Microwave filters for communication systems : fundamentals, design, and applications

There have been significant advances in the synthesis and physical realization of microwave filter networks over the last three decades. This book provides a coherent and readable description of system requirements and constraints for microwave filters, fundamental considerations in the theory and design of microwave filters, up-to-date modern synthesis techniques with examples and technology considerations in the choice of hardware.

Author Notes

Richard J. Cameron is the retired technical director of COM DEV Europe, Visiting Professor at the University of Leeds (UK), and is a Fellow of IEE and IEEE
Dr. Chandra M. Kudsia is Adjunct Professor at the University of Waterloo, a Fellow of IEEE, AIAA and EIC, and the retired chief scientist of COM DEV Space Group
Dr. Raafat R. Mansour is a Professor at the University of Waterloo, former director of R&D at COM DEV International, and is a Fellow of IEEE

Foreword	p. xxi
Preface	p. xxiii
Acknowledgments	p. xxxi
1 Radio Frequency (RF) Filter Networks for Wireless Communications-The System Perspective	p. 1
Part I Introduction to a Communication System, Radio Spectrum, and Information	p. 2
1.1 Model of a Communication System	p. 2
1.1.1 Building Blocks of a Communication System	p. 3
1.2 Radio Spectrum and its Utilization	p. 7
1.2.1 Radio Propagation at Microwave Frequencies	p. 7
1.2.2 Radio Spectrum as a Natural Resource	p. 9
1.3 Concept of Information	p. 10
1.4 Communication Channel and Link Budgets	p. 12
1.4.1 Signal Power in a Communication Link	p. 12
1.4.2 Transmit and Receive Antennas	p. 13
Part II Noise in a Communication Channel	p. 18
1.5 Noise in Communication Systems	p. 18
1.5.1 Adjacent Copolarized Channel Interference	p. 18
1.5.2 Adjacent Cross-Polarized Channel Interference	p. 19
1.5.3 Multipath Interference	p. 19
1.5.4 Thermal Noise	p. 20
1.5.5 Noise in Cascaded Networks	p. 26
1.5.6 Intermodulation (IM) Noise	p. 29
1.5.7 Distortion Due to Channel Imperfections	p. 31
1.5.8 RF Link Design	p. 34
1.6 Modulation-Demodulation Schemes in a Communication System	p. 37
1.6.1 Amplitude Modulation	p. 37
1.6.2 Formation of a Baseband Signal	p. 39
1.6.3 Angle-Modulated Signals	p. 40
1.6.4 Comparison of FM and AM Systems	p. 43
1.7 Digital Transmission	p. 46
1.7.1 Sampling	p. 46
1.7.2 Quantization	p. 47
1.7.3 PCM Systems	p. 47
1.7.4 Quantization Noise in PCM Systems	p. 48
1.7.5 Error Rates in Binary Transmission	p. 49
1.7.6 Digital Modulation and Demodulation Schemes	p. 50
1.7.7 Advanced Modulation Schemes	p. 53
1.7.8 Quality of Service and S/N Ratio	p. 58
Part III Impact of System Design on the Requirements of Filter Networks	p. 58
1.8 Communication Channes in a Satellite System	p. 58
1.8.1 Receive Section	p. 61
1.8.2 The Channelizer Section	p. 62
1.8.3 High-Power Amplifiers (HPAs)	p. 64
1.8.4 Transmitter Section Architecture	p. 67
1.9 RF Filters in Cellular Systems	p. 71
1.10 Impact of System Requirements on RF Filter Specifications	p. 74
1.11 Impact of Satellite and Cellular Communications on Filter Technology	p. 77
Summary	p. 78
References	p. 78
Appendix 1A Intermodulation Distortion Summary	p. 80
2 Fundamentals of Circuit Theory Approximation	p. 83
2.1 Linear Systems	p. 83
2.1.1 Concept of Linearity	p. 84
2.2 Classification of Systems	p. 84
2.2.1 Time-Invariant and Time-Variant Systems	p. 85
2.2.2 Lumped and Distributed Systems	p. 85
