Richard J. Cameron, Chandra M. Kudsia, Raafat R. Mansour
Microwave Filters for Communication Systems (eBook, ePUB)
Fundamentals, Design, and Applications
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Richard J. Cameron, Chandra M. Kudsia, Raafat R. Mansour
Microwave Filters for Communication Systems (eBook, ePUB)
Fundamentals, Design, and Applications
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An in-depth look at the state-of-the-art in microwave filter design, implementation, and optimization Thoroughly revised and expanded, this second edition of the popular reference addresses the many important advances that have taken place in the field since the publication of the first edition and includes new chapters on Multiband Filters, Tunable Filters and a chapter devoted to Practical Considerations and Examples. One of the chief constraints in the evolution of wireless communication systems is the scarcity of the available frequency spectrum, thus making frequency spectrum a primary…mehr
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An in-depth look at the state-of-the-art in microwave filter design, implementation, and optimization Thoroughly revised and expanded, this second edition of the popular reference addresses the many important advances that have taken place in the field since the publication of the first edition and includes new chapters on Multiband Filters, Tunable Filters and a chapter devoted to Practical Considerations and Examples. One of the chief constraints in the evolution of wireless communication systems is the scarcity of the available frequency spectrum, thus making frequency spectrum a primary resource to be judiciously shared and optimally utilized. This fundamental limitation, along with atmospheric conditions and interference have long been drivers of intense research and development in the fields of signal processing and filter networks, the two technologies that govern the information capacity of a given frequency spectrum. Written by distinguished experts with a combined century of industrial and academic experience in the field, Microwave Filters for Communication Systems: * Provides a coherent, accessible description of system requirements and constraints for microwave filters * Covers fundamental considerations in the theory and design of microwave filters and the use of EM techniques to analyze and optimize filter structures * Chapters on Multiband Filters and Tunable Filters address the new markets emerging for wireless communication systems and flexible satellite payloads and * A chapter devoted to real-world examples and exercises that allow readers to test and fine-tune their grasp of the material covered in various chapters, in effect it provides the roadmap to develop a software laboratory, to analyze, design, and perform system level tradeoffs including EM based tolerance and sensitivity analysis for microwave filters and multiplexers for practical applications. Microwave Filters for Communication Systems provides students and practitioners alike with a solid grounding in the theoretical underpinnings of practical microwave filter and its physical realization using state-of-the-art EM-based techniques.
Produktdetails
- Produktdetails
- Verlag: John Wiley & Sons
- Seitenzahl: 928
- Erscheinungstermin: 3. April 2018
- Englisch
- ISBN-13: 9781119292388
- Artikelnr.: 57006924
- Verlag: John Wiley & Sons
- Seitenzahl: 928
- Erscheinungstermin: 3. April 2018
- Englisch
- ISBN-13: 9781119292388
- Artikelnr.: 57006924
Richard J. Cameron, isthe formerTechnical Director at COM DEV International. Visiting Professor at the University of Leeds (UK), and is a Fellow of IEE and IEEE. Chandra M. Kudsia, PhD, is an Adjunct Professor at the University of Waterloo and former Chief Scientist, COM DEV International. He is a Fellow of IEEE, AIAA, CAE, EIC and IETE. Raafat R. Mansour, PhD, is a Professor at the University of Waterloo and a former Director of R&D at COM DEV International. He is a Fellow of IEEE, CAE and EIC.
Preface xxiii 1 Radio Frequency (RF) Filter Networks forWireless
Communications--The SystemPerspective 1 Part I Introduction to a
Communication System, Radio Spectrum, and Information 1 1.1 Model of a
Communication System 1 1.2 Radio Spectrum and its Utilization 6 1.3 Concept
of Information 8 1.4 Communication Channel and Link Budgets 10 Part II
Noise in a Communication Channel 15 1.5 Noise in Communication Systems 15
1.6 Modulation-Demodulation Schemes in a Communication System 32 1.7
Digital Transmission 39 Part III Impact of SystemDesign on the Requirements
of Filter Networks 50 1.8 Communication Channels in a Satellite System 50
1.9 RF Filters in Cellular Systems 62 1.10 UltraWideband (UWB)Wireless
Communication 66 1.11 Impact of System Requirements on RF Filter
Specifications 68 1.12 Impact of Satellite and Cellular Communications on
Filter Technology 72 Summary 72 References 72 Appendix 1A 74
Intermodulation Distortion Summary 74 2 Fundamentals of Circuit Theory
Approximation 75 2.1 Linear Systems 75 2.2 Classification of Systems 76 2.3
Evolution of Electrical Circuits: A Historical Perspective 77 2.4 Network
Equation of Linear Systems in the Time Domain 78 2.5 Network Equation of
Linear Systems in the Frequency-Domain Exponential Driving Function 80 2.6
Steady-State Response of Linear Systems to Sinusoidal Excitations 83 2.7
Circuit Theory Approximation 84 Summary 85 References 86 3 Characterization
of Lossless Lowpass Prototype Filter Functions 87 3.1 The Ideal Filter 87
3.2 Characterization of Polynomial Functions for Doubly Terminated Lossless
