Average Current-Mode Control of DC-DC Power Converters

An authoritative one-stop guide to the analysis, design, development, and control of a variety of power converter systems

Average Current-Mode Control of DC-DC Power Converters provides comprehensive and up-to-date information about average current-mode control (ACMC) of pulse-width modulated (PWM) dc-dc converters. This invaluable one-stop resource covers both fundamental and state-of-the-art techniques in average current-mode control of power electronic converters???featuring novel small-signal models of non-isolated and isolated converter topologies with joint and disjoint switching elements and coverage of frequency and time domain analysis of controlled circuits.

The authors employ a systematic theoretical framework supported by step-by-step derivations, design procedures for measuring transfer functions, challenging end-of-chapter problems, easy-to-follow diagrams and illustrations, numerous examples for different power supply specifications, and practical tips for developing power-stage small-signal models using circuit-averaging techniques. The text addresses all essential aspects of modeling, design, analysis, and simulation of average current-mode control of power converter topologies, such as buck, boost, buck-boost, and flyback converters in operating continuous-conduction mode (CCM). Bridging the gap between fundamental modeling methods and their application in a variety of switched-mode power supplies, this book:

• Discusses the development of small-signal models and transfer functions related to the inner current and outer voltage loops
• Analyzes inner current loops with average current-mode control and describes their dynamic characteristics
• Presents dynamic properties of the poles and zeros, time-domain responses of the control circuits, and comparison of relevant modeling techniques
• Contains a detailed chapter on the analysis and design of control circuits in time-domain and frequency-domain
• Provides techniques required to produce professional MATLAB plots and schematics for circuit simulations, including example MATLAB codes for the complete design of PWM buck, boost, buck-boost, and flyback DC-DC converters
• Includes appendices with design equations for steady-state operation in CCM for power converters, parameters of commonly used power MOSFETs and diodes, SPICE models of selected MOSFETs and diodes, simulation tools including introductions to SPICE, MATLAB, and SABER, and MATLAB codes for transfer functions and transient responses

Average Current-Mode Control of DC-DC Power Converters is a must-have reference and guide for researchers, advanced graduate students, and instructors in the area of power electronics, and for practicing engineers and scientists specializing in advanced circuit modeling methods for various converters at different operating conditions.

Marian K. Kazimierczuk, PhD, Professor of Electrical Engineering, Wright State University, Dayton, Ohio, USA. He has taught undergraduate and graduate electronics courses in the field of high-frequency power electronics for more than 35 years. Professor Kazimierczuk has performed an extensive research on PWM and resonant power converters, electronic ballasts, high-frequency magnetic components, high-efficiency RF power amplifiers, modeling and control of power converters, active power factor correction, wireless power transfer, renewable energy sources, power MOSFET drivers, and wide-bandgap GaN and SiC semiconductor devices. He has published over 500 papers in IEEE Transactions, IET journals, and IEEE international conferences, has written eight textbooks, and holds 7 patents. He is a Life Fellow of the IEEE.

Dalvir K. Saini, PhD, Research Engineer, Failure Analysis Lab, University of Dayton Research Institute, Wright Patterson Air Force Base, Dayton, Ohio, USA. She has been pursuing the area of failure analysis of electrical systems and components related to aircraft safety, and has published several journal and conference publications in the field of modeling of switched-mode power converters.

Agasthya Ayachit, PhD, Senior System Engineer, Mercedes-Benz Research & Development North America, Redford, Michigan, USA. He has been actively contributing to the design and development of power conversion stages in electric vehicle battery charging and e-drive systems. He has published several journal papers in IEEE Transactions, IET journals, and IEEE conferences in the field of small-signal modeling of power converters. His research interests are in the field of circuit topologies, modeling and design of power converters, wireless charging, and wide-bandgap semiconductor devices (GaN/SiC).

