[内容简介]

This book describes a new concept in analyzing circuits, which includes optoisolation elements. The analysis is based on nonlinear dynamics and chaos models and shows comprehensive benefits and results. All conceptual optoisolation circuits are innovative and can be broadly implemented in engineering applications. The dynamics of optoisolation circuits provides several ways to use them in a variety of applications covering wide areas. The presentation fills the gap of analytical methods for optoisolation circuits analysis, concrete examples, and geometric examples. The optoisolation circuits analysis is developed systematically, starting with basic optoisolation circuits differential equations and their bifurcations, followed by Fixed points analysis, limit cycles and their bifurcations. Optoisolation circuits can be characterized as Lorenz equations, chaos, iterated maps, period doubling and attractors. This book is aimed at electrical and electronic engineers, students and researchers in physics as well.

A Unique features of the book are its emphasis on practical and innovative engineering applications. These include optocouplers in a variety topological structures, passive components, conservative elements, dissipative elements, active devices, etc., In each chapter, the concept is developed from the basic assumptions up to the final engineering outcomes. The scientific background is explained at basic and advance levels and closely integrated with mathematical theory. Many examples are presented in this book and it is also ideal for an intermediate level courses at graduate level studies. It is also ideal for engineer who has not had formal instruction in nonlinear dynamics, but who now desires to fill the gap between innovative optoisolation circuits and advance mathematical analysis methods.

[目录]

