Chaos Analysis and Chaotic EMI Suppression of DC–DC Converters

Introduces chaos theory, its analytical methods and the means to apply chaos to the switching power supply design DC-DC converters are typical switching systems which have plenty of nonlinear behaviors, such as bifurcation and chaos. The nonlinear behaviors of DC-DC converters have been studied heavily over the past 20 years, yet researchers are still unsure of the practical application of bifurcations and chaos in switching converters. The electromagnetic interference (EMI), which resulted from the high rates of changes of voltage and current, has become a major design criterion in DC-DC converters due to wide applications of various electronic devices in industry and daily life, and the question of how to reduce the annoying, harmful EMI has attracted much research interest. This book focuses on the analysis and application of chaos to reduce harmful EMI of DC-DC converters. After a review of the fundamentals of chaos behaviors of DC-DC converters, the authors present some recent findings such as Symbolic Entropy, Complexity and Chaos Point Process, to analyze the characters of chaotic DC-DC converters. Using these methods, the statistic characters of chaotic DC-DC converters are extracted and the foundations for the following researches of chaotic EMI suppression are reinforced. The focus then transfers to estimating the power spectral density of chaotic PWM converters behind an introduction of basic principles of spectrum analysis and chaotic PWM technique. Invariant Density, and Prony and Wavelet analysis methods are suggested for estimating the power spectral density of chaotic PWM converters. Finally, some design-oriented applications provide a good example of applying chaos theory in engineering practice, and illustrate the effectiveness on suppressing EMI of the proposed chaotic PWM. * Introduces chaos theory, its analytical methods and the means to apply chaos to the switching power supply design * Approaches the subject in a systematic manner from analyzing method, chaotic phenomenon and EMI characteristics, analytical methods for chaos, and applying chaos to reduce EMI (electromagnetic interference) * Highlights advanced research work in the fields of statistic characters of nonlinear behaviors and chaotic PWM technology to suppress EMI of switching converters * Bridges the gap between numerical theory and real-world applications, enabling power electronics designers to both analyze the effects of chaos and leverage these effects to reduce EMI

Table of Contents:
About the Authors xi Preface xiii Acknowledgments xv 1 Nonlinear Models and Behaviors of DC DC Converters 1 1.1 Introduction 1 1.2 Overview of PWM DC DC Converters 2 1.2.1 Principle of Pulse Width Modulation 2 1.2.2 Basic Topologies of DC DC Converters 3 1.2.3 Operation Modes of DC DC Converters 6 1.2.4 State-Space Model of DC DC Converters 7 1.2.5 Discrete Model of DC DC Converters 9 1.3 Overview of the Nonlinear Behavior of DC DC Converters 10 1.4 Review of Basic Dynamics Concepts 13 1.4.1 Dynamical System 14 1.4.2 Linear and Nonlinear Dynamical Systems 16 1.4.3 Characterization of Nonlinear Behavior 18 1.5 Conclusions 24 References 24 2 Symbolic Analysis of the Nonlinear Behavior of DC DC Converters 27 2.1 Introduction 27 2.2 Overview of the Time Series Principle of Discrete Systems 28 2.2.1 Symbolic Dynamics and Symbolic Time Series 28 2.2.2 Symbolization Method 30 2.2.3 Symbolic Dynamics of a Period-Doubling Cascade 32 2.3 Block Entropy 34 2.4 Symbolic Time Series Analysis of DC DC Converters 38 2.4.1 Period-Doubling Bifurcation and Chaos of DC DC Converters 39 2.4.2 Border Collision Bifurcation and Chaos of DC DC Converters 43 2.5 Conclusions 46 References 46 3 Complexity of the Nonlinear Behavior of DC DC Converters 49 3.1 Introduction 49 3.2 Lempel Ziv Complexity and Analysis of Nonlinear Behavior of DC DC Converters Based on L Z Complexity 51 3.2.1 Lempel Ziv Complexity 51 3.2.2 Analysis of Lempel Ziv Complexity of Buck Converter 52 3.3 Switching Block of DC DC Converters 53 3.4 Weight Lempel Ziv Complexity and Analysis of Nonlinear Behavior of DC DC Converters Based on Weight L Z Complexity 56 3.4.1 Weight Lempel Ziv Complexity 57 3.4.2 Weight Lempel Ziv Complexity of Buck Converter 57 3.4.3 Qualitative Analysis of Bifurcation Phenomena Based on Complexity 58 3.5 Duplicate Symbolic Sequence and Complexity 61 3.5.1 Main Switching Block and Main Symbolic Sequence 61 3.5.2 Secondary