MICROWAVE FILTERS FOR COMMUNICATION SYSTEMS: FUNDAMENTALS, DESIGN, AND APPLICATIONS

RICHARD J. CAMERON CHANDRA M. KUDSIA RAAFAT R. MANSOUR

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WILEY-INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION

CONTENTS

FOREWORD xxi

PREFACE xxiii

ACKNOWLEDGMENTS xxxi

1 RADIO FREQUENCY (RF) FILTER NETWORKS FOR WIRELESS COMMUNICATIONS—THE SYSTEM PERSPECTIVE 1

Part I Introduction to a Communication System, Radio Spectrum, and Information / 2

1.1 Model of a Communication System / 2 1.1.1 Building Blocks of a Communication System / 3

1.2 Radio Spectrum and its Utilization / 7

1.2.1 Radio Propagation at Microwave Frequencies / 7 1.2.2 Radio Spectrum as a Natural Resource / 9

1.3 Concept of Information / 10 1.4 Communication Channel and Link Budgets / 12

1.4.1 Signal Power in a Communication Link / 12

1.4.2 Transmit and Receive Antennas / 13

Part II Noise in a Communication Channel / 18

1.5 Noise in Communication Systems / 18 1.5.1 Adjacent Copolarized Channel Interference / 18

vii

VIII CONTENTS

1.5.2 Adjacent Cross-Polarized Channel Interference / 19 1.5.3 Multipath Interference / 19 1.5.4 Thermal Noise / 20

1.5.5 Noise in Cascaded Networks / 26 1.5.6 Intermodulation (IM) Noise / 29 1.5.7 Distortion Due to Channel Imperfections / 31 1.5.8 RF Link Design / 34

1.6 Modulation-Demodulation Schemes in a Communication System / 37 1.6.1 Amplitude Modulation / 37 1.6.2 Formation of a Baseband Signal / 39

1.6.3 Angle-Modulated Signals / 40 1.6.4 Comparison of FM and AM Systems / 43

1.7 Digital Transmission / 46 1.7.1 Sampling / 46 1.7.2 Quantization / 47

1.7.3 PCM Systems / 47 1.7.4 Quantization Noise in PCM Systems / 48 1.7.5 Error Rates in Binary Transmission / 49

1.7.6 Digital Modulation and Demodulation Schemes / 50

1.7.7 Advanced Modulation Schemes / 53 1.7.8 Quality of Service and S/N Ratio / 58

Part III Impact of System Design on the Requirements of Filter Networks / 58

1.8 Communication Channels in a Satellite System / 58 1.8.1 Receive Section / 61

1.8.2 The Channelizer Section / 62 1.8.3 High-Power Amplifiers (HPAs) / 64

1.8.4 Transmitter Section Architecture / 67 1.9 RF Filters in Cellular Systems / 71

1.10 Impact of System Requirements on RF Filter Specifications / 74

1.11 Impact ofSatellite and Cellular Communications on Filter Technology / 77 Summary / 78 References / 78 Appendix 1A Intermodulation Distortion Summary / 80

2 FUNDAMENTALS OF CIRCUIT THEORY APPROXIMATION 83

2.1 Linear Systems / 83 2.1.1 Concept of Linearity / 84

2.2 Classification of Systems / 84

CONTENTS JX

2.2.1 Time-Invariant and Time-Variant Systems / 85

2.2.2 Lumped and Distributed Systems / 85 2.2.3 Instantaneous and Dynamic Systems / 85 2.2.4 Analog and Digital Systems / 85

2.3 Evolution of Electrical Circuits—A Historical Perspective / 86 2.3.1 Circuit Elements / 86

2.4 Network Equation of Linear Systems in the Time Domain / 87 2.5 Network Equation of Linear Systems in the Frequency-Domain

Exponential Driving Function / 89 2.5.1 Complex Frequency Variable / 90 2.5.2 Transfer Function / 91

