Technol., Pa......Page 45
I. I NTRODUCTION......Page 47
Fig.€4. SM-LRM modeling method.......Page 48
1) Device Analysis by the Schwarz Christoffel Transformation: To......Page 49
IV. R ESULTS......Page 50
TABLE V
$\beta_{i}$ C OEFFICIENTS FOR PKI-LRM M ETHOD AND M ICR......Page 51
M. Horno, Calculation of quasi-static characteristic of microstr......Page 52
M. T. Hagan and M. Menhaj, Training feedforward networks with th......Page 53
I. I NTRODUCTION......Page 54
B. Phantom Materials......Page 55
III. S IGNAL P ROCESSING......Page 56
B. Focusing......Page 57
B. Tumor Detection and Skin Subtraction......Page 58
Fig.€9. Signal-to-clutter ratio received when changing the permi......Page 59
J. M. Sill, Second generation experimental system for tissue sen......Page 60
D. W. Winters, E. J. Bond, S. C. Hagness, and B. D. Van Veen, Es......Page 61
A. GA Design......Page 62
B. Numerical Analysis......Page 63
Fig.€5. Fabricated FSSs.......Page 64
A. Equivalent Circuit for Closely Spaced FSSs......Page 65
C. Design Example......Page 66
C. H. Chan, K. T. Ng, and A. B. Kouki, A mixed spectral-domain a......Page 67
R. Takaichi, T. Aoki, and Y. Kobayashi, Back-side relative condu......Page 68
Fig.€1. Discharge characteristics of a conventional carbon-elect......Page 69
Fig. 2. Predistorter using $(I ^{2} +Q ^{2})$ component.......Page 70
Fig.€5. Comparison between simulated ACPR and measured ACPR with......Page 71
III. S IMULATION......Page 72
Fig.€10. Simulated ACPR at 5-MHz offset as a function of third-o......Page 73
B. Low-Voltage Operation......Page 74
S. Kusunoki, K. Kawakami, and T. Hatsugai, Load impedance and bi......Page 75
3rd generation partnership project; Technical specification grou......Page 76
Fig.€1. Schematic for the SP6T MEMS switch based on metal-contac......Page 77
B. Fabrication......Page 78
Fig.€5. (a) Setup schematic for measuring the switching times. (......Page 79
Fig.€7. (a) and (b) Extracted parameters for CPW 1 and CPW 2 and......Page 80
Fig.€8. Comparison of the measured and modeled RF performance fo......Page 81
B. Small-Signal Modeling......Page 82
Fig.€13. Comparison of the measured and the modeled isolation pe......Page 83
Fig.€15. (a) Setup schematic for measuring RF power handling. (b......Page 84
L. Dussopt and G. M. Rebeiz, Intermodulation distortion and powe......Page 85
I. I NTRODUCTION......Page 87
1) Resonant Frequency of the Inductive Coupled-Ring Resonator: F......Page 88
B. Production of the Polymer-Dispersed Liquid-Crystal Material......Page 89
Fig.€6. Polymer-dispersed liquid crystal made by mixing 5 wt% NO......Page 90
V. V ARIATION OF R ESPONSE T IME W ITH P OLYMER C ONCENTRATION......Page 91
Fig. 14. $\Delta \varepsilon{'}$ versus applied electric field (......Page 92
VII. P OLYMER -D ISPERSED L IQUID -C RYSTAL L OADED V ARIABLE P......Page 93
VIII. C ONCLUSION......Page 94
T. Kamei, Y. Utsumi, H. Moritake, K. Toda, and H. Suzuki, Measur......Page 95
II. D YNAMIC P ERFORMANCE OF EMI R ECEIVERS......Page 96
A. SNR......Page 97
2) Dynamic Range: The dynamic range is the difference between th......Page 98
1) Optimum Amplitude Intervals: A sample that is digitized withi......Page 99
A. Dead Times of Limiters......Page 100
2) Limiter With Improved Matching: The multiresolution time-doma......Page 101
4) Simulations: Time-domain simulations where performed with SPI......Page 102
VII. M EASUREMENT R ESULTS......Page 103
Fig.€19. Overload factor of the multiresolution system with thre......Page 104
F. Viehböck and H. Fürst, A novel fast high resolution ADC-struc......Page 105
II. T HEORY......Page 106
III. FDTD F ORMULATION......Page 107
IV. N UMERICAL R ESULTS......Page 108
Fig. 5. (a) (c) Wavefront images of the particle velocities $v_{......Page 109
Fig. 8. (a) (c) Wavefront images of the particle velocities $v_{......Page 110
A. Taflove and S. C. Hagness, Computational Electrodynamics: The......Page 111
M. Takeuchi, H. Odagawa, M. Tanaka, and K. Yamanouchi, SAW trans......Page 112
Fig.€1. (a) Layout of eight radial slotlines. Black stripes indi......Page 113
Fig.€2. Axial magnetic field contours of the resonator for all s......Page 114
Fig.€5. Calculated tuning parameter as function of the slotline......Page 115
IV. R ESONATOR D ESIGN AND E XPERIMENTAL R ESULTS......Page 116
Fig.€9. Traces of signals due to switching of the frequency of t......Page 117
V. D ISCUSSION AND C ONCLUSION......Page 118
A. C. Polycarpou et al., Radiation and scattering from ferrite-t......Page 119
Fig.€1. Summary of previously reported DA gain and BW performanc......Page 120
Fig.€4. Gain cell of first DA version employing a cascode config......Page 121
Fig.€6. Eye diagrams of MUX output signal at 80 Gbit/s. The on-w......Page 122
A. Circuit Design......Page 123
C. Discussion......Page 124
A. Circuit Design......Page 125
TABLE II B IAS C ONDITIONS AND P OWER C ONSUMPTION FOR M AXIMUM......Page 126
VI. C ONCLUSION AND O UTLOOK......Page 127
J. G. Proakis, Digital Communications, 2nd ed. New York: McGraw-......Page 128
I. I NTRODUCTION......Page 130
B. DDJ......Page 131
Fig.€3. Ensemble of normalized DDJ values for different ratios o......Page 132
Fig.€5. Deviation of the threshold-crossing time due to the effe......Page 133
B. Peak-to-Peak Jitter and Scale-One DDJ......Page 134
A. Discrete Systems......Page 135
B. Integrated TIA......Page 136
TABLE II C OMPARING M EASURED ${\rm DDJ}_{1}$ AND P REDICTIONS O......Page 137
B. Analui and A. Hajimiri, Bandwidth enhancement for trans-imped......Page 138
II. 0.15- $\mu{\hbox {m}}$ GaAs pHEMT MMIC T ECHNOLOGY......Page 140
Fig. 4. Characteristics of $I_{\rm DS}$ and $I_{\rm G}$ versus $......Page 141
Fig.€7. Light emission spectrum induced by impact ionization $I_......Page 142
V. RF-D RIVEN $I_{\rm G}$ I NDUCED DC/RF D EGRADATION......Page 143
VI. E MPIRICAL M ODEL FOR $P_{\rm OUT}$ L ONG -T ERM P REDICTION......Page 144
VII. C ONSIDERATION OF P OWER P ERFORMANCE B UDGET......Page 145
Y. C. Chou, R. Grundbacher, R. Lai, B. R. Allen, B. Osgood, A. S......Page 146
Y. C. Chou, G. P. Li, Y. C. Chen, C. S. Wu, K. K. Yu, and T. A.......Page 147
A. Waveform Symmetry and $1/f$ Noise Upconversion......Page 149
Fig.€1. Examples of symmetrical and asymmetrical oscillation wav......Page 150
A. Push Push Oscillator......Page 151
B. Triple-Push Oscillator......Page 152
A. Device $1/f$ Noise Measurement......Page 153
C. Triple-Push Oscillator......Page 154
L. Dussopt and G. M. Rebeiz, A low phase noise silicon 18-GHz pu......Page 155
I. I NTRODUCTION......Page 157
III. D ESIGN......Page 158
Fig.€5. Fabrication process.......Page 159
Fig.€8. Measurement configuration of in vitro measurement using......Page 160
Fig.€11. Measured results of in vivo measurements using mice. (a......Page 161
H. Hwang, J. Yim, J. W. Cho, C. Cheon, and Y. Kwon, 110 GHz broa......Page 162
II. RBFNN......Page 164
III. E XPERIMENTAL......Page 165
A. Modeling......Page 166
Fig.€7. Normalized spectra for the input signal, measured output......Page 167
B. Predistortion......Page 168
V. C ONCLUSION......Page 169
J. Tsimbinos and K. V. Lever, Computational complexity of Volter......Page 170
II. D UAL -B AND R ESONATORS AND F ILTER D ESIGN P ROCEDURES......Page 171
A. Type-I Filter......Page 172
Fig. 6. Design curves of: (a) $\theta_{1}$ and $\theta_{2}$ . (b......Page 173
Fig.€9. Structure of dual-band inverter for type-I filter.......Page 174
B. Coupled-Line Sections in the Middle Stages......Page 175
TABLE I C IRCUIT P ARAMETERS OF F ILTER A......Page 176
Fig.€18. (a) Circuit configuration and parameters of filter B. (......Page 177
B. Filter Design With Type-II Filter......Page 178
Fig.€21. Design flows of type-I and type-II filters.......Page 179
J. T. Kuo and H. S. Cheng, Design of quasi-elliptic function fil......Page 180
C. Monzon, A small dual-frequency transformer in two sections, I......Page 181
II. G ENERAL D ISTRIBUTED S MALL -S IGNAL E QUIVALENT -C IRCUIT......Page 182
A. Generation of Starting Value of SSM Parameters......Page 183
Fig.€5. T-network representation of a cold pinchoff FET equivale......Page 184
Fig.€7. Resistance estimation from the cold forward stripped $Z$......Page 185
B. Model Parameter Optimization......Page 186
IV. I NTRINSIC P ARAMETER E XTRACTION......Page 187
Fig.€13. Errors between simulated and measured $S$ -parameters.......Page 188
P. Ladbrooke, MMIC Design GaAs FET's and HEMTs . Norwood, MA: Ar......Page 189
I. I NTRODUCTION......Page 191
A. Formulation of the Above-Cutoff Dispersion Model......Page 192
Fig.€2. Static drain current measurements carried out at differe......Page 193
A. Model Extraction......Page 194
Fig. 7. Pulsed transconductance of a 0.25- $\mu\hbox{m}$ Triquin......Page 195
Fig. 10. GaAs 0.25- $\mu\hbox{m}$ pHEMT $S$ -parameters (opportu......Page 196
C. High-Frequency Model Validation......Page 197
Fig. 13. Variations $\Delta(I/C)_{P_{\rm out}}^{Z_{1},Z_{2}}$ in......Page 198
J. B. Scott, J. G. Rathmell, A. E. Parker, and M. Sayed, Pulsed......Page 199
C. Fiegna, F. Filicori, G. Vannini, and F. Venturi, Modeling the......Page 200
I. I NTRODUCTION......Page 202
Fig.€2. (a) Equivalent-circuit model of the unit-cell CRLH CPW w......Page 203
Fig. 3. Measured $\mu_{\rm eff},\varepsilon_{\rm eff}$, and the......Page 204
A. Reduced-Size CRLH CPW Resonator......Page 205
Fig. 8. (a) Geometry of the two-pole CRLH CPW BPF ( $\ell_{1}= 0......Page 206
C. Caloz, A. Sanada, and T. Itoh, A novel composite right-/left-......Page 207
S.-G. Mao and Y.-Z. Chueh, Broadband composite right/left-handed......Page 208
II. T HEORETICAL A NALYSIS......Page 209
III. MEMS S WITCH F ABRICATION AND M EASUREMENT......Page 210
Fig.€4. Typical CV characteristic of a capacitive MEMS switch at......Page 211
B. Capacitance Transients......Page 212
Fig.€9. Arrhenius plot of the time scale of the stretched expone......Page 213
C. L. Henley, Critical Ising spin dynamics on percolation cluste......Page 214
A. Significance of Proposed Research......Page 216
1) UWB Transmitter: The UWB transceiver architecture is shown in......Page 217
Fig.€6. BER comparison for a standard and proposed test for a Bl......Page 218
2) Proposed BER Test Method: We investigate how BER changes in t......Page 219
Fig.€10. BER comparison for standard and proposed test for GSM 9......Page 220
3) GSM 900 Interferer: For GSM 900, the maximum allowable signal......Page 221
J. H. Friedman, Multivariate adaptive regression splines, Annals......Page 222
A. Test Set Description......Page 224
TABLE I SRAV P ARAMETER FOR D IFFERENT T YPES OF S WITCHES AND D......Page 225
A. Dielectric Conduction Mechanism......Page 226
V. M ODELING OF THE D IELECTRIC C HARGING P HENOMENON......Page 227
Fig.€11. FOM for the dielectric of switches of type A and switch......Page 228
X. Rottenberg, B. Nauwelaers, W. De Raedt, and H. A. C. Tilmans,......Page 229
I. I NTRODUCTION......Page 231
Fig.€2. Frequency response of a one-unit cell CW-SRRTL analyzed......Page 232
B. Case II......Page 233
Fig.€11. $S$ -parameters of the CW-LHTL with eight SRRs/CLSs in......Page 234
Fig.€15. Dispersion diagram of the CW-LHTL.......Page 235
Fig.€18. Comparison between the $S$ -parameters of CW-LHTL unit......Page 236
Fig.€22. Schematic of a T-junction with a left-handed section.......Page 237
C. Caloz, C. Chang, and T. Itoh, Full-wave verification of the f......Page 238
I. I NTRODUCTION......Page 240
Fig.€1. Bluetooth and WLAN packet transmission timing diagram.......Page 241
B. Measurement and Characterization......Page 242
A. Cancellation Approach......Page 243
B. Proposed Canceller Unit......Page 244
IV. CMOS IC I MPLEMENTATION......Page 245
Fig.€8. (a) Variation of VGA gain magnitude with frequency. (b)......Page 246
Fig.€9. (a) Simplified diagram showing phase shifter operation.......Page 247
Fig.€13. Schematic of on-board tunable bandpass emulation filter......Page 248
Digital Cellular Telecommunications System (Phase 2 $+$, GSM): R......Page 249
Fig.€1. ISI versus distance plot with different bandwidth-distan......Page 251
B. FFE......Page 252
Fig.€3. FFE configuration with passive LC ladder delay line and......Page 253
Fig.€5. DC gain characteristic of the multiplier cell.......Page 254
Fig.€7. Passive delay-line performance with $Ts/3$ tap spacing.......Page 255
E. Output Buffer Stage......Page 256
A. Measurement of the FFE With Passive Delay Line......Page 257
Fig.€17. FFE performance measurement setup over the 500-m MMF op......Page 258
Fig.€22. Microphotograph of the FFE with active delay-line appro......Page 259
T. H. Lee, The Design of CMOS Radio-Frequency Integrated Circuit......Page 260
I. I NTRODUCTION......Page 262
A. Sensitivity Analysis of Lossy Subsections......Page 263
B. Sensitivity Analysis of Lossless Subsections......Page 264
1) Sensitivity of Modal Voltages and Currents: It can be proved......Page 265
2) Sensitivity of Modal Transformation Matrices: The next step i......Page 266
D. Unified Sensitivity Equations......Page 267
Example 2: This example demonstrates the use of the proposed sen......Page 268
TABLE€I C OMPUTATIONAL C OST C OMPARISON......Page 269
D ERIVATION OF S ENSITIVITY E QUATIONS FOR M ODAL V OLTAGES AND......Page 270
J. W. Bandler, W. Kellermann, and K. Madsen, A superlinearly con......Page 271
Fig.€2. Conceptual schematic of the SPST ridge-waveguide switch......Page 273
III. RF MEMS M ULTIPORT W AVEGUIDE S WITCH......Page 274
Fig.€6. Simulation results for proposed C-type switch with ideal......Page 275
A. SPST RF MEMS Coaxial Switches......Page 276
Fig.€12. Measured results for the proposed RF MEMS coaxial SPST......Page 277
Fig.€16. Measurement results for the proposed RF MEMS coaxial C-......Page 278
J. Muldavin, R. Boisvert, C. Bozler, S. Rabe, and C. Keast, Powe......Page 279
I. I NTRODUCTION......Page 280
A. Time-Domain Adjoint Sensitivity Analysis......Page 281
B. Derivative Computation......Page 282
2) Summary: The above derivations can be summed up as follows. C......Page 283
Fig.€6. Pseudocode description for the proposed algorithm (conti......Page 284
B. Time-Domain Sensitivity......Page 285
C. Optimization of Time-Domain Waveforms......Page 286
Fig. 18. $V_{1}$ response.......Page 287
VI. C ONCLUSION......Page 288
J. Vlach and K. Singhal, Computer Methods for Circuit Analysis a......Page 289
I. I NTRODUCTION......Page 290
II. S YSTEM C ONCEPT......Page 291
III. S UB -A RRAY A NALYSIS......Page 292
IV. S YSTEM O PERATION /A RRAY P ERFORMANCE......Page 293
Fig.€10. Bistatic pattern for two source incidence along with DO......Page 294
Fig.€12. Test setup for communication link test.......Page 295
Fig.€15. ( top ) Transmitted modulating waveform from location 1......Page 296
H. Steyskal, R. A. Shore, and R. L. Haupt, Methods for null cont......Page 297
D. S. Goshi, K. M. K. H. Leong, and T. Itoh, A retrodirective ar......Page 298
A. Lateral IMPATT Diode......Page 299
Fig.€5. Measured IMPATT impedance after deembedding at 77 GHz an......Page 300
C. Bias T......Page 301
TABLE€I C ALCULATED AND M EASURED P OWER......Page 302
P. J. Stabile and B. Lalevic, Lateral IMPATT diodes, IEEE Electr......Page 303
II. T HEORY......Page 304
III. R ESULTS......Page 306
IV. C ONCLUSION......Page 307
J.-F. Lee and R. Dyczij-Edlinger, Automatic mesh generation usin......Page 308
I. I NTRODUCTION......Page 310
III. C HANNEL P ARAMETER V ARIATION......Page 311
Fig.€5. Changes in insertion loss and eye height of a typical in......Page 312
B. Modeling and Analysis Methodologies of Active System......Page 313
Fig.€8. Eye diagrams of the chip-to-chip interconnect system: th......Page 314
Fig.€10. Response waveforms of the active system at the receiver......Page 315
Fig.€12. Measured and simulated single-bit responses at the rece......Page 316
Fig.€17. Eye diagram of the input waveform with add Gaussian jit......Page 317
W. J. Dally and J. W. Poulton, Digital Systems Engineering . Cam......Page 318
Fiber channel Methodologies for jitter specification, Nat. Commi......Page 319
I. I NTRODUCTION......Page 320
II. W IDE -B AND RF T RANSMITTER P ROTOTYPE......Page 321
Fig.€5. AM/PM curve smoothed versus the raw measurement AM/PM da......Page 322
IV. I NFLUENCE OF T IME D ELAY ON M EMORY -E FFECT I DENTIFICATI......Page 323
Fig.€11. Measured transmitter AM/PM characteristic comparison wi......Page 324
Fig.€13. Spectrum comparison among the spectra of memoryless mod......Page 325
A. Inclusive Memory-Effect Model......Page 326
VII. E XPERIMENTAL S ETUP AND N EWLY P ROPOSED M ODEL V ALIDATIO......Page 327
C. P. Silva, A. A. Moulthrop, and M. S. Muha, Introduction to po......Page 328
K. A. Remley, M. M. P. Schreurs, D. F. Williams, and J. Wood, Ex......Page 329
I. I NTRODUCTION......Page 330
A. Miniature Horn Antennas With Waveguide Feeds......Page 331
Fig.€7. Simulated difference in cross-polarization power from th......Page 332
C. Beam Control Circuitry......Page 333
IV. M EASURED S YSTEM P ERFORMANCE......Page 334
V. R ADAR M EASUREMENTS AND C HARACTERIZATION......Page 335
S. Ortiz and A. Mortazawi, A perpendicular aperture-fed patch an......Page 336
I. I NTRODUCTION......Page 337
A. Discretized Port Plane......Page 338
IV. F IELD -B ASED W AVE S EPARATION......Page 339
V. O RTHOGONALITY OF M ODES......Page 340
A. Full-Wave Approach for Guides With Homogeneous Cross Section......Page 341
B. Extension to Guides With Inhomogeneous Cross Section......Page 342
A. Coaxial-Torus Resonator......Page 343
C. $H$ -Plane Step Discontinuity......Page 344
Fig.€14. Comparison between FVTD and MM results of the transmiss......Page 345
VIII. C ONCLUSION......Page 346
F. E. Gardiol, Higher-order modes in dielectrically loaded recta......Page 347
I. I NTRODUCTION......Page 348
A. MMIC Broad-Band PA Design......Page 349
1) First Stage Design With Programmable Predistortion: The desig......Page 350
Fig.€5. Simulation result of the first stage power performance.......Page 351
Fig.€7. Frequency tuning range with normalized $C1$ and $C2$ .......Page 352
Fig.€10. Small signal measurement results of the MMIC broad-band......Page 353
TABLE€I P1dB C OMPARISON OF PAM W ITH D IFFERENT B IASING C OND......Page 354
P. Savary, A. Girardot, G. Montoriol, F. Dupis, B. Thibaud, R. J......Page 355
Fig.€1. Drawing of switch geometry. ( top ) Side view. ( bottom......Page 357
Fig.€4. Resistance variation as a function of signal frequency.......Page 358
Fig.€5. Plot of test resistance data for switches run to a maxim......Page 359
V. D ETERMINATION OF R ESISTANCE V ARIATION W ITH C ONTACT F ORC......Page 360
VI. C ONTACT F ORCE AND M ECHANICAL R ESONANCE......Page 361
R. Holmes, Calculation of constriction resistances with constant......Page 362
Fig.€1. Batch-fabricated bandpass filters on a single panel; eac......Page 363
B. Probabilistic Diagnosis Based on Statistical Analysis: Concep......Page 364
TABLE I S HOWING S IMULATION M ATRIX S ETUP......Page 365
C. Extraction of pdfs of Performance Measures......Page 366
TABLE II S HOWING S TATISTICAL P ARAMETERS OF F ILTER P ERFORMAN......Page 367
D. Parametric Yield......Page 368
1) Number of Performance Measures Less Than Number of Physical P......Page 369
1) Bandpass Filter: A bandpass filter with a layout similar to t......Page 370
K. Singhal and J. F. Pinel, Statistical design centering and tol......Page 371
M. H. Kutner, C. J. Nachtscheim, W. Wasserman, and J. Neter, App......Page 372
A. Role of the Grid......Page 373
A. Components of the TLM-G System......Page 374
B. Relation Between YATWAD, YATD, and the Components of the GT i......Page 375
B. Bowtie Antenna in a TLM-G System......Page 376
C. Circular Cylindrical Cavity Resonator......Page 377
I. Foster, C. Kesselman, and S. Tuecke, The anatomy of the Grid:......Page 378
P. Lorenz and P. Russer, Hybrid transmission line matrix multipo......Page 379
I. I NTRODUCTION......Page 380
B. Microcellular Porous Titania Using Microfabrication of Cerami......Page 381
III. M ATERIAL C HARACTERIZATION......Page 382
B. Porous Titania With Microcellular Structure......Page 383
Fig.€9. Measurement setup for anisotropic samples inside a cavit......Page 384
A. Stratified-Medium-Loaded Cavity Resonator......Page 385
Fig.€15. (a) Stratified-medium-loaded resonator before metalliza......Page 386
C. DRA......Page 387
A. Buerkle, K. Sarabandi, and H. Mosallaei, Compact slot and die......Page 388
G. P. Junker, A. A. Kishk, A. W. Glisson, and D. Kajfez, Effect......Page 389
II. I DEAL T RANSMISSION -L INE M ODEL......Page 390
A. Single Dielectric Thin-Film Thickness......Page 391
Fig.€5. Representative flow of $c$ - and $\pi$ -mode currents in......Page 392
B. Detailed Modeling of the Balun......Page 393
Fig.€11. (a) Measured insertion and return losses of a pair of b......Page 394
B. Time-Domain Measurement......Page 395
G. Keiser, Optical Fiber Communications, 3rd ed. New York: McGra......Page 396
I. I NTRODUCTION......Page 398
II. PHD M ODEL F ORMULATION......Page 399
III. E XCITATION D ESIGN......Page 400
TABLE I O UTPUT OF SM S IMULATION $F_{0}=3~{\hbox{GHz}}$, $M=2$,......Page 401
V. D ISCUSSION......Page 402
Fig.€2. Simulation-based PHD model (solid lines), compared to un......Page 403
Fig.€6. Simulated trajectory diagrams. (a) Circuit-level model (......Page 404
VII. C ONCLUSIONS......Page 405
Agilent HMMC-5200 DC 20 GHz HBT series-shunt amplifier, Agilent......Page 406
Fig.€1. Multifinger GSGGSG coplanar probes placed: (a) on a doub......Page 407
III. C OAXIAL I MPLEMENTATION AND T ESTS OF A H ALF -L EAKY M UL......Page 408
IV. O N -W AFER I MPLEMENTATION OF A H ALF -L EAKY M ULTIPORT......Page 409
Fig. 11. Crosstalk parameters ( $S_{13}$ and $S_{14}$, probe dis......Page 410
V. C ONCLUSION......Page 411
W. Lin and C. Ruan, Measurement and calibration of a universal s......Page 412
V. Teppati, A. Ferrero, D. Parena, and U. Pisani, A simple calib......Page 413
A. Design......Page 414
C. Power Handling Modeling......Page 415
E. High-Power Measurements: Hot Tuning Range......Page 416
III. I MPEDANCE T UNER......Page 417
Fig.€12. Simulated tuner impedance coverage at 31.5, 33, and 35......Page 418
R. E. Collin, Foundations for Microwave Engineering . New York:......Page 419
J. Tuovinen, T. Vaha-Heikkila, J. Varis, and G. M. Rebeiz, A $V$......Page 420
540 - 01528823......Page 421
550 - 01528824......Page 422
560 - 01528825......Page 423
570 - 01528826......Page 424

Citation preview

NOVEMBER 2005

VOLUME 53

NUMBER 11

IETMAB

(ISSN 0018-9480)

SPECIAL ISSUE ON 2005 INTERNATIONAL MICROWAVE SYMPOSIUM

2005 Symposium Issue

"The Flagship of Microwaves" was the theme of the 2005 IEEE MTT-S International Microwave Symposium, held on 12-17 June 2005 in Long Beach, CA, USA.

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Digital Object Identifier 10.1109/TMTT.2005.860911

NOVEMBER 2005

VOLUME 53

NUMBER 11

IETMAB

(ISSN 0018-9480)

SPECIAL ISSUE ON 2005 INTERNATIONAL MICROWAVE SYMPOSIUM 2005 Symposium Issue Guest Editorial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. Jackson

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MICROWAVE SYMPOSIUM PAPERS

Design Techniques for Dual-Passband Filters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G. Macchiarella and S. Tamiazzo On the Derivation of Coupled-Line Models From EM Simulators and Application to MoM Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M. Farina, A. Morini, and T. Rozzi Attenuation Characteristics of Coplanar Waveguides at Subterahertz Frequencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J. Zhang, S. Alexandrou, and T. Y. Hsiang Direct-Coupled Microwave Filters With Single and Dual Stopbands . . . . . . . . . . . . .R. J. Cameron, M. Yu, and Y. Wang Rectangular Waveguide With Dielectric-Filled Corrugations Supporting Backward Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I. A. Eshrah, A. A. Kishk, A. B. Yakovlev, and A. W. Glisson Empirical Model Generation Techniques for Planar Microwave Components Using Electromagnetic Linear Regression Models . . . . . . . . . . . . . . . . . . . . G. Doménech-Asensi, J. Hinojosa, J. Martínez-Alajarín, and J. Garrigós-Guerrero Tissue Sensing Adaptive Radar for Breast Cancer Detection—Experimental Investigation of Simple Tumor Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J. M. Sill and E. C. Fear Novel Waveguide Filters With Multiple Attenuation Poles Using Dual-Behavior Resonance of Frequency-Selective Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M. Ohira, H. Deguchi, M. Tsuji, and H. Shigesawa Third- and Fifth-Order Baseband Component Injection for Linearization of the Power Amplifier in a Cellular Phone. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . N. Mizusawa and S. Kusunoki A Low-Loss Single-Pole Six-Throw Switch Based on Compact RF MEMS Switches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J. Lee, C. H. Je, S. Kang, and C.-A. Choi Increasing the Speed of Microstrip-Line-Type Polymer-Dispersed Liquid-Crystal Loaded Variable Phase Shifter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Y. Utsumi, T. Kamei, K. Saito, and H. Moritake A Low-Noise Multiresolution High-Dynamic Ultra-Broad-Band Time-Domain EMI Measurement System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S. Braun and P. Russer

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(Contents Continued on Page 3262)

(Contents Continued from Page 3261) Analysis of the Frequency Response of SAW Filters Using Finite-Difference Time-Domain Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . K.-Y. Wong and W.-Y. Tam Dielectric Resonator With Discrete Electromechanical Frequency Tuning . . . . . . . . .G. I. Panaitov, R. Ott, and N. Klein Comparison of InP/InGaAs DHBT Distributed Amplifiers as Modulator Drivers for 80-Gbit/s Operation . . . . . . . . . . . . . . . . . . . . . . .K. Schneider, R. Driad, R. E. Makon, H. Maßler, M. Ludwig, R. Quay, M. Schlechtweg, and G. Weimann Data-Dependent Jitter in Serial Communications . . . . . . . . . . . . . . . . . . . . B. Analui, J. F. Buckwalter, and A. Hajimiri The Effect of RF-Driven Gate Current on DC/RF Performance in GaAs pHEMT MMIC Power Amplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Y.-C. Chou, R. Lai, T. R. Block, A. Sharma, Q. Kan, D. L. Leung, D. Eng, and A. Oki Noise Upconversion . . . . J. Choi and A. Mortazawi Design of Push–Push and Triple-Push Oscillators for Reducing In Vitro and In Vivo Measurement for Biological Applications Using Micromachined Probe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J.-M. Kim, D. Oh, J. Yoon, S. Cho, N. Kim, J. Cho, Y. Kwon, C. Cheon, and Y.-K. Kim Wide-Band Dynamic Modeling of Power Amplifiers Using Radial-Basis Function Neural Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .M. Isaksson, D. Wisell, and D. Rönnow Planar Filter Design With Fully Controllable Second Passband . . . . . . . . . . . . . . C.-M. Tsai, H.-M. Lee, and C.-C. Tsai A New Small-Signal Modeling Approach Applied to GaN Devices . . . . . . . . . . . . . . . . . . . . A. Jarndal and G. Kompa Accurate pHEMT Nonlinear Modeling in the Presence of Low-Frequency Dispersive Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Raffo, A. Santarelli, P. A. Traverso, G. Vannini, F. Palomba, F. Scappaviva, M. Pagani, and F. Filicori Modeling of Symmetric Composite Right/Left-Handed Coplanar Waveguides With Applications to Compact Bandpass Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S.-G. Mao, M.-S. Wu, Y.-Z. Chueh, and C. H. Chen Temperature Study of the Dielectric Polarization Effects of Capacitive RF MEMS Switches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .G. Papaioannou, M.-N. Exarchos, V. Theonas, G. Wang, and J. Papapolymerou Production Test Technique for Measuring BER of Ultra-Wideband (UWB) Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .S. Bhattacharya, R. Senguttuvan, and A. Chatterjee Reliability Modeling of Capacitive RF MEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S. Mellé, D. De Conto, D. Dubuc, K. Grenier, O. Vendier, J.-L. Muraro, J.-L. Cazaux, and R. Plana Analysis, Modeling, and Applications of Coaxial Waveguide-Based Left-Handed Transmission Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H. Salehi and R. Mansour Analysis and Design of an Interference Canceller for Collocated Radios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .A. Raghavan, E. Gebara, E. M. Tentzeris, and J. Laskar 0.18- m CMOS Equalization Techniques for 10-Gb/s Fiber Optical Communication Links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M. Maeng, F. Bien, Y. Hur, H. Kim, S. Chandramouli, E. Gebara, and J. Laskar Delay-Extraction-Based Sensitivity Analysis of Multiconductor Transmission Lines With Nonlinear Terminations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . N. M. Nakhla, A. Dounavis, M. S. Nakhla, and R. Achar Multiport MEMS-Based Waveguide and Coaxial Switches . . . . . . . . . . . . . . . . . . . M. Daneshmand and R. R. Mansour An Adjoint-Based Approach to Computing Time-Domain Sensitivity of Multiport Systems Described by Reduced-Order Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T. Ahmed, E. Gad, and M. C. E. Yagoub A Secure High-Speed Retrodirective Communication Link . . . . . . . . . . . . . .D. S. Goshi, K. M. K. H. Leong, and T. Itoh Monolithic Integrated Millimeter-Wave IMPATT Transmitter in Standard CMOS Technology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T. Al-Attar and T. H. Lee Hybrid Surface Integral-Equation/Mode-Matching Method for the Analysis of Dielectric Loaded Waveguide Filters of Arbitrary Shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. Catina, F. Arndt, and J. Brandt Performance Analysis and Model-to-Hardware Correlation of Multigigahertz Parallel Bus With Transmit Pre-Emphasis Equalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . W. T. Beyene, J. Feng, N. Cheng, and X. Yuan Deembedding Static Nonlinearities and Accurately Identifying and Modeling Memory Effects in Wide-Band RF Transmitters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .T. Liu, S. Boumaiza, and F. M. Ghannouchi A Compact Dual-Polarized Multibeam Phased-Array Architecture for Millimeter-Wave Radar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .L. Schulwitz and A. Mortazawi Field-Based Scattering-Matrix Extraction Scheme for the FVTD Method Exploiting a Flux-Splitting Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. Baumann, C. Fumeaux, and R. Vahldieck Broad-Band Power Amplifier With a Novel Tunable Output Matching Network . . . . . . . H. Zhang, H. Gao, and G.-P. Li Determination of Intermodulation Distortion in a Contact-Type MEMS Microswitch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J. Johnson, G. G. Adams, and N. E. McGruer Statistical Analysis and Diagnosis Methodology for RF Circuits in LCP Substrates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S. Mukherjee, M. Swaminathan, and E. Matoglu

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(Contents Continued on Page 3263)

(Contents Continued from Page 3262) TLM-G—A Grid-Enabled Time-Domain Transmission-Line-Matrix System for the Analysis of Complex Electromagnetic Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P. Lorenz, J. V. Vital, B. Biscontini, and P. Russer Tailored and Anisotropic Dielectric Constants Through Porosity in Ceramic Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .X. Gong, W. H. She, E. E Hoppenjans, Z. N. Wing, R. G. Geyer, J. W. Halloran, and W. J. Chappell Development of Low-Loss Broad-Band Planar Baluns Using Multilayered Organic Thin Films. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. C. Chen, A.-V. Pham, and R. E. Leoni III Broad-Band Poly-Harmonic Distortion (PHD) Behavioral Models From Fast Automated Simulations and Large-Signal Vectorial Network Measurements . . . . . . . . . . . . . . . . D. E. Root, J. Verspecht, D. Sharrit, J. Wood, and A. Cognata On-Wafer Calibration Algorithm for Partially Leaky Multiport Vector Network Analyzers . . . . V. Teppati and A. Ferrero High-Power MEMS Varactors and Impedance Tuners for Millimeter-Wave Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Y. Lu, L. P. B. Katehi, and D. Peroulis Information for Authors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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CALLS FOR PAPERS

2006 IEEE Radio Frequency Integrated Circuits Symposium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 53, NO. 11, NOVEMBER 2005

Guest Editorial

O

NCE AGAIN, the November issue of this TRANSACTIONS highlights expanded papers from the 2005 IEEE Microwave Theory and Techniques Society (IEEE MTT-S) International Microwave Symposium (IMS) held June 11–17, 2005, Long Beach, CA. An outstanding technical program was assembled through the leadership of the following individuals. IMS General Chair Charlie Jackson Tatsuo Itoh IMS Vice-Chair Dave Rutledge TPC Chairman Mike Delisio TPC Associate-Chairman Robert York TPC Associate-Chairman Jonathon Hacker Electronic Paper Submission Arvind Sharma Secretary Hector De Los Santos Interactive Forum Ethan Wang Workshops and Tutorials Emilio Severo Panel Sessions Alina Moussessian Focused Sessions John Horton Special Memorial Sessions Scott Wedge Student Paper Contest Debabani Choudhury Digest A total of 984 papers were originally submitted to the IEEE MTT-S IMS Technical Program Committee (TPC) in December 2004 for possible presentation at the IEEE MTT-S IMS in June 2005. Of those papers, 491 (a 50% acceptance rate) were accepted at the IEEE MTT-S IMS. Each of the authors was then invited to expand their papers for consideration in this TRANSACTIONS’ Special Issue. 121 expanded papers were submitted by the April 1, 2005 deadline. Of these, 46 papers have been accepted for publication in this TRANSACTIONS (38%

Digital Object Identifier 10.1109/TMTT.2005.858386

acceptance rate). However, the review of 8 papers was not completed in time and they will be included in future issues of this TRANSACTIONS. This year, the process for reviewing the expanded papers was based on last year’s process. Instead of having a team of guest editors handle the papers, the associate editors of this TRANSACTIONS split the responsibility of handling all of this TRANSACTIONS’ Special Issue papers along with their allotment of regular issue papers. This new process provided several benefits, including the following: 1) consistent editorial review process between regular papers and special issue papers; 2) extensive editorial reviewer database from which to draw instead of just TPC membership; 3) minimal guest editor training because the associate editors handled all of this TRANSACTIONS’ Special Issue papers; 4) significantly reduced cost because the review process “infrastructure” was already in place; 5) publication of this TRANSACTIONS’ Special Issue in November instead of the previous December publication. On behalf of the IEEE MTT-S IMS Steering Committee and this TRANSACTIONS Editorial Staff, I would like to thank all of the reviewers and associate editors for their time and commitment to making this TRANSACTIONS such a well-respected publication.

CHARLIE JACKSON, General Chair, 2005 IEEE MTT-S IMS Raytheon Company Space and Airborne Systems El Segundo, CA 90245 USA

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Design Techniques for Dual-Passband Filters Giuseppe Macchiarella, Member, IEEE, and Stefano Tamiazzo

Abstract—This paper introduces two possible approaches to the design of microwave filters presenting two passbands separated by one rejection band, which is created by suitably placing transmission zeros in the stopband. In the first method, the two passbands have almost equal extension and the transmission zeros are symmetrically placed in the stopband; the second method instead allows the synthesis of filters with different passbands width and all the transmission zeros in the stopband placed at the same frequency. Both design methods are based on suitably defined frequency transformations and employ well-established prototype synthesis techniques; the practical implementation is performed through the classical multiple-coupled cavity topology. Two test filters operating in the global system for mobile communication 800-MHz band, designed with the described procedures and actually fabricated, have validated the novel design methods. Index Terms—Chebyshev filters, circuit synthesis, elliptic filters, microwave filters.

I. INTRODUCTION

T

HE SYNTHESIS of microwave filters presenting two passbands has been faced in the past using frequency-variable transformations based on the Zolatarev function [1], [2]; this approach, however, does not allow to control the attenuation between the two passbands (the inner stopband). Let us consider, in fact, the case where a strong attenuation is required inside a filter passband; the actual frequency characteristic to be realized is that of a dual-passband filter (DPBF) with a required stopband specified between the two passbands. The synthesis of these kinds of filters could be analytically approached with a general pole-zero placing technique (few examples using this approach can actually be found in the literature [3], [4]); however, since this technique is based on numerical optimization, the convergence is not always guaranteed and its effectiveness may be questionable (especially in the case of high-selectivity requirements). Another technique proposed for designing DPBFs consists of cascading a wide bandpass filter with a narrow stopband filter (notch) [5]; however, also in this case, the design is substantially based on numerical optimization. In this paper, we present two design techniques for DPBFs; the first method [6] refers to symmetrical DPBFs, i.e., with the frequency response geometrically symmetric with respect to located inside the inner stopband. The second a frequency method is instead applicable to filters with arbitrary passbands widths having, however, all the transmission zeros at the same frequency inside the stopband. Both design methods do not rely upon numerical optimization: they are, in fact, based on a frequency transformation followed by the synthesis of a low-pass

Manuscript received March 7, 2005; revised May 16, 2005. G. Macchiarella is with the Dipartimento di Elettronica e Informazione, Politecnico di Milano, 32 20133 Milan, Italy (e-mail: [email protected]). S. Tamiazzo is with the Forem (an Andrew Company), 20041 Agrate Brianza, Italy (e-mail: [email protected]). Digital Object Identifier 10.1109/TMTT.2005.855749

Fig. 1.

Low-pass prototype response of symmetrical dual-band filters.

prototype. The first technique allows realizing the DPBF as a classical multiple-coupled cavity filter (with the coupling coefficients and the tuning frequencies as characteristic design parameters); the second method produces an inline filter configuration with rejection resonators suitably coupled to bandpass resonators (again, the design parameters are the coupling coefficients and tuning frequencies). It is worth observing that a similar approach has been employed in [13] to realize DPBFs in microstrip technology; the design technique employed in that paper, however, is not suitable to realize high-selectivity coupled-cavity filters (such as those considered here). In Sections II and III, the two novel design methods for DPBFs are introduced and discussed. In Section IV, the design of two test DPBFs with the novel methods is presented and the measurements realized on fabricated prototypes are illustrated. Conclusions are drawn in Section V. II. DESIGN METHOD A Let consider the typical response of a low-pass prototype associated to a geometrically symmetric DPBF (Fig. 1); this normalized response is obtained by applying the usual bandpass low-pass frequency transformation to a geometrically symmetric bandpass response around . This means that the rejection band limits, as well as the inner passbands limits, are assumed geometrically symmetric with respect to . Let consider now the asymmetrical single-passband response shown in Fig. 2, which is defined in a different normalized frequency domain ; the following frequency transformation is introduced, which allows mapping the imaginary axis of into the imaginary axis of : (1) The following correspondence is then imposed in the two frequency domains:

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(2)

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Fig. 2. Asymmetrical single passband response.

From the above requirements, the parameters computed as follows:

and

can be

(3) Finally, using (1) and (3), the transformed frequencies can be expressed as a function of the original frequencies as follows: (4) Let us now see how to perform the synthesis of the dual-band prototype using the above equations. First, the number of poles must be even and of the prototype is assigned; this number also represents the overall number of reflection zeros in the two of transmission zeros are passbands. An even number and (symmetrical then symmetrically placed between zeros in the domain ) and are transformed into domain using (4). A prototype of order with transmission zeros at can be then synthesized in this domain (several techniques to this purpose are available in the literature, determining the generalized Chebyshev characteristic [7]–[9]); actu, , and associated ally, only the polynomials to the prototype scattering parameters and have to be evaluated. Let be the : they are pure imaginary numbers representing roots of the reflection zeros frequencies in the domain; using (1), the reflections zeros in the domain are evaluated as follows:

(5) Being also the transmission zeros defined in the do, , and can be evaluated: main, the polynomial and are generated first, the normalized polynomial from and by imposing equal to one the highest degree coefficients; following the Cameron notation [10], and are and as follows: then obtained from (6) where and is always unitary, but in the case when it assumes the value given in [10]. and are defined, the unitary of requires that Once ; the poles can be then be obtained by evaluating the roots of the above expression and by selecting those with a negative real part. The polynomial

is generated from the poles by imposing equal to one the highest degree coefficient [10]. The procedure described above allows the evaluation of the characteristic polynomials of the dual-band prototype; from these polynomials, following one of the available techniques in the literature, a canonical prototype can be synthesized (the most simple is the transversal one introduced by Cameron in [10]). Using the coupling matrix rotation technique, the prototype topology can further modified; in particular, a convenient symmetric topology applicable here is the cascade of the quadruplet sections (each introducing a pair of symmetric imaginary zeros); the technique illustrated in [11] can be employed for this topology transformation. of the seAs a final result, the normalized coupling matrix lected filter topology is obtained. For de-normalizing the prototype, a reference frequency must be defined: all the passbands and stopband limits must be geometrically symmetric around . Let us assume and are the de-normalized frequenin the normalized domain , then cies corresponding to and . From , , and , the following de-normalized parameters can then be evaluated:

(7) where are the coupling coefficients between cavities and and is the external of the first/last cavity. Using the above parameters, the practical dimensioning of the filter structure can be performed following several well-established methods available in the literature. III. DESIGN METHOD B The second synthesis method starts with the classical all-pole Chebyshev prototype of order ; as is well known, this can be represented through shunt capacitances of a unit value coupled by admittance inverters with a parameter value ( are the low-pass prototype parameters [12]). bandpass frequency transforNow the following low-pass mation is adopted for de-normalizing the prototype: (8)

where is the de-normalized radian frequency, is the normal, and are the parameters that ized frequency, and , , define the transformation. It can be observed that this transformation can be practically implemented by replacing each unit capacitance in the prototype with the dual-band resonator shown in Fig. 3. This resonator presents two parallel and one series resohaving coincident nances; a dual-band filter of order can then be realized with restransmission zeros at onators of this kind (Fig. 4). It is interesting to observe that, in this case, the response is not necessarily symmetric around the stopband; this means that the two passbands may have different widths.

MACCHIARELLA AND TAMIAZZO: DESIGN TECHNIQUES FOR DUAL-PASSBAND FILTERS

Fig. 3. Dual-band resonator obtained with the transformation (8). The parameters (! , b ) represent the radian resonant frequency and the susceptance slope parameter of the two resonators.

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Fig. 5. Scheme of the dual-band filter obtained with the design method B.

Using (11) and (12), the parameters defining the transformation ( , , ) can finally be expressed as a function of the passbands limits

Fig. 4. Schematic response for the dual-band filter employing the resonators in Fig. 3.

The four parameters that define the transformation (8) can be analytically evaluated by imposing suitable requirements. In particular, it can be assumed that the lower limits of the two , ) map to in the normalized domain , passbands ( , ) map to . Using (8) and while the upper limits ( taking into account the odd symmetry of , these conditions can be expressed as (9) Now let us consider the function whose zeros , , , ); it is possible are just the frequencies ( to represent as the ratio of two polynomials by substituting (8) for

(13) Once the above parameters are known, the dual-band resonators in Fig. 3 are also completely defined. The overall filter scheme is depicted in Fig. 5. Note that all the equivalent bandpass resonators have resonant and susceptance slope parameter , while the frequency stopband resonators (those with an apex in Fig. 5) have these and , respectively. parameters equal to Once the susceptance slope parameters of the resonators are known, the coupling coefficients required for the practical dimensioning of the filter structure can be obtained using the following well-known expressions: bandpass resonators

(10)

bandstop resonators

where The external formulas:

(14)

’s can also be evaluated using the following

(15)

IV. SYNTHESIS OF TWO TEST FILTERS For evaluating the performances of the design procedures introduced here, two dual-band filters have been designed employing these methods. (11) Now, being ( , , , ) the zeros of coefficients can also be expressed as

, the

(12)

A. Test Filter 1 The first test filter specifications are the following: • outer limits of passbands: 834 and 895 MHz; • inner limits of passbands: 849.5 and 878.67 MHz; • stopband: 851–877.12 MHz; • passband return loss (RL): 20 dB; • minimum attenuation in stopband: 35 dB. For the low-pass prototype synthesis, the frequency has been assumed as the geometric mean of the two outer passbands

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Fig. 7. Dual-band prototype response (

coefficients: P = [6:27e-3 0 1:27e-3

domain).