Lowpass Prototype Filter Networks 88 3.3 Characteristic Polynomials for
Idealized Lowpass Prototype Networks 93 3.4 Lowpass Prototype
Characteristics 95 3.5 Characteristic Polynomials versus Response Shapes 96
3.6 Classical Prototype Filters 98 3.7 Unified Design Chart (UDC)
Relationships 108 3.8 Lowpass Prototype Circuit Configurations 109 3.9
Effect of Dissipation 113 3.10 Asymmetric Response Filters 115 Summary 118
References 119 Appendix 3A 121 Unified Design Charts 121 4 Computer-Aided
Synthesis of Characteristic Polynomials 129 4.1 Objective Function and
Constraints for Symmetric Lowpass Prototype Filter Networks 129 4.2
Analytic Gradients of the Objective Function 131 4.3 Optimization Criteria
for Classical Filters 134 4.4 Generation of Novel Classes of Filter
Functions 136 4.5 Asymmetric Class of Filters 138 4.6 Linear Phase Filters
142 4.7 Critical Frequencies for Selected Filter Functions 143 Summary 144
References 144 Appendix 4A 145 5 Analysis of Multiport Microwave Networks
147 5.1 Matrix Representation of Two-Port Networks 147 5.2 Cascade of Two
Networks 160 5.3 Multiport Networks 167 5.4 Analysis of Multiport Networks
169 Summary 174 References 175 6 Synthesis of a General Class of the
Chebyshev Filter Function 177 6.1 Polynomial Forms of the Transfer and
Reflection Parameters S21(S) and S11(S) for a Two-port network 177 6.2
Alternating Pole Method for the Determination of the Denominator Polynomial
E(S) 186 6.3 General Polynomial SynthesisMethods for Chebyshev Filter
Functions 189 6.4 Predistorted Filter Characteristics 200 6.5
Transformation for Symmetric Dual-Passband Filters 208 Summary 211
References 211 Appendix 6A 212 Complex Terminating Impedances in Multiport
Networks 212 6A.1 Change of Termination Impedance 213 References 213 7
Synthesis of Network-Circuit Approach 215 7.1 Circuit Synthesis Approach
216 7.2 Lowpass Prototype Circuits for Coupled-Resonator Microwave Bandpass
Filters 221 7.3 Ladder Network Synthesis 229 7.4 Synthesis Example of an
Asymmetric (4-2) Filter Network 235 Summary 244 References 245 8 Synthesis
of Networks: Direct Coupling Matrix SynthesisMethods 247 8.1 The Coupling
Matrix 247 8.2 Direct Synthesis of the Coupling Matrix 258 8.3 Coupling
Matrix Reduction 261 8.4 Synthesis of the N + 2 Coupling Matrix 268 8.5
Even- and Odd-Mode Coupling Matrix Synthesis Technique: the Folded Lattice
Array 282 Summary 292 References 293 9 Reconfiguration of the Folded
Coupling Matrix 295 9.1 Symmetric Realizations for Dual-Mode Filters 295
9.2 Asymmetric Realizations for Symmetric Characteristics 300 9.3
"Pfitzenmaier" Configurations 301 9.4 Cascaded Quartets (CQs): Two Quartets
in Cascade for Degrees Eight and Above 304 9.5 Parallel-Connected Two-Port
Networks 306 9.6 Cul-de-Sac Configuration 311 Summary 321 References 321 10
Synthesis and Application of Extracted Pole and Trisection Elements 323
10.1 Extracted Pole Filter Synthesis 323 10.2 Synthesis of Bandstop Filters
Using the Extracted Pole Technique 335 10.2.1 Direct-Coupled Bandstop
Filters 338 10.2.1.1 Cul-de-Sac Forms for the Direct-Coupled Bandstop
Matrix 341 10.3 Trisections 343 10.4 Box Section and Extended Box
Configurations 361 Summary 371 References 371 11 Microwave Resonators 373
11.1 Microwave Resonator Configurations 373 11.2 Calculation of Resonant
Frequency 376 11.3 Resonator Unloaded Q Factor 383 11.4 Measurement of
Loaded and Unloaded Q Factor 387 Summary 393 References 393 12 Waveguide
and Coaxial Lowpass Filters 395 12.1 Commensurate-Line Building Elements
395 12.2 Lowpass Prototype Transfer Polynomials 396 12.3 Synthesis and
Realization of the Distributed Stepped Impedance Lowpass Filter 401 12.4
Short-Step Transformers 410 12.5 Synthesis and Realization of Mixed
Lumped/Distributed Lowpass Filters 411 Summary 425 References 426 13
Waveguide Realization of Single- and Dual-Mode Resonator Filters 427 13.1
Synthesis Process 428 13.2 Design of the Filter Function 428 13.3
Realization and Analysis of the Microwave Filter Network 434 13.4 Dual-Mode
Filters 440 13.5 Coupling Sign Correction 442 13.6 Dual-Mode Realizations
for Some Typical Coupling Matrix Configurations 444 13.7 Phase- and
Direct-Coupled Extracted Pole Filters 447 13.8 The "Full-Inductive"
Dual-Mode Filter 450 Summary 454 References 454 14 Design and Physical
Realization of Coupled Resonator Filters 457 14.1 Circuit Models for
Chebyshev Bandpass Filters 459 14.2 Calculation of Interresonator Coupling
463 14.3 Calculation of Input/Output Coupling 467 14.4 Design Example of
Dielectric Resonator Filters Using the Coupling Matrix Model 468 14.5
Design Example of aWaveguide Iris Filter Using the Impedance InverterModel
475 14.6 Design Example of a Microstrip Filter Using the J-Admittance
InverterModel 478 Summary 483 References 484 15 Advanced EM-Based Design
Techniques for Microwave Filters 485 15.1 EM-Based Synthesis Techniques 485
15.2 EM-Based Optimization Techniques 486 15.3 EM-Based Advanced Design
Techniques 496 Summary 513 References 514 16 Dielectric Resonator Filters
517 16.1 Resonant Frequency Calculation in Dielectric Resonators 517 16.2
Rigorous Analyses of Dielectric Resonators 521 16.3 Dielectric Resonator
Filter Configurations 524 16.4 Design Considerations for Dielectric
Resonator Filters 528 16.5 Other Dielectric Resonator Configurations 531
16.6 Cryogenic Dielectric Resonator Filters 534 16.7 Hybrid
Dielectric/Superconductor Filters 536 16.8 Miniature Dielectric Resonators
538 Summary 542 References 543 17 Allpass Phase and Group Delay Equalizer
Networks 545 17.1 Characteristics of Allpass Networks 545 17.2
Lumped-Element Allpass Networks 547 17.3 Microwave Allpass Networks 551
