Reflectionless Filters

Reflectionless Filters

by Matthew A. Morgan

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Product Details

ISBN-13: 9781630813277
Publisher: Artech House, Incorporated
Publication date: 01/31/2017
Pages: 280
Product dimensions: 6.10(w) x 9.10(h) x 0.90(d)

About the Author

Matthew A. Morgan is a scientist/research engineer at the Central Development Lab (CDL) at the National Radio Astronomy Observatory (NRAO) in Charlottesville, VA. He received his M.S. and Ph.D. degrees in electrical engineering from California Institute of Technology and his B.S. degree in electrical engineering from the University of Virginia.

Table of Contents

Preface xi

Acknowledgments xvii

Chapter 1 Passive Microwave Networks 1

1.1 Two-Port Networks 1

1.2 Properties of Immittance and Transfer Functions 4

1.2.1 The Laplace Frequency Domain 4

1.2.2 Immittance Functions 5

1.2.3 Transfer Functions 5

1.3 Duality 6

1.4 Filter Transfer Functions 8

1.4.1 Pole-Zero Configuration 8

1.4.2 Butterworth Filter Response 10

1.4.3 Chebyshev Type I Filter Response 11

1.4.4 Chebyshev Type II Filter Response 12

1.4.5 Elliptic Filter Response 14

1.4.6 Group Delay 16

1.5 Conventional Filter Topologies 17

1.5.1 Frequency Transformations 19

1.6 Even- and Odd-Mode Analysis 21

1.7 Transmission Lines 25

1.7.1 The Telegrapher's Equations and Wave Solutions 25

1.7.2 The Standard Transmission-Line Model 27

1.7.3 Special Cases 28

1.7.4 Impedance and Scattering Parameters 30

1.7.5 Coupled Transmission Lines 31

References 32

Chapter 2 Classical Absorptive Filters 35

2.1 Diplexers 35

2.2 Directional Filters 37

2.3 Hybrid-Coupled Filters 38

2.4 Empirical Approaches 40

2.4.1 Damped Resonators 40

2.4.2 Absorptive Gaussian Filters 41

2.4.3 Absorptive Transmission-Line Equalizers 41

2.5 Constant-Resistance Networks 45

2.5.1 Topologies 45

2.5.2 Readability 46

2.5.3 Chebyshev Type I Example 47

2.5.4 Higher-Order Solutions 53

References 53

Chapter 3 Foundations of Reflectionless Filters 55

3.1 Basic Filter Derivation 55

3.1.1 Methodology 55

3.1.2 Procedure 56

3.1.3 Performance 59

3.1.4 Third-Order Case 60

3.2 Normalized Element Scaling 63

3.2.1 Stop-Band Specification (ωs = 1) 63

3.2.2 Pass-Band 3 dB Corner Specification (ω3dB = 1) 64

3.2.3 Pass-Band 1 dB Corner Specification (ω1dB = 1) 65

3.2.4 Pass-Band Ripple Factor Specification (ε) 65

3.3 Nonuniqueness 65

3.4 Auxiliary Components 67

3.5 Frequency Transformations 69

3.6 Design Example 71

3.6.1 Monolithic Implementation 72

3.6.2 Experimental Results 75

3.7 The Problem of Discovering New Topologies 76

3.7.1 Nonuniqueness of Dual Networks 76

3.7.2 Nontrivial Equivalent Circuits 77

References 79

Chapter 4 Subnetwork Expansion 81

4.1 The Reflectionless Filter as a Diplexer 81

4.2 Subnetworks 84

4.2.1 Internal Subnetwork Analysis 84

4.2.2 Subnetwork Attenuator 85

4.2.3 Cross-Connected Subnetwork Analysis 86

4.3 Compound Reflectionless Filters 88

4.3.1 Third-Rank Compound Filter 90

4.3.2 Design Example 91

4.4 Combination Filters 92

4.4.1 Second-Rank Filter with Subnetwork Attenuator 92

4.4.2 Second-Rank Filter with Auxiliary Elements 94

4.4.3 Reflectionless Notch Filters 95

4.5 Cascade Combinations 96

4.5.1 Cascaded High-/Low-Order Low-Pass Filters 97

4.5.2 Cascaded High-/Low-Frequency Low-Pass Filters 97

4.5.3 Cascaded High-/Low-Pass Ultrawideband Filters 98