Polynomials

0 0 022 -5], = = Fig. 6. Asymmetrical prototype response (

domain). [1 0 3 3 0 4 32 0 2 85 0 0 998 0 0 176 0 0 012], = [0 2833 0 7535 00 4882], [1 1 039 3 845 3 019 5 529 3 211 3 77 1 544 1 278 0 335 0 205 0 0266 Polynomials coefficients: = [1 0 9869 1 1426 1 1774 0 2084 0 2663 00 0118], = [1 2 0 + 0 0123]. 0 987 3 15+2 06 2 8+3 324 1 5+3 09 0 22+1 82 00 148+0 46 ]. :

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limits MHz. Note that the inner passband limits and the stopbands limits are also geometrically symmetric with respect to . Now, applying the usual bandpass–low-pass frequency transformation, the characteristic frequencies in the normalized domain (Fig. 1) can be obtained, , . i.e., In order to satisfy the selectivity requirements, it has found that 12 poles and four zeros are required; initially the transmission zeros are uniformly displaced in the stopband, i.e., . The first step is the synthesis of the asymmetric prototype of in the domain,imposing the transformed transorder . The polynomials mission zeros , , and associated with this prototype are shown in Fig. 6 together with the corresponding frequency response. Following the guidelines given above, the polynomials , , and of the dual-band prototype are then evaluated, determining the response shown in Fig. 7 (together with the polynomials coefficients). It can be observed from Fig. 7 that the prototype response does not satisfy the attenuation requirement in the stopband (this is due to the initially assigned transmission zeros); it is, however, possible, after a few attempts, to find a suitable placement for the transmission zeros that determines an equiripple response also in the stopband. With this optimized zeros position, the polynomials , , and result with the values shown in the equation at the bottom of this page. From the above polynomials, the coupling matrix of the transversal canonical prototype is derived with the procedure described in [11]; using the matrix rotation technique, this canonical prototype is then transformed into a cascaded-blocks inline topology [11]. In the case considered here, the blocks are

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Fig. 8. Topology of the inline prototype synthesized. Each black node represents a unit capacitance; the lines are admittance inverters (coupling coefficients). Source and load have unit conductance.

represented by two quadruplets, which allow to obtain four symmetrical transmission zeros; the final filter topology is schematically represented in Fig. 8. associated The nonzero elements of the coupling matrix to the inline prototype are as shown in the first equation at the bottom of the following page. Note that, for the symmetry of the frequency characteristic, all the elements on the main diagonal are zero (synchronous resonators). of De-normalizing the prototype (7), the following values for the coupling coefficients and external ’s are finally obtained as shown in the second equation at the bottom of the following MHz. page. Note that all resonators are tuned at The response evaluated for the designed filter is reported in Fig. 9; as expected, it presents an equiripple response also in the stopband. B. Test Filter 2 For the second test filter, design method B has been employed; to put into evidence the possibility of an asymmetric response offered by this method, the following specifications have been assumed: • passband 1: 840–862 MHz; • passband 2: 888–899 MHz

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Fig. 10. Topology of the second dual-band filter synthesized. Each black node represents a passband resonator; the lines are admittance inverters (coupling coefficients).

Fig. 9. Frequency response of the dual-band filter (design method A).

• passband RL: 20 dB; • number of poles : 12. Note that the two passbands have different widths (22 and 11 MHz, respectively); note also that, in this case, the requirement on the stopband is not specified (the transmission zeros are all at the same frequency and cannot be assigned a priori). The first step in the design is the synthesis of an all-poles and dB; the inprototype of order are given by the third equation shown verter parameters at the bottom of this page. Employing (11)–(13), the parameters defining the dual-band resonators in the filter are then evaluated as follows: MHz MHz

Finally, using (14) and (15), the following de-normalized dualband filter parameters are obtained:

Main path Nonadjacent couplings

– –

Fig. 11.

Frequency response of the dual-band filter (design method B).

Fig. 10 shows the topology of the dual-band filter obtained with the second design method; the computed response is reported in Fig. 11. C. Comparisons Between the Two Design Methods The two design methods seem to determine filters with very different topologies; the filter configuration in Fig. 10 can actually be obtained even with design method A by imposing six transmission zeros all at . In fact, in this case, the topology ) degenof Fig. 8 (with three quadruplets, i.e., with erates because the couplings 2 and 3, 6 and 7, and 10 and 11 vanish after the matrix rotations of the canonical prototype. It is not possible, however, to obtain an asymmetric frequency response with design method A and, thus, the topology obtained with design method B offers greater flexibility in defining the

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Fig. 12. Fabricated dual-band test filters (the cover with the tuning screws is removed). Test filter 1 is in the upper box, while test filter 2 is in the lower box. Fig. 13.

Measured response of test filter 1 (design method A).

Fig. 14.

Measured response of test filter 2 (design method B).

two passbands at the expense of less selectivity in the stopband (for the same overall number of resonators). One can wonder if it should be possible, generally speaking, to obtain a frequency asymmetric DPBF with an equiripple response both in the passbands and stopband. As a preliminary study, we have investigated this question by performing the synthesis of the inline prototype (Fig. 8) through direct optimization; the (very preliminary) results obtained have shown that an equiripple response is possible with different width passbands only if the RL in the two passbands is different (larger in the narrower passband). However, a direct synthesis method for this kind of response has not yet been found. V. EXPERIMENTAL VERIFICATIONS For a definitive validation of the design methods for DPBFs introduced here, the two test filters designed above have actually been fabricated using multiple-coupled coaxial resonators. The coaxial cavities have a square external cross section; the inner conductor (short circuited at one end) has a circular cross section. The relevant dimensions are as follows: • cavity width: 40 mm; • cavity height: 60 mm; • inner conductor diameter: 13 mm; • inner conductor length: 57.5 mm. Note that the length of the inner conductor is approximately , then a capacitive susceptance is required for obtaining the resonance (it is realized partly with the cover of the cavity and partly with a tuning screw). The positive couplings are realized by removing part of the common wall of the coupled (adjacent) cavities; capacitive probes are used for the negative couplings. The input (output) coupling to the first (last) resonator is obtained with a tap in the inner conductor of the cavity (the taps distances from the short circuit are determined by imposing the required external ’s). All the couplings have been dimensioned using the even/odd resonance frequencies technique (finite-element commercial software has been employed for this purpose). Fig. 12 presents a photograph of the fabricated structure without cover and tuning screws; the two filters have been realized in a single box, sharing a sidewall (the upper structure is test filter 1 and the lower one is test filter 2). This photograph clearly shows how the negative (capacitive) couplings in filter

1 have been realized; the input/output couplings through taps in the first/last resonators can also be observed. Figs. 13 and 14 report the measured response (attenuation and return loss) of the two fabricated and tuned filters. It can be immediately observed that the measured responses are very similar to the theoretical curves obtained in Section IV (Figs. 9 and 11); the small differences are partly due to very critical requirements (i.e., small transition bandwidths, particularly for the test filter 1) and partly due to the tuning process, which is not yet well established for these kinds of filters. In any case, the measured responses clearly indicate the effectiveness of the dual-band design procedures introduced here.

VI. CONCLUSION This paper has focused on the design of microwave filters that present two passbands separated by one stopband (filters with these frequency characteristics are becoming of particular interest in base stations for mobile communications). Two original methods for designing these kinds of filters have been introduced. The first method allows to obtain a geometrically symmetric frequency characteristic (around a frequency in the stopband) with an arbitrary number of transmission zeros suitably displaced in the stopband; with the second method, two passbands with different widths can be obtained, while the stopband transmission zeros all placed at the same is determined by frequency ( being the order of the filter).

MACCHIARELLA AND TAMIAZZO: DESIGN TECHNIQUES FOR DUAL-PASSBAND FILTERS

The proposed design methods have been successfully tested through the design and fabrication of two filters employing multiple-coupled coaxial cavities with capacitive loading. ACKNOWLEDGMENT The authors thank G. Ronco and A. Dell’Orto, both of Forem (an Andrew Company), Agrate Brianza, Italy, for performing the tuning of the test filters. REFERENCES [1] R. Levy, “Generalized rational function approximation in finite intervals using Zolotarev functions,” IEEE Trans. Microw. Theory Tech., vol. MTT-18, no. 12, pp. 1052–1064, Dec. 1970. [2] H. C. Bell, “Zolotarev bandpass filters,” in IEEE MTT-S Int. Microwave Symp. Dig., Phoenix, AZ, May 2001, pp. 1495–1498. [3] J. Lee, M. S. Uhm, and I. B. Yom, “A dual-passband filter of canonical structure for satellite applications,” IEEE Microw. Wireless Compon. Lett., vol. 14, no. 6, pp. 271–273, Jun. 2004. [4] S. Holme, “Multiple passband filters for satellite applications,” in Proc. 20th AIAA Int. Communications Satellite Systems Conf. and Exhibit, Montreal, QC, Canada, May 2002, pp. 1993–1996. [5] L. C. Tsai and C. W. Hsue, “Dual-band bandpass filters using equallength coupled-serial-shunted lines and -transform technique,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 4, pp. 1111–1117, Apr. 2004. [6] G. Macchiarella and S. Tamiazzo, “A design technique for symmetric dual-band filters,” presented at the IEEE MTT-S Int. Microwave Symp., Long Beach, CA, Jun. 2005. [7] R. J. Cameron, “General coupling matrix synthesis methods for Chebyshev filtering functions,” IEEE Trans. Microw. Theory Tech., vol. 47, no. 4, pp. 433–442, Apr. 1999. [8] G. Macchiarella, “Accurate synthesis of in-line prototype filters using cascaded triplet and quadruplet sections,” IEEE Trans. Microw. Theory Tech., vol. 50, no. 7, pp. 1779–1783, Jul. 2002. [9] S. Amari, “Synthesis of cross-coupled resonator filters using an analytical gradient-based optimization technique,” IEEE Trans. Microw. Theory Tech., vol. 48, no. 9, pp. 1559–1564, Sep. 2000. [10] R. J. Cameron, “Advanced coupling matrix synthesis techniques for microwave filters,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 1, pp. 1–10, Jan. 2003.

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[11] S. Tamiazzo and G. Macchiarella, “An analytical technique for the synthesis of cascaded -tuplets cross-coupled resonators microwave filters using matrix rotations,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 5, pp. 1693–1698, May 2005. [12] G. Matthaei, L. Young, and E. M. T. Jones, Microwave Filter, Impedance-Matching Networks, and Coupling Structures. Norwood, MA: Artech House, 1980, ch. 4. [13] C. Quendo, E. Rius, and C. Person, “Narrow bandpass filters using dualbehavior resonators,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 3, pp. 734–743, Mar. 2003.

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Giuseppe Macchiarella (M’88) was born in Milan, Italy, in 1952. He received the Laurea degree in electronic engineering from the Politecnico di Milano, Milan, Italy, in 1975. From 1977 to 1987, he was a Researcher with the National Research Council of Italy, where he was involved in studies on microwave propagation. In 1987, he became an Associate Professor of microwave engineering with the Dipartimento di Elettronica e Informazione, Politecnico di Milano. He is also the Scientific Coordinator of the PoliEri Laboratory, a monolithic microwave integrated circuit (MMIC) research laboratory, which is jointly supported by the Politecnico di Milano and Ericsson Lab Italy. His current research concerns the field of microwave circuits with special emphasis on microwave filters synthesis and power-amplifier linearization. He has authored or coauthored over 80 papers and conference presentations.

Stefano Tamiazzo received the Laurea degree in telecommunication engineering from the Politecnico di Milano, Milan, Italy, in 2002, and the Master degree in information technology from Cefriel, Milan, Italy, in 2003. He is currently with Forem (an Andrew Company), Agrate Brianza, Italy, where he is involved in the design of microwave filters and combiners for wireless applications.

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On the Derivation of Coupled-Line Models From EM Simulators and Application to MoM Analysis Marco Farina, Member, IEEE, Antonio Morini, and Tullio Rozzi, Fellow, IEEE

Abstract—This paper addresses the problem of deriving an actual coupled-line model from the “spot frequency” characteristics of transmission media derived by means of a numerical electromagnetic simulator. For a given set of coupled lines, possibly asymmetric and lossy, one of the main issues is to recover a model whose parameters are physically and practically meaningful. In order to satisfy the requirements, the model ought to basically yield a natmodes for ural generalization of the well-known even/odd and couples of lines, and collapse to a set of uncoupled lines when coupling is negligible. Hence, part of this study is devoted to discussing and evaluating models that satisfy such requirements. The end result is a Weissfloch-type equivalent circuit made up of uncoupled lines and input and output ideal transformers. The algorithm is then applied to the network parameters of coupled lines. The latter are evaluated by a full-wave method of moments approach, and a subsequent short-open calibration (SOC) procedure. Finally, a new algorithm is introduced that is able to evaluate and remove the contribution of the naked discontinuity due to ports, usually not directly available from the SOC routine. Index Terms—Calibration, coupled lines, method of moments (MoM).

I. INTRODUCTION

T

HE PROBLEM of the analysis of coupled lines occurs in a number of cases, spanning from signal integrity problems in digital electronics to RF and microwave circuits. In this framework, it is a compelling issue, actively investigated by most computer-aided engineering (CAE) producers. The model produced by an electromagnetic (EM)—namely, a “full-wave”—analysis is a “spot-frequency” network representation, often a - or an -matrix, regardless of the internal structure of the device being simulated, knowledge of which is, in fact, lost. Our aim is to process such a matrix in order to recover a coupled-line model, which more closely represents our actual “device-under-test” (DUT). This task is performed by using a so-called modal decoupling technique. The modal decoupling technique is a powerful approach widely employed both in circuit theory and EM analysis under several forms. In circuit theory, it has been used for more than three decades in order to analyze problems involving multiconductor transmission lines [1]–[3]. In particular, a number of authors have applied it to solve problems in the time and frequency domains, and some of them Manuscript received March 1, 2005; revised July 7, 2005. The authors are with the Dipartimento di Elettromagnetismo e Bioingegneria, Università Politecnica delle Marche, Ancona 60131, Italy (e-mail: [email protected]). Digital Object Identifier 10.1109/TMTT.2005.857125

(e.g., [4] and [5]) have exploited modal decomposition to develop SPICE-compatible models of coupled lines. Modal decomposition gives origin to a natural generalization of the even/odd-mode decomposition for pairs of symmetric lines, while encompassing the - and -mode decomposition for asymmetric line pairs. Hence, the latter are just special cases of the more general theory, carefully reviewed in [6]. In almost all of the above references, the problem may be formulated as follows: given the impedance and admittance matrices per unit length, telegrapher’s equations are investigated with the purpose of deriving a modal description of the solution. The modal description is subsequently manipulated, e.g., aiming to a SPICE model derivation. Our current study addresses the problem from a slightly different perspective in which those matrices are not known, and it reconsiders in depth the concepts outlined in [7]. As stated above, the problem typically arises when using a three-dimensional (3-D) EM solver in order to derive the response of a coupled-line circuit. In fact, once the analysis of a section of coupled lines is performed by means of the EM solver, be it either 3-D or two-and-one-half-dimensional (2.5-D), the result is a set of “spot-frequency” network parameters describing the behavior of the circuit at its ports. Note that although the actual topology of the lines may be quite complicated, involving complex substrates and exotic cross-sectional geometries, the overall network description is nonetheless obtained regardless of the “coupled-line” nature of the analyzed circuit. Our aim is to recover a coupled-line description starting from such network parameters, while clarifying some concepts that appeared in different contexts in the literature. Such a description has to be physically and practically meaningful: it ought to be a natural generalization of even/odd- and -mode concepts widely used for couples of lines, and it should collapse to a group of uncoupled lines described by the standard parameters when coupling is negligible. Those requirements make the algorithm suitable for implementation in almost any full-wave CAE tool. In order to be more concrete about the last statement, let us consider a simple yet practical problem that could arise when designing and simulating a circuit in a commercial tool (e.g., Microwave Office from AWR, El Segundo, CA, or em from Sonnet Software, Syracuse, NY, or many others). Let us imagine that we have designed two strongly coupled lines used, for example, in order to build a 3-dB hybrid, and nearby, not close, but parallel to, the coupled pair, an additional single line. In this context, we are interested in evaluating the even- and odd-mode

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FARINA et al.: ON THE DERIVATION OF COUPLED-LINE MODELS FROM EM SIMULATORS AND APPLICATION TO MoM ANALYSIS

characteristic impedances for the coupled lines and the standard characteristic impedance for the line alone, but most—if not every—software package will not provide any information. As matter of fact, it will likely provide data only when a single line is present—evaluating propagation constant and characteristic impedance—as in this case, those quantities are unambiguously defined. An algorithm complying with the requirements listed above, and described in Section II, allows circumventing such a limitation. The starting point is the powerful decomposition introduced in [1] in a different framework, generalized here to the case of lossy lines. The proposed idea is applied in particular (but it is not limited) to a method of moments (MoM) approach, which is able to handle structures with multiple conductors and conductor and dielectric losses while accounting for conductor thickness. In this application, a short-open calibration (SOC) algorithm developed by the authors in [8] is used in order to remove the effect of ports, needed for the deterministic 3-D analysis, and part of the feeding lines. An interesting point is that the error network, accounting for port discontinuities, as well as for part of the feeding lines, is available as a by-product. The error network is, however, defined without any assumption about its topology. In a recent letter [9], it has been highlighted that SOC would be more attractive if able to produce explicit information about the shear port discontinuity and the characteristic parameters of the feeding lines. Hence, in this study, it is shown how to perform this preliminary step, namely, to recover network parameters of the coupled lines starting from the error network. The theory discussed in Section II is then applied with a view to recovering a coupled-line model. In this context, a Weissfloch-type decoupled-line model fed by input and output ideal transformers is derived. Remarkably, a completely similar problem linking the calibration issues with the problem of calculating parameters of coupled lines is encountered in the measurement process (see, e.g., [10]). Hence, the same approach may be used in an experimental framework. Finally, the sensitivity issue is addressed by investigating the “optimal” conditions in which to apply the whole algorithm.

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Fig. 1. Coupled lines and reference system.

respect to and by substituting the first in the second and viceversa, one obtains

(2) The solution of (2) is straightforward, namely, omitting the frequency dependence for the sake of simplicity [11] as follows:

(3) where

is the characteristic admittance matrix (4)

while and are constant vectors to be obtained by imposing boundary conditions, which is in analogy to what is done for a standard single line. Note that, in this case, the characteristic admittance matrix is the image admittance matrix of the system, namely, the matrix “seen” at any section of the set of coupled lines, once they are terminated on it. In fact, for a given length of a set of lines, if , namely, it is terminated on (5) one obtains

II. THEORY

and, consequently, (6)

The incremental section of a general set of isotropic coupled lines is represented by a series impedance matrix and a shunt admittance matrix per unit length (see, e.g., [11]); both matrices are symmetric owing to reciprocity. The telegrapher’s equations in the frequency domain are (Fig. 1)

Let us now define

(7)

(1)

according to the notation used in [8]; in this case, the whole admittance matrix describing a finite section of coupled lines is indicated as

and are voltage and current vectors at where section . By differentiating each of the equations of (1) with

(8)

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In writing the above expression, we have exploited the symin metry of the structure with respect to the plane Fig. 1. Such a symmetry holds for any isotropic and uniform set are also individually symmetric of coupled lines. Blocks blocks are symmetric as a conseby virtue of reciprocity. . quence of the symmetry with respect to plane Matrix (8) is what we obtain as output of a 3-D (or 2.5-D) fullwave EM simulation of a section of line after port discontinuities are suitably deembedded or from a measurement process. Incidentally, the theory is developed using admittance matrices, as they are the primitive quantities calculated by most MoM solvers dedicated to the analysis of planar and quasi-planar circuits. , in particular, relates by definition and when , namely, when all terminals of the coupled lines at are shorted to ground. In the MoM framework, this condition is achieved by means of perfect electric conducting (PEC) walls obtained either by physically imposing PEC boundary conditions (e.g., ports in shielded structures) or by exploiting symmetries (e.g., by using odd excitations, one obtains a PEC condition in the symmetry plane. This is done for example in the SOC algorithm). so that by using (3)–(8), Under these conditions, one obtains

Evaluation of the matrix function on right-hand side of in (15)—as well as the square root needed to evaluate (14)—requires the eigenvalues and eigenvectors of said matrices. Hence, if an eigenvalue decomposition is applied to the argument

(9)

(17)

(10) relates

where

is a diagonal matrix whose elements are the eigenvalues of the matrix on the left-hand is a matrix whose columns are the corresponding side, and eigenvectors, the inverse of the hyperbolic cosine in (15) has to . be evaluated for each of the eigenvalues of It is noted that, from a purely mathematical standpoint, diagonalization (16) is possible only when the geometrical multiequals their plicity of the eigenvalues of the matrix algebraic multiplicity. In principle, such a condition is not satisfied a priori, however, as will be discussed below, due to their specific physical meaning, eigenvectors of (16) are independent and span the whole space even when associated to the same eigenvalue. In fact, we can look at a canonical representation of the solutions of (2), namely, by using a spectral decomposition. We dependence seek solutions of (2) having a so that the first equation of (2) gives

; hence,

and the term in square brackets is just

On the other hand, Under these conditions,

(16)

and

when

.

(11)

For each eigenvalue , one obtains a distribution of voltages and currents flowing in the conductors and ; for -coupled lines (plus ground), one obtains n-independent modes. This occurs even when they correspond to same (degenerate) eigenvalues, such as in a standard TEM structure. The modes are, in fact, a complete basis for the telegrapher’s equations. The terminal voltages and currents at any section may be expressed as a linear superposition of these independent vectors

Hence, by some manipulations of (3) and (11), one obtains (12) It is worth noting that all the above exponential functions have the same matrix argument so that they share the same eigenvectors. As a consequence, they are fully commutative and simplification of the exponential terms is possible. Hence, (12) yields (13) By combining (10) and (13), one obtains

(14) so that (15)

(18) and are unknown excitation amplitudes fixed by where the boundary conditions. For a given section of line of length , their elimination yields the overall admittance matrix appearing in (8), e.g., as done in [12]. Hence, (18) is a representation alternative to (3) of the total voltages and currents in which the contribution of each single mode is made explicit. As an additional note, to any eigenvalue of the matrix may be added , where is any integer number, and the resulting matrix will still be a solution of (15). In the general case, the ambiguity of cannot be removed easily, unless we introduce some additional hypotheses or “measurements.” In the special lossless case, we can use the known physical bounds over the effective permittivity of each mode in order to set correctly. Generally, an optimal can be selected, as will be discussed in Section III.

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Incidentally, note also that the left-hand side of (14) bears a resemblance to the well-known scalar expression for the image admittance matrix. Note also that, according to (15) and (16), (19) Our main goal is to obtain the modal characteristic parameters starting from the total admittance matrix of a section of line, but comparing (17) and (19), it appears that (20) Hence, by knowing and in (8), we have been able to evaluate the propagation constants for each mode of the coupled lines. A further step consists of extracting some suitable informa, which is tion from the characteristic admittance matrix available from (14). In fact, the modal expansion (18) gives voltages and currents of modes appearing with a modal distribution of voltages and currents across the -conductors. For a given mode , each voltage is generally related to any of the currents, namely, the and is nondiagonal. As a matter of fact, matrix relating is also generally nondiagonal. However, a set of coupled lines may be described as a set of uncoupled lines, fed and terminated by a transformer network [1], [4], namely, a set of “congruence transformers” [1]. This description looks extremely attractive, being a natural generalization of the even/odd-mode concept to the general nonsymmetric case. For the sake of the clarity, it is stressed here that the even/odd-mode concept refers to the mode propagating along the coupled lines; the symmetry plane concerned is parallel to the -axis. In the remainder of this paper, we are going to generalize results introduced in [1] to the general lossy case in the framework of the above discussion. It is worth noting that what we are going to introduce may also be considered a generalization of Weissfloch’ theorem, stating that any lossless reciprocal two-port may be described as a section of line embedded between two transformers (see, e.g., [11]). However, Weissfloch’ theorem for a two-port network is only valid at a spot frequency; in our case, due to the underlying physical identity between the system being described and a set of coupled lines, the extracted model is valid over a whole range of frequencies. By using symbols similar to those adopted in [1], we can build a symmetric matrix involving and and diagonalize it (note, in fact, that while and are both complex symmetric matrices due to reciprocity, their product generally is not) as follows:

Fig. 2. Decomposition of a set of n-coupled lines in n-uncoupled lines plus ideal transformers.

possible for practical low-loss structures, where the effect of losses is not dominant. In the particular, but noteworthy case of commuting and , (21) becomes identical to (19) for which diagonalization by eigenvectors is guaranteed owing to physical reasons, as discussed after (16)—regardless of the complex nature of the matrices involved. This, again, is strong evidence in support of our conjecture. Note also that because of the symmetry of the left-hand side of (21), if decomposition (21) does exist, it is always possible to by a diagonal matrix and define a in such right multiply a way that [13] (22) In fact, it can be shown that, if the columns of eigenvectors of a symmetric complex matrix, onal matrix and

are the is a diag-

(23) satisfies (22). is still an eigenvector matrix for (21), as we have only right multiplied an eigenvector matrix by a diagonal matrix. Hence, (21) may be rewritten as (24) We can now introduce a suitable change of basis (see Fig. 2) from to and from to as follows:

(25) (21) From a mathematical point-of-view, one should observe that, when and are complex, there is no guarantee that diagonalization (21) is even possible [13]. However, from a physical standpoint, complex symmetric matrices arise as the effect of losses, and diagonalization (21) does exist in the limiting lossless case. Hence, we can conjecture that decomposition (21) is

Here, defines a congruence transformer network. Note that the relationship between the two expressions of (25) ensures that power is conserved in the transformation. In particular, one can verify that by selecting (26)

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telegrapher’s equations (1) become decoupled in the being

domain

identifying (35) with (26). In fact, by substituting (35) in (26), one obtains (36)

(27) since, thanks to (24) and (26), matrices relating and in (27) are diagonal. In (26), are, thus far, convenient, but arbitrary are the propagation constants along the admittances, while decoupled lines. At this point, the characteristic impedance for and is also diagonal being

Hence, are the eigenvalues of . This fact suggests selecting according to such relationship with the eigenvalues of ; this way, the standard definition of the even and odd modes is recovered in the algorithm as the natural limit case of symmetric lines. Such a choice complies with all the requirements listed in Section I and looks suitable for implementation in commercial full-wave packages. III. SENSITIVITY ANALYSIS

(28) and involving all diagonal matrices, while the propagation constants are given by (29) Note also that (25) implies (30) Several remarks are now in order. The first one is that the above decomposition is not unique. This is apparent considering that are arbitrary, reflecting the fact that an eigenvector matrix, such as , may be right multiplied by an arbitrary diagonal matrix and still be an eigenvector matrix of the original problem. The second important remark is that in (21) are generally not in (18) and (20). In fact, the left-hand-side expresequal to sion of (21) may be expressed as

The set of relationships derived in Section II will be used in the context of MoM analysis, while also being suitable for an experimental measurement process. In both cases, numerical errors or noise will affect the overall admittance matrix of the multiconductor line or any of its alternative representations. In this context, it is relevant to evaluate the sensitivity of the parameters in order to verify the existence of an optimal length of the line section. Let us consider relationships (10) and (13), linking the blocks of the “measured” -matrix to the length of the section . It is possible to estimate the sensitivity of such blocks, normalized with respect to the characteristic admittance matrix , in terms of their derivatives with respect to as follows:

(31) or, by substituting decomposition (19),

(37) (32)

In comparison with (21), it appears that if (33) (38)

then (34) and become equal to the modal . This condition is satisfied commute so that they share the same eigenvector if and is symmetric, while and are basis. This happens if individually symmetric matrices. With complex symmetric, can be suitably normalized so as to its eigenvector matrix satisfy (33). This property is satisfied in a noteworthy case, namely, that of two symmetric coupled lines since, in this case, we can choose directly

A positive number that is often used in order to express sensitivity is the uniform norm of the above matrices (39) In our case,

(35) Now, in fact, and share the same eigenvectors as so that, according to (30), the characteristic impedances of the decoupled lines—namely, the values in —are the eigenvalues of . Apparently, choice (35) is completely independent from the allows transformation (26). Actually, a proper selection of

(40)

FARINA et al.: ON THE DERIVATION OF COUPLED-LINE MODELS FROM EM SIMULATORS AND APPLICATION TO MoM ANALYSIS

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TABLE I ERROR AS FUNCTION OF LINE LENGTH FOR TWO IDEAL COUPLED STRIPLINES

(41)

Now, considering that

, the following results:

Fig. 3. General deembedding problem for the MoM, as discussed in [8].

(42) In the lossless case is maximum, i.e., when

, the minimum occurs when (42)

(43) according to (41). Hence, (43) indicates that the first optimal length is approximately a quarter-wavelength. Table I shows an example of this. We have calculated the -parameters for a section of two ideal coupled striplines suspended in air (for which the solution is known analytically) and added a uniformly random error; the error is selected to be within 1/100 of the Euclidean norm of the matrix. The relative error is the “measured” deviation (percentage) from the expected value of the effective permittivity, namely, 1, for one of the two modes. Due to the random nature of the test, different measurements produce different results, but basically worst measurements always appear to result for quite short lines and for those close to a half-wavelength. IV. APPLICATION TO MOM ANALYSIS In [8], we introduced a calibration procedure aimed at deembedding results evaluated by MoM approaches, either 2.5-D and 3-D, by way of removing the effect of discontinuities arising as a consequence of port definition. In that procedure, the analysis of the DUT, including ports and feeding lines, was complemented by the additional analysis of a structure involving the feeding lines and ports alone, namely, a standard structure. Ports actually were grouped according to their position in the box (left, right, top, and bottom box walls), being possibly coupled, and for each group, a standard was built and analyzed. Once the result of this analysis is duly “subtracted” from the response of the DUT, the desired net or calibrated response remains, thus removing the effects of port discontinuity and of

Fig. 4.

Assumed topology for the error network.

part of the feeding lines, possibly coupled. For the sake of completeness, the general calibration problem, as discussed in [8], is reported in Fig. 3. In [8], no assumption was made about the topology of the error network, providing a powerful and general calibration approach. However, in this way, it was not possible to calibrate out only the port effects, i.e., to have reference planes coincident with the port planes, as the naked port discontinuities were not directly available from the calibration procedure. Actually, the reference planes may be translated to the location of the ports by using a simple procedure described in the following without any need for further analysis. To this aim, we need to make some hypotheses about the topology of the error networks, exploiting our information about their origin. They are assumed to be the result of two cascaded networks, and a section of coupled lines namely, a port discontinuity described by (Fig. 4). has the block structure described by (8). The topology in Fig. 4 allows to deduce the relationships re, and malating the admittance matrix of the error network trices and . In fact, the following relationships hold:

(44)

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Fig. 5. General topology for the error network: suitable for excitation schemes not assuming PEC-backed delta-gap generators.

Fig. 6. Topology for the error network evaluated by a double-length standard.

Consequently the

-matrix for the “naked” discontinuity is (45)

In order to remove the port discontinuity alone and, thus, make available the response at the port reference plane, one only in the raw simulation, which includes needs to introduce an error network plus a DUT. As a by-product, a “clean” matrix (8) of the section of coupled lines is available, and the procedure developed in Section II may be used to deduce its characteristic parameters. In the more general case, where the port discontinuities cannot be assumed to simply contribute as a shunt admittance -port network — being matrix, we need a complete the number of coupled lines—in order to completely represent the naked discontinuity, as shown in Fig. 5. This happens, for example, if the SOC is applied to unshielded structures, where a different excitation scheme is needed. Of course, the number of unknown parameters is now doubled, and an additional standard is needed. A suitable standard is described in Fig. 6, being identical to the previous one, but where lines have double lengths: in this ’ is constituted by the same port case, the new error network cascaded with twice the line section. discontinuity , The next step is to evaluate a “correction block” from and exnamely, by changing the sign of the elements of changing even and odd ports (namely, left and right ports), as described in [8]. If we connect the correction block on the left-hand ’ in Fig. 6, the port discontinuity and the first secside of are cancelled out, leaving out only the desired tion of line section of line. Hence, cascading the correction block to the ad’ directly provides the calibrated line ditional error network parameters. V. EXAMPLES The most significant examples are the ones for which the exact solution is known, as indicated in [14]. Hence, according to [14], a section of two symmetric coupled striplines is analyzed by the MoM approach, and its odd and even characteristic impedances are calculated following the procedure introduced

Fig. 7. Comparison between theory and results from EmSight from AWR: S -parameters for two coupled striplines (see text for parameters). Calibration performed at the port plane (only the discontinuity due to the ports was removed).

in Section II. The section is 5-mm long; the two strips are 1-mm wide, spaced 1 mm. The distance from both grounds is 1.5 mm—so that the inter-ground spacing is 3 mm—and the dielectric relative permittivity is 3. Fig. 7 compares results obtained by the procedure described in Section IV, namely, by applying the SOC and subtracting the naked port discontinuity alone, and those obtained by using EmSight from AWR. Results are nearly indistinguishable, and both are indistinguishable from the analytic results (not reported). In both cases, the precision is controlled by the quality of the mesh. Once the pure port discontinuity is calculated, the “clean” -parameters for the feeding lines are available from the calibration itself, regardless of the DUT, and may be used in order to directly calculate their characteristic parameters. All results in the following are directly derived from the error network, and they are consequently sensitive to the way we decouple line and port contributions in the error network.

FARINA et al.: ON THE DERIVATION OF COUPLED-LINE MODELS FROM EM SIMULATORS AND APPLICATION TO MoM ANALYSIS

Fig. 8. Effective permittivity for the modes of two coupled striplines (see text for parameters) calculated by (15).

The structure supports two pure TEM modes; hence, the effective permittivity, calculated according to (15), should be 3 for both modes; Fig. 8 shows results obtained in our case. It should be noted that, owing to the standard used during calibration, there is an additional effect not accounted for in the sensitivity analysis of Section III, but playing a role in the precision obtainable from this calculation. In fact, if the calibration standard is too short with respect to the wavelength, direct coupling between the ports on the opposite side of the structure may be significant regardless of the presence of the lines (e.g., in Fig. 4, ports 1 and 2 may direct couple to ports 3 and 4). The consequence is that the error network deriving from the calibration procedure [8] may not be sufficiently accurate. In any case, indications coming from (43) do not conflict with such an additional requirement on the standard. Along with , (14) provides the characteristic admittance . According to what has been discussed in Section II matrix diagonalize any for two symmetric lines, eigenvectors of , of the significant immittance matrices and its eigenvalues coincide with the characteristic admittances of the even and odd modes. Fig. 9 shows a comparison between the eigenvalues of and the characteristic impedances analytically calculated. The above examples discuss lossless cases, while one of our purposes here is to check the validity for the general lossy case. The main difficulty with lossy cases is to select structures for which analytical results are known. The solution is to build an analytical example for which the result is exactly defined. Fig. 10 describes two strongly coupled copper coaxial cables, embedded in a very lossy dielectric . The example is also interesting, as it does not describe a planar device. Moreover, it is addressed by a finite-element approach instead of a MoM: this fact highlights how theory of Section II may be applied to a very large class of problem. In fact, such a device is analyzed by splitting the structure in two substructures, both involving just one conductor and both simulated by Ansoft HFSS, the first one obtained by replacing

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Fig. 9. Comparison between analytical and calculated characteristic impedances for the even and odd modes in a stripline (see text for parameters).

Fig. 10.

Coupled coaxial cables in lossy dielectric (" = 2; tan  = 0:5).

the longitudinal symmetry plane by a perfect magnetic conducting (PMC) wall, and the second exploiting a PEC wall in the same position. Obviously, the first substructure models an even mode propagating across the whole DUT, while the second one describes an odd mode. After simulating both structures, the characteristic impedances are rigorously evaluated (even and odd, respectively), simply being the image impedances for each of the two-ports. These impedances will be our “analytical” reference below. In fact, the full four-port response is recovered by suitably superimposing the results from the two substructures and are two-port network owing to the symmetry. If and parameters for the even- and odd-mode simulations, for the four-port are

for

(46)

where if if At this point, we can evaluate by (14), and according to the , theory of Section II, we derive the complex eigenvalues of to be compared with the analytical reference. Fig. 11 shows such

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[6] G. T. Lei, G. W. Pan, and B. K. Gilbert, “Examination, clarification, and simplification of modal decoupling method for multiconductor transmission lines,” IEEE Trans. Microw. Theory Tech., vol. 43, no. 9, pp. 2090–2100, Sep. 1995. [7] M. Farina, A. Morini, and T. Rozzi, “On the definition and the derivation of the characteristic parameters for coupled lines, and its application to MoM analysis,” presented at the IEEE MTT-S Int. Microwave Symp., 2005. [8] M. Farina and T. Rozzi, “A short-open de-embedding technique for method of moments based electromagnetic analyses,” IEEE Trans. Microw. Theory Tech., vol. 49, no. 4, pp. 624–628, Apr. 2001. [9] J. C. Rautio, “On deembedding of port discontinuities in full-wave CAD models of multiport circuits,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 10, pp. 2448–2449, Oct. 2004. [10] T. M. Winkel, L. S. Dutta, and H. Grabinski, “An accurate determination of the characteristic impedance matrix of coupled symmetric lines on chips, based on high-frequency S -parameters measurements,” in IEEE MTT-S Int. Microwave Symp. Dig., 1997, pp. 1769–1772. [11] G. C. Corazza, Fondamenti di Campi Elettromagnetici e Circuiti. Bologna, Italy: Casa Editrice Patron, 1973. [12] W. Heinrich and H. Hartnagel, “Wave propagation on MESFET electrodes and its influence on transistor gain,” IEEE Trans. Microw. Theory Tech., vol. MTT-35, no. 1, pp. 1–8, Jan. 1987. [13] R. A. Horn and C. R. Johnson, Matrix Analysis. Cambridge, U.K.: Cambridge Univ. Press, 1985. [14] J. C. Rautio, “An ultrahigh precision benchmark for validation of planar electromagnetic analyses,” IEEE Trans. Microw. Theory Tech., vol. 42, no. 11, pp. 2046–2050, Nov. 1994.

Fig. 11. Comparison between characteristic impedances evaluated according to Section II and the analytical ones (see text) for the two coupled lossy coaxial cables.

a comparison, for both even and odd modes, real and imaginary part, highlighting a perfect coincidence with the expected results. VI. CONCLUSION In this paper, we have shown how to recover information about the feeding lines and the port discontinuity from a SOC procedure, particularly as applied to the MoM. In this framework, definition and derivation of the characteristic parameters for coupled, possibly lossy, lines have been discussed. REFERENCES [1] F. Y. Chang, “Transient analysis of lossless coupled transmission lines,” IEEE Trans. Microw. Theory Tech., vol. MTT-18, no. 9, pp. 616–626, Sep. 1970. [2] K. D. Marx, “Propagation modes, equivalent circuits and characteristic terminations for multiconductor transmission lines with inhomogeneous dielectrics,” IEEE Trans. Microw. Theory Tech., vol. MTT-21, no. 7, pp. 450–457, Jul. 1973. [3] C. R. Paul, “On uniform multimode transmission lines,” IEEE Trans. Microw. Theory Tech., vol. MTT-21, no. 8, pp. 556–558, Aug. 1973. [4] F. Romeo and M. Santomauro, “Time-domain simulation of n coupled transmission lines,” IEEE Trans. Microw. Theory Tech., vol. MTT-35, no. 2, pp. 131–136, Feb. 1987. [5] A. R. Djordjevic, “SPICE-compatible models for multiconductor transmission lines in Laplace transform,” IEEE Trans. Microw. Theory Tech., vol. 45, no. 5, pp. 569–579, May 1997.

Marco Farina (M’98) received the M. Eng. (summa cum laude) degree in electronics and Ph.D. degree from the University of Ancona, Ancona, Italy, in 1990 and 1995, respectively. From 1991 to 1992, he was a Technical Officer in the Italian Army. Since 1992, he has been with the Department of Electromagnetics and Bioengineering, University of Ancona, where he is an Assistant Professor. In 2002, he became an Associate Professor. He is also a Consulting Engineer in electronics. He coauthored Advanced Electromagnetic Analysis of Passive and Active Planar Structures (London, U.K.: IEE Press, 1999). He has developed the full-wave software package for 3-D structures EM3DS. Antonio Morini received the Laurea degree (summa cum laude) in electronics and Ph.D. degree in electromagnetism from the University of Ancona, Ancona, Italy, in 1987 and 1992, respectively. He is currently an Associate Professor of electromagnetism and microwaves with the Università Politecnica delle Marche, Ancona, Italy. His research is mainly devoted to the modeling and design of passive millimetric components, such as filters, multiplexers, and antennas. Tullio Rozzi (M’66–SM’74–F’90) received the Dottore degree in physics from the University of Pisa, Pisa, Italy, in 1965, the Ph.D. degree in electronic engineering from The University of Leeds, Leeds, U.K., in 1968, and the D.Sc. degree from the University of Bath, Bath, U.K., in 1987. From 1968 to 1978, he was a Research Scientist with Philips Research Laboratories, Eindhoven, The Netherlands. In 1975, he spent one year with the Antenna Laboratory, University of Illinois at Urbana–Champaign. In 1978, he became the Chair of Electrical Engineering with the University of Liverpool. In 1981, he became the Chair of Electronics and Head of the Electronics Group, University of Bath, where he was also the Head of the School of Electrical Engineering on an alternate three-year basis. Since 1988, he has been a Professor with the Dipartimento di Elettromagnetismo e Bioingegneria, Università Politecnica delle Marche, Ancona, Italy, where he is also Head of the department. Dr. Rozzi was the recipient of the 1975 Microwave Prize presented by the IEEE Microwave Theory and Technique Society (IEEE MTT-S).

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Attenuation Characteristics of Coplanar Waveguides at Subterahertz Frequencies Jingjing Zhang, Student Member, IEEE, Sotiris Alexandrou, and Thomas Y. Hsiang, Senior Member, IEEE

Abstract—We present experimental and simulation data of subterahertz attenuation of coplanar waveguides (CPWs) with wide and narrow ground planes. Experimental data are obtained by using a subpicosecond measurement technique based on electrooptic sampling. While time-domain data qualitatively describe the attenuation characteristics, they are converted to the frequency domain by a Fourier transform to give a quantitative interpretation. Simulation data are obtained by full-wave analysis and compared with the experimental results. It is shown that the simulation results consistently agree with experimental results. Furthermore, in the case of CPWs with wide ground planes, both of them are consistent with analytical theory. While CPWs with narrow ground planes have not been analytically studied, our results show that they suffer considerably lower attenuation, which we attribute to a reduced coupling between the CPW mode and substrate modes. The effects of ground-plane width and line dimensions on the attenuation characteristics are discussed in detail. Index Terms—Attenuation, coplanar waveguides (CPWs), electromagnetic radiation effects, microwave propagation.

I. INTRODUCTION

C

OPLANAR waveguides (CPWs) are used extensively in ultrafast devices and circuits and their characteristics have been well studied. In particular, the attenuation at high frequencies up to subterahertz has become an essential topic for the design of practical devices and circuits. Since Grischkowsky et al. [1] experimentally demonstrated that the radiation loss dominates over 200 GHz for a 5- m coplanar transmission line, many of the subsequent studies have outlined the subterahertz attenuation characteristics of CPWs theoretically and/or experimentally [2]–[4]. However, most of the research thus far have been conducted on CPWs with wide ground planes. Although CPWs with narrow ground planes provide important advantages for microwave applications such as its flexibility and low parasitics, they have not been sufficiently analyzed. Schnieder et al.. [5] have derived analytic formulas to model the radiation loss of conductor-backed CPW with narrow ground planes. However, their results were not verified by experiments; furthermore, a CPW with a finitely thick substrate, but without backside metallization, still needs to be investigated. Manuscript received April 11, 2005. This work was supported in part by the Laboratory for Laser Energetics. J. Zhang and T. Y. Hsiang are with the Laboratory for Laser Energetics and the Department of Electrical and Computer Engineering, University of Rochester, Rochester, NY 14627-0231 USA (e-mail: [email protected]). S. Alexandrou was with the Laboratory for Laser Energetics and the Department of Electrical and Computer Engineering, University of Rochester, Rochester, NY 14627-0231 USA. He is now with the Cyprus Telecommunication Authority, Nicosia 1396, Cyprus. Digital Object Identifier 10.1109/TMTT.2005.857124

Fig. 1. Cross section of the CPW: (a) with wide ground planes and (b) with narrow ground planes.

Previously [6], we have reported preliminary results of simulations of the subterahertz attenuation of CPWs with wide and narrow ground planes. In this paper, detailed experimental results are described and compared with the simulations. The effects of ground-plane width and line dimensions on the attenuation characteristics in the subterahertz frequency domain are investigated. II. THEORY CPWs are a family of transmission lines consisting of a center conductor strip and two ground conductor planes with variable widths. All three conductors are placed on the same side of a dielectric substrate, as shown in Fig. 1. The ideal CPW structure has a semi-infinitely thick substrate and two semi-infinitely wide ground planes. The actual implementation of CPW mainly modifies the ideal structure in the following two ways. First, the substrate has a finite thickness , sometimes with backside metallization. Second, the ground planes have a finite width and, although the conductors are very thin, their thickness is larger than the skin depth. In our study, the width of the center conductor on CPWs is designed to be the same as the width of separation between the center conductor and ground planes . The ground-plane width plays an important role in affecting the performance of CPWs. When an electromagnetic wave propagates on a CPW, it suffers three types of attenuations, which are: 1) conductor loss; 2) dielectric loss; and 3) radiation loss. Dielectric loss is proportional to the loss tangent of the substrate, which is strongly influenced by the dielectric relaxation and the conductivity of the dielectric substrate. In high-quality semiconductor substrates,

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which have dielectric relaxation in the range of several terahertz, the loss tangent has a small value as long as the conductivity is kept low by avoiding high doping. Under these conditions, dielectric loss is very small compared to conductor loss and radiation loss and can be neglected [7], [8]. is evaluated in terms of the surface The conductor loss is resistivity. In the case of CPWs with wide ground planes, given by [9]

(dB/unit length) Fig. 2. Radiation loss of CPWs with different lateral dimensions: 10, 20, and 50 m, respectively.

