Pierre Jarry, PhD, began his research in the area of microwaves at the University of Limoges in France and at Dublin University in Ireland. He was later appointed professor at the University of Brest (France), where he created and directed the Laboratory of Electronics and Telecommunication Systems, which is affiliated with the French National Science Research Center (CNRS). Dr. Jarry now serves as Professor at the University of Bordeaux (France) and the CNRS laboratory IMS (Intégration du Materiau au Système). His research focuses on the areas of microwave filters, distributed filters, multimode filters, and genetic microwave filters, among others. Jacques Beneat, PhD, is an Assistant Professor at Norwich University in Vermont. His research interests include microwave and filter design, radio propagation measurements, and modeling for emerging wireless networks.

• Foreword xiiiPreface xvPART I MICROWAVE FILTER FUNDAMENTALS 11 Scattering Parameters and ABCD Matrices 31.1 Introduction 31.2 Scattering Matrix of a Two-Port System 41.2.1 Definitions 41.2.2 Computing the S Parameters 61.2.3 S-Parameter Properties 101.3 ABCD Matrix of a Two-Port System 101.3.1 ABCD Matrix of Basic Elements 111.3.2 Cascade and Multiplication Property 121.3.3 Input Impedence of a Loaded Two-Port 141.3.4 Impedance and Admittance Inverters 141.3.5 ABCD-Parameter Properties 171.4 Conversion from Formulation S to ABCD and ABCD to S 181.5 Bisection Theorem for Symmetrical Networks 181.6 Conclusions 21References 212 Approximations and Synthesis 232.1 Introduction 232.2 Ideal Low-Pass Filtering Characteristics 242.3 Functions Approximating the Ideal Low-Pass Magnitude Response 252.3.1 Butterworth Function 252.3.2 Chebyshev Function 262.3.3 Elliptic Function 272.3.4 Generalized Chebyshev (Pseudoelliptic) Function 292.4 Functions Approximating the Ideal Low-Pass Phase Response 302.4.1 Bessel Function 302.4.2 Rhodes Equidistant Linear-Phase Function 312.5 Low-Pass Lumped Ladder Prototypes 322.5.1 General Synthesis Technique 322.5.2 Normalized Low-Pass Ladders 362.6 Impedance and Frequency Scaling 392.6.1 Impedance Scaling 392.6.2 Frequency Scaling 402.7 LC Filter Example 412.8 Impedance and Admittance Inverter Ladders 412.8.1 Low-Pass Prototypes 412.8.2 Scaling Flexibility 422.8.3 Bandpass Ladders 442.8.4 Filter Examples 452.9 Conclusions 46References 463 Waveguides and Transmission Lines 493.1 Introduction 493.2 Rectangular Waveguides and Cavities 493.2.1 Rectangular Waveguides 493.2.2 Rectangular Cavities 523.3 Circular Waveguides and Cavities 533.3.1 Circular Waveguides 533.3.2 Cylindrical Cavities 553.4 Evanescent Modes 563.5 Planar Transmission Lines 573.6 Distributed Circuits 603.7 Conclusions 63References 644 Categorization of Microwave Filters 674.1 Introduction 674.2 Minimum-Phase Microwave Filters 684.2.1 General Design Steps 684.2.2 Minimum-Phase Filter Examples 704.3 Non-Minimum-Phase Symmetrical Response Microwave Filters 704.3.1 General Design Steps 714.3.2 Non-Minimum-Phase Symmetrical Response Filter Examples 734.3.3 Microwave Linear-Phase Filters 734.4 Non-Minimum-Phase Asymmetrical Response Microwave Filters 744.4.1 General Design Steps 744.4.2 Non-Minimum-Phase Asymmetrical Response Filter Examples 774.4.3 Multimode Microwave Filters by Optimization 794.5 Conclusions 79References 80PART II MINIMUM-PHASE FILTERS 835 Capacitive-Gap