Microwave Network Design Using the Scattering Matrix
Microwave Network Design Using the Scattering Matrix

Microwave Network Design Using the Scattering Matrix

by Janusz Dobtowolski

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Product Details

ISBN-13: 9781608071296
Publisher: Artech House, Incorporated
Publication date: 10/31/2010
Pages: 280
Product dimensions: 6.20(w) x 9.20(h) x 0.80(d)

About the Author

Janusz A. Dobrowolski is a professor and head of the Microwave Circuits and Instrumentation Division of the Institute of Electronic Systems at the Warsaw University of Technology. He holds an M.Sc., Ph.D. and D.Sc. in electrical engineering from that same university.

Table of Contents

1 Introduction 1

References 4

2 Theory of Uniform Waveguides 7

2.1 Modal Electromagnetic Fields 8

2.2 Power Transmitted in a Waveguide 9

2.3 Characteristic Impedance 11

2.4 Normalization of Waveguide Voltage and Current 13

2.5 Transmission Line Equivalent Circuit of a Waveguide 14

References 15

3 Theory of Transmission Lines 17

3.1 Lumped Elements Circuit Model of a Transmission Line 18

3.2 Voltage and Current Wave Propagation in a Transmission Line 18

3.3 Terminated Transmission Line 21

3.4 Terminated Transmission Line Special Cases 24

References 26

4 Wave Variables and the Scattering Matrix 27

4.1 Voltage Traveling Waves and the Scattering Matrix 28

4.1.1 Physical Interpretation of Scattering Parqameters 30

4.1.2 A Shift in Reference Plane 32

4.1.3 Scattering Matrix Properties 34

4.1.4 Conversions Between the Scattering Matrix and Other Matrix Descriptions of Microwave Networks 35

4.2 Normalized Voltage Traveling Waves and the Generalized Scattering Matrix 36

4.2.1 Physical Interpretation of Generalized Scattering Parameters 37

4.3 Traveling Wave Intensities and the True Scattering Matrix 39

4.4 Pseudowaves and the Pseudoscattering Matrix 42

4.4.1 Pseudoscattering Matrix Properties 44

4.4.2 Conversions Between the Pseudoscattering Matrix and other Matrix Descriptions of Microwave Networks 48

4.4.3 Change of Reference Impedances 51

4.4.4 One-Port Reference Impedance Transformation 53

4.4.5 Multiport Network Reference Impedance Transformation 55

4.4.6 Two-Port Reference Impedance Transformation 55

4.4.7 Three-Port to Two-Port Network Scattering Matrix Transformation 56

4.4.8 Scattering Matrix of the Cascade of Two-Port Networks 60

4.4.9 Scattering Matrix of an Embedded Multiport Network 62

4.5 Generalized Multiport Network Cascade Matrix 64

4.5.1 T-Matrix to S-Matrix and S-Matrix to T-Matrix Transformation for Multiport Network with the Same Number of Input and Output Ports (Balanced Networks) 68

4.5.2 T-Matrix to S-Matrix and S-Matrix to T-Matrix Transformation for Multiport Networks with Different Numbers of Input and Output Ports (Unbalanced Networks) 69

4.6 Load Impedance 71

4.7 Power Waves and the Power Scattering Matrix 72

4.7.1 Physical Interpretation of Power Waves 75

4.7.2 Physical Interpretation of Power Scattering Parameters 77

4.7.3 Conversions Between Power Wave Scattering Matrix and Other Matrix Descriptions of Microwave Networks 83

4.7.4 Power Scattering Matrix Properties 84

4.7.5 Port Connections 85

References 87

5 Signal Analysis of Multiport Networks 89

5.1 Wave Relations For Basic Elements of Multiport Networks 90

5.1.1 Signal Source 90

5.1.2 Load 92

5.2 Microwave Network Analysis Using Scattering Parameters and Signal Flow Graphs 96

5.3 Signal Analysis of Two-Port Networks 100

5.3.1 Transducer Power Gain 100

5.3.2 Power Gain 102

5.3.3 Available Power Gain 103

5.3.4 Stability Consideration for Active Two-Port Networks 103

5.3.5 Maximum Power Gain 108

5.3.6 Constand Power Gain Circles 109

5.3.7 Constand Available Power Gain Circles 110

5.3.8 Insertion Loss 110

5.3.9 Voltage Gain 112

5.3.10 Voltage Transfer Gain 113

5.4 Multiport Network Analysis 114

5.5 Multielement Multiport Network Analysis Using Connection Scattering Matrix Approach 120

References 125

6 Mode Wave Variables and Mixed Mode Scattering Matrix of Differential Networks 127

6.1 Differential and Common Mode Definitions 128

6.2 Mode-Specific Waves and Impedances 130

6.3 Mixed Mode Scattering Parameters 132

6.4 Transformation Between Standard-and Mixed-Mode Scattering Parameters 134

6.5 Generalized Mixed-Mode Pseudoscattering Matrix 138

6.6 Mixed-Mode Cascade Matrix 158

References 163

7 Noise Wave Variables and the Scattering Matrix 165

7.1 Noise Waves 166

7.1.1 Noise Power Waves 166

7.1.2 Noise Pseudowaves 167

7.2 Noise Wave Representation of Microwave Networks 168

7.3 Other Noise Representations of Noisy Networks and Their Transformations to Noise Wave Parameters 171

7.3.1 Chain Matrix Noise Representation 171

7.3.2 Cascade Matrix Noise Representation 175

7.3.3 Impedance Matrix and Admittance Matrix Noise Representations 179

7.4 Noise Modeling of Microwave Network Elements 181

7.4.1 Noise Wave Correlation Matrices of Passive Multiport Networks 181

7.4.2 Noise Correlation Matrices of Passive Multiport Networks Embedded in Lossy Waveguides 185

7.4.3 Noise Wave Correlation Matrices of Active Two-Port Networks 186

7.5 Two-Port to Three-Port Noise Wave Transformation 190

7.6 Noise Wave Correlation Matrices of Embedded Multiport Networks 196

7.7 Deembedding Noise Wave Parameters of Cascaded Noisy Two-Port Networks 198

References 200

8 Noise Analysis of Multiport Networks 203

8.1 Basic Relationships For Noisy Multiport Networks 204

8.2 Classical Two-Port Network Noise Theory 205

8.3 Noise Figure of a Two-Port Network 208

8.3.1 Constant Noise Figure Circles 209

8.4 Two-Port Network Noise Analysis Using Scattering Matrix 211

8.5 Noise Analysis of Two-Port Networks Using Noise Waves And Cascade (Transfer Scattering) Matrix 215

8.5.1 Noise Wave Parameters Of Cascade Connected Two-Port Networks 218

8.6 Noise Analysis of Multielement Multiport Networks Using Connection Scattering Matrix Approach 220

8.6.1 Noise Figure 223

8.6.2 Signal-to-Noise Ratio 227

8.7 Noise Analysis of Multiport Networks 228

8.7.1 Noise Figure 230

8.7.2 Signal-to-Noise Ratio 231

References 238

9 Scattering Functions in Nonlinear Modeling of Microwave Devices 241

9.1 Large-Signal Scattering Functions 242

9.2 Linearization of Scattering Functions 245

9.3 The Time Reference 250

9.4 Application of the Response Coefficients Matrices S and S′ to Predict Nonlinear Device Performance 252

9.5 Experimental Determination of the Response Coefficients Matrices S and S′ 254

References 258

Appendix 261

About the Author 265

Index 267

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