(1) where is the surface resistivity of the conductors and has a square-root frequency dependence as long as the skin depth is is the much smaller than the thickness of the conductors, is the characteristic effective permittivity of the substrate, is a geometry-dependent paimpedance of the CPW, and rameter. The surface resistivity accounts for the conductor loss and the value of increases as the line dimensions become smaller. At low frequencies, the skin depth can become comparable or even larger than the thickness of the conductors and, in this case, conductor loss tends to saturate to a constant value. For CPWs with narrow ground planes, no closed-form expression of conductor loss has been derived. When the CPW mode propagates along the transmission line at a velocity faster than that of the substrate mode, the coupling between the CPW mode and substrate mode forces energy to radiate from the transmission line into the substrate at an angle [10] given by (2) where and are the propagation constants of the guided CPW mode and the substrate modes, respectively, and is the relative permittivity of the substrate. The electromagnetic energy leaking into the substrate in the form of radiation loss, for the case of wide ground planes, is given by [2]

mm (3) is the frewhere is the speed of light in free space, is a geometry-dependent parameter defined by quency, is the complete elliptic integral of the . At high frequencies first kind, and where the value of starts to increase, the angle is reduced so that the rate of increase of radiation loss is limited below the dependence. Equation (3) also suggests that, as shown in

Fig. 2, CPWs with smaller lateral dimensions suffer reduced radiation loss while this reduction inevitably leads to an increase in the conductor loss. III. EXPERIMENTS A. Fabrication and Measurement The CPWs used in our experiments were fabricated on semi-insulating GaAs substrates with a thickness of 500 m. The substrate was not intentionally doped and had a high cm. The electron mobility was resistivity of more than 10 5000 cm /V s and the substrate’s orientation was . The transmission lines were first patterned with evaporated gold using a “liftoff” process and the wafers were subsequently annealed in inert argon atmosphere at a temperature of 350 C for 20 minutes in order to improve the contact between the evaporated conductors and the substrate. The annealing temperature was kept relatively low to avoid diffusion of gold into the semiconductor. Subsequent measurements indicated that the thickness of the gold film was 290 nm. Two separate sets of transmission lines were fabricated: CPWs with wide ground planes and CPWs with narrow ground planes. All transmission lines had the dimension the same as with a value of 10 or 50 m. CPWs with wide ground m, while for planes had a ground-plane width CPWs with narrow ground planes, the value of was reduced to the size of the line dimensions. The transmission lines were incorporated into two chips. The first chip included the above two types of CPWs with lateral dimensions of 50 m. The second chip included the smaller version of the same CPWs with lateral dimensions of 10 m. After patterning, the wafers were diced and each chip was mounted on a sample holder to facilitate high-speed measurements on the transmission lines. Each CPW included a gap in its center conductor that formed a photoconductive switch in series with the transmission line. An optical beam from a femtosecond Ti : sapphire laser illuminated the switches, generating subpicosecond electrical pulses, which propagated on the CPW. The electrical pulses were generated by the method of nonuniform gap illumination [11], [12], which permits the generation of subpicosecond pulses even on semi-insulating

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Fig. 3. Configuration of subpicosecond electrooptic sampling on CPW.

GaAs substrates that have a relatively long carrier lifetime. With this method, the laser only illuminates the positive edge of the photoconductive switch instead of the whole gap. Since most of the switch gap is never illuminated, drift currents are suppressed. Thus, the generation of transients with long fall times due to the long carrier lifetime of substrate is avoided. Under these conditions, it is possible to generate electrical pulses with ultrashort fall times utilizing the effect of field screening, which does not depend on carrier lifetime. It should be mentioned that such a pulse-generation scheme is flexible, repeatable, and requires no special lithographic or substrate processing steps. More importantly, it can be implemented on virtually any high-quality semiconductor substrate such as GaAs, InP, and silicon. A detailed experimental and theoretical characterization of this effect has been presented elsewhere [11], [13], [14]. The generated electrical pulses were probed with a subpicosecond electrooptic sampling system [15]. In this system, light from a femtosecond laser is divided into two beams, the first of which is used to generate the electrical pulses. The second beam is reflected through an LiTaO crystal positioned at consecutive positions along the CPW and senses the electric field of the propagating pulses as a change in polarization. In this manner, the electrical profile of the propagating waveforms was mapped as a function of time at consecutive positions along each CPW. In all of our reported data, we restrict the observation time window to be shorter than the return time for the pulse to be reflected from the CPW termination and reappear at the observation point (typically hundreds of picoseconds). In this way, we avoided the complication in accounting for the imperfect (and frequency-dependent) termination in the analysis. Geometry of the above sampling process is demonstrated in Fig. 3. The evolution of the electrical signals was first studied in the time domain and then analyzed in the frequency domain. With this methodology, we are able to give a description of the characteristics of each transmission line over a broad bandwidth. B. Time-Domain Analysis In the time domain, it is easy to give a qualitative evaluation of the relative contributions of attenuation by focusing our at-

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Fig. 4. Electrical pulses probed at 0.25, 1, 3, and 5 mm on two 50-m CPWs with ground-plane width of 500 (solid line) and 50 m (dotted line).

tention on the pulse ringing and the peak-amplitude reduction and broadening. The waveforms of electrical pulses probed on two CPWs with lateral dimensions of 50 m are shown in Fig. 4. One CPW had wide ground planes with a width of 500 m and the other had narrow ground planes with a width of 50 m. It is worth noting that, at the first measurement position, the signals are essentially identical even though they were generated by different switches on separate lines. At this position, the main pulses in both CPWs have a temporal duration of approximately 1 ps. The first observation about the evolution of these signals is that as the pulses propagate along CPWs, they become broader and their peak amplitude is reduced. A closer look at the experimental data reveals some differences between the propagation characteristics of the two CPWs. The signals on the CPW with wide ground planes suffer a larger reduction in peak amplitude, have a broader temporal width, and show reduced “ringing.” This is most noticeable in the last set of traces, measured at the propagation distance of 5 mm. These observations are consistent with a higher loss of high-frequency components in the CPW with wide ground planes. These findings are in agreement with predictions of [3] where it was suggested that a reduction of the ground-plane width limits the leakage from the CPW mode to the substrate modes and reduces radiation loss. A similar comparison between the waveforms propagated on 10- m CPWs with wide and narrow ground planes, as shown in Fig. 5, indicates that again the loss is substantially lower in the CPW with narrow ground planes. Our results show that a reduction of the ground-plane width improves the attenuation characteristics of these CPWs. This observation will be further reinforced with the results of our frequency-domain analysis. The lateral dimensions of CPWs have a strong effect on their characteristics. The influence of this parameter is investigated with the results in Fig. 6, which shows a comparison of the electrical waveforms propagated on CPWs with narrow ground planes with lateral dimensions of 10 and 50 m. The initial pulses, both of which were probed at 0.25 mm from the switch have strong similarities, with the waveform from the 10- m CPW being slightly narrower. At longer distances, the signals propagated on the 10- m CPW evolve in a distinctly different

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Fig. 5. Electrical pulses probed at 0.5, 1, 3, and 5 mm on a 10-m CPW with ground-plane width of 500 m (solid line) and electrical pulses probed at 0.25, 1, 3, and 5 mm on a 10-m CPW with ground-plane width of 10 m (dotted line).

Fig. 7. Spectral representation of some time-domain data measured on a 10-m CPW with narrow ground planes. Thin lines refer to magnitude of measured pulses. Bold lines refer to phase of measured pulses. A super-Gaussian gating function has been used to smooth out the transformed results.

As the signals propagate on a CPW, their phase increases and their amplitude is reduced because of attenuation. The spectral distribution of the waveforms is altered in a way that is directly related to their complex propagation factor . The factor can give a complete description of the CPW, with its real part representing the attenuation suffered by the signal as it travels along the CPW, and its imaginary part being inversely proportional to the phase velocity. At a moment and a propagation distance , the initial pulse is modified to . The spectral distribution of is related to the initial pulse by (4) Fig. 6. Electrical pulses probed at 0.25, 1, 3, and 5 mm on 10-m (solid line) and 50-m (dotted line) CPWs with narrow ground planes.

where (5)

way compared to the pulses on the 50- m CPW. In sharp contrast to the pulses on the 50- m CPW, which are heavily distorted, the waveforms from the narrow transmission line are only marginally broadened and show very little ringing indicating that high-frequency loss is comparatively limited. On the other hand, the pulses from the 10- m CPW have progressively smaller peak amplitudes: a clear indication of increased low-frequency attenuation dominated by conductor loss. With time-domain analysis, we have been able to present a qualitative description of the attenuation characteristics of CPWs. When the data are analyzed in the frequency domain, they pave the way for quantitative interpretation and verification of theory, as discussed in Section III-C. C. Frequency-Domain Analysis In order to facilitate frequency-domain characterization of CPWs, our time-domain data were filtered by a gating function and converted to the frequency domain by Fourier transform. An example of such a transformation is seen in Fig. 7. The pulses measured on a 10- m CPW with narrow ground planes, also shown in Fig. 6 in the time domain, are displayed as frequency-dependent functions of amplitude and phase.

By expressing the input and the propagated signals and as functions of frequency, as shown in Fig. 7, can be evaluated. Since time-domain data the attenuation are readily available not in just two, but several measurement positions, we can use a least square fit for the calculation of to improve the accuracy of the measurement. Frequency-domain data and analysis will be further studied in Section V. IV. FULL-WAVE ANALYSIS To facilitate a comparison with experiments, a numerical computation of attenuation characteristics needs to be developed since no closed-form analysis is available. We first note that, when the electrical signals propagate along a CPW, longitudinal components of both the electric and magnetic fields are present. Pure TE and TM modes cannot be supported any more. In order to fully describe the wave propagation, quasi-static assumption has to be replaced by a full-wave analysis. The electric and magnetic fields can be considered as superposition of TE and TM modes and expressed as a weighed sum of these modes. TE and TM modes are chosen to be orthogonal sets, which form a basis for the expansion of the electric

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Fig. 8.

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Equivalent two-port network of CPW.

and magnetic fields. Fourier transform is taken along the direction parallel to the substrate and perpendicular to the transmission line. In the Fourier transform domain, applying appropriate boundary conditions gives rise to equations of current distribution on the transmission line. This set of equations can be solved by using several methods [9]. For analyzing electromagnetic fields by the method of moments, we use Sonnet Suites [16], a high-frequency electromagnetic software, to simulate the scattering matrix of the microwave network consisting of CPW. The software employs a modified method of moments based on Maxwell’s equations to perform a three-dimensional full-wave analysis of predominantly planar structures. As appropriate parameters are set in Sonnet Suites input interface, dielectric and radiation losses can be taken into account. In the dielectric-layer settings, we choose GaAs for the substrate is set to 12.9, the material. The relative dielectric constant dielectric loss tangent is set to 0.006, and the dielectric conductivity is set to 0. The dielectric loss is then determined by the dielectric loss tangent. Besides choosing gold, with a conductivity of 4.09 10 S/m, the thickness of conductors is set to 0.29 m. Hence, both the direct current resistivity and the skin-effect surface impedance have been taken into account in the calculation of conductor loss. In order to sufficiently implement the summation of waveguide modes to approximate the radiation, both of the lateral substrate dimensions are set to be greater than one or two wavelengths. The sidewalls of the boundary are far enough from the center conductor strip such that they have no effect on the radiating structure. By adding air layers above and below the substrate and setting both the top and bottom covers of the boundary as free space, the radiation loss is fully evaluated in the simulation. Sonnet Suites calculates - -, and -parameters for planar circuits and antennas including CPWs. Fig. 8 shows a CPW of length , which can be regarded as a two-port network. The incident and reflected waves in ports 1 and 2 are and , respectively. The scattering matrix equation can be written as (6) Assuming an impedance match exists between the CPW and load, i.e., , (6) gives rise to the following relationships:

(7)

Fig. 9. Simulated and experimental attenuation of CPWs with a 50-m center conductor. Sim-wg refers to simulated attenuation of the CPW with wide ground planes. Exp-wg refers to experimental attenuation of the CPW with wide ground planes. Sim-ng refers to simulated attenuation of the CPW with narrow ground planes. Exp-ng refers to experimental attenuation of the CPW with narrow ground planes.

where is the net power delivered to the CPW, is the net is the net power delivpower reflected from the CPW, and ered to the load. According to expressions for the voltage and current in the two-port network, the power ratios can also be expressed as follows: (8) Substituting (7) for the power ratios in (8), the attenuation per unit length can be defined by (9) While Sonnet Suites defines the loss factor [16] by Loss Factor

(10)

we adopt (9) to facilitate a direct comparison with experiments. Further, in the experiments, reflected signals are excluded from the results by restricting the observation time window to the into main pulse [17], [18], and it is unnecessary to take account. The attenuation is then defined by simplifying (9) as (11) It should be pointed out that, due to the virtual box walls in Sonnet Suites, resonance peaks in electric fields, which do not exist in actual CPWs, may be introduced into the simulations. Therefore, the simulated attenuation will show a ripple behavior. These resonance points are individually identified and removed. V. RESULTS AND DISCUSSION Fig. 9 shows the attenuation of CPWs with a 50- m center conductor as a function of frequency. The experimental attenuation curve for the wide ground-planes CPW, which is roughly the same as the simulated attenuation curve, is given to assess the validity of the full-wave analysis. We present the simulated and experimental attenuations of CPWs with both wide and

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The study thus far reveals that CPWs with narrow ground planes suffer lower attenuation than CPWs with wide ground planes. On the basis of the obtained results, we proceed to further investigate the effect of lateral dimensions on the performance of CPWs with narrow ground planes. The lateral dimensions of both center conductors and ground planes are chosen to be 10 or 50 m. Fig. 11 shows their attenuation in detail. At low frequencies up to 300 GHz, the CPW with larger lateral dimensions yields lower attenuation mainly arising from lower conductor loss. As the frequency increases up to 1 THz, the CPW with smaller lateral dimensions performs better with lower attenuation due to lower radiation loss. Fig. 10. Simulated and experimental attenuation of CPWs with a 10-m center conductor. Sim-wg refers to simulated attenuation of the CPW with wide ground planes. Exp-wg refers to experimental attenuation of the CPW with wide ground planes. Sim-ng refers to simulated attenuation of the CPW with narrow ground planes. Exp-ng refers to experimental attenuation of the CPW with narrow ground planes.

Fig. 11. Simulated and experimental attenuation of CPWs with narrow ground planes. The lateral dimensions are 10 and 50 m, respectively. Sim-10 refers to simulated attenuation of the CPW with a 10-m center conductor. Exp-10 refers to experimental attenuation of the CPW with a 10-m center conductor. Sim-50 refers to simulated attenuation of the CPW with a 50-m center conductor. Exp-50 refers to experimental attenuation of the CPW with a 50-m center conductor.

narrow ground planes for comparison. As expected, the attenuation of CPW with narrow ground planes is much lower than that of CPW with wide ground planes over 200 GHz, where the radiation loss dominates. The reduction of radiation loss arises from the reduction of overlap between the quasi-TEM CPW mode and the substrate modes. Therefore, reducing the width of ground planes leads to an obvious decrease of radiation loss and, consequently, this causes the decrease of total attenuation at subterahertz frequencies. In addition, the subterahertz attenuation of CPWs with a 10- m center conductor has also been simulated and compared to the corresponding experimental data. Fig. 10 demonstrates that, again, the CPW with narrower ground planes has a strongly lower attenuation over 200 GHz. On the other hand, Fig. 10 shows a higher attenuation for CPW with narrow ground planes up to 200 GHz. As for the frequency range below 200 GHz, conductor loss is a more important factor than radiation loss so that the attenuation characteristics is different than at high frequencies.

VI. CONCLUSION In this paper, we have presented a detailed study on the attenuation characteristics of a family of CPWs at subterahertz frequencies. The simple transmission-line designs only require a single fabrication step and can be readily implemented on high-quality semiconductor substrates suitable for ultrafast devices and circuits. Our experimental results have demonstrated that the attenuation characteristics of CPWs with wide ground planes are well described by existing theory up to very high frequencies. At the same time, we have simulated attenuations of CPWs with wide and narrow ground planes by exploiting a full-wave analysis software. The simulation results agree well with the experimental data at up to subterahertz frequencies. It is shown that reducing the width of the ground planes leads to a significant reduction in radiation loss. Furthermore, simulated and experimental attenuations of narrow ground-planes CPWs with a 50- and 10- m center conductor have been compared. At high frequencies above 300 GHz, CPW with smaller lateral dimensions performs with lower attenuation. At low frequencies, the CPW with larger lateral dimensions does better. Considering their effects on performance of CPWs, we need to investigate not only attenuation, but also dispersion. Experiments and simulations on dispersion characteristics of CPWs will be reported in a future study. ACKNOWLEDGMENT The authors wish to acknowledge the assistance of and discussion with B. Mu, Y. Zhu, and Y. Wang, all of the Rochester Institute of Technology, Rochester, NY. REFERENCES [1] D. Grischkowsky, I. N. Duling III, J. C. Chen, and C.-C. Chi, “Electromagnetic shock waves from transmission lines,” Phys. Rev. Lett., vol. 59, no. 15, pp. 1663–1666, Oct. 1987. [2] M. Y. Frankel, S. Gupta, J. A. Valdmanis, and G. A. Mourou, “Terahertz attenuation and dispersion characteristics of coplanar transmission lines,” IEEE Trans. Microw. Theory Tech., vol. 39, no. 6, pp. 910–915, Jun. 1991. [3] M. Tsuji, H. Shigesawa, and A. A. Oliner, “New interesting leakage behavior on coplanar waveguides of finite and infinite widths,” IEEE Trans. Microw. Theory Tech., vol. 39, no. 12, pp. 2130–2137, Dec. 1991. [4] J. Zehentner and J. Machac, “Properties of CPW in the sub-mm wave range and its potential to radiate,” in IEEE MTT-S Int. Microwave Symp. Dig., vol. 2, Jun. 2000, pp. 1061–1064. [5] F. Schnieder, T. Tischler, and W. Heinrich, “Modeling dispersion and radiation characteristics of conductor-backed CPW with finite ground,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 1, pp. 137–143, Jan. 2003.

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[6] J. Zhang and T. Y. Hsiang, “Subterahertz attenuation in coplanar waveguides,” presented at the IEEE MTT-S Int. Microwave Symp., Jun. 2005. [7] D. S. Phatak, N. K. Das, and A. P. Defonzo, “Dispersion characteristics of optically excited coplanar striplines: Comprehensive full wave analysis,” IEEE Trans. Microw. Theory Tech., vol. 38, no. 11, pp. 1719–1730, Nov. 1990. [8] C. Shu, X. Wu, E. S. Yang, X. C. Zhang, and D. H. Auston, “Propagation characteristics of picosecond electrical pulses on a periodically loaded coplanar,” IEEE Trans. Microw. Theory Tech., vol. 39, no. 6, pp. 930–935, Jun. 1991. [9] K. C. Gupta, R. Garg, and I. J. Bahl, Microstrip Lines and Slotlines. Norwood, MA: Artech House, 1979, ch. 7. [10] D. S. Rutledge, D. P. Neikirk, and D. P. Kasilingham, Infrared and Millimeter Waves. New York: Academic, 1983, ch. 1. [11] S. Alexandrou, C.-C. Wang, R. Sobolewski, and T. Y. Hsiang, “Generation of subpicosecond electrical pulses by nonuniform illumination of GaAs transmission line gaps,” IEEE J. Quantum Electron., vol. 30, no. 5, pp. 1332–1338, May 1994. [12] D. Krokel, D. Grischkowsky, and M. B. Ketchen, “Subpicosecond electrical pulse generation using photoconductive switches with long carrier lifetimes,” Appl. Phys. Lett., vol. 54, no. 11, pp. 1046–1047, Mar. 1989. [13] C.-C. Wang, M. Currie, R. Sobolewski, and T. Y. Hsiang, “Subpicosecond electrical pulse generation by edge illumination of silicon and indium phosphide photoconductive switches,” Appl. Phys. Lett., vol. 67, no. 1, pp. 79–81, Jul. 1995. [14] X. Zhou, S. Alexandrou, and T. Y. Hsiang, “Monte Carlo investigation of the intrinsic mechanism of subpicosecond pulse generation by nonuniform illumination,” J. Appl. Phys., vol. 77, no. 2, pp. 706–711, Jan. 1995. [15] S. Alexandrou, R. Sobolewski, and T. Y. Hsiang, “Time-domain characterization of bent coplanar waveguides,” IEEE J. Quantum Electron., vol. 28, no. 10, pp. 2325–2332, Oct. 1992. [16] Sonnet User’s Guide Release 9, Sonnet Software Inc., Syracuse, NY, 2003. [17] S. Alexandrou, “The bent coplanar waveguide at sub-terahertz frequencies,” Ph.D. dissertation, Dept. Elect. Comput. Eng., Univ. Rochester, Rochester, NY, 1994. [18] T. Y. Hsiang, S. Alexandrou, and C. C. Wang, “Terahertz dispersion of coplanar waveguides and waveguide bends,” in Proc. PIERS’95 Symp., 1995, p. 789.

Jingjing Zhang (S’05) received the Bachelor’s degree in optical engineering from the Beijing Institute of Technology, Beijing, China, in 1995, the Master’s degree in electrical engineering from the University of Rochester, Rochester, NY, in 2002, and is currently working toward the Ph.D. degree in electrical engineering at the University of Rochester. Her research interests include electromagnetic simulation, design and analysis of transmission lines, and opto-electronics.

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Sotiris Alexandrou was born in Nicosia, Cyprus, in 1964. He received the B.S. degree from Lehigh University, Bethlehem, PA, in 1989, and the Ph.D. degree from the University of Rochester, Rochester, NY, in 1994, both in electrical engineering. From 1990 to 1994, he was a Frank Horton Fellow with the University of Rochester. From 1994 to 1996, he was with the IBM T. J. Watson Research Center. In 1996, he returned to Cyprus to complete his military service and joined the Cyprus Telecommunication Authority, Nicosia, Cyprus, in 1998. His research interests include ultrafast studies of electronic devices and transmission structures, the physics of semiconductor devices, and the development of femtosecond laser systems.

Thomas Y. Hsiang (M’81–SM’88) received the M.A. and Ph.D. degrees in physics from the University of California at Berkeley, in 1973 and 1977, respectively. Since 1981, he has been on the faculty of the University of Rochester, Rochester, NY, where, in 1988, he became a Professor of electrical and computer engineering. During the 1987–1988 academic year, he was a Visiting Professor with National Taiwan University. From 1990 to 1991, he was the Director of the Solid State and Microstructures Program at the National Science Foundation. While with the University of Rochester, he has performed pioneering research in the field of ultrafast studies in superconducting and semiconductor electronic devices and transmission structures. Dr. Hsiang is a Fellow of the American Physical Society.

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Direct-Coupled Microwave Filters With Single and Dual Stopbands Richard J. Cameron, Fellow, IEEE, Ming Yu, Senior Member, IEEE, and Ying Wang

Abstract—This paper presents new ideas for the design and implementation of microwave filters with single and dual stopbands. They can be realized with waveguide, coaxial, dielectric resonators, or in a planar technology. The new methods represent an advance over present methods in that the resonators are direct coupled, thus avoiding the need for transmission line phase lengths between resonator stubs that tend to degrade performance due to their dispersion and are difficult to adjust during tuning. Three bandstop (BS) configurations are presented. The first will accommodate even or odd characteristics and also asymmetric responses, although some negative or diagonal cross-couplings will be needed. The second resembles the cul-de-sac configuration for bandpass filters and needs no diagonal or negative couplings even for asymmetric characteristics. The third is an application of the cul-de-sac synthesis technique to dual-band bandstop (DBBS) filters. All these BS designs are very similar to regular bandpass filters in their design and realization. The design of a DBBS filter is presented and compared with an equivalent bandpass filter to demonstrate its advantages. Finally, the simulated and measured results of a fourth-degree BS filter design in the novel cul-de-sac configuration are presented. Index Terms—Bandstop (BS) filters, coupling matrix, direct coupling, dual-band filters, filter synthesis, microwave filter.

I. INTRODUCTION

M

ICROWAVE bandstop (BS) filters are widely used for suppression of spurious outputs from high power transmitters. They become more important in the design of telecommunication and broadcast systems, to prevent interference with other users. These interfering signals may take the form of harmonics from a nonlinear power amplifier, or spurious passbands (breakthrough) in a bandpass cover filter within the transmit subsystem. Normally, these interfering signals are suppressed with low-pass filters with wide reject bands, but these do not discriminate between frequency ranges that are inherently spurious free and those with spurious/harmonic content. This sometimes leads to a complicated low-pass device where design for lowest insertion loss/size and high power handling can become problematic. When spurious signals are well defined and restricted to relatively narrow frequency bands, it becomes more efficient in terms of insertion loss, compactness, and power handling to use a BS filter, providing rejection only over the limited bandwidth. In the past, these BS filters have been realized as an array of BS stub elements separated by lengths of transmission line, usually about 3/4 in length. In practice, the performance of these BS Manuscript received April 1, 2005; revised July 18, 2005. R. J. Cameron is with COM DEV Ltd., Aylesbury, Bucks HP22 5SX, U.K. M. Yu and Y. Wang are with COM DEV Ltd., Cambridge, ON, Canada N1R 7H6 (e-mail: [email protected]). Digital Object Identifier 10.1109/TMTT.2005.859032

filters may be degraded by dispersive effects and thermal expansion in the interstub phase lengths, and are difficult to adjust during development and production. This paper presents a new approach to the design of single and dual BS filters, where resonators are directly coupled by irises or some other coupling element, rather than by phase lengths, making the techniques used for their design and construction very similar to those used for bandpass filters. Three variants of the direct-coupled BS filter are described, the first similar in style to a regular folded-geometry bandpass filter, and the second resembling the cul-de-sac bandpass filter topology [1], [6], requiring no negative or diagonal couplings even for asymmetric characteristics. Finally, it is shown that the BS synthesis technique may be applied to dual-band characteristics, and a comparison is made with an equivalent bandpass filter to demonstrate the advantages. II. SYNTHESIS OF THE PROTOTYPE POLYNOMIALS It was noted in [2] and [3] that to generate a BS characteristic from regular low-pass prototype (LPP) polynomials, it was only necessary to exchange the reflection and transfer functions (including the constants)

(1) and share a common denominator polySince , the unitary conditions for a passive lossless netnomial work are preserved. If the characteristics are Chebyshev, then the original prescribed equiripple return loss characteristic becomes the transfer response, with a minimum reject level equal to the original prescribed return loss level. Because the degree is of the new numerator polynomial for , the network that is synnow the same as its denominator thesized will be fully canonical. The new numerator of is and the original transfer function numerator polynomial of prescribed TZs provided may have any number , the degree of the characteristic. If , then the constant 1 [1]. The synthesis of the coupling matrix for the BS network follows very similar lines to the synthesis of fully canonical LPPs for bandpass filters as described in [1] and later amplified in [4]. (degree ) and (degree Firstly, exchange the ) polynomials, and then form the polynomials for the rational and for the short circuit admittance parameters

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network. For an even-degree double-terminated network with source and load terminations of 1

(2a) and for an odd-degree network

(2b) Fig. 1. Direct-coupled BS filter realizing a symmetric 4–2 characteristic. (a) Coupling and routing diagram. (b) Possible realization with coaxial resonant cavities.

where

and and , 0 1 2 3 , are the complex coefficients and , respectively. If is less than (which of is the usual case), then the highest degree coefficient of is zero. and Having built up the numerator polynomials and the denominator polynomial , the coupling matrix synthesis proceeds in exactly the same way as described is now the same degree in [1]. Because the numerator of as its denominator, the characteristic is now fully canonical and the coupling matrix representing it will need to incorporate a . is calculated as [1] direct source–load coupling (3)

If the original bandpass characteristic is noncanonical, i.e., the degree of is less than and therefore , it 1 may be seen from (2) that the leading coefficient of [2]. For a Chebyshev characteristic, the leading coefficient of always equals unity, as does for noncanonical cases, 1. In other words, and so from (3) it may be seen that

the direct source–load coupling inverter has the same characteristic impedance as the interfacing transmission lines from the source and to the load and may be constructed simply from a 90 section of that line. For fully canonical characteristics, e.g., will be slightly less than unity and will provide the 4–4, finite return loss at infinite frequency that the fully canonical prototype requires. The rest of the synthesis of the coupling matrix proceeds as for the LPP for a bandpass filter. Fig. 1(a) gives an example of a symmetric fourth-degree BS device in folded configuration, showing that the main signal path is through the direct . An interesting implementation in input–output coupling microstrip may be found in [5]. A. Example of Synthesis In general, it is not desirable to include complex couplings in direct-coupled BS filters in folded form, so it is best to restrict applications to symmetric prototypes. An example is given of a symmetric fourth-degree characteristic with 22-dB return loss (which will become the stopband reject level) and two transmis2.0107 sion zeros (TZs) (actually “reflection zeros” now) at to give an out-of-band (return loss) lobe level of 30 dB. After synthesizing the folded ladder network, the coupling matrix is obtained as (4a), shown at the bottom of this page. Note that the direct input–output coupling is unity for this noncanonical case, meaning that this coupling inverter has

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the same characteristic admittance as the input and output lines part of that and may actually be formed from a 90 line carrying the main signal power, between the input and output tap points to the main body of the filter. Fig. 1(b) shows a possible realization with coaxial cavities; however, coupling is negative in (4a) and will have to be realized as a probe in this example. It is interesting to note that with BS transfer and reflection characteristics, when the number of reflection zeros (formerly (i.e., ), TZs) is less than the degree of the filter a second solution is possible by working with the dual of the network. The dual network is obtained simply by multiplying the coefficients of the transfer and reflection numerator polynoand by 1, and is equivalent to placing unit mials inverters at the input and output of the network. If this is done for the 4–2 symmetric example and the BS matrix resynthesized, the coupling matrix, shown in (4b) at the bottom of this page, is obtained with all-positive couplings. However, in general, this uniformity of coupling sign will not occur.

Fig. 2. Cul-de-sac forms for direct-coupled BS filters. (a) Sixth degree. (b) Seventh degree.

III. CUL-DE-SAC FORMS FOR THE DIRECT-COUPLED BS MATRIX If the number of reflection zeros of the BS characteristic is as above), and the less than the degree of the network ( network is double terminated between equal source and load terminations, then a cul-de-sac form [1] for the BS network, similar to that for bandpass filters, may be obtained by introducing two unity-impedance 45 phase lengths at either end of the network. and polynomials This is equivalent to multiplying the by , which has no effect on the overall transfer and reflection responses of the network apart from the 90 phase changes in and . Synthesizing the network using the direct coupling matrix approach described above yields networks such as shown in Fig. 2. These networks are characterized by the square-shaped “core” quartet of couplings, with the source and load terminals at adjacent corners at the “input/output” end, while the other resonators are strung out in two chains from the other two corners, in equal numbers if is even and one more than the other if is odd. There are no diagonal couplings even for asymmetric characteristics, and all couplings are of the same sign. For these charac, the direct source–load coupling teristics where will always be unity in value. An example is taken of a 4–2 asymmetric characteristic with 22-dB return loss and two TZs on the upper side at 1.3127 and 1.8082, there producing two rejection and lobes at 30 dB each. Exchanging the

Fig. 3. 4–2 direct-coupled cul-de-sac BS filter. (a) Coupling and routing diagram. (b) Possible realization with waveguide cavities.

polynomials, multiplying them by , and synthesizing the folded coupling matrix as described above yield the coupling matrix, shown in (5), at the bottom of the following page. Fig. 3 shows the corresponding coupling and routing diagram and a possible realization with waveguide resonators. The section of waveguide transmission line between the input and output connections forms the direct input–output coupling and may be an odd number of quarter wavelengths—the less, the better. Finally, Fig. 4 shows the results of analyzing the prototype BS coupling matrix, where it may be seen that the transfer and reflection characteristics have exchanged. The original 22-dB return loss level has now become the BS reject level and the

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CAMERON et al.: DIRECT-COUPLED MICROWAVE FILTERS WITH SINGLE AND DUAL STOPBANDS

Fig. 4. 4–2 direct-coupled cul-de-sac BS filter rejection and return loss performance.

30-dB lobe levels, originally designed for the rejection characteristic, now apply to the return loss characteristic. As with the bandpass cul-de-sac configuration, the BS cul-de-sac will have the minimum number of couplings for a finite-position given filtering characteristic with up to TZs. For the bandpass case, it was shown in [6] that the sensitivity of the cul-de-sac configuration to thermal fluctuations and manufacturing tolerances is likely to be greater than filters with other coupling configurations giving the same response. It is expected that the same will apply to the BS cul-de-sac configuration, and it is recommended to keep the BS cul-de-sac design as simple as possible for a less complex prototype characteristics implementation. For the same reasons, it is not recommended to design a BS rejection level for greater than about 25–30 dB, depending on design bandwidth (DBW). IV. TRANSFORMATION FOR DUAL-BAND FILTERS Occasionally, applications arise for filters that exhibit two passbands within the confines of the passband of the original regular single-passband filter [7], [8]. An example may be envisaged where there are two distinct signals multiplexed into a single channel, each requiring a high degree of selectivity to reject close-to-band noise and interference, or where extra linearity is required near the extremes of the channel for a signal whose main energy is concentrated near the edges of its bandwidth rather than at the center. An application is also seen for dual-band bandstop (DBBS) filters in high power systems for the suppression of close-toband intermodulation sidebands caused by a high power amplifier operating in a nonlinear mode, e.g., close to or at saturation (spectrum spreading) [8]. Typically, a quaternary phase-

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shift keying (QPSK) signal passing through a saturated traveling wave tube amplifier (TWTA) will acquire spectral sidelobes about 18 dB down in level relative to the peak power at midband, and extending for about one bandwidth on either side of the main band. Although it will not contribute to far-out-ofband rejection by itself, simulations have shown that the DBBS filtering characteristic will suppress the contiguous sidebands with significantly less insertion loss and higher power handling than the equivalent bandpass filter. The particularly simple con-band and struction lends itself to high power applications at above. The dual-band characteristic may be generated from a regular single-passband LPP filtering characteristic by the application of a symmetric mapping formula. The mapping transforms the original equiripple behavior (if the original LP filtering characteristic is Chebyshev) of the single passband over two subbands. The lower band ranges from the lower edge of the original passto , and the upper passband extends band at to , where the fractional parameters from are the prescribed frequency points within the main passband that define the inner edges of the two subbands (see Fig. 5). The effect of applying the transform is to double the degree of filtering characteristic and the number of any TZs ( 2 , 2 ), but the original equiripple level and the levels of any rejection lobes (apart from the central lobe) are preserved. The dual-band characteristic will be symmetric about zero frequency even if the original LPP filtering function was asymmetric. The dual-band characteristic is obtained by applying a symmetric frequency transform (6) where is the frequency variable mapped from the prototype -plane. The constants and may be found by considering the boundary conditions at at giving and

(7)

Substituting back into (6) yields the transform formula

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TABLE I SINGULARITIES OF TRANSFER AND REFLECTION POLYNOMIALS. (a) 4–2 LOW-PASS PROTOTYPE. (b) AFTER TRANSFORMATION TO 8–4 DUAL-BAND LOW–PASS PROTOTYPE CHARACTERISTIC WITH x 0.4

=

Fig. 5. Dual-band filters. (a) 4–2 asymmetric LPP filter. (b) After transformation to dual-band LPP with x 0.4.

=6

and (8) for 1 2 . Using this transform, the -plane sinand polynomials and the singularities of the polynomial of the LPP may be mapped gularities of the to the 2 and 2 singularities, respectively, of the dual-band characteristic. Network synthesis may then proceed as normal on the double-size polynomials to realize the dual-band filter. Any TZs below the main passband of the LPP will map to frequencies between the two passbands of the dual-band char1 acteristic. Inspection of (8) shows that a TZ at 1 will map to 0, which imposes a limit to how far away from the lower band edge of the LPP that a TZ may be placed, and still map into a pair of TZs in the dual-band char0.4 and 1.3809, acteristic. For example, when any TZ with a position more negative than this in the LPP will map into a pair of real axis zeros in the dual-band response. Fig. 5(b) shows an eighth-degree dual-band filter with four TZs 0.4, formed by the transformation of a 4–2 asymand metric filter with 20-dB return loss level and optimized such that the rejection lobe level nearest to the passband and the point at 1.3809 (which will transform to 0) are both 23 dB

Fig. 6. Coupling matrices for 8–4 dual-band filtering characteristics. (a) Dual-band bandpass prototype network (here shown in cascade quartet configuration). (b) DBBS prototype network (cul-de-sac configuration).

[see Fig. 5(a)]. After transformation, this will give an equiripple rejection level of 23 dB in the interband region. Table I gives the -plane locations of the original 4–2 asymmetric filtering function together with their transformed positions for the 8–4 symmetric dual-band LPP filter. Fig. 6(a) gives the coupling matrix (shown here in cascade quartet configuration) synthesized from the transformed singularities using the methods described in [1]. Note that the dual-band coupling matrix is synchronously tuned even though the original prototype was asymmetric. The DBBS coupling matrix may now be generated in the same way as for the single-band BS matrix as described above. and polynomials from the transForming the formed singularities in Table I(b), exchanging them, multiplying them by , and then synthesizing the network as for the singleband BS filter yield the cul-de-sac coupling matrix shown in Fig. 6(b). Note that all couplings are positive and symmetric in

CAMERON et al.: DIRECT-COUPLED MICROWAVE FILTERS WITH SINGLE AND DUAL STOPBANDS

Fig. 7.

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8–4 DBBS filter coupling and routing diagram.

value about the physical center of the network and that the resonators are conjugately tuned. The coupling and routing diagram corresponding to the DBBS coupling matrix is given in Fig. 7, showing that there are no diagonal cross couplings even though the original prototype was asymmetric. Analyzing the matrix in Fig. 6(b) will give the same characteristics as shown in Fig. 5(b), but with the transfer and reflection responses exchanged. V. DBBS FILTER—RF DESIGN To assess the advantages of a DBBS filter at RF frequencies, the eighth-degree DBBS filter prototype designed above will be analyzed at a center frequency of 12 GHz and 120 MHz DBW, and compared with a symmetric 8–2 bandpass filter with the same center frequency. The DBW and TZs of the bandpass filter have been adjusted to give approximately the same rejection slopes in the vicinity of the band edges of the 40 MHz usable of 8000 bandwidth (UBW) channel as the DBBS filter. A has been assumed for both filters. The cul-de-sac configuration is particularly attractive for the realization of the DBBS because it gives all-positive couplings that are minimum in number and symmetric in value about the line of symmetry of the network, enabling a simple mechanical design with waveguide or dielectric resonators to be made. The return loss and rejection characteristics of the DBBS filter are shown in Fig. 8(a), and the rejection response is compared with that of the bandpass filter in Fig. 8(b). It may be clearly seen here that the DBBS rejection is very much limited to the suppression of spectral sidelobes, and a separate cover filter will be required if rejection further out of band is needed. However, the intrinsic insertion loss of the DBBS is significantly less. Fig. 9(a) compares the insertion loss variations of the dual-BS filter and the bandpass filter over the channel UBW, showing that the insertion loss of the DBBS filter is approximately 25% that of the BP filter at midband (0.35 dB versus 1.4 dB). The group delay variations of the two filters over the UBW are compared in Fig. 9(b), showing that because of its wider DBW the absolute group delay of the DBBS filter is less, but variation over the UBW is about the same. A. Voltage Multiplication Factors (VMFs) Within Resonant Cavities—Comparison Between DBBS and Bandpass Filters For comparison of the high power handling performances of different filters, the VMF associated with each cavity in the filter makes a useful parameter. The VMF of each resonant cavity is the factor by which the voltage incident at the input to the filter is

Fig. 8. DBBS filter comparison of rejection characteristic with 8–2 bandpass filter (simulations). (a) Rejection (solid line) and return loss (dotted line) of DBBS filter. (b) Rejection characteristic compared with 8–2 bandpass filter.

multiplied to obtain the voltage in the cavity, and may be easily computed using the methods outlined in [9]. In Fig. 10, the plots for the VMFs in the eight cavities in the DBBS filter and the equivalent bandpass filter are shown. The BP filter voltages are symmetric about the center frequency, but because of the conjugate tuning of the DBBS filter, corresponding pairs of cavities have conjugate asymmetry, e.g., the voltage characteristics of reversed, etc. cavity 8 are the same as cavity 1 reversed, In Fig. 10(a) and (b), the plots corresponding to cavities with the highest midband VMFs are shown in bold. In the case of the BP filter, the VMF is approximately 8 (in cavity 3) at midband (where the majority of the signal power is typically present), while the worst-case VMF of the DBBS is about 5 (cavities 2 and 7) at midband, equivalent to about 2.6 times greater power handling. The band center voltages of the other cavities in the DBBS filter are relatively low. At band edge, the VMF of the DBBS filter is approximately 13 (cavities 4 and 5) while that of the BP filter is approximately 11 (again cavity 3). Since the highest voltages at midband occur in only two of the eight cavities of the DBBS, it may be possible to construct them with larger dimensions or with a different type of resonator with greater power handling properties. This will be helpful when mass and volume of the filter are important considerations.

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Fig. 9. DBBS filter comparison with bandpass filter (simulations). (a) Insertion loss variations. (b) Group delay variations over UBW.

Fig. 10. VMFs within rectangular waveguide cavities. (a) DBBS filter. (b) Equivalent bandpass filter.

B. DBBS Filter Construction lid or as The DBBS filter may be realized as a housing two half-housings; in either case, the manufacturing operations are milling from solid or fabrication. Input/output and inter-resonator couplings are all aperture—no probes or diagonal couplings are required—and are screw adjustable. The cavity layout has a certain amount of flexibility, but the “dog-leg” coupling topology shown in Figs. 7 and 11 is particularly suitable for mode resonance in cylindrical cavities, supthe high mode. Dissipated RF energy pressing the degenerate may be efficiently transferred to a cooling baseplate through the flat base of the filter. C. Sensitivity Considerations At the time of writing, a practical model had not been constructed and tested to assess the sensitivity of the DBBS filter to environmental fluctuations and manufacturing tolerances. In [10], the design and testing of a 12th-degree dual-band bandpass filter is described, and it is noted there that the device is quite sensitive due to the narrow transition bandwidths of the rejection characteristic. The cul-de-sac configuration for the DBBS filter will be inherently more sensitive because of the reduced number of couplings, although the situation will be improved because negative couplings are not needed.

Fig. 11. Possible cavity layout with square waveguide cavities. Coupling values are all the same sign and are symmetric about the center, i.e., , , etc.

M =M M =M

VI. HARDWARE VALIDATION In order to confirm the design procedure and to assess sensitivity to manufacturing tolerances (random) and dimensional changes due to variations in the thermal environment (unidirectional), a waveguide model of a cul-de-sac BS filter was designed and simulated. The prototype characteristic was a fourth-degree symmetric Chebyshev with 22-dB return loss (to become the stopband reject level) and two TZs at

CAMERON et al.: DIRECT-COUPLED MICROWAVE FILTERS WITH SINGLE AND DUAL STOPBANDS

Fig. 12. 4–2 direct-coupled cul-de-sac BS filter. (a) Model for EM simulation. (b) Photograph of -band model.

Ku

1.9140 to give rejection lobe levels of 25 dB (which will become the out-of-band return loss lobe levels on either side of the reject band). The design reject bandwidth is 500 MHz centered at 13.35 GHz, with the main signal power in the range 10.9–12.5 GHz. The BS resonators are to be realized with -mode rectangular waveguide WR75 cavities, -plane coupled to the main waveguide run. The coupling matrix for this BS filter is given by (9), shown at the bottom of this page, and an outline sketch and a photograph of the model upon which the measurements were made are shown in Fig. 12. The model was dimensioned and analyzed using full-wave EM optimization software, and a laboratory model was built and tested. The results are shown in Fig. 13, where Fig. 13(a)

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Fig. 13. 4–2 direct-coupled cul-de-sac BS filter simulated and measured performance. (a) Simulated rejection and return loss performance. (b) Insertion loss detail.

compares the simulated and measured rejection and return loss performances. It may be seen that a rejection level of 19 dB is being achieved over the band 13.1–13.6 GHz, while 20-dB return loss level is maintained over the 11.25–12.3 GHz range and 15 dB over the 12.3–12.5 GHz range. The advantages of using a BS filter for this application now become evident—it is estimated that a seventh-degree bandpass filter operating over the 10.9–12.5 GHz band would be needed to provide 20 dB rejection over the 13.1–13.6 GHz band. Fig. 13(b) gives some detail of the simulated/measured rejection characteristic in the passband and around the stopband, demonstrating the very high selectivity and low insertion loss levels that are achievable.

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The measured response agrees well with the simulated. The somewhat “skewed” appearance of the return loss characteristic is due to the relatively wide reject band that the filter was designed for, which meant that some of the coupling apertures are quite large especially in the vicinity of the junctions with the main waveguide. Coupling matrix deembedding analysis indicates that some stray coupling is present in this region, which mainly accounts for the asymmetry. These stray coupling themselves, couplings actually provide enough aperture to be omitted for this particular allowing the case. Also, for ideal performance, the electrical distance between the input and output apertures should remain constant radians. Dispersive with frequency at an odd multiple of effects within the waveguide cause a variation in this electrical length with frequency, which will tend to contribute to the skewing effect. The stray coupling effect will be mitigated somewhat by increasing the spacing of the input/output couradians, but dispersive effects will then plings to say begin to become troublesome.