17.4 Physical Realization of Allpass Networks 554 17.5 Synthesis of
Reflection-Type Allpass Networks 557 17.6 Practical Narrowband
Reflection-Type Allpass Networks 558 17.7 Optimization Criteria for Allpass
Networks 561 17.8 Dissipation Loss 566 17.9 Equalization Tradeoffs 567
Summary 567 References 568 18 Multiplexer Theory and Design 569 18.1
Background 569 18.2 Multiplexer Configurations 571 18.3 RF Channelizers
(Demultiplexers) 575 18.4 RF Combiners 581 18.5 Transmit-Receive Diplexers
601 Summary 606 References 607 19 Computer-Aided Diagnosis and Tuning of
Microwave Filters 609 19.1 Sequential Tuning of Coupled Resonator Filters
610 19.2 Computer-Aided Tuning Based on Circuit Model Parameter Extraction
615 19.3 Computer-Aided Tuning Based on Poles and Zeros of the Input
Reflection Coefficient 619 19.4 Time-Domain Tuning 622 19.5 Filter Tuning
Based on Fuzzy Logic Techniques 627 19.6 Automated Setups for Filter Tuning
637 Summary 639 References 640 20 High-Power Considerations in Microwave
Filter Networks 643 20.1 Background 643 20.2 High-Power Requirements
inWireless Systems 643 20.3 High-Power Amplifiers (HPAs) 645 20.4 Gas
Discharge 645 20.5 Multipaction Breakdown 651 20.6 High-Power Bandpass
Filters 662 20.7 Passive Intermodulation (PIM) Consideration for High-Power
Equipment 670 Summary 674 Acknowledgment 675 References 675 21 Multiband
Filters 679 21.1 Introduction 679 21.2 Approach I: Multiband Filters
Realized by Having Transmission Zeros Inside the Passband of a Bandpass
Filter 681 21.3 Approach II: Multiband Filters Employing Multimode
Resonators 683 21.4 Approach III: Multiband Filters Using Parallel
Connected Filters 700 21.5 Approach IV: Multiband Filter Implemented Using
Notch Filters Connected in Cascade with aWideband Bandpass 701 21.6 Use of
Dual-Band Filters in Diplexer and Multiplexer Applications 703 21.7
Synthesis of Multiband Filters 705 Summary 727 References 728 22 Tunable
Filters 731 22.1 Introduction 731 22.2 Major Challenges in Realizing High-Q
3D Tunable Filters 733 22.3 Combline Tunable Filters 734 22.4 Tunable
Dielectric Resonator Filters 752 22.5 Waveguide Tunable Filters 772 22.6
Filters with Tunable Bandwidth 776 Summary 778 References 779 23 Practical
Considerations and Design Examples 785 ChandraM. Kudsia, Vicente E. Boria,
and Santiago Cogollos 23.1 System Considerations for Filter Specifications
in Communication Systems 785 23.2 Filter Synthesis Techniques and
Topologies 796 23.3 Multiplexers 827 23.4 High-Power Considerations 839
23.5 Tolerance and Sensitivity Analysis in Filter Design 851 Summary 858
Acknowledgments 858 Appendix 23A 858 Thermal Expansion 858 References 859 A
Physical Constants 861 B Conductivities of Metals 863 C Dielectric
Constants and Loss Tangents of Some Materials 865 D RectangularWaveguide
Designation 867 E Impedance and Admittance Inverters 869 E.1 Filter
Realization with Series Elements 869 E.2 Normalization of the Element
Values 872 E.3 General Lowpass Prototype Case 873 E.4 Bandpass Prototype
874 References 878 Index 879
Communications--The SystemPerspective 1 Part I Introduction to a
Communication System, Radio Spectrum, and Information 1 1.1 Model of a
Communication System 1 1.2 Radio Spectrum and its Utilization 6 1.3 Concept
of Information 8 1.4 Communication Channel and Link Budgets 10 Part II
Noise in a Communication Channel 15 1.5 Noise in Communication Systems 15
1.6 Modulation-Demodulation Schemes in a Communication System 32 1.7
Digital Transmission 39 Part III Impact of SystemDesign on the Requirements
of Filter Networks 50 1.8 Communication Channels in a Satellite System 50
1.9 RF Filters in Cellular Systems 62 1.10 UltraWideband (UWB)Wireless
Communication 66 1.11 Impact of System Requirements on RF Filter
Specifications 68 1.12 Impact of Satellite and Cellular Communications on
Filter Technology 72 Summary 72 References 72 Appendix 1A 74
Intermodulation Distortion Summary 74 2 Fundamentals of Circuit Theory
Approximation 75 2.1 Linear Systems 75 2.2 Classification of Systems 76 2.3
Evolution of Electrical Circuits: A Historical Perspective 77 2.4 Network
Equation of Linear Systems in the Time Domain 78 2.5 Network Equation of
Linear Systems in the Frequency-Domain Exponential Driving Function 80 2.6
Steady-State Response of Linear Systems to Sinusoidal Excitations 83 2.7
Circuit Theory Approximation 84 Summary 85 References 86 3 Characterization
of Lossless Lowpass Prototype Filter Functions 87 3.1 The Ideal Filter 87
3.2 Characterization of Polynomial Functions for Doubly Terminated Lossless
Lowpass Prototype Filter Networks 88 3.3 Characteristic Polynomials for
Idealized Lowpass Prototype Networks 93 3.4 Lowpass Prototype
Characteristics 95 3.5 Characteristic Polynomials versus Response Shapes 96
3.6 Classical Prototype Filters 98 3.7 Unified Design Chart (UDC)
Relationships 108 3.8 Lowpass Prototype Circuit Configurations 109 3.9
Effect of Dissipation 113 3.10 Asymmetric Response Filters 115 Summary 118
References 119 Appendix 3A 121 Unified Design Charts 121 4 Computer-Aided
Synthesis of Characteristic Polynomials 129 4.1 Objective Function and
Constraints for Symmetric Lowpass Prototype Filter Networks 129 4.2
Analytic Gradients of the Objective Function 131 4.3 Optimization Criteria
for Classical Filters 134 4.4 Generation of Novel Classes of Filter
Functions 136 4.5 Asymmetric Class of Filters 138 4.6 Linear Phase Filters
142 4.7 Critical Frequencies for Selected Filter Functions 143 Summary 144
References 144 Appendix 4A 145 5 Analysis of Multiport Microwave Networks
147 5.1 Matrix Representation of Two-Port Networks 147 5.2 Cascade of Two
