Chaos Analysis and Chaotic EMI Suppression of DC-DC Converters

Professor Bo Zhang, School of Electric Power, South China University of Technology, Guangzhou, China>Professor Zhang obtained his PhD in 1994 from Nanjing University of Aeronautics and Astronautics, China, and was a Visiting Scholar at Iowa State University, USA from 2005-6. His research interests include nonlinear analysis and control of power electronic systems, power electronic systems and device, and motor and driving control systems. Professor Wang is the author of numerous journal articles and conference proceedings, and holds 8 Science and Technology awards of province/ministry-grade.? He has been an evaluation expert of 863 Projects, and is currently Chairman of the Power Supply Society of Guangdong Province, China. Dr Xuemei Wang, Associate Professor, School of Electric Power, South China University of Technology, Guangzhou, ChinaDr Wang obtained his PhD in 2009 from South China University of Technology and has been an associate professor for four years. He lectures in power electronics, analogue and digital electronic technology, and soft switching technology of DC switching supply. Dr Wang's areas of expertise include non-linear analysis and control of power electronic systems.

• About the Authors xiPreface xiiiAcknowledgments xv1 Nonlinear Models and Behaviors of DC–DC Converters 11.1 Introduction 11.2 Overview of PWM DC–DC Converters 21.2.1 Principle of Pulse Width Modulation 21.2.2 Basic Topologies of DC–DC Converters 31.2.3 Operation Modes of DC–DC Converters 61.2.4 State-Space Model of DC–DC Converters 71.2.5 Discrete Model of DC–DC Converters 91.3 Overview of the Nonlinear Behavior of DC–DC Converters 101.4 Review of Basic Dynamics Concepts 131.4.1 Dynamical System 141.4.2 Linear and Nonlinear Dynamical Systems 161.4.3 Characterization of Nonlinear Behavior 181.5 Conclusions 24References 242 Symbolic Analysis of the Nonlinear Behavior of DC–DC Converters 272.1 Introduction 272.2 Overview of the Time Series Principle of Discrete Systems 282.2.1 Symbolic Dynamics and Symbolic Time Series 282.2.2 Symbolization Method 302.2.3 Symbolic Dynamics of a Period-Doubling Cascade 322.3 Block Entropy 342.4 Symbolic Time Series Analysis of DC–DC Converters 382.4.1 Period-Doubling Bifurcation and Chaos of DC–DC Converters 392.4.2 Border Collision Bifurcation and Chaos of DC–DC Converters 432.5 Conclusions 46References 463 Complexity of the Nonlinear Behavior of DC–DC Converters 493.1 Introduction 493.2 Lempel–Ziv Complexity and Analysis of Nonlinear Behavior of DC–DC Converters Based on L–Z Complexity 513.2.1 Lempel–Ziv Complexity 513.2.2 Analysis of Lempel–Ziv Complexity of Buck Converter 523.3 Switching Block of DC–DC Converters 533.4 Weight Lempel–Ziv Complexity and Analysis of Nonlinear Behavior of DC–DC Converters Based on Weight L–Z Complexity 563.4.1 Weight Lempel–Ziv Complexity 573.4.2 Weight Lempel–Ziv Complexity of Buck Converter 573.4.3 Qualitative Analysis of Bifurcation Phenomena Based on Complexity 583.5 Duplicate Symbolic Sequence and Complexity 613.5.1 Main Switching Block and Main Symbolic Sequence 613.5.2 Secondary Switching Block and Secondary Symbolic Sequence 613.5.3 Duplicate Symbolic Sequence 623.5.4 Analysis of Border Collision and Bifurcation in DC–DC Converters Based on Duplicate Symbolic Sequence 633.6 Applied Example 653.7 Conclusions 72References 724 Invariant Probability Distribution of DC–DC Converters 754.1 Introduction 754.2 Invariant Probability Distribution of Chaotic Map 764.3 Calculating Invariant Probability Distribution of the Chaotic Discrete-Time Maps with Eigenvector Method 784.4 Invariant Probability Distribution of the Chaotic Mapping of the Boost Converter 794.5 Application Examples of Invariant Probability