2.2.3 Instantaneous and Dynamic Systems	p. 85
2.2.4 Analog and Digital Systems	p. 85
2.3 Evolution of Electrical Circuits-A Historical Perspective	p. 86
2.3.1 Circuit Elements	p. 86
2.4 Network Equation of Linear Systems in the Time Domain	p. 87
2.5 Network Equation of Linear Systems in the Frequency-Domain Exponential Driving Function	p. 89
2.5.1 Complex Frequency Variable	p. 90
2.5.2 Transfer Function	p. 91
2.5.3 Signal Representation by Continuous Exponentials	p. 92
2.5.4 Transfer Functions of Electrical Networks	p. 92
2.6 Steady-State Response of Linear Systems to Sinusoidal Excitations	p. 93
2.7 Circuit Theory Approximation	p. 94
Summary	p. 96
References	p. 96
3 Characterization of Lossless Lowpass Prototype Filter Functions	p. 97
3.1 The Ideal Filter	p. 97
3.1.1 Distortionless Transmission	p. 97
3.1.2 Maximum Power Transfer in Two-Port Networks	p. 98
3.2 Characterization of Polynomial Functions for Doubly Terminated Lossless Lowpass Prototype Filter Networks	p. 99
3.2.1 Reflection and Transmission Coefficients	p. 101
3.2.2 Normalization of the Characteristic Polynomials	p. 104
3.3 Characteristic Polynomials for Idealized Lowpass Prototype Networks	p. 105
3.4 Lowpass Prototype Characteristics	p. 107
3.4.1 Amplitude Response	p. 107
3.4.2 Phase Response	p. 107
3.4.3 Phase Linearity	p. 108
3.5 Characteristic Polynomials Versus Response Shapes	p. 109
3.5.1 All-Pole Prototype Filter Functions	p. 109
3.5.2 Prototype Filter Functions with Finite Transmission Zeros	p. 109
3.6 Classical Prototype Filters	p. 111
3.6.1 Maximally Flat Filters	p. 111
3.6.2 Chebyshev Approximation	p. 112
3.6.3 Elliptic Function Filters	p. 115
3.6.4 Odd-Order Elliptic Function Filters	p. 118
3.6.5 Even-Order Elliptic Function Filters	p. 119
3.6.6 Filters with Transmission Zeros and a Maximally Flat Passband	p. 121
3.6.7 Lineal-Phase Filters	p. 121
3.6.8 Comparison of Maximally Flat, Chebyshev, and Elliptic Function Filters	p. 122
3.7 Unified Design Chart (UDC) Relationships	p. 123
3.7.1 Ripple Factor	p. 124
3.8 Lowpass Prototype Circuit Configurations	p. 125
3.8.1 Scaling of Prototype Networks	p. 126
3.8.2 Frequency Response of Scaled Networks	p. 127
3.9 Effect of Dissipation	p. 130
3.9.1 Relationship of Dissipation Factor [delta] and Quality Factor Q[subscript 0]	p. 132
3.9.2 Equivalent [delta] for Lowpass and Highpass Filters	p. 134
3.9.3 Equivalent [delta] for Bandpass and Bandstop Filters	p. 134
3.10 Asymmetric Response Filters	p. 136
3.10.1 Positive Functions	p. 137
Summary	p. 140
References	p. 141
Appendix 3A Unified Design Charts	p. 143
4 Computer-Aided Synthesis of Characteristic Polynomials	p. 151
4.1 Objective Function and Constraints for Symmetric Lowpass Prototype Filter Networks	p. 152
4.2 Analytic Gradients of the Objective Function	p. 154
4.2.1 Gradient of the Unconstrained Objective Function	p. 155
4.2.2 Gradient of the Inequality Constraint	p. 156
4.2.3 Gradient of the Equality Constraint	p. 157
4.3 Optimization Criteria for Classical Filters	p. 158
4.3.1 Chebyshev Function Filters	p. 158
4.3.2 Inverse Chebyshev Filters	p. 159
4.3.3 Elliptic Function Filters	p. 159
4.4 Generation of Novel Classes of Filter Functions	p. 161
4.4.1 Equiripple Passbands and Stopbands	p. 161
4.4.2 Nonequiripple Stopband with an Equiripple Passband	p. 163
4.5 Asymmetric Class of Filters	p. 163
4.5.1 Asymmetric Filters with Chebyshev Passband	p. 164