VII. CONCLUSION In this paper, a method for the synthesis of the coupling matrices for three different forms of direct-coupled BS filter has been presented. All of them with the resonant cavities are direct coupled so wide-band performance is potentially better than conventional phase-coupled stub BS realization, and because the cavities are tuned to frequencies within the stopband, the main signal power will route through the direct input–output coupling, bypassing the resonators and giving minimal insertion loss and relatively high power handling. Other advantages accrue in terms of simple and compact construction, flexible layout possibilities, and ease of manufacture and of tuning on the production line. The second form resembles the cul-de-sac bandpass filter that has been previously presented, and is able to realize asymmetric BS characteristics without the need for negative or diagonal couplings. A technique for the design of DBBS filters has also been presented. Possible applications include the suppression of close-to-band intermodulation products generated by nonlinearity in high power amplifiers. A comparison with a bandpass filter with the same function has been made, showing that significantly lower insertion loss and higher power handling may be obtained, although a separate cover filter, to provide rejection in regions more than a bandwidth away from the channel band edges, will possibly be needed. The EM simulated results of a fourth-degree waveguide model have been presented and compared with the measured results of a breadboard model, showing good correlation. Possible future applications for the direct-coupled BS filter might include high-power signal diplexing when ultralow loss is important but where out-of-band rejection is not a serious problem (or is provided by a low-loss wide-band cover filter) and large levels of isolation are not required. For a diplexer

application, each of the two BS filters will be tuned to reject the frequency of the channel on the opposite arm of the combination point. ACKNOWLEDGMENT The authors wish to thank D. J. Smith and W. Fitzpatrick, both of COM DEV Ltd., Cambridge, ON, Canada, for their help on filter tuning and testing. REFERENCES [1] R. J. Cameron, “Advanced coupling matrix synthesis techniques for microwave filters,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 1, pp. 1–10, Jan. 2003. [2] J. R. Qiang and W. C. Zhuang, “New narrow-band dual-mode bandstop waveguide filters,” IEEE Trans. Microw. Theory Tech., vol. MTT-31, no. 12, pp. 1045–1050, Dec. 1983. [3] R. J. Cameron, “General prototype network synthesis methods for microwave filters,” ESA J., vol. 6, no. 2, pp. 193–206, 1982. [4] S. Amari and U. Rosenberg, “Direct synthesis of a new class of bandstop filters,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 2, pp. 607–616, Feb. 2004. [5] R. Wu, S. Amari, and U. Rosenberg, “New cross-coupled microstrip band-reject filter,” in IEEE MTT-S Int. Microwave Symp. Dig., Fort Worth, TX, Jun. 2004, pp. 1597–1600. [6] R. J. Cameron, A. R. Harish, and C. J. Radcliffe, “Synthesis of advanced microwave filters without diagonal cross-couplings,” IEEE Trans. Microw. Theory Tech., vol. 50, no. 12, pp. 2862–2872, Dec. 2002. [7] J. Lee, M. S. Uhm, and I.-B. Yom, “A dual-passband filter of canonical structure for satellite applications,” IEEE Microw. Compon. Lett., vol. 14, no. 6, pp. 271–273, Jun. 2004. [8] H. Uchida et al., “Dual band-rejection filter for distortion reduction in RF transmitters,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 11, pp. 2550–2556, Nov. 2004. [9] A. Sivadas, M. Yu, and R. J. Cameron, “A simplified analysis for high power microwave bandpass filter structures,” in IEEE MTT-S Int. Microwave Symp. Dig., Boston, MA, 2000, pp. 1771–1774. [10] G. Macchiarella and S. Tamiazzo, “A design technique for symmetric dualband filters,” in IEEE MTT-S Int. Microwave Symp. Dig., Long Beach, CA, Jun. 2005. [CD ROM].

Richard J. Cameron (M’83–SM’94–F’02) received the B.Sc. degree in telecommunications and electronic engineering from Loughborough University, Loughborough, U.K., in 1969. In 1969, he joined Marconi Space and Defence Systems, Stanmore, U.K., where his activities included small earth-station design, telecommunication satellite system analysis, and computer-aided RF circuit and component design. In 1975, he joined the European Space Agency’s technical establishment (ESTEC, The Netherlands), where he was involved in the research and development of advanced microwave active and passive components and circuits with applications in telecommunications, scientific, and earth observation spacecraft. Since joining COM DEV Ltd., Aylesbury, Bucks, U.K., in 1984, he has been involved in the software and methods for the design of high-performance components and subsystems for both space and terrestrial application. Mr. Cameron is a Fellow of the Institution of Electrical Engineers (IEE), U.K.

CAMERON et al.: DIRECT-COUPLED MICROWAVE FILTERS WITH SINGLE AND DUAL STOPBANDS

Ming Yu (S’90–M’93–SM’01) received the Ph.D. degree in electrical engineering from the University of Victoria, Victoria, BC, Canada, in 1995. In 1993, while working on his doctoral dissertation, he joined COM DEV Ltd., Cambridge, ON, Canada, as a Member of the Technical Staff. He was involved in designing passive microwave/RF hardware from 300 MHz to 60 GHz, insuring compliance with specifications, cost, and schedules. He was also a Principal Developer of a variety of COM DEV proprietary software for microwave filters and multiplexers. His varied experience also includes being the Manager of Filter/Multiplexer Technology (Space Group) and Staff Scientist of Corporate Research and Development (R&D). He is currently the Director of R&D. He is responsible for overseeing the development of the company R&D Roadmap and next-generation product development. He is also an Adjunct Associate Professor with the University of Waterloo, Waterloo, ON, Canada. He has authored or coauthored over 60 publications. He holds 12 patents with six pending. His research interests include computer-aided design, tuning, electromagnetic (EM) modeling, and optimization of microwave filter/multiplexer for both space- and ground-based applications. Dr. Yu is a member of the IEEE Technical Coordinating Committee (TCC, MTT-8) and a frequent reviewer of many IEEE and Institution of Electrical Engineers (IEE) publications. He is the cochair of the IEEE Microwave Theory and Techniques Society (IEEE MTT) Technical Program Committee (TPC-10). He was the recipient of the 1995 COM DEV Ltd. Achievement Award for the development of a computer-aided tuning system for microwave filters and multiplexers.

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Ying Wang received the B.Eng. and M.Eng. degrees in electrical engineering from the Nanjing University of Science and Technology, Nanjing, China, in 1993 and 1996, respectively, and the Ph.D. degree in electrical engineering from the University of Waterloo, Waterloo, ON, Canada, in 2000. In 2000, she joined COM DEV Ltd., Cambridge, ON, Canada, where she is currently a Senior Member of the Technical Staff. Since joining COM DEV Ltd., she has been involved in the development of computer-aided design (CAD) software for design, simulation, and optimization of microwave circuits for space application.

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Rectangular Waveguide With Dielectric-Filled Corrugations Supporting Backward Waves Islam A. Eshrah, Student Member, IEEE, Ahmed A. Kishk, Fellow, IEEE, Alexander B. Yakovlev, Senior Member, IEEE, and Allen W. Glisson, Fellow, IEEE

Abstract—A new application for corrugated waveguides as left-handed (LH) meta-material guided-wave structures is investigated. The waveguide is operated below the cutoff of the dominant mode, where the waveguide has an inherent shunt inductance. The dielectric-filled corrugations are used to provide a series capacitance, which, along with the shunt inductance, create the necessary environment to support backward waves. A simple equivalent-circuit model is constructed, and proves quite accurate in determining the dispersion, as well as the scattering characteristics of the structure. Experimental verification of the occurrence of backward waves in the corrugated waveguide is presented. Very good agreement between the results obtained using the equivalent-circuit model and the full-wave finite-difference time-domain solution is achieved. The effect of the various design parameters on the LH propagation bandwidth is investigated. The advantages and possible applications of the structure are discussed. Index Terms—Corrugated waveguide, metamaterial transmission lines, moment methods, periodic structure.

I. INTRODUCTION

W

ITH THE increasing interest in meta-material transmission lines (TLs) [1]–[4] that exhibit negative refraction resulting in left-handed (LH) propagation [5]–[11], attention was drawn toward guided-wave structures that manifest the same behavior [12]–[15]. Such structures have the advantage of being closed and, thus, have minimal radiation losses and do not suffer from any extraneous effects. In [13], an LH waveguide was realized by inserting printed split-ring resonators along the direction of propagation in the conventional rectangular waveguide. In terms of the TL equivalent-circuit model, the reason of using these insertions is to realize series capacitance and shunt inductance simultaneously within the frequency range in which LH propagation is desired. In this paper, the series capacitance is achieved by introducing dielectric-filled transverse corrugations to the waveguide broad wall, as shown in the geometry in Fig. 1. Corrugated waveguides have been traditionally used with corrugated horn antennas [16] to support hybrid modes that improve the radiation characteristics. With the proper choice of the corrugation parameters, however, they can serve as a capacitive immittance surface instead. Operating the waveguide below the cutoff frequency, where an

Fig. 1. Rectangular waveguide with dielectric-filled corrugations supporting LH propagation.

inherent shunt inductance occurs, in the presence of the capacitive corrugations provides the required environment for supporting the LH propagation regime. In [14], a brief description of the analysis of the corrugated waveguide using an equivalent TL model was discussed. The analysis was based on determining the per-unit-length parameters of the equivalent TL model and identifying the passband and stopband. In addition to the simple circuit model that can accurately predict the behavior of the structure, a full-wave modal solution of this waveguide was performed in [15], where spectral analysis of the infinite periodically corrugated waveguide is presented and the dispersion characteristics of the structure were investigated. In Section II, the circuit model of the unit cell, i.e., one corrugation, is presented in detail. From the circuit analysis, the propagation constant is estimated. Experimental results illustrating the occurrence of LH propagating waves are presented in Section III, along with results showing the phase advance phenomenon. The effect of the various parameters on the bandwidth of the LH operation is also presented in Section III. The results obtained using the circuit analysis are compared to those obtained using the finite-difference time-domain (FDTD) method and exhibit very good agreement. Conclusions and discussions are presented in Section IV. II. EQUIVALENT-CIRCUIT MODEL

Manuscript received March 31, 2005; revised May 23, 2005. This work was supported in part by the Army Research Office under Grant DAAD19-02-10074. The authors are with the Department of Electrical Engineering, The University of Mississippi, University, MS 38677 USA (e-mail: [email protected]; [email protected]; [email protected]; [email protected]). Digital Object Identifier 10.1109/TMTT.2005.855748

The physical and electrical parameters of the corrugated waveguide are given in Fig. 2. The waveguide is assumed to and . The corrugation length be air filled, i.e., does not necessarily have a wall-to-wall extent, i.e., . The corrugations are filled with a material having constitutive parameters and , and have width, depth, and period , ,

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ESHRAH et al.: RECTANGULAR WAVEGUIDE WITH DIELECTRIC-FILLED CORRUGATIONS SUPPORTING BACKWARD WAVES

Fig. 2. Rectangular waveguide with dielectric-filled (a) Transverse section. (b) Longitudinal (top) section.

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corrugations.

and , respectively. The waveguide height is measured from the corrugation interface to the other wall of the waveguide. The TL or telegrapher’s equations for the modal voltage and current of the conventional rectangular waveguide [17] imply that the equivalent circuit of a differential TL element depends on the mode type (TE or TM) and the mode state (propagating mode of the waveor evanescent) [14]. For the dominant guide, the TL equations may be written as

Fig. 3. Transverse slot loaded with a short-circuited waveguide section. (a) A cut through one corrugated cell. (b) Equivalent-circuit model.

(1) where and are the per-unit-length inductance and capacitance of the equivalent TL, respectively, and may be expressed as (2) where , is the cutoff frequency of the waveis constant and guide dominant mode, and the impedance depends on the adopted definition of the waveguide characteristic impedance. For the power–voltage definition of the waveis given by guide characteristic impedance [18], (3) It can be readily seen from (2) that, above the cutoff frequency, the conventional series shunt model is obtained. Below the cutoff, however, a series shunt circuit model rebecomes flects the evanescent nature of the TE mode since . Thus, an inherent shunt inductance ocnegative for curs for the evanescent TE mode. To realize the series shunt circuit model that supports LH propagation, a capacitive series waveguide discontinuity is required. Transverse broad wall slots, which are known to be modeled as series loads, may be loaded with a capacitive impedance to yield the required series capacitance. One possible load that satisfies this requirement is a short-circuited waveguide section with cross-sectional dimensions equal to that of the slot. To support propagating waves and have a cutoff frequency less than that of the waveguide, the short-circuited waveguide should be filled with a dielectric with sufficiently high permittivity. The slot with the short-circuited section can be regarded as a dielectric-filled corrugation depicted

in Fig. 3(a). A simple equivalent-circuit model for waveguide transverse slots was constructed in [19] and, thus, the equivalent-circuit model of the corrugation may be obtained as depicted in Fig. 3(b). The LC parallel combination in Fig. 3(b) models the slot, whereas the transformer accounts for the change in impedance definition from the main waveguide to the secondary waveguide of the corrugation. Thus, the admittance introduced by one corrugation may be given by (4) are the propagation constant and the characterwhere and istic impedance of the corrugation waveguide. For sufficiently narrow slots and sufficiently small period of the corrugations, , the effective per-unit-length inductance and i.e., capacitance of the TL model of the corrugated waveguide may be found using (5) Within some frequency range higher than the corrugation waveguide cutoff and lower than the main waveguide cutoff, and with the proper choice of the corrugation depth and period, and are negative corresponding to a shunt inductance and series capacitance, respectively. The typical behavior of the per-unit-length effective parameters is depicted in Fig. 4. is negaIt is clear that below the cutoff frequency , tive, yielding a shunt inductance. Within the frequency range where the contribution of the capacitance provided by the corrugation exceeds that of the waveguide inductance, a series capacitance is achieved and, thus, LH propagation can be supported. Whereas Fig. 4 shows the case , different dimensions may result where

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Fig. 4. Typical curves for the effective per-unit-length inductance and capacitance of the TL model. The scale of the inductance and capacitance is not the same.

Fig. 5. Manufactured corrugated waveguide prototype showing the artificial conducting wall, the corrugations inserted in the waveguide, and some pieces of the laminate before stacking them to form the corrugations.

in . The propagation constant may thus be computed in the different frequency ranges using (6) elsewhere and . In where (6), the first and second branches correspond to right-handed (RH) and LH propagation, respectively, and the third branch corresponds to evanescence occurring when the per-unit-length parameters have opposite signs. Alternatively, the propagation constant may be obtained using the Bloch–Floquet theorem as (7) Notice that (6) is the first-order approximation of (7) for a suffiand can be comciently small period. The frequencies puted by letting go to and 0, respectively, yielding (8) which can be solved for these two frequencies numerically. It is important to notice that for relatively electrically long slots that have wall-to-wall extent, the effect of the slot admittance is dominated by the short-circuit waveguide admittance. Moreover, the transformer turns ratio is unity. This facilitates the analysis of the structure even more, alleviates the need of determining the slot circuit parameters, and hence, helps speed up the design procedure using the circuit model. III. RESULTS A. Verifications and Experimental Results To verify the wave propagation below the cutoff, a prototype of the corrugated waveguide was realized as shown in Fig. 5. The corrugations were built by stacking rectangular pieces milled off a Rogers high-frequency laminate (RO3010) and thickness of having a dielectric constant of mm. The rectangles have dimensions of mm mm. An artificial wall was inserted in a standard and

Fig. 6. Insertion loss for a rectangular waveguide with and without the corrugations. The simulation results are plotted for the cases with and without an air gap between the corrugation and bottom wall.

-band waveguide section of length 8.8 mm to reduce the width mm and raise the cutoff frequency to GHz. to Fig. 6 shows the measured insertion loss with and without the corrugations. Experimental results are compared with those obtained using FDTD commercial software.1 The waveguide is excited using standard -band adapters connected to an HP8510 network analyzer. The discrepancies between the experimental and simulation results are attributed to the imperfections in the hand-assembly manufacturing process of this simple prototype, namely, the air gap between the laminate pieces and the bottom wall of the waveguide, which is very crucial in the operation of the structure since it is based on the fact that the corrugations are short circuited. The effect of the air gap on the transmission coefficient is also shown in Fig. 6, where the simulation results with and without an air gap of 0.1 mm are depicted. Other sources 1QuickWave3D: A General Purpose Electromagnetic Simulator Based on Conformal Finite-Difference Time-Domain Method, ver. 2.2, QWED Sp. Z o.o, Warsaw, Poland, Dec. 1998.

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Fig. 8. Corrugated waveguide excited by an incident TE mode of a wider noncorrugated waveguide. (a) Original geometry. (b) Equivalent-circuit model. Fig. 7. Comparison between the phase of the transmission coefficient S a reference waveguide section and a longer section.

of

of discrepancy include the possible nonuniform air gap between the corrugations and the artificial wall inserted in the waveguide and the air gaps between the corrugations themselves. It is worth mentioning that the effect of the dielectric and conductor losses was taken into consideration in the FDTD simulation. That is why the transmission in the LH band experiences some attenuation, which is dominated by the dielectric losses (a loss tangent of 0.0023 at 10 GHz). For lossless dielectric, total transmission is observed in the LH band. The ripples in the transmission bands are due to the mismatch between the waveguide ports and the corrugated waveguide section, which results in standing waves that vary the response of the system with frequency. To verify the phase advance phenomenon within the LH propagation band, the method suggested in [13] is employed, for a where the phase of the transmission coefficient reference waveguide section is compared to that obtained for slightly longer sections having four and eight more cells. The phase advance over a portion of the LH band is plotted in Fig. 7, as obtained from the simulation. Notice the linear increase in phase with the increase in the number of cells at every frequency point. B. Bandwidth Control and Parametric Studies The effect of the various design parameters on the LH propagation bandwidth and dispersion characteristics is studied by considering the setup shown in Fig. 8(a) for which the equivalent circuit is depicted in Fig. 8(b). The broad wall of the port waveguides and the corrugated waveguide measure 22.86 and 17 mm, respectively. In the equivalent-circuit model, the ports are designated by the characteristic impedance . Every unit cell in Fig. 8(b) is made of the circuit in Fig. 3(b). Notice that the discontinuity is not modeled in the circuit model. First, the effect of the waveguide height-to-width ratio is investigated. Figs. 9 and 10 show that the bandwidth increases as the air-filled height decreases. This can be explained in terms of equivalent-circuit model as the per-unit-length inductance

Fig. 9. Effect of the waveguide height b on the dispersion behavior of the corrugated waveguide. The solid and dashed lines represent the real and imaginary parts, respectively. The curves are plotted for b (mm) = 6:46; 4:46; and 2:46 designated by (+), (), and (), respectively.

decreases and, thus, will change its sign over a wider frequency range. In Fig. 9, the upper frequency of the LH band decreases, whereas the lower frequency is the increases as tends to decrease same. Notice that the stopband decreases, approaching a balanced condition for the comas posite waveguide [4], i.e., . Indeed, at mm, , resulting in a vanishing bandgap. For lower values of , is greater than , which causes the LH passband to occur in , the RH passband in the range , the range and the stopband in the range , as observed in the mm in Fig. 9. The narrow stopband in this case with case results in a smoother transition from the LH to RH passbands, as shown in Fig. 10(b), compared to the case depicted in Fig. 10(a). The plots in Fig. 10 also show a comparison between the circuit model results obtained using Agilent’s Advanced Design System (ADS) [20] and the full-wave FDTD results obtained using Quickwave 3-D.

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Fig. 11. Effect of the corrugations width-to-period ratio on the dispersion behavior of the corrugated waveguide. The solid and dashed lines represent the real and imaginary parts, respectively. The curves are plotted for w = 1:27 mm, and p (mm) = 1:37; 1:905; and 2:54 designated by (+), (), and (), respectively.

Fig. 10. Effect of the waveguide height b on the transmission coefficient S . (a) b = 6:46 mm. (b) b = 2:46 mm.

An increase in the corrugation width for a fixed period is reflected positively on the bandwidth, as depicted in Fig. 11. This can be expected since the average capacitance offered by the increases. However, for a concorrugations increases as stant width-to-period ratio, varying the period has virtually no effect on the dispersion characteristics, provided that the narrow slot approximation is not violated and the period is small relative to the wavelength. This can be understood from the expression where the term is a function of the width-to-peof riod ratio. Decreasing the length of the corrugation results in an increase in the corrugation waveguide cutoff frequency and, thus, an increase in the corrugation wavelength . This results in a and, consedecrease in the corrugation electrical depth quently, a positive shift in the LH band. Also, since the corrugation characteristic impedance increases as decreases, the decreases, and thus, the bandcapacitive susceptance of width of the LH operation decreases for shorter corrugations. IV. CONCLUSION A circuit model analysis for a rectangular waveguide with dielectric-filled corrugations was presented. The results obtained

using the equivalent-circuit model, being in very good agreement with the full-wave FDTD solution, show that this structure can support LH propagation and predict with high accuracy its frequency band. The simplicity of the analysis of this structure makes it an attractive tool to gain more insight into the physics of the LH propagation phenomenon in guided-wave structures, especially since the modal solution of the corrugated waveguide is available. The possibility of designing a dual-band LH waveguide by using corrugations with different depths either on opposite walls or alternating on the same wall was also considered. It is also interesting to notice that the dimensions of the waveguide may be miniaturized while supporting the LH propagating waves. An interesting potential application for the composite RH/LH waveguide is its use in waveguide slot antenna arrays, where the scanning capability can be improved by frequency scanning through the RH and LH passbands. A well-known problem for waveguide antenna arrays is the fact that the waveguide wavelength is larger than the free-space wavelength. Thus, the elements are separated by a distance larger than half the free-space wavelength (to guarantee equiphase excitation), which may lead to the appearance of grating lobes while scanning the frequency. In the LH band, the guided propagation constant can be equal to or larger than its free-space counterpart (in magnitude) and its gradient with frequency is much higher, allowing large scan angles with small frequency change. This alleviates the need to use elements with wide radiation pattern bandwidth since a small frequency sweep causes a large change in the propagation constant and, thus, a wide range of progressive phase shift between the array elements. The waveguide slots may be on the broad wall opposite to the corrugated wall or the narrow wall in the case of a two-walled corrugated waveguide. Future study involves deeper investigation of the analysis of this periodic structure and understanding the behavior of the supported modes within this environment. Although this structure may be rather difficult to fabricate as compared to

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other designs, such as split-ring resonator insertions in rectangular waveguide, it triggers the analysis of other structures that may exhibit the same effect including printed dipoles and slots, dielectric slabs with holes, strip-loaded dielectric slabs, and printed dipoles with vias.

ACKNOWLEDGMENT The authors wish to thank the Rogers Corporation, Chandler, AZ, for providing a free sample of the high-frequency laminate under the Rogers University Program.

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Islam A. Eshrah (S’00) was born in Cairo, Egypt, in 1977. He received the B.Sc. and M.Sc. degrees in electronics and telecommunications engineering from Cairo University, Cairo, Egypt, in 2000 and 2002, respectively, and is currently working toward the Ph.D. degree in electrical engineering at The University of Mississippi, University. From 2000 to 2002, he was a Teaching Assistant with the Department of Electronics and Telecommunications Engineering, Cairo University. His research interests include dielectric-resonator antennas, integral-equation numerical methods, modeling of microwave structures, phasedarray systems, and metamaterial guided-wave structures. Mr. Eshrah is a member of Phi Kappa Phi. He was the recipient of the 2004 Young Scientist Award presented at the URSI International Symposium on Electromagnetics, Pisa, Italy, the 2005 Young Scientist Award presented at the URSI General Assembly, New Delhi, India, and the 2005 Raj Mittra Junior Researcher Award presented at the Antennas and Propagation Symposium, Washington DC.

REFERENCES [1] G. V. Eleftheriades, A. K. Iyer, and P. C. Kremer, “Planar negative refractive index media using periodically L–C loaded transmission lines,” IEEE Trans. Microw. Theory Tech., vol. 50, no. 12, pp. 2702–2712, Dec. 2002. [2] G. V. Eleftheriades, O. Siddiqui, and A. K. Iyer, “Transmission line models for negative refractive index media and associated implementations without excess resonators,” IEEE Microw. Wireless Compon. Lett., vol. 13, no. 2, pp. 51–53, Feb. 2003. [3] T. Decoopman, O. Vanbésien, and D. Lippens, “Demonstration of a backward wave in a single split ring resonator and wire loaded finline,” IEEE Microw. Wireless Compon. Lett., vol. 14, no. 11, pp. 507–509, Nov. 2004. [4] A. Lai, C. Caloz, and T. Itoh, “Composite right/left-handed transmission line metamaterials,” IEEE Micro, vol. 5, no. 3, pp. 34–50, Sep. 2004. [5] V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of " and ,” Sov. Phys.–Usp., vol. 10, no. 4, pp. 509–514, 1968. [6] J. B. Pendry, “Negative refraction makes a perfect lense,” Phys. Rev. Lett., vol. 85, no. 18, pp. 3966–3969, 2000. [7] D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Shultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett., vol. 84, no. 18, pp. 4184–4187, 2000. [8] N. Engheta, “An idea for thin subwavelength cavity resonators using metamaterials with negative permittivity and permeability,” IEEE Antennas Wireless Propag. Lett., vol. 1, no. 1, pp. 10–13, Dec. 2002. [9] A. Alù and N. Engheta, “Pairing an epsilon-negative slab with a mu-negative slab: Resonance, tunneling and transparency,” IEEE Trans. Antennas Propag., vol. 51, no. 10, pp. 2558–2571, Oct. 2003. [10] R. A. Shelby, D. R. Smith, and S. Shultz, “Experimental verification of a negative index of refraction,” Science, vol. 292, no. 5514, pp. 77–79, 2001. [11] 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. 2075–2081, Nov. 1999. [12] R. Marques, J. Martel, F. Mesa, and F. Medina, “Left-handed-media simulation and transmission of EM waves in subwavelength split-ring-resonator-loaded metallic waveguides,” Phys. Rev. Lett., pp. 183 901–183 904, Oct. 2002. [13] S. Hrabar, J. Bartolic, and Z. Sipus, “Waveguide miniaturization using uniaxial negative permeability metamaterial,” IEEE Trans. Antennas Propag., vol. 53, no. 1, pp. 110–119, Jan. 2005. [14] I. A. Eshrah, A. A. Kishk, A. B. Yakovlev, and A. W. Glisson, “Evanescent rectangular waveguide with corrugated walls: A composite right/left-handed metaguide,” in IEEE MTT-S Int. Microwave Symp. Dig., 2005 [CD ROM]. [15] , “Modal analysis of corrugated rectangular waveguides supporting left-hand propagation,” in IEEE AP-S Int. Symp. Dig., 2005 [CD ROM]. [16] P. J. B. Clarricoats and A. D. Olver, Corrugated Horns for Microwave Antennas. London, U.K.: Peregrinus, 1984. [17] N. Marcuvitz, Waveguide Handbook. London, U.K.: Peregrinus, 1986. [18] P. A. Rizzi, Microwave Engineering: Passive Circuits. Englewood Cliffs, NJ: Prentice-Hall, 1988. [19] I. A. Eshrah, A. A. Kishk, A. B. Yakovlev, and A. W. Glisson, “Loadindependent equivalent circuit model for transverse waveguide slots,” in IEEE AP-S Int. Symp. Dig., 2005 [CD ROM]. [20] Advanced Design System 2003A, User’s Guide, Agilent Technol., Palo Alto, CA, 2003.

Ahmed A. Kishk (S’84–M’86–SM’90–F’98) received the B.S. degree in electrical engineering from Cairo University, Cairo, Egypt, in 1977, the B.S. degree in applied mathematics from Ain-Shams University, Cairo, Egypt, in 1980, and the M.Eng. and Ph.D. degrees in electrical engineering from the University of Manitoba, Winnipeg, MB, Canada, in 1983 and 1986, respectively. From 1977 to 1981, he was a Research Assistant and an Instructor with the Faculty of Engineering, Cairo University. From 1981 to 1985, he was a Research Assistant with the Department of Electrical Engineering, University of Manitoba. From December 1985 to August 1986, he was a Research Associate Fellow with the same department. In 1986, he joined the Department of Electrical Engineering, The University of Mississippi, University, as an Assistant Professor. He was on sabbatical leave with Chalmers University of Technology during the 1994–1995 academic year. He is currently a Professor with The University of Mississippi (since 1995). He was an Editor (1997) and Editor-in-Chief (1998–2001) of the ACES Journal. He was the Chair of the Physics and Engineering Division, Mississippi Academy of Science (2001–2002). He has authored or coauthored over 150 refereed journal papers and book chapters. He coauthored Microwave Horns and Feeds book (London, U.K.: IEE, 1994; Piscataway, NJ: IEEE Press, 1994) and coauthored Chapter 2 of Handbook of Microstrip Antennas (Stevenage, U.K.: Peregrinus, 1989). His research interest includes the design of millimeter frequency antennas, feeds for parabolic reflectors, dielectric-resonator antennas, microstrip antennas, soft and hard surfaces, phased-array antennas, and computer-aided design for antennas. Dr. Kishk is a member of Sigma Xi, the U.S. National Committee of International Union of Radio Science (URSI) Commission B, the Applied Computational Electromagnetics Society, the Electromagnetic Academy, and Phi Kappa Phi. He is currently an editor of the IEEE Antennas and Propagation Magazine. He was the recipient of the 1995 Outstanding Paper Award for a paper published in the Applied Computational Electromagnetic Society Journal. He was the recipient of the 1997 Outstanding Engineering Educator Award presented by Memphis Section of the IEEE. He was the recipient of the Outstanding Engineering Faculty Member of 1998. He was the recipient of the 2001 Faculty Research Award for outstanding performance in research and the 2005 School of Engineering Senior Faculty Research Award. He was also the recipient of the Valued Contribution Award for Outstanding Invited Presentation, “EM Modeling of Surfaces with STOP or GO Characteristics—Artificial Magnetic Conductors and Soft and Hard Surfaces” presented by the Applied Computational Electromagnetic Society. He was the recipient of the 2004 IEEE Microwave Theory and Techniques Society (IEEE MTT-S) Microwave Prize.

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Alexander B. Yakovlev (S’94–M’97–SM’01) was born on June 5, 1964, in the Ukraine. He received the Ph.D. degree in radiophysics from the Institute of Radiophysics and Electronics, National Academy of Sciences, Kharkov, Ukraine, in 1992, and the Ph.D. degree in Electrical Engineering from the University of Wisconsin at Milwaukee, in 1997. From 1992 to 1994, he was an Assistant Professor with the Department of Radiophysics, Dniepropetrovsk State University, Dniepropetrovsk, Ukraine. From 1994 to 1997, he was a Research and Teaching Assistant with the Department of Electrical Engineering and Computer Science, University of Wisconsin at Milwaukee. From 1997 to 1998, he was a Research and Development Engineer with the Compact Software Division, Ansoft Corporation, Paterson, NJ, and with the Ansoft Corporation, Pittsburgh, PA. From 1998 to 2000, he was a Post-Doctoral Research Associate with the Electrical and Computer Engineering Department, North Carolina State University, Raleigh. In Summer 2000, he joined the Department of Electrical Engineering, The University of Mississippi, University, as an Assistant Professor, and became an Associate Professor in Summer 2004. His research interests include mathematical methods in applied electromagnetics, modeling of high-frequency interconnection structures and amplifier arrays for spatial and quasi-optical power combining, integrated-circuit elements and devices, theory of leaky waves, and singularity theory. Dr. Yakovlev is a member of URSI Commission B. He was the recipient of the 1992 Young Scientist Award presented at the URSI International Symposium on Electromagnetic Theory, Sydney, Australia, and the 1996 Young Scientist Award presented at the International Symposium on Antennas and Propagation, Chiba, Japan.

Allen W. Glisson (S’71–M’78–SM’88–F’02) received the B.S., M.S., and Ph.D. degrees in electrical engineering from The University of Mississippi, University, in 1973, 1975, and 1978, respectively. In 1978, he joined the faculty of The University of Mississippi, where he is currently a Professor and Chair of the Department of Electrical Engineering. His current research interests include the development and application of numerical techniques for treating electromagnetic radiation and scattering problems, and modeling of dielectric resonators and dielectric-resonator antennas. He is an Associate Editor for Radio Science, and Co-Editor-in-Chief of the Applied Computational Electromagnetics Society Journal. Dr. Glisson is a member of Commission B of URSI and the Applied Computational Electromagnetics Society. Since 1984, he has served as the associate editor for book reviews and abstracts for the IEEE Antennas and Propagation Society Magazine. He recently served as the editor-in-chief of the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION. He currently serves on the Board of Directors of the Applied Computational Electromagnetics Society and is a member of the IEEE Antennas and Propagation Society (IEEE AP-S) Press Liaison Committee. He previously served as a member of the IEEE AP-S Administrative Committee (AdCom) and as the secretary of Commission B of the U.S. National Committee of URSI. He was selected as the Outstanding Engineering Faculty Member in 1986, 1996, and 2004. He was the recipient of the 1989 Ralph R. Teetor Educational Award and 2002 Faculty Service Award of the School of Engineering. He was also the recipient of a Best Paper Award presented by the SUMMA Foundation. He twice received a citation for excellence in refereeing from the American Geophysical Union. He was a recipient of the 2004 Microwave Prize presented by the IEEE Microwave Theory and Techniques Society (IEEE MTT-S).

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Empirical Model Generation Techniques for Planar Microwave Components Using Electromagnetic Linear Regression Models Ginés Doménech-Asensi, Member, IEEE, Juan Hinojosa, Juan Martínez-Alajarín, Student Member, IEEE, and Javier Garrigós-Guerrero, Member, IEEE

Abstract—Accurate and efficient empirical model generation techniques of microwave devices, for a large range of geometric and material parameters opportunely chosen, are presented. The empirical models are based on multiple linear regression approach, which compensates the error between an initial inaccurate empirical model and an electromagnetic (EM) full-wave solver (or measurement data). The aim of these techniques is to generate accurate empirical models, which are computationally very efficient with respect to any EM technique. These simple models could be integrated in a toolbox of any commercially available computed-aided design tools for RF/microwave circuits. Comparisons with artificial neural networks and linear-regression-based models are listed and discussed for the dispersion of a microstrip transmission line propagating the quasi-TEM mode and a microwave tunable phase shifter propagating the even mode. Index Terms—Anisotropic media, computer-aided design (CAD), coplanar, microstrip, modeling, tunable circuits and devices.

I. INTRODUCTION

M

ANY computer-aided design (CAD) tools for radio frequency (RF)/microwave circuits, such as the Advanced Design System (ADS), Microwave Office, Sonnet, etc., allow the design and optimization of microwave circuits. The simulations are fast and the results are in good agreement with the experimental measurements. Unfortunately, many CAD tools do not allow carrying out simulations for certain geometrical dimensions of device, novel devices, and specific materials (anisotropic, ferroelectric, etc.). In this case, it is necessary to use field simulation and analysis techniques based on frequency-domain or time-domain electromagnetic (EM) numerical methods like, for example, [1]–[3]. However, these EM numerical methods require intensive computations in the central processing unit (CPU) and make device optimization a formidable task. Recently, hybrid methods have been developed to model microwave circuits with artificial neural networks (ANNs) [4]. These hybrid methods combine computational efficiency of Manuscript received April 1, 2005; revised July 20, 2005. This work was supported in part by the Ministerio de Ciencia y Tecnología under Grant TIC200201266 and by the Fundación Séneca de la Región de Murcia, Spain, under Grant PB/39/FS/02. The authors are with the Departamento de Electrónica, Tecnología de Computadoras y Proyectos, Universidad Politécnica de Cartagena, Cartagena 30202, Spain (e-mail: [email protected]; [email protected]). Digital Object Identifier 10.1109/TMTT.2005.857331

coarse models (CMs) with the accuracy of fine models (FMs) by means of ANNs. CMs are initial empirical models with a limited validity range for their parameters whose simulation results may become inaccurate. FMs can be provided by an EM simulator or even by direct measurements. These techniques decrease the cost of needed data, improve generalization ability, and are suitable for novel device modeling. However, there are some aspects of these approaches that require expertise such as that of finding the optimal set of the internal parameters of the ANN, the most appropriate iteration number, the learning algorithm, etc. Moreover, models so obtained are most difficult to be integrated in a toolbox of any commercially available CAD tool for RF/microwave circuits than any empirical model. The aim of this paper is to suggest novel approaches exploiting linear regression models (LRMs) [5], substituting ANN in the hybrid neural methods, which can serve as a basis for constructing a set of empirical models to generate the stipulated input–output data of a given device. Models so obtained combine high accuracy, large range of geometrical and material parameters opportunely chosen, and reduced CPU time. In this paper, the empirical model generation techniques developed in [6] have been extended to space mapping (SM) technology [4]. Moreover, the modeling techniques are illustrated for two examples. One is a microstrip line whose dispersion model for the quasi-transverse electromagnetic (TEM) mode has been obtained and the other is a microwave tunable phase shifter whose model for the even mode has been achieved for a set of parameters extended with respect to the works in [6]. The microwave tunable phase shifter is based on a coplanar waveguide (CPW) supporting a nematic liquid crystal [7]. Initial quasi-static empirical models of these devices are provided from known Hammerstad and Jensen model [8] for the microstrip line, and extracted from Schwarz–Christoffel mapping [9] and then using Szentkuti’s transformation [10] for the microwave tunable phase shifter device. This paper is organized as follows. Section II describes the empirical model generation techniques of microwave devices using LRMs. Section III presents the initial empirical models of the microstrip transmission line and microwave tunable phase shifter. Comparisons with hybrid neural and LRM modeling methods are provided in Section IV for the microstrip transmission line and microwave tunable phase shifter. Finally, conclusions are presented in Section V.

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Fig. 4. SM-LRM modeling method. Fig. 1.

Classical approach.

Figs. 1–4, vector represents the design parameters and fre, quency of the initial empirical model, FM, and LRM. , and are the respective model responses. is . much faster to calculate, but less accurate than In the EM-LRM method [11] illustrated in Fig. 2, the differbetween the responses of both CM and FM is used ence to find the coefficients of the LRM, reducing the number of FM simulations or measurements due to a simpler input–output relationship (2)

Fig. 2.

Thus, the response of the EM-LRM model given input data is

EM-LRM modeling method.

for a (3)

For the PKI-LRM method [12] shown in Fig. 3, the CM output is used as input for the LRM in addition to other inputs (design parameters and frequency). The coefficients of the LRM are found such that its response is approximately equal to the FM response. The aim of the PKI-LRM method is to find such that an appropriate response Fig. 3.

PKI-LRM modeling method.

(4)

II. EMPIRICAL MODEL GENERATION TECHNIQUES For microwave problems and in the case of a classical approach (Fig. 1), large amounts of data are needed to ensure model accuracy either by EM simulation or by measurement. This is very time expensive, since the simulations or measurements must be performed for many combinations of different values of geometric, material, process, and input signal paramis expressed as eters. The response (1) is the FM response obtained either by EM simulawhere tion or by measurement. In order to reduce the data needed, we have applied the same innovate strategies than those used in [4]. Among these strategies, we have used the following techniques: the hybrid electromagnetic linear regression model (EM-LRM) modeling approach (Fig. 2); the prior knowledge input (PKI-LRM) modeling method (Fig. 3); and the space mapping (SM-LRM)-based modeling technique (Fig. 4). For all these approaches, an initial empirical model is required as CM, which will be optimized in order to provide an accurate device modeling. This initial empirical model can be obtained by using quasi-static analysis. In

In the SM-LRM method [13] shown in Fig. 4, the LRM is used to obtain a set of design parameters and frequencies , which makes the CM response to be as close as possible to the FM response. The aim of the SM-LRM method is to find an such that appropriate response (5) Using this last technique (SM-LRM), there are several ways from , , and [14], [15]. Instead of to obtain working with all parameters , we have used only selected preassigned parameters, which is a special type of SM method called implicit space mapping (ISM) [16]. Starting from this basis, we have used a noniterative process in the following two steps. Step 1) Parameter extraction is performed using initial empirical model to obtain the FM response. This gives a set of values such that (6) Step 2) Linear regression is applied to find a function such that (7)

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paper, we have chosen to use the quasi-static empirical model presented in [8] as initial empirical model (CM). B. Initial Empirical Model of the Microwave Tunable Device The microwave tunable device (Fig. 6) is based on a CPW supporting a material with specific properties. The dielectric and thickness is isotropic. substrate with the permittivity is a frequency-agile material The substrate with a thickness with uniaxial anisotropic properties whose permittivity tensor is Fig. 5.

Cross section of the microstrip transmission line.

(9) where

(10)

Fig. 6.

Cross section of the microwave liquid crystal tunable phase shifter.

The general form of the LRMs for variables used in all of the above modeling approaches is [5]

(8)

where independent variables are the input vector (design parameters, frequency, ) of the LRM. Coefficients can be obtained using several optimization algorithms. In this paper, we have determined them by means of a least square optimization have been determined, empirical method. Once coefficients models are immediately available for fast accurate simulations. III. INITIAL EMPIRICAL MODELS OF THE MICROWAVE DEVICES The above-described techniques have been applied to a microstrip transmission line (Fig. 5) and a microwave tunable device realizing the phase shifter electronics function (Fig. 6). A. Initial Empirical Model of the Microstrip Transmission Line In the case of the microstrip transmission line, accurate quasistatic and dispersion empirical models for the quasi-TEM mode is isotropic [8], [17]. are well known when the permittivity It is worth mentioning here that the purpose of using this device is to show that LRM-based modeling techniques described in Section II in conjunction with an initial quasi-static empirical model can be applied to obtain empirical dispersion models with a high degree of accuracy. The modeling of dispersive relations is a topic of practical interest in microwave devices. In this

The frequency-agile material is a nematic liquid crystal [7] as in [18]. An initial optical axis ( ) orientation of the molecules parallel to the RF measuring electric field is carried out. It is obtained by depositing a polyimide (not shown in Fig. 6) on and the liquid the interface between the isotropic material . Polyimide is annealed and brushed in order to give crystal to the liquid crystal molecules. a planar orientation When a bias voltage is applied perpendicularly to the initial optical axis of the molecules in addition to RF signal, it is possible to control the orientation of the molecules according to the angle , so that the effective relative permittivity of the CPW-based device is modified. This variation of the effective relative permittivity carries out a modification of the guided wavelength and, therefore, a phase shift according to the following relationship: (11) where is the length of the CPW-based device, is the frequency, is the light speed, and the applied electric field. Initial empirical model of this device for the even mode can be provided from Schwarz–Christoffel mapping [9] and then using Szentkuti’s transformation [10]. 1) Device Analysis by the Schwarz–Christoffel Transformation: To analyze the microwave tunable phase shifter (Fig. 6) by the Schwarz–Christoffel transformation [9], we assume that the strip and ground planes are perfect conductors, the strip is m , and the ground planes are infininfinitesimally thin itely large. We also suppose the interface between the isotropic and the anisotropic substrate with substrate of permittivity permittivity tensor , except where the strip resides, represents a perfect magnetic surface. It should be noted that this assumption is exact only when the upper and lower regions are identical and, thus, maintain a perfect symmetry. For the considered CPW-based device, this symmetry does not exist and, thus, error in calculations is expected. Nevertheless, this error will be corrected with the methods presented in this paper. By using the Schwarz–Christoffel transformation, we obtain the capacitances

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TABLE I

REGION OF INTEREST FOR THE MICROSTRIP TRANSMISSION LINE

TABLE II REGION OF INTEREST FOR THE TUNABLE MICROWAVE PHASE SHIFTER Fig. 7. Equivalent device after Szentkuti’s transformation.

per unit length and, therefore, the static effective permittivity ) and characteristic impedance. Consider the substrates ( , as isotropic (12)

(13)

The parameters device

,

,

, and

are bounds of the CPW-based

(14)

. and are, respectively, the characteristic impedances of the CPW-based device in Figs. 6 and 7, when the dielectric . is obtained substrates are replaced with air from (13) with . is also obtained from (13) with , substituting for from (16). Therefore, quasi-static characteristic impedance and effective permittivity of the microwave tunable phase shifter can be obtained from the following relationships: (20)

(15) and are obtained from (14) and (15), respectively, by replacing by . , , , and are the and complete elliptical integrals of first order of moduli and complementary moduli and . These integrals are obtained from analytical relationships [19]. 2) Szentkuti’s Transformation: Consider now the device is isotropic and is anisotropic. Using Szenof Fig. 6. tkuti’s transformation [10], the anisotropic substrate can be transformed into an isotropic one (Fig. 7) with (16) (17) Quasi-static characteristic impedance of the CPW-based device filled with isotropic and anisotropic substrates shown in in Fig. 7, can be obtained as Fig. 6, and equivalent line follows [20]: (18) (19) and are, respectively, the capacitances per unit where length of the devices shown in Figs. 6 and 7, defined as

(21) and is computed from (12), where substituting for from (16) and for from (17). Dispersion model for this device is not required, since several tests with commercial finite element simulator have shown that the quasi-TEM mode dispersion is very low. IV. RESULTS The LRM-based modeling techniques described in Section II (EM-LRM, PKI-LRM, and SM-LRM) have been applied to the microstrip line (Fig. 5) and the microwave tunable phase shifter (Fig. 6). Desired output data (FM) have been obtained from the spectral domain approach (SDA) method [3] and a commercially available finite element simulator for the mentioned devices, respectively, in the regions of interest shown in Tables I and II. The data of the microwave tunable phase shifter have been extended with respect to works in [6] with some parameters ; m; considered constant, namely: GHz. In this section, the simulation results of the and LRM-based models are compared with those obtained from hybrid neural (EM-ANN, PKI-ANN, and SM-ANN) [4] modeling methods. Different regression models depending on the approach used have been applied. In all cases, we have use second-order polycoefficients have been obtained nomial regression models.