Filters for Millimeter Waves 855.1 Introduction 855.2 Capacitive-Gap Filters 865.2.1 Capacitive-Gap Filter Structure 865.2.2 Design Procedures 875.2.3 Step-by-Step Design Example 915.2.4 Filter Realizations 935.3 Extension to Millimeter Waves 955.3.1 Millimeter-Wave Technology 955.3.2 Fifth-Order Chebyshev Capacitive-Gap Filter at 35 GHz 965.4 Electromagnetic Characterization of SSS 995.5 Conclusions 102References 1026 Evanescent-Mode Waveguide Filters with Dielectric Inserts 1056.1 Introduction 1056.2 Evanescent-Mode Waveguide Filters 1066.2.1 Scattering and ABCD Descriptions of the Structure 1086.2.2 Equivalent Circuit of the Structure 1106.2.3 Filter Design Procedure 1156.2.4 Design Examples and Realizations 1176.3 Folded Evanescent-Mode Waveguide Filters 1216.3.1 Scattering and ABCD Descriptions of the Additional Elements 1236.3.2 Filter Design Procedure 1256.3.3 Design Examples and Realizations 1256.4 Conclusions 127References 1287 Interdigital Filters 1317.1 Introduction 1317.2 Interdigital Filters 1317.3 Design Method 1357.3.1 Prototype Circuit 1357.3.2 Equivalent Circuit 1377.3.3 Input and Output 1407.3.4 Case of Narrowband Filters 1417.3.5 Frequency Transformation 1417.3.6 Physical Parameters of the Interdigital Filter 1427.4 Design Examples 1457.4.1 Wideband Example 1457.4.2 Narrowband Example 1477.5 Realizations and Measured Performance 1487.6 Conclusions 150References 1518 Combline Filters Implemented in SSS 1538.1 Introduction 1538.2 Combline Filters 1538.3 Design Method 1568.3.1 Prototype Circuit 1568.3.2 Equivalent Circuit 1578.3.3 Input and Output 1598.3.4 Feasibility 1628.3.5 Physical Parameters of the Combline Structure 1628.4 Design Example 1658.5 Realizations and Measured Performance 1688.6 Conclusions 169References 170PART III NON-MINIMUM-PHASE SYMMETRICAL RESPONSE FILTERS 1719 Generalized Interdigital Filters with Conditions on Amplitude and Phase 1739.1 Introduction 1739.2 Generalized Interdigital Filter 1749.3 Simultaneous Amplitude and Phase Functions 1759.3.1 Minimum-Phase Functions with Linear Phase 1759.3.2 Non-Minimum-Phase Functions with Simultaneous Conditions on the Amplitude and Phase 1779.3.3 Synthesis of Non-Minimum-Phase Functions with Simultaneous Conditions on the Amplitude andPhase 1809.4 Design Method 1829.4.1 Even-Mode Equivalent Circuit 1829.4.2 Frequency Transformation 1869.4.3 Physical Parameters of the Interdigital Structure 1879.5 Design Example 1919.6 Realizations and Measured Performance 1949.7 Conclusions 195References 19710 Temperature-Stable Narrowband Monomode TE011 Linear-Phase Filters 19910.1 Introduction 19910.2 TE011 Filters 20010.3 Low-Pass Prototype 20010.3.1 Amplitude 20010.3.2 Delay 20110.3.3 Synthesis of the Low-Pass Prototype 20210.4 Design Method 20410.4.1 Matching the Coupling 20410.4.2 Selecting the Cavities 20710.4.3 Defining the Coupling 20810.5 Design Example 21010.6 Realizations and Measured Performance 21310.6.1 Amplitude and Phase Performance 21310.6.2 Temperature Performance 21410.7 Conclusions 215References 217PART IV NON-MINIMUM-PHASE ASYMMETRICAL RESPONSE FILTERS 21911 Asymmetrical Capacitive-Gap Coupled Line Filters 22111.1 Introduction 22111.2 Capacitive-Gap Coupled Line Filters 22211.3 Synthesis of Low-Pass Asymmetrical Generalized Chebyshev Filters 22211.3.1 In-Line Network 22511.3.2 Analysis of the In-Line Network 22611.3.3 Synthesis of