SYNCHRONOUS AND RESONANT DC/DC CONVERSION TECHNOLOGY, FACTOR, AND MATHEMATICAL ENERGY MODELING Fang Lin Luo NanyangTechnological University Singapore HongYe NanyangTechnological University Singapore Uf&) Taylor &. Francis >V J Taylor &i Francis Group Boca Raton London New York A CRC title, part of the Taylor & Francis imprint, a member of the Taylor & Francis Group, the academic division of T&F Informa plc.
Contents 1 Synchronous Rectifier DC/DC Converters 1 1.1 Introduction 2 1.2 Fiat Transformer Synchronous Rectifier Luo-Converter 5 1.2.1 Transformer Is in Magnetizing Process 5 1.2.2 Switching-On 6 1.2.3 Transformer Is in Demagnetizing Process 6 1.2.4 Switching-Off 6 1.2.5 Summary 7 1.3 Active Clamped Synchronous Rectifier Luo-Converter 7 1.3.1 Transformer Is in Magnetizing 8 1.3.2 Switching-On 8 1.3.3 Transformer Is in Demagnetizing 8 1.3.4 Switching-Off 9 1.3.5 Summary 9 1.4 Double Current Synchronous Rectifier Luo-Converter 9 1.4.1 Transformer Is in Magnetizing 10 1.4.2 Switching-On 11 1.4.3 Transformer Is in Demagnetizing 11 1.4.4 Switching-Off 11 1.4.5 Summary 11 1.5 Zero-Current-Switching Synchronous Rectifier Luo-Converter 12 1.5.1 Transformer Is in Magnetizing 13 1.5.2 Resonant Period 13 1.5.3 Transformer Is in Demagnetizing 13 1.5.4 Switching-Off 14 1.5.5 Summary 14 1.6 Zero-Voltage-Switching Synchronous Rectifier Luo-Converter 14 1.6.1 Transformer Is in Magnetizing 15 1.6.2 Resonant Period 16 1.6.3 Transformer Is in Demagnetizing 16 1.6.4 Switching-Off 16 1.6.5 Summary 16 Bibliography 17 2 Multiple Energy-Storage Element Resonant Power Converters 19 2.1 Introduction 19
2.1.1 Two-Element RPC 20 2.1.2 Three-Element RPC 21 2.1.3 Four-Element RPC 22 2.2 Bipolar Current and Voltage Source 24 2.2.1 Bipolar Voltage Source 26 2.2.1.1 Two Voltage Source Circuit 26 2.2.1.2 One Voltage Source Circuit 27 2.2.2 Bipolar Current Source 29 2.2.2.1 Two Voltage Source Circuit 30 2.2.2.2 One Voltage Source Circuit 30 2.3 A Two-Element RPC Analysis 31 2.3.1 Input Impedance 31 2.3.2 Current Transfer Gain 32 2.3.3 Operation Analysis 33 2.3.4 Simulation Results 37 2.3.5 Experimental Results 38 Bibliography 38 3 Il-CLL Current Source Resonant Inverter 41 3.1 Introduction 41 3.1.1 Pump Circuits 41 3.1.2 Current Source 41 3.1.3 Resonant Circuit 42 3.1.4 Load 42 3.1.5 Summary 42 3.2 Mathematic Analysis 43 3.2.1 Input Impedance 43 3.2.2 Components' Voltages and Currents 44 3.2.3 Simplified Impedance and Current Gain 45 3.2.4 Power Transfer Efficiency 52 3.3 Simulation Results 53 3.4 Discussion 54 3.4.1 Function of the Il-CLL Circuit 54 3.4.2 Applying Frequency to this Il-CLL CSRI 55 3.4.3 Explanation of g > 1 55 3.4.4 DC Current Component Remaining 55 3.4.5 Efficiency 55 Bibliography 55 4 Cascade Double T-CL Current Source Resonant Inverter 57 4.1 Introduction 57 4.2 Mathematic Analysis 57 4.2.1 Input Impedance 58 4.2.2 Components, Voltages, and Currents 59 4.2.3 Simplified Impedance and Current Gain 60
