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### Summary

### Summary

In today's globally competitive wireless industry, the design-to-production cycle is critically important. Circuit and system engineers must be able to develop robust designs that can be mass produced. To accomplish this, engineers need to learn the requirements of, and solutions leading to, optimum performance. The first of a two-volume set, this text takes a practical approach to RF (radio frequency) circuit design, offering an understanding of the fundamental concepts that practitioners need to know and use for their work in this industry. It seeks to lay the groundwork for efficient passive circuit design.

### Author Notes

Rowan Gilmore holds a D.Sc. and MSEE degrees from Washington University in St. Louis, and a B.E. degree in electrical engineering from the University of Queensland, Brisbane, Australia.

Mr. Gilmore is an experienced consulting engineer who introduced the worlds first commercial harmonic-balance CAD simulator while Vice-President Engineering at Compact Software. He has held numerous design and management posts in industry, including Central Microwave, Schlumberger, Telstra and SITA. A senior member of the IEEE. He has nearly fifteen years of teaching experience with Besser Associates and CEI Europe.

050

### Table of Contents

Preface | p. xv |

Acknowledgments | p. xix |

1 Introduction | p. 1 |

1.1 Defining RF | p. 1 |

1.2 Circuits and systems | p. 3 |

1.2.1 System specification | p. 3 |

1.2.2 System design | p. 4 |

1.2.3 Circuit design | p. 4 |

1.3 Wireless | p. 5 |

1.4 Conclusion | p. 6 |

Reference | p. 7 |

2 RF circuit fundamentals | p. 9 |

2.1 Introduction | p. 9 |

2.2 The decibel scale | p. 9 |

2.2.1 Illustrative example: decibel calculations | p. 12 |

2.2.2 Absolute power level reference | p. 13 |

2.2.3 Illustrative exercise: power conversions | p. 14 |

2.3 Complex number review | p. 15 |

2.4 Normalization | p. 17 |

2.5 R-L-C voltage-current relationships | p. 18 |

2.6 Complex impedance and admittance systems | p. 20 |

2.7 Unloaded and loaded Q definitions | p. 22 |

2.8 Complex series impedance of RF components | p. 23 |

2.9 Complex parallel admittance of RF components | p. 24 |

2.9.1 Illustrative exercise: computing elements from admittance specifications | p. 27 |

2.10 Series and parallel L-C resonant circuits | p. 27 |

2.11 Series and parallel conversions of lumped R-L-C networks | p. 30 |

2.11.1 Illustrative example: converting a series parallel equivalence | p. 32 |

2.12 One-port and multiport networks | p. 33 |

2.13 Importance of power transfer when cascading system components | p. 35 |

2.14 Importance of impedance matching | p. 36 |

2.15 RF components and related issues | p. 37 |

2.15.1 Parasitic inductances and capacitances | p. 38 |

2.15.2 Limited range of practical element values | p. 38 |

2.15.3 Measurement and test-fixture considerations | p. 39 |

2.15.4 Grounding and coupling effects | p. 39 |

2.16 Lumped elements versus transmission lines | p. 40 |

2.16.1 Illustrative example: fractional wavelength calculations | p. 42 |

2.16.2 Two-conductor transmission lines | p. 43 |

2.16.3 Transmission line characterizations | p. 46 |

2.16.4 Various TEM transmission line configurations | p. 48 |

2.16.5 Reflected waves on transmission lines | p. 51 |

2.16.6 Transmission line stubs | p. 54 |

2.16.7 Illustrative example: open-circuited parallel stub computation | p. 57 |

2.16.8 Directional couplers | p. 58 |

2.17 Circuit parameters using wave relations | p. 59 |

2.17.1 Reflection coefficient definitions | p. 59 |

2.17.2 Return loss | p. 62 |

2.17.3 Voltage standing wave ratio | p. 63 |

2.17.4 Mismatch loss | p. 64 |

2.17.5 Difference between mismatch loss and return loss | p. 65 |

2.18 Impedance transformation and matching | p. 65 |

2.19 Single-ended versus differential circuits | p. 66 |

2.19.1 Single-ended RF circuits | p. 67 |

2.19.2 Differential RF circuits | p. 68 |

2.19.3 Electromagnetic compatibility and interference | p. 72 |

2.20 Time domain versus frequency domain | p. 73 |

2.20.1 Periodic waveform definitions | p. 73 |