1 Introduction 8

1.1 Principle of Operation of Conventional Average Current-Mode Control Technique 11

1.2 Principle of Operation of Modified Average Current-Mode Control Technique 12

1.3 Steady-State Operation 14

2 Average Current-Mode Control of Buck DC-DC Converter 17

2.1 Circuit Description, DC Characteristics, and Design 18

2.1.1 Circuit Description 18

2.1.2 DC Model 18

2.1.3 Design Example 21

2.2 Large-Signal and Small-Signal Models of PWM Buck Converter in CCM 22

2.3 Power Stage Transfer Functions 23

2.3.1 Duty Cycle-to-Output Voltage Transfer Function T_p 25

2.3.2 Duty Cycle-to-Inductor Current Transfer Function T_pi 27

2.3.3 Input Voltage-to-Output Voltage Transfer Function M_v 29

2.3.4 Input Voltage-to-Inductor Current Transfer Function Mv_i 31

2.3.5 Reverse Current Gain A_i 32

2.3.6 Open-Loop Input Impedance Z_i 34

2.3.7 Open-Loop Output Impedance Z_o 35

2.4 Inner-Current Loop 38

2.4.1 Transfer Function of Filter and Non-Inverting Amplifier T_f 39

2.4.2 Transfer Function of Pulse-Width Modulator T_m 41

2.4.3 Uncompensated Loop Gain T_ki 42                                                                                      

2.4.4 Transfer Function of Control Circuit for Inner-Current Loop T_ci 42

2.4.5 Compensated Loop Gain of Inner-Current Loop T_i 45

2.5 Closed-Loop Transfer Functions for Inner-Current Loop 46

2.5.1 Reference Voltage-to-Inductor Current Transfer Function T_icl 47

2.5.2 Reference Voltage-to-Output Voltage Transfer Function T_picl 48

2.5.3 Input Voltage-to-Inductor Current Transfer Function M_icl 48

2.5.4 Input Voltage-to-Output Voltage Transfer Function M_vicl 49

2.5.5 Input Impedance Z_iicl 51

2.5.6 Output Impedance Z_oicl 53

2.6 Outer-Voltage Loop 55

2.6.1 Transfer Function of Feedback Network β 56

2.6.2 Uncompensated Loop Gain for Outer-Voltage Loop T_kv 57

2.6.3 Transfer Function of Control Circuit for Outer-Voltage Loop T_cv 57

2.6.4 Compensated Loop Gain of Outer-Voltage Loop T_v 60

2.7 Closed-Loop Transfer Functions for Outer-Voltage Loop 60

2.7.1 Reference Voltage-to-Output Voltage Transfer Function T_pcl 61

2.7.2 Input Voltage to Duty-Cycle Transfer Function M_dv 61

2.7.3 Input Voltage-to-Output Voltage Transfer Function M_vcl 64

2.7.4 Input Impedance Z_ivcl 65

2.7.5 Output Impedance Z_ovcl 68

2.8 Comparison of Closed-Loop and Open-Loop Step Responses 70

2.8.1 Response of Output Voltage to Step Change in Input Voltage 70

2.8.2 Response of Output Voltage to Step Change in Duty Cycle, Current-Loop reference Voltage, and Voltage-Loop Reference Voltage 70