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TABLE III ERRORS BETWEEN DESIRED OUTPUTS AND INITIAL EMPIRICAL, CLASSICAL APPROACH-LRM, EM-LRM, PKI-LRM, SM-LRM, EM-ANN, PKI-ANN, SM-ANN MODEL OUTPUTS FOR THE MICROSTRIP LINE

TABLE IV ERRORS BETWEEN DESIRED OUTPUTS AND INITIAL EMPIRICAL, CLASSICAL APPROACH-LRM, EM-LRM, PKI-LRM, SM-LRM, EM-ANN, PKI-ANN, SM-ANN MODEL OUTPUTS FOR THE MICROWAVE TUNABLE PHASE SHIFTER

using a least square optimization method. In our case, we have used statistics toolbox from MATLAB, which implements these calculations. The confidence value has been set to 0.01. The number of coefficients for a single model depends on the . According to (8), 10, 15, and number of input parameters 21 coefficients are needed, respectively, for 3–5 input parameters. We must consider that each output parameter requires its single model. Thus, in the case of the EM-LRM approach, 10 and 15 coefficients for the modeling of microstrip line and microwave tunable phase shifter, respectively, have been used for and ). For the same respective each output required ( devices, the PKI-LRM method has required 15 and 21 coeffiand ). In the case of the SM-LRM cients for each output ( method, we have selected for the microstrip line and and for the microwave tunable phase shifter as preassigned pawith the LRM. rameters, and we have obtained , , and and ), To obtain the output parameters of the devices ( two LRMs have been required for each preassigned parameter. The number of input parameters is the same that initially, i.e., 3 for the microstrip line and 4 for the microwave tunable phase shifter. This yields 10 and 15 coefficients for the same respective devices and for each output parameter. In the case of the hybrid neural modeling techniques, an ANN using a three-layer perceptron [21] has been adapted. It has been implemented on MATLAB and trained with the Levenberg–Marquardt’s learning algorithm [22] during 500 iterations. We have used 30 neurons for the hidden layer and two neurons for the output layer for all the methods and both devices. The input layers of the EM-ANN and SM-ANN methods have as many inputs (Tables I and II). The input layer of the neurons as PKI-ANN method has two additional neurons corresponding to , ). The available outputs the outputs of the CM ( for the EM-ANN of the ANNs are the pair of data for the PKI-ANN method, method, the pair of data and the preassigned parameters ( , and ) for the SM-ANN method. The mean and max errors over initial empirical models and generated model outputs ( and ) with respect to expected ones (FM results) are shown in Tables III and IV for both devices. The generated models exploiting LRMs and ANNs have been obtained for all parameters of Tables I and II. Half of data have been used for training and the other half for validation. We

COEFFICIENTS FOR PKI-LRM METHOD AND MICROSTRIP LINE

TABLE V

can see that the classical approach based on LRM presents large errors with respect to others. Therefore, a second-order polynomial regression model is not sufficient to model the devices in the regions of interest presented in Tables I and II. EM-LRM, PKI-LRM, and SM-LRM methods show an improvement of and with respect to the initial emthe accuracy for pirical model, although the PKI-LRM approach is definitely coefficients, in four decimal digits the best one. Thus, only format, for the PKI method are shown for the microstrip line and microwave phase shifter in Tables V and VI, respectively, in order not to overdraw this paper. On the other hand, the three hybrid neural methods (EM-ANN, PKI-ANN, and SM-ANN) provide better results on the mean error than any models exploiting LRMs. This shows that the ability of neural networks to model nonlinear systems is better than LRMs. However, the advantages of the LRM-based modeling methods with respect to equivalent ANN-based methods are their standardization and their simplicity and easiness to be implemented and to be integrated in a toolbox of any commercially available CAD tools for RF/microwave circuits. Moreover, their simplicity implies faster model generations. In the case of the devices implicated here, LRM-based modeling methods took between 2–4 s to build a

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TABLE VI

COEFFICIENTS FOR PKI-LRM METHOD AND MICROWAVE PHASE SHIFTER

methods exploiting LRMs. However, LRM-based models are simpler empirical models that are easier to implement and to compute than any ANN-based method that requires expertise to find the optimal structure of the ANN, the most appropriate iteration number, etc. Therefore, the LRM-based techniques are suitable to generate accurate empirical model for planar microwave components. REFERENCES

model, while ANN-based models required between 200–300 s to do the same process, depending on the approach used (EM, PKI, or SM). Note also the accuracy of the generated empirical models can still be improved by dividing into several ranges the input parameters and using as many LRMs as needed. As example, the mean and max errors for the dispersive relations of the miand crostrip line can be less than 0.18% and 2.16% for , respectively, by dividing into three 0.13% and 1.27% for ranges (1–13, 14–24, and 25–40 GHz) the frequency parameter in the PKI-LRM method. Therefore, the empirical model generation techniques exploiting LRMs, except for classical approach, are suitable to be used for accurate modeling of planar microwave components with a large range of geometrical, frequency, and material parameters opportunely chosen. V. CONCLUSION In this paper, three simple and accurate techniques have been developed to perform the modeling of planar microwave components for a large range of geometrical, frequency, and material parameters. These techniques compensate the error between an initial empirical model and an EM simulator (or measurement data) by means of LRMs. They allow decreasing the number of data needed to ensure model accuracy, to improve generalization ability, and to reduce the order polynomial of the regression model with respect to the classical approach. The models obtained with these techniques are accurate empirical models. The three modeling techniques have been applied to two microwave devices (microstrip transmission line and a microwave tunable phase shifter) and compared to equivalent ANN-based methods. These last methods have offered better results than the

[1] J. S. Hornsby and A. Gopinath, “Numerical analysis of a dielectric loaded waveguide with a microstrip line—Finite difference methods,” IEEE Trans. Microw. Theory Tech., vol. 17, no. 9, pp. 684–690, Sep. 1969. [2] S. Akhtarzad and P. B. Johns, “Generalized elements for TLM method of numerical analysis,” Proc. Inst. Elect. Eng., vol. 122, no. 12, pp. 1349–1352, Dec. 1975. [3] T. Itoh and R. Mittra, “Spectral-domain approach for calculating the dispersion characteristics of microstrip lines,” IEEE Trans. Microw. Theory Tech., vol. MTT-21, no. 7, pp. 496–499, Jul. 1973. [4] J. W. Bandler, M. A. Ismail, J. E. Rayas-Sánchez, and Q.-J. Zhang, “Neuromodeling of microwave circuits exploiting space-mapping technology,” IEEE Trans. Microw. Theory Tech., vol. 47, no. 12, pp. 2417–2427, Dec. 1999. [5] M. H. DeGroot, Probability and Statistics, 2nd ed. Reading, MA: Addison-Wesley, 1986. [6] J. Hinojosa, G. Doménech, J. Martínez, and J. Garrigós, “Empirical model generations techniques for planar microwave components using electromagnetic linear regression models,” presented at the IEEE MTT-S Int. Microwave Symp., Long Beach, CA, 2005. [7] P. G. De Gennes and J. Prost, The Physics of Liquid Crystal, 2nd ed. Oxford, U.K.: Clarendon, 1993. [8] E. Hammerstad and O. Jensen, “Accurate models for microstrip computer aided design,” in IEEE MTT-S Int. Microwave Symp. Dig., Washington, DC, 1980, pp. 407–409. [9] R. E. Collin, Field Theory of Guided Waves, 2nd ed. New York: IEEE Press, 1976, pp. 259–273. [10] B. T. Szentkuti, “Simple analysis of anisotropic microstrip lines by a transform method,” Electron. Lett., vol. 12, no. 25, pp. 672–673, Dec. 1976. [11] P. M. Watson and K. C. Gupta, “EM-ANN models for microstrip vias and interconnects in dataset circuits,” IEEE Trans. Microw. Theory Tech., vol. 44, no. 12, pp. 2495–2503, Dec. 1996. [12] P. M. Watson, K. C. Gupta, and R. L. Mahajan, “Development of knowledge based artificial neural network models for microwave components,” in IEEE MTT-S Int. Microwave Symp. Dig., Baltimore, MD, 1998, pp. 9–12. [13] J. W. Bandler, R. M. Biernacki, S. H. Chen, P. A. Grobelny, and R. H. Hammers, “Space-mapping technique for electromagnetic optimization,” IEEE Trans. Microw. Theory Tech., vol. 42, no. 12, pp. 2536–2544, Dec. 1994. [14] J. W. Bandler, R. M. Biernacki, S. H. Chen, R. H. Hemmers, and K. Madsen, “Electromagnetic optimization exploiting aggressive space mapping,” IEEE Trans. Microw. Theory Tech., vol. 43, no. 12, pp. 2874–2882, Dec. 1995. [15] J. W. Bandler, Q. S. Cheng, S. A. Dakroury, A. S. Mohamed, M. H. Bakr, K. Madsen, and J. Sondergaard, “Space-mapping: The state of the art,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 1, pp. 337–361, Jan. 2004. [16] J. W. Bandler, Q. S. Cheng, N. K. Nikolova, and M. A. Ismail, “Implicit space mapping optimization exploiting preassigned parameters,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 1, pp. 378–385, Jan. 2004. [17] M. Kirschning and R. H. Jansen, “Accurate model for effective dielectric constant of microstrip with validity up to millimeter-wave frequencies,” Electron. Lett., vol. 18, no. 6, pp. 272–273, Mar. 1982. [18] D. Dolfi, M. Labeyrie, P. Joffre, and J. P. Huignard, “Liquid crystal microwave phase shifter,” Electron. Lett., vol. 29, no. 10, pp. 926–928, May 1993. [19] W. Hilberg, “From approximations to exact relations for characteristic impedances,” IEEE Trans. Microw. Theory Tech., vol. MTT-17, no. 5, pp. 259–265, May 1969. [20] M. Horno, “Calculation of quasi-static characteristic of microstrip on anisotropic substrate using mapping method,” in IEEE MTT-S Int. Microwave Symp. Dig., Washington, DC, 1980, pp. 450–452.

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[21] D. E. Rumelhart, G. E. Inton, and R. J. Williams, “Learning internal representations by error propagation,” in Parallel Data Processing, D. E. Rumelhart and J. L. McClelland, Eds. Cambridge, MA: MIT Press, 1986, vol. 1, pp. 318–362. [22] M. T. Hagan and M. Menhaj, “Training feedforward networks with the Marquardt algorithm,” IEEE Trans. Neural Netw., vol. 5, no. 6, pp. 989–993, Nov. 1994.

Ginés Doménech-Asensi (S’96–A’03–M’04) was born in Barcelona, Spain, in 1972. He received the B.Sc. and M.Sc. degrees in industrial engineering from the Universidad de Murcia, Murcia, Spain, in 1993 and 1996, respectively, and the Ph.D. degree from the Universidad Politécnica de Cartagena, Cartagena, Spain, in 2002. Since 1997, he has been an Assistant Professor with the Departamento de Electrónica y Tecnología de Computadoras, Universidad de Murcia, and since 1999, with the Universidad Politécnica de Cartagena. His current research is within the field of electronic design automation tools, development of tools and methods for analog microelectronics synthesis, and microwave devices modeling.

Juan Hinojosa was born in Dunkerque, France, in 1965. He received the Diplôme d’Etudes Approffondies (D.E.A.) and Ph.D. degrees in electronics from the Université des Sciences et Technologies de Lille (USTL), Lille, France, in 1990 and 1995, respectively. In 1990, he joined the Hyper-Frequency and Semiconductor Department, Nanotechnologies and Microelectronics, Electronics Institute, as a Research Student, where he was involved in the development of EM characterization techniques of materials in the microwave frequency range. In 1999, he joined the Universidad Politécnica de Cartagena, Cartagena, Spain, where he is currently involved with teaching and research activities. His research interests include EM characterization techniques of materials in the microwave frequency range and microwave circuit and device modeling techniques for novel microwave passive circuit and device design.

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Juan Martínez-Alajarín (S’98) was born in Cartagena, Spain, in 1972. He received the B.Sc. and M.Sc. degrees in electrical and electronic engineering (both with honors) from the Universidad de Murcia, Murcia, Spain, in 1994 and 1998, respectively, and is currently working toward the Ph.D. degree in electronic engineering at the Universidad Politécnica de Cartagena, Cartagena, Spain. He is currently an Assistant Lecturer with the Departamento de Electrónica y Tecnología de Computadoras, Universidad Politécnica de Cartagena. His research interests include image and signal processing, modeling and pattern recognition, and ANNs.

Javier Garrigós-Guerrero (S’96–A’97–M’04) received the B.Sc. and M.Sc. degrees in electrical engineering from the Universidad de Murcia, Murcia, Spain, in 1992 and 1995, respectively, and the Ph.D. degree from the Universidad Politécnica de Cartagena, Cartagena, Spain, in 2002. From 1995 to 1996, he was with the Universidad de Zaragoza, Zaragoza, Spain, as an Invited Researcher. From 1997 to 2002, he was an Assistant Professor with the Department of Computer Engineering and Technology, Universidad de Murcia, and later at the Universidad Politécnica de Cartagena, where he is currently an Assistant Professor with the Departmento de Electrónica y Tecnología de Computadoras. His research interests are in the field of soft computing such as fuzzy ANNs and evolutionary computation and their computational efficiency by improving algorithms and developing parallel or application-specific processing architectures.

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Tissue Sensing Adaptive Radar for Breast Cancer Detection—Experimental Investigation of Simple Tumor Models Jeff M. Sill, Student Member, IEEE, and Elise C. Fear, Member, IEEE

Abstract—Microwave breast cancer detection is based on differences in electrical properties between healthy and malignant tissues. Tissue sensing adaptive radar (TSAR) has been proposed as a method of microwave breast imaging for early tumor detection. TSAR senses all tissues in the volume of interest and adapts accordingly. Simulation results have shown the feasibility of this system for detecting tumors of 4 mm in diameter. In this paper, the secondgeneration experimental system for TSAR is presented. Materials with electrical properties similar to those in the breast are used for the breast model. A resistively loaded Wu–King monopole antenna is fabricated, and reflections from the breast model over the frequency range of 1–10 GHz are recorded. The reflected signals are processed with the TSAR algorithm, which includes improved skin subtraction and TSAR focusing algorithms. Various tumor models are examined; specifically, a 1-cm tumor is detected with a signal-to-clutter ratio of 10.41 dB. Tumor detection with the experimental system is evaluated and compared to simulation results. Index Terms—Breast cancer detection, experimental verification, microwave imaging, tissue sensing adaptive radar.

I. INTRODUCTION

B

REAST cancer is a significant health issue for women and affects one in every seven women [1]. The current method of detection is mammography, which involves X-ray imaging of a compressed breast. X-ray mammography creates images of the density of breast tissues and the images are used to locate suspicious areas. Although mammography is the gold standard, concerns related to the false-positive and false-negative rates exist [2]. There is need for a complementary, safe, and reasonably priced method [3]. Microwave breast cancer detection has been introduced as a complementary method for breast cancer detection. Microwave breast cancer detection relies on differences in electrical properties between malignant and fatty tissues as summarized in [4]. Microwave breast imaging methods include hybrid, passive, and active approaches. Hybrid methods include thermoacoustic tomography, which uses microwaves to selectively heat tumors and ultrasound approaches to create images [5]–[7]. One passive approach, microwave radiometry, measures the increased temperature of the tumor compared

Manuscript received March 31, 2005; revised July 12, 2005. This work was supported by the Natural Sciences and Engineering Research Council of Canada and by the Canadian Breast Cancer Foundation. The authors are with the Department of Electrical and Computer Engineering, University of Calgary, Calgary, AB, Canada T2N 1N4 (e-mail: [email protected]). Digital Object Identifier 10.1109/TMTT.2005.857330

to the normal tissue [7]–[9]. Active microwave approaches include tomography and radar-based imaging. Microwave tomography records the transmission of waves through the breast and creates an electrical property map of the region of interest [7]. Radar-based approaches, first presented by Hagness et al. [10], involve focusing reflections from the breast in order to determine the location of significant scatterers (i.e., tumors). Radar-based imaging systems include microwave imaging via space time (MIST) beamforming [11], [12] and tissue sensing adaptive radar (TSAR) [13], [14]. The MIST system features a woman lying supine with the antennas scanned over the naturally flattened breast. In the TSAR system, the woman lies prone, the breast falls through a hole in the examination table, and antennas are scanned around the breast. The MIST system uses advanced clutter reduction algorithms to create an image. Simulations have shown that the MIST system can detect a 2-mm tumor in a two-dimensional (2-D) breast model derived from magnetic resonance imaging [11]. The TSAR algorithm uses simple clutter reduction methods; however, tumors of 4 mm have been detected in a three-dimensional (3-D) cylindrical breast model [15]. The experimental verification of each imaging system is the next step before their clinical application. In a realistic system, practical issues such as antenna fabrication, the electrical properties of breast tissues, and breast shape must be considered. The first experimental system for testing radar-based breast cancer detection was presented in [16]. This system was designed for preliminary method verification and included a polyvinyl chloride (PVC) pipe, wood, and air to represent the breast, tumor, and fatty tissues, respectively. The materials used had similar contrasts in electrical properties to those expected in the breast. Detection of a 3-mm-diameter wooden dowel was possible in a 2-D experiment. A quasi-3-D system was presented in [17] and showed detection of a 3-D tumor in a 2-D model. Experimental verification was presented in [12] for the MIST system. The breast model consisted of a printed circuit board (skin), diacetin-water solution (tumor), and soybean oil (fatty tissue). The materials were chosen based on availability, cost, toxicity, and stability. Because the soybean oil has lower dielectric properties than the actual fatty tissue, the materials selected for the skin and tumor were correspondingly lower in properties. Tumors of 4-mm diameter were detected in a 6 cm 6 cm breast model scanned at 49 antenna locations. While this system is more complex than the first-generation experimental TSAR system, the electrical properties are again based on the property contrasts. Therefore, the goal of the second-generation

0018-9480/$20.00 © 2005 IEEE

SILL AND FEAR: TISSUE SENSING ADAPTIVE RADAR FOR BREAST CANCER DETECTION

Fig. 1. TSAR experimental system. The tank is shown on the left and the VNA is on the right. The coaxial cable is held with stands to reduce flex and movement.

experimental TSAR system is to use materials with electrical properties similar to realistic breast tissues. This paper reports the experiments and results with the second-generation TSAR prototype. Specifically, it expands on the preliminary results presented in [18], where a 1-cm tumor immersed in canola oil was detected. The aims of this paper are to test and characterize an antenna, implement an improved TSAR algorithm, and detect tumors in a realistic breast model. Section II discusses the experimental system, including the materials used for the breast model and antenna fabrication. The improved signal processing for the skin subtraction algorithm and the TSAR focusing algorithm is presented in Section III. In Section IV, the tumor detection results are presented for various breast models. Section V draws conclusions based on the results and outlines future work with the experimental TSAR system. II. EXPERIMENTAL SYSTEM This section describes the TSAR experimental system. The experimental setup, equipment used, and data acquisition techniques are outlined. As well, the electrical properties of each material in the breast model are discussed. Finally, a description of the antenna fabrication is presented. A. Experimental Setup The experimental system is shown in Fig. 1. The system is composed of a Plexiglas tank, immersion liquid, ground plane, antenna, and breast phantom. The top of the tank is a ground plane, which is implemented to simplify the antenna design. This places limitations on the imaging capabilities of the system; however, this setup is similar to preliminary simulations in [19]. Therefore, it is acceptable for preliminary experimental tests. Holes are placed in the ground plane for placement of the antenna, breast model, and tumors. The entire tank, with the exception of the ground plane, is fabricated without metal, thus reducing reflections from the tank. The dimensions are shown in Fig. 2. are In all experiments, reflections from the antenna recorded with an 8719ES vector network analyzer (VNA) (Agilent Technologies, Palo Alto, CA) connected to a 50- coaxial

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Fig. 2. Test setup with a monopole antenna, immersion liquid, and breast phantom. (a) Top-down view. (b) Side view.

cable. Data are recorded at 1601 frequency points and 16 samples are averaged at each frequency. The frequency range over which data are acquired is from 1 to 10 GHz. In the experiments, the phantom plate (Fig. 2) is rotated in increments of 22.5 or 45 . These rotations are performed to simulate scanning the antenna around the tumor or breast model. Reflections are recorded after each rotation. B. Phantom Materials The breast model is represented by a cylinder with a diameter of 10 cm and a height of 30 cm. A hemispherical tumor is attached to the ground plane and placed in the breast model, as shown in Fig. 2. Here, the length of the breast model is selected such that the antenna does not detect the end of the model (i.e., via method of images, this represents a 2-D model). However, the tumor is 3-D in order to provide a more challenging detection task, as the imaging task involves detecting the 3-D tumor in a plane perpendicular to the cylinder axis and containing the tumor. The breast model is composed of materials with similar electrical properties to skin, fatty tissue, and tumors. The properties of each material are measured using an open-ended borosilicate dielectric probe [20]. The results are summarized in Fig. 3 and Table I. The skin is composed of a flexible silicone sheet loaded with dielectric fillers named LDF-32 (Eccosorb) (Emerson and Cumming Microwave Products, Randolph, MA). The electrical properties of the skin are shown in Fig. 3. The sheet of material is formed into a cylinder by joining the sheet with TP-50 epoxy (Eccobond TP-50) (Emerson and Cumming Microwave Prodand ucts). This epoxy has electrical properties of S/m at 4 GHz; however, this value may vary as air microbubbles are dispersed throughout the material. The fatty tissue is created from flour, canola oil, and 0.9% saline [21] in a ratio by weight of 500 : 225 : 25. The fatty tissue mixture is a dough that is packed in the interior of the skin cylinder. The electrical properties of the fat dough (Fig. 3) were monitored for a three-week period. The electrical properties decreased by 10% as the water evaporated. As a first approximation, the electrical properties are selected to represent mainly the

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Fig. 4. Fabricated Wu–King monopole antenna soldered to an SMA connector and attached to a metal plug.

Fig. 3. Electrical properties of materials in the breast model. All properties are measured with an open-ended borosilicate dielectric probe [20]. (a) Relative permittivity and (b) conductivity as a function of frequency. TABLE I ELECTRICAL PROPERTIES USED IN THE EXPERIMENTAL SYSTEM. ALL MATERIALS ARE MEASURED WITH AN OPEN-ENDED BOROSILICATE DIELECTRIC PROBE [20] AT 4 GHz

fatty tissue inside the breast and hence have lower permittivity than the average properties used in [10]. Tumors are fabricated using Alginate powder (Alginmax) (Major Proditti Dentari S.P.A., Moncalieri, Italy), water, and salt in a ratio by weight of 115 : 250 : 14 [22]. The tumors are covered with a thin layer of epoxy (Eccostock HiK cement) (Emerson and Cumming Microwave Products). The epoxy and S/m) creates a layer between the oil ( and the tumor to prevent diffusion of the tumor in the oil. Furthermore, this conserves the electrical properties (Fig. 3) of the tumor. Over a three-week period, measurements demonstrated

minimal change in properties. The thickness of the epoxy layer is difficult to control; however, the size of the tumor is measured based on the tumor and epoxy size combined. Therefore, as investigated in [18], the epoxy layer reduces reflections from the tumor, which creates a more difficult tumor detection scenario. As described in [18], the tumors are attached to metal plugs and inserted into the ground plane of the tank. An immersion liquid is needed to improve the match between interior and exterior of the breast. Therefore, the tank , is filled with an immersion liquid of canola oil ( S/m). Canola oil is similar to the liquid investigated in [14], which provides excellent tumor detection and localization. Additionally, fewer antennas are required to scan a given volume than with a higher permittivity liquid [14]. Furthermore, canola oil is minimally dispersive over the frequency range of interest and has low loss. The electrical properties of the breast model at 4 GHz are listed in Table I. The materials have a relatively small change in permittivity over the frequency range (Fig. 3) and the changes correspond to those observed in real tissues (e.g., [23]). Furthermore, the materials used to represent the breast have similar electrical properties to those of real tissues [7]. C. Antenna Fabrication The antenna used to illuminate the breast model is a resistively loaded Wu–King monopole [24], [25]. The resistively loaded monopole is selected as it provides acceptable performance over the ultrawideband frequency range of interest. The monopole has length of 10.8 mm and is designed in a lossless liquid similar to oil with . The design and characterization of the antenna are outlined in [14] and [18]. The antenna is fabricated using high-frequency chip resistors (Vishay 0603HF) (Malvern, PA) soldered to a high-frequency substrate (Rogers RO3203 series) (Rogers Corporation, Chandler, AZ). The suband S/m) has electrical properties strate ( similar to those of the canola oil. The antenna is soldered to a subminiature A (SMA) connector and attached to a metal plug. The fabricated antenna (Fig. 4) is inserted into the ground plane of the tank. III. SIGNAL PROCESSING The signal processing includes converting signals from frequency to time, and the TSAR image formation algorithm. The

SILL AND FEAR: TISSUE SENSING ADAPTIVE RADAR FOR BREAST CANCER DETECTION

initial signal processing step is converting the frequency-domain data to the time domain for use in the image formation algorithms. As in [16], the measured data are weighted with a differentiated Gaussian signal with center frequency of 4 GHz and full-width half maximum extent from 1.3 to 7.6 GHz. The data are transformed with an inverse chirp z transform to produce the time-domain signal. The TSAR image formation algorithm is similar to that of [16]; however, improvements to the skin subtraction and focusing step are implemented. The first step is calibration, which involves subtracting the reflections recorded without an object present. This removes clutter in the signals, such as reflections from the Plexiglas tank. The remaining signal contains antenna mismatch, skin reflection, and tumor reflection. The next steps in the TSAR algorithm are skin subtraction and focusing, discussed in this section.

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Defining (5) (6) (7) permits us to write

as (8)

Minimization of the mean squared error with respect to results in the basic Wiener–Holf equation

A. Skin Subtraction

(9)

The skin subtraction algorithm previously implemented was an adaptive correlation method named Woody averaging [13], [26]. This method provided effective skin subtraction; however, a residual skin response remained. Therefore, an improved skin subtraction algorithm is desired. The proposed skin subtraction algorithm is based on the recursive least squares (RLS) algorithm, which is an adaptive filtering method. The method is adapted from a beamformer approach in [27]. A single signal is selected as the target signal and the remaining signals are weighted and summed to approximate the target signal. The desired signal is defined as or , a vector where is the sample at time . The input signal or remaining signals can be defined as and is a matrix where is the number of input signals. The weight vector at time is and is defined as a vector. The approximation to the desired signal at time is defined as (1) and the error in the approximation is calculated as (2) At time , the sum of the squared error is defined as (3) where is the forgetting factor and is the current sample number. Expanding to include the definition of results in

(4)

Solving for approach equates

recursively using the standard brute force

(10) and (11) However, to solve (9) requires a matrix inversion. Therefore, the matrix inversion lemma is used to solve for as in [27]. This method differs from the MIST skin subtraction approach presented in [11], as the weight vectors are updated recursively after each time step. In contrast, the method proposed in [11] has a constant weight vector, which is shifted through the selected window. When applied to TSAR signals, the RLS algorithm and Woody averaging methods are combined. The RLS algorithm estimates the skin response and is therefore applied from the start of the signal to a point corresponding to the interior of the breast. This is obtained from the skin location and thickness estimates [28]. The Woody averaging algorithm is applied from the interior of the breast to the remaining portion of the signal. Therefore, signals estimated with the RLS algorithm and Woody averaging are combined, creating a total estimated signal. The total estimated signal is subtracted from the target signal. This process is repeated with the signal received at each antenna as the target signal. B. Focusing The skin-subtracted signals are integrated and focused similar to [28]. The focusing is performed by identifying a focal point inside the region bounded by the synthetic antenna array and calculating the travel time from each antenna to the focal point. The selected contribution from each signal is summed and the process is repeated as the focal point is scanned through the focusing region. The resulting image indicates the location of significantly scattering objects as reflections from these objects

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Fig. 5. Experimental, simulated, and theoretical VSWR calculated from the reflection coefficient [18].

add coherently [16]. To improve selectivity of focus, several additions are made to the algorithm [29]. Mathematically, pixel can be described by intensity at location

(12) , is identiThe contribution from antenna , fied using the travel time between the antenna and the pixel gives more weight to the location. Weighting antennas closest to the current focal point. Signal compensation includes variable compensation and in-breast compensation (13) In-breast compensation is the distance traveled in breast tissue and is determined using the estimated skin has a value of zero location. Variable compensation if the pixel location is outside of the skin, one if the location is if between the skin and the array center, and decreases as the location is beyond the array center, where is the distance from the antenna. The skin location is calculated as in [28]. The images are evaluated using the signal-to-clutter ratio. The signal-to-clutter ratio is calculated as the maximum tumor response compared to the maximum response in the same image with the tumor response removed [28]. IV. RESULTS AND DISCUSSION A. Antenna Three antennas are fabricated with the same profile and compared to simulations to confirm correct operation. The impedance of the simulated antenna in [14] is converted to represent a monopole. The theoretical impedance is calculated from [30]. The voltage standing wave ratios (VSWRs) for the fabricated, simulated, and theoretical antennas are shown in Fig. 5. The results demonstrate a good match between all fabricated antennas and the simulated antenna. The VSWR is below 2 between 7–10 GHz. The poor VSWRs at lower frequencies are expected as matching to 50 was not a design goal. However, the input impedance of the antenna is relatively

Fig. 6.

Transmission between two antennas (S ).

constant over the frequency range of interest and the design of an impedance transformer is feasible. Transmission between two antennas is measured by con. necting an antenna to each port of the VNA and measuring The antennas are placed in the immersion liquid and separated by 7 cm as this is sufficiently in the far field of the antennas. is measured using the same reference Transmission antenna, which is similar to the antennas in Fig. 5. The results demonstrate a transmission of approximately 38 dB at 4 GHz as shown in Fig. 6. This low transmission can be attributed to the poor VSWR and the resistive profile of the antenna. The decrease in transmission at higher frequencies may be in part due to the variation in resistors at higher frequencies. The efficiency of the antenna is calculated using definitions in [31] and finite-difference time-domain (FDTD) simulations. Specifically, we compute the power radiated through a closed surface surrounding the antenna and divide this by the input power. The efficiency ranges from 1.9% to 15.8% over the frequency range from 2 to 8 GHz. At maximum power of 5 dBm from the VNA, the total power radiated at 4 GHz is 6.2 dBm. Although this antenna has poor performance, it is still implemented for tumor detection due to simplicity. Furthermore, if tumor detection is possible with an inefficient antenna, improved detection capabilities are expected with an improved antenna. B. Tumor Detection and Skin Subtraction In a preliminary experiment, a tumor was placed in the immersion liquid and rotated around the center of the tank. Reflections were recorded at eight antenna positions and imaged with the focusing algorithm [18]. The tumor was clearly decm and tected with maximum response located at cm while the actual physical location was cm and cm. The signal-to-clutter ratios were 8.21 and 7.19 dB for the 2- and 1-cm tumors, respectively. The signal-to-clutter ratio decreased with tumor size, as expected. The results were promising as tumor detection was possible with very little clutter [18]. The next experiment includes the skin and the interior of the skin filled with canola oil. The two skin subtraction algorithms, Woody averaging and the RLS–Woody combination, are applied to the data and the skin response is compared before

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TABLE II SIGNAL-TO-CLUTTER RATIOS FOR EACH BREAST MODEL

Fig. 7. Plot of a single skin-subtracted response using the Woody averaging method and the RLS algorithm. This shows the effectiveness of the RLS skin subtraction method.

Fig. 9. Signal-to-clutter ratio received when changing the permittivity in the TSAR focusing algorithm. The highest signal-to-clutter ratios occur when the permittivity value used for calculation is the same as the measured value.

Fig. 8. Image of 1-cm tumor in the complete breast model. The white circle is a postprocessing step to illustrate the actual location of the skin cylinder. The exterior line represents the antenna locations. Strongly scattering objects are indicated with lighter intensities while darker pixels indicate areas of weak scattering.

and after skin subtraction. Fig. 7 demonstrates the effectiveness of the RLS algorithm compared to the Woody averaging results. The peak-to-peak of the skin response is calculated prior to and after skin subtraction, and the ratio of these quantities is calculated. Here, the peak-to-peak results are 26.33 and 107.87 dB for Woody averaging and the RLS algorithm, respectively. The skin-subtracted data recorded at 15 antenna positions are focused using the TSAR focusing algorithm. The signal-to-clutter ratios for a 1-cm tumor are calculated to be 6.63 dB for Woody averaging and 14.37 dB for the RLS–Woody combination. These results further demonstrate the effectiveness of the RLS–Woody combination, which is selected as the skin subtraction method for the remainder of this paper. C. TSAR Images The final experiment is the most complex and includes the skin, tumor, and fatty tissue. Reflections are recorded and the TSAR algorithm is applied to the data. The results are plotted in Fig. 8 for a 1-cm tumor. The tumor is detected with maximum cm and cm, while the response located at

cm and cm. The signal-tophysical location is clutter ratios are 13.74 and 10.41 dB for the 2- and 1-cm tumors, respectively. To confirm and compare the results, simulations are performed with the FDTD method [32]. The simulation setup is as in [14]; however, the breast interior is homogeneous, and material properties are the same as discussed in Section II. The recorded reflections from the simulations are focused, and the signal-to-clutter ratio for the 1-cm tumor is 23.38 dB. As expected, the signal-to-clutter ratio is higher for simulations than experiments. Simulations provide a relatively noise-free environment and a homogeneous breast interior. In addition, oscillations are introduced in the measured signal when converting from the frequency to the time domain, as the weighting function is band limited. The signal-to-clutter ratios for each of the three experiments are shown in Table II. As expected, the signal-to-clutter ratio decreases as the tumor size decreases. The tumor-only simulations have low signal-to-clutter ratios compared to the skin tumor case as only eight antenna positions are used to create an image. Finally, as the complexity of the system increases, the signal-to-clutter ratios decrease. These results are promising, as tumor detection is possible using an inefficient antenna to record the reflections. Therefore, with an improved antenna, improved tumor detection capability is anticipated. Finally, the robustness of the algorithm to changes in breast permittivity is tested. The permittivity of the fatty tissue in the interior of the breast is varied from 3 to 6 in the postprocessing algorithm. This variation changes the travel time from the antenna to focal point. The signal-to-clutter ratios are calculated as the permittivity values are changed in 0.1 increments and shown in Fig. 9. The results indicate that, for small tumors, the largest signal-to-clutter ratio is obtained when the electrical properties are similar to the measured value of the fatty tissue. This demonstrates the necessity of prior information on the

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electrical properties inside the breast to achieve the highest signal-to-clutter ratio. In the case of inhomogeneous breast tissue, an average permittivity value is necessary to compute the travel time through the breast tissue. Algorithms for estimating the average permittivity in the breast have been introduced in [33]. With an estimate of the average properties, the focusing algorithms described here have detected tumors in simple breast models containing variations in properties of 10% [14]. V. CONCLUSION This paper presents the second-generation TSAR experimental system. The materials used to represent the breast and the corresponding electrical properties were presented. The RLS algorithm was introduced as an improved skin subtraction algorithm compared to the previous method of Woody averaging. Tumor detection and localization were possible in three breast phantoms of increasing complexity. These results are promising as the materials used to represent the breast have similar electrical properties to those in a realistic breast. Furthermore, this is the most complex breast model currently under investigation for radar-based tumor detection. The tumors examined here are larger in diameter than the 4-mm tumors detected with a 3-D model reported in [14]. Testing detection of smaller tumors is planned with a 3-D system. Although promising results are obtained with this simple system, experiments in 3-D are not performed. Currently, the antenna is the limiting factor for 3-D experiments. An improved antenna is under development, and improved performance and directivity are expected. This should increase the tumor detection capabilities of the TSAR system. Another challenge is the development of a 3-D breast model, including more realistic shape and inhomogeneities. The materials and methods reported here may be used to develop this realistic model. Finally, a scanning system must be developed to scan the improved antenna around the new model. This may involve a vertical scan in addition to the rotation of the model reported here. Therefore, this paper with a simple model provides a foundation for expansion to a 3-D system. ACKNOWLEDGMENT The authors would like to acknowledge the technical support of S. Foster, I. Choi, F. Hickli, and J. Shelley, all of the University of Calgary, Calgary, AB, Canada. REFERENCES [1] American Cancer Society, “Cancer facts and figures 2005,” Amer. Cancer Soc,, Atlanta, GA, 2005. [2] Mammography and Beyond: Developing Technologies for the Early Detection of Breast Cancer. Washington, DC: Inst. Med., Nat. Academy Press, 2001. [3] Saving Women’s Lives: Strategies for Improving Breast Cancer Detection and Diagnosis. Washington, DC: Inst. Med., Nat. Academy Press, 2004. [4] E. C. Fear, “Microwave imaging of the breast,” Technol. Cancer Res. Treat., vol. 4, no. 1, pp. 69–82, Feb. 2005. [5] R. A. Kruger, K. K. Kpoecky, A. M. Aisen, D. R. Reinecke, G. A. Kruger, and W. L. Kiser Jr., “Thermoacoustic CT with radio waves: A medical imaging paradigm,” Radiology, vol. 211, no. 1, pp. 275–278, 1999.

[6] L. V. Wang, X. Zhao, H. Sun, and G. Ku, “Microwave-induced acoustic imaging of biological tissues,” Rev. Sci. Instrum., vol. 70, no. 9, pp. 3744–3748, 1999. [7] E. C. Fear, S. C. Hagness, P. M. Meaney, M. Okoniewski, and M. A. Stuchly, “Enhancing breast tumor detection with near-field imaging,” IEEE Micro, vol. 3, no. 1, pp. 48–56, Mar. 2002. [8] S. Mouty, B. Bocquet, R. Ringot, N. Rocourt, and P. Devos, “Microwave radiometric imaging for the characterization of breast tumors,” Eur. Phys. J.: Appl. Phys., vol. 38, pp. 73–78, 2000. [9] K. L. Carr, P. Cevasco, P. Dunlea, and J. Shaeffer, “Radiometric sensing: An adjuvant to mammography to determine breast biopsy,” in IEEE MTT-S Int. Microwave Symp. Dig., Boston, MA, Jun. 2000, pp. 929–932. [10] 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. [11] E. J. Bond, X. Li, S. C. Hagness, and B. D. Van Veen, “Microwave imaging via space time beamforming for early detection of breast cancer,” IEEE Trans. Antennas Propag., vol. 51, no. 8, pp. 1690–1705, Aug. 2003. [12] 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 tumour detection in multilayer breast phantoms,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 8, pp. 1856–1865, Aug. 2004. [13] E. C. Fear and J. Sill, “Preliminary investigations of tissue sensing adaptive radar for breast tumour detection,” in Proc. Engineering Medicine and Biology Society, Cancun, Mexico, Sep. 2003, pp. 3787–3790. [14] J. M. Sill and E. C. Fear, “Tissue sensing adaptive radar for breast cancer detection: A study of immersion liquid,” Electron. Lett., vol. 41, no. 3, pp. 113–115, Feb. 2005. [15] J. M. Sill, T. C. Williams, and E. C. Fear, “Tissue sensing adaptive radar for breast tumour detection: Investigation of issues for system implementation,” in Int. Zurich Electromagnetic Compatibility Symp., Zurich, Switzerland, Feb. 2005, pp. 71–74. [16] 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. , “Experimental feasibility of breast tumor detection and localiza[17] tion,” in IEEE MTT-S Int. Microwave Symp. Dig., Philadelphia, PA, Jun. 2003, pp. 383–386. [18] J. M. Sill and E. C. Fear, “Tissue sensing adaptive radar for breast cancer detection: Preliminary experimental results,” in IEEE MTT-S Int. Microwave Symp. Dig., Long Beach, CA, Jun. 2005. [CD ROM]. [19] E. C. Fear and M. A. Stuchly, “Microwave system for breast tumor detection,” IEEE Microw. Guided Wave Lett., vol. 9, no. 11, pp. 470–472, Nov. 1999. [20] D. M. Hagl, D. Popovic, S. C. Hagness, J. H. Booske, and M. Okoniewski, “Sensing volume of open-ended coaxial probes for dielectric characterization of breast tissue at microwave frequencies,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 4, pp. 1194–1206, Apr. 2003. [21] J. J. W. Lagendijk and P. Nilsson, “Hyperthermia dough: A fat and bone equivalent phantom to test microwave/radio frequency hyperthermia heating systems,” Phys. Med. Biol., vol. 30, no. 7, pp. 709–712, 1985. [22] X. Yun, E. C. Fear, and R. Johnston, “Compact antenna for radar-based breast cancer detection,” IEEE Trans. Antennas Propag., vol. 53, no. 8, pp. 2374–2380, Aug. 2005. [23] K. R. Foster and H. P. Schwan, “Dielectric properties of tissues and biological materials: A critical review,” Crit. Rev. Biomed. Eng., vol. 17, no. 1, pp. 25–104, 1989. [24] T. Wu and R. King, “The cylindrical antenna with nonreflecting resistive loading,” IEEE Trans. Antennas Propag., vol. AP-13, no. 3, pp. 369–373, May 1965. , “Corrections to ‘The cylindrical antenna with nonreflecting resis[25] tive loading’,” IEEE Trans. Antennas Propag., vol. AP-13, no. 11, p. 998, Nov. 1965. [26] C. D. Woody, “Characterization of an adaptive filter for the analysis of variable latency neuroelectric signals,” Med. Biol. Eng., vol. 5, no. 6, pp. 539–553, 1967. [27] S. Haykin, Adaptive Filter Theory. Upper Saddle River, NJ: PrenticeHall, 1996. [28] E. C. Fear, X. Li, S. C. Hagness, and M. A. Stuchly, “Confocal microwave imaging for breast cancer detection: Localization of tumors in three dimensions,” IEEE Trans. Biomed. Eng., vol. 49, no. 8, pp. 812–822, Aug. 2002. [29] J. M. Sill, “Second generation experimental system for tissue sensing adaptive radar,” M.S. thesis, Univ. Calgary, Calgary, AB, Canada, 2005.

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[30] J. G. Maloney and G. S. Smith, “A study of transient radiation from the Wu–King resistive monopole—FDTD analysis and experimental measurements,” IEEE Trans. Antennas Propag., vol. 41, no. 5, pp. 668–676, May 1993. [31] C. A. Balanis, Antenna Theory: Analysis and Design. New York: Wiley, 1997. [32] A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite Difference Time Domain Method. Boston, MA: Artech House, 2000. [33] D. W. Winters, E. J. Bond, S. C. Hagness, and B. D. Van Veen, “Estimation of average breast tissue properties at microwave frequencies using a time-domain inverse scattering technique,” in Int. Zurich Electromagnetic Compatibility Symp., Zurich, Switzerland, Feb. 2005, pp. 59–64.

Jeff M. Sill (S’02–05) received the B.Eng. degree in electrical engineering from the University of Victoria, Victoria, BC, Canada, in 2002 and the M.Sc. degree from the University of Calgary, Calgary, AB, Canada, in 2005. He is currently a Research Engineer with the University of Calgary. His research interests include microwave breast cancer detection and biomedical applications for signal processing.

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Elise C. Fear (S’96–M’01) received the B.A.Sc. degree in systems design engineering from the University of Waterloo, Waterloo, ON, Canada, in 1995, and the M.A.Sc. and Ph.D. degrees in electrical engineering from the University of Victoria, Victoria, BC, Canada, in 1997 and 2001, respectively. She was a Natural Sciences and Engineering Research Council of Canada (NSERC) Post-Doctoral Fellow of electrical engineering with the University of Calgary, Calgary, AB, Canada, from 2001 to 2002, and is currently an Associate Professor with the same department. Her research interests involve the interaction of electromagnetic fields with living systems, including the interaction of low-frequency fields with biological cells and microwave breast cancer detection. Dr. Fear is currently an associate editor for the IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING.

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Novel Waveguide Filters With Multiple Attenuation Poles Using Dual-Behavior Resonance of Frequency-Selective Surfaces Masataka Ohira, Student Member, IEEE, Hiroyuki Deguchi, Member, IEEE, Mikio Tsuji, Member, IEEE, and Hiroshi Shigesawa, Life Fellow, IEEE

Abstract—This paper develops novel waveguide filters consisting of frequency-selective surfaces (FSSs) in order to realize both the drastic size reduction and multiple attenuation poles in stopbands at both sides of passband. The FSS provides not only a passband but also attenuation-pole frequencies in stopbands since the FSS has both the aperture-element and the patch-element behaviors. In the present design method, the shape of each FSS is designed by a genetic algorithm so that the resonant curve of FSS can be fitted to that obtained from an equivalent-circuit approach. By using such FSSs and quarter-wavelength waveguides, a bandpass filter with six attenuation poles like an elliptic-function filter has been constructed. Furthermore, a technique of the size reduction by controlling adequately the resonant response of each FSS is presented. In this filter, the FSSs are closely located at the interval of the length much shorter than a quarter wavelength. It is shown from the design example that the half longitudinal length of the former example can be obtained, keeping both the passband response and attenuation poles in stopbands. The effectiveness of the waveguide filters with FSSs is validated by good agreement between the calculated and the measured results. Index Terms—Frequency-selective surfaces (FSSs), genetic algorithms (GAs), resonance, waveguide filters.

I. INTRODUCTION

W

AVEGUIDE filters having attenuation poles like an elliptic-function filter have been investigated in order to realize sharp cutoff skirts out of band and low insertion loss in band. For this purpose, the attenuation poles in stopband have been generated so far by utilizing evanescent modes in a cavity [1], asymmetric irises between cavity resonators [2], bypass coupling through nonresonating modes [3], circuit elements such as stubs [4], [5], and so on. However, such filters using a cavity resonator cannot avoid being relatively large and heavy. On the other hand, resonant irises have been used as resonators for more compact and lightweight filters. This type of filter consists of thin resonant irises and quarter-wavelength waveguide sections. For example, the resonant-aperture filter has improved out-of-band rejection [6], [7]; also, the combination of resonant irises and waveguide cavity modes has realized a pseudoelliptic filter [8]. Furthermore, slot apertures have been studied numerically and experimentally as transverse sections

Manuscript received April 1, 2005; revised June 24, 2005 and July 21, 2005. This work was supported in part by the Japan Society for the Promotion of Science under Grant-in Aid for Scientific Research (C) (2) 14550384. The authors are with the Department of Electronics, Doshisha University, Kyotanabe, Kyoto 610-0321, Japan. Digital Object Identifier 10.1109/TMTT.2005.857334

for a bandpass filter [9]. However, bandpass filters using only irises have not realized multiple attenuation poles in stopbands at both sides of a passband like an elliptic-function filter yet. The reason is that the resonance of conventional irises works as full transmission for constructing a passband, and also their iris shapes are mainly determined only by a passband property. Therefore, a new type of resonator having an arbitrarily shaped resonant element [10] has been proposed, which is called hereafter a frequency-selective surface (FSS) [11], [12]. This paper develops two novel waveguide filters consisting of the FSSs. The proposed single-layer FSS provides one resonance (full transmission) in a passband and one antiresonance (full reflection) in each of the stopbands, that is, a dual-behavior resonance. Such a resonant property has been utilized in the design of microstrip planar filters [13], [14], but it has not been realized for waveguide filter applications yet. Introducing such FSSs makes it possible to design a waveguide filter having multiple attenuation poles and also realize a drastic size-reduced filter, just by controlling a resonant curve of each FSS without any additional couplings and structures. This paper is organized as follows. In Section II, a design method of the FSSs using a genetic algorithm (GA) [15]–[18] is first presented. Section III shows a design example of a waveguide filter constructed by three FSSs and quarter-wavelength waveguides to realize multiple attenuation poles. In addition, the effect to the insertion loss due to lossy materials is investigated numerically and experimentally. Furthermore, Section IV presents an equivalent-circuit approach for a design of a waveguide filter with closely spaced FSSs, of which the interval is much shorter than a quarter wavelength. The second design example shows that both a drastic size reduction and multiple attenuation poles can be realized by controlling the resonant response of the FSSs. The validity of the waveguide filters with the FSSs is proven by the comparison of the calculated results by the method of moments (MoM) and the experimental results at the -band. II. DESIGN OF FSS IN WAVEGUIDE A. GA Design Fig. 1 shows an example of the proposed waveguide filter, which consists of arbitrarily shaped FSSs working as resonators waveguides (length in this and quarter-wavelength will be figure) as inverters. The design method for . shown in Section IV. The section size of the waveguide is

0018-9480/$20.00 © 2005 IEEE

OHIRA et al.: NOVEL WAVEGUIDE FILTERS USING DUAL-BEHAVIOR RESONANCE OF FSSs

Fig. 1. Waveguide filter consisting of three FSSs.