the In-Line Network 22911.3.4 Frequency Transformation 23211.4 Design Method 23311.5 Design Example 23811.6 Realization of the CGCL Filter 24311.7 Conclusions 244References 24512 Asymmetrical Dual-Mode TE102/TE301 Thick Iris Rectangular In-Line Waveguide Filters with Transmission Zeros 24712.1 Introduction 24712.2 TE102/TE301 Filters 24812.3 Synthesis of Low-Pass Asymmetrical Generalized Chebyshev Filters 24812.3.1 Fundamental Element 24912.3.2 Analysis of the In-Line Network 25012.3.3 Synthesis by Simple Extraction Techniques 25212.3.4 Frequency Transformation 25412.4 Design Method 25612.4.1 Equivalent Circuit of Monomode and Bimode Cavities 25612.4.2 Optimization Approach 25612.5 Design Example 26212.6 Realizations and Measured Performance 26612.6.1 Third-Order Filter with One Transmission Zero 26612.6.2 Fourth-Order Filter with Two Transmission Zeros 26812.7 Conclusions 269References 27013 Asymmetrical Cylindrical Dual-Mode Waveguide Filters with Transmission Zeros 27313.1 Introduction 27313.2 Dual-Mode Cylindrical Waveguide Filters 27413.3 Synthesis of Low-Pass Asymmetrical Generalized Chebyshev Filters 27513.3.1 Synthesis From a Cross-Coupled Prototype 27513.3.2 Extracting the Elements from the Chain Matrix 27713.3.3 Coupling Graph and Frequency Transformation 28113.4 Design Method 28413.4.1 Rotation Matrix 28413.4.2 Cruciform Iris 28613.4.3 Physical Parameters of the Irises 29013.5 Realizations and Measured Performance 29213.5.1 Fourth-Order Filter with One Transmission Zero on the Left 29213.5.2 Fourth-Order Filter with Two Ransmission Zeros on the Right 29313.5.3 Sixth-Order Filter with One Transmission Zero on the Right 29513.6 Conclusions 296References 29614 Asymmetrical Multimode Rectangular Building Block Filters Using Genetic Optimization 29914.1 Introduction 29914.2 Multimode Rectangular Waveguide Filters 30014.3 Optimization-Based Design 30214.3.1 Genetic Algorithm 30214.3.2 Example 30814.4 Realizations 31314.4.1 Fourth-Order Filter with Two Transmission Zeros 31314.4.2 Seventh-Order Filter with Four Transmission Zeros 31414.4.3 Extension to a Tenth-Order Filter with Six Transmission Zeros 31814.5 Conclusions 320References 320Appendix 1: Lossless Systems 323Appendix 2: Redundant Elements 325Appendix 3: Modal Analysis of Waveguide Step Discontinuities 328Appendix 4: Trisections with Unity Inverters on the Inside or on the Outside 338Appendix 5: Reference Fields and Scattering Matrices for Multimodal Rectangular Waveguide Filters 340Index 353

Pierre Jarry, PhD, began his research in the area of microwaves at the University of Limoges in France and at Dublin University in Ireland. He was later appointed professor at the University of Brest (France), where he created and directed the Laboratory of Electronics and Telecommunication Systems, which is affiliated with the French National Science Research Center (CNRS). Dr. Jarry now serves as Professor at the University of Bordeaux (France) and the CNRS laboratory IMS (Intégration du Materiau au Système). His research focuses on the areas of microwave filters, distributed filters, multimode filters, and genetic microwave filters, among others. Jacques Beneat, PhD, is an Assistant Professor at Norwich University in Vermont. His research interests include microwave and filter design, radio propagation measurements, and modeling for emerging wireless networks.

