Microwave Network Design Using the Scattering Matrix (Artech House Microwave Library)

287 Pages·2010·2.07 MB·English

by  Janusz A. Dobrowolski

Microwave Network Design
Using the Scattering Matrix
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Microwave Network Design
Using the Scattering Matrix
Janusz A. Dobrowolski
artechhouse.com
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British Library Cataloguing in Publication Data
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ISBN 13: 978-1-60807-129-6
Cover design by Vicki Kane
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10 9 8 7 6 5 4 3 2 1
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

i Microwave Network Design Using the Scattering Matrix
3 Theory of Transmission Lines 17
3.1 Lumped Element Circuit Model of a
Transmisssion 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 Parameters 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
Contents ii
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
Networks 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
iii Microwave Network Design Using the Scattering Matrix
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 Constant Power Gain Circles 109
5.3.7 Constant 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
Contents ix
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