Switching Block and Secondary Symbolic Sequence 61 3.5.3 Duplicate Symbolic Sequence 62 3.5.4 Analysis of Border Collision and Bifurcation in DC DC Converters Based on Duplicate Symbolic Sequence 63 3.6 Applied Example 65 3.7 Conclusions 72 References 72 4 Invariant Probability Distribution of DC DC Converters 75 4.1 Introduction 75 4.2 Invariant Probability Distribution of Chaotic Map 76 4.3 Calculating Invariant Probability Distribution of the Chaotic Discrete-Time Maps with Eigenvector Method 78 4.4 Invariant Probability Distribution of the Chaotic Mapping of the Boost Converter 79 4.5 Application Examples of Invariant Probability Distribution 82 4.5.1 Power Spectral Density of the Input Current in a DC DC Converters 83 4.5.2 Average Switching Frequency 86 4.5.3 Parameter Design with Invariant Probability Distribution 88 4.6 Conclusions 90 References 90 5 EMI and EMC of Switching Power Converters 93 5.1 Introduction 93 5.2 EMI Origin of Electric Circuits 94 5.3 Characteristics of Switching Processes of Power Semiconductors 94 5.4 Overview of EMI and EMC 98 5.4.1 Basic Principles of EMI 98 5.4.2 EMC Regulations 99 5.5 EMI of Power Electronic Converters 101 5.5.1 Parasitic Parameters of Flyback Converters 102 5.5.2 Primary Rectifying Circuit 104 5.5.3 Switching Loop 104 5.6 Conclusions 107 References 107 6 Discrete Subsystem Chaotic Point Process of DC DC Converters and EMI Suppression 109 6.1 Introduction 109 6.2 Description of Chaotic Point Process of DC DC Converters 110 6.2.1 Model of Chaotic Point Process of DC DC Converters 110 6.2.2 Statistical Characteristics of the Chaotic Point Process in Converter 111 6.3 Spectral Quantification Analysis of the PWM Pulse Process 113 6.3.1 Spectral Quantification Analysis of the Periodic PWM Pulse 113 6.3.2 Spectral Quantification Analysis of PWM Chaotic SPSP 118 6.4 Conclusions 121 References 121 7 Basis of Spectral Analysis 123 7.1 Introduction 123 7.2 Some Concepts 124 7.3 Fourier Analysis and Fourier Transform 125 7.4 Spectral Density 127 7.4.1 Energy Signals and Power Signals 128 7.4.2 Energy Spectral Density 129 7.4.3 Power Spectral Density 130 7.5 Autocorrelation Function and Power Spectral Density 131 7.6 Classic Power Spectrum Estimation 133 7.6.1 Periodogram 133 7.6.2 Bartlett 134 7.6.3 Welch 135 7.6.4 Blackman and Tukey Method 136 7.6.5 Summary of Classic PSD Estimators 137 7.7 Modern Spectral Density Estimation 138 7.8 Conclusions 139 References 139 8 Dynamic Chaos Spectrum of Chaotic Switching Converters I: Wavelet Method 141 8.1 Introduction 141 8.1.1 Lack of Time and Frequency Positioning 141 8.1.2 Limitation for the Time-Variant Signals 141 8.1.3 Limitation for Resolution 142 8.2 Basic Principle of Wavelet Analysis 143 8.3 Multiresolution Analysis and Orthogonal Wavelets Basis 146 8.4 Wavelet Transform and Filter Bank 148 8.5 Wavelet Analysis of Chaotic PWM 148 8.5.1 Basic Principle of Chaotic PWM Control 148 8.5.2 Wavelet Analysis 149 8.5.3 Wavelet Reconstruction of Chaotic PWM 151 8.5.4 Time-Frequency Analysis of the Chaotic PWM 158 8.5.5 Information on the Time Frequency Image of P(t) 162 8.6 Conclusions 169 References 169 9 Dynamic Chaos Spectrum of Chaotic Switching Converters II: Prony Method 173 9.1 Introduction 173 9.2 Prony Method 174 9.2.1 Basic Principle of Prony Method 175 9.2.2 Classical Computing Process of Prony Analysis 178 9.3 Estimating PSD Using the Prony Method 179 9.4 Chaotic Spectral Estimation of DC DC Converters Based on the Prony Method 182 9.5 Conclusions 186 References 186 10 Chaotic PWM Suppressing EMI of Power Electronic Converters 189 10.1 Introduction 189 10.2 The Principle of Chaotic PWM Suppressing EMI 190 10.2.1 Basic Theory of Frequency Modulation 190 10.2.2 The Frequency Characteristics of Fixed Frequency PWM Wave 194 10.2.3 Frequency Characteristics of Spreading Frequency PWM Wave 195 10.2.4 The Principle of Chaotic PWM Suppressing EMI 196 10.3 The Key Techniques of Chaotic PWM for Power Electronic Converters 198 10.3.1 Parameter Selection of Chaotic PWM 198 10.3.2 Choice of a Chaotic PWM Modulation Signal 202 10.4 Chaotic PWM Suppressing EMI Experiments 204 10.4.1 Modulation Circuit of Piecewise-Linear Capacitor Chaos Circuit 205 10.4.2 The DC DC Converter Suppressing EMI Based on UC3842 208 10.4.3 EMI Suppression of Full Bridge Inversion Based on SG3525 214 10.5 EMI Suppression of Commercial Switching Power Supply 216 10.6 Characteristics of Chaotic Modulated by Different Chaotic Maps 231 10.7 Conclusions 234 References 235 Index 237