• Foreword xiiiPreface xvPART I MICROWAVE FILTER FUNDAMENTALS 11 Scattering Parameters and ABCD Matrices 31.1 Introduction 31.2 Scattering Matrix of a Two-Port System 41.2.1 Definitions 41.2.2 Computing the S Parameters 61.2.3 S-Parameter Properties 101.3 ABCD Matrix of a Two-Port System 101.3.1 ABCD Matrix of Basic Elements 111.3.2 Cascade and Multiplication Property 121.3.3 Input Impedence of a Loaded Two-Port 141.3.4 Impedance and Admittance Inverters 141.3.5 ABCD-Parameter Properties 171.4 Conversion from Formulation S to ABCD and ABCD to S 181.5 Bisection Theorem for Symmetrical Networks 181.6 Conclusions 21References 212 Approximations and Synthesis 232.1 Introduction 232.2 Ideal Low-Pass Filtering Characteristics 242.3 Functions Approximating the Ideal Low-Pass Magnitude Response 252.3.1 Butterworth Function 252.3.2 Chebyshev Function 262.3.3 Elliptic Function 272.3.4 Generalized Chebyshev (Pseudoelliptic) Function 292.4 Functions Approximating the Ideal Low-Pass Phase Response 302.4.1 Bessel Function 302.4.2 Rhodes Equidistant Linear-Phase Function 312.5 Low-Pass Lumped Ladder Prototypes 322.5.1 General Synthesis Technique 322.5.2 Normalized Low-Pass Ladders 362.6 Impedance and Frequency Scaling 392.6.1 Impedance Scaling 392.6.2 Frequency Scaling 402.7 LC Filter Example 412.8 Impedance and Admittance Inverter Ladders 412.8.1 Low-Pass Prototypes 412.8.2 Scaling Flexibility 422.8.3 Bandpass Ladders 442.8.4 Filter Examples 452.9 Conclusions 46References 463 Waveguides and Transmission Lines 493.1 Introduction 493.2 Rectangular Waveguides and Cavities 493.2.1 Rectangular Waveguides 493.2.2 Rectangular Cavities 523.3 Circular Waveguides and Cavities 533.3.1 Circular Waveguides 533.3.2 Cylindrical Cavities 553.4 Evanescent Modes 563.5 Planar Transmission Lines 573.6 Distributed Circuits 603.7 Conclusions 63References 644 Categorization of Microwave Filters 674.1 Introduction 674.2 Minimum-Phase Microwave Filters 684.2.1 General Design Steps 684.2.2 Minimum-Phase Filter Examples 704.3 Non-Minimum-Phase Symmetrical Response Microwave Filters 704.3.1 General Design Steps 714.3.2 Non-Minimum-Phase Symmetrical Response Filter Examples 734.3.3 Microwave Linear-Phase Filters 734.4 Non-Minimum-Phase Asymmetrical Response Microwave Filters 744.4.1 General Design Steps 744.4.2 Non-Minimum-Phase Asymmetrical Response Filter Examples 774.4.3 Multimode Microwave Filters by Optimization 794.5 Conclusions 79References 80PART II MINIMUM-PHASE FILTERS 835 Capacitive-Gap Filters for Millimeter Waves 855.1 Introduction 855.2 Capacitive-Gap Filters 865.2.1 Capacitive-Gap Filter Structure 865.2.2 Design Procedures 875.2.3 Step-by-Step Design Example 915.2.4 Filter Realizations 935.3 Extension to Millimeter Waves 955.3.1 Millimeter-Wave Technology 955.3.2 Fifth-Order Chebyshev Capacitive-Gap Filter at 35 GHz 965.4 Electromagnetic Characterization of SSS 995.5 Conclusions 102References 1026 Evanescent-Mode Waveguide Filters with Dielectric Inserts 1056.1 Introduction 1056.2 Evanescent-Mode Waveguide Filters 1066.2.1 Scattering and ABCD Descriptions of the Structure 1086.2.2 Equivalent Circuit of the Structure 1106.2.3 Filter Design Procedure 1156.2.4 Design Examples and Realizations 1176.3 Folded Evanescent-Mode Waveguide Filters 1216.3.1 Scattering and ABCD Descriptions of the Additional Elements 1236.3.2 Filter Design Procedure 1256.3.3 Design Examples and Realizations 1256.4 Conclusions 127References 1287 Interdigital Filters 1317.1 Introduction 1317.2 Interdigital Filters 1317.3 