4.5.4 Predistortion Filters 99

4.5.5 Slope Equalizers 103

References 105

Chapter 5 Duality Reduction 107

5.1 Dual Reflectionless Filter Network 107

5.1.1 Properties of Dual Multiport Networks 107

5.1.2 Derivation 110

5.1.3 Alternative Derivation 111

5.2 Compound Filter Reduction 112

5.3 Layout Considerations 115

5.3.1 Monolithic Versions 115

5.3.2 Discrete-Element Versions 117

References 119

Chapter 6 Generalized Reflectionless Filters 121

6.1 ReEvaluation of Prior Topologies 121

6.1.1 Compound High-Pass Filters 121

6.1.2 Clues in the Pole-Zero Configuration 123

6.2 Generalized Compound Topologies 125

6.2.1 Seventh-Order Derivation 125

6.2.2 Customized Responses 127

6.3 Chebyshev Type II Reflectionless Filters 127

6.3.1 Chebyshev Prototype Parameters 128

6.3.2 Ripple Factor 129

6.3.3 Stop-Band Rejection 131

6.3.4 Normalized Element Scaling 132

6.4 Expanded Topology For Larger Ripple Factor 133

6.4.1 Generalized Auxiliary Elements 133

6.4.2 Transformer-Coupled Generalized Topology 134

6.5 Dual Topology 136

6.6 High-Pass and Band-Pass Filters 137

6.7 Chebyshev Type I Reflectionless Filters 141

6.8 Zolotarev Reflectionless Filters 143

6.9 Delta-Wye Transformation 145

6.10 Component Sensitivity 147

References 151

Chapter 7 Transmission-Line Reflectionless Filters 153

7.1 Derivation 153

7.1.1 Richard's Transformation 153

7.1.2 Kuroda's Identity 155

7.1.3 Application to Reflectionless Filters 157

7.1.4 A Three-Port Transmission-Line Identity 159

7.1.5 Final Topology and Component Values 162

7.1.6 Frequency Response 166

7.1.7 Lumped-Element Correspondence 166

7.2 Alternative Forms 168

7.2.1 Reversed Input Coupling 169

7.2.2 Cascade Resonators 171

7.2.3 Mixed Resonators 173

7.3 Design Example 174

References 175

Chapter 8 Reflectionless Multiplexers 177

8.1 Dipiexers 177

8.2 Triplexers 180

8.2.1 Design Example 181

8.3 Multiplexers 184

8.3.1 Low-Pass Arrays 185

8.3.2 High-Pass Arrays 186

8.4 High-Rejection Multiplexers 188

8.5 Contiguous Channels 189

References 189

Chapter 9 Applications of Reflectionless Filters 191

9.1 With Up-/Down-Converters 191

9.1.1 Image Termination 191

9.1.2 Image Rejection Stability 193

9.1.3 Inter modulation Expansion 194

9.2 With Multiplier Chains 195

9.3 With Broadband Amplifiers 197

9.4 With Analog-to-Digital Converters 198

9.5 Distributed Filtering 199

9.6 With Conventional Filters 200

9.7 Slope Equalizers 202

9.8 Time-Domain Applications 203

9.8.1 Measures of Performance in the Time Domain 203

9.8.2 Latency 205

9.8.3 Intersymbol Interference 206

9.8.4 Low-Selectivity Time-Domain Filters 209

References 210

Chapter 10 Tools for Advanced Topology Creation 213

10.1 Split Symmetry-Plane Representation 213

10.1.1 Chebyshev Type II Example 213

10.1.2 Chebyshev Type II Alternate Forms 215

10.1.3 A Pseudo-Elliptic Reflectionless Filter 216

10.1.4 Modification of Prior Topologies 219

10.2 Unusual Forms of Symmetry 220

10.2.1 Antiparallel Subnetworks 220

10.2.2 Nonplanar Forms 224

10.3 Conclusion 229

References 230

Appendix A Delta-Wye Transformations 231

Appendix B Zolotarev Filter Prototypes 235

References 239

Appendix C Transmission-Line Identities 241

C.1 Two-Port Identities 241

C.2 Three-Port Identities 248

C.3 Four-Port Identities 248

C 4 Periodic Kuroda's Identity 249

References 249

About the Author 251

Index 253

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