Networks 160 5.3 Multiport Networks 167 5.4 Analysis of Multiport Networks
169 Summary 174 References 175 6 Synthesis of a General Class of the
Chebyshev Filter Function 177 6.1 Polynomial Forms of the Transfer and
Reflection Parameters S21(S) and S11(S) for a Two-port network 177 6.2
Alternating Pole Method for the Determination of the Denominator Polynomial
E(S) 186 6.3 General Polynomial SynthesisMethods for Chebyshev Filter
Functions 189 6.4 Predistorted Filter Characteristics 200 6.5
Transformation for Symmetric Dual-Passband Filters 208 Summary 211
References 211 Appendix 6A 212 Complex Terminating Impedances in Multiport
Networks 212 6A.1 Change of Termination Impedance 213 References 213 7
Synthesis of Network-Circuit Approach 215 7.1 Circuit Synthesis Approach
216 7.2 Lowpass Prototype Circuits for Coupled-Resonator Microwave Bandpass
Filters 221 7.3 Ladder Network Synthesis 229 7.4 Synthesis Example of an
Asymmetric (4-2) Filter Network 235 Summary 244 References 245 8 Synthesis
of Networks: Direct Coupling Matrix SynthesisMethods 247 8.1 The Coupling
Matrix 247 8.2 Direct Synthesis of the Coupling Matrix 258 8.3 Coupling
Matrix Reduction 261 8.4 Synthesis of the N + 2 Coupling Matrix 268 8.5
Even- and Odd-Mode Coupling Matrix Synthesis Technique: the Folded Lattice
Array 282 Summary 292 References 293 9 Reconfiguration of the Folded
Coupling Matrix 295 9.1 Symmetric Realizations for Dual-Mode Filters 295
9.2 Asymmetric Realizations for Symmetric Characteristics 300 9.3
"Pfitzenmaier" Configurations 301 9.4 Cascaded Quartets (CQs): Two Quartets
in Cascade for Degrees Eight and Above 304 9.5 Parallel-Connected Two-Port
Networks 306 9.6 Cul-de-Sac Configuration 311 Summary 321 References 321 10
Synthesis and Application of Extracted Pole and Trisection Elements 323
10.1 Extracted Pole Filter Synthesis 323 10.2 Synthesis of Bandstop Filters
Using the Extracted Pole Technique 335 10.2.1 Direct-Coupled Bandstop
Filters 338 10.2.1.1 Cul-de-Sac Forms for the Direct-Coupled Bandstop
Matrix 341 10.3 Trisections 343 10.4 Box Section and Extended Box
Configurations 361 Summary 371 References 371 11 Microwave Resonators 373
11.1 Microwave Resonator Configurations 373 11.2 Calculation of Resonant
Frequency 376 11.3 Resonator Unloaded Q Factor 383 11.4 Measurement of
Loaded and Unloaded Q Factor 387 Summary 393 References 393 12 Waveguide
and Coaxial Lowpass Filters 395 12.1 Commensurate-Line Building Elements
395 12.2 Lowpass Prototype Transfer Polynomials 396 12.3 Synthesis and
Realization of the Distributed Stepped Impedance Lowpass Filter 401 12.4
Short-Step Transformers 410 12.5 Synthesis and Realization of Mixed
Lumped/Distributed Lowpass Filters 411 Summary 425 References 426 13
Waveguide Realization of Single- and Dual-Mode Resonator Filters 427 13.1
Synthesis Process 428 13.2 Design of the Filter Function 428 13.3
Realization and Analysis of the Microwave Filter Network 434 13.4 Dual-Mode
Filters 440 13.5 Coupling Sign Correction 442 13.6 Dual-Mode Realizations
for Some Typical Coupling Matrix Configurations 444 13.7 Phase- and
Direct-Coupled Extracted Pole Filters 447 13.8 The "Full-Inductive"
Dual-Mode Filter 450 Summary 454 References 454 14 Design and Physical
Realization of Coupled Resonator Filters 457 14.1 Circuit Models for
Chebyshev Bandpass Filters 459 14.2 Calculation of Interresonator Coupling
463 14.3 Calculation of Input/Output Coupling 467 14.4 Design Example of
Dielectric Resonator Filters Using the Coupling Matrix Model 468 14.5
Design Example of aWaveguide Iris Filter Using the Impedance InverterModel
475 14.6 Design Example of a Microstrip Filter Using the J-Admittance
InverterModel 478 Summary 483 References 484 15 Advanced EM-Based Design
Techniques for Microwave Filters 485 15.1 EM-Based Synthesis Techniques 485
15.2 EM-Based Optimization Techniques 486 15.3 EM-Based Advanced Design
Techniques 496 Summary 513 References 514 16 Dielectric Resonator Filters
517 16.1 Resonant Frequency Calculation in Dielectric Resonators 517 16.2
Rigorous Analyses of Dielectric Resonators 521 16.3 Dielectric Resonator
Filter Configurations 524 16.4 Design Considerations for Dielectric
Resonator Filters 528 16.5 Other Dielectric Resonator Configurations 531
16.6 Cryogenic Dielectric Resonator Filters 534 16.7 Hybrid
Dielectric/Superconductor Filters 536 16.8 Miniature Dielectric Resonators
538 Summary 542 References 543 17 Allpass Phase and Group Delay Equalizer
Networks 545 17.1 Characteristics of Allpass Networks 545 17.2
Lumped-Element Allpass Networks 547 17.3 Microwave Allpass Networks 551
17.4 Physical Realization of Allpass Networks 554 17.5 Synthesis of
Reflection-Type Allpass Networks 557 17.6 Practical Narrowband
Reflection-Type Allpass Networks 558 17.7 Optimization Criteria for Allpass
Networks 561 17.8 Dissipation Loss 566 17.9 Equalization Tradeoffs 567
Summary 567 References 568 18 Multiplexer Theory and Design 569 18.1
Background 569 18.2 Multiplexer Configurations 571 18.3 RF Channelizers
(Demultiplexers) 575 18.4 RF Combiners 581 18.5 Transmit-Receive Diplexers
601 Summary 606 References 607 19 Computer-Aided Diagnosis and Tuning of
Microwave Filters 609 19.1 Sequential Tuning of Coupled Resonator Filters
610 19.2 Computer-Aided Tuning Based on Circuit Model Parameter Extraction
615 19.3 Computer-Aided Tuning Based on Poles and Zeros of the Input
Reflection Coefficient 619 19.4 Time-Domain Tuning 622 19.5 Filter Tuning
Based on Fuzzy Logic Techniques 627 19.6 Automated Setups for Filter Tuning
637 Summary 639 References 640 20 High-Power Considerations in Microwave
