1 Overview of Quadrature Hybrids ............................... 1
1.1 From Distributed to Lumped Element Design ............... 1
1.2 Applications ............................................ 8
1.3 Analysis of Quadrature Error ........................... 13
1.4 Conclusion ............................................. 15
References .................................................. 16
2 Basic Theory ................................................ 19
2.1 Lossless Circuits ...................................... 19
2.2 Hybrid Circuits ........................................ 20
2.3 Lumped Element Quadrature Hybrids ...................... 24
2.4 Approximate-Phase Quadrature Hybrids ................... 30
2.5 Conclusion ............................................. 33
References .................................................. 34
3 Approximations .............................................. 35
3.1 Optimization Goal ...................................... 36
3.2 Polynomial Form of F(ω) ................................ 36
3.3 Rational Form of F(ω) .................................. 38
3.4 Second-Order Optimum Rational Function ................. 45
3.5 Higher-Order Optimum Rational Functions ................ 48
3.6 Transfer Functions in Terms of the Complex Variable .... 64
3.7 Numerator Part of the Optimum Transfer Functions ....... 67
3.8 Transfer Functions of Optimum Approximate-Phase
Hybrids ................................................ 71
3.9 Conclusion ............................................. 72
References .................................................. 73
4 Passive Synthesis ........................................... 75
4.1 Even-and Odd-Mode Analysis ............................. 76
4.2 The First-Order Quadrature Hybrid ...................... 79
4.3 Higher-Order Lowpass Prototypes ........................ 81
4.4 Use of Transmission Lines .............................. 93
4.5 Optimum Rational Function Second-Order Prototypes ...... 96
4.6 Higher-Order Optimum Rational Function Hybrids ........ 104
4.7 Hybrid Synthesis Using Cascaded Sections .............. 107
4.8 Cascades of First-Order Sections ...................... 109
4.9 Cascades of Second-Order Sections ..................... 112
4.10 Further Cascade Arrangements .......................... 113
4.11 Approximate-Phase Hybrids ............................. 117
4.12 Approximate-Amplitude Hybrids Based on Phase Delay
Networks .............................................. 124
4.13 Conclusion ............................................ 126
References ................................................. 127
5 Practical Design ........................................... 129
5.1 The First-Order Circuit Coupled Inductor Design ....... 130
5.2 A 435-MHz Ground Inductor Hybrid Design ............... 135
5.3 A 1.27-GHz First-Order Microstrip Hybrid .............. 137
5.4 A 100-200-MHz Third-Order Polynomial-Based Hybrid ..... 138
5.5 A 1-3-GHz Mixed Element Hybrid ........................ 140
5.6 A 2.5—6-GHz Hybrid with Coupled Transmission Lines .... 144
5.7 Optimum Second-Order Hybrids .......................... 146
5.8 A 50-150-MHz Second-Order Hybrid ...................... 150
5.9 Higher-Order Symmetrical Optimum Hybrids .............. 151
5.10 A 2-32-MHz First-Order Cascade Hybrid ................. 152
5.11 A 10-100-MHz Second-Order Cascade Hybrid .............. 154
5.12 A 10-100-MHz Approximate-Phase Hybrid ................. 157
5.13 A 1-300-MHz Approximate-Amplitude Hybrid Based on
Phase Delay Networks .................................. 164
5.14 Conclusion ............................................ 167
Reference .................................................. 168
6 Special Topics ............................................. 169
6.1 Active Circuits ....................................... 169
6.2 Unequal Division and Nonquadrature Hybrids ............ 181
6.3 Power Handling ........................................ 190
6.4 Graphical Techniques for Cascaded Couplers ............ 192
6.5 A 50-550-MHz Hybrid with Sections of Different
Topology .............................................. 196
6.6 Conclusion ............................................ 201
References ................................................. 202
Glossary ...................................................... 203
Bibliography .................................................. 207
About the Author .............................................. 211
Index ......................................................... 213
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