Preface v

Introduction xv

1 Optoisolation Products Descriptions 1

1.1 Optocouplers General Description 1

1.2 Opto Negative Differential Resistance (NDR) 8

1.3 Absolute Negative Differential Resistance (NDR) 11

1.4 Optocoupler (LED, Photo Transistor) as a Basic Negative Differential Resistance (NDR) Circuit 11

1.5 Optocoupler (LED, Photo Transistor) NDR Circuit Mathematical Analysis 14

1.6 Controlling NDR Characteristics by Optocoupler (LED, Phototransistor) Parameters 18

1.7 Optocoupler (LED, Photo Transistor) Computer Analysis 20

1.8 Oscillations and Regenerative Amplification Using Opto Negative Differential Resistance (NDR) 22

1.9 Radio FM Generation - Parameter Variation Method Using Opto NDR as Compensation Elements 26

1.10 Multi Channel Bi Directional Digital Optocoupler 28

1.11 Exercises 35

2 Optoisolation One Dimensional Flow and Bifurcation 37

2.1 Optocoupler Flow on the Line 37

2.2 Optocoupler Fixed Point and Stability 41

2.3 Optocoupler Fixed Point and Stability Analysis using Taylor Expansion Estimation 47

2.4 Optocoupler Saddle - Node Bifurcation 67

2.5 Optocoupler Transcritical Bifurcation 77

2.6 Optocoupler Pitchfork Bifurcation 81

2.6.1 Optocoupler Supercritical Pitchfork Bifurcation 81

2.6.2 Optocoupler Subcritical Pitchfork Bifurcation 86

2.7 Optocoupler Imperfect Bifurcations and Catastrophes 90

2.8 Optocoupler Flow on the Circle 94

2.9 Optocoupler Flow on the Circle Uniform Oscillation 98

2.10 Optocoupler Flow on the Circle Non-Uniform Oswcillation 98

2.11 Exercises 100

3 Optoisolation Negative Differential Resistance (NDR) Circuits as a Dynamical System 103

3.1 OPTO NDR Basic Dynamical Circuit (Case I) 104

3.2 OPTO NDR Fixed Points and Stability (Case I) 114

3.3 OPTO NDR Basic Dynamical Circuit (Case II) 123

3.4 OPTO NDR Fixed Points and Stability (Case II) 137

3.5 OPTO NDR Linear Stability Analysis 139

3.6 OPTO NDR Bifurcation 142

3.7 OPTO NDR Cascade Structure 143

3.8 Exercises 173

4 Optoisolation Negative Differential Resistance (NDR) Circuits in a Topologic Structures 177

4.1 OPTO NDR Flow on the Line 177

4.2 OPTO NDR Fixed points and Stability 190

4.3 OPTO NDR Circuit Dynamic with Oscillation Source 201

4.4 OPTO NDR Circuit Dynamic with Inductor and Output Capacitor 210

4.5 OPTO NDR Circuit Dynamic with Serial Capacitor 225

4.6 Exercises 239

5 Photocoupled FET's Structure Negative Differential Resistance (NDR) Circuits 245

5.1 Photocoupled FET General Description 245

5.2 Combinational Connection of Photocoupled FET's - Negative Differential Resistance (NDR) Circuit 258

5.3 Photocoupled FET's Circuit (NDR) Flow on the Line 265

5.4 Photocoupled FET's Circuit (NDR) one dimensional Map discrete time 279

5.5 Photocoupled FET's Circuit (NDR) One Dimensional R_{d, ONQ2} Map Discrete Time 286

5.6 Photocoupled FET's Circuit (NDR) One Dimensional R_{d, ONQ2} Chaos and Periodic Windows 296

5.7 Exercises 301

6 Optoisolation's Circuits Two Dimensional Flow 305

6.1 Optoisolation's Circuits Two Dimensional Flow Linear/Nonlinear Systems Analysis using Taylor Expansion Estimation 305

6.2 Optoisolation's Circuits Two Dimensional Flow Linear/Nonlinear Systems Analysis using Taylor expansion estimation - Fixed Points, Stability 326

6.3 Optoisolation's Circuits Two Dimensional Flow Linear/Nonlinear Systems (exponential terms) 336

6.4 Optoisolation's Circuits Two Dimensional Flow Bifurcation 347

6.5 Optoisolation's Circuits Two Dimensional Flow Center 354

6.6 Optoisolation's Circuits Two Dimensional Flow k2 = 0, V2 = 0, k1 = 0 or k1 <> 0 354

6.7 Exercises 358

7 Optoisolation's Circuits with Time Delay Parameters 363

7.1 Delayed Optoisolation Circuit General Description 364

7.2 Delayed OptoNDR Circuit Dynamic Analysis 373

7.3 OptoNDR Circuit Stability Analysis Under Delayed Variables in Time 387

7.4 OptoNDR Circuit Stability Switching Under Parameters Variations 400

7.5 Delayed Optoisolation System (Higher Order Characteristic Equation) Dynamic Analysis 410

7.6 Delayed Optoisolation System Stability Switching Under Parameters Variations 425

7.7 Exercises 433

8 Optoisolation's Circuits Time Periodic Delay Differential Equation (DDE) 437

8.1 Delayed Optoisolation Circuit with Periodic Source Mathieu Equation 438

8.2 Delayed Optoisolation Circuit Implementation with Periodic Source 451

8.3 Delayed OptoNDR Circuit Implementation with Periodic Source 463

8.4 Delayed OptoNDR Circuit Implementation with Periodic Source Stability Analysis 477

8.5 Delayed OptoNDR Circuit Characteristic Equation with Periodic Source Stability Analysis 492

8.6 Exercises 501

9 Optoisolation's Circuits Chaos Characteristics 505

9.1 Optoisolation Lorenz System 506

9.2 Lorenzian Optoisolation System Properties 526

9.3 Lorenzian Optoisolation System Chaos and Attractors 533

9.4 Optoisolation Circuit Lorenz Map and System Parameters Space 543

9.5 Optoisolation System One Dimensional Map 548

9.6 Optoisolation System One Dimensional Maps Fixed Points and Logistic Map 554

9.7 Exercises 562

10 Optoisolation's Bifurcation Behaviors - Investigation, Comparison and Conclusions 565

Appendix A Optoisolation Circuit Taylor Series Approximation 577

Appendix B Operational Amplifiers Application in Optoisolation Circuits 599

Appendix C Optocoupler Equivalent Circuit Based on LED and Photodiode 629

References 643