4.5.2 Asymmetrical Filters with Arbitrary Response	p. 166
4.6 Linear Phase Filters	p. 168
4.7 Critical Frequencies for Selected Fitter Functions	p. 169
Summary	p. 169
References	p. 170
Appendix 4A Critical Frequencies for an Unconventional 8-Pole Filter	p. 171
5 Analysis of Multiport Microwave Networks	p. 173
5.1 Matrix Representation of Two-Port Networks	p. 174
5.1.1 Impedance [Z] and Admittance [Y] Matrices	p. 174
5.1.2 The [ABCD] Matrix	p. 175
5.1.3 The Scattering [S] Matrix	p. 178
5.1.4 The Transmission Matrix [T]	p. 183
5.1.5 Analysis of Two-Port Networks	p. 185
5.2 Cascade of Two Networks	p. 189
5.3 Multiport Networks	p. 198
5.4 Analysis of Multiport Networks	p. 200
Summary	p. 205
References	p. 206
6 Synthesis of a General Class of the Chebyshev Filter Function	p. 207
6.1 Polynomial forms of the Transfer and Reflection Parameters S[subscript 21](s) and S[subscript 11](s) for a Two-Port Network	p. 207
6.1.1 Relationships Between [epsilon] and [epsilon subscript R]	p. 215
6.2 Alternating Pole Method for Determination of the Denominator Polynomial E(s)	p. 216
6.3 General Polynomial Synthesis Methods for Chebyshev Filter Functions	p. 219
6.3.1 Polynomial Synthesis	p. 220
6.3.2 Recursive Technique	p. 225
6.3.3 Polynomial Forms for Symmetric and Asymmetric Filtering Functions	p. 229
6.4 Predistorted Filter Characteristics	p. 230
6.4.1 Synthesis of the Predistorted Filter Network	p. 236
6.5 Transformation for Dual-Band Bandpass Filters	p. 238
Summary	p. 241
References	p. 242
7 Synthesis of Network-Circuit Approach	p. 243
7.1 Circuit Synthesis Approach	p. 245
7.1.1 Buildup of [ABCD] Matrix for the Third-Degree Network	p. 246
7.1.2 Network Synthesis	p. 247
7.2 Lowpass Prototype Circuits for Coupled-Resonator Microwave Bandpass Filters	p. 250
7.2.1 Synthesis of the [ABCD] Polynomials for Circuits with Inverters	p. 251
7.2.2 Synthesis of the [ABCD] Polynomials for the Singly Terminated Filter Prototype	p. 258
7.3 Ladder Network Synthesis	p. 260
7.4 Synthesis Example of an Asymmetric (4-2) Filter Network	p. 269
Summary	p. 276
References	p. 277
8 Coupling Matrix Synthesis of Filter Networks	p. 279
8.1 Coupling Matrix	p. 279
8.1.1 Bandpass and Lowpass Prototypes	p. 281
8.1.2 Formation of the General N x N Coupling Matrix and its Analysis	p. 282
8.1.3 Formation of the Coupling Matrix from the Lowpass Prototype Circuit Elements	p. 286
8.1.4 Analysis of the Network Represented by the Coupling Matrix	p. 288
8.1.5 Direct Analysis	p. 291
8.2 Direct Synthesis of the Coupling Matrix	p. 292
8.2.1 Direct Synthesis of the N x N Coupling Matrix	p. 293
8.3 Coupling Matrix Reduction	p. 295
8.3.1 Similarity Transformation and Annihilation f Matrix Elements	p. 296
8.4 Synthesis of the N + 2 Coupling Matrix	p. 303
8.4.1 Synthesis of the Transversal Coupling Matrix	p. 304
8.4.2 Reduction of the N + 2 Transversal Matrix to the Folded Canonical Form	p. 311
8.4.3 Illustrative Example	p. 312
Summary	p. 315
References	p. 316
9 Reconfiguration of the Folded Coupling Matrix	p. 319
9.1 Symmetric Realizations for Dual-Mode Filters	p. 320
9.1.1 Sixth-Degree Filter	p. 322
9.1.2 Eighth-Degree Filter	p. 322
9.1.3 10th-Degree Filter	p. 323
9.1.4 12th-Degree Filter	p. 323
9.2 Asymmetric Realizations for Symmetric Characteristics	p. 325
9.3 "Pfitzenmaier" Configurations	p. 326
9.4 Cascaded Quartets (CQs)-Two Quartets in Cascade for Degrees 8 and Above	p. 328
9.5 Parallel-Connected Two-Port Networks	p. 331
