Pierre Jarry, PhD, is a professor at the University of Bordeaux, France, and also serves the French National Science Research Center (CNRS) laboratory IMS (Intégration du Materiau au Système). Previously he was professor at the University of Brest, Brest, France, where he created and directed the Laboratory of Electronics and Telecommunication Systems, which is affiliated with the CNRS. His research focuses on the areas of microwave filters (localized, distributed, multimode, and genetic), and microwave amplifiers (lumped, distributed and lossy distributed, power, and multi-stage).Jacques N. Beneat, PhD, is Professor of Electrical and Computer Engineering at Norwich University, Vermont, USA. He received his PhD in electrical and computer engineering from Worcester Polytechnic Institute, Massachusetts, USA, with a focus in advanced microwave structures for satellite communications.

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• Foreword viiPreface ixAcknowledgments xiii1 Microwave Amplifier Fundamentals 11.1 Introduction 21.2 Scattering Parameters and Signal Flow Graphs 21.3 Reflection Coefficients 51.4 Gain Expressions 71.5 Stability 91.6 Noise 101.7 ABCD Matrix 141.7.1 ABCD Matrix of a Series Impedance 141.7.2 ABCD Matrix of a Parallel Admittance 151.7.3 Input Impedance of Impedance Loaded Two-Port 151.7.4 Input Admittance of Admittance Loaded Two-Port 161.7.5 ABCD Matrix of the Cascade of Two Systems 161.7.6 ABCD Matrix of the Parallel Connection of Two Systems 171.7.7 ABCD Matrix of the Series Connection of Two Systems 171.7.8 ABCD Matrix of Admittance Loaded Two-Port Connected in Parallel 171.7.9 ABCD Matrix of Impedance Loaded Two-Port Connected in Series 191.7.10 Conversion Between Scattering and ABCD Matrices 191.8 Distributed Network Elements 201.8.1 Uniform Transmission Line 201.8.2 Unit Element 211.8.3 Input Impedance and Input Admittance 221.8.4 Short-Circuited Stub Placed in Series 231.8.5 Short-Circuited Stub Placed in Parallel 241.8.6 Open-Circuited Stub Placed in Series 241.8.7 Open-Circuited Stub Placed in Parallel 251.8.8 Richard’s Transformation 251.8.9 Kuroda Identities 28References 352 Introduction to the Real Frequency Technique: Multistage Lumped Amplifier Design 372.1 Introduction 372.2 Multistage Lumped Amplifier Representation 382.3 Overview of the RFT 402.4 Multistage Transducer Gain 412.5 Multistage VSWR 432.6 Optimization Process 442.6.1 Single-Valued Error and Target Functions 442.6.2 Levenberg–Marquardt–More Optimization 462.7 Design Procedures 482.8 Four-Stage Amplifier Design Example 492.9 Transistor Feedback Block for Broadband Amplifiers 572.9.1 Resistive Adaptation 572.9.2 Resistive Feedback 572.9.3 Reactive Feedback 572.9.4 Transistor Feedback Block 582.10 Realizations 592.10.1 Three-Stage Hybrid Amplifier 592.10.2 Two-Stage Monolithic Amplifier 622.10.3 Single-Stage GaAs Technology Amplifier 64References 643 Multistage Distributed Amplifier Design 673.1 Introduction 673.2 Multistage Distributed Amplifier Representation 683.3 Multistage Transducer Gain 703.4 Multistage VSWR 713.5 Multistage Noise Figure 733.6 Optimization Process 743.7 Transistor Bias Circuit Considerations 753.8 Distributed Equalizer Synthesis 783.8.1 Richard’s Theorem 783.8.2 Stub Extraction 803.8.3 Denormalization 823.8.4 UE Impedances Too Low 833.8.5 UE Impedances Too High 853.9 Design Procedures 883.10 Simulations and Realizations 923.10.1 Three-Stage 2–8 GHz Distributed Amplifier 923.10.2 Three-Stage 1.15–1.5 GHz Distributed Amplifier 943.10.3 Three-Stage 1.15–1.5 GHz Distributed Amplifier (Noncommensurate) 943.10.4 Three-Stage 5.925–6.425 GHz Hybrid Amplifier 96References 994 Multistage