2.5.3 Signal Representation by Continuous Exponentials / 92 2.5.4 Transfer Functions of Electrical Networks / 92

2.6 Steady-State Response of Linear Systems to Sinusoidal Excitations / 93

2.7 Circuit Theory Approximation / 94 Summary / 96

References / 96

3 CHARACTERIZATION OF LOSSLESS LOWPASS PROTOTYPE FILTER FUNCTIONS 97

3.1 The Ideal Filter / 97 3.1.1 Distortionless Transmission / 97 3.1.2 Maximum Power Transfer in Two-Port Networks / 98

3.2 Characterization of Polynomial Functions for Doubly Terminated Lossless Lowpass Prototype Filter Networks / 99 3.2.1 Reflection and Transmission Coefficients / 101 3.2.2 Normalization of the Characteristic Polynomials / 104

3.3 Characteristic Polynomials for Idealized Lowpass Prototype Networks / 105

3.4 Lowpass Prototype Characteristics / 107 3.4.1 Amplitude Response / 107

3.4.2 Phase Response / 107 3.4.3 Phase Linearity / 108

3.5 Characteristic Polynomials Versus Response Shapes / 109

3.5.1 All-Pole Prototype Filter Functions / 109 3.5.2 Prototype Filter Functions with Finite Transmission Zeros / 109

3.6 Classical Prototype Filters / 111 3.6.1 Maximally Fiat Filters / 111

3.6.2 Chebyshev Approximation / 112 3.6.3 Elliptic Function Filters / 115

CONTENTS

3.6.4 Odd-Order Elliptic Function Filters / 118 3.6.5 Even-Order Elliptic Function Filters / 119

3.6.6 Filters with Transmission Zeros and a Maximally Fiat Passband / 121

3.6.7 Linear Phase Filters / 121 3.6.8 Comparison of Maximally Fiat, Chebyshev, and

Elliptic Function Filters / 122

3.7 Uniried Design Chart (UDC) Relationships / 123 3.7.1 Ripple Factor / 124

3.8 Lowpass Prototype Circuit Configurations / 125

3.8.1 Scaling of Prototype Networks / 126 3.8.2 Frequency Response of Scaled Networks / 127

3.9 Effect of Dissipation / 130

3.9.1 Relationship of Dissipation Factor 8 and Quality Factor ß 0 / 132

3.9.2 Equivalent 8 for Lowpass and Highpass Filters / 134

3.9.3 Equivalent 8 for Bandpass and Bandstop Filters / 3.10 Asymmetrie Response Filters / 136

3.10.1 Positive Functions / 137 Summary / 140 References / 141 Appendix 3A Unified Design Charts / 143

COMPUTER-AIDED SYNTHESIS OF CHARACTERISTIC POLYNOMIALS

4.1 Objective Function and Constraints for Symmetrie Lowpass Prototype Filter Networks / 152

4.2 Analytic Gradients of the Objective Function / 154

4.2.1 Gradient of the Unconstrained Objective Function / 155

4.2.2 Gradient of the Inequality Constraint / 156

4.2.3 Gradient of the Equality Constraint / 157 4.3 Optimization Criteria for Classical Filters / 158

4.3.1 Chebyshev Function Filters / 158 4.3.2 Inverse Chebyshev Filters / 159 4.3.3 Elliptic Function Filters / 159

4.4 Generation of Novel Classes of Filter Functions / 161 4.4.1 Equiripple Passbands and Stopbands / 161

CONTENTS Xi

4.4.2 Nonequiripple Stopband with an Equiripple Passband / 163

4.5 Asymmetrie Class of Filters / 163 4.5.1 Asymmetrie Filters with Chebyshev

Passband / 164 4.5.2 Asymmetrical Filters with Arbitrary

Response / 166 4.6 Linear Phase Filters / 168 4.7 Critical Frequencies for Selected Filter Functions / 169 Summary / 169

References / 170 Appendix 4A Critical Frequencies for an Unconventional 8-Pole Filter / 171

5 ANALYSIS OF MULTIPORT MICROWAVE NETWORKS 173

5.1 Matrix Representation of Two-Port Networks / 174 5.1.1 Impedance [Z] and Admittance [T] Matrices / 174 5.1.2 The [ABCD] Matrix / 175