2.20.2 Jitter | p. 76 |

2.20.3 Eye diagram | p. 77 |

2.21 Summary | p. 78 |

References | p. 79 |

Selected bibliography | p. 80 |

3 The radio as typical RF system | p. 81 |

3.1 Receiver architecture | p. 81 |

3.1.1 The simple detector receiver | p. 81 |

3.1.2 The direct conversion (homodyne) receiver | p. 83 |

3.1.3 The superheterodyne receiver--analog system | p. 85 |

3.1.4 The superheterodyne receiver--digital system | p. 88 |

3.2 Receiver characterization | p. 94 |

3.2.1 The communications channel | p. 94 |

3.2.2 Receiver noise | p. 95 |

3.2.3 Receiver sensitivity | p. 98 |

3.2.4 System nonlinearity | p. 100 |

3.2.5 Receiver dynamic range | p. 109 |

3.2.6 Receiver selectivity | p. 113 |

3.2.7 Receiver frequency response | p. 125 |

3.3 Analysis of a CDMA receiver handset | p. 125 |

3.3.1 Receiver component specification | p. 130 |

3.3.2 Receiver response | p. 135 |

Problems | p. 144 |

References | p. 146 |

4 The Smith chart and S-parameters | p. 147 |

4.1 Introduction | p. 147 |

4.2 The Smith chart: a polar plot of reflection coefficient | p. 148 |

4.2.1 Impedance manipulations on the Smith chart | p. 151 |

4.2.2 Adding series inductors on the Smith chart | p. 151 |

4.2.3 Adding series capacitors on the Smith chart | p. 152 |

4.2.4 Adding series resistors on the Smith chart | p. 152 |

4.3 The admittance Smith chart | p. 154 |

4.3.1 Adding parallel capacitors on the admittance Smith chart | p. 156 |

4.3.2 Adding parallel inductors on the admittance Smith chart | p. 158 |

4.3.3 Adding parallel resistors on the admittance Smith chart | p. 159 |

4.4 Circuit manipulations using series and parallel components | p. 159 |

4.5 The immitance (Z-Y) Smith chart | p. 160 |

4.5.1 Series R-L-C contours on the immitance Smith chart | p. 161 |

4.5.2 Shunt R-L-C contours on the immitance Smith chart | p. 162 |

4.5.3 Lowpass L-C transformers | p. 162 |

4.5.4 Highpass L-C transformers | p. 163 |

4.5.5 Bandpass transformer sections | p. 163 |

4.5.6 Illustrative exercise: series-to-parallel circuit conversions | p. 164 |

4.5.7 Illustrative exercise: impedance transformations | p. 165 |

4.6 Constant Q curves on the Smith chart | p. 169 |

4.7 Negative reactive elements | p. 169 |

4.7.1 Illustrative example: removing the effect of parasitic inductance | p. 170 |

4.8 Negative resistance and the extended Smith chart | p. 171 |

4.9 Transmission line manipulations on the Smith chart | p. 172 |

4.9.1 Cascade transmission lines | p. 172 |

4.9.2 Parallel transmission line stubs | p. 175 |

4.9.3 Important points to remember about transmission lines | p. 176 |

4.9.4 Illustrative example: impedance transformation with transmission line and lumped elements | p. 177 |

4.9.5 Illustrative example: computing transmission line lengths with the Smith chart | p. 178 |

4.9.6 Illustrative example: troubleshooting a matching network with the Smith chart | p. 179 |

4.10 Matrix descriptions of networks | p. 180 |

4.11 The scattering (S) matrix | p. 183 |

4.12 The network analyzer | p. 185 |

4.13 S-parameter measurements | p. 188 |

4.13.1 Measurement errors | p. 188 |

4.13.2 One-port calibration | p. 190 |

4.13.3 Two-port calibrations | p. 191 |

4.13.4 Time-domain reflectometry | p. 192 |

4.14 Two-port gain expressions in terms of S-parameters | p. 193 |

4.14.1 Illustrative exercise: transducer gain versus insertion loss | p. 195 |

4.14.2 Illustrative exercise: transistor gain calculations--1 | p. 196 |

4.14.3 Illustrative exercise: transistor gain calculations--2 | p. 198 |

4.15 Cascading two-ports with S-parameters | p. 200 |

4.15.1 Illustrative exercise: performance of two cascaded filters | p. 201 |

4.15.2 Mismatch error | p. 203 |

4.15.3 The cascadable scattering transfer matrix | p. 204 |

4.16 Multiport S-parameters | p. 205 |

4.17 Generalized two-port S-parameters | p. 206 |

4.18 Mixed-mode S-parameters | p. 209 |

4.18.1 Standard S-parameter to mixed-mode S-parameter transformations | p. 213 |

4.18.2 Illustrative example: characterization of a SAW filter | p. 215 |

4.19 Summary | p. 217 |

References | p. 218 |

Selected bibliography | p. 218 |