2.8.3 Response of Input Current to Step Change in Input Voltage 71

2.8.4 Response of Output Voltage to Step Change in Load Current 72

2.9 Summary 73

3 Average Current-Mode Control of Boost DC-DC Converter 75

3.1 Circuit Description, DC Characteristics, and Design 76

3.1.1 Circuit Description 76

3.1.2 DC Model 76

3.1.3 Design Example 79

3.2 Large-Signal and Small-Signal Models of PWM Boost Converter for CCM 80

3.3 Power-Stage Transfer Functions 82

3.3.1 Duty Cycle-to-Output Voltage Transfer Function T_p 83

3.3.2 Duty Cycle-to-Inductor Current Transfer Function T_pi 89

3.3.3 Input Voltage-to-Output Voltage Transfer Function M_v 96

3.3.4 Input Voltage-to-Inductor Current Transfer Function M_vi 97

3.3.5 Reverse Current Gain A_i 99

3.3.6 Open-Loop Input Impedance Z_i 101

3.3.7 Open-Loop Output Impedance Z_o 102

3.4 Inner-Current Loop 105

3.4.1 Transfer Function of Filter and Non-Inverting Amplifier T_f 106

3.4.2 Transfer Function of Pulse-Width Modulator Tm 107

3.4.3 Uncompensated Loop Gain T_ki 108

3.4.4 Transfer Function of Control Circuit T_ci 108

3.4.5 Loop Gain of Inner-Current Loop T_i 111

3.5 Closed-Loop Transfer Functions for Inner-Current Loop 112

3.5.1 Reference Voltage-to-Inductor Current Transfer Function T_icl 112

3.5.2 Reference Voltage-to-Output Voltage Transfer Function T_picl 113

3.5.3 Input Voltage-to-Inductor Current Transfer Function M_icl 115

3.5.4 Input Voltage-to-Output Voltage Transfer Function M_vicl 116

3.5.5 Input Voltage-to-Duty Cycle Transfer Function M_di 118

3.5.6 Input Impedance Z_iicl 119

3.5.7 Output Impedance Z_oicl 120

3.6 Outer-Voltage Loop 122

3.6.1 Transfer Function of Feedback Network β 122

3.6.2 Uncompensated Loop Gain for Outer-Voltage Loop T_kv 123

3.6.3 Transfer Function of Control Circuit for Outer-Voltage Loop T_cv 123

3.6.4 Compensated Loop Gain of Outer-Voltage Loop T_v 127

3.7 Closed-Loop Transfer Functions for Outer-Voltage Loop 128

3.7.1 Reference Voltage-to-Output Voltage Transfer Function T_pcl 128

3.7.2 Input Voltage-to-duty cycle Transfer Function M_dv 129

3.7.3 Input Voltage-to-Output Voltage Transfer Function M_vcl 131

3.7.4 Input Impedance Z_ivcl 133

3.7.5 Output Impedance Z_ovcl 135

3.8 Comparison of Closed-Loop and Open-Loop Step Responses 137

3.8.1 Response of Output Voltage to Step Change in Input Voltage 137

3.8.2 Response of Output Voltage to Step Change in Duty Cycle, Current-Loop reference Voltage, and Voltage-Loop Reference Voltage 138

3.8.3 Response of Input Current to Step Change in Input Voltage 139

3.8.4 Response of Output Voltage to Step Change in Load Current 140

3.9 Summary 141

4 Average Current-Mode Control of Buck-Boost DC-DC Converter 143

4.1 Circuit Description, DC Model, and Design 144

4.1.1 Circuit Description 144

4.1.2 DC Model 144

4.1.3 Design Example 147

4.2 Large-Signal and Small-Signal Models of PWM Buck-Boost Converter in CCM 149

4.3 Power Stage Transfer Functions 150

4.3.1 Duty Cycle-to-Output Voltage Transfer Function T_p 152

4.3.2 Duty Cycle-to-Inductor Current Transfer Function T_pi 159

4.3.3 Input Voltage-to-Output Voltage Transfer Function M_v 165

4.3.4 Input Voltage-to-Inductor Current Transfer Function M_vi 167

4.3.5 Reverse Current Gain A_i 168

4.3.6 Open-Loop Input Impedance Z_i 170

4.3.7 Open-Loop Output Impedance Z_o 172

4.4 Inner-Current Loop 176

4.4.1 Transfer Function of Filter T_f 177

4.4.2 Transfer Function of Pulse-Width Modulator T_m 178

4.4.3 Uncompensated Loop Gain T_ki 179

4.4.4 Transfer Function of Compensation Circuit T_ci 180

4.4.5 Compensated Loop Gain T_i 183

4.5 Closed-Inner Loop Transfer Functions 183

4.5.1 Reference Voltage-to-Inductor Current Transfer Function T_icl 185

4.5.2 Reference Voltage-to-Output Voltage Transfer Function T_picl 187

4.5.3 Input Voltage-to-Inductor Current Transfer Function M_icl 188

4.5.4 Input Voltage-to-Output Voltage Transfer Function M_vicl 190

4.5.5 Input Voltage-to-Duty Cycle Transfer Function M_di 191

4.5.6 Input Impedance Z_iicl 193

4.5.7 Output Impedance Z_oicl 195

4.6 Outer-Voltage Loop 196

4.6.1 Transfer Function of Feedback Network β 198

4.6.2 Uncompensated Loop Gain T_kv 198

4.6.3 Transfer Function of Control Circuit for Outer-Voltage Loop T_cv 200

4.6.4 Compensated Loop Gain T_v 202

4.7 Closed-Loop Transfer Functions for Outer-Voltage Loop 202

4.7.1 Reference Voltage-to-Output Voltage Transfer Function T_pcl 203

4.7.2 Input Voltage-to-Duty Cycle Transfer Function M_dv 205

4.7.3 Input Voltage-to-Output Voltage Transfer Function M_vcl 206

4.7.4 Input Impedance Z_ivcl 209

4.7.5 Output Impedance Z_ovcl 211

4.8 Comparison of Closed-Loop and Open-Loop Step Responses 213

4.8.1 Response of Output Voltage to Step Change in Input Voltage 213

4.8.2 Response of Output Voltage to Step Change in Duty Cycle, Current-Loop reference Voltage, and Voltage-Loop Reference Voltage 214