5.1.3 The Scattering [S] Matrix / 178 5.1.4 The Transmission Matrix [T] / 183

5.1.5 Analysis of Two-Port Networks / 185 5.2 Cascade of Two Networks / 189 5.3 Multiport Networks / 198

5.4 Analysis of Multiport Networks / 200 Summary / 205

References / 206

6 SYNTHESIS OF A GENERAL CLASS OF THE CHEBYSHEV FILTER FUNCTION 207

6.1 Polynomial forms of the Transfer and Reflection Parameters S2i(s) and Sj ,0) for a Two-Port Network / 207 6.1.1 Relationship Between e and eR / 215

6.2 Alternating Pole Method for Determination of the Denominator Polynomial E(s) / 216

6.3 General Polynomial Synthesis Methods for Chebyshev Filter Functions / 219 6.3.1 Polynomial Synthesis / 220 6.3.2 Recursive Technique / 225

6.3.3 Polynomial Forms for Symmetrie and Asymmetrie Filtering Functions / 229

XII CONTENTS

6.4 Predistorted Filter Characteristics / 230 6.4.1 Synthesis of the Predistorted Filter Network / 236

6.5 Transformation for Dual-Band Bandpass Filters / 238 Summary / 241

References / 242

7 SYNTHESIS OF NETWORK-CIRCUIT APPROACH 243

7.1 Circuit Synthesis Approach / 245

7.1.1 Buildup of [ABCD] Matrix for the Third-Degree Network / 246

7.1.2 Network Synthesis / 247 7.2 Lowpass Prototype Circuits for Coupled-Resonator

Microwave Bandpass Filters / 250 7.2.1 Synthesis of the [ABCD ] Polynomials for

Circuits with Inverters / 251 7.2.2 Synthesis of the [ABCD] Polynomials for the Singly

Terminated Filter Prototype / 258 7.3 Ladder Network Synthesis / 260 7.4 Synthesis Example of an Asymmetrie (4-2)

Filter Network / 269

Summary / 276 References / 277

8 COUPLING MATRIX SYNTHESIS OF FILTER NETWORKS 279

8.1 Coupling Matrix / 279

8.1.1 Bandpass and Lowpass Prototypes / 281 8.1.2 Formation of the General N x N Coupling Matrix and

its Analysis / 282 8.1.3 Formation of the Coupling Matrix from the Lowpass

Prototype Circuit Elements / 286

8.1.4 Analysis of the Network Represented by the Coupling Matrix / 288

8.1.5 Direct Analysis / 291 8.2 Direct Synthesis of the Coupling Matrix / 292

8.2.1 Direct Synthesis of the N x N Coupling Matrix / 293 8.3 Coupling Matrix Reduction / 295

8.3.1 Similarity Transformation and Annihilation of Matrix Elements / 296

8.4 Synthesis of the N + 2 Coupling Matrix / 303

CONTENTS XIII

8.4.1 Synthesis of the Transversal Coupling Matrix / 304 8.4.2 Reduction of the N + 2 Transversal Matrix to

the Folded Canonical Form / 311 8.4.3 Illustrative Example / 312

Summary / 315

References / 316

9 RECONFIGURATION OF THE FOLDED COUPLING MATRIX 319

9.1 Symmetrie Realizations for Dual-Mode Filters / 320 9.1.1 Sixth-Degree Filter / 322 9.1.2 Eighth-Degree Filter / 322

9.1.3 lOth-Degree Filter / 323

9.1.4 12th-Degree Filter / 323 9.2 Asymmetrie Realizations for Symmetrie Charaeteristies / 325 9.3 "Pfitzenmaier" Configurations / 326 9.4 Cascaded Quartets (CQs)—Two Quartets

in Cascade for Degrees 8 and Above / 328 9.5 Parallel-Connected Two-Port Networks / 331