Filter Networks 643 20.1 Background 643 20.2 High-Power Requirements
inWireless Systems 643 20.3 High-Power Amplifiers (HPAs) 645 20.4 Gas
Discharge 645 20.5 Multipaction Breakdown 651 20.6 High-Power Bandpass
Filters 662 20.7 Passive Intermodulation (PIM) Consideration for High-Power
Equipment 670 Summary 674 Acknowledgment 675 References 675 21 Multiband
Filters 679 21.1 Introduction 679 21.2 Approach I: Multiband Filters
Realized by Having Transmission Zeros Inside the Passband of a Bandpass
Filter 681 21.3 Approach II: Multiband Filters Employing Multimode
Resonators 683 21.4 Approach III: Multiband Filters Using Parallel
Connected Filters 700 21.5 Approach IV: Multiband Filter Implemented Using
Notch Filters Connected in Cascade with aWideband Bandpass 701 21.6 Use of
Dual-Band Filters in Diplexer and Multiplexer Applications 703 21.7
Synthesis of Multiband Filters 705 Summary 727 References 728 22 Tunable
Filters 731 22.1 Introduction 731 22.2 Major Challenges in Realizing High-Q
3D Tunable Filters 733 22.3 Combline Tunable Filters 734 22.4 Tunable
Dielectric Resonator Filters 752 22.5 Waveguide Tunable Filters 772 22.6
Filters with Tunable Bandwidth 776 Summary 778 References 779 23 Practical
Considerations and Design Examples 785 ChandraM. Kudsia, Vicente E. Boria,
and Santiago Cogollos 23.1 System Considerations for Filter Specifications
in Communication Systems 785 23.2 Filter Synthesis Techniques and
Topologies 796 23.3 Multiplexers 827 23.4 High-Power Considerations 839
23.5 Tolerance and Sensitivity Analysis in Filter Design 851 Summary 858
Acknowledgments 858 Appendix 23A 858 Thermal Expansion 858 References 859 A
Physical Constants 861 B Conductivities of Metals 863 C Dielectric
Constants and Loss Tangents of Some Materials 865 D RectangularWaveguide
Designation 867 E Impedance and Admittance Inverters 869 E.1 Filter
Realization with Series Elements 869 E.2 Normalization of the Element
Values 872 E.3 General Lowpass Prototype Case 873 E.4 Bandpass Prototype
874 References 878 Index 879
Preface xxiii 1 Radio Frequency (RF) Filter Networks forWireless
Communications--The SystemPerspective 1 Part I Introduction to a
Communication System, Radio Spectrum, and Information 1 1.1 Model of a
Communication System 1 1.2 Radio Spectrum and its Utilization 6 1.3 Concept
of Information 8 1.4 Communication Channel and Link Budgets 10 Part II
Noise in a Communication Channel 15 1.5 Noise in Communication Systems 15
1.6 Modulation-Demodulation Schemes in a Communication System 32 1.7
Digital Transmission 39 Part III Impact of SystemDesign on the Requirements
of Filter Networks 50 1.8 Communication Channels in a Satellite System 50
1.9 RF Filters in Cellular Systems 62 1.10 UltraWideband (UWB)Wireless
Communication 66 1.11 Impact of System Requirements on RF Filter
Specifications 68 1.12 Impact of Satellite and Cellular Communications on
Filter Technology 72 Summary 72 References 72 Appendix 1A 74
Intermodulation Distortion Summary 74 2 Fundamentals of Circuit Theory
Approximation 75 2.1 Linear Systems 75 2.2 Classification of Systems 76 2.3
Evolution of Electrical Circuits: A Historical Perspective 77 2.4 Network
Equation of Linear Systems in the Time Domain 78 2.5 Network Equation of
Linear Systems in the Frequency-Domain Exponential Driving Function 80 2.6
Steady-State Response of Linear Systems to Sinusoidal Excitations 83 2.7
Circuit Theory Approximation 84 Summary 85 References 86 3 Characterization
of Lossless Lowpass Prototype Filter Functions 87 3.1 The Ideal Filter 87
3.2 Characterization of Polynomial Functions for Doubly Terminated Lossless
Lowpass Prototype Filter Networks 88 3.3 Characteristic Polynomials for
Idealized Lowpass Prototype Networks 93 3.4 Lowpass Prototype
Characteristics 95 3.5 Characteristic Polynomials versus Response Shapes 96
3.6 Classical Prototype Filters 98 3.7 Unified Design Chart (UDC)
Relationships 108 3.8 Lowpass Prototype Circuit Configurations 109 3.9
Effect of Dissipation 113 3.10 Asymmetric Response Filters 115 Summary 118
References 119 Appendix 3A 121 Unified Design Charts 121 4 Computer-Aided
Synthesis of Characteristic Polynomials 129 4.1 Objective Function and
Constraints for Symmetric Lowpass Prototype Filter Networks 129 4.2
Analytic Gradients of the Objective Function 131 4.3 Optimization Criteria
for Classical Filters 134 4.4 Generation of Novel Classes of Filter
Functions 136 4.5 Asymmetric Class of Filters 138 4.6 Linear Phase Filters
142 4.7 Critical Frequencies for Selected Filter Functions 143 Summary 144
References 144 Appendix 4A 145 5 Analysis of Multiport Microwave Networks
147 5.1 Matrix Representation of Two-Port Networks 147 5.2 Cascade of Two
Networks 160 5.3 Multiport Networks 167 5.4 Analysis of Multiport Networks
169 Summary 174 References 175 6 Synthesis of a General Class of the
Chebyshev Filter Function 177 6.1 Polynomial Forms of the Transfer and
Reflection Parameters S21(S) and S11(S) for a Two-port network 177 6.2
Alternating Pole Method for the Determination of the Denominator Polynomial
E(S) 186 6.3 General Polynomial SynthesisMethods for Chebyshev Filter
Functions 189 6.4 Predistorted Filter Characteristics 200 6.5
Transformation for Symmetric Dual-Passband Filters 208 Summary 211
References 211 Appendix 6A 212 Complex Terminating Impedances in Multiport
Networks 212 6A.1 Change of Termination Impedance 213 References 213 7
Synthesis of Network-Circuit Approach 215 7.1 Circuit Synthesis Approach
216 7.2 Lowpass Prototype Circuits for Coupled-Resonator Microwave Bandpass
Filters 221 7.3 Ladder Network Synthesis 229 7.4 Synthesis Example of an