Transimpedance Amplifiers 1014.1 Introduction 1014.2 Multistage Transimpedance Amplifier Representation 1024.3 Extension to Distributed Equalizers 1044.4 Multistage Transimpedance Gain 1064.5 Multistage VSWR 1094.6 Optimization Process 1104.7 Design Procedures 1114.8 Noise Model of the Receiver Front End 1144.9 Two-Stage Transimpedance Amplifier Example 116References 1185 Multistage Lossy Distributed Amplifiers 1215.1 Introduction 1215.2 Lossy Distributed Network 1225.3 Multistage Lossy Distributed Amplifier Representation 1275.4 Multistage Transducer Gain 1305.5 Multistage VSWR 1325.6 Optimization Process 1335.7 Synthesis of the Lossy Distributed Network 1355.8 Design Procedures 1415.9 Realizations 1445.9.1 Single-Stage Broadband Hybrid Realization 1445.9.2 Two-Stage Broadband Hybrid Realization 145References 1496 Multistage Power Amplifiers 1516.1 Introduction 1516.2 Multistage Power Amplifier Representation 1526.3 Added Power Optimization 1546.3.1 Requirements for Maximum Added Power 1546.3.2 Two-Dimensional Interpolation 1566.4 Multistage Transducer Gain 1596.5 Multistage VSWR 1626.6 Optimization Process 1636.7 Design Procedures 1646.8 Realizations 1666.8.1 Realization of a One-Stage Power Amplifier 1666.8.2 Realization of a Three-Stages Power Amplifier 1676.9 Linear Power Amplifiers 1726.9.1 Theory 1726.9.2 Arborescent Structures 1756.9.3 Example of an Arborescent Linear Power Amplifier 176References 1797 Multistage Active Microwave Filters 1817.1 Introduction 1817.2 Multistage Active Filter Representation 1827.3 Multistage Transducer Gain 1847.4 Multistage VSWR 1867.5 Multistage Phase and Group Delay 1877.6 Optimization Process 1887.7 Synthesis Procedures 1897.8 Design Procedures 1957.9 Simulations and Realizations 1987.9.1 Two-Stage Low-Pass Active Filter 1987.9.2 Single-Stage Bandpass Active Filter 2007.9.3 Single-Stage Bandpass Active Filter MMIC Realization 202References 2068 Passive Microwave Equalizers for Radar Receiver Design 2078.1 Introduction 2078.2 Equalizer Needs for Radar Application 2088.3 Passive Equalizer Representation 2098.4 Optimization Process 2128.5 Examples of Microwave Equalizers for Radar Receivers 2138.5.1 Sixth-Order Equalizer with No Transmission Zeros 2138.5.2 Sixth-Order Equalizer with Two Transmission Zeros 214References 2179 Synthesis of Microwave Antennas 2199.1 Introduction 2199.2 Antenna Needs 2199.3 Antenna Equalizer Representation 2219.4 Optimization Process 2229.5 Examples of Antenna-Matching Network Designs 2239.5.1 Mid-Band Star Antenna 2239.5.2 Broadband Horn Antenna 224References 227Appendix A: Multistage Transducer Gain 229Appendix B: Levenberg–Marquardt–More Optimization Algorithm 239Appendix C: Noise Correlation Matrix 245Appendix D: Network Synthesis Using the Transfer Matrix 253Index 271

Pierre Jarry, PhD, is a professor at the University of Bordeaux, France, and also serves the French National Science Research Center (CNRS) laboratory IMS (Intégration du Materiau au Système). Previously he was professor at the University of Brest, Brest, France, where he created and directed the Laboratory of Electronics and Telecommunication Systems, which is affiliated with the CNRS. His research focuses on the areas of microwave filters (localized, distributed, multimode, and genetic), and microwave amplifiers (lumped, distributed and lossy distributed, power, and multi-stage).Jacques N. Beneat, PhD, is Professor of Electrical and Computer Engineering at Norwich University, Vermont, USA. He received his PhD in electrical and computer engineering from Worcester Polytechnic Institute, Massachusetts, USA, with a focus in advanced microwave structures for satellite communications.