9.5.1 Even-Mode and Odd-Mode Coupling Submatrices / 335 9.6 Cul-de-Sac Configuration / 337

9.6.1 Further Cul-de-Sac Forms / 340 9.6.2 Sensitivity Considerations / 345

Summary / 345 References / 347

10 SYNTHESIS AND APPLICATION OF EXTRACTED POLE AND TRISECTION ELEMENTS 349

10.1 Extracted Pole Filter Synthesis / 349

10.1.1 Synthesis of the Extracted Pole Element / 350 10.1.2 Example of Synthesis of Extracted

Pole Network / 354

10.1.3 Analysis of the Extracted Pole Filter Network / 357

10.1.4 Direct-Coupled Extracted Pole Filters / 360 10.2 Synthesis of Bandstop Filters Using

the Extracted Pole Technique / 364

10.2.1 Direct-Coupled Bandstop Filters / 366 10.3 Trisections / 371

10.3.1 Synthesis of the Trisection—Circuit Approach / 373

XIV CONTENTS

10.3.2 Cascade Trisections—Coupling Matrix Approach / 379

10.3.3 Techniques Based on the Trisection for Synthesis of Advanced Circuits / 387

10.4 Box Section and Extended Box Configurations / 392 10.4.1 Box Sections / 393 10.4.2 Extended Box Sections / 397

Summary / 401

References / 402

11 MICROWAVE RESONATORS 405

11.1 Microwave Resonator Configurations / 405 11.2 Calculation of Resonant Frequency / 409

11.2.1 Resonance Frequency of Conventional Transmission-Line Resonators / 409

11.2.2 Resonance Frequency Calculation Using the Transverse Resonance Technique / 412

11.2.3 Resonance Frequency of Arbitrarily Shaped Resonators / 413

11.3 Resonator Unloaded Q Factor / 416

11.3.1 Unloaded Q Factor of Conventional Resonators / 418 11.3.2 Unloaded Q of Arbitrarily Shaped Resonators / 421

11.4 Measurement of Loaded and Unloaded Q Factor / 421

Summary / 428

References / 429

12 WAVEGUIDE AND COAXIAL LOWPASS FILTERS 431

12.1 Commensurate-Line Building Elements / 432 12.2 Lowpass Prototype Transfer Polynomials / 433

12.2.1 Chebyshev Polynomials of the Second Kind / 433

12.2.2 Achieser-Zolotarev Functions / 436 12.3 Synthesis and Realization of the Distributed Stepped

Impedance Lowpass Filter / 438

12:3.1 Mapping the Transfer Function S2] from the w Plane to the 0 Plane / 439

12.3.2 Synthesis of the Stepped Impedance Lowpass Prototype Circuit / 441

12.3.3 Realization / 443

CONTENTS XV

12.4 Short-Step Transformers / 448 12.5 Synthesis and Realization of Mixed Lumped/Distributed

Lowpass Filter / 451 12.5.1 Formation of the Transfer and

Reflection Polynomials / 452

12.5.2 Synthesis of the Tapered-Corrugated Lowpass Prototype Circuit / 454

12.5.3 Realization / 458 Summary / 466

References / 466

13 WAVEGUIDE REALIZATION OF SINGLE- AND DUAL-MODE RESONATOR FILTERS 469

13.1 Synthesis Process / 470 13.2 Design of the Filter Function / 471

13.2.1 Amplitude Optimization / 471 13.2.2 Rejection Lobe Optimization / 472

13.2.3 Group Delay Optimization / 474 13.3 Realization and Analysis of the Microwave

Filter Network / 479

13.4 Dual-Mode Filters / 485 13.4.1 Virtual Negative Couplings / 486

13.5 Coupling Sign Correction / 488

13.6 Dual-Mode Realizations for Some Typical Coupling Matrix Configurations / 489 13.6.1 Folded Array / 490

13.6.2 Pfitzenmaier Configuration / 491 13.6.3 Propagating Forms / 492 13.6.4 Cascade Quartet / 492 13.6.5 Extended Box / 492