Asymmetric (4-2) Filter Network 235 Summary 244 References 245 8 Synthesis
of Networks: Direct Coupling Matrix SynthesisMethods 247 8.1 The Coupling
Matrix 247 8.2 Direct Synthesis of the Coupling Matrix 258 8.3 Coupling
Matrix Reduction 261 8.4 Synthesis of the N + 2 Coupling Matrix 268 8.5
Even- and Odd-Mode Coupling Matrix Synthesis Technique: the Folded Lattice
Array 282 Summary 292 References 293 9 Reconfiguration of the Folded
Coupling Matrix 295 9.1 Symmetric Realizations for Dual-Mode Filters 295
9.2 Asymmetric Realizations for Symmetric Characteristics 300 9.3
"Pfitzenmaier" Configurations 301 9.4 Cascaded Quartets (CQs): Two Quartets
in Cascade for Degrees Eight and Above 304 9.5 Parallel-Connected Two-Port
Networks 306 9.6 Cul-de-Sac Configuration 311 Summary 321 References 321 10
Synthesis and Application of Extracted Pole and Trisection Elements 323
10.1 Extracted Pole Filter Synthesis 323 10.2 Synthesis of Bandstop Filters
Using the Extracted Pole Technique 335 10.2.1 Direct-Coupled Bandstop
Filters 338 10.2.1.1 Cul-de-Sac Forms for the Direct-Coupled Bandstop
Matrix 341 10.3 Trisections 343 10.4 Box Section and Extended Box
Configurations 361 Summary 371 References 371 11 Microwave Resonators 373
11.1 Microwave Resonator Configurations 373 11.2 Calculation of Resonant
Frequency 376 11.3 Resonator Unloaded Q Factor 383 11.4 Measurement of
Loaded and Unloaded Q Factor 387 Summary 393 References 393 12 Waveguide
and Coaxial Lowpass Filters 395 12.1 Commensurate-Line Building Elements
395 12.2 Lowpass Prototype Transfer Polynomials 396 12.3 Synthesis and
Realization of the Distributed Stepped Impedance Lowpass Filter 401 12.4
Short-Step Transformers 410 12.5 Synthesis and Realization of Mixed
Lumped/Distributed Lowpass Filters 411 Summary 425 References 426 13
Waveguide Realization of Single- and Dual-Mode Resonator Filters 427 13.1
Synthesis Process 428 13.2 Design of the Filter Function 428 13.3
Realization and Analysis of the Microwave Filter Network 434 13.4 Dual-Mode
Filters 440 13.5 Coupling Sign Correction 442 13.6 Dual-Mode Realizations
for Some Typical Coupling Matrix Configurations 444 13.7 Phase- and
Direct-Coupled Extracted Pole Filters 447 13.8 The "Full-Inductive"
Dual-Mode Filter 450 Summary 454 References 454 14 Design and Physical
Realization of Coupled Resonator Filters 457 14.1 Circuit Models for
Chebyshev Bandpass Filters 459 14.2 Calculation of Interresonator Coupling
463 14.3 Calculation of Input/Output Coupling 467 14.4 Design Example of
Dielectric Resonator Filters Using the Coupling Matrix Model 468 14.5
Design Example of aWaveguide Iris Filter Using the Impedance InverterModel
475 14.6 Design Example of a Microstrip Filter Using the J-Admittance
InverterModel 478 Summary 483 References 484 15 Advanced EM-Based Design
Techniques for Microwave Filters 485 15.1 EM-Based Synthesis Techniques 485
15.2 EM-Based Optimization Techniques 486 15.3 EM-Based Advanced Design
Techniques 496 Summary 513 References 514 16 Dielectric Resonator Filters
517 16.1 Resonant Frequency Calculation in Dielectric Resonators 517 16.2
Rigorous Analyses of Dielectric Resonators 521 16.3 Dielectric Resonator
Filter Configurations 524 16.4 Design Considerations for Dielectric
Resonator Filters 528 16.5 Other Dielectric Resonator Configurations 531
16.6 Cryogenic Dielectric Resonator Filters 534 16.7 Hybrid
Dielectric/Superconductor Filters 536 16.8 Miniature Dielectric Resonators
538 Summary 542 References 543 17 Allpass Phase and Group Delay Equalizer
Networks 545 17.1 Characteristics of Allpass Networks 545 17.2
Lumped-Element Allpass Networks 547 17.3 Microwave Allpass Networks 551
17.4 Physical Realization of Allpass Networks 554 17.5 Synthesis of
Reflection-Type Allpass Networks 557 17.6 Practical Narrowband
Reflection-Type Allpass Networks 558 17.7 Optimization Criteria for Allpass
Networks 561 17.8 Dissipation Loss 566 17.9 Equalization Tradeoffs 567
Summary 567 References 568 18 Multiplexer Theory and Design 569 18.1
Background 569 18.2 Multiplexer Configurations 571 18.3 RF Channelizers
(Demultiplexers) 575 18.4 RF Combiners 581 18.5 Transmit-Receive Diplexers
601 Summary 606 References 607 19 Computer-Aided Diagnosis and Tuning of
Microwave Filters 609 19.1 Sequential Tuning of Coupled Resonator Filters
610 19.2 Computer-Aided Tuning Based on Circuit Model Parameter Extraction
615 19.3 Computer-Aided Tuning Based on Poles and Zeros of the Input
Reflection Coefficient 619 19.4 Time-Domain Tuning 622 19.5 Filter Tuning
Based on Fuzzy Logic Techniques 627 19.6 Automated Setups for Filter Tuning
637 Summary 639 References 640 20 High-Power Considerations in Microwave
Filter Networks 643 20.1 Background 643 20.2 High-Power Requirements
inWireless Systems 643 20.3 High-Power Amplifiers (HPAs) 645 20.4 Gas
Discharge 645 20.5 Multipaction Breakdown 651 20.6 High-Power Bandpass
Filters 662 20.7 Passive Intermodulation (PIM) Consideration for High-Power
Equipment 670 Summary 674 Acknowledgment 675 References 675 21 Multiband
Filters 679 21.1 Introduction 679 21.2 Approach I: Multiband Filters
Realized by Having Transmission Zeros Inside the Passband of a Bandpass
Filter 681 21.3 Approach II: Multiband Filters Employing Multimode
Resonators 683 21.4 Approach III: Multiband Filters Using Parallel
Connected Filters 700 21.5 Approach IV: Multiband Filter Implemented Using
Notch Filters Connected in Cascade with aWideband Bandpass 701 21.6 Use of
Dual-Band Filters in Diplexer and Multiplexer Applications 703 21.7
Synthesis of Multiband Filters 705 Summary 727 References 728 22 Tunable
Filters 731 22.1 Introduction 731 22.2 Major Challenges in Realizing High-Q