Design Method 1357.3.1 Prototype Circuit 1357.3.2 Equivalent Circuit 1377.3.3 Input and Output 1407.3.4 Case of Narrowband Filters 1417.3.5 Frequency Transformation 1417.3.6 Physical Parameters of the Interdigital Filter 1427.4 Design Examples 1457.4.1 Wideband Example 1457.4.2 Narrowband Example 1477.5 Realizations and Measured Performance 1487.6 Conclusions 150References 1518 Combline Filters Implemented in SSS 1538.1 Introduction 1538.2 Combline Filters 1538.3 Design Method 1568.3.1 Prototype Circuit 1568.3.2 Equivalent Circuit 1578.3.3 Input and Output 1598.3.4 Feasibility 1628.3.5 Physical Parameters of the Combline Structure 1628.4 Design Example 1658.5 Realizations and Measured Performance 1688.6 Conclusions 169References 170PART III NON-MINIMUM-PHASE SYMMETRICAL RESPONSE FILTERS 1719 Generalized Interdigital Filters with Conditions on Amplitude and Phase 1739.1 Introduction 1739.2 Generalized Interdigital Filter 1749.3 Simultaneous Amplitude and Phase Functions 1759.3.1 Minimum-Phase Functions with Linear Phase 1759.3.2 Non-Minimum-Phase Functions with Simultaneous Conditions on the Amplitude and Phase 1779.3.3 Synthesis of Non-Minimum-Phase Functions with Simultaneous Conditions on the Amplitude andPhase 1809.4 Design Method 1829.4.1 Even-Mode Equivalent Circuit 1829.4.2 Frequency Transformation 1869.4.3 Physical Parameters of the Interdigital Structure 1879.5 Design Example 1919.6 Realizations and Measured Performance 1949.7 Conclusions 195References 19710 Temperature-Stable Narrowband Monomode TE011 Linear-Phase Filters 19910.1 Introduction 19910.2 TE011 Filters 20010.3 Low-Pass Prototype 20010.3.1 Amplitude 20010.3.2 Delay 20110.3.3 Synthesis of the Low-Pass Prototype 20210.4 Design Method 20410.4.1 Matching the Coupling 20410.4.2 Selecting the Cavities 20710.4.3 Defining the Coupling 20810.5 Design Example 21010.6 Realizations and Measured Performance 21310.6.1 Amplitude and Phase Performance 21310.6.2 Temperature Performance 21410.7 Conclusions 215References 217PART IV NON-MINIMUM-PHASE ASYMMETRICAL RESPONSE FILTERS 21911 Asymmetrical Capacitive-Gap Coupled Line Filters 22111.1 Introduction 22111.2 Capacitive-Gap Coupled Line Filters 22211.3 Synthesis of Low-Pass Asymmetrical Generalized Chebyshev Filters 22211.3.1 In-Line Network 22511.3.2 Analysis of the In-Line Network 22611.3.3 Synthesis of the In-Line Network 22911.3.4 Frequency Transformation 23211.4 Design Method 23311.5 Design Example 23811.6 Realization of the CGCL Filter 24311.7 Conclusions 244References 24512 Asymmetrical Dual-Mode TE102/TE301 Thick Iris Rectangular In-Line Waveguide Filters with Transmission Zeros 24712.1 Introduction 24712.2 TE102/TE301 Filters 24812.3 Synthesis of Low-Pass Asymmetrical Generalized Chebyshev Filters 24812.3.1 Fundamental Element 24912.3.2 Analysis of the In-Line Network 25012.3.3 Synthesis by Simple Extraction Techniques 25212.3.4 Frequency Transformation 25412.4 Design Method 25612.4.1 Equivalent Circuit of Monomode and Bimode Cavities 25612.4.2 Optimization Approach 25612.5 Design Example 26212.6 Realizations and Measured Performance 26612.6.1 Third-Order Filter with One Transmission Zero 26612.6.2 Fourth-Order Filter with Two Transmission Zeros 26812.7 Conclusions 269References 27013 Asymmetrical Cylindrical Dual-Mode Waveguide Filters with Transmission Zeros 27313.1 Introduction 27313.2 Dual-Mode Cylindrical Waveguide Filters 27413.3 Synthesis of Low-Pass Asymmetrical Generalized Chebyshev Filters 27513.3.1 Synthesis From a Cross-Coupled Prototype 