Distribution 824.5.1 Power Spectral Density of the Input Current in a DC–DC Converters 834.5.2 Average Switching Frequency 864.5.3 Parameter Design with Invariant Probability Distribution 884.6 Conclusions 90References 905 EMI and EMC of Switching Power Converters 935.1 Introduction 935.2 EMI Origin of Electric Circuits 945.3 Characteristics of Switching Processes of Power Semiconductors 945.4 Overview of EMI and EMC 985.4.1 Basic Principles of EMI 985.4.2 EMC Regulations 995.5 EMI of Power Electronic Converters 1015.5.1 Parasitic Parameters of Flyback Converters 1025.5.2 Primary Rectifying Circuit 1045.5.3 Switching Loop 1045.6 Conclusions 107References 1076 Discrete Subsystem Chaotic Point Process of DC–DC Converters and EMI Suppression 1096.1 Introduction 1096.2 Description of Chaotic Point Process of DC–DC Converters 1106.2.1 Model of Chaotic Point Process of DC–DC Converters 1106.2.2 Statistical Characteristics of the Chaotic Point Process in Converter 1116.3 Spectral Quantification Analysis of the PWM Pulse Process 1136.3.1 Spectral Quantification Analysis of the Periodic PWM Pulse 1136.3.2 Spectral Quantification Analysis of PWM Chaotic SPSP 1186.4 Conclusions 121References 1217 Basis of Spectral Analysis 1237.1 Introduction 1237.2 Some Concepts 1247.3 Fourier Analysis and Fourier Transform 1257.4 Spectral Density 1277.4.1 Energy Signals and Power Signals 1287.4.2 Energy Spectral Density 1297.4.3 Power Spectral Density 1307.5 Autocorrelation Function and Power Spectral Density 1317.6 Classic Power Spectrum Estimation 1337.6.1 Periodogram 1337.6.2 Bartlett 1347.6.3 Welch 1357.6.4 Blackman and Tukey Method 1367.6.5 Summary of Classic PSD Estimators 1377.7 Modern Spectral Density Estimation 1387.8 Conclusions 139References 1398 Dynamic Chaos Spectrum of Chaotic Switching Converters I: Wavelet Method 1418.1 Introduction 1418.1.1 Lack of Time and Frequency Positioning 1418.1.2 Limitation for the Time-Variant Signals 1418.1.3 Limitation for Resolution 1428.2 Basic Principle of Wavelet Analysis 1438.3 Multiresolution Analysis and Orthogonal Wavelets Basis 1468.4 Wavelet Transform and Filter Bank 1488.5 Wavelet Analysis of Chaotic PWM 1488.5.1 Basic Principle of Chaotic PWM Control 1488.5.2 Wavelet Analysis 1498.5.3 Wavelet Reconstruction of Chaotic PWM 1518.5.4 Time-Frequency Analysis of the Chaotic PWM 1588.5.5 Information on the Time–Frequency Image of P(t) 1628.6 Conclusions 169References 1699 Dynamic Chaos Spectrum of Chaotic Switching Converters II: Prony Method 1739.1 Introduction 1739.2 Prony Method 1749.2.1 Basic Principle of Prony Method 1759.2.2 Classical Computing Process of Prony Analysis 1789.3 Estimating PSD Using the Prony Method 1799.4 Chaotic Spectral Estimation of DC–DC Converters Based on the Prony Method 1829.5 Conclusions 186References 18610 Chaotic PWM Suppressing EMI of Power Electronic Converters 18910.1 Introduction 18910.2 The Principle of Chaotic PWM Suppressing EMI 19010.2.1 Basic Theory of Frequency Modulation 19010.2.2 The Frequency Characteristics of Fixed Frequency PWM Wave 19410.2.3 Frequency Characteristics of Spreading Frequency PWM Wave 19510.2.4 The Principle of Chaotic PWM Suppressing EMI 19610.3 The Key Techniques of Chaotic PWM for Power Electronic Converters 19810.3.1 Parameter Selection of Chaotic PWM 19810.3.2 Choice of a Chaotic PWM Modulation Signal 20210.4 Chaotic PWM Suppressing EMI Experiments 20410.4.1 Modulation Circuit of Piecewise-Linear Capacitor Chaos Circuit 20510.4.2 The DC–DC Converter Suppressing EMI Based on UC3842 20810.4.3 EMI Suppression of Full Bridge Inversion Based on SG3525 21410.5 EMI Suppression of Commercial Switching Power Supply 21610.6 Characteristics of Chaotic Modulated by Different Chaotic Maps 23110.7 Conclusions 234References 235Index 237