13.7 Phase- and Direct-Coupled Extracted Pole Filters / 494 13.8 The "Füll Inductive" Dual-Mode Filter / 496

13.8.1 Synthesis of the Equivalent Circuit / 498

Summary / 499 References / 500

14 DESIGN AND PHYSICAL REALIZATION OF COUPLED RESONATOR FILTERS 501

14.1 Circuit Models for Chebyshev Bandpass Filters / 502

XVI CONTENTS

14.2 Calculation of Interresonator Coupling / 507 14.2.1 The Use of Electric Wall and Magnetic

Wall Symmetry / 507

14.2.2 Interresonator Coupling Calculation Using S Parameters / 509

14.3 Calculation of Input/Output Coupling / 511 14.3.1 Frequency Domain Method / 511

14.3.2 Group Delay Method / 512 14.4 Design Example of Dielectric Resonator Filters Using the Coupling

Matrix Model / 513 14.4.1 Calculation of Dielectric Resonator Cavity

Configuration / 515 14.4.2 Calculation of Iris Dimensions for

Interresonator Coupling / 516 14.4.3 Calculation of Input/Output Coupling / 518

14.5 Design Example of a Waveguide Iris Filter Using the Impedance Inverter Model / 521

14.6 Design Example of a Microstrip Filter Using the /-Admittance Inverter Model / 524

Summary / 529 References / 530

15 ADVANCED EM-BASED DESIGN TECHNIQUES FOR MICROWAVE FILTERS 531

15.1 EM-Based Synthesis Techniques / 532 15.2 EM-Based Optimization Techniques / 532

15.2.1 Optimization Using an EM Simulator / 534 15.2.2 Optimization Using Semi-EM-Based Simulator / 535

15.2.3 Optimization Using an EM Simulator with Adaptive Frequency Sampling / 537

15.2.4 Optimization Using EM-Based Neural Network Models / 538

15.2.5 Optimization Using EM-Based Multidimensional Cauchy Technique / 543

15.2.6 Optimization Using EM-Based Fuzzy Logic / 544 15.3 EM-Based Advanced Design Techniques / 544

15.3.1 Space Mapping Techniques / 545

15.3.2 Calibrated Coarse Model (CCM) Techniques / 553 15.3.3 Generalized Calibrated Coarse Model Technique

for Filter Design / 559 Summary / 563

CONTENTS XVÜ

References / 564

DIELECTRIC RESONATOR FILTERS 567

16.1 Resonant Frequency Calculation in Dielectric Resonators / 568

16.2 Rigorous Analyses of Dielectric Resonators / 572

16.2.1 Mode Charts for Dielectric Resonators / 574

16.3 Dielectric Resonator Filter Configurations / 576 16.4 Design Considerations for Dielectric

Resonator Filters / 580 16.4.1 Achievable Filter Q Value / 580 16.4.2 Spurious Performance of Dielectric Resonator

Filters / 581

16.4.3 Temperature Drift / 582 16.4.4 Power Handling Capability / 583

16.5 Other Dielectric Resonator Configurations / 583 16.6 Cryogenic Dielectric Resonator Filters / 587 16.7 Hybrid Dielectric/Superconductor Filters / 589 Summary / 592

References / 593

ALLPASS PHASE AND GROUP DELAY EQUALIZER NETWORKS 595

17.1 Characteristics of Allpass Networks / 596

17.2 Lumped-Element Allpass Networks / 597

17.2.1 Resistively Terminated Symmetrie Lattice Networks / 599 17.2.2 Network Realizations / 601

17.3 Microwave Allpass Networks / 603

17.4 Physical Realization of Allpass Networks / 608 17.4.1 Transmission-Type Equalizers / 609 1 7.4.2 Reftection-Type Allpass Networks / 609

17.5 Synthesis of Reflection-Type Allpass Networks / 610

11.6 Practical Narrowband Reflection-Type Allpass Networks / 612

17.6.1 C-Section Allpass Equalizer in Waveguide Structure / 613 17.6.2 D-Section Allpass Equalizer in Waveguide Structure / 615

17.6.3 Narrowband TEM Reactance Networks / 615

17.7 Optimization Criteria for Allpass Networks / 616 17.8 Effect of Dissipation / 620

17.8.1 Dissipation Loss of a Lumped-Element First-Order Allpass Equalizer / 620

XVIII CONTENTS

17.8.2 Dissipation Loss of a Second-Order Lumped Equalizer / 621

17.8.3 Effect of Dissipation in Distributed Allpass Networks / 621

17.9 Equalization Tradeoffs / 622 Summary / 623 References / 623

18 MULTIPLEXER THEORY AND DESIGN 625

18.1 Background / 625 18.2 Multiplexer Configurations / 627

18.2.1 Hybrid Coupled Approach / 627 18.2.2 Circulator-Coupled Approach / 629 18.2.3 Directional Filter Approach / 630

18.2.4 Manifold-Coupled Approach / 630

18.3 RF Channelizers (Demultiplexers) / 632 18.3.1 Hybrid Branching Network / 633 18.3.2 Circulator-Coupled MUX / 634 18.3.3 En Passant Distortion / 636