9.5.1 Even-Mode and Odd-Mode Coupling Submatrices	p. 335
9.6 Cul-de-Sac Configuration	p. 337
9.6.1 Further Cul-de-Sac Forms	p. 340
9.6.2 Sensitivity Considerations	p. 345
Summary	p. 345
References	p. 347
10 Synthesis and Application of Extracted Pole and Trisection Elements	p. 349
10.1 Extracted Pole Filter Synthesis	p. 349
10.1.1 Synthesis of the Extracted Pole Element	p. 350
10.1.2 Example of Synthesis of Extracted Pole Network	p. 354
10.1.3 Analysis of the Extracted Pole Filter Network	p. 357
10.1.4 Direct-Coupled Extracted Pole Filters	p. 360
10.2 Synthesis of Bandstop Filters Using the Extracted Pole Technique	p. 364
10.2.1 Direct-Coupled Bandstop Filters	p. 366
10.3 Trisections	p. 371
10.3.1 Synthesis of the Trisection-Circuit Approach	p. 373
10.3.2 Cascade Trisections-Coupling Matrix Approach	p. 379
10.3.3 Techniques Based on the Trisection for Synthesis of Advanced Circuits	p. 387
10.4 Box Section and Extended Box Configurations	p. 392
10.4.1 Box Sections	p. 393
10.4.2 Extended Box Sections	p. 397
Summary	p. 401
References	p. 402
11 Microwave Resonators	p. 405
11.1 Microwave Resonator Configurations	p. 405
11.2 Calculation of Resonant Frequency	p. 409
11.2.1 Resonance Frequency of Conventional Transmission-Line Resonators	p. 409
11.2.2 Resonance Frequency Calculation Using the Transverse Resonance Technique	p. 412
11.2.3 Resonance Frequency of Arbitrarily Shaped Resonators	p. 413
11.3 Resonator Unloaded Q Factor	p. 416
11.3.1 Unloaded Q Factor of Conventional Resonators	p. 418
11.3.2 Unloaded Q of Arbitrarily Shaped Resonators	p. 421
11.4 Measurement of Loaded and Unloaded Q Factor	p. 421
Summary	p. 428
References	p. 429
12 Waveguide and Coaxial Lowpass Filters	p. 431
12.1 Commensurate-Line Building Elements	p. 432
12.2 Lowpass Prototype Transfer Polynomials	p. 433
12.2.1 Chebyshev Polynomials of the Second Kind	p. 433
12.2.2 Achieser-Zolotarev Functions	p. 436
12.3 Synthesis and Realization of the Distributed Stepped Impedance Lowpass Filter	p. 438
12.3.1 Mapping the Transfer Function S[subscript 21] from the [omega] Plane to the [theta] Plane	p. 439
12.3.2 Synthesis of the Stepped Impedance Lowpass Prototype Circuit	p. 441
12.3.3 Realization	p. 443
12.4 Short-Step Transformers	p. 448
12.5 Synthesis and Realization of Mixed Lumped/Distributed Lowpass Filter	p. 451
12.5.1 Formation of the Transfer and Reflection Polynomials	p. 452
12.5.2 Synthesis of the Tapered-Corrugated Lowpass Prototype Circuit	p. 454
12.5.3 Realization	p. 458
Summary	p. 466
References	p. 466
13 Waveguide Realization of Single- and Dual-Mode Resonator Filters	p. 469
13.1 Synthesis Process	p. 470
13.2 Design of the Filter Function	p. 471
13.2.1 Amplitude Optimization	p. 471
13.2.2 Rejection Lobe Optimization	p. 472
13.2.3 Group Delay Optimization	p. 474
13.3 Realization and Analysis of the Microwave Filter Network	p. 479
13.4 Dual-Mode Filters	p. 485
13.4.1 Virtual Negative Couplings	p. 486
13.5 Coupling Sign Correction	p. 488
13.6 Dual-Mode Realizations for Some Typical Coupling Matrix Configurations	p. 489
13.6.1 Folded Array	p. 490
13.6.2 Pfitzenmaier Configuration	p. 491
13.6.3 Propagating Forms	p. 492
13.6.4 Cascade Quartet	p. 492
13.6.5 Extended Box	p. 492
13.7 Phase- and Direct-Coupled Extracted Pole Filters	p. 494
13.8 The "Full Inductive" Dual-Mode Filter	p. 496
13.8.1 Synthesis of the Equivalent Circuit	p. 498
Summary	p. 499
References	p. 500