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• Foreword viiPreface ixAcknowledgments xiii1 Microwave Amplifier Fundamentals 11.1 Introduction 21.2 Scattering Parameters and Signal Flow Graphs 21.3 Reflection Coefficients 51.4 Gain Expressions 71.5 Stability 91.6 Noise 101.7 ABCD Matrix 141.7.1 ABCD Matrix of a Series Impedance 141.7.2 ABCD Matrix of a Parallel Admittance 151.7.3 Input Impedance of Impedance Loaded Two-Port 151.7.4 Input Admittance of Admittance Loaded Two-Port 161.7.5 ABCD Matrix of the Cascade of Two Systems 161.7.6 ABCD Matrix of the Parallel Connection of Two Systems 171.7.7 ABCD Matrix of the Series Connection of Two Systems 171.7.8 ABCD Matrix of Admittance Loaded Two-Port Connected in Parallel 171.7.9 ABCD Matrix of Impedance Loaded Two-Port Connected in Series 191.7.10 Conversion Between Scattering and ABCD Matrices 191.8 Distributed Network Elements 201.8.1 Uniform Transmission Line 201.8.2 Unit Element 211.8.3 Input Impedance and Input Admittance 221.8.4 Short-Circuited Stub Placed in Series 231.8.5 Short-Circuited Stub Placed in Parallel 241.8.6 Open-Circuited Stub Placed in Series 241.8.7 Open-Circuited Stub Placed in Parallel 251.8.8 Richard’s Transformation 251.8.9 Kuroda Identities 28References 352 Introduction to the Real Frequency Technique: Multistage Lumped Amplifier Design 372.1 Introduction 372.2 Multistage Lumped Amplifier Representation 382.3 Overview of the RFT 402.4 Multistage Transducer Gain 412.5 Multistage VSWR 432.6 Optimization Process 442.6.1 Single-Valued Error and Target Functions 442.6.2 Levenberg–Marquardt–More Optimization 462.7 Design Procedures 482.8 Four-Stage Amplifier Design Example 492.9 Transistor Feedback Block for Broadband Amplifiers 572.9.1 Resistive Adaptation 572.9.2 Resistive Feedback 572.9.3 Reactive Feedback 572.9.4 Transistor Feedback Block 582.10 Realizations 592.10.1 Three-Stage Hybrid Amplifier 592.10.2 Two-Stage Monolithic Amplifier 622.10.3 Single-Stage GaAs Technology Amplifier 64References 643 Multistage Distributed Amplifier Design 673.1 Introduction 673.2 Multistage Distributed Amplifier Representation 683.3 Multistage Transducer Gain 703.4 Multistage VSWR 713.5 Multistage Noise Figure 733.6 Optimization Process 743.7 Transistor Bias Circuit Considerations 753.8 Distributed Equalizer Synthesis 783.8.1 Richard’s Theorem 783.8.2 Stub Extraction 803.8.3 Denormalization 823.8.4 UE Impedances Too Low 833.8.5 UE Impedances Too High 853.9 Design Procedures 883.10 Simulations and Realizations 923.10.1 Three-Stage 2–8 GHz Distributed Amplifier 923.10.2 Three-Stage 1.15–1.5 GHz Distributed Amplifier 943.10.3 Three-Stage 1.15–1.5 GHz Distributed Amplifier (Noncommensurate) 943.10.4 Three-Stage 5.925–6.425 GHz Hybrid Amplifier 96References 994 Multistage Transimpedance Amplifiers 1014.1 Introduction 1014.2 Multistage Transimpedance Amplifier Representation 1024.3 Extension to Distributed Equalizers 1044.4 Multistage Transimpedance Gain 1064.5 Multistage VSWR 1094.6 Optimization Process 1104.7 Design Procedures 1114.8 Noise Model of the Receiver Front End 1144.9 Two-Stage Transimpedance Amplifier Example 116References 1185 Multistage Lossy Distributed Amplifiers 1215.1 Introduction 1215.2 Lossy Distributed Network 1225.3 Multistage Lossy Distributed Amplifier Representation 1275.4 Multistage Transducer Gain 1305.5 Multistage VSWR 1325.6 Optimization Process 1335.7 Synthesis of the Lossy Distributed Network 1355.8 Design Procedures 1415.9 Realizations 1445.9.1 Single-Stage Broadband Hybrid Realization 1445.9.2 Two-Stage Broadband Hybrid Realization 145References 1496 Multistage Power Amplifiers 1516.1 Introduction 1516.2 Multistage Power Amplifier Representation 1526.3 Added Power Optimization 1546.3.1 Requirements for Maximum Added Power 1546.3.2 Two-Dimensional Interpolation 1566.4 Multistage Transducer Gain 1596.5 Multistage VSWR 1626.6 Optimization Process 1636.7 Design Procedures 1646.8 Realizations 1666.8.1 Realization of a One-Stage Power Amplifier 1666.8.2 