4.2.4 Power Transfer Efficiency 66 4.3 Simulation Result 67 4.3.1 ß = \,f= 33.9 khz, T = 29.5 us 69 4.3.2 ß = 1.4142,/= 48.0 khz, T = 20.83 us 69 4.3.3 ß = 1.59,/= 54 khz, T = 18.52 us 70 4.4 Experimental Result 71 4.5 Discussion 73 4.5.1 Function of the Double T-CL Circuit 73 4.5.2 Applying Frequency to This Double T-CL CSRI 73 4.5.3 Explanation of g > 1 73 Bibliography 73 5 Cascade Reverse Double T-LC Resonant Power Converter 75 5.1 Introduction 75 5.2 Steady-State Analysis of Cascade Reverse Double T-LCRPC 76 5.2.1 Topology and Circuit Description 76 5.2.2 Classical Analysis on AC Side 77 5.2.2.1 Basic Operating Principles 77 5.2.2.2 Equivalent Load Resistance 77 5.2.2.3 Equivalent AC Circuit and Transfer Functions 78 5.2.2.4 Analysis of Voltage Transfer Gain and the Input Impedance 80 5.2.3 Simulation and Experimental Results 84 5.2.3.1 Simulation Studies 85 5.2.3.2 Experimental Results 86 5.3 Resonance Operation and Modeling 86 5.3.1 Operating Principle, Operating Modes, and Equivalent Circuits 87 5.3.2 State-Space Analysis 89 5.4 Small-Signal Modeling of Cascade Reverse Double T-LC RPC 92 5.4.1 Small-Signal Modeling 93 5.4.1.1 Model Diagram 93 5.4.1.2 Nonlinear State Equation 93 5.4.1.3 Harmonie Approximation 94 5.4.1.4 Extended Describing Function 95 5.4.1.5 Harmonie Balance 96 5.4.1.6 Perturbation and Linearization 97 5.4.1.7 Equivalent Circuit Model 98 5.4.2 Closed-Loop System Design 99 5.5 Discussion 104 5.5.1 Characteristics of Variable-Parameter Resonant Converter 105 5.5.2 Discontinuous Conduction Mode (DCM) 108 Bibliography 114 Appendix: Parameters Used in Small-Signal Modeling 116
6 DC Energy Sources for DC/DC Converters 117 6.1 Introduction 117 6.2 Single-Phase Half-Wave Diode Rectifier 118 6.2.1 Resistive Load 118 6.2.2 Inductive Load 119 6.2.3 Pure Inductive Load 122 6.2.4 Back EMF Plus Resistor Load 123 6.2.5 Back EMF Plus Inductor Load 125 6.3 Single-Phase Bridge Diode Rectifier 125 6.3.1 Resistive Load 127 6.3.2 Back EMF Load 129 6.3.3 Capacitive Load 131 6.4 Three-Phase Half-Bridge Diode Rectifier 133 6.4.1 Resistive Load 133 6.4.2 Back EMF Load (0.5 J2V in < E < /2VJ 134 6.4.3 Back EMF Load (E < 0.5 /2VJ 136 6.5 Three-Phase Full-Bridge Diode Rectifier with Resistive Load 136 6.6 Thyristor Rectifiers 138 6.6.1 Single-Phase Half-Wave Rectifier with Resistive Load 139 6.6.2 Single-Phase Half-Wave Thyristor Rectifier with Inductive Load 140 6.6.3 Single-Phase Half-Wave Thyristor Rectifier with Pure Inductive Load 141 6.6.4 Single-Phase Half-Wave Rectifier with Back EMF Plus Resistive Load 142 6.6.5 Single-Phase Half-Wave Rectifier with Back EMF Plus Inductive Load 144 6.6.6 Single-Phase Half-Wave Rectifier with Back EMF Plus Pure Inductor 145 6.6.7 Single-Phase Full-Wave Semicontrolled Rectifier with Inductive Load 147 6.6.8 Single-Phase Full-Controlled Rectifier with Inductive Load 148 6.6.9 Three-Phase Half-Wave Rectifier with Resistive Load 149 6.6.10 Three-Phase Half-Wave Thyristor Rectifier with Inductive Load 151 6.6.11 Three-Phase Full-Wave Thyristor Rectifier with Resistive Load 152 6.6.12 Three-Phase Full-Wave Thyristor Rectifier with Inductive Load 153 Bibliography 155 7 Control Circuit: EMI and Application Examples of DC/DC Converters 157 7.1 Introduction 157