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Fig. 3. GA design of FSS geometry.

the FSS metals and the waveguide wall in order to avoid the instability of the connection between them in the experiment. The whole FSS geometry is symmetrical with respect to both horizontal and vertical axes of the waveguide. The characteristics of the GA-generated FSS are evaluated according to the fitness value, so that the FSS can realize an ideal resonant curve. The fitness function is defined here as fitness Fig. 2. (a) Example of transmission response of single-layer FSS having both an aperture-type and a patch-type behaviors. (b) Its equivalent circuit.

(1)

and (2)

The FSS conductor is assumed to be infinitesimally thin and is supported by a dielectric of the relative permittivity and the thickness . The loss of the conductor and the dielectric is omitted here for simplicity of a design. Our single-layer FSS has a transmission response shown in Fig. 2(a), where the passband and the attenuation-pole frequencies are provided by a resonance (full transmission at ) and and ), respectively. Such antiresonances (full reflection at a transmission response can be easily realized by using an arbitrarily shaped FSS based on the GA design. The response in Fig. 2(a) is represented by the equivalent-circuit model in Fig. 2(b), where two networks are equivalent [19]. In case of quarter-wavelength inverters, the impedance of the parallel resbecomes infinity at the center frequency so onant circuit that the passband is produced, while the series resonant cirand determines the antiresonant frequencies cuits and , respectively. From the view point of FSS geometry, the present FSS works as an aperture-type FSS at the resonant frequency and a patch-type FSS at the antiresonant frequencies, respectively. To design a waveguide bandpass filter with multiple attenuation poles, we first calculate an ideal frequency characteristic of dual-behavior resonance of each FSS by using the equivalent-circuit approach [10], [20]. Once an ideal resonant response of each FSS is obtained, the shape of each FSS element is designed using the GA. The GA-operated region is shown in Fig. 3. To give an arbitrarily shaped FSS, the FSS is divided into subsections in the MoM analysis [21], [22]. The FSS geometry is represented in terms of 1s and 0s in the GA. The 1s and 0s correspond to the nonmetal parts of FSS (blank pixels in Fig. 3) and the conductors (hatched pixels), respectively. In the present method, the GA operates on one quarter region of the FSS geometry, except for the pixels at the boundary between

where , and are posis the number of sampling freitive weighting constants, is the quency points at around attenuation-pole frequencies, number of sampling frequency points at around a passband, and are the transmission coefficients at sampling frequency obtained by the MoM and circuit, respectively. The flowchart of the GA optimization used in this paper can be referred in [18]. If the search of the GA converges in some generations, then the FSS geometry is recognized as a designed one. Otherwise, the reproduction cycle to the next generation is repeated until an FSS with an ideal resonant curve is obtained. When the FSSs designed by the GA are inserted in a main rectangular waveguide at the interval of the length , -approximation design is finished. B. Numerical Analysis The frequency responses of GA-generated FSSs are calculated by the MoM that solves the magnetic field integral equation (MFIE) for unknown magnetic currents at the nonmetal parts of the FSS [21]. The magnetic fields can be expressed using the magnetic-type spectral-domain dyadic Green’s function, which can be obtained by the spectral-domain immittance method [23], [24] in consideration of a dielectric effect. Here, the unknown magnetic current is expressed in terms of the rooftop subdomain basis functions. Applying Galerkin’s procedure to solve the MFIE, the matrix equation can be obtained. To avoid difficult computations of the waveguide-mode summations, an efficient numerical technique using the fast Fourier technique (FFT), which has been proposed for the analysis of shielded microstrip circuits [22], is applied to the waveguide discontinuity problem (the geometry resolutions and must

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be a power of 2). Finally, can be calculated from the known magnetic currents. The characteristics of a waveguide filter with FSSs as shown in Fig. 1 are calculated by means of the coupled-integral-equations technique (see [21] and [25] for the formulation), which accurately takes higher order mode interaction between the adjacent FSSs into account. The coupled magnetic field integral equation is obtained by enforcing the boundary conditions at all the FSSs. Then one matrix equation that involves the unknown magnetic currents of all the FSSs is derived. By solving the equation, one gets the insertion and the return losses of a designed filter. III. DESIGN EXAMPLE AND EXPERIMENTS A. Waveguide Filter With GA-Designed FSSs We show a design example of the waveguide filter constructed waveguides. The passband response is by three FSSs and approximated by a three-pole 0.01-dB Chebyshev filter at the GHz and the frequency bandwidth center frequency MHz. At the stopband, the filter has six attenuaand tion poles. Therefore, the antiresonant frequencies of each FSS are set as follows: GHz GHz GHz

GHz GHz GHz

The main rectangular waveguide is a WR-90 ( mm mm). Each FSS is supported by a dielectric (BT and Resins Glass Cloth, , mm). One quarter of the FSS geometry are encoded into a 49-bit binary code to divide the FSS geometry into 16 16 subsections. The GA evalin 9.5–10.5 GHz at around the passband as well as uates at around the attenuation-pole frequencies. In the GA design, the individuals are reproduced through the tournament selecof 0.8 and the tion, the single-point crossover with the rate of 0.02. The population size is chosen mutation with the rate to be 50. In addition, the weighting coefficients and in (2) are chosen to be 4.0 and 1.0, respectively. The sampling freand are set to be 11 in the passband and 5 quency points in each of the stopbands at both sides of passband, respectively. Fig. 4 shows the FSS geometries obtained by the GA design and the comparison of the calculated and the measured transmission responses for each FSS. The ideal curves obtained from prototype are also shown in the figure. The predicted rethe sults are calculated by the MoM using 32 16 resolutions for the FSS geometries. Fig. 5 displays the photograph of the FSSs fabricated by a milling machine. To insert them into a waveguide, each FSS is fitted into the metallic frame of the same rectangular aperture as the -band waveguide and also the same thickness as the dielectric substrate. The calculated and the measured results agree well over the frequency range, although the measured results shift to a little higher frequency side due to the tolerances in the fabrication and the estimation error of the dielectric constant. Hence, it is confirmed numerically and experimentally that the GA-designed FSSs work well at each resonant frequency.

Fig. 4. Designed FSSs and the comparison of transmission response between the calculated and measured results. (a) FSS1. (b) FSS2. (c) FSS3.

Fig. 5. Fabricated FSSs.

Fig. 6 shows the frequency characteristics of the designed filter by means of the coupled-integral-equations technique. The structures is displayed in the inset of the figure. The length of the interval between the FSSs is 9.61 mm shorter than a quarter wavelength for constructing the specified passband in consideration of the dielectric. The designed filter can realize the low insertion loss in the passband and also six attenuation poles in the stopband at both sides of the passband. The waveguide filter has high skirt selectivity by using the antiresonances 9 and 11 GHz of the FSS3. The calculated and the measured results exhibit good agreement, although the measured responses shift to a little

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Fig. 7. (a) Equivalent circuit for passband design of a compact waveguide filter. (b) Admittance-inverter expression at a passband.

Fig. 6. Calculated and measured insertion loss and return loss for the waveguide filter with six attenuation poles using the GA-designed FSSs.

higher frequency side for the same reason as Fig. 4. The cause of the insertion loss (1.4–1.7 dB) in the passband observed in the experiment is discussed later. Nevertheless, the fabricated filter can provide successfully the passband and the attenuation poles. From the good agreement of both results, the effectiveness of the waveguide filter utilizing the resonances of the FSS can be validated.

value of three FSSs. According to the formula, [19, eq. (3.62)], using the unloaded quality factor in our design yields the insertion loss about 1.3 dB at the center frequency, of which the value is close to the measured insertion loss of 1.6 dB in Fig. 6 at the center frequency. The cause of the difference between the estimated and the measured insertion losses is partly because the passband is not sufficiently constructed due to the resonant-frequency shift of each FSS. As shown above, the insertion loss of the filter in Fig. 6 is mainly due to the loss of three FSSs, that is, low unloaded quality factors. For a practical use, a lower loss material is required to improve the unloaded quality factors. IV. SIZE-REDUCTION TECHNIQUE

B. Loss Considerations

A. Equivalent Circuit for Closely Spaced FSSs

Here, we give some considerations to the insertion loss observed in the experiments. In this type of waveguide filter, it is considered that the losses are mainly caused by two factors, namely: 1) loss of the conductor that composes the element shape and 2) loss of the dielectric that supports the FSS. These losses can be estimated by the MoM taking the loss effects into account. The loss tangent and the back-side surface resistance of the copper-clad dielectric substrate (BT Resins Glass Cloth) is assumed to be 4.54 10 and 64.4 m ( 26.5 m of the top-side surface resistance), respectively [26]. It is observed from the numerical results that the losses of the FSS1, the FSS2, and the FSS3 are about 0.26, 0.43, and 0.29 dB at the center frequency, respectively. On the other hand, the experimental results show about 0.35, 0.50, and 0.37 dB, respectively. These values are higher than those of the MoM simulation. The differences between the experimental and the numerical results may be caused by the fabrication error and the estimation error of the material constant. In addition, we confirm numerically that the effect of the conductor loss is almost same as that of the dielectric loss in case of BT Resins Glass Cloth. Furthermore, the unloaded quality factor of the FSS can be estimated from the loss of the experimental results. The unloaded is defined here by , where , quality factor , and represent the angular frequency at , the capacitance value of the parallel resonant circuit of the th FSS, and the dissipative element in the resonant circuit, respectively. As a result, is obtained as the average the unloaded quality factor

Up to the previous section, we have demonstrated the waveguide filter consisting of quarter-wavelength inverters. In this section, a waveguide filter with closely spaced FSSs, whose interval is much shorter than a quarter wavelength, will be presented. The proposed filter can make its whole filter size more compact without any additional structures, such as an inductive iris inserted between resonant irises. That is, instead of using a quarter-wavelength ideal inverter, we introduce FSS resonators including a part of ideal inverter as follows. Fig. 7 shows a modified inverter expression, where the shunt admittance is loaded on each side of the transmission line to construct an ideal inrepresents the admittance of the th verter, and ( is electrical length), the FSS. Then, by giving matrix of the network surrounded by the dashed line as inverter in Fig. 7 is obtained as (3) where the characteristic admittance for the normalization. The matrix indicates that the network works as an ideal inverter having the parameter . Hence, the compact waveguide filter can also be expressed as the equivalent filter network shown in Fig. 7(b), where the inverters connected to , and those the input/output waveguides have . In this equivabetween the FSSs have lent-circuit expression in Fig. 7, the admittances of equivalent

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resonators can be represented by using the admittances of the resonators (that is, FSS) needed here in the following forms:

(4a)

(4b)

(4c) where and denote the parameters of parobtained from a conventional inverter allel resonant circuits and denote those of approach [20], while the FSSs needed here. These equations support only the characteristic at around the passband because they include the frequency-dependent parameter of the electrical length . It should for the resonator of the conbe noted here that for the present resventional method, whereas onators, that is, the FSSs do not resonate at the center frequency . In addition, the network expression in Fig. 7 makes it possible to choose an arbitrary length of the interval between FSSs. Using the above results, a passband for compact waveguide filters can be designed. First, the physical length between the FSSs and the passband specifications are given. Then the paramand for the equivalent resonators can be easily eters obtained from a conventional filter design [20] using and , where represents the electrical length at the center frequency . Next, the parameters and of the FSS are determined to satisfy the relations in (4a)–(4c) within the specified passband. After the above proceare required because the dure, little adjustments of and inverter parameter actually depends on the frequency. When the frequency response is satisfied with the specification, the passband design using the equivalent circuit is finished. B. Optimization The shape of the FSS can be designed easily by following the method described in Section II. However, in the present case of closely spaced FSSs, the effect of the evanescent modes between the adjacent FSSs cannot be neglected. Therefore, after designing each FSS geometry based on the resonant-curve fitting, the GA optimization of the FSS geometries is performed again by evaluating the insertion and the return losses of the waveguide filter with the FSSs. Since the calculation by means of the coupled-integral-equations technique takes computation time though the FFT is used, the micro-GA [17] with a small

Fig. 8. Transmission responses of GA-designed FSSs calculated by the MoM in comparison with those of the equivalent circuit approach. (a) FSSs 1 and 3. (b) FSS 2.

population size is applied to the optimization. function in (1) is defined here as

in the fitness

(5) and in decibels of the overall filter strucwhere ture represent the -parameters obtained from the MoM. The GA starts with the initial population, of which the one population has the FSS geometries designed by the resonant-curve fitting and the rest are generated by the random numbers. When the GA optimization is converged, the filter design is finished. C. Design Example Finally, we deign a compact waveguide filter, of which the passband specification and the main rectangular waveguide are the same as the design examples in Section III. As an example, prototype design is chosen here to be 5 mm the length for . The attenuation-pole frequencies and that is about are set for designing a symmetric filter as follows: GHz GHz GHz GHz GHz GHz Each FSS is supported by the dielectric with the relative permitand the thickness mm. The GA evalutivity in 9.8–10.2 GHz and in 8.4–9.4 and 10.6–11.6 GHz ates and the population size 5. The with the crossover rate weighting coefficients and and the sampling frequency and are the same as those of Section III. points Fig. 8 shows the GA-optimized FSS geometries and their transmission characteristics. The FSS1 and the FSS2 are de-

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REFERENCES

Fig. 9. Frequency characteristics of the size-reduced waveguide filter designed by the GA-optimization technique. The whole longitudinal length is about half of the filter presented in Section III.

signed to resonate at the frequency and below the center frequency , respectively. Although any FSSs do not resonate at the center frequency , the compact filter using these FSSs can provide successfully the same passband as the filter with quarter-wavelength inverters, as shown in Fig. 9, where the length between the FSSs is 4.8 mm for constructing the passband in consideration of the dielectric effect. The whole longitudinal length of the present filter is 10.80 mm, while that of the filters shown in the Section III is 20.42 mm. The designed filter can realize the drastic size reduction, keeping the four attenuation poles. The numerical results shown here prove the effectiveness of the size-reduction technique for the waveguide filter with the FSSs. V. CONCLUSION In this paper, two waveguide filters with the FSSs have been developed as resonators. To design such filters, the design method based on an equivalent-circuit approach and a GA has been shown first. The application was made to a three-pole Chebyshev bandpass filter with six attenuation poles. The design example shows that the attenuation poles in stopband at both sides of a passband can easily be set by utilizing the antiresonances of the FSSs. In addition, the size-reduction technique, in which the FSSs are placed at the interval of the length shorter than a quarter wavelength, have been presented. The present equivalent-circuit approach allows us to design a waveguide filter with closely spaced FSSs having the same passband response as the filter with quarter-wavelength waveguides, just by changing adequately the resonant response of each FSS. As an example, a drastic size-reduced filter with four attenuation poles, of which the total length becomes about half of the former design example, is designed. The numerical and experimental verifications for the design examples have proven the usefulness of the proposed waveguide filter and its design method.

[1] K. Iguchi, M. Tsuji, and H. Shigesawa, “Negative coupling between TE and TE modes for use in evanescent-mode bandpass filters and their field-theoritic CAD,” in IEEE MTT-S Int. Microwave Symp. Dig., San Diego, CA, May 1994, pp. 727–730. [2] F. Arndt, T. Duschak, U. Papziner, and P. Rolappe, “Asymmetric iris coupled filters with stopband poles,” in IEEE MTT-S Int. Microwave Symp. Dig., Dallas, TX, May 1990, pp. 215–218. [3] U. Rosenberg, S. Amari, and J. Bornemann, “Inline TM -mode filters with high-design flexibility by utilizing bypass couplings of nonresonating TE modes,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 6, pp. 1735–1742, Jun. 2003. [4] S. Amari and J. Bornemann, “Using frequency-dependent coupling to generate finite attenuation poles in direct-coupled resonator bandpass filters,” IEEE Microw. Guided Wave Lett., vol. 9, no. 10, pp. 404–406, Oct. 1999. [5] S. Amari, J. Bornemann, and U. Rosenberg, “Pseudo-elliptic waveguide filters without cross coupling,” in Proc. 31st Eur. Microwave Conf., vol. 3, London, U.K., Sep. 2001, pp. 429–432. [6] M. Piloni, R. Ravenelli, and M. Guglielmi, “Resonant aperture filters in rectangular waveguide,” in IEEE MTT-S Int. Microwave Symp. Dig., Anaheim, CA, Jun. 1999, pp. 911–914. [7] M. Capurso, M. Piloni, and M. Guglielmi, “Resonant aperture filters: Improved out-of-band rejection and size reduction,” in Proc. 31st Eur. Microwave Conf., vol. 1, London, U.K., Sep. 2001, pp. 331–334. [8] U. Rosenberg, S. Amari, and J. Bornemann, “Mixed-resonance compact in-line pseudo-elliptic filters,” in IEEE MTT-S Int. Microwave Symp. Dig., Philadelphia, PA, Jun. 2003, pp. 479–482. [9] R. D. Seager, J. C. Vardaxoglou, and D. S. Lockyer, “Close coupled resonant aperture inserts for waveguide filtering applications,” IEEE Microw. Compon. Lett., vol. 11, no. 3, pp. 112–114, Mar. 2001. [10] M. Ohira, H. Deguchi, M. Tsuji, and H. Shigesawa, “Novel waveguide filters with multiple attenuation poles using frequency selective surfaces,” presented at the IEEE MTT-S Int. Microwave Symp., Long Beach, CA, Jun. 2005. [11] J. A. Arnaud and F. A. Pelow, “Resonant-grid quasi-optical diplexers,” Bell Syst. Tech. J., vol. 54, no. 2, pp. 263–283, Feb. 1975. [12] B. A. Munk, Frequency Selective Surfaces: Theory and Design. New York: Wiley, 2000. [13] C. Quendo, E. Rius, and C. Person, “Narrow bandpass filters using dualbehavior resonators,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 3, pp. 734–743, Mar. 2003. [14] , “Narrow bandpass filters using dual-behavior resonators based on stepped-impedance stubs and different-length stubs,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 3, pp. 1034–1044, Mar. 2004. [15] J. M. Johnson and Y. Rahmat-Samii, “Genetic algorithms in engineering electromagnetics,” IEEE Antennas Propag. Mag., vol. 39, no. 4, pp. 7–25, Aug. 1997. [16] D.S. Weile and E. Michielssen, “Genetic algorithm optimization applied to electromagnetics: A review,” IEEE Trans. Antennas Propag., vol. 45, no. 3, pp. 343–353, Mar. 1997. [17] M. Ohira, H. Deguchi, M. Tsuji, and H. Shigesawa, “Optimized singlelayer frequency selective surface and its experimental verification,” in Proc. 32nd Eur. Microwave Conf., Milan, Italy, Sep. 2002, pp. 981–984. [18] , “Multiband single-layer frequency selective surface designed by combination of genetic algorithm and geometry-refinement technique,” IEEE Trans. Antennas Propag., vol. 52, no. 11, pp. 2925–2931, Nov. 2004. [19] J.-S. G. Hong and M. J. Lancaster, Microstrip Filters for RF/Microwave Applications. New York: Wiley, 2001. [20] G. L. Matthaei, L. Young, and E. M. T. Jones, Microwave Filters, Impedance-Matching Networks, and Coupling Structures. New York: McGraw-Hill, 1964. [21] A. B. Yakovlev, A. I. Khalil, C. W. Hicks, A. Mortazawi, and M. B. Steer, “The generalized scattering matrix of closely spaced strip and slot layers in waveguide,” IEEE Trans. Microw. Theory Tech., vol. 48, no. 1, pp. 126–137, Jan. 2000. [22] A. Hill and V. K. Tripathi, “An efficient algorithm for the three-dimensional analysis of passive microstrip components and discontinuities for microwave and millimeter-wave integrated circuits,” IEEE Trans. Microw. Theory Tech., vol. 39, no. 1, pp. 83–91, Jan. 1991. [23] C. H. Chan, K. T. Ng, and A. B. Kouki, “A mixed spectral-domain approach for dispersion analysis of suspended planar transmission lines with pedestals,” IEEE Trans. Microw. Theory Tech., vol. 37, no. 11, pp. 1716–1723, Nov. 1989.

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[24] T. Itoh, “Spectral domain immitance approach for dispersion characteristics of generalized printed transmission lines,” IEEE Trans. Microw. Theory Tech., vol. 28, no. 7, pp. 733–736, Jul. 1980. [25] S. Amari, J. Bornemann, and R. Vahldieck, “Fast and accurate analysis of waveguide filters by the coupled-integral-equations technique,” IEEE Trans. Microw. Theory Tech., vol. 45, no. 9, pp. 1611–1618, Sep. 1997. [26] R. Takaichi, T. Aoki, and Y. Kobayashi, “Back-side relative conductivity measurements of three types of copper-clad dielectric substrates,” presented at the Proc. IEICE Gen. Conf., Tokyo, Japan, 2004, C-2-125.

Masataka Ohira (S’03) was born in Osaka, Japan, on July 21, 1978. He received the B.E. and M.E. degrees from Doshisha University, Kyoto, Japan, in 2001 and 2003, respectively, and is currently working toward the D.E. degree at Doshisha University. He is currently with the Graduate School of Electric Engineering, Doshisha University. His current research activities are concerned with the analysis and design of frequency-selective surfaces and their applications. Mr. Ohira is a student member of the Institute of Electronics, Information and Communication Engineers (IEICE), Japan, and the Institute of Electrical Engineers (IEE), Japan. He was the recipient of the 2005 IEICE Young Engineer Award.

Hiroyuki Deguchi (M’92) was born in Osaka, Japan, on August 24, 1962. He received the B.E., M.E., and D.E. degrees from Doshisha University, Kyoto, Japan, in 1986, 1988, and 1999, respectively. From 1988 to 2000, he was with the Mitsubishi Electric Corporation, where he was engaged in the research and development of very large reflector antennas, deployable antennas, horn antennas, and radome antennas. Since 2000, he has been with Doshisha University, where he is currently an Associate Professor. His current research activities are concerned with microwave and millimeter-wave aperture antennas and antenna measurements. Dr. Deguchi is a member of the Institute of Electronics, Information and Communication Engineers (IEICE), Japan, and the Institute of Electrical Engineers (IEE), Japan. He was the recipient of the 1992 IEICE Young Engineer Award.

Mikio Tsuji (S’78–M’81) was born in Kyoto, Japan, on September 10, 1953. He received the B.E., M.E., and D.E. degrees from Doshisha University, Kyoto, Japan, in 1976, 1978, and 1985, respectively. Since 1981, he has been with Doshisha University, where he is currently a Professor. His current research activities are concerned with microwave and millimeter-wave guiding structures and devices and scattering problems of electromagnetic waves. Dr. Tsuji is a member of the Institute of Electronics, Information and Communication Engineers (IEICE), Japan, and the Institute of Electrical Engineers (IEE), Japan.

Hiroshi Shigesawa (S’62–M’63–SM’85–F’94– LF’05) was born in Hyogo, Japan, on January 5, 1939. He received the B.E., M.E., and D.E. degrees from Doshisha University, Kyoto, Japan, in 1961, 1963, and 1969, respectively. Since 1963, he has been with Doshisha University. From 1979 to 1980, he was a Visiting Scholar with the Microwave Research Institute, Polytechnic Institute of New York, Brooklyn, NY. He is currently a Professor with the Faculty of Engineering, Doshisha University. His current research activities involve microwave and millimeter-wave guiding structures and devices and scattering problems of electromagnetic waves. Dr. Shigesawa is a Fellow of the Institute of Electronics, Information and Communication Engineers (IEICE), Japan. He is a member of the Institute of Electrical Engineers (IEE), Japan, and the Optical Society of America (OSA).

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Third- and Fifth-Order Baseband Component Injection for Linearization of the Power Amplifier in a Cellular Phone Nishiki Mizusawa and Shigeo Kusunoki, Member, IEEE

Abstract—This paper proposes a new predistortion technique to improve the adjacent channel power ratio of the power amplifier (PA) in a cellular phone. This technique injects the thirdand fifth-order distortion components in the baseband block, and eliminates the fundamental component from the injected signals in order to operate effectively up to near power saturation. We show this technique can raise the distortion-compensation limit, through mathematical analysis, and confirm it with simulation. We also examine the distortion compensation performance of the PA using a wide-band code-division multiple-access uplink signal and a high-speed downlink packet access signal, and the possibility of applying a new low-voltage high-capacity battery. Index Terms—Cellular phone, compensation, intermodulation distortion, power amplifier (PA), predistortion.

I. INTRODUCTION

T

Fig. 1. Discharge characteristics of a conventional carbon-electrode Li-ion battery and a new alloy-electrode Li-ion battery.

Manuscript received April 1, 2005; revised June 3, 2005. The authors are with Sony Ericsson Mobile Communications Japan Inc., Tokyo 108-0075, Japan (e-mail: [email protected]). Digital Object Identifier 10.1109/TMTT.2005.855747

There have been numerous approaches to compensating for distortion in cellular phones [3]. Predistortion [4] has many advantages, such as little extra cost and stable operation, and is well suited to baseband implementation using a digital signal processor (DSP), but predistortion needs a lookup table (LUT), which is necessary to index with either the instantaneous input power or the amplitude of the complex baseband signal. Predistortion increases the DSP processing power and power consumption. Second-harmonic injection [5], [6] and harmonic and baseband injection [7] reduce distortion by mixing the second harmonic of the RF signal and its fundamental component. These techniques are simple and low cost. However, second-harmonic injection requires both precise gain and phase adjustment for the perfect cancellation of the distortion, and harmonic and baseband injection requires both precise adjustment of harmonicsignal gain and baseband-signal gain. These adjustment blocks cannot be easily integrated. This paper proposes a new predistortion technique that injects distortion components in the baseband block. Since the distortion components are generated directly from in-phase and quadrature ( and ) signals, it is not necessary to index the LUT with either the instantaneous input power or the amplitude of the complex baseband signal. The LUT has only to index with the average output power. Both gain and phase adjustment for cancellation of distortion is possible in the baseband block. The

HIRD-GENERATION (3G) cellular-phone systems are now widely used. Since these systems use a varying envelope signal, a linear power amplifier (PA) is needed, and this makes the operation of the PA less efficient. Still, a highly efficient PA is required to maximize standby and talk time. The development of highly efficient semiconductor devices with high linearity addresses this problem [1]. Current cellular phones, however, are presenting new problems. For example, the output power of the PA must be raised because the multiple-code transmission signal, such as the high-speed downlink packet access (HSDPA) uplink signal, increases the peak-to-average ratio (PAR). An even more critical problem is the need for a higher capacity battery. Fig. 1 shows the discharge characteristics of a conventional carbon-electrode Li-ion battery and a new alloy-electrode Li-ion battery. The conventional carbon-electrode Li-ion battery maintains an output voltage of 3.5 V for a considerable period. The new alloy-electrode Li-ion battery has a 50% higher capacity, but the output voltage goes down to 2.7 V [2] and, at this voltage, a cellular phone cannot be operated. To fully utilize this new battery, the PA should be able to operate at 2.7 V. To meet these requirements, distortion must be compensated, but this has been difficult in small cellular phones because additional components are needed. Furthermore, any approach to distortion compensation should not increase power consumption.

0018-9480/$20.00 © 2005 IEEE

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proposed predistorter can be easily integrated and no additional components are needed. When an injection technique is used, there is a distortioncompensation limit [8] and distortion compensation is necessary up to near power saturation. However, using the proposed technique, the distortion-compensation limit is raised. Section II presents the basic principle of two baseband distortion component injection techniques using a digital modulation signal. In Section III, a typical PA for a wide-band code-division multiple-access (W-CDMA) handset is modeled. The simulation of adjacent channel power ratio (ACPR) improvement and the distortion-compensation limit is shown. This paper also examines the distortion-compensation performance of a W-CDMA PA using a W-CDMA uplink signal and an HSDPA uplink signal, and demonstrates the application of a new low-voltage high-capacity battery. II. ANALYSIS We assume that the amplifier nonlinearity can be expressed in terms of a power series up to the fifth degree by the expression (1) where is the output voltage and is the input voltage of the PA, and , , etc. are coefficients of the nonlinear terms. The input voltage when the digital modulation format is used , phase , and carrier frequency, which has magnitude can be written as

(2)

Fig. 2.

Predistorter using (I + Q ) component.

for injection, and is the voltage ratio of the desired signal and the third-order distortion component. Fig. 2 shows the block diagram of the predistorter, which injects the third-order distortion component that corresponds to (4). is defined as the relative phase between the desired signal and the third-order distortion component. The baseband block in Fig. 2 generates the desired signals and and the component. The component is multiplied by and by separately and multiplied by for amplitude tuning and rotated for phase tuning, and added to the original and signals. These signals are then converted to an analog signal and passed through the low-pass filter. These signals are then modin the quadratic modulator (QM), ulated and multiplied by then input to the PA. By substituting (4) into (1), the distorted output voltage that appears at the fundamental frequency can be expressed as in (5), which is truncated beyond third-degree nonlinearity

, , and where average , therefore, average . By substituting (2) into (1), the distorted output voltage appears at the fundamental frequency given by

(3)

(5)

In (3), the second term is the third-order distortion, which is caused by the third-degree nonlinearity of the PA, and the third term is the fifth-order distortion, which is caused by the fifthdegree nonlinearity of the PA. If we now add the cube of the desired signal as the third-order distortion component to the PA input voltage (2), the following equation is obtained:

In (5), the term that has is ignored because it is small. The third term in (5) is the original third-order distortion, which is caused by the third-degree nonlinearity of the PA without distortion compensation. The second, fourth, and fifth terms are generated by the injected distortion component. In a weakly nonlinear region, since input voltage is small, the fourth and fifth terms in (5) can be ignored and (5) is a first-order equation of . In this case, the dominant distortion products of the second and third terms of (5) can be canceled out by adjusting in the following conditions:

(4) where is the amplitude of the PA input signal, which consists of the desired signal and the third-order distortion component

(6)

MIZUSAWA et al.: THIRD- AND FIFTH-ORDER BASEBAND COMPONENT INJECTION FOR LINEARIZATION OF PA IN CELLULAR PHONE

Equation (6) means and . The influence of the fourth and fifth terms in (5) increases as increases. The fourth and fifth terms in (5) become a factor of the distortion-compensation limit [8], and restrict the distortion-compensation performance [9]. The fourth and fifth terms in (5) are generated from the desired signal and the injected distortion component by the third-degree nonlinearity of the PA. In order to raise the distortion-compensation limit, the distortion component power should be suppressed. When the input signal and , the cubic nonlinearity generis a two-tone signal at ates lower and higher third-order intermodulation (IM3) prodand , and the fundamental tones and ucts at , which are 9.5 dB higher than the IM3 products [10]. Similarly, when the digital modulation format is used, the injected distortion component of the Fig. 2 predistorter contains the fundamental component. The fundamental component is 9.5 dB higher than the third-order distortion product. The injected distortion component is generated by multiplying the desired signal . When we subtract dc from to generate by the new distortion component, the distortion component power is suppressed 10 dB by eliminating the fundamental component from the distortion component. This does not change the distoris tion-compensation performance where the dc of defined as average in this paper. If we now add the new third-order distortion component to the PA input voltage (2), the following equation is obtained:

Fig. 3.

Block diagram of the proposed predistorter.

Fig. 4.

Quadrature Taylor-series amplifier model.

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(7) Replacing (4) with (7) and substituting (7) into (1), the distorted output voltage that appears at the fundamental frequency can be expressed as (8), which is truncated beyond third-degree nonlinearity as follows:

Fig. 5. Comparison between simulated ACPR and measured ACPR without injection.

(8) The second term of (8) eliminates the fundamental component from the distortion component. Comparing (5) with (8), we see that the additional third-order distortion components in the fifth and sixth terms of (8) are suppressed rather than the fourth and fifth terms of (5). In addition, the increase of causes an increase of the fifth-order distortion product. When distortion compensation is required near the power-saturation point of the PA, the injection of the third- and fifth-order distortion components is necessary. Fig. 3 is the block diagram of the proposed predistorter, which is deinjects the distortion components expressed by (7).

fined as the relative phase between the desired signal and the is defined as the relthird-order distortion component, and ative phase between the desired signal and the fifth-order distortion component. The baseband block in Fig. 3 generates the and desired signals and and the components. The component is multiplied by and by separately and multiplied by for amplitude tuning and rotated for phase tuning to generate the third-order distortion component. The component is multiplied by and by separately and multiplied by for amplitude tuning for phase tuning to generate the fifth-order disand rotated tortion component. These distortion components are then added to the original and signals.

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Fig. 6. Simulated spectrum at PA input. (a) Desired signal. (b) Third-order distortion component using the Fig. 2 predistorter . (c) Third-order distortion component using the Fig. 3 predistorter.

These signals are then converted to an analog signal and passed through the low-pass filter. These signals are then modulated and multiplied by in the QM, then input to the PA. III. SIMULATION In order to simulate distortion-compensation performance, we used the quadrature Taylor-series amplifier shown in Fig. 4. This approach allows us to describe the complex gain and in the form of a Taylor series of input as follows:

The output voltage of the amplifier can be written as AmpOut

(11)

A typical PA for a W-CDMA handset, which has a maximum output power of 26.5 dBm, has complex gains and of

(12)

(9) (13) (10) where

and

are constants.

The output spectrum and ACPR were simulated by inputting the voltage waveform of the W-CDMA uplink signal (DPCCH DPDCH, 3.84 Mc/s) to this amplifier.

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Fig. 7. Simulated ACPR at 5-MHz offset with and without injection.

Fig. 9. Simulated optimized relative phase between the desired signal and the distortion components.

Fig. 8. Simulated optimized distortion-component power at PA input.

Before simulation of distortion compensation, it is necessary to confirm that this model is sufficiently accurate for the simulation of ACPR. Fig. 5 compares the simulated ACPR and measured ACPR without injection. Since the measurement and dBm, simulation results correspond well around Fig. 5 shows that the model is sufficiently accurate for the simulation of distortion compensation. Fig. 6 shows the simulated spectrums of the W-CDMA uplink desired signal, the third-order distortion component used in Fig. 2, and the third-order distortion component used in Fig. 3 at the input of the PA. The spectrum of the desired signal is ob, and the third-order distortion compotained by setting . It can be seen that the funnents are obtained by setting damental component, which is included in the third-order distortion component of Fig. 6(c), is 10 dB less than that in Fig. 6(b). Fig. 7 shows the simulation of ACPR improvement using the proposed predistorter. This figure shows that the effect of distortion compensation with the Fig. 2 predistorter is up to dBm, but the Fig. 3 predistorter suppresses ACPR dBm. by 10 dB at shown in Fig. 7 is obtained by optimizing , , , and Fig. 3 in order to minimize ACPR. Fig. 8 shows the optimized

Fig. 10. Simulated ACPR at 5-MHz offset as a function of third-order distortion-component power.

distortion component power at the PA input. In Fig. 8, the difference between the power of the fundamental input signal and the third-order distortion component corresponds to , and the difference between the power of the fundamental input signal and the fifth-order distortion component corresponds to . In Fig. 8, an increase of the output power causes an increase of the fifth-order distortion-component power. This indicates that the fifth-order distortion component also plays a part in suppressing ACPR near the saturated-power region. Fig. 8 also shows that the Fig. 3 predistorter needs 10 dB less the distortion-component power than the Fig. 2 predistorter. Fig. 9 shows the optimized relative phase between the desired signal and the distortion components. In Fig. 9, the phase of the third-order distortion component corresponds to and the phase of the fifth-order distortion component corresponds to Fig. 10 shows the simulated 5-MHz offset ACPR as a function of third-order distortion-component power at dBm. Fig. 11 shows the simulated 5-MHz offset ACPR as a function of the relative phase between the

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Fig. 11. Simulated ACPR at 5-MHz offset as a function of relative phase between the desired signal and the third-order distortion component.

Fig. 12. Comparison between simulated and measured 5-MHz offset ACPR with and without injection under W-CDMA uplink signal.

desired signal and the third-order distortion component at dBm. Since the ACPR at 5-MHz offset in dBm without injection is 40 dBc, Fig. 10 shows that a gain accuracy of 5 dB is necessary to suppress the ACPR by 10 dB, and Fig. 11 shows that a phase accuracy of 30 is necessary to suppress the ACPR by 10 dB. IV. EXPERIMENTAL RESULTS A. Distortion Compensation Under W-CDMA Signal To verify the effectiveness of the proposed predistorter, the ACPR was measured using the Fig. 3 predistorter and the PA for W-CDMA consisting of a two-stage InGaP HBT. This PA is the same as that in Section III. The maximum output power of this PA is designed as 26.5 dBm, as are most PA modules, because the maximum output power of a power class 3 handset is specified as 24 dBm by the 3GPP specification [11], and estimated loss of 2.5 dB between an antenna and the PA. As this study focused on the ACPR improvement of a PA using the proposed predistorter, this result was obtained by using the signals, and , and the distortion components generated beforehand. The distortion components were generated without using a DSP. Fig. 12 shows the ACPR at 5-MHz offset using the Fig. 2 predistorter and theFig. 3 predistorter using the W-CDMA uplink signal (DPCCH DPDCH, 3.84 Mc/s), and compares the measured results with the simulated results. In Fig. 12, the measured results agree well with the simulated results. In both results, disdBm. Using the Fig. 2 predistortion is low up to dBm and at torter, distortion increases rapidly at dBm, which is the desired output power, around the predistorter is no longer effective. This rapid increase of distortion is due to the distortion-compensation limit expressed in (5). On the other hand, the Fig. 3 predistorter functions effectively dBm and output power can be inup to around creased to 28 dBm under dBc at 5-MHz offset. is effective as distortion comThis suggests that pensation. Fig. 13 shows the ACPR at 10-MHz offset. As shown

Fig. 13. signal.

Measured results of 10-MHz offset ACPR under W-CDMA uplink

in this figure, the predistorter also functions effectively on the ACPR at 10-MHz offset. Fig. 14 shows spectrum regrowth with and without a Fig. 3 predistorter under a W-CDMA uplink signal (DPCCH DPDCH, 3.84 Mc/s) at dBm. The power-added efficiency (PAE) is 43% at dBm and the dBc without predistortion. The Fig. 3 predistorter raises the to 28 dBm and improves dBc, this the PAE 48%, while maintaining the improvement of PAE does not include the DSP consumption. B. Low-Voltage Operation As previously mentioned, we checked operation under low supply voltage in order to use a new battery with large capacity. Fig. 15 shows ACPR versus supply voltage to the PA. In this figure, for all supply voltages, the output power of the PA is maintained at 26.5 dBm using a W-CDMA uplink signal (DPCCH DPDCH, 3.84 Mc/s). The ACPR degrades as the supply voltage decreases. Using the Fig. 3 predistorter, ACPR improves with all voltages. ACPR at 5-MHz offset under

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recovered. In addition, ACPR at 10-MHz offset maintains the low specified value of 43 dBc. C. Under HSDPA Signal Operation

Fig. 14. Measured output spectrum of the HBT PA under W-CDMA uplink signal at 26.5-dBm output.

As previously mentioned, we checked operation under an HSDPA signal. The composition of the HSDPA signal is DPCCH DPDCH HS DPCCH, , and dB at . Fig. 16 shows the measured results of ACPR at 5-MHz offset and ACRP at 10-MHz offset with and without predistortion. ACPR at 5-MHz offset using the HSDPA signal is degraded 5 dB more than when using a W-CDMA uplink signal at dBm. However, when the proposed predistorter is used, ACPR at 5 MHz is improved 5 dB, and the specified value of 33 dBc is recovered. V. CONCLUSION A new predistortion technique, which injects distortion components in the baseband block, has been presented. The new technique injects the third- and fifth-order distortion components, and eliminates the fundamental component from the distortion components in order to operate effectively up to near power saturation. The new technique raises the distortion-compensation limit dBc and the output power to 28 dBm under at 5-MHz offset. The new technique enables the PA to operate satisfactorily under a 2.7-V supply voltage. The new technique also enables the PA to operate under an HSDPA signal without changing the saturation power. ACKNOWLEDGMENT

Fig. 15. Measured ACPR versus supply voltage to the PA under W-CDMA uplink signal.

The authors thank the members of the PA team of Sony Ericsson Mobile Communications Japan Inc., Tokyo, Japan. REFERENCES

Fig. 16. Measured results of 5-MHz offset ACPR and 10-MHz offset ACPR under HSDPA uplink signal.

the

V improved with distortion compensation, and 33-dBc value specified by the 3GPP specification [11] is

[1] Y. Hasegawa, Y. Ogata, I. Nagasako, N. Iwata, M. Kanamori, and T. Ito, “3.4 V operation power amplifier multi-chip IC’s for digital cellular phone,” in IEEE GaAs IC Symp. Dig., 1995, pp. 63–66. [2] T. Momma, N. Shiraishi, A. Yoshizawa, T. Osaka, A. Gedanken, J. Zhu, and L. Sominski, “SnS anode for rechargeable lithium battery,” J. Power Sources, pp. 198–200, 97–98(2001). [3] S. Mann, M. Beach, P. Warr, and J. McGeehan, “Increasing the talk-time of mobile radios with efficient linear transmitter architectures,” Electron. Commun. Eng. J., pp. 65–76, Apr. 2001. [4] J. K. Cavers, “Amplifier linearization using a digital predistorter with fast adaptation and low memory requirements,” IEEE Trans. Veh. Technol., vol. 39, no. 11, pp. 374–382, Nov. 1990. [5] K. Joshin, Y. Nakasya, T. Iwai, T. Miyashita, and S. Ohara, “Harmonic feedback circuit effects on intermodulation products and adjacent channel leakage power in HBT power amplifier for 1.9 GHz wide-band CDMA cellular phones,” IEICE Trans. Electron., vol. E82-C, no. 5, pp. 725–729, May 1999. [6] D. Jing, W. S. Chan, and C. W. Li, “New linearization method using interstage second harmonic enhancement,” IEEE Microw. Guided Wave Lett., vol. 8, no. 11, pp. 402–404, Nov. 1998. [7] C. W. Fan and K. K. M. Cheng, “Theoretical and experimental study of amplifier linearization based on harmonic and baseband signal injection technique,” IEEE Trans. Microw. Theory Tech., vol. 50, no. 7, pp. 1801–1806, Jul. 2002. [8] S. Kusunoki, K. Kawakami, and T. Hatsugai, “Load impedance and biasnetwork dependence of power amplifier with second-harmonic injection,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 9, pp. 2169–2176, Sep. 2004.

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[9] N. Mizusawa and S. Kusunoki, “Third and fifth order base-band component injection for linearization of the power amplifier in a cellular phone,” presented at the IEEE MTT-S Int. Microwave Symp., Jun. 2005, Paper TH2B-6. [10] J. Vuolevi and T. Rahkonen, Memoryless Spectral Regrowth Distortion in RF Power Amplifiers. Norwood, MA: Artech House, 2003, ch. 2, sec. 3, pp. 21–24. [11] 3rd generation partnership project; Technical specification group terminals, “Terminal conformance specification: Radio transmission and reception (FDD),”, TS 34.121 V 6.0.0, Mar. 2005.

Nishiki Mizusawa received the B.E. degree from the Musashi Institute of Technology, Tokyo, Japan, in 1986. In 1986, he joined the Anritsu Corporation, and in 1991, the Sony Corporation, where he was involved in design and implementation of PDC and W-CDMA mobile phones. He is currently with Sony Ericsson Mobile Communications Japan Inc., Tokyo, Japan, where he is engaged in research and development of high-efficiency PAs for wireless handset terminals.

Shigeo Kusunoki (M’02) received the B.E., M.E., and D.E. degrees from the University of Electro-Communications, Tokyo, Japan, in 1979, 1981 and 2005, respectively. In 1981, he joined the NEC Corporation, and in 1991, the Sony Corporation, where he has been with the Sony Research Center and Semiconductor Industrial Department engaged in the research and development of GaAs monolithic microwave integrated circuits (MMICs). He is currently with Sony Ericsson Mobile Communications Japan Inc., Tokyo, Japan. Dr. Kusunoki is a member of the Institute of Electronics, Information and Communication Engineers (IEICE), Japan.

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A Low-Loss Single-Pole Six-Throw Switch Based on Compact RF MEMS Switches Jaewoo Lee, Member, IEEE, Chang Han Je, Sungweon Kang, Member, IEEE, and Chang-Auck Choi

Abstract—A low-loss single-pole six-throw (SP6T) switch using very compact metal-contact RF microelectromechanical system (MEMS) series switches is presented. The metal-contact MEMS switch has an extremely compact active area of 0.4 mm 0.3 mm, thus permitting the formation of an SP6T MEMS switch into the RF switch with a total area of 1 mm2 . The MEMS switch shows an effective spring constant of 746 N/m and an actuation time of 8.0 s. It has an isolation loss from 64.4 to 30.6 dB and an insertion loss of 0.08–0.19 dB at 0.5–20 GHz. Furthermore, in order to evaluate RF performances of the SP6T MEMS switch, as well as those of the single-pole single-throw RF MEMS series switch, we have performed small-signal modeling based on a parameter-extraction method. Accurate agreement between the measured and modeled RF performances demonstrates the validity of the small-signal model. The SP6T switch performed well with an isolation loss from 62.4 to 39.1 dB and an insertion loss of 0.19–0.70 dB from dc to 6 GHz between the input port and each output port. Index Terms—Microelectromechanical parameter estimation, switches.

devices,

modeling,

I. INTRODUCTION

S

INGLE-POLE multithrow (SPMT) RF switches are widely applied to switching systems, multiband selectors, and filter banks, which consist mainly of GaAs MESFETs [1] or GaAs pseudomorphic high electron-mobility transistors (pHEMTs) [2]. The SPMT RF switches are easily integrated with other modules so they have been effectively used for a variety of the monolithic microwave integrated circuits (MMICs). Up to 2 GHz, the GaAs MESFET switches present good RF performances for an insertion loss of 0.7 dB and isolation of 33 dB. GaAs pHEMTs show an insertion loss of 0.6 dB and isolation loss of 30 dB. However, as the frequency range increases, it is difficult that the RF switch module is directly applied to high-frequency applications due to their inherent parasitic parameters, which may be junction capacitances, parasitic capacitances, or pad resistances. Instead, the RF switch module has to be revised completely for the applications. Therefore, the SPMT switches composed of solid-state devices can be limited to RF performances at a high frequency in spite of their compact size and compatibility with other RF modules. One of the promising components is an RF microelectromechanical systems (MEMS) switch. Recently, many researchers have

Manuscript received March 31, 2005. This work was supported by the Korea Ministry of Information and Communication. The authors are with the Basic Research Laboratory, Electronics and Telecommunications Research Institute, Daejeon 305-350, Korea (e-mail: [email protected]; [email protected]; [email protected]; [email protected]). Digital Object Identifier 10.1109/TMTT.2005.855746

Fig. 1. Schematic for the SP6T MEMS switch based on metal-contact RF MEMS series switches.

studied metal-contact MEMS switches [3], [4], which have a much lower insertion loss and higher isolation characteristic than solid-state devices. For better RF performance, the RF MEMS switches have been successfully applied to dual-path power amplifiers for wireless communication systems [5], to 4-bit true time delay (TTD) phase shifters in phased-array antennas [6], to a -band single-pole double-throw (SPDT) circuit [7], and to a single-pole four-throw (SP4T) switch using lateral switches [8]. Although the RF MEMS switches show excellent RF performances at higher frequency, they may have some limitations with respect to application in communication systems because their active area is 2–4 times larger than that of the RF switch. Therefore, to overcome the bottleneck for both RF performances and the area issue, it is necessary to design an SPMT switch based on compact RF MEMS switches. In this paper, we present a low-loss single-pole six-throw (SP6T) switch with a total area of 1 mm using small metal-contact RF MEMS switches, each of which has an area of 0.4 mm 0.3 mm. The SP6T MEMS switch is comprised of a transmission line and six MEMS switches, as shown in Fig. 1, and its dc and RF characteristics have previously been presented [9]. In order to evaluate RF performances of the fabricated MEMS switch, we have performed small-signal modeling. Conventional small-signal models for on-state modeling are generally inaccurate because the fringing capacitances are not expected to occur at the front end of each broken signal line. On account of this inaccuracy, we adapted a physically based parameter-extraction method to the small-signal modeling [10], which has been used for modeling solid-state devices [11]–[13], where we can more accurately find the on-state and off-state upper capacitance from resistance measured data. Subsequently, coplanar waveguide (CPW) lines were also modeled to lumped RLC equivalent circuits by the extraction method so each section of the transmission line in the SP6T switch can be modeled to “T-shape” equivalent circuits. The modeled -parameters indicate that the modeling is valid in the whole range of frequency.