18.4 RFCombiners / 638 18.4.1 Circulator-Coupled MUX / 640 18.4.2 Hybrid-Coupled Filter Combiner Module (HCFM)

Multiplexer / 640

18.4.3 Directional Filter Combiner / 643 18.4.4 Manifold Multiplexer / 645

18.5 Transmit-Receive Diplexers / 661

18.5.1 Internal Voltage Levels in Tx/Rx Diplexer Filters / 665

Summary / 668 References / 669

19 COMPUTER-AIDED DIAGNOSIS AND TUNING OF MICROWAVE FILTERS 671

19.1 Sequential Tuning of Coupled Resonator Filters / 672 19.2 Computer-Aided Tuning Based on Circuit Model Parameter

Extraction / 678 19.3 Computer-Aided Tuning Based on Poles and Zeros of the

Input Reflection Coefficient / 683

19.4 Time-Domain Tuning / 687

CONTENTS XIX

19.4.1 Time-Domain Tuning of Resonator Frequencies / 688

19.4.2 Time-Domain Tuning of Interresonator Coupling / 689

19.4.3 Time-Domain Response of a Golden Filter / 691

19.5 Filter Tuning Based on Fuzzy Logic Techniques / 692 19.5.1 Description of Fuzzy Logic Systems / 693

19.5.2 Steps in Building the FL System / 694 19.5.3 Comparison Between Boolean Logic and

Fuzzy Logic / 697 19.5.4 Applying Fuzzy Logic to Filter

Tuning / 700 19.6 Automated Setups for Filter Tuning / 703 Summary / 706

References / 707

20 HIGH-POWER CONSIDERATIONS IN MICROWAVE FILTER NETWORKS 711

20.1 Background / 711 20.2 High-Power Requirements in Wireless Systems / 712

20.3 High-Power Amplifiers (HPAs) / 713 20.4 High-Power Breakdown Phenomena / 714

20.4.1 Gaseous Breakdown / 715

20.4.2 Mean Free Path / 715 20.4.3 Diffusion / 716

20.4.4 Attachment / 716 20.4.5 Breakdown in Air / 716 20.4.6 Critical Pressure / 717 20.4.7 Power Rating of Waveguides and Coaxial

Transmission Lines / 719

20.4.8 Derating Factors / 720 20.4.9 Impact of Thermal Dissipation on

Power Rating / 721

20.5 High-Power Bandpass Filters / 722 20.5.1 Bandpass Filters Limited by Thermal

Dissipation / 723

20.5.2 Bandpass Filters Limited by Voltage Breakdown / 724

20.5.3 Filter Prototype Network / 724

XX CONTENTS

20.5.4 Lumped To Distributed Scaling / 725 20.5.5 Resonator Voltages from Prototype

Network / 726

20.5.6 Example and Verification Via FEM Simulation / 727

20.5.7 Example of High Voltages in a Multiplexer / 729

20.6 Multipaction Breakdown / 730 20.6.1 Dependence on Vacuum Environment / 730

20.6.2 Dependence on Applied RF Voltage / 730 20.6.3 Dependence on / x d Product / 731 20.6.4 Dependence on Surface Conditions

of Materials / 732 20.6.5 Detection and Prevention of Multipaction / 732

20.6.6 Design Margins in Multipaction / 733 20.6.7 Multipactor Breakdown Levels / 737

20.7 Passive Intermodulation (PIM) Consideration for High-Power Equipment / 739 20.7.1 PIM Measurement / 740 20.7.2 PIM Control Guidelines / 741

Summary / 742

References / 743

APPENDIX A

APPENDIX B

APPENDIX C

APPENDIX D

INDEX

745

747

749

751

753