Realization of a Three-Stages Power Amplifier 1676.9 Linear Power Amplifiers 1726.9.1 Theory 1726.9.2 Arborescent Structures 1756.9.3 Example of an Arborescent Linear Power Amplifier 176References 1797 Multistage Active Microwave Filters 1817.1 Introduction 1817.2 Multistage Active Filter Representation 1827.3 Multistage Transducer Gain 1847.4 Multistage VSWR 1867.5 Multistage Phase and Group Delay 1877.6 Optimization Process 1887.7 Synthesis Procedures 1897.8 Design Procedures 1957.9 Simulations and Realizations 1987.9.1 Two-Stage Low-Pass Active Filter 1987.9.2 Single-Stage Bandpass Active Filter 2007.9.3 Single-Stage Bandpass Active Filter MMIC Realization 202References 2068 Passive Microwave Equalizers for Radar Receiver Design 2078.1 Introduction 2078.2 Equalizer Needs for Radar Application 2088.3 Passive Equalizer Representation 2098.4 Optimization Process 2128.5 Examples of Microwave Equalizers for Radar Receivers 2138.5.1 Sixth-Order Equalizer with No Transmission Zeros 2138.5.2 Sixth-Order Equalizer with Two Transmission Zeros 214References 2179 Synthesis of Microwave Antennas 2199.1 Introduction 2199.2 Antenna Needs 2199.3 Antenna Equalizer Representation 2219.4 Optimization Process 2229.5 Examples of Antenna-Matching Network Designs 2239.5.1 Mid-Band Star Antenna 2239.5.2 Broadband Horn Antenna 224References 227Appendix A: Multistage Transducer Gain 229Appendix B: Levenberg–Marquardt–More Optimization Algorithm 239Appendix C: Noise Correlation Matrix 245Appendix D: Network Synthesis Using the Transfer Matrix 253Index 271

Pierre Jarry, PhD, is a professor at the University of Bordeaux, France, and also serves the French National Science Research Center (CNRS) laboratory IMS (Intégration du Materiau au Système). Previously he was professor at the University of Brest, Brest, France, where he created and directed the Laboratory of Electronics and Telecommunication Systems, which is affiliated with the CNRS. His research focuses on the areas of microwave filters (localized, distributed, multimode, and genetic), and microwave amplifiers (lumped, distributed and lossy distributed, power, and multi-stage).Jacques N. Beneat, PhD, is Professor of Electrical and Computer Engineering at Norwich University, Vermont, USA. He received his PhD in electrical and computer engineering from Worcester Polytechnic Institute, Massachusetts, USA, with a focus in advanced microwave structures for satellite communications.

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• Foreword viiPreface ixAcknowledgments xiii1 Microwave Amplifier Fundamentals 11.1 Introduction 21.2 Scattering Parameters and Signal Flow Graphs 21.3 Reflection Coefficients 51.4 Gain Expressions 71.5 Stability 91.6 Noise 101.7 ABCD Matrix 141.7.1 ABCD Matrix of a Series Impedance 141.7.2 ABCD Matrix of a Parallel Admittance 151.7.3 Input Impedance of Impedance Loaded Two-Port 151.7.4 Input Admittance of Admittance Loaded Two-Port 161.7.5 ABCD Matrix of the Cascade of Two Systems 161.7.6 ABCD Matrix of the Parallel Connection of Two Systems 171.7.7 ABCD Matrix of the Series Connection of Two Systems 171.7.8 ABCD Matrix of Admittance Loaded Two-Port Connected in Parallel 171.7.9 ABCD Matrix of Impedance Loaded Two-Port Connected in Series 191.7.10 Conversion Between Scattering and ABCD Matrices 191.8 Distributed Network Elements 201.8.1 Uniform Transmission Line 201.8.2 Unit Element 211.8.3 Input Impedance and Input Admittance 221.8.4 Short-Circuited Stub Placed in Series 231.8.5 Short-Circuited Stub Placed in Parallel 241.8.6 Open-Circuited Stub Placed in Series 241.8.7 Open-Circuited Stub Placed in Parallel 251.8.8 Richard’s Transformation 251.8.9 Kuroda Identities 28References 352 Introduction to the Real Frequency Technique: Multistage Lumped Amplifier Design 372.1 Introduction 372.2 Multistage Lumped Amplifier Representation 382.3 Overview of the RFT 402.4 Multistage Transducer Gain 412.5 Multistage VSWR 432.6 Optimization Process 442.6.1 Single-Valued Error and Target