27513.3.2 Extracting the Elements from the Chain Matrix 27713.3.3 Coupling Graph and Frequency Transformation 28113.4 Design Method 28413.4.1 Rotation Matrix 28413.4.2 Cruciform Iris 28613.4.3 Physical Parameters of the Irises 29013.5 Realizations and Measured Performance 29213.5.1 Fourth-Order Filter with One Transmission Zero on the Left 29213.5.2 Fourth-Order Filter with Two Ransmission Zeros on the Right 29313.5.3 Sixth-Order Filter with One Transmission Zero on the Right 29513.6 Conclusions 296References 29614 Asymmetrical Multimode Rectangular Building Block Filters Using Genetic Optimization 29914.1 Introduction 29914.2 Multimode Rectangular Waveguide Filters 30014.3 Optimization-Based Design 30214.3.1 Genetic Algorithm 30214.3.2 Example 30814.4 Realizations 31314.4.1 Fourth-Order Filter with Two Transmission Zeros 31314.4.2 Seventh-Order Filter with Four Transmission Zeros 31414.4.3 Extension to a Tenth-Order Filter with Six Transmission Zeros 31814.5 Conclusions 320References 320Appendix 1: Lossless Systems 323Appendix 2: Redundant Elements 325Appendix 3: Modal Analysis of Waveguide Step Discontinuities 328Appendix 4: Trisections with Unity Inverters on the Inside or on the Outside 338Appendix 5: Reference Fields and Scattering Matrices for Multimodal Rectangular Waveguide Filters 340Index 353

Pierre Jarry, PhD, began his research in the area of microwaves at the University of Limoges in France and at Dublin University in Ireland. He was later appointed professor at the University of Brest (France), where he created and directed the Laboratory of Electronics and Telecommunication Systems, which is affiliated with the French National Science Research Center (CNRS). Dr. Jarry now serves as Professor at the University of Bordeaux (France) and the CNRS laboratory IMS (Intégration du Materiau au Système). His research focuses on the areas of microwave filters, distributed filters, multimode filters, and genetic microwave filters, among others. Jacques Beneat, PhD, is an Assistant Professor at Norwich University in Vermont. His research interests include microwave and filter design, radio propagation measurements, and modeling for emerging wireless networks.

• Foreword xiiiPreface xvPART I MICROWAVE FILTER FUNDAMENTALS 11 Scattering Parameters and ABCD Matrices 31.1 Introduction 31.2 Scattering Matrix of a Two-Port System 41.2.1 Definitions 41.2.2 Computing the S Parameters 61.2.3 S-Parameter Properties 101.3 ABCD Matrix of a Two-Port System 101.3.1 ABCD Matrix of Basic Elements 111.3.2 Cascade and Multiplication Property 121.3.3 Input Impedence of a Loaded Two-Port 141.3.4 Impedance and Admittance Inverters 141.3.5 ABCD-Parameter Properties 171.4 Conversion from Formulation S to ABCD and ABCD to S 181.5 Bisection Theorem for Symmetrical Networks 181.6 Conclusions 21References 212 Approximations and Synthesis 232.1 Introduction 232.2 Ideal Low-Pass Filtering Characteristics 242.3 Functions Approximating the Ideal Low-Pass Magnitude Response 252.3.1 Butterworth Function 252.3.2 Chebyshev Function 262.3.3 Elliptic Function 272.3.4 Generalized Chebyshev (Pseudoelliptic) Function 292.4 Functions Approximating the Ideal Low-Pass Phase Response 302.4.1 Bessel Function 302.4.2 Rhodes Equidistant Linear-Phase Function 312.5 Low-Pass Lumped Ladder Prototypes 322.5.1 General Synthesis Technique 322.5.2 Normalized Low-Pass Ladders 362.6 Impedance and Frequency Scaling 392.6.1 Impedance Scaling 392.6.2 Frequency Scaling 402.7 LC Filter Example 412.8 Impedance and