14 Design and Physical Realization of Coupled Resonator Filters	p. 501
14.1 Circuit Models for Chebyshev Bandpass Filters	p. 502
14.2 Calculation of Interresonator Coupling	p. 507
14.2.1 The Use of Electric Wall and Magnetic Wall Symmetry	p. 507
14.2.2 Interresonator Coupling Calculation Using S Parameters	p. 509
14.3 Calculation of Input/Output Coupling	p. 511
14.3.1 Frequency Domain Method	p. 511
14.3.2 Group Delay Method	p. 512
14.4 Design Example of Dielectric Resonator Filters Using the Coupling Matrix Model	p. 513
14.4.1 Calculation of Dielectric Resonator Cavity Configuration	p. 515
14.4.2 Calculation of Iris Dimensions for Interresonator Coupling	p. 516
14.4.3 Calculation of Input/Output Coupling	p. 518
14.5 Design Example of a Waveguide Iris Filter Using the Impedance Inverter Model	p. 521
14.6 Design Example of a Microstrip Filter Using the J-Admittance Inverter Model	p. 524
Summary	p. 529
References	p. 530
15 Advanced EM-Based Design Techniques for Microwave Filters	p. 531
15.1 EM-Based Synthesis Techniques	p. 532
15.2 EM-Based Optimization Techniques	p. 532
15.2.1 Optimization Using an EM Simulator	p. 534
15.2.2 Optimization Using Semi-EM-Based Simulator	p. 535
15.2.3 Optimization Using an EM Simulator with Adaptive Frequency Sampling	p. 537
15.2.4 Optimization Using EM-Based Neural Network Models	p. 538
15.2.5 Optimization Using EM-Based Multidimensional Cauchy Technique	p. 543
15.2.6 Optimization Using EM-Based Fuzzy Logic	p. 544
15.3 EM-Based Advanced Design Techniques	p. 544
15.3.1 Space Mapping Techniques	p. 545
15.3.2 Calibrated Coarse Model (CCM) Techniques	p. 553
15.3.3 Generalized Calibrated Coarse Model Technique for Filter Design	p. 559
Summary	p. 563
References	p. 564
16 Dielectric Resonator Filters	p. 567
16.1 Resonant Frequency Calculation in Dielectric Resonators	p. 568
16.2 Rigorous Analyses of Dielectric Resonators	p. 572
16.2.1 Mode Charts for Dielectric Resonators	p. 574
16.3 Dielectric Resonator Filter Configurations	p. 576
16.4 Design Considerations for Dielectric Resonator Filters	p. 580
16.4.1 Achievable Filter Q Value	p. 580
16.4.2 Spurious Performance of Dielectric Resonator Filters	p. 581
16.4.3 Temperature Drift	p. 582
16.4.4 Power Handling Capability	p. 583
16.5 Other Dielectric Resonator Configurations	p. 583
16.6 Cryogenic Dielectric Resonator Filters	p. 587
16.7 Hybrid Dielectric/Superconductor Filters	p. 589
Summary	p. 592
References	p. 593
17 Allpass Phase and Group Delay Equalizer Networks	p. 595
17.1 Characteristics of Allpass Networks	p. 596
17.2 Lumped-Element Allpass Networks	p. 597
17.2.1 Resistively Terminated Symmetric Lattice Networks	p. 599
17.2.2 Network Realizations	p. 601
17.3 Microwave Allpass Networks	p. 603
17.4 Physical Realization of Allpass Networks	p. 608
17.4.1 Transmission-Type Equalizers	p. 609
17.4.2 Reflection-Type Allpass Networks	p. 609
17.5 Synthesis of Reflection-Type Allpass Networks	p. 610
17.6 Practical Narrowband Reflection-Type Allpass Networks	p. 612
17.6.1 C-Section Allpass Equalizer in Waveguide Structure	p. 613
17.6.2 D-Section Allpass Equalizer in Waveguide Structure	p. 615
17.6.3 Narrowband TEM Reactance Networks	p. 615
17.7 Optimization Criteria for Allpass Networks	p. 616
17.8 Effect of Dissipation	p. 620
17.8.1 Dissipation Loss of a Lumped-Element First-Order Allpass Equalizer	p. 620
17.8.2 Dissipation Loss of a Second-Order Lumped Equalizer	p. 621