5 Impedance matching techniques | p. 221 |

5.1 The impedance match | p. 222 |

5.2 Transmission zero definitions | p. 225 |

5.2.1 Illustrative exercise: determine the order of L-C networks | p. 228 |

5.3 Impedance matching into complex termination | p. 232 |

5.3.1 Illustrative example: matching a 50-[Omega] source to a complex load | p. 233 |

5.4 Impedance matching with uneven resistive terminations | p. 236 |

5.5 The Q matching technique with L-C sections | p. 239 |

5.5.1 Illustrative example: impedance matching of two resistive terminations | p. 241 |

5.5.2 Bandwidth of L-C matching sections | p. 244 |

5.6 Impedance matching of complex terminations | p. 247 |

5.6.1 Absorbing the parasitics of the terminations | p. 247 |

5.6.2 Resonating excessive parasitic inductance or capacitance | p. 248 |

5.6.3 Illustrative exercise: impedance matching complex terminations with the Smith chart | p. 251 |

5.7 Multisection impedance matching to increase bandwidth | p. 254 |

5.7.1 Illustrative exercise: two-section impedance match for wider bandwidth | p. 257 |

5.8 Multisection impedance matching to decrease bandwidth | p. 260 |

5.8.1 Illustrative exercise: two-section impedance match for narrow bandwidth | p. 262 |

5.9 Impedance matching with transmission line components | p. 264 |

5.9.1 Impedance matching with a single cascade transmission line | p. 264 |

5.9.2 Illustrative exercise: impedance matching with a cascade transmission line | p. 266 |

5.10 Impedance matching with transmission lines on the Smith chart | p. 267 |

5.10.1 Illustrative exercise: impedance matching with a cascade transmission line | p. 269 |

5.10.2 Parallel stub manipulations on the Smith chart | p. 271 |

5.11 Impedance matching of balanced circuits | p. 272 |

5.11.1 Illustrative exercise: impedance matching of differential amplifiers | p. 272 |

5.12 Answers to illustrative exercise of Section 5.2.1 (circuit 4) | p. 273 |

5.13 Summary | p. 275 |

References | p. 276 |

Selected bibliography | p. 276 |

6 CAE/CAD of linear RF/MW circuits | p. 277 |

6.1 Introduction | p. 277 |

6.2 Historical review | p. 279 |

6.3 Analysis versus synthesis and optimization | p. 281 |

6.4 Circuit simulation techniques | p. 282 |

6.4.1 DC and transient analysis | p. 282 |

6.4.2 AC steady-state circuit analysis | p. 283 |

6.5 Impedance mapping | p. 284 |

6.6 Component tuning | p. 286 |

6.7 Circuit optimization | p. 286 |

6.7.1 Error function definitions | p. 289 |

6.7.2 Illustrative exercise: weighting factor determinations | p. 290 |

6.7.3 Component sensitivities | p. 293 |

6.7.4 Constrained versus unconstrained optimization | p. 294 |

6.7.5 Search techniques | p. 294 |

6.7.6 Illustrative exercise: matching network optimization | p. 295 |

6.8 Statistical design techniques | p. 298 |

6.8.1 Yield-oriented design | p. 299 |

6.8.2 Component tolerance distributions--probability density functions | p. 301 |

6.8.3 Statistical sensitivities | p. 303 |

6.8.4 Illustrative exercise: design centering of a 500-MHz lowpass filter | p. 307 |

6.9 Circuit synthesis | p. 314 |

6.9.1 Parasitic absorption | p. 316 |

6.9.2 Ripple, slope, and minimum insertion loss specifications | p. 317 |

6.9.3 Illustrative example: matching network synthesis | p. 318 |

6.10 Electromagnetic field simulation | p. 321 |

6.10.1 Categories by geometries | p. 322 |

6.10.2 Illustrative example: layout and cosimulation of a 6-GHz Wilkinson power divider | p. 324 |

6.11 CAD program descriptions | p. 327 |

6.11.1 Agilent Advanced Design System | p. 327 |

6.11.2 Ansoft Designer | p. 329 |

6.11.3 AWR Microwave Office | p. 331 |

6.11.4 Eagleware Genesys | p. 333 |

6.12 Summary | p. 334 |

References | p. 334 |

7 Passive component models | p. 337 |

7.1 Introduction | p. 337 |

7.2 Resistance, self-inductance, and stray capacitance of conductors | p. 339 |

7.2.1 Resistance changes of conductors at RF | p. 339 |

7.2.2 RF considerations of resistor types | p. 341 |

7.2.3 Inductance of a straight wire (far from ground and shielding) | p. 342 |

7.2.4 Parallel-plate and edge-coupled capacitance | p. 344 |

7.3 Frequency response of physical resistors | p. 346 |