Admittance Inverter Ladders 412.8.1 Low-Pass Prototypes 412.8.2 Scaling Flexibility 422.8.3 Bandpass Ladders 442.8.4 Filter Examples 452.9 Conclusions 46References 463 Waveguides and Transmission Lines 493.1 Introduction 493.2 Rectangular Waveguides and Cavities 493.2.1 Rectangular Waveguides 493.2.2 Rectangular Cavities 523.3 Circular Waveguides and Cavities 533.3.1 Circular Waveguides 533.3.2 Cylindrical Cavities 553.4 Evanescent Modes 563.5 Planar Transmission Lines 573.6 Distributed Circuits 603.7 Conclusions 63References 644 Categorization of Microwave Filters 674.1 Introduction 674.2 Minimum-Phase Microwave Filters 684.2.1 General Design Steps 684.2.2 Minimum-Phase Filter Examples 704.3 Non-Minimum-Phase Symmetrical Response Microwave Filters 704.3.1 General Design Steps 714.3.2 Non-Minimum-Phase Symmetrical Response Filter Examples 734.3.3 Microwave Linear-Phase Filters 734.4 Non-Minimum-Phase Asymmetrical Response Microwave Filters 744.4.1 General Design Steps 744.4.2 Non-Minimum-Phase Asymmetrical Response Filter Examples 774.4.3 Multimode Microwave Filters by Optimization 794.5 Conclusions 79References 80PART II MINIMUM-PHASE FILTERS 835 Capacitive-Gap Filters for Millimeter Waves 855.1 Introduction 855.2 Capacitive-Gap Filters 865.2.1 Capacitive-Gap Filter Structure 865.2.2 Design Procedures 875.2.3 Step-by-Step Design Example 915.2.4 Filter Realizations 935.3 Extension to Millimeter Waves 955.3.1 Millimeter-Wave Technology 955.3.2 Fifth-Order Chebyshev Capacitive-Gap Filter at 35 GHz 965.4 Electromagnetic Characterization of SSS 995.5 Conclusions 102References 1026 Evanescent-Mode Waveguide Filters with Dielectric Inserts 1056.1 Introduction 1056.2 Evanescent-Mode Waveguide Filters 1066.2.1 Scattering and ABCD Descriptions of the Structure 1086.2.2 Equivalent Circuit of the Structure 1106.2.3 Filter Design Procedure 1156.2.4 Design Examples and Realizations 1176.3 Folded Evanescent-Mode Waveguide Filters 1216.3.1 Scattering and ABCD Descriptions of the Additional Elements 1236.3.2 Filter Design Procedure 1256.3.3 Design Examples and Realizations 1256.4 Conclusions 127References 1287 Interdigital Filters 1317.1 Introduction 1317.2 Interdigital Filters 1317.3 Design Method 1357.3.1 Prototype Circuit 1357.3.2 Equivalent Circuit 1377.3.3 Input and Output 1407.3.4 Case of Narrowband Filters 1417.3.5 Frequency Transformation 1417.3.6 Physical Parameters of the Interdigital Filter 1427.4 Design Examples 1457.4.1 Wideband Example 1457.4.2 Narrowband Example 1477.5 Realizations and Measured Performance 1487.6 Conclusions 150References 1518 Combline Filters Implemented in SSS 1538.1 Introduction 1538.2 Combline Filters 1538.3 Design Method 1568.3.1 Prototype Circuit 1568.3.2 Equivalent Circuit 1578.3.3 Input and Output 1598.3.4 Feasibility 1628.3.5 Physical Parameters of the Combline Structure 1628.4 Design Example 1658.5 Realizations and Measured Performance 1688.6 Conclusions 169References 170PART III NON-MINIMUM-PHASE SYMMETRICAL RESPONSE FILTERS 1719 Generalized Interdigital Filters with Conditions on Amplitude and Phase 1739.1 Introduction 1739.2 Generalized Interdigital Filter 1749.3 Simultaneous Amplitude and Phase Functions 1759.3.1 Minimum-Phase Functions with Linear Phase 1759.3.2 Non-Minimum-Phase Functions with Simultaneous Conditions on the Amplitude and Phase 1779.3.3 Synthesis of Non-Minimum-Phase Functions with Simultaneous Conditions on the Amplitude andPhase 1809.4 Design Method 1829.4.1 Even-Mode Equivalent Circuit 1829.4.2 Frequency Transformation 