Functions 442.6.2 Levenberg–Marquardt–More Optimization 462.7 Design Procedures 482.8 Four-Stage Amplifier Design Example 492.9 Transistor Feedback Block for Broadband Amplifiers 572.9.1 Resistive Adaptation 572.9.2 Resistive Feedback 572.9.3 Reactive Feedback 572.9.4 Transistor Feedback Block 582.10 Realizations 592.10.1 Three-Stage Hybrid Amplifier 592.10.2 Two-Stage Monolithic Amplifier 622.10.3 Single-Stage GaAs Technology Amplifier 64References 643 Multistage Distributed Amplifier Design 673.1 Introduction 673.2 Multistage Distributed Amplifier Representation 683.3 Multistage Transducer Gain 703.4 Multistage VSWR 713.5 Multistage Noise Figure 733.6 Optimization Process 743.7 Transistor Bias Circuit Considerations 753.8 Distributed Equalizer Synthesis 783.8.1 Richard’s Theorem 783.8.2 Stub Extraction 803.8.3 Denormalization 823.8.4 UE Impedances Too Low 833.8.5 UE Impedances Too High 853.9 Design Procedures 883.10 Simulations and Realizations 923.10.1 Three-Stage 2–8 GHz Distributed Amplifier 923.10.2 Three-Stage 1.15–1.5 GHz Distributed Amplifier 943.10.3 Three-Stage 1.15–1.5 GHz Distributed Amplifier (Noncommensurate) 943.10.4 Three-Stage 5.925–6.425 GHz Hybrid Amplifier 96References 994 Multistage Transimpedance Amplifiers 1014.1 Introduction 1014.2 Multistage Transimpedance Amplifier Representation 1024.3 Extension to Distributed Equalizers 1044.4 Multistage Transimpedance Gain 1064.5 Multistage VSWR 1094.6 Optimization Process 1104.7 Design Procedures 1114.8 Noise Model of the Receiver Front End 1144.9 Two-Stage Transimpedance Amplifier Example 116References 1185 Multistage Lossy Distributed Amplifiers 1215.1 Introduction 1215.2 Lossy Distributed Network 1225.3 Multistage Lossy Distributed Amplifier Representation 1275.4 Multistage Transducer Gain 1305.5 Multistage VSWR 1325.6 Optimization Process 1335.7 Synthesis of the Lossy Distributed Network 1355.8 Design Procedures 1415.9 Realizations 1445.9.1 Single-Stage Broadband Hybrid Realization 1445.9.2 Two-Stage Broadband Hybrid Realization 145References 1496 Multistage Power Amplifiers 1516.1 Introduction 1516.2 Multistage Power Amplifier Representation 1526.3 Added Power Optimization 1546.3.1 Requirements for Maximum Added Power 1546.3.2 Two-Dimensional Interpolation 1566.4 Multistage Transducer Gain 1596.5 Multistage VSWR 1626.6 Optimization Process 1636.7 Design Procedures 1646.8 Realizations 1666.8.1 Realization of a One-Stage Power Amplifier 1666.8.2 Realization of a Three-Stages Power Amplifier 1676.9 Linear Power Amplifiers 1726.9.1 Theory 1726.9.2 Arborescent Structures 1756.9.3 Example of an Arborescent Linear Power Amplifier 176References 1797 Multistage Active Microwave Filters 1817.1 Introduction 1817.2 Multistage Active Filter Representation 1827.3 Multistage Transducer Gain 1847.4 Multistage VSWR 1867.5 Multistage Phase and Group Delay 1877.6 Optimization Process 1887.7 Synthesis Procedures 1897.8 Design Procedures 1957.9 Simulations and Realizations 1987.9.1 Two-Stage Low-Pass Active Filter 1987.9.2 Single-Stage Bandpass Active Filter 2007.9.3 Single-Stage Bandpass Active Filter MMIC Realization 202References 2068 Passive Microwave Equalizers for Radar Receiver Design 2078.1 Introduction 2078.2 Equalizer Needs for Radar Application 2088.3 Passive Equalizer Representation 2098.4 Optimization Process 2128.5 Examples of Microwave Equalizers for Radar Receivers 2138.5.1 Sixth-Order Equalizer with No Transmission Zeros 2138.5.2 Sixth-Order Equalizer with Two Transmission Zeros 214References 2179 Synthesis of Microwave Antennas 2199.1 Introduction 2199.2 Antenna Needs 2199.3 Antenna Equalizer Representation 2219.4 Optimization Process 2229.5 Examples of Antenna-Matching Network Designs 2239.5.1 Mid-Band Star Antenna 2239.5.2 Broadband Horn Antenna 224References 227Appendix A: Multistage Transducer Gain 229Appendix B: Levenberg–Marquardt–More Optimization Algorithm 239Appendix C: Noise Correlation Matrix 245Appendix D: Network Synthesis Using the Transfer Matrix 253Index 271