4.8.3 Response of Input Current to Step Change in Input Voltage 215

4.8.4 Response of Output Voltage to Step Change in Load Current 216

4.9 Summary 217

5 Average Current-Mode Control of Flyback DC-DC Converter 219

5.1 Circuit Description, DC Model, and Design 220

5.1.1 Circuit Description 220

5.1.2 DC Model 222

5.1.3 Derivation of Equivalent Averaged Resistance 225

5.1.4 Design Example 229

5.2 Large-Signal and Small-Signal Models of PWM Flyback Converter in CCM 229

5.3 Power Stage Transfer Functions 233

5.3.1 Duty Cycle-to-Output Voltage Transfer Function T_p 236

5.3.2 Duty Cycle-to-Inductor Current Transfer Function T_pi 243

5.3.3 Input Voltage-to-Output Voltage Transfer Function M_v 249

5.3.4 Input Voltage-to-Inductor Current Transfer Function M_vi 251

5.3.5 Reverse Current Gain A_i 253

5.3.6 Open-Loop Input Impedance Z_i 255

5.3.7 Open-Loop Output Impedance Z_o 256

5.4 Inner-Current Loop 260

5.4.1 Transfer Function of Filter and Non-Inverting Amplifier T_f 261

5.4.2 Transfer Function of Pulse-Width Modulator T_m 263

5.4.3 Uncompensated Loop Gain T_ki 263

5.4.4 Transfer Function of Compensation Circuit T_ci 265

5.4.5 Compensated Loop Gain T_i 267

5.5 Closed-Loop Transfer Functions for Inner-Current Loop 268

5.5.1 Reference Voltage-to-Inductor Current Transfer Function T_icl 269

5.5.2 Reference Voltage-to-Output Voltage Transfer Function T_picl 271

5.5.3 Input Voltage-to-Inductor Current Transfer Function M_icl 272

5.5.4 Input Voltage-to-Output Voltage Transfer Function M_vicl 274

5.5.5 Input Voltage-to-Duty Cycle Transfer Function M_di 275

5.5.6 Input Impedance Z_iicl 277

5.5.7 Output Impedance Z_oicl 278

5.6 Outer-Voltage Loop 280

5.6.1 Transfer Function of Feedback Network β 281

5.6.2 Uncompensated Loop Gain T_kv 283

5.6.3 Transfer Function of Compensation Circuit T_cv 284

5.6.4 Compensated Loop Gain T_v 286

5.7 Closed-Loop Transfer Functions for Outer-Voltage Loop 286

5.7.1 Reference Voltage-to-Output Voltage Transfer Function T_pcl 287

5.7.2 Input Voltage-to-Duty Cycle Transfer Function M_dv 287

5.7.3 Input Voltage-to-Output Voltage Transfer Function M_vcl 290

5.7.4 Input Impedance Z_ivcl 292

5.7.5 Output Impedance Z_ovcl 294

5.8 Comparison of Closed-Loop and Open-Loop Step Responses 296

5.8.1 Response of Output Voltage to Step Change in Input Voltage 296

5.8.2 Response of Output Voltage to Step Change in Duty Cycle, Current-Loop reference Voltage, and Voltage-Loop Reference Voltage 297

5.8.3 Response of Input Current to Step Change in Input Voltage 298

5.8.4 Response of Output Voltage to Step Change in Load Current 299

5.9 Summary 299

6 Bibliography 302

Appendices 307

A Design Equations for Continuous-Conduction Mode 308

B MOSFET Parameters 310

C Diode Parameters 311

D Selected MOSFETs Spice Models 312

E Selected Diodes Spice Models 314

F Simulation Tools 316

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