3D Tunable Filters 733 22.3 Combline Tunable Filters 734 22.4 Tunable
Dielectric Resonator Filters 752 22.5 Waveguide Tunable Filters 772 22.6
Filters with Tunable Bandwidth 776 Summary 778 References 779 23 Practical
Considerations and Design Examples 785 ChandraM. Kudsia, Vicente E. Boria,
and Santiago Cogollos 23.1 System Considerations for Filter Specifications
in Communication Systems 785 23.2 Filter Synthesis Techniques and
Topologies 796 23.3 Multiplexers 827 23.4 High-Power Considerations 839
23.5 Tolerance and Sensitivity Analysis in Filter Design 851 Summary 858
Acknowledgments 858 Appendix 23A 858 Thermal Expansion 858 References 859 A
Physical Constants 861 B Conductivities of Metals 863 C Dielectric
Constants and Loss Tangents of Some Materials 865 D RectangularWaveguide
Designation 867 E Impedance and Admittance Inverters 869 E.1 Filter
Realization with Series Elements 869 E.2 Normalization of the Element
Values 872 E.3 General Lowpass Prototype Case 873 E.4 Bandpass Prototype
874 References 878 Index 879
Communications--The SystemPerspective 1 Part I Introduction to a
Communication System, Radio Spectrum, and Information 1 1.1 Model of a
Communication System 1 1.2 Radio Spectrum and its Utilization 6 1.3 Concept
of Information 8 1.4 Communication Channel and Link Budgets 10 Part II
Noise in a Communication Channel 15 1.5 Noise in Communication Systems 15
1.6 Modulation-Demodulation Schemes in a Communication System 32 1.7
Digital Transmission 39 Part III Impact of SystemDesign on the Requirements
of Filter Networks 50 1.8 Communication Channels in a Satellite System 50
1.9 RF Filters in Cellular Systems 62 1.10 UltraWideband (UWB)Wireless
Communication 66 1.11 Impact of System Requirements on RF Filter
Specifications 68 1.12 Impact of Satellite and Cellular Communications on
Filter Technology 72 Summary 72 References 72 Appendix 1A 74
Intermodulation Distortion Summary 74 2 Fundamentals of Circuit Theory
Approximation 75 2.1 Linear Systems 75 2.2 Classification of Systems 76 2.3
Evolution of Electrical Circuits: A Historical Perspective 77 2.4 Network
Equation of Linear Systems in the Time Domain 78 2.5 Network Equation of
Linear Systems in the Frequency-Domain Exponential Driving Function 80 2.6
Steady-State Response of Linear Systems to Sinusoidal Excitations 83 2.7
Circuit Theory Approximation 84 Summary 85 References 86 3 Characterization
of Lossless Lowpass Prototype Filter Functions 87 3.1 The Ideal Filter 87
3.2 Characterization of Polynomial Functions for Doubly Terminated Lossless
Lowpass Prototype Filter Networks 88 3.3 Characteristic Polynomials for
Idealized Lowpass Prototype Networks 93 3.4 Lowpass Prototype
Characteristics 95 3.5 Characteristic Polynomials versus Response Shapes 96
3.6 Classical Prototype Filters 98 3.7 Unified Design Chart (UDC)
Relationships 108 3.8 Lowpass Prototype Circuit Configurations 109 3.9
Effect of Dissipation 113 3.10 Asymmetric Response Filters 115 Summary 118
References 119 Appendix 3A 121 Unified Design Charts 121 4 Computer-Aided
Synthesis of Characteristic Polynomials 129 4.1 Objective Function and
Constraints for Symmetric Lowpass Prototype Filter Networks 129 4.2
Analytic Gradients of the Objective Function 131 4.3 Optimization Criteria
for Classical Filters 134 4.4 Generation of Novel Classes of Filter
Functions 136 4.5 Asymmetric Class of Filters 138 4.6 Linear Phase Filters
142 4.7 Critical Frequencies for Selected Filter Functions 143 Summary 144
References 144 Appendix 4A 145 5 Analysis of Multiport Microwave Networks
147 5.1 Matrix Representation of Two-Port Networks 147 5.2 Cascade of Two
Networks 160 5.3 Multiport Networks 167 5.4 Analysis of Multiport Networks
169 Summary 174 References 175 6 Synthesis of a General Class of the
Chebyshev Filter Function 177 6.1 Polynomial Forms of the Transfer and
Reflection Parameters S21(S) and S11(S) for a Two-port network 177 6.2
Alternating Pole Method for the Determination of the Denominator Polynomial
E(S) 186 6.3 General Polynomial SynthesisMethods for Chebyshev Filter
Functions 189 6.4 Predistorted Filter Characteristics 200 6.5
Transformation for Symmetric Dual-Passband Filters 208 Summary 211
References 211 Appendix 6A 212 Complex Terminating Impedances in Multiport
Networks 212 6A.1 Change of Termination Impedance 213 References 213 7
Synthesis of Network-Circuit Approach 215 7.1 Circuit Synthesis Approach
216 7.2 Lowpass Prototype Circuits for Coupled-Resonator Microwave Bandpass
Filters 221 7.3 Ladder Network Synthesis 229 7.4 Synthesis Example of an
Asymmetric (4-2) Filter Network 235 Summary 244 References 245 8 Synthesis
of Networks: Direct Coupling Matrix SynthesisMethods 247 8.1 The Coupling
Matrix 247 8.2 Direct Synthesis of the Coupling Matrix 258 8.3 Coupling
Matrix Reduction 261 8.4 Synthesis of the N + 2 Coupling Matrix 268 8.5
Even- and Odd-Mode Coupling Matrix Synthesis Technique: the Folded Lattice
Array 282 Summary 292 References 293 9 Reconfiguration of the Folded
Coupling Matrix 295 9.1 Symmetric Realizations for Dual-Mode Filters 295
9.2 Asymmetric Realizations for Symmetric Characteristics 300 9.3
"Pfitzenmaier" Configurations 301 9.4 Cascaded Quartets (CQs): Two Quartets
in Cascade for Degrees Eight and Above 304 9.5 Parallel-Connected Two-Port
Networks 306 9.6 Cul-de-Sac Configuration 311 Summary 321 References 321 10
Synthesis and Application of Extracted Pole and Trisection Elements 323
10.1 Extracted Pole Filter Synthesis 323 10.2 Synthesis of Bandstop Filters
Using the Extracted Pole Technique 335 10.2.1 Direct-Coupled Bandstop
Filters 338 10.2.1.1 Cul-de-Sac Forms for the Direct-Coupled Bandstop