17.8.3 Effect of Dissipation in Distributed Allpass Networks	p. 621
17.9 Equalization Tradeoffs	p. 622
Summary	p. 623
References	p. 623
18 Multiplexer Theory and Design	p. 625
18.1 Background	p. 625
18.2 Multiplexer Configurations	p. 627
18.2.1 Hybrid Coupled Approach	p. 627
18.2.2 Circulator-Coupled Approach	p. 629
18.2.3 Directional Filter Approach	p. 630
18.2.4 Manifold-Coupled Approach	p. 630
18.3 RF Channelizers (Demultiplexers)	p. 632
18.3.1 Hybrid Branching Network	p. 633
18.3.2 Circulator-Coupled MUX	p. 634
18.3.3 En Passant Distortion	p. 636
18.4 RF Combiners	p. 638
18.4.1 Circulator-Coupled MUX	p. 640
18.4.2 Hybrid-Coupled Filter Combiner Module (HCFM) Multiplexer	p. 640
18.4.3 Directional Filter Combiner	p. 643
18.4.4 Manifold Multiplexer	p. 645
18.5 Transmit-Receive Diplexers	p. 661
18.5.1 Internal Voltage Levels in Tx/Rx Diplexer Filters	p. 665
Summary	p. 668
References	p. 669
19 Computer-Aided Diagnosis and Tuning of Microwave Filters	p. 671
19.1 Sequential Tuning of Coupled Resonator Filters	p. 672
19.2 Computer-Aided Tuning Based on Circuit Model Parameter Extraction	p. 678
19.3 Computer-Aided Tuning Based on Poles and Zeros of the Input Reflection Coefficient	p. 683
19.4 Time-Domain Tuning	p. 687
19.4.1 Time-Domain Tuning of Resonator Frequencies	p. 688
19.4.2 Time-Domain Tuning of Interresonator Coupling	p. 689
19.4.3 Time-Domain Response of a Golden Filter	p. 691
19.5 Filter Tuning Based on Fuzzy Logic Techniques	p. 692
19.5.1 Description of Fuzzy Logic Systems	p. 693
19.5.2 Steps in Building the FL System	p. 694
19.5.3 Comparison Between Boolean Logic and Fuzzy Logic	p. 697
19.5.4 Applying Fuzzy Logic to Filter Tuning	p. 700
19.6 Automated Setups for Filter Tuning	p. 703
Summary	p. 706
References	p. 707
20 High-Power Considerations in Microwave Filter Networks	p. 711
20.1 Background	p. 711
20.2 High-Power Requirements in Wireless Systems	p. 712
20.3 High-Power Amplifiers (HPAs)	p. 713
20.4 High-Power Breakdown Phenomena	p. 714
20.4.1 Gaseous Breakdown	p. 715
20.4.2 Mean Free Path	p. 715
20.4.3 Diffusion	p. 716
20.4.4 Attachment	p. 716
20.4.5 Breakdown in Air	p. 716
20.4.6 Critical Pressure	p. 717
20.4.7 Power Rating of Waveguides and Coaxial Transmission Lines	p. 719
20.4.8 Derating Factors	p. 720
20.4.9 Impact of Thermal Dissipation on Power-Rating	p. 721
20.5 High-Power Bandpass Filters	p. 722
20.5.1 Bandpass Filters Limited by Thermal Dissipation	p. 723
20.5.2 Bandpass Filters Limited by Voltage Breakdown	p. 724
20.5.3 Filter Prototype Network	p. 724
20.5.4 Lumped To Distributed Scaling	p. 725
20.5.5 Resonator Voltages from Prototype Network	p. 726
20.5.6 Example and Verification Via FEM Simulation	p. 727
20.5.7 Example of High Voltages in a Multiplexer	p. 729
20.6 Multipaction Breakdown	p. 730
20.6.1 Dependence on Vacuum Environment	p. 730
20.6.2 Dependence on Applied RF Voltage	p. 730
20.6.3 Dependence on f x d Product	p. 731
20.6.4 Dependence on Surface Conditions of Materials	p. 732
20.6.5 Detection and Prevention of Multipaction	p. 732
20.6.6 Design Margins in Multipaction	p. 733
20.6.7 Multipactor Breakdown Levels	p. 737
20.7 Passive Intermodulation (PIM) Consideration for High-Power Equipment	p. 739
20.7.1 PIM Measurement	p. 740
20.7.2 PIM Control Guidelines	p. 741
Summary	p. 742
References	p. 743
Appendix A p. 745
Appendix B p. 747
Appendix C p. 749
Appendix D p. 751
Index	p. 753

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