7.2 Luo-Resonator 157 7.2.1 Circuit Explanation 158 7.2.2 Calculation Formulae 159 7.2.3 A Design Example 160 7.2.4 Discussion 160 7.3 EMI, EMS, and EMC 161 7.3.1 EMI/EMC Analysis 161 7.3.2 Comparison to Hard-Switching and Soft-Switching 163 7.3.3 Measuring Method and Results 163 7.3.4 Designing Rule to Minimize EMI/EMC 167 7.4 Some DC/DC Converter Applications 168 7.4.1 A 5000 V Insulation Test Bench 168 7.4.2 MIT 42/14 V 3 KW DC/DC Converter 169 7.4.3 IBM 1.8 V/200 A Power Supply 171 Bibliography 173 8 Energy Factor (EF) and Mathematical Modeling for Power DC/DC Converters 175 8.1 Introduction 175 8.2 Pumping Energy (PE) 177 8.2.1 Energy Quantization 177 8.2.2 Energy Quantization Function 177 8.3 Stored Energy (SE) 177 8.3.1 Stored Energy in Continuous Conduction Mode (CCM) 178 8.3.1.1 Stored Energy (SE) 178 8.3.1.2 Capacitor-Inductor Stored Energy Ratio (CIR) 178 8.3.1.3 Energy Losses (EL) 179 8.3.1.4 Stored Energy Variation on Inductors and Capacitors (VE) 179 8.3.2 Stored Energy in Discontinuous Conduction Mode(DCM) 180 8.4 Energy Factor (EF) 182 8.5 Variation Energy Factor (EF V ) 183 8.6 Time Constant t and Damping Time Constant x d 183 8.6.1 Time Constant t 183 8.6.2 Damping Time Constant x rf 184 8.6.3 Time Constants Ratio t, 184 8.6.4 Mathematical Modeling for Power DC/DC Converters 185 8.7 Examples of Applications 186 8.7.1 A Bück Converter in CCM 186 8.7.1.1 Bück Converter without Energy Losses (r L = 0 Q.)..186 8.7.1.2 Bück Converter with Small Energy Losses (r L = 1.5 Ü.) 190 8.7.1.3 Bück Converter with Energy Losses (r L = 4.5 Q.) 192
8.7.1.4 Bück Converter with Large Energy Losses (r L = 6 Q) 196 8.7.2 A Super-Lift Luo-Converter in CCM 198 8.7.3 A Boost Converter in CCM (No Power Losses) 201 8.7.4 A Buck-Boost Converter in CCM (No Power Losses) 206 8.7.5 Positive Output Luo-Converter in CCM (No Power Losses) 209 8.8 Small Signal Analysis 211 8.8.1 A Bück Converter in CCM without Energy Losses (r L = 0)...214 8.8.2 Buck-Converter with Small Energy Losses (r L = 1.5 ü) 215 8.8.3 Super-Lift Luo-Converter with Energy Losses (r L = 0.12 Q.) 218 Bibliography 223 Appendix A: A Second-Order Transfer Function 225 AI Very Small Damping Time Constant 225 A2 Small Damping Time Constant 226 A3 Critical Damping Time Constant 228 A4 Large Damping Time Constant 228 Appendix B: Some Calculation Formulas Derivations 231 Bl Transfer Function of Bück Converter 231 B2 Transfer Function of Super-Lift Luo-Converter 231 B3 Simplified Transfer Function of Super-Lift Luo-Converter...232 B4 Time Constants x and x d, and Ratio t, 232 Index 235