Matrix 341 10.3 Trisections 343 10.4 Box Section and Extended Box
Configurations 361 Summary 371 References 371 11 Microwave Resonators 373
11.1 Microwave Resonator Configurations 373 11.2 Calculation of Resonant
Frequency 376 11.3 Resonator Unloaded Q Factor 383 11.4 Measurement of
Loaded and Unloaded Q Factor 387 Summary 393 References 393 12 Waveguide
and Coaxial Lowpass Filters 395 12.1 Commensurate-Line Building Elements
395 12.2 Lowpass Prototype Transfer Polynomials 396 12.3 Synthesis and
Realization of the Distributed Stepped Impedance Lowpass Filter 401 12.4
Short-Step Transformers 410 12.5 Synthesis and Realization of Mixed
Lumped/Distributed Lowpass Filters 411 Summary 425 References 426 13
Waveguide Realization of Single- and Dual-Mode Resonator Filters 427 13.1
Synthesis Process 428 13.2 Design of the Filter Function 428 13.3
Realization and Analysis of the Microwave Filter Network 434 13.4 Dual-Mode
Filters 440 13.5 Coupling Sign Correction 442 13.6 Dual-Mode Realizations
for Some Typical Coupling Matrix Configurations 444 13.7 Phase- and
Direct-Coupled Extracted Pole Filters 447 13.8 The "Full-Inductive"
Dual-Mode Filter 450 Summary 454 References 454 14 Design and Physical
Realization of Coupled Resonator Filters 457 14.1 Circuit Models for
Chebyshev Bandpass Filters 459 14.2 Calculation of Interresonator Coupling
463 14.3 Calculation of Input/Output Coupling 467 14.4 Design Example of
Dielectric Resonator Filters Using the Coupling Matrix Model 468 14.5
Design Example of aWaveguide Iris Filter Using the Impedance InverterModel
475 14.6 Design Example of a Microstrip Filter Using the J-Admittance
InverterModel 478 Summary 483 References 484 15 Advanced EM-Based Design
Techniques for Microwave Filters 485 15.1 EM-Based Synthesis Techniques 485
15.2 EM-Based Optimization Techniques 486 15.3 EM-Based Advanced Design
Techniques 496 Summary 513 References 514 16 Dielectric Resonator Filters
517 16.1 Resonant Frequency Calculation in Dielectric Resonators 517 16.2
Rigorous Analyses of Dielectric Resonators 521 16.3 Dielectric Resonator
Filter Configurations 524 16.4 Design Considerations for Dielectric
Resonator Filters 528 16.5 Other Dielectric Resonator Configurations 531
16.6 Cryogenic Dielectric Resonator Filters 534 16.7 Hybrid
Dielectric/Superconductor Filters 536 16.8 Miniature Dielectric Resonators
538 Summary 542 References 543 17 Allpass Phase and Group Delay Equalizer
Networks 545 17.1 Characteristics of Allpass Networks 545 17.2
Lumped-Element Allpass Networks 547 17.3 Microwave Allpass Networks 551
17.4 Physical Realization of Allpass Networks 554 17.5 Synthesis of
Reflection-Type Allpass Networks 557 17.6 Practical Narrowband
Reflection-Type Allpass Networks 558 17.7 Optimization Criteria for Allpass
Networks 561 17.8 Dissipation Loss 566 17.9 Equalization Tradeoffs 567
Summary 567 References 568 18 Multiplexer Theory and Design 569 18.1
Background 569 18.2 Multiplexer Configurations 571 18.3 RF Channelizers
(Demultiplexers) 575 18.4 RF Combiners 581 18.5 Transmit-Receive Diplexers
601 Summary 606 References 607 19 Computer-Aided Diagnosis and Tuning of
Microwave Filters 609 19.1 Sequential Tuning of Coupled Resonator Filters
610 19.2 Computer-Aided Tuning Based on Circuit Model Parameter Extraction
615 19.3 Computer-Aided Tuning Based on Poles and Zeros of the Input
Reflection Coefficient 619 19.4 Time-Domain Tuning 622 19.5 Filter Tuning
Based on Fuzzy Logic Techniques 627 19.6 Automated Setups for Filter Tuning
637 Summary 639 References 640 20 High-Power Considerations in Microwave
Filter Networks 643 20.1 Background 643 20.2 High-Power Requirements
inWireless Systems 643 20.3 High-Power Amplifiers (HPAs) 645 20.4 Gas
Discharge 645 20.5 Multipaction Breakdown 651 20.6 High-Power Bandpass
Filters 662 20.7 Passive Intermodulation (PIM) Consideration for High-Power
Equipment 670 Summary 674 Acknowledgment 675 References 675 21 Multiband
Filters 679 21.1 Introduction 679 21.2 Approach I: Multiband Filters
Realized by Having Transmission Zeros Inside the Passband of a Bandpass
Filter 681 21.3 Approach II: Multiband Filters Employing Multimode
Resonators 683 21.4 Approach III: Multiband Filters Using Parallel
Connected Filters 700 21.5 Approach IV: Multiband Filter Implemented Using
Notch Filters Connected in Cascade with aWideband Bandpass 701 21.6 Use of
Dual-Band Filters in Diplexer and Multiplexer Applications 703 21.7
Synthesis of Multiband Filters 705 Summary 727 References 728 22 Tunable
Filters 731 22.1 Introduction 731 22.2 Major Challenges in Realizing High-Q
3D Tunable Filters 733 22.3 Combline Tunable Filters 734 22.4 Tunable
Dielectric Resonator Filters 752 22.5 Waveguide Tunable Filters 772 22.6
Filters with Tunable Bandwidth 776 Summary 778 References 779 23 Practical
Considerations and Design Examples 785 ChandraM. Kudsia, Vicente E. Boria,
and Santiago Cogollos 23.1 System Considerations for Filter Specifications
in Communication Systems 785 23.2 Filter Synthesis Techniques and
Topologies 796 23.3 Multiplexers 827 23.4 High-Power Considerations 839
23.5 Tolerance and Sensitivity Analysis in Filter Design 851 Summary 858
Acknowledgments 858 Appendix 23A 858 Thermal Expansion 858 References 859 A
Physical Constants 861 B Conductivities of Metals 863 C Dielectric
Constants and Loss Tangents of Some Materials 865 D RectangularWaveguide
Designation 867 E Impedance and Admittance Inverters 869 E.1 Filter
Realization with Series Elements 869 E.2 Normalization of the Element
Values 872 E.3 General Lowpass Prototype Case 873 E.4 Bandpass Prototype
874 References 878 Index 879