1869.4.3 Physical Parameters of the Interdigital Structure 1879.5 Design Example 1919.6 Realizations and Measured Performance 1949.7 Conclusions 195References 19710 Temperature-Stable Narrowband Monomode TE011 Linear-Phase Filters 19910.1 Introduction 19910.2 TE011 Filters 20010.3 Low-Pass Prototype 20010.3.1 Amplitude 20010.3.2 Delay 20110.3.3 Synthesis of the Low-Pass Prototype 20210.4 Design Method 20410.4.1 Matching the Coupling 20410.4.2 Selecting the Cavities 20710.4.3 Defining the Coupling 20810.5 Design Example 21010.6 Realizations and Measured Performance 21310.6.1 Amplitude and Phase Performance 21310.6.2 Temperature Performance 21410.7 Conclusions 215References 217PART IV NON-MINIMUM-PHASE ASYMMETRICAL RESPONSE FILTERS 21911 Asymmetrical Capacitive-Gap Coupled Line Filters 22111.1 Introduction 22111.2 Capacitive-Gap Coupled Line Filters 22211.3 Synthesis of Low-Pass Asymmetrical Generalized Chebyshev Filters 22211.3.1 In-Line Network 22511.3.2 Analysis of the In-Line Network 22611.3.3 Synthesis of the In-Line Network 22911.3.4 Frequency Transformation 23211.4 Design Method 23311.5 Design Example 23811.6 Realization of the CGCL Filter 24311.7 Conclusions 244References 24512 Asymmetrical Dual-Mode TE102/TE301 Thick Iris Rectangular In-Line Waveguide Filters with Transmission Zeros 24712.1 Introduction 24712.2 TE102/TE301 Filters 24812.3 Synthesis of Low-Pass Asymmetrical Generalized Chebyshev Filters 24812.3.1 Fundamental Element 24912.3.2 Analysis of the In-Line Network 25012.3.3 Synthesis by Simple Extraction Techniques 25212.3.4 Frequency Transformation 25412.4 Design Method 25612.4.1 Equivalent Circuit of Monomode and Bimode Cavities 25612.4.2 Optimization Approach 25612.5 Design Example 26212.6 Realizations and Measured Performance 26612.6.1 Third-Order Filter with One Transmission Zero 26612.6.2 Fourth-Order Filter with Two Transmission Zeros 26812.7 Conclusions 269References 27013 Asymmetrical Cylindrical Dual-Mode Waveguide Filters with Transmission Zeros 27313.1 Introduction 27313.2 Dual-Mode Cylindrical Waveguide Filters 27413.3 Synthesis of Low-Pass Asymmetrical Generalized Chebyshev Filters 27513.3.1 Synthesis From a Cross-Coupled Prototype 27513.3.2 Extracting the Elements from the Chain Matrix 27713.3.3 Coupling Graph and Frequency Transformation 28113.4 Design Method 28413.4.1 Rotation Matrix 28413.4.2 Cruciform Iris 28613.4.3 Physical Parameters of the Irises 29013.5 Realizations and Measured Performance 29213.5.1 Fourth-Order Filter with One Transmission Zero on the Left 29213.5.2 Fourth-Order Filter with Two Ransmission Zeros on the Right 29313.5.3 Sixth-Order Filter with One Transmission Zero on the Right 29513.6 Conclusions 296References 29614 Asymmetrical Multimode Rectangular Building Block Filters Using Genetic Optimization 29914.1 Introduction 29914.2 Multimode Rectangular Waveguide Filters 30014.3 Optimization-Based Design 30214.3.1 Genetic Algorithm 30214.3.2 Example 30814.4 Realizations 31314.4.1 Fourth-Order Filter with Two Transmission Zeros 31314.4.2 Seventh-Order Filter with Four Transmission Zeros 31414.4.3 Extension to a Tenth-Order Filter with Six Transmission Zeros 31814.5 Conclusions 320References 320Appendix 1: Lossless Systems 323Appendix 2: Redundant Elements 325Appendix 3: Modal Analysis of Waveguide Step Discontinuities 328Appendix 4: Trisections with Unity Inverters on the Inside or on the Outside 338Appendix 5: Reference Fields and Scattering Matrices for Multimodal Rectangular Waveguide Filters 340Index 353