Nonlinear Microwave Circuit Design

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Nonlinear Microwave Circuit Design

Chapter 1 Nonlinear Analysis Methods 1
1.1 Introduction 1
1.2 Time-Domain Solution 4
1.2.1 General Formulation 4
1.2.2 Steady State Analysis 7
1.2.3 Convolution Methods 9
1.3 Solution Through Series Expansion 13
1.3.1 Volterra Series 13
1.3.2 Fourier Series 22
1.3.2.1 Basic formulation (single tone) 23
1.3.2.2 Multi-tone analysis 33
1.3.2.3 Envelope analysis 43
1.3.2.4 Additional remarks 45
1.3.2.5 Describing function 46
1.3.2.6 Spectral balance 47
1.4 The Conversion Matrix 49
1.5 Bibliography 56
Chapter 2 Nonlinear Measurements 61
2.1 Introduction 61
2.2 Load/Source Pull 62
2.3 The Vector Nonlinear Network Analyser 71
2.4 Pulsed Measurements 74
2.5 Bibliography 80
Chapter 3 Nonlinear Models 83
3.1 Introduction 83
3.2 Physical Models 84
vi CONTENTS
3.2.1 Introduction 84
3.2.2 Basic Equations 86
3.2.3 Numerical Models 88
3.2.4 Analytical Models 92
3.3 Equivalent-Circuit Models 95
3.3.1 Introduction 95
3.3.2 Linear Models 96
3.3.3 From Linear to Nonlinear 102
3.3.4 Extraction of an Equivalent Circuit from Multi-bias Small-signal
Measurements 121
3.3.5 Nonlinear Models 133
3.3.6 Packages 139
3.4 Black-Box Models 142
3.4.1 Table-based Models 142
3.4.2 Quasi-static Model Identified from Time-domain Data 143
3.4.3 Frequency-domain Models 144
3.4.4 Behavioural Models 146
3.5 Simplified Models 148
3.6 Bibliography 151
Chapter 4 Power Amplifiers 159
4.1 Introduction 159
4.2 Classes of Operation 168
4.3 Simplified Class-A Fundamental-frequency Design for High Efficiency 170
4.3.1 The Methodology 170
4.3.2 An Example of Application 180
4.4 Multi-harmonic Design for High Power and Efficiency 182
4.4.1 Introduction 182
4.4.2 Basic Assumptions 187
4.4.3 Harmonic Tuning Approach 194
4.4.4 Mathematical Statements 197
4.4.5 Design Statements 205
4.4.6 Harmonic Generation Mechanisms and Drain Current Waveforms 207
4.4.7 Sample Realisations and Measured Performances 212
4.5 Bibliography 226
Chapter 5 Oscillators 229
5.1 Introduction 229
5.2 Linear Stability and Oscillation Conditions 230
5.3 From Linear to Nonlinear: Quasi-large-signal Oscillation and Stability
Conditions 243
5.4 Design Methods 252
CONTENTS vii
5.5 Nonlinear Analysis Methods for Oscillators 259
5.5.1 The Probe Approach 260
5.5.2 Nonlinear Methods 261
5.6 Noise 269
5.7 Bibliography 276
Chapter 6 Frequency Multipliers and Dividers 279
6.1 Introduction 279
6.2 Passive Multipliers 280
6.3 Active Multipliers 282
6.3.1 Introduction 282
6.3.2 Piecewise-linear Analysis 283
6.3.3 Full-nonlinear Analysis 298
6.3.4 Other Circuit Considerations 306
6.4 Frequency Dividers – the Regenerative (Passive) Approach 308
6.5 Bibliography 311
Chapter 7 Mixers 315
7.1 Introduction 315
7.2 Mixer Configurations 318
7.2.1 Passive and Active Mixers 318
7.2.2 Symmetry 322
7.3 Mixer Design 329
7.4 Nonlinear Analysis 332
7.5 Noise 337
7.6 Bibliography 339
Chapter 8 Stability and Injection-locked Circuits 341
8.1 Introduction 341
8.2 Local Stability of Nonlinear Circuits in Large-signal Regime 341
8.3 Nonlinear Analysis, Stability and Bifurcations 349
8.3.1 Stability and Bifurcations 349
8.3.2 Nonlinear Algorithms for Stability Analysis 356
8.4 Injection Locking 359
8.5 Bibliography 368
Appendix 371
A.1 Transformation in the Fourier Domain of the Linear Differential Equation 371
A.2 Time-Frequency Transformations 372
A.3 Generalised Fourier Transformation for the Volterra Series Expansion 372
viii CONTENTS
A.4 Discrete Fourier Transform and Inverse Discrete Fourier Transform for
Periodic Signals 373
A.5 The Harmonic Balance System of Equations for the Example Circuit with
N = 3 375
A.6 The Jacobian Matrix 378
A.7 Multi-Dimensional Discrete Fourier Transform and Inverse Discrete
Fourier Transform for Quasi-periodic Signals 379
A.8 Oversampled Discrete Fourier Transform and Inverse Discrete Fourier
Transform for Quasi-Periodic Signals 380
A.9 Derivation of Simplified Transport Equations 382
A.10 Determination of the Stability of a Linear Network 382
A.11 Determination of the Locking Range of an Injection-Locked Oscillator 384
Index 387

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