7.3.1 Fitting a model to measured resistor data | p. 348 |

7.4 Modeling physical inductors | p. 350 |

7.4.1 Inductor self-capacitance and loss resistances | p. 353 |

7.4.2 Planar printed inductors | p. 353 |

7.4.3 Effective inductance calculations | p. 354 |

7.4.4 Q-factor calculation | p. 355 |

7.4.5 Multilayer inductors | p. 357 |

7.4.6 Inductors with magnetic core | p. 360 |

7.5 Ferrite beads | p. 362 |

7.6 Physical capacitor models | p. 364 |

7.6.1 Interdigital capacitors | p. 367 |

7.6.2 Illustrative example of effective capacitance calculations | p. 367 |

7.6.3 Secondary resonances in multifinger capacitors | p. 370 |

7.7 Via hole models | p. 372 |

7.7.1 Grounding-path inductance effects | p. 375 |

7.8 Planar transmission lines for RF/MW applications | p. 377 |

7.8.1 Comparison of planar transmission line forms | p. 378 |

7.8.2 Coupled transmission lines | p. 381 |

7.8.3 Transmission line discontinuities | p. 383 |

7.9 Dielectric board materials | p. 387 |

7.10 Transformers | p. 389 |

7.10.1 Transformer equivalent circuit with conventional windings | p. 390 |

7.10.2 Baluns | p. 392 |

7.11 Crystal resonators and models | p. 395 |

7.11.1 Crystal orientation | p. 396 |

7.11.2 Doubly rotated cuts | p. 397 |

7.11.3 Crystal resonator equivalent circuit | p. 397 |

7.11.4 Applications | p. 403 |

7.12 Surface acoustic wave resonators | p. 403 |

7.13 Dielectric resonators | p. 405 |

7.14 Component measurements and modeling | p. 408 |

7.15 Summary | p. 410 |

References | p. 411 |

8 Filters and resonant circuits | p. 415 |

8.1 Introduction | p. 415 |

8.2 Filter specifications | p. 417 |

8.3 Various filter types | p. 421 |

8.4 Low-frequency versus RF/MW filters | p. 423 |

8.4.1 Baseband filters | p. 423 |

8.4.2 RF filters | p. 429 |

8.5 Comparison of filter responses | p. 441 |

8.6 Multiplexer filters | p. 442 |

8.7 Filter design outline | p. 444 |

8.7.1 Lowpass filter design using filter tables | p. 444 |

8.7.2 Illustrative exercise: 400-MHz Chebyshev filter design with lumped components | p. 451 |

8.8 Transmission line (distributed-element) filters | p. 457 |

8.8.1 Illustrative example: converting a lumped filter to distributed type using Richard's transformation | p. 458 |

8.9 Network transformations | p. 460 |

8.9.1 Transformations to change the filter's response | p. 461 |

8.9.2 Transformations to change termination ratio or element type | p. 462 |

8.9.3 Transformations to change termination ratios and/or circuit topologies of transmission line networks | p. 468 |

8.9.4 Transformations to change element values | p. 474 |

8.10 L-C resonant circuits in filter design | p. 475 |

8.10.1 Illustrative example: bandpass resonant circuit design | p. 476 |

8.10.2 Illustrative exercise: synthesis and transformations of a capacitively coupled resonator filter | p. 482 |

8.11 Other forms of resonators | p. 484 |

8.11.1 Illustrative example: coupled transmission line filter synthesis using CAD | p. 485 |

8.11.2 Dielectric resonators | p. 488 |

8.11.3 Crystal resonators | p. 488 |

8.12 Summary | p. 489 |

References | p. 490 |

Selected bibilography | p. 491 |

9 Similarities and differences of RF and high-speed digital designs | p. 493 |

9.1 Historical perspective of analog RF and digital designs | p. 493 |

9.2 Time-domain and voltage-current parameters (transition times, delays, skew, and signal levels) | p. 496 |

9.3 Crosstalk versus coupling | p. 500 |

9.4 R-L-C models for digital applications | p. 503 |

9.4.1 Resistors | p. 503 |

9.4.2 Inductors | p. 505 |

9.4.3 Capacitors | p. 507 |

9.5 Parasitics of passive interconnects, loading, vias, and losses | p. 509 |

9.6 Frequency-domain versus time-domain considerations | p. 513 |

9.6.1 When frequency domain is essential: clock networks | p. 513 |

9.6.2 When frequency domain is useful: power distribution | p. 514 |

9.7 Measurement and simulation considerations | p. 516 |

References | p. 520 |

Selected bibliography | p. 521 |

Appendix | p. 523 |

Summary of Basic Formulas - 1 | p. 523 |

Summary of Basic Formulas - 2 | p. 525 |

About the Authors | p. 527 |

Index | p. 529 |