Broadband direct-coupled and matching RF networks

Description

Contents 1. Introduction 1.1 Purpose 1.2 Overview 1.3 Related Software 1.4 Revisions 2. Fundamentals 2.1 Power Transfer 2.1.1 Complex Source to Complex Load 2.1.2 Generalized Reflection Coefficient 2.1.3 Circle to Circle Mapping 2.1.4 Doubly-Terminated Networks 2.1.5 Singly-Terminated Networks 2.2 Major Response Shapes 2.2.1 Lowpass to Bandpass Transformation 2.2.2 Insertion Loss Behavior 2.2.3 Reflection Coefficient Behavior 2.2.4 Flat Loss 2.2.5 Stopband Ripple 2.2.6 Effects of Component Dissipation 2.3 Significance of Loaded Q 2.3.1 Series-Parallel Conversion 2.3.2 Resonator VA/W 2.3.3 Resonator Efficiency 2.4 Ladder Network Topologies 2.4.1 Lowpass Prototype Networks 2.4.2 Classical Bandpass Prototype Networks 2.4.3 Direct-Coupled Prototype Bandpass Networks 2.4.4 Transformations in Bandpass Networks 2.4.5 Duality 2.5 Network Component Values 2.5.1 Equal-Element Lowpass Prototype 2.5.2 Program ALLCHEBY.EXE 2.5.3 Elliptic Function Lowpass Prototype 2.5.4 Scaling 2.6 Network Analysis 2.6.1 ABCD Two-Port Parameters 2.6.2 Cascading Two-Port Subnetworks ......................... : 2.6.3 Scattering Parameters 2.6.4 Special Relations for ABCD Parameters 2.6.5 Hilbert Transform 2.7 Summary of Fundamentals 3. Direct-Coupled Filters 3.1 Prior Technology 3.1.1 Classical Filters 3.1.2 Coupled Resonator Concept 3.2 Properties 3.2.1 Topologies 3.2.2 Resonators 3.2.3 Inverters 3.2.4 Narrowband Choices in Parallel Resistance Space 3.3 Response Characteristics 3.3.1 Stopband Selectivity 3.3.2 Passband Width 3.3.3 Mismatched Terminations 3.3.4 Effects of Dissipation 3.3.5 Passband Distortion 3.4 Eliminating Passband Distortion 3.4.1 Stagger-Tuning Two Resonators 3.4.2 Stagger-Tuning Three Resonators 3.4.3 Exact Replacement of Resonators 3.4.3.1 Replacing External Series Resonators 3.4.3.2 Replacing Internal Series Resonators 3.4.3.3 Replacing Internal Series Resonators Having Traps 3.4.4 All Possible All-Pole Topologies 3.4.5 Wideband Choices in Parallel Resistance Space 3.5 The Method of Choices 3.5.1 A Spreadsheet for Four Resonators 3.5.2 A Spreadsheet for Five Resonators 3.5.3 A Spreadsheet for a Four Resonator Elliptic Filter 3.6 Tuning 3.6.1 Alternating Open- and Short-Circuit Method 3.6.2 Reactive Input Reflection Function 3.6.3 Narrow-Band Reflection Poles and Zeros 3.6.4 Wideband Networks Having Exact Responses 3. 7 Summary of Direct-Coupled Filters 4. Comprehensive Equal-Ripple Filters 4.1 Purpose 4.2 Response Continuum 4.2.1 Transducer and Characteristic Functions 4.2.2 Transmission Zeros 4.2.3 Passband Selectivity 4.2.4 Stop band Selectivity 4.3 Challenges of Polynomial Synthesis 4.3.1 Underlying Concepts 4.3.2 Mathematical Operations and Sensitivities 4.3.3 The Approximation Problem 4.3.4 Realization of Element Values 4.3.5 Road Map for Topologies 4.4 Element Responses at Discrete Frequencies 4.4.1 Filters 4.4.2 Single-Match Broadband Networks 4.4.3 Double-Match Broadband Networks 4.4.4 Lessons Learned 4.5 Synthesis by Iterated Analysis 4.5.1 Zeros and Poles of the Characteristic Function 4.5.2 Characteristic Zeros of Ladder Filters 4.5.3 Balancing Variables and Constraints 4.5.4 Efficient Network Analysis 4.5.5 Efficient Optimization 4.6 Summary of Comprehensive Equal-Ripple Filters 5. Matching Networks 5.1 Single-Frequency Matching 5.1.1 Zero Reflectance 5.1.2 El Sections Matching Resistances 5.1.3 El Sections Matching Impedances 5.1.4 Pi and T Sections 5.1.5 Cascade Transmission Lines 5.2 Analytic Gain-Bandwidth Theory 5.2.1 Gain-Bandwidth Limitation 5.2.2 The Single-Match Minimization Problem 5.2.3 Single-Match Optimal Results 5.2.4 Chebyshev Network Element Values 5.2.5 Other Terminal Impedances 5.2.6 Measured Loaded Q 5.3 Real-Frequency Technique 5.3.1 Non-Analytic Real-Frequency Data 5.3.2 Approximating the Network Resistance Function 5.3.3 Synthesis of a Resistance Function 5.3.4 Double-Matching Using the RFT 5.3.5 Double-Matching Using Brune Functions 5.3.6 Double-Matching Active Devices 5.4 Introduction to GRABIM 5.4.1 Thesis 5.4.2 Overview 5.4.3 Branch Parameter and Reactance Effects 5.4.4 The Response Surface 5.5 Algorithms for GRABIM 5.5.1 Efficient Network Selection and Analysis 5.5.2 Grid Searches 5.5.3 Constrained Optimization for Element Removal 5.6 Examples Using GRABIM 5.6.1 Example of a Non-Analytic Bandpass Problem 5.6.2 Example of a Distributed Interstage Network 5.6.3 Example of Neighborhood Matching 5.6.4 Example of Topological Simplification and Sampling 5.7 Summary of Matching Networks 6. GRABIM in Detail 6.1 Formulation 6.1.1 The General Problem 6.1.2 The General Solution 6.1.3 The Specific Problem 6.2 Network Analysis 6.2.1 Transducer Function and Its Derivatives 6.2.2 Derivatives with Respect to the Variable Space 6.2.3 Lossless Ladder Network Analysis Equations 6.2.4 Lossless Ladder Network Analysis Algorithm 6.3 Grid Search 6.3.1 Minimax Objective Function 6.3.2 Pattern Searches 6.3.3 Grid Geometry 6.3.4 Grid Algorithm 6.3.5 Other Factorial Search Algorithms 6.4 Method of Multipliers 6.4.1 The Problem 6.4.2 Quadratic Penalty Functions 6.4.3 Adjusting the Multipliers 6.4.4 Gauss-Newton Unconstrained Minimizer 6.4.5 Alternative Constrained Optimization Methods 6.4.6 Frequency Sampling Strategy 6.5 Summary of GRABIM in Detail Appendices Appendix A - Circle Mapping A.1 Bilinear Mapping A.1.1 Right-Half Plane to Circle Mappings A.1.2 Circle to Circle Mapping A.2 Interior Circular Images A.2.1 Concentric Circle in a Unit Circle A.2.2 Eccentric Circle in a Unit Circle A.2.3 Neighborhood Parameters A.3 Planar Lines to Circles A.3.1 Constant Resistance A.3.2 Constant Q A.3.3 Eccentric Vector Magnitude Appendix B - Abbreviations and Symbols Prefece References Autor Index Subject Index