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Fig. 3.

Simulation result of a quarter membrane at the on-state mode.

Fig. 4.

SEM photographs of the RF MEMS series switch.

Fig. 2. Schematic views about each part dimension and the switching part for the metal-contact RF MEMS series switch.

In Section II, we present the design, fabrication, and characterization issues of the MEMS switch. In Section III, we investigate the design and results of the SP6T MEMS switch, and we present our conclusion in Section IV. II. SPST SWITCH DESIGN AND CHARACTERIZATION A. Design Fig. 2 shows schematic views of each part dimension and the switching part for the metal-contact RF MEMS series switch. The metal-contact MEMS switch has a CPW line of 28/40/28 m ( , 50 ) and two electrodes of 65 m, whose active area is 400 m 300 m. 200 m The center wedge (CW), which is located in the middle of the switching part due to an anchor role, has an area of 5 m. For conventional metal-contact MEMS series 5 m switches, the isolation characteristic generally depends on two and ). refers to the off-state off-state parameters ( signal-line coupling capacitance that is due to the gap between refers only to the off-state contact each broken signal line; depends solely on the distance of the overcapacitance. lapping part between the front end of the signal line and the is contact metal of the switching part in the membrane. If an arbitrary value, the isolation feature can be improved by decreasing , which is inversely proportional to the RF open signal line gap. As shown in Fig. 2, we have designed a broad signal line gap to be associated with the release process. The goal of this design is to enhance the isolation characteristic such that, at the same time, the release process does not affect the RF performance. In consideration of this factor, the determined signal line gap is 140 m. Another factor addressed in the design is the RF line in the switching part. To control the membrane spring constant properly, the inner part of the switching part is removed. Also, in order to obtain a depth of a

contact metal, an electromechanical simulation using ANSYS Multiphysics has been performed with the quarter model of the membrane, as shown in Fig. 3. The result indicates that is applied, the gap between when a pull-down voltage the RF signal line and the contact metal is 0.2 m rather than 0 m because the CW plays the anchor in the switching part of membrane. Therefore, the depth of the contact metal could be determined to 0.2 m. B. Fabrication We first deposited Au of 0.85 m for a CPW on a GaAs substrate of 625 m. Next, we coated a polyimide (PI2556) of 0.9- m height, and we cured it as a sacrificial layer to form a contact metal (Au of 0.2 m). The membrane for the fabricated MEMS switch was composed of the first membrane with a PECVD SiN dielectric of 0.3 m, the second membrane with an Au upper electrode of 2.3 m, and the third membrane with a PECVD SiN dielectric of 0.3 m. Finally, we used a polyimide stripper to remove the sacrificial layer. The fabricated RF MEMS switch had of 27.5 V. Fig. 4 shows scanning electron microscopy (SEM) photographs of the fabricated switch and its anchor and switching part.

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TABLE I PHYSICAL DIMENSIONS AND MATERIAL CONSTANTS

C. Electromechanical Response The dynamic mechanical response of the MEMS switch is characterized with the equation given by the d’Alembert principle [14] as (1) where is the membrane displacement, is the effective memis the effective damping coefficient, is the brane mass, effective spring constant, and is the external force. By using the physical dimension and material constant of the metal-contact MEMS switch in Table I, the solution of (1) can be obtained. is composed Considering the moving part of the membrane, of Au effective mass and SiN effective mass : both and are Au and SiN mass, respectively, excluding is dependent on the concerned the mass of the anchor. Since device, it has been determined by calculating (1) with the other can be easily obtained by I–V plots for the MEMS values. switch. Fig. 5 shows the setup schematic for measuring switching times and the plots of measured switching times. Biasing a square wave of 0/36 V with a frequency of 1 kHz at the dc-bias pad and inputting a constant voltage of 1 V at the RF input port, we have measured the actuation/release time. A voltage drop was detected at the RF input port, where the RF output port is grounded in order to make the electrically closed loop at the on-state mode. The measured actuation and release time are 8.0 and 5.0 s, respectively. With this measured actuation time, we can determine the of 0.0095 kg/s. It is worthy of noting that the release time is less than the actuation time, in contrast with the calculated value . This of 75 s for the constant damping condition result may be due to the physical structure, which is divided into two parts: one is the electrode area into which the electrostatic force is inserted, and the other is the switching part, which only handles the RF signal. In Table II, the characteristics were presented for the MEMS switch. D. Small-Signal Modeling To evaluate the RF performance for fabricated metal-contact MEMS switches, we need a small-signal model. Two-port se-

Fig. 5. (a) Setup schematic for measuring the switching times. (b) Actuation time. (c) Release time.

ries-impedance models (series model), which characterize the RF performances of metal-contact MEMS switches, are generally used in the manner presented in [3] and [4]. However, there are some difficulties with the conventional modeling. For instance, because of the nonphysically based solutions derived from the numerical approach, it is hard to obtain the model’s pa, which includes the contact resistances rameters, especially and ). Moreover, using the series model without the ( fringing capacitances may be improper even though this model can approximately characterize RF performances in terms of loss. Since they strongly depend on the bias mode, the fringing capacitances must affect the small-signal modeling. Therefore, we use the small-signal model instead of the series model.

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TABLE II CHARACTERISTICS OF THE SPST MEMS SWITCH

Fig. 6. Structure-based: (a) off-state and (b) on-state equivalent circuit and (c) their  small-signal model of the RF MEMS series switch.

Fig. 6 shows the structure-based small-signal models for the MEMS series switch [10]. The extracted parameters related to the small-signal model were presented in Fig. 6. The transmission lines in Fig. 6(c) are a CPW line (28/40/28 m, 50 , CPW 1) with the length of 80 m, where a “T-shape” circuit is assumed to their equivalent circuit. Using RF through test pattern, , , and ) have been extracted their parameters ( as shown in Fig. 7(a) and (b). Moreover, for a transmission line of the SP6T switch, a CPW line (14/20/14 m, 50 , CPW , , and 2) has been fabricated and their parameters ( ) have been extracted. Extracted (440 m), (220 m), and (220 m) at 5–20 GHz were 79.4–83.1 fF, 80.5–103.5 pH, and 0.01–0.61 , respectively, and their fitted values were 80 fF, 95 pH, and 0.23 . The others were listed in Table III. For modeling the off-state mode, an RF open test pattern has been fabricated additionally. The open pattern is identical to the MEMS switch without the membrane so we can exand fringing capacitances ( tract the gap capacitance and ). In the off-state circuit, there are the series combina-

Fig. 7. (a) and (b) Extracted parameters for CPW 1 and CPW 2 and (c) and (d) for the fabricated SPST MEMS switch.

tion of overlapped contact capacitances between the membrane and a signal line and off-state membrane fringing and ) considered to the effect of the capacitances ( , and , where we can igmembrane, in addition to , and innore the impedance value of the line resistance ductance of the switching part due to their relatively small

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TABLE III EXTRACTED PARAMETERS OF THE SPST MEMS SWITCH

Fig. 8. Comparison of the measured and modeled RF performance for the metal-contact RF MEMS series switch.

, , and . To calculate , we added to for describing the “ shape” scheme shown in Fig. 6. is . The -parameter equation for the model equal to is more intricate because fringing capacitances are added to the can be exseries model. Similarly, using the model, pressed to where

(3) values. Fitted and were 0.65 and 5 fF, respectively. Exwas 2.1–2.4 fF at 5–20 GHz. As is added tracted in a parallel combination, can be determined to , which was 3.08–3.14 fF. As by had the value of 6.9–8.7 fF, could be determined to 2.6–2.7 fF, which represented the off-state fringing effect of the membrane. The on-state model comprises on-state fringing capacitances ( and ), , and , where is divided into contact resistances and the line resistance. As shown was not constant, and remained in Fig. 7(d), the extracted at 5–20 GHz due to the skin effect at between 1.11–1.68 higher frequency. As , could , which was be extracted by could be regarded as the lumped re0.54–0.82 . Since sistance of CPW 1 with the length of 140 m, its value could be determined as 0.04 . Like , could be obtained. Exwas 55.1–62.3 pH and their fitted value was 60 pH. tracted was extracted to 12.1–26.7 fF at 5–20 GHz, As could be determined easily on 17.8–20.7 fF by using . It is reasonable that as is two or more , the fringing capacitances, which times higher than that of are strongly dependent on the bias mode, should be considered for the model parameter of the small-signal modeling. E. RF Performances In the off-state mode, determined [10] by

of the

model

can be

(2)

of the model In the on-state mode, and instead of mined with of (2), where . Thus,

can be deterand and is calculated as (4)

As is an admittance composed of and being , it is easy to see that the physical data as well as must include the physically based data. Despite the complexity for (4), we can extensively improve the modeling accuracy by in (4). This inclusion enables us to drastically including in the on-state mode, especially reduce the average error for the imaginary part for . of the model in the on-state is given by mode (5) Fig. 8 shows the measured and modeled RF performance for the fabricated MEMS switch. In the off-state mode, the isolation loss from derived by (3) agrees well with the measured data. The measured characteristic from 64.4 to 30.6 dB at 0.5–20 GHz indicates that the fabricated MEMS switch has a good isolation characteristic. Presumably, the isolation charac, which can be teristic can be improved simply with a lower due to the large signal-line gap. The inachieved with a low sertion loss was 0.08–0.19 dB at 0.5–20 GHz, whereas that of the return loss was from 39.1 to 22.0 dB. The validity of the model is demonstrated by the fact that its RF performances are almost the same as that of the measured data, as shown in Fig. 8. The excellent agreement shows that the model can be used for

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Fig. 10. Schematic views of the SP6T switch by using the metal-contact RF MEMS series switches.

Fig. 9. (a) Setup schematic for measuring IMD3. (b) Measured result for the fabricated MEMS series switch.

designing an optimized device with respect to specific applications, and for precisely evaluating the performance of the entire system, including MEMS devices. Fig. 9 presents the experimental setup for measuring the third intermodulation distortion (IMD3) at 2 GHz (0 dBm) with the offset of 100 kHz and the result for the fabricated MEMS series switch, where the measured IMD3 is 71.7 dBc. III. SP6T SWITCH DESIGN AND CHARACTERIZATION A. Design Top views of the SP6T switch layout using metal-contact MEMS series switches are shown in Fig. 10. In order to fabricate the SP6T switch within an area of 1 mm , we located each MEMS switch as close as possible to the adjacent switches so the area of the SP6T switch has been determined to 1.3 mm 0.8 mm. As a result of the optimization, all transmissionline structures between the input port and each output port are not identical, but symmetrical with respect to the input port. From the input port through each port, CPW 2 (14/20/14 m, 50 ) has been used to satisfy the demands of both an RF input matching and size considerations. The length of CPW 2 from Port1 (P1) to Port2 (P2) is 250 m, where the probe-pad length of 40 m is included. A CPW 2 of 250 m is only used in the case of P2 and Port7 (P7), but to the others, the CPW 2 line of 440 m is added linearly. Moreover, for an RF signal to be propagated to an output port, another CPW 2 of 50 m is additionally used in the vertical direction of the input signal. To control the RF signal as a port, the SPST MEMS switch is then placed next to CPW 2 of 50 m, where CPW 1 of 80 m has also been placed on both sides of the active membrane area in

Fig. 11.

Equivalent circuit of the SP6T MEMS switch between P1 and P4.

the MEMS switch. The ground plane of each CPW 2 used as the transmission line in the SP6T switch is linked together by an air-bridge metal, as shown in Fig. 10. B. Small-Signal Modeling Fig. 11 shows the small-signal equivalent circuit of the SP6T MEMS switch, where P4 is only in the on-state mode and the other ports are in the off-state mode. Both the on- and off-state model for the MEMS switch are used in the equivalent circuit because the other ports are in the off-state mode if one port is actuated. As mentioned before, considering that each CPW has its “T-shape” equivalent circuit, CPW 2 of 250 m near , as shown in Fig. 11. P1 has been modeled to , , and (51 fF), (57 pH), and (0.1 ) by We have obtained , , and , respectively. CPW 2 using extracted

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Fig. 12. SEM photographs of the SP6T switch with an area of 1 mm based on an RF MEMS series switch.

of 440 m, which links the input part of P2 (or P7) with that of (90 fF), (100 pH), and the others, has been modeled to (0.175 ). The third section of CPW 2 is CPW 2 of 50 m, which is used in the vertical direction of the input signal. Fitted , , and were 10.2 fF, 11.4 pH, and 0.02 , respectively. For the MEMS switch, since we performed the small-signal modeling above, we have used simply the fitted parameters of the model. Since there is each CPW 1 of 80 m on either side of the active area of the MEMS switch, it has been also modeled to the “T-shape” equivalent circuit. Fitted , , and were 14.5 fF, 17.3 pH, and 0.02 , respectively. In the on-state (22 fF), (22 fF), (60 pH), and mode, (1.273 ) have been applied to the model parameters, whereas in (8 fF), (8 fF), and (2.2 fF) the off-state mode, are applied.

Fig. 13. Comparison of the measured and the modeled isolation performance for the fabricated SP6T MEMS switch.

C. RF Performance The SP6T switch has been fabricated using the same process as that employed for the SPST MEMS switch. Fig. 12 shows SEM photographs of the SP6T switch with an area of 1 mm based on an RF MEMS series switch. In the off-state mode, the measured isolation characteristics of the SP6T switch between the input port and each output port (P2, P3, and P4) at 6 GHz were 40.0, 39.1, and 39.2 dB, respectively, whereas those of the modeled isolation were 43.7, 42.9, and 39.2 dB, respectively, as shown in Fig. 13. The features indicate that its excellent isolation characteristic of approximately 40 dB at 6 GHz results from the fabricated MEMS switch with the broad signal-line gap of 140 m, despite an intricate coupling path with each port in the SP6T switch. Fig. 14 provides a comparison of the measured and modeled RF performances for the SP6T switch in the on-state mode. The measured insertion losses between the input port and each output port (P2, P3,

and P4) at 6 GHz were 0.70, 0.53, and 0.43 dB, respectively and the modeled insertion losses were 0.75, 0.50, and 0.37 dB, respectively. Both the measured and modeled return losses were better than 9.0 dB up to 6 GHz. The other characteristics were listed in Table IV. The modeled results demonstrate that the small-signal modeling based on the parameter-extraction method can accurately evaluate the RF performances of the SP6T switch. Therefore, when the P2 switch was in the on-state mode, the isolation characteristics between the input port and the other off-state ports can be obtained by using the modeled equivalent circuit, as shown in Fig. 14(d), which were around 47 dB. Fig. 15 presents the experimental setup for measuring RF power handling of 35 dBm at 0.5 GHz and the measured RF response, where we use an amplifier of Mini-circuits (ZHL-5W). The output power was detected linearly up to 35 dBm without a self-actuation phenomenon.

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TABLE IV MEASURED RF PERFORMANCES OF THE SP6T MEMS SWITCH AT 6 GHz

SIMULATED

AND

Fig. 15. (a) Setup schematic for measuring RF power handling. (b) Measured response for the SP6T MEMS switch.

Fig. 14. Comparison of the measured and modeled RF performances for the SP6T MEMS switch in the on-state mode.

D. Hermetic Test To determine how much the hermetic condition affects the membrane actuation, we fabricated a hermetic chamber with a

range of 0.01–1 mbar, which is made of acryl of 20 mm. Fig. 16 presents the experimental setup for measuring with a parameter analyzer (HP4155B) as a function of the hermetic condition, where we fabricate and use an evaluation board for the SP6T switch in order for the discrete device to be loaded to the hermetic chamber instead of an on-wafer measurement. With a voltage sweep of 0–36 V at the bias pad taken, we determined and the leakage current under the hermetic condition, while biasing a constant voltage (1 V) at one RF port and detecting the on/off state of the compliance current (1 mA) at the other and leakage current on the port. Fig. 17 shows the measured hermetic condition. is 27.5 V at 0.01–1 mbar, but the leakage has a few different values at 26.1–27.5 A. Concurrent at sidering shows a constant value rather than a variable dependent on the pressure condition, it is evident that the damping coefficient for the fabricated RF MEMS switch should have a constant value.

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Dr. J. Lee, Knowledge*on, IKsan, Korea, for their technical assistance. REFERENCES

Fig. 16. Setup schematic and photographs for measuring hermetic condition for the SP6T MEMS switch.

V under the

Fig. 17. Measured pull-down voltage and leakage current on the hermetic condition for the SP6T MEMS switch.

IV. CONCLUSION The design, fabrication, and characterization of an SP6T switch based on compact RF MEMS series switches have been presented. The fabricated SP6T switch not only has a substantially reduced active area and displays excellent RF performances. In addition, RF performances of the SP6T switch have been evaluated with a small-signal model by the parameter-extraction method alongside those of the metal-contact MEMS series switch. For both switches, the good agreement of the measured and modeled RF performances demonstrates the validity of the model. The result shows that the model can be used either for designing an optimized device with respect to specific applications or for precisely evaluating the performance of an entire system, including MEMS devices. ACKNOWLEDGMENT The authors would like to thank C. Hyoung, Elctronics and Telecommunication Research Institute, Daejeon, Korea, and

[1] J. Smuk, M. Mahfoudi, D. Belliveau, and M. Shifrin, “Multi-throw plastic MMIC switches up to 6 GHz with integrated positive control logic,” in Proc. 21st Gallium Arsenide Integrated Circuit Symp., Oct. 17–20, 1999, pp. 259–262. [2] H. Tosaka, T. Fujii, K. Miyakoshi, K. Ikenaka, and M. Takahashi, “An antenna switch MMIC using E/D mode p-HEMT for GSM/DCS/PCS/WCDMA bands application,” in IEEE Radio Frequency Integrated Circuits Symp. Dig., 2003, pp. 519–522. [3] G. M. Rebeiz and J. B. Muldavin, “RF MEMS switches and switch circuits,” IEEE Micro, vol. 2, no. 4, pp. 54–71, Dec. 2001. [4] G. M. Rebeiz, RF MEMS—Theory, Design, and Technology. New York: Wiley, 2003. [5] M. Kim, J. B. Hacker, R. E. Mihailovich, and J. F. DeNatale, “A monolithic MEMS switched dual-path power amplifier,” IEEE Microw. Wireless Compon. Lett., vol. 11, no. 7, pp. 285–286, Jul. 2001. [6] G.-L. Tan, R. E. Mihailovich, J. B. Hacker, J. F. DeNatale, and G. M. Rebeiz, “Low-loss 2- and 4-bit TTD MEMS phase shifters based on SP4T switches,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 1, pp. 297–304, Jan. 2003. [7] J.-H. Park, S. Lee, J.-M. Kim, Y. Kwon, and Y.-K. Kim, “A 35–60 GHz single-pole double-throw (SPDT) switching circuit using direct control MEMS switches and double resonance technique,” in Proc. 12th Int. Solid State Sensors, Actuators and Microsystems Conf., Boston, MA, Jun. 8–12, 2003, pp. 1796–1799. [8] A. Q. Liu, W. Palei, M. Tang, and A. Alphones, “Single-pole-four-throw using high-aspect-ratio lateral switches,” Electron. Lett., vol. 40, no. 18, pp. 1125–1126, Sep. 2004. [9] J. Lee, C.-H. Je, S. Kang, and C.-A. Choi, “A single-pole 6-throw (SP6T) antenna switch using metal-contact RF MEMS switches for multi-band applications,” presented at the IEEE MTT-S Int. Microwave Symp., Jun. 2005. [10] J. Lee, W.-S. Yang, C. Hyoung, S. Kang, and C.-A. Choi, “A  smallsignal model of MEMS series switches based on the parameter-extraction method,” in Proc. Int. MEMS, NANO, and Smart Systems Conf., Aug. 25–27, 2004, pp. 447–453. [11] D. Costa, W. U. Liu, and J. S. Harris, Jr., “Direct extraction of the AlGaAs/GaAs heterojuction bipolar transistor small-signal equivalent circuit,” IEEE Trans. Electron Devices, vol. 38, no. 9, pp. 2018–2024, Sep. 1991. [12] B. Li, S. Prasad, L.-W. Yang, and S. C. Wang, “A semianalytical parameter-extraction procedure for HBT equivalent circuit,” IEEE Trans. Microw. Theory Tech., vol. 46, no. 10, pp. 1427–1435, Oct. 1998. [13] C. V. Niekerk, P. Meyer, D. M. M.-P. Schreurs, and P. B. Winson, “A robust integrated multibias parameter-extraction method for MESFET and HEMT models,” IEEE Trans. Microw. Theory Tech., vol. 48, no. 5, pp. 777–786, May 2000. [14] L. Dussopt and G. M. Rebeiz, “Intermodulation distortion and power handling in RF MEMS switches, varactors, and tunable filters,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 4, pp. 1247–1256, Apr. 2003.

Jaewoo Lee (M’03) was born in Jangsu, Jeonbuk, Korea, in 1972. He received the B.S. degree in electronic engineering from Korea University, Seoul, Korea, in 2000, and the M.S. degree in information and communication engineering from Gwang-Ju Institute of Science and Technology (GIST), Gwangju, Korea, in 2002. In September 2002, he joined the Electronics and Telecommunications Research Institute (ETRI), Daejeon, Korea, as a Member of Engineering Staff, where he been with the Basic Research Laboratory focusing on MEMS devices. His current research interests include the design, fabrication, and characterization of electrostatic MEMS devices, especially RF MEMS switches, for applications to telecommunication systems. Mr. Lee is a member of the IEEE Microwave Theory and Techniques Society (IEEE MTT-S) and the IEEE Electron Device Society (IEEE ED-S).

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Chang Han Je was born in Jinju, Korea, in 1977. He received the B.S. degree in mechanical engineering from Yonsei University, Seoul, Korea, in 2002, and the M.S. degree in mechanical engineering from the Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Korea, in 2004. Since 2004, he has been with the Electronics and Telecommunications Research Institute (ETRI), Daejeon, Korea, as a Member of Engineering Staff, where he has been with the Microsystems Research Department. His research interests include the design, fabrication, and characterization of MEMS devices and MEMS packaging.

Sungweon Kang (M’91) was born in Busan, Korea, in February 1964. He received the B.S. degree and M.S. degree in electronic engineering from Kyung Pook National University, Daegu, Korea, in 1987 and 1989, respectively, and the Ph.D. degree in electrical engineering from the Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Korea, in 2004. While with Kyung Pook National University, he performed many pioneering studies for silicon-on-insulator (SOI) structures and SOI devices. In 1989, he joined the Electronics and Telecommunications Research Institute (ETRI), Daejeon, Korea, where he is currently a Senior Engineer with the Semiconductor Department. He has also been a Team Reader and a Project Director of RF MEMS and microsystems with the ETRI. From 1989 to 1995, he was involved with next-generation devices for 1-Gb three-dimensional (3-D) SOI dynamic random access memory (DRAM). Since 1996, his research interests have focused on RF circuits, devices, and basebands for mobile hand set and multimedia devices. He is currently involved with next-generation body area network (BAN) communication technology. His research interests include RF MMICs, MEMS devices, nanoscale device modeling, and simulations. Dr. Kang was a reviewer of the IEEE Electron Device Society. He has been a member of the Semiconductor Equipment and Materials Institute (SEMI) since 1993.

Chang-Auck Choi was born in Daegu, Korea, in 1954. He received the M.S. and Ph.D. degrees in electronic engineering from Kyungpook National University, Taegu, Korea, in 1988 and 1999, respectively. Since 1980, he has been with the Electronics and Telecommunications Research Institute (ETRI), Daejeon, Korea, where he is involved with the development of MEMS devices and advanced semiconductor process technology. He is currently the Director of the IT-BT Technology Development Department, ETRI. His current research involves microoptoelectromechanical systems (MOEMS), semiconductor sensors, and bio-MEMS.

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Increasing the Speed of Microstrip-Line-Type Polymer-Dispersed Liquid-Crystal Loaded Variable Phase Shifter Yozo Utsumi, Fellow, IEEE, Toshihisa Kamei, Member, IEEE, Katsuhiko Saito, and Hiroshi Moritake

Abstract—We discuss a method for the production of microwave polymer-dispersed liquid-crystal devices. We also show how to obtain a fine grained uniform fibrous polymer network. We then measure how the microwave-band dielectric properties and response-time characteristics of microstrip-line-type polymer-dispersed liquid-crystal devices vary with polymer concentration, and we measure how their response-time characteristics vary with the thickness of the polymer-dispersed liquid-crystal layer. With a layer thickness of 50 m, an applied voltage of 100 V and a polymer concentration of 7 wt%, we show that the decay time can be reduced to approximately 1/30th that of a plain liquid crystal at the expense of an increase in rise time of approximately 2.5 times and a deterioration of dielectric birefringence of approximately 50%. Finally, we discuss the results obtained with a prototype polymer-dispersed liquid-crystal loaded variable phase shifter in the 15-GHz band. By comparing the variable phase and response time of this phase shifter with basic experimental data obtained by the microwave resonance method, we verified the validity of these values. Index Terms—Delay lines, liquid-crystal devices, microstrip resonators, phase shifter.

I. INTRODUCTION

I

N A liquid-crystal device with a microstrip-line structure, microwave-band insertion losses make it impossible to use an extremely thin liquid-crystal layer as in liquid-crystal display applications. On the other hand, the decay time of a liquidcrystal device increases in proportion to the square of the layer thickness [1], thus, with a liquid-crystal layer thickness of approximately 100 m, as used in the configuration of most microwave liquid-crystal devices, the decay time ends up being approximately 1000 times greater than the rise time [2]. It is thus hoped that a way can be found to substantially reduce the decay time even if this entails a slight increase in rise time and deterioration of the dielectric properties. A promising means of achieving this involves substituting the liquid-crystal layer with a so-called polymer-dispersed liquid crystal consisting of a polymer dispersed into a nematic liquid crystal at a suitable concentration [3].

Manuscript received April 1, 2005; revised July 4, 2005. This work was supported in part by the 2004 Hoso Bunka (Broadcasting Culture) Foundation. Y. Utsumi, T. Kamei, and H. Moritake are with the Department of Communications Engineering, National Defense Academy, Yokosuka, Kanagawa 239-8686, Japan (e-mail: [email protected]; [email protected]; [email protected]). K. Saito was with the Department of Communications Engineering, National Defense Academy, Yokosuka, Kanagawa 239-8686, Japan. He is now with the Japan Maritime Self-Defense Force, 237-0076 Yokosuka, Japan. Digital Object Identifier 10.1109/TMTT.2005.857123

A number of our earlier studies have touched on this subject. Reference [2] proposes a method (called a “microwave resonance method”) for measuring microwave-band response-time characteristics in devices that use plain nematic liquid crystals, and analyzes the results of measurements made using this method. Reference [4] describes the ability to increase the speed of polymer-dispersed liquid-crystal devices by measuring the response-time characteristics and dielectric properties obtained when the polymer concentration is varied while keeping the applied voltage and polymer-dispersed liquid-crystal layer thickness constant, and by measuring the response-time characteristics obtained when the polymer-dispersed liquid-crystal layer thickness is varied while keeping the applied electric field and polymer concentration constant. References [5] and [6] propose a method (also called a “microwave resonance method”) for measuring microwave-band dielectric properties in devices that use plain nematic liquid crystals. In particular, they clarify the concept of an effective alignment coefficient based on incomplete alignment of liquid-crystal molecules, which is a problem when the device structure consists of a microstrip-line structure. In this paper, our chief aim is to demonstrate quantitatively how the decay times of devices using polymer-dispersed liquid crystals can be improved in order to address a serious issue described in [2]—namely, the large value of the decay time in plain liquid-crystal devices. In order to take direct measurements of the liquid-crystal device characteristics in the microwave band when measuring the response-time characteristics and dielectric properties of microstrip-line structure polymer-dispersed liquid-crystal devices, we used a microwave resonance method based on an inductive coupled-ring resonator that we developed [5], [6]. The novel aspects of this paper compared with [2], [5], and [6] can be summarized as follows. 1) We discuss the production technique of microwave-band polymer-dispersed liquid-crystal devices and the optical method for verifying this production technique. Investigating the importance of the temperature during the polymer-dispersed liquid-crystal mixing, we found guidelines for the selection of liquid-crystal material related to the nematic–isotropic (N–I) phase temperature and the polymer concentration. In order to make the problem of the mixing temperature clear, we made a production test for the two kinds of liquid-crystal material having the different N–I phase temperature.

0018-9480/$20.00 © 2005 IEEE

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2) We quantitatively show how the response-time characteristics and dielectric properties vary with polymer concentration in microstrip-line devices made with polymer-dispersed liquid crystals, and we clarify the physical significance of this variation. 3) We quantitatively show how the response-time characteristics of polymer-dispersed liquid crystals vary with layer thickness, and we clarify the physical significance of this variation. 4) We quantitatively show that the use of polymer-dispersed liquid crystal allows the decay time to be improved by a factor of approximately 30, but at the expense of an increase in rise time by a factor of approximately 2.5 and an impairment of dielectric properties of approximately 50%. 5) As an example of a specific application, we used a polymer-dispersed liquid crystal with a polymer concentration of 9% (by weight of pre-polymer) to produce a prototype 15-GHz-band variable phase shifter with a microstrip meander-line structure having a layer thickness of 100 m and a characteristic impedance of 50 , and we show that its phase characteristics and response-time characteristics match the basic experimental data obtained with the microwave resonance method. Our paper also contains various additions compared with [4]. For example, we have added new discussions of items 1) and 5); with regard to item 3), we have added new data relating to a polymer concentration of 9 wt%, thereby yielding new experimental results on the layer thickness dependence of response times when the concentration is varied and helping us understand the physical significance of this phenomenon, and we have added a comment to illustrate the time-domain data obtained in the microwave resonance method. II. IMPROVING THE DECAY TIME OF POLYMER-DISPERSED LIQUID-CRYSTAL DEVICES When a plain liquid crystal is injected between two parallel plates that have been subjected to a rubbing process, the rise and decay time are expressed as follows [1]: time (1) (2) Here, is the coefficient of viscosity, and are the bias electric field and threshold electric field, is the dielectric birefringence, is the thickness of the liquidcrystal layer, and is the elastic constant. As (2) shows, the decay time increases in proportion to the square of the liquidcrystal layer thickness so once the layer thickness has been set, the device’s response time is more or less predetermined. The thickness of the liquid-crystal layer for microwave devices is relatively large at approximately 100 m, in which case, the rubbed substrate surfaces are only able to apply a weak aligning force to the molecular orientation of the liquid crystal so that the rise time is only a few milliseconds while the decay time is much longer at several tens of seconds.

Fig. 1. Inductive coupled-ring resonator with polymer-dispersed liquid crystal from [4].

Thus, since the use of a polymer-dispersed liquid crystal causes the liquid-crystal molecules to be subjected to a strong aligning force from the neighboring polymer interfaces, the same effect is obtained when the liquid-crystal layer is made thinner, allowing the decay time to be improved. However, this effect involves tradeoffs associated with the disadvantages of increased threshold voltage, lower dielectric birefringence, and increased rise time.

III. MEASURING THE RESPONSE TIME OF A MICROWAVE RING RESONATOR FILLED WITH POLYMER-DISPERSED LIQUID CRYSTAL A. Microwave Resonance Method 1) Resonant Frequency of the Inductive Coupled-Ring Resonator: Fig. 1 shows the structure of an inductive coupled-ring resonator filled with polymer-dispersed liquid-crystal material. The ring surface of the glass substrate is oriented toward the ground conductor, the polymer-dispersed liquid-crystal material fills the gap between the ring surface and the ground conductor, and the polymer-dispersed liquid-crystal material is allowed to come into direct contact with the ring. With regard to the rubbing between the ring surface and the ground conductor surface, we performed experiments with polymer-dispersed liquid-crystal layers having a parallel nematic (PN) (in which the polyimide films on the upper and lower surfaces of the cell have parallel rubbing directions) structure. When a square wave bias voltage is applied to the gap between the ring and ground plane, the longitudinal axes of the liquid-crystal molecules in the PN structure align themselves parallel with the propagating RF electric field, resulting in a rel. When no square wave bias voltage is ative permittivity of applied, the liquid-crystal molecules align themselves perpendicular to the RF electric field due to the mechanical aligning force of the rubbed polyimide film and dispersed polymer, re. sulting in a relative permittivity of when a 1-kHz bias We measured the resonant frequency voltage is applied corresponds to the substrate’s permittivity , and the resonant frequency when no bias voltage . is applied corresponds to

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Fig. 3. Time-domain data in microwave resonance method (BL011 PDLC 9 wt%, d = 50 m). TABLE I NEMATIC LIQUID CRYSTAL (Merck) USED FOR OUR MEASUREMENTS Fig. 2. Some of the resonant frequencies of an inductive coupled-ring resonator filled with polymer-dispersed liquid-crystal material (measured values) from [4].

2) Principle of Response-Time Measurements: The rise (voltage on time) indicates the time taken for the time resonant peak to shift from to , and can be determined by measuring the output of an RF detector with a digital oscilloscope. Similarly, the decay time (voltage off time) can be to . determined by observing the shift from Fig. 2 shows the resonant peaks in the 20-GHz band corre(under bias voltage) and sponding to the permittivity (with no bias voltage) of the inductive coupled-ring resonator shown in Fig. 1 when filled with the polymer-dispersed liquidcrystal material. When the bias voltage is turned on, the resonant frequency to . The frequency shift shifts from corresponds to the dielectric birefringence . When the detector output is observed on an oscilloscope, it is possible to observe the transient response-time characteristics of the shift in the resonant peak corresponding to the change in to . permittivity from Strictly speaking, is regarded as the time taken for the permittivity of the polymer-dispersed liquid-crystal layer to change to from the instant the voltage is from is taken to be the time for the permittivity turned on, and to change from to from the instant the voltage is turned off. Fig. 3 shows an example of the time-domain data obtained when observing the temporal characteristics of the transient response to a shift in the resonant peak. Specifically, this figure shows the result of measuring the decay time when a material consisting of 9 wt% polymer in BL011 liquid crystal (Merck) is filled into a 50- m gap and subjected to a bias voltage of 100 V. The decay time was measured by observing the time to taken for the resonant frequency to shift from —corresponding to a change in dielectric constant equal —after switching off to 90% of the dielectric birefringence the bias voltage. This change of resonant frequency was observed on an oscilloscope by applying a continuous wave (CW) to the ring resonator shown in signal with a frequency of Fig. 1 and detecting the output from this ring resonator. At the

instant the resonant peak frequency (which shifts as the applied voltage is switched on and off) coincides with the frequency of the CW signal, the output shown on the oscilloscope reaches its peak value. In each case, we measured the time taken for the detection output to reach a peak value. In the example shown in Fig. 3, the measurement was made with a CW signal at a fre, yielding a value of ms. quency of B. Production of the Polymer-Dispersed Liquid-Crystal Material The gap of the PN-aligned ring resonator shown in Fig. 1 was filled with a polymer-dispersed liquid crystal made by mixing a nematic liquid crystal with a photo setting pre-polymer (acryl urethane based, NOA65 made by Norand, Cranbury, NJ, refractive index 1.524). The polymer-dispersed liquid crystal was produced by the phase separation method with photopolymerization. An optical test cell was produced to facilitate observation of the formation of a uniform fibrous polymer network, which is desirable in a microwave use. Considering that the polymer-dispersed liquid crystal would be applied to microwave-band variable delay lines and the like, the polymer-dispersed liquid-crystal test cell was produced using the nematic liquid crystals BL006 and BL011 in the 20-GHz band. (Merck), which have relatively large Table I lists the parameters of these two liquid-crystal materials measured in the 20-GHz band and the values shown in the manufacturer’s catalog. The pre-polymer was stirred for several hours while keeping it heated beyond the temperature at which BL006 becomes C). isotropic (the N–I phase transition temperature The pre-polymer was mixed in at a ratio of 5 wt%. A test cell was produced by filling the space between two homogeneously aligned indium–tin–oxide (ITO) glass plates with a uni-

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Fig. 4. Photopolymer phase separation mechanism. (a) T . (c) After curing.

N –I

> N –I

C. (b) T

s

TEPPATI AND FERRERO: ON-WAFER CALIBRATION ALGORITHM FOR PARTIALLY LEAKY MULTIPORT VNAs

[13] J. Helton and R. Speciale, “A complete and unambiguous solution to the super-TSD multiport-calibration problem,” in IEEE MTT-S Int. Microwave Symp. Dig., vol. 83, May 1983, pp. 251–252. [14] M. Schoon, “A semi-automatic 3-port network analyzer,” IEEE Trans. Microw. Theory Tech., vol. 41, no. 6, pp. 974–978, Jun. 1993. [15] W. V. Moer and Y. Rolain, “Proving the usefulness of a three-port nonlinear vectorial network analyzer through mixer measurements,” IEEE Trans. Instrum. Meas., vol. 52, no. 12, pp. 1834–1837, Dec. 2003. [16] F. Sanpietro, A. Ferrero, U. Pisani, and L. Brunetti, “Accuracy of a multiport network analyzer,” IEEE Trans. Instrum. Meas., vol. 44, no. 2, pp. 304–307, Apr. 1995. [17] A. Ferrero, U. Pisani, and K. Kerwin, “A new implementation of a multiport automatic network analyzer,” IEEE Trans. Microw. Theory Tech., vol. 40, no. 11, pp. 2078–2085, Nov. 1992. [18] A. Ferrero, F. Sanpietro, and U. Pisani, “Multiport vector network analyzer calibration: A general formulation,” IEEE Trans. Microw. Theory Tech., vol. 42, no. 12, pp. 2455–2461, Dec. 1994. [19] A. Ferrero and F. Sanpietro, “A simplified algorithm for leaky network analyzer calibration,” IEEE Microw. Guided Wave Lett., vol. 5, no. 4, pp. 119–121, Apr. 1995. [20] J. V. Butler, D. K. Rytting, M. F. Iskander, R. D. Pollard, and M. V. Bossche, “16-term error model and calibration procedure for on-wafer network analysis measurements,” IEEE Trans. Microw. Theory Tech., vol. 39, no. 12, pp. 2211–2217, Dec. 1991. [21] H. V. Hamme and M. V. Bossche, “Flexible vector network analyzer calibration with accuracy bounds using an 8-term or a 16-term error correction model,” IEEE Trans. Microw. Theory Tech., vol. 42, no. 6, pp. 976–987, Jun. 1994. [22] K. Silvonen, “LMR 16-a self-calibration procedure for a leaky network analyzer,” IEEE Trans. Microw. Theory Tech., vol. 45, no. 7, pp. 1041–1049, Jul. 1997. [23] H. Heuermann and B. Schiek, “Calibration of network analyzer measurements with leakage errors,” Electron. Lett., vol. 30, no. 1, pp. 52–53, Jan. 1994. [24] R. Speciale, “A generalization of the TSD network-analyzer calibration procedure, covering n-port scattering-parameter measurements, affected by leakage errors,” IEEE Trans. Microw. Theory Tech., vol. MTT-25, no. 12, pp. 1100–1115, Dec. 1977.

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[25] V. Teppati, A. Ferrero, D. Parena, and U. Pisani, “A simple calibration algorithm for partially leaky model multiport vector network analyzers,” in 65th ARFTG Dig., Jun. 2005, pp. 1–4.

Valeria Teppati (S’00–M’04) was born in Turin, Italy, on October 2 , 1974. She received the Electronics Engineering degree and Ph.D. in electronic instrumentation from the Politecnico di Torino, Turin, Italy, in 1999 and 2003, respectively. Since 2003, she has been a Research and Teaching Assistant with the Politecnico di Torino. Her research interests and activities include microwave devices design, linear and nonlinear measurements design, calibration, and uncertainty.

Andrea Ferrero (S’86–M’88) was born in Novara, Italy, on November 7, 1962. He received the Electronic Engineering degree and Ph.D. degree in electronics from the Politecnico di Torino, Turin, Italy, in 1987 and 1992, respectively. In 1988, he joined Aeritalia as a Microwave Consultant. During 1991, he was a summer student with the Microwave Technology Division, Hewlett-Packard, Santa Rosa, CA. In 1995, he was a Guest Researcher with the Electrical Engineering Department, Ecole Polytechnique de Montrèal, Montrèal, QC, Canada. In 1998, he became an Associate Professor of electronic measurements with the Politecnico di Torino. His main research activities are in the area of microwave measurement techniques, calibration, and modeling.

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High-Power MEMS Varactors and Impedance Tuners for Millimeter-Wave Applications Yumin Lu, Member, IEEE, Linda P. B. Katehi, Fellow, IEEE, and Dimitrios Peroulis, Member, IEEE

Abstract—A high-power contactless RF microelectromechanical system (MEMS) varactor and an impedance tuner that utilizes this varactor and is simultaneously optimized for maximum impedance coverage and power handling are presented in this paper. The proposed varactor can successfully handle 4 W of RF power (hot tuning) for more than 108 cycles when tested with no hermetic packaging or nitrogen protection. This is the highest power handling under hot tuning conditions reported to date. In addition to this MEMS device, a 30-GHz four-varactor impedance tuner optimized for high-power operation is demonstrated. The power handling capability of this tuner is 4.5 times higher than conventional designs. These results experimentally demonstrate for the first time the significant advantages of contactless MEMS devices over contact-based structures (e.g., switches) for high-power applications. Index Terms—Contactless operation, high-power microelectromechanical system (MEMS), impedance tuner, MEMS reliability, MEMS varactors.

I. INTRODUCTION

A

LARGE number of microelectromechanical system (MEMS) devices have already been developed over the past 15 years [1] for a variety of high-frequency communication systems. During this period, the majority of researchers have primarily focused their attention to devices that either have no movable parts (such as MEMS inductors [2], [3] and bulk acoustic resonators [4]) or have movable parts with impacting and rubbing surfaces (such as RF MEMS switches) [5]. While the first approach significantly enhances the components’ RF performance, reconfigurable communication systems require devices with movable parts that can be actuated by electrostatic, magnetostatic, thermal, or piezoelectric forces. RF MEMS switches are currently considered to be among the most promising tunable devices due to their excellent RF performance (loss 0.2 dB, 66 dBm, isolation 30 dB, third-order intercept point bandwidth 40 GHz [1]) and virtually zero power consumption. Despite these advantages, however, a number of serious reliability and cost issues remain unanswered for MEMS

switches. The most important of these include: 1) contact area damage and wear that lead to contact resistance degradation even for relatively low power levels [6]; 2) poor power handling caused by the limited actual contact area. This issue becomes particularly difficult to address for RF power levels 500 mW and/or for hot-switching applications [7]; 3) dielectric charging caused by trapped charges inside the thin dielectric layers commonly found in MEMS switches. Dielectric charging leads to uncontrollable changes of the actuation voltages versus time and eventually complete device failure [8]; and 4) lack of low-cost hermetic packaging that protects the MEMS devices at harsh environments. Additionally, the optimum gas microenvironment for the reliable operation of MEMS switches is still unknown today. It is interesting to note that these reliability and packaging concerns in today’s MEMS switching technology are directly linked to their designed mode of operation that relies on some type of direct metal-to-metal [9] or metal-to-dielectric contact [10]. Other MEMS devices that operate in completely contactless modes, such as the Analog Devices accelerometers and the Agilent film bulk acoustic resonator (FBAR) filters, do not exhibit these difficulties, have already become commercially available, and are massively produced. Although their design and complexity are comparable to MEMS switches, their crucial advantage lies on the lack of any type of contact. Motivated by these devices, this paper focuses on a high-performance contactless MEMS varactor and its application into a unique impedance tuner simultaneously optimized for maximum power handling and impedance coverage. The results, backed by simulated and measured data, prove that, unlike switches, contactless MEMS devices can be reliably employed in high-power applications. This paper is organized as follows. Section II presents the power handling capabilities of the varactor. Section III discusses the design and implementation of the impedance tuner. Finally, Section IV discusses the tuner’s bandwidth from 27 to 35 GHz. II. CONTACTLESS MEMS VARACTOR

Manuscript received April 1, 2005; revised June 18, 2005 and August 23, 2005. This work was supported by the Multifunctional Adaptive Radio, Radar and Sensors Multiuniversity Research Initiative Project under Award 2001-0694-02 and by the Collaborative Technology Alliances in Advanced Sensors Program sponsored by the U.S. Army Research Laboratory under Contract DAAD-19-01-2-0008. Y. Lu is with the Radiation Laboratory, Electrical Engineering and Computer Science Department, The University of Michigan at Ann Arbor, Ann Arbor, MI 48109-2122 USA and also with M/A-COM, Lowell, MA 01853 USA. L. P. B. Katehi and D. Peroulis are with the School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907 USA (e-mail: [email protected]; [email protected]). Digital Object Identifier 10.1109/TMTT.2005.859031

A. Design Fig. 1 shows the MEMS device studied in this paper. The design, fabrication details, and low-power tuning range have been presented elsewhere [12], [13] and will not be repeated here. The design is based on the extended tuning range approach [14] and will only be summarized briefly here. The varactor is composed of two beams, namely, the lower and upper beams, which are 1- and 10- m thick, respectively. The lower beam is suspended approximately 4 m above

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Fig. 1. Contactless analog RF MEMS varactor [13].

