If you are working with circuits based on solid state devices, diodes and transistors, designing radio-frequency circuits, or regularly involved in any area requiring a functional knowledge of nonlinear oscillations and stability concepts, this volume offers an in-depth look at the very complex and unforeseen behaviour of nonlinear circuits. There is detailed coverage of circuits used in power amplifiers, voltage-controlled oscillators, frequency dividers, frequency multipliers, self-oscillating mixers, and phase-locked loops. This resource should give the reader greater insight into the design solutions that nonlinear circuits offer, presenting explanations and detection techniques for many "anomalous" phenomena often encountered in practice. It also aims to provide a better understanding of nonlinear oscillation theory and stability issues as you learn new techniques for the efficient steady-state simulation of these circuits.
Author(s): Almudena Suarez
Year: 2003
Language: English
Pages: 356
Stability Analysis of Nonlinear Microwave Circuits......Page 2
Contents v......Page 6
Preface xi......Page 12
Acknowledgments xv......Page 16
1 Steady-State Solutions of Nonlinear Circuits 1......Page 18
1.1 Autonomous and Nonautonomous Dynamical Systems 2......Page 19
1.2 Oscillations in Linear and Nonlinear Systems 10......Page 27
1.3 Phase-Space Representation of Solutions 16......Page 33
1.4 Stability of Limit Sets 29......Page 46
1.5 Poincare Map 44......Page 61
1.6 Entrainment: Phase-Locked Solutions in the Torus 52......Page 69
References 57......Page 74
2 Nonlinear Analysis Techniques 61......Page 78
2.1 Time-Domain Simulation 62......Page 79
2.2 Harmonic Balance for Nonautonomous Circuits 66......Page 83
2.3 Harmonic Balance for Autonomous and Sychronized Circuits 75......Page 92
2.4 Envelope Transient 91......Page 108
2.5 Continuation Techinque for Tracing Solution Curves Versus a Circuit Parameter 96......Page 113
2.6 Analysis of Autonomous and Synchronized Circuits in Closed Harmonic-Balance Programs 100......Page 117
References 112......Page 129
3 Local Stability Analysis 117......Page 134
3.1 Stability Concept for Linear and Nonlinear Circuits 118......Page 135
3.2 Derivation of the Characteristic System in the Harmonic-Balance Formulation 131......Page 148
3.3 The Open-Loop Approach 152......Page 169
References 171......Page 188
Appendix 3A 172......Page 189
4 Bifurcation Analysis of Nonlinear Circuits 177......Page 194
4.1 Local Bifurcations 178......Page 195
4.2 Bifurcations of the Poincare Map 196......Page 213
4.3 Global Bifurcations 211......Page 228
4.4 Analysis of Bifurcations from the Harmoinc-Balance Characteristic System 216......Page 233
4.5 Harmonic-Balance Analysis of Bifurcations with the Aid of an Auxiliary Generator 227......Page 244
References 240......Page 257
5 Global Stability of Microwave Circuits 243......Page 260
5.1 Global Behavior of Free-Running Oscillators 244......Page 261
5.2 Global Behavior of Synchronized Oscillators 247......Page 264
5.3 Global Behavior of Frequency Dividers by Two 252......Page 269
5.4 Global Behavior of Self-Oscillating Mixers 266......Page 283
5.5 Global Behavior of Frequency Doublers 273......Page 290
5.6 Global Behavior of Phase-Locked Loops 278......Page 295
References 292......Page 309
6 Bifurcaion Routes to Chaos 295......Page 312
6.1 Homoclinicity 296......Page 313
6.2 Quasiperiodic Route to Chaos 301......Page 318
6.3 Period-Doubling Route to Chaos 305......Page 322
6.4 Torus-Doubling Route to Chaos 311......Page 328
6.5 Intermittence 315......Page 332
References 320......Page 337
About the Authors 323......Page 340
Index 325......Page 342