Fig. 2. Simple schematic diagram of the RF MEMS analog varactor. A1 and A2 are the areas of the RF plate and the dc actuation pads, respectively. The varactor is connected to the ground plane of the CPW line with four crab-leg springs (not shown in this figure).

the center conductor of a 70/120/70- m coplanar waveguide (CPW) and is anchored at its ground planes. The upper beam is approximately 8 m above the substrate and extends over two square pads that are used for actuating the device. These square pads are completely isolated from the CPW line. Fig. 2 shows a simplified schematic of these ideas. The upper beam cannot deflect substantially due to its large stiffness. As a result, it pushes the lower beam downwards when an electrostatic potential is applied between the varactor and the actuation pads. Because of the height difference between the two beams, the pull-in instability for the upper beam does not occur until it moves by approximately 2.5 m downwards. Consequently, the tuning range of the varactor can be very high. As shown in this section though, it is limited by the desired power handling. Fig. 1 also shows a dielectric layer covering the center conductor of the CPW. This was only included for precaution in the initial tests and is not necessary because the lower beam and the CPW line are always at the same dc potential. B. Low-Power Measurements First, a small signal measurement was performed with an 8510 C vector network analyzer to measure the -parameters of a typical varactor from 2 to 40 GHz at various bias voltages. The effects of the probes and the connecting cables were de-embedded by standard line-reflect-reflect-match (LRRM)

Fig. 3. (a) Measured and simulated return of the MEMS varactor for several bias voltages. (b) Extracted C –V curve and equivalent circuit of the varactor.

calibration with Wincal.1 The varactor’s capacitance was then extracted from the measured -parameters and the techniques reported in [10]. Fig. 3 shows typical measured and simulated reflection coefficients and the extracted – curve. The simulated -parameter data have been obtained by the Sonnet software package.2 The – curve and the equivalent circuit parameters were extracted by the Agilent Advanced Design System (ADS).3 The varactor has a low capacitance of 0.095 pF at no bias and a maximum capacitance of 0.3 pF at a bias voltage of 55 V. This corresponds to a tuning range of approximately 3.15 : 1. C. Power Handling Modeling Lack of any contact renders the device at hand immune to welding-induced stiction. As a result, self-actuation will be the dominant power-induced failure mechanism. Following the analysis in [11] and by referring to Fig. 2, the self-actuation power can be approximated to be (1) 1Wincal 3.1 Calibration Software, Cascade Microtech Inc., Beaverton, OR, 2002. 2High Frequency Electromagnetic Software (HFSS), ver. 9.52, Sonnet Software, North Syracuse, NY. 3ADS, ver. 2003A, Agilent Technol., Palo Alto, CA.

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D. Experimental Apparatus for High-Power Measurements

TABLE I BASIC VARACTOR PARAMETERS

Fig. 4. Minimum capacitor gap (simulated) and maximum available tuning range as a function of the incident power.

where N/m [13] is the -directed spring constant of the varactor, m is the initial gap of the lower beam, is the operating frequency, is the varactor’s capacitance, is the system impedance, and m is the RF actuation area. All of the varactor’s parameters are summarized in Table I. The fringing field effect has been taken into account above by the linear approximation m

(2)

where is the lower beam gap and varies between 1 and 4 m. This equation results in a fringing field capacitance of 34% and and m, respectively. This is consistent 1% when with the measurements of Fig. 3, since the parallel plate capacm and m are 0.095 and 0.301 pF, itances for respectively. Based on this analysis, Fig. 4 shows the calculated minimum allowable gap between the lower beam and the CPW center conductor before self-actuation occurs. The calculation has been GHz. Notice that although the minimum performed at gap increases as a function of the incident power, the device remains functional but with a reduced tuning range. Fig. 4 also shows the calculated and measured (please see next subsection) tuning ranges as a function of the incident power. This graph shows that the 1- and 10-W tuning ranges are 2.3 : 1 and 1.25 : 1, respectively. It is worth noting that the device provides a reasonable tuning range even at powers as high as 10 W. The experimental data associated with this graph are discussed in the next subsection.

The high-power experimental characterization of the device is performed using the apparatus shown in Fig. 5. An -band traveling-wave tube (TWT) amplifier is used to get high input power, and a directional coupler (HP11692D) is employed to monitor the incident and reflected powers. The magnitude of reflection of the device-under-test (DUT) can then be calcuand . However, when such a setup lated from is used to measure devices with very low reflections such as MEMS varactors, special attention needs to be paid to the measurement errors. In particular, there are two major contributors from the test setup that introduce errors in the measurement, which are: 1) the coupler directivity and 2) the reflections from the connecting cable and probes. The HP11692D is a 2–18-GHz broad-band 22-dB coupler with directivity higher than 26 dB from 8 to 18 GHz. The high directivity of the coupler greatly reduces the effect of the input signal (port 1) on the reflection port (port 2). However, a typical Picoprobe 40 A microwave probe from GGB Industries Inc., Naples, FL, has a better than 18-dB return loss from dc to 40 GHz.4 The signal reflected by the cables/probes then combines with the reflected signal from the DUT and introduces inaccuracies. This error can be quite high if the DUT’s return loss is close to that of cables and probes. In order to calibrate these errors out, the following procedure is followed. The varactor is first tested with the setup shown in Fig. 5 at very low power level (10 dBm). Power meter 1 is used to monitor the input power while power meter 2 is used to record the reflected power. We then relate these data (we will call it power reflection) with the capacitance value extracted from the network analyzer measurements. For example, when the bias voltage is 30 V, we measured a power reflection of 14.43 dB. From the – curve in Fig. 3, we know the capacitance is 0.115 pF at 30 V. Therefore, we relate a power reflection of 14.43 dB to 0.115 pF. This one-to-one mapping between the power reflection and the capacitance is performed for all capacitances from 0.095 fF to 0.3 pF. Effectively, the power reflection data collected at low input power level (10 dBm) serve as our calibration scheme. E. High-Power Measurements: Hot Tuning Range After this mapping is completed, the high-power – curve can be extracted from the power measurements. Fig. 6 shows these capacitance values at different input power levels ranging from 0.01 to 4 W. In these measurements, the hot tuning range of the varactor was extracted for every incident power level. From these curves, we readily observe that there were no powerrelated failures for powers as high as 4 W. The maximum output power of the TWT was limited to 6 W, which did not allow us to test these devices at higher power levels (approximately 2 W is lost in the cables and transitions from the TWT to the varactor). It is interesting to note, however, that at high-power levels, the hot tuning range of the varactor is reduced due to self-actuation. For example, at 4-W input power, the maximum capacitance that the varactor can provide is about 0.18 pF at 35.5 V. This corresponds to about 40% reduction of the tuning range. Fig. 4 4GGB

Industries Inc., Naples, FL. [Online]. Available: http://www.ggb.com

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Fig. 5. Experimental setup designed and implemented for high-power characterization.

Fig. 6. Measured varactor tuning range at different input power levels (hot tuning).

summarizes these data. Good agreement is observed between simulated and measured results. The 8%–15% error is due to the approximations involved in the simple 1-D model. The same setup for hot tuning range measurement in Fig. 5 is used to cycle the varactor at an input power of 3.2 W (hot tuning). The dc bias source is replaced with a square wave generator that generates a 0–37-V square wave at 2 kHz. A 3-V safe margin from the pull down voltage (40 V) is used to avoid self-actuation during this cycling test. The varactor is cycled up to 100 million cycles in an open laboratory environment with no nitrogen protection or hermetic packaging. Fig. 7 shows the varW after 15, 29, and 100 million actor – curves at cycles. The varactor’s performance is quite consistent during the whole cycling process except that the – curve shifts slightly toward the low voltage side. After the cycling test is finished, the hot tuning rage of the varactor at various input power levels is measured again following the previous procedure. Fig. 8 shows the measured results after 100 million hot cycling tests as a function of bias voltage and input RF power. The measurement results agree very well with the results shown in Fig. 6 that were taken before the cycling test. The consistency can be clearly seen from the maximum capacitance value that the varactor provides and the corresponding pull-down voltages at different power levels before and after cycling tests. The measurements shown in Fig. 8 were taken several days after the experiments had been started. During this period, the TWT’s maximum power level was dropped by 0.6 dB, which explains the difference between the maximum power reported in Figs. 6 and 8. It is also worth noting that the devices

Fig. 7. Measured varactor C –V curve before and after 15, 29, and 100 million hot cycles at an input power of 3.2 W.

Fig. 8. Measured varactor C –V curves at various power levels (hot tuning range) after 100 million cycling test with 3.2-W power.

were perfectly functional after the hot cycling tests were stopped at 100 million cycles. III. IMPEDANCE TUNER By employing four of these devices, we have designed and implemented an impedance tuner simultaneously optimized for maximum impedance coverage and power handling [15]. While several researchers have demonstrated wide-range impedance tuners [15]–[20], none of these designs have considered the issue of power handling. In fact, they all use a large number of MEMS switches whose power handling is severely limited by stiction and welding. Furthermore, no hot switching is possible in these designs.

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Fig. 9. Microphotograph of the fabricated impedance tuner. The tuner occupies an area of 0.49 0.12 mm .

2

Fig. 11. Measured and simulated tuner impedance coverage at 27, 28.5, and 30 GHz.

Fig. 12.

Fig. 10. Simulated time-domain voltage waveforms for the four varactors of the tuner for all possible bias voltages. Each waveform is normalized to the amplitude of the voltage at the load. The maximum amplitude for each varactor is listed in Table II (design 1).

TABLE II MAXIMUM RMS VOLTAGE OF THE FOUR MEMS VARACTORS. DESIGN 1 IS THE OPTIMIZED DESIGN WHILE DESIGN 2 IS A CONVENTIONAL DESIGN THAT DOES NOT OPTIMIZE THE TUNER’S POWER HANDLING. DETAILS OF THE DESIGNS CAN BE FOUND IN [15]

The fundamental idea in this new tuner is to optimize the placement of MEMS varactors so each varactor exhibits approximately the same voltage swing. This ensures that self-actuation due to high RF power [13] is minimized for the whole tuner. The impedance tuner design is presented in detail in [15] and will not be repeated here. The final four-capacitor tuner is shown in Fig. 9. Fig. 10 presents the ADS-simulated time-domain varactor voltages for all possible bias voltages. These waveforms are normalized to the voltage of the load so they are independent of the input power level. The maximum voltage swing for each varactor of this design is summarized and compared to a conventional design in Table II. More details about the conventional design can be found in [15]. The maximum power that the tuner

Simulated tuner impedance coverage at 31.5, 33, and 35 GHz.

can deliver to the load increases from 0.19 W (design 2, conventional) to 0.84 W (design 1, optimized). This is about 4.5 times improvement in terms of the power that the tuner can deliver. The optimized impedance tuner is fabricated on a 10 000- cm Si substrate. Due to a condition change of the sputter tool at the Solid State Electronics Laboratory, The University of Michigan at Ann Arbor, the deposited lower beam had a somewhat higher residual stress level than expected. This resulted in a reduced capacitor range of the MEMS varactors because the varactor’s minimum capacitance was increased to about 0.15 pF instead of the nominal 0.1 pF. Due to these fabrication issues, the tuner presented its optimum performance at 30 GHz instead of the originally designed 25 GHz. Fig. 11 presents the simulated and experimental results for various frequencies. At frequencies lower than the design frequency, the tuner’s functionality is primarily limited by the reduced impedance coverage due to the reduction of the transmission lines’ electrical lengths as well as the reduction of the capacitors’ admittances. Limited coverage is not a major concern at high frequencies unless the frequency is significantly higher than the design frequency. Fig. 12 proves this for frequencies up to 35 GHz. At high frequencies, however, the maximum rms voltages increase rapidly. Table III summarizes these data. Please note that this is an analog tuner and it is impossible to measure all different configurations. The simulated data in Figs. 11 and 12 are presented for six distinct capacitance values per varactor. About 190 experimental points were collected from the continuous range. As a comparison between simulated and measured data, Fig. 13 shows the -parameters of the tuner with all varactors in the up and down states. Very good agreement is observed between the designed and the acquired values.

LU et al.: HIGH-POWER MEMS VARACTORS AND IMPEDANCE TUNERS FOR MILLIMETER-WAVE APPLICATIONS

TABLE III SIMULATED TUNER LOSS AND MAXIMUM RMS VOLTAGES OF THE VARACTORS AT VARIOUS FREQUENCIES. MAXIMUM POWER IS CALCULATED WITH VARACTOR SELF-ACTUATION VOLTAGE OF 24 V

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swing on each of the MEMS varactors. Design issues including the optimization on the transmission line length, the effect of the added MIM capacitor, and the tuner loss are discussed in detail. This is the first demonstration of high-power RF MEMS devices and clearly illustrates the benefits of using contactless RF MEMS devices as opposed to conventional MEMS switches. REFERENCES [1] G. M. Rebeiz, RF MEMS, Theory, Design and Technology. New York: Wiley, 2003. [2] J.-B. Yoon, B.-I. Kim, Y.-S. Choi, and E. Yoon, “3-D construction of monolithic passive components for RF and microwave ICs using thick-metal surface micromachining technology,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 1, pp. 279–288, Jan. 2003. [3] G. W. Dahlmann, E. M. Yeatman, P. R. Young, I. D. Robertson, and S. microwave inductors using solder surface Lucyszyn, “MEMS high tension self-assembly,” in IEEE MTT-S Int. Microwave Symp. Dig., vol. 1, Phoenix, AZ, May 2001, pp. 329–332. [4] E. Benes, M. Groschl, W. Burger, and M. Schmid, “Sensors based on piezoelectric resonators,” Sens. Actuators A, Phys., vol. 48, no. 1, pp. 1–21, May 1995. [5] G. M. Rebeiz and J. B. Muldavin, “RF MEMS switches and switch circuits,” IEEE Micro, vol. 2, no. 4, pp. 59–71, Dec. 2001. [6] D. Hyman and M. Mehregany, “Contact physics of gold microcontacts for MEMS switches,” IEEE Trans. Compon. Packag. Technol., vol. 22, no. 3, pp. 357–364, Sep. 1999. [7] J. Wellman and A. Garcia, “High power ( 1 W) application of RF MEMS lifetime performance evaluation,” Jet Propulsion Lab., Pasadena, CA, Evaluation Rep., Jan. 2003. [Online]. Available: http://nepp. nasa.gov/DocUploads/5FAB12BE-15FE-4A30-BA522BC13547FE60/ RFMEMSX.pdf. [8] X. Yuan, S. Cherepko, J. Hwang, C. L. Goldsmith, C. Nordqusit, and C. Dyck, “Initial observation and analysis of dielectric-charging effects on RF MEMS capacitive switches,” in IEEE MTT-S Int. Microwave Symp. Dig., vol. 3, Fort Worth, TX, Jun. 2004, pp. 1943–1946. [9] R. E. Mihailovich, M. Kim, J. B. Hacker, E. A. Sovero, J. Studer, J. A. Higgins, and J. F. DeNatale, “MEM relay for reconfigurable RF circuits,” IEEE Microw. Wireless Compon. Lett., vol. 11, no. 2, pp. 53–55, Feb. 2001. [10] D. Peroulis, S. P. Pacheco, K. Sarabandi, and L. P. B. Katehi, “Electromechanical considerations in developing low-voltage RF MEMS switches,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 1, pp. 259–270, Jan. 2003. [11] D. Peroulis, S. P. Pacheco, and L. P. B. Katehi, “RF MEMS switches with enhanced power-handling capabilities,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 1, pp. 59–68, Jan. 2004. [12] D. Peroulis and L. P. B. Katehi, “Electrostatically-tunable analog RF MEMS varactors with measured capacitance range of 300%,” in IEEE MTT-S Int. Microwave Symp. Dig., vol. 3, Philadelphia, PA, Jun. 2003, pp. 1793–1796. [13] D. Peroulis, Y. Lu, and L. P. B. Katehi, “Highly reliable analog MEMS varactors,” in IEEE MTT-S Int. Microwave Symp. Dig., vol. 2, Fort Worth, TX, Jun. 2004, pp. 869–872. [14] J. Zou, C. Liu, and J. Schutt-Aine, “Development of a wide tuning-range two-parallel-plate tunable capacitor for integrated wireless communication systems,” Int. J. RF Microwave Computer-Aided Eng., vol. 11, no. 5, pp. 322–329, Sep. 2001. [15] Y. Lu, L. P. B. Katehi, and D. Peroulis, “A novel MEMS impedance tuner simultaneously optimized for maximum impedance range and power handling,” in IEEE MTT-S Int. Microwave Symp. Dig., Long Beach, CA, Jun. 2005. [CD ROM]. [16] C. L. Goldsmith, A. Malczewski, J. Papapolymerou, K. L. Lange, 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, Jan. 2003. [17] K. Kang, J.-H. Park, Y.-K. Kim, H.-T. Kim, S. Jung, and Y. Kwon, “Low-loss analog and digital micromachined impedance tuners at the -band,” IEEE Trans. Microw. Theory Tech., vol. 49, no. 12, pp. 2394–2400, Dec. 2001. [18] J. Tuovinen, T. Vaha-Heikkila, J. Varis, and G. M. Rebeiz, “A reconfigurable 6–20 GHz RF MEMS impedance tuner,” in IEEE MTT-S Int. Microwave Symp. Dig., vol. 2, Fort Worth, TX, Jun. 2004, pp. 729–732. [19] R. E. Collin, Foundations for Microwave Engineering. New York: McGraw-Hill, 1997.

Q

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Fig. 13. Measured and simulated -parameters of the tuner when all varactors are in the: (a) up and (b) down positions.

IV. CONCLUSION This paper studied the power handling capability of a contactless RF MEMS varactor and an impedance tuner that employs this varactor. Reliable operation with at least 4 W of RF power is experimentally demonstrated for more than 100 million cycles. All measurements are performed under high RF power (hot tuning) in a typical laboratory space without hermetic protection or the help of a nitrogen atmosphere. The tradeoffs of power handling and tuning range are also carefully characterized for different power levels. This varactor is employed in a new impedance tuner design that optimizes the tuner’s power handling capability by ensuring a uniform maximum voltage

Ka

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[20] T. Vaha-Heikkila and G. M. Rebeiz, “A 20–50 GHz reconfigurable matching network for power amplifier applications,” in IEEE MTT-S Int. Microwave Symp. Dig., vol. 2, Fort Worth, TX, Jun. 2004, pp. 717–720. [21] J. Tuovinen, T. Vaha-Heikkila, J. Varis, and G. M. Rebeiz, “A V -band single-stub RF MEMS impedance tuner,” in 34th Eur. Microwave Conf. Dig., Amsterdam, The Netherlands, Oct. 2004, pp. 1301–1304.

Yumin Lu (S’02–M’05) received the B.Sc. degree in materials science and engineering from Fudan University, Shanghai, China, in 1996, the M.Sc. degree in materials science and engineering from the Ohio State University, Columbus, in 2001, and the Ph.D. degree in electrical engineering from The University of Michigan at Ann Arbor, in 2005. His doctoral research concerned reconfigurable RF/microwave circuits with RF MEMS devices. Upon completion of his doctoral degree, he joined Strategic Research and Development, M/A-COM, Lowell, MA, as a Senior Engineer, where he is currently involved in the development of RF integrated circuits (RFICs) for the next-generation automotive short-range radar system.

Linda P. B. Katehi (S’81–M’84–SM’89–F’95) received the B.S.E.E. degree from the National Technical University of Athens, Athens, Greece, in 1977, and the M.S.E.E. and Ph.D. degrees from the University of California at Los Angeles, in 1981 and 1984, respectively. In September 1984, she joined the faculty of the Electrical Engineering and Computer Science (EECS) Department, The University of Michigan at Ann Arbor, as an Assistant Professor and then became an Associate Professor in 1989 and a Professor in 1994. She served in many administrative positions including Director of Graduate Programs at the College of Engineering (1995–1996), Elected Member of the College Executive Committee (1996–1998), Associate Dean for Graduate Education (1998–1999), and Associate Dean for Academic Affairs (1999–2001). In January 2002, she joined Purdue University, West Lafayette, IN, as the John A. Edwardson Dean of Engineering and as a Professor of electrical and computer engineering. She has authored or coauthored 450 papers published in referred journals and symposia proceedings. She holds five patents. Prof. Katehi is a member of the IEEE Antennas and Propagation Society (IEEE AP-S), the IEEE Microwave Theory and Techniques Society (IEEE MTT-S), Sigma Xi, Hybrid Microelectronics, and International Scientific Radio Union (URSI) Commission D. She was a member of the IEEE AP-S Administrative Committee (AdCom) (1992–1995). She currently serves on the IEEE MTT-S AdCom. He was an associate editor for the IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES and the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION. She was the recipient of the 1984 IEEE AP-S W. P. King (Best Paper Award for a Young Engineer), the 1985 IEEE AP-S S. A. Schelkunoff Award (Best Paper Award), the 1987 National Science Foundation (NSF) Presidential Young Investigator Award, the 1987 URSI Booker Award, the 1994 Humboldt Research Award, the 1994 University of Michigan Faculty Recognition Award, the 1996 IEEE MTT-S Microwave Prize, the 1997 International Microelectronics and Packaging Society (IMAPS) Best Paper Award, the 2000 IEEE Third Millennium Medal, the 2000 Institution of Electrical Engineers (IEE), U.K., Marconi Prize, and the 2002 IEEE MTT-S Distinguished Educator Award.

Dimitrios Peroulis (S’99–M’04) was born in Athens, Greece, on 1975. He received the Diploma degree in electrical and computer engineering from the National Technical University of Athens, Athens, Greece, in 1993, and the M.S.E. and Ph.D. degrees in electrical engineering from The University of Michigan at Ann Arbor, in 1999 and 2003, respectively. Since August 2003, he has been an Assistant Professor with the School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN. His current research work is focused on MEMS for multifunctional communications systems, radars, and bio-sensors. Dr. Peroulis was the recipient of the Third Place Award of the Student Paper Competition presented at the 2001 IEEE Microwave Theory and Techniques Society (IEEE MTT-S) International Microwave Symposium (IMS), Phoenix, AZ, and the 2002 Rackham Graduate School Predoctoral Fellowship presented by The University of Michigan at Ann Arbor. He was also the recipient of two Student Paper Awards (honorable mentions) of the Student Paper Competitions presented at the 2001 IEEE Antennas and Propagation (IEEE AP-S) International Symposium, Boston, MA, and the 2002 IEEE MTT-S IMS, Seattle, WA.

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Digital Object Identifier 10.1109/TMTT.2005.856786

Digital Object Identifier 10.1109/TMTT.2005.860915

EDITORIAL BOARD Editor: M. STEER Associate Editors:A. CANGELLARIS, A. CIDRONALI, M. DO, K. ITOH, S. MARSH, A. MORTAZAWI, Y. NIKAWA, J. PEDRO, Z. POPOVIC, S. RAMAN, V. RIZZOLI, D. WILLIAMS, R. WU, A. YAKOVLEV REVIEWERS M. Abdul-Gaffoor M. Abe R. Abou-Jaoude M. Abouzahra A. Abramowicz L. Accatino R. Achar D. Adam E. Adler M. Adlerstein K. Agarwal D. Ahn H.-R Ahn M. Aikawa C. Aitchison M. Akaike C. Akyel A. Akyurtlu B. Albinsson F. Alessandri A. Alexanian C. Algani W. Ali-Ahmad F. Alimenti B. Allen D. Allsopp D. Allstot R. Alm B. Alpert A. Alphones A. Altintas A. Alvarez-Melcom M. Alzona S. Amari L. Andersen B. Anderson Y. Ando O. Anegawa K.-S. Ang I. Angelov R. Anholt Y. Antar G. Antonini D. Antsos K. Anwar I. Aoki R. Aparicio K. Araki J. Archer P. Arcioni F. Arndt R. Arora U. Arz M. Asai P. Asbeck K. Ashby H. Ashok J. Atherton A. Atia I. Awai K. Aygun S. Ayuz Y. Baeyens T. Bagwell Z. Baharav I. Bahl D. Baillargeat S. Bajpai J. Baker-Jarvis E. Balboni S. Banba J. Bandler I. Bandurkin R. Bansal D. Barataud I. Barba F. Bardati I. Bardi S. Barker D. Barlage J. Barr D. Batchelor B. Bates H. Baudrand S. Beaussart R. Beck D. Becker K. Beilenhoff B. Beker V. Belitsky D. Belot H. Bell T. Benson M. Berroth G. Bertin S. Best W. Beyenne A. Beyer S. Bharj K. Bhasin P. Bhattacharya Q. Bi M. Bialkowski E. Biebl P. Bienstman R. Bierig R. Biernacki S. Bila L. Billonnet T. Bird B. Bishop G. Bit-Babik D. Blackham B. Blalock M. Blank P. Blondy P. Blount D. Boccoli B. Boeck F. Bögelsack L. Boglione R. Boix J. Booske N. Borges de Carvalho V. Boria V. Borich O. Boric-Lubecke E. Borie J. Bornemann R. Bosisio H. Boss S. Bousnina P. Bouysse M. Bozzi E. Bracken P. Bradley R. Bradley T. Brazil G. Brehm K. Breuer B. Bridges L. Briones T. Brookes S. Broschat E. Brown G. Brown R. Brown S. Brozovich S. Bruce

S. Bryan H. Bu D. Budimir T. Budka M. Bujatti C. Buntschuh J. Burghartz P. Burghignoli O. Buric-Lubecke D. Butler Q. Cai M. Calcatera C. Caloz E. Camargo R. Cameron N. Camilleri R. Camisa S. Cammer C. Campbell R. Campbell M. Campovecchio F. Canavero A. Cangellaris F. Capolino A. Cappy J.-L. Carbonero G. Carchon J. Carlin G. Carrer R. Carter F. Casas A. Cassinese J. Catala R. Caverly M. Celik M. Celuch-Marcysiak Z. Cendes B. Cetiner J. Cha N. Chaing H. Chaloupka M. Chamberlain C.-H. Chan C.-Y. Chang C. Chang F. Chang H.-C. Chang K. Chang H. Chapell W. Chappell W. Charczenko K. Chatterjee G. Chattopadhyay S. Chaudhuri S. Chebolu C.-C. Chen C.-H. Chen D. Chen H.-S. Chen J. Chen J.-I. Chen J. Chen K. Chen S. Chen W.-K. Chen Y.-J. Chen Y.-K. Chen Z. Chen K.-K. Cheng S. Cherepko W. Chew W.-C. Chew C.-Y. Chi Y.-C. Chiang T. Cho D. Choi J. Choi C.-K. Chou D. Choudhury Y. Chow C. Christopoulos S. Chung R. Cicchetti A. Cidronali T. Cisco J. Citerne D. Citrin R. Clarke J. Cloete E. Cohen L. Cohen A. Coleman R. Collin F. Colomb B. Colpitts G. Conciauro A. Connelly D. Consonni H. Contopanagos F. Cooray I. Corbella J. Costa E. Costamagna A. Costanzo C. Courtney J. Cowles I. Craddock G. Creech J. Crescenzi S. Cripps D. Cros T. Crowe M. Crya R. Culbertson C. Curry W. Curtice Z. Czyz S. D’Agostino C. Dalle G. Dambrine K. Dandekar A. Daryoush B. Das N. Das M. Davidovich M. Davidovitz B. Davis I. Davis L. Davis G. Dawe H. Dayal F. De Flaviis H. De Los Santos P. De Maagt D. De Zutter B. Deal A. Dec J. Deen J. Dees J. DeFalco D. Degroot C. Deibele J. Del Alamo A. Deleniv M. DeLisio S. Demir J. DeNatale E. Denlinger N. Deo

A. Deutsch Y. Deval T. Dhaene A. Diaz-Morcillo G. D’Inzeo C. Diskus B. Dixon T. Djordjevic M. A. Do J. Doane J. Dobrowolski W. Domino S. Dow C. Dozier P. Draxler R. Drayton A. Dreher F. Drewniak S. Dudorov S. Duffy L. Dunleavy V. Dunn J. Dunsmore A. Dutta D. Duvanaud A. Duzdar S. Dvorak L. Dworsky M. Dydyk L. Eastman J. Ebel R. Egri R. Ehlers T. Eibert H. Eisele B. Eisenstadt G. Eisenstein G. Eleftheriades I. Elfadel S. El-Ghazaly F. Ellinger T. Ellis B. Elsharawy R. Emrick N. Engheta B. Engst Y. Eo H. Eom N. Erickson J. Eriksson C. Ernst M. Eron L. Escotte M. Essaaidi J. Everard G. Ewell A. Ezzeddine M. Faber C. Fager D.-G. Fang N. Farhat M. Farina W. Fathelbab A. Fathy A. Fazal E. Fear R. Feinaugle M. Feldman P. Feldman A. Ferendeci C. Fernandes A. Fernandez A. Ferrero I. Fianovsky J. Fiedziuszko I. Filanovsky P. Filicori D. Filipovic A. Fliflet P. Focardi B. Fornberg K. Foster P. Foster G. Franceschetti A. Franchois M. Freire R. Freund A. Freundorfer F. Frezza R. Fujimoto V. Fusco G. Gabriel T. Gaier Z. Galani I. Galin D. Gamble B.-Q. Gao M. Garcia K. Gard R. Garver G. Gauthier B. Geller V. Gelnovatch P. Genderen G. Gentili N. Georgieva W. Geppert J. Gerber F. Gerecht F. German S. Gevorgian R. Geyer O. Ghandi F. Ghannouchi K. Gharaibeh G. Ghione D. Ghodgaonkar F. Giannini A. Gibson S. Gierkink J. Gilb B. Gilbert B.Gimeno E.Glass A. Glisson M. Goano E. Godshalk J. Goel M. Goldfarb C. Goldsmith P. Goldsmith M. Golio R. Gómez R. Gonzalo S. Goodnick S. Gopalsami A. Gopinath R. Gordon P. Gould K. Goverdhanam J. Graffeuil L. Gragnani B. Grant G. Grau A. Grebennikov B. Green T. Gregorzyk I. Gresham E. Griffin

J. Griffith A. Griol G. Groskopf C. Grossman T. Grzegorczyk M. Guglielmi P. Guillon K.-H. Gundlach A. Gupta K. Gupta R. Gupta F. Gustrau R. Gutmann W. Gwarek R. Haas J. Hacker G. Haddad S. Hadjiloucas C. Hafner M. Hagmann S. Hagness H.-K. Hahn A. Hajimiri D. Halchin A. Hallac B. Hallford K. Halonen R. Ham K. Hamaguchi M. Hamid J.-H. Han A. Hanke V. Hanna V. Hansen G. Hanson Y. Hao L. Harle M. Harris L. Hartin H. Hartnagel J. Harvey H. Hasegawa K.-Y. Hashimoto K. Hashimoto J. Haslett G. Hau S. Hay H. Hayashi J. Hayashi L. Hayden B. Haydl S. He T. Heath J. Heaton I. Hecht G. Hegazi P. Heide E. Heilweil W. Heinrich G. Heiter M. Helier R. Henderson R. Henning D. Heo J. Herren K. Herrick N. Herscovici J. Hesler J. Heston M. Heutmaker C. Hicks R. Hicks A. Higgins M. Hikita D. Hill G. Hiller W. Hioe J. Hirokawa T. Hirvonen V. Ho W. Hoefer R. Hoffmann M. Hoft J. Hong S. Hong W. Hong K. Honjo G. Hopkins Y. Horii D. Hornbuckle J. Horng J. Horton K. Hosoya R. Howald H. Howe J.-P. Hsu Q. Hu C.-C. Huang C. Huang F. Huang H.-C. Huang J. Huang P. Huang T.-W. Huang A. Huber D. Huebner H.-T. Hui A. Hung C. Hung H. Hung I. Hunter J. Hurrell M. Hussein B. Huyart I. Huynen H.-Y. Hwang J. Hwang K.-P. Hwang J. Hwu C. Icheln T. Idehara S. Iezekiel P. Ikonen K. Ikossi K. Inagaki A. Ishimaru T. Ishizaki Y. Ismail K. Itoh T. Itoh F. Ivanek A. Ivanov T. Ivanov C. Iversen D. Iverson D. Jablonski D. Jachowski C. Jackson D. Jackson R. Jackson A. Jacob M. Jacob H. Jacobsson D. Jaeger N. Jaeger N. Jain R. Jakoby G. James R. Janaswamy

Digital Object Identifier 10.1109/TMTT.2005.860912

V. Jandhyala W. Jang R. Jansen J. Jargon B. Jarry P. Jarry A. Jelenski W. Jemison S.-K. Jeng M. Jensen E. Jerby G. Jerinic T. Jerse P. Jia D. Jiao J.-M. Jin J. Johansson R. Johnk W. Joines K. Jokela S. Jones U. Jordan L. Josefsson K. Joshin J. Joubert R. Kagiwada T. Kaho M. Kahrs D. Kajfez S. Kalenitchenko B. Kalinikos H. Kamitsuna R. Kamuoa M. Kanda S.-H. Kang P. Kangaslahtii B. Kapilevich K. Karkkainen M. Kärkkäinen A. Karpov R. Karumudi A. Kashif T. Kashiwa L. Katehi A. Katz R. Kaul S. Kawakami S. Kawasaki M. Kazimierczuk R. Keam S. Kee S. Kenney A. Kerr O. Kesler L. Kettunen M.-A. Khan J. Kiang O. Kilic H. Kim I. Kim J.-P. Kim W. Kim C. King R. King A. Kirilenko V. Kisel A. Kishk T. Kitamura T. Kitazawa M.-J. Kitlinski K. Kiziloglu R. Knerr R. Knöchel L. Knockaert K. Kobayashi Y. Kobayashi G. Kobidze P. Koert T. Kolding N. Kolias B. Kolner B. Kolundzija J. Komiak A. Komiyama G. Kompa B. Kopp B. Kormanyos K. Kornegay M. Koshiba T. Kosmanis J. Kot A. Kraszewski T. Krems J. Kretzschmar K. Krishnamurthy C. Krowne V. Krozer J. Krupka W. Kruppa H. Kubo C. Kudsia S. Kudszus E. Kuester Y. Kuga W. Kuhn T. Kuki M. Kumar J. Kuno J.-T. Kuo P.-W. Kuo H. Kurebayashi T. Kuri F. KurokI L. Kushner N. Kuster M. Kuzuhara Y.-W. Kwon I. Lager R. Lai J. Lamb P. Lampariello M. Lanagan M. Lancaster U. Langmann G. Lapin T. Larsen J. Larson L. Larson J. Laskar M. Laso A. Lauer J.-J. Laurin G. Lazzi F. Le Pennec J.-F. Lee J.-J. Lee J.-S. Lee K. Lee S.-G. Lee T. Lee K. Leong T.-E. Leong Y.-C. Leong R. Leoni M. Lerouge K.-W. Leung Y. Leviatan R. Levy L.-W. Li

Y.-M. Li L. Ligthart C.-L. Lin J. Lin G. Linde S. Lindenmeier A. Lindner C. Ling H. Ling D. Linkhart P. Linnér D. Lippens F. Little A. Litwin L. Liu Q.-H. Liu S.-I. Liu Y.-W. Liu O. Llopis S. Lloyd C. Lohmann J. Long U. Lott D. Lovelace K. Lu L.-H. Lu S. Lu W.-T. Lu V. Lubecke S. Lucyszyn R. Luebbers L. Lunardi S. Luo J. Luy C. Lyons G. Lyons Z. Ma S. Maas G. Macchiarella S. Maci T. Mader M. Madihian A. Madjar M. Magana T. Magath C. Mahle S. Mahmoud I. Maio M. Majewski M. Makimoto J. Malherbe J. Mallat R. Mallavarpu D. Malocha L. Maloratsky V. Manasson C. Mann H. Manohara R. Mansour S. March V. Mark F. Marliani R. Marques G. Marrocco S. Marsh J. Martens L. Martens J. Marti A. Martin E. Martinez A. Massa D. Masse K. Masterson A. Materka K. Matsunaga A. Matsushima R. Mattauch M. Mattes G. Matthaei P. Mayer W. Mayer J. Mazierska J. Mazur G. Mazzarella K. McCarthy P. McClay T. McKay J. McKinney R. McMillan R. McMorrow D. McPherson D. McQuiddy E. McShane F. Medina D. Meharry C. Meng H.-K. Meng W. Menzel F. Mesa R. Metaxas P. Mezzanotte K. Michalski E. Michielssen A. Mickelson V. Mikhnev R. Miles E. Miller M. Miller P. Miller R. Minasian J. Mink S. Mirabbasi J. Miranda D. Mirshekar T. Miura S. Miyahara H. Miyashita M. Miyazaki K. Mizuno S. Mizushina C. Mobbs M. Mohamed A. Mohammadian A. Mohan A. Mondal T. Monediere R. Mongia M. Mongiardo C. Monzon C. Moore J. Morente M. Morgan A. Morini J. Morsey A. Mortazawi H. Mosallaei J. Mosig A. Moulthrop G. Mourou A. Moussessian M. Mrozowski J.-E. Mueller T. Mueller J. Muldavin M. Muraguchi V. Nair K. Naishadham T. Nakagawa M. Nakatsugawa

M. Nakhla C. Naldi J. Nallatamby S. Nam T. Namiki G. Narayanan T. Narhi M. Nasir A. Natarajan J. Nath B. Nauwelaers J. Navarro J. Nebus D. Neikirk B. Nelson A. Neto E. Newman H. Newman M. Ney E. Ngoya C. Nguyen T. Nichols K. Niclas E. Niehenke S. Nightingale Y. Nikawa P. Nikitin A. Niknejad N. Nikolova K. Nikoskinen M. Nisenoff T. Nishikawa G. Niu S. Nogi T. Nojima T. Nomoto A. Nosich B. Notaros K. Noujeim D. Novak T. Nozokido G. Nusinovich E. Nyfors D. Oates J. Obregon J. O’Callahan M. Odyneic H. Ogawa K.-I. Ohata T. Ohira H. Okazaki V. Okhmatovski A. Oki M. Okoniewski G. Olbrich A. Oliner S. Oliver J. Olsson F. Olyslager A. Omar B.-L. Ooi A. Orlandi R. Orta S. Ortiz J. Osepchuk J. Ou W. Ou T. Oxley R. Paglione T. Palenius W. Palmer D.-S. Pan S.-K. Pan C. Panasik R. Panock C. Papanicolopoulos J. Papapolymerou S. Parisi D.-C. Park H. Park D. Parker T. Parker R. Parry D. Pasalic W. Pascher M. Pastorino S. Patel P. Pathak A. Pavio J. Pavio T. Pavio J. Pearce W. Pearson J. Pedro B. Pejcinovic S.-T. Peng R. Pengelly J. Pereda L. Perregrini M. Petelin A. Peterson D. Peterson O. Peverini U. Pfeiffer A.-V. Pham J. Phillips L. Pierantoni B. Piernas J. Pierro P. Pieters B. Pillans M. Pirola W. Platte A. Platzker C. Pobanz A. Podell R. Pogorzelski P. Poire R. Pollard G. Ponchak Z. Popovic M. Pospieszalski V. Postoyalko N. Pothecary D. Pozar S. Prasad D. Prather R. Pregla D. Prescott M. Prigent S. Pritchett Y. Prokopenko S. Prosvirnin J. Pulliainen L. Puranen D. Purdy J. Putz Y. Qian T. Quach D. Quak P. Queffelec R. Quere F. Raab V. Radisic L. Raffaelli M. Raffetto C. Railton O. Ramahi S. Raman

J. Randa R. Ranson T. Rappaport J.-P. Raskin P. Ratanadecho J. Rathmell C. Rauscher J. Rautio J. Rayas-Sánchez H. Reader G. Rebeiz B. Redman-White E. Reese R. Reid H.-M. Rein J. Reinert I. Rekanos R. Remis K. Remley L. Reynolds A. Reynoso-Hernandez E. Rezek A. Riddle E. Rius J. Rius B. Rizzi V. Rizzoli I. Robertson P. Roblin S. Rockwell A. Roden A. Rodriguez M. Rodwell H. Rogier A. Rong Y. Rong J. Roos D. Root N. Rorsman L. Roselli A. Rosen J. Rosenberg U. Rosenberg F. Rotella E. Rothwell L. Roy J. Roychowdury T. Rozzi J. Rubio R. Ruby A. Rudiakova M. Rudolph A. Ruehli P. Russer D. Rutledge A. Rydberg D. Rytting T. Saad C. Saavedra K. Sabet M. Sachidananda G. Sadowniczak A. Safavi-Naeini A. Safwat M. Sagawa M. Salazar M. Salazar-Palma A. Sanada M. Sanagi A. Sangster W. Sansen K. Sarabandi T. Sarkar C. Sarris P. Saunier S. Savov D. Schaubert I. Scherbatko G. Schettini F. Schettino M. Schetzen B. Schiek M. Schindler M. Schlechtweg E. Schmidhammer L. Schmidt D. Schmitt F. Schmückle F. Schnieder J. Schoukens D. Schreurs G. Schreyer W. Schroeder H. Schumacher J. Schutt-Aine F. Schwering W. Scott F. Sechi A. Seeds J. Sercu R. Settaluri J. Sevic O. Sevimli D. Shaeffer L. Shafai O. Shanaa Z. Shao M. Shapiro A. Sharma V. Shastin P. Shastry R. Shavit T. Shen T. Shibata A. Shibib H. Shigesawa Y.-C. Shih T. Shiozawa M. Shirokov W. Shiroma Y. Shoji N. Shuley M. Shur P. Siegel D. Sievenpiper B. Sigmon A. Sihvola C. Silva M. Silveira M. Silveirinha K. Silvonen W. Simbuerger R. Simons F. Sinnesbichler J. Sitch N. Skou Z. Skvor R. Sloan D. Smith G. Smith P. Smith C. Snowden R. Snyder R. So H. Sobol E. Sobolewski A. Sochava N. Sokal V. Sokolov

M. Solano K. Solbach M. Solomon B.-S. Song M. Sorolla Ayza R. Sorrentino C. Soukoulis N. Soveiko E. Sovero J. Sowers T. Sowlati R. Sparks S. Spiegel P. Staecker D. Staiculescu J. Stake D. Stancil P. Starski J. Staudinger P. Stauffer P. Steenson A. Stelzer J. Stenarson K. Stephan M. Stern C. Stevens S. Stitzer M. Stone B. Strassner P. Stuart M. Stubbs M. Stuchly R. Sturdivant A. Suarez N. Suematsu T. Suetsugu Y. Suh F. Sullivan C. Sun L. Sundstrom S. Sussman-Fort K. Suyama J. Svacina D. Swanson B. Szendrenyi A. Szu W. Tabbara A. Taflove G. Tait Y. Tajima Y. Takayama M. Taki Y. Takimoto S. Talisa K. Tan W.-C. Tang E. Taniguchi R. Tascone J. Taub J. Tauritz D. Teeter F. Teixeira M. Tentzeris S.-A. Teo K. Thakur H. Thal W. Thiel H.-W. Thim B. Thompson G. Thoren M. Thumm N. Tilston W. Tinga I. Tittonen G. Tkachenko M.-R. Tofighi T. Tokumitsu K. Tomiyasu P. Tommasino A. Toropainen M. Toupikov I. Toyoda C. Trask S. Tretyakov R. Trew A. Trifiletti C. Trueman P. Truffer A. Truitt C.-M. Tsai R. Tsai J. Tsalamengas L. Tsang H.-Q. Tserng J. Tsui M. Tsuji T. Tsujiguchi R. Tucker J. Tuovinen C.-K. Tzuang T. Ueda K. Uehara S. Ueno J. Uher A. Uhlir T. Ulrich Y. Umeda T. Uwano N. Uzunoglu R. Vahldieck M. Vaidyanathan P. Vainikainen M. Valtonen N. Van der Meijs D. Van der Weide P. Van Genderen E. Van Lil C. Van Niekerk M. Vanden Bossche G. Vandenbosch A. Vander Vorst D. Vanhoenacker-Janvie K. Varian L. Vegni G. Venanzoni I. Vendik S. Verdeyme V. Veremey R. Vernon J. Verspecht L. Verweyen H. Vickes A. Victor L. Vietzorreck A. Viitanen F. Villegas D. Vinayak C. Vittoria S. Vitusevich D. Viveiros E. Viveiros J. Volakis V. Volman J. Vuolevi K. Wagner K. Wakino P. Waldow A.-A. Walid T. Walid

D. Walker V. Walker P. Wallace J. Walsh C. Wan A. Wang B.-Z. Wang C. Wang E. Wang H. Wang J. Wang K.-C. Wang L. Wang T.-H. Wang W. Wang Y. Wang Z. Wang K. Warnick K. Washio T. Watanabe R. Waterhouse R. Waugh D. Webb J. Webb K. Webb R. Webster S. Wedge C.-J. Wei R. Weigel T. Weiland A. Weily S. Weinreb J. Weiss S. Weiss A. Weisshaar C. Weitzel K. Weller T. Weller C.-P. Wen W. Weng M. Wengler S. Wentworth C. Westgate C. Whelan J. Whelehan L. Whicker J. Whitaker P. White S. Whiteley K. Whites W. Wiesbeck G. Wilkins A. Wilkinson D. Williams B. Wilson J. Wiltse P. Winson K. Wong K.-L. Wong T. Wong J. Woo J. Wood G. Woods G. Wrixon B.-L. Wu H. Wu K.-L. Wu R.-B. Wu T. Wu Y.-S. Wu R. Wylde G. Xiao H. Xin H.-Z. Xu S.-J. Xu Y. Xu Q. Xue A. Yakovlev S. Yamamoto C.-H. Yang F. Yang H.-Y. Yang Y. Yang H. Yano H. Yao K. Yashiro S. Ye J. Yeo K. Yeo S.-P. Yeo S.-J. Yi W.-Y. Yin H. Ymeri S. Yngvesson T. Yoneyama C.-K. Yong H.-J. Yoo J.-G. Yook R. York N. Yoshida S. Yoshikado A. Young L. Young G. Yu M. Yu A. Zaghoul K. Zaki J. Zamanillo P. Zampardi J. Zapata J. Zehentner Q.-J. Zhang R. Zhang A. Zhao L. Zhao L. Zhu N.-H. Zhu Y.-S. Zhu Z. Zhu R. Zhukavin R. Ziolkowski H. Zirath A. Zolfaghari T. Zwick