Pulsewidth Modulated DC-to-DC Power Conversion Circuits, Dynamics, and Control Designs
, by Choi, Byungcho
- ISBN: 9781118180631 | 1118180631
- Cover: Hardcover
- Copyright: 7/22/2013
This book provides engineers in the power electronics field with complete guidance to pulsewidth modulated (PWM) DC-to-DC power converters. It explains the circuit and operation of PWM DC-to-DC converters and their dynamic characteristics along with in-depth discussion of the current mode control scheme for PWM DC-to-DC converters. Topics include the functional basics, dynamic modeling and analysis, compensation design, and applications of current mode control. Fully tested problems and simulation examples are included, as well as downloadable lecture slides and ready-to-run PSpice programs.
BYUNGCHO CHOI is a professor in the School of Electrical Engineering and Computer Science at Kyungpook National University, Daegu, Korea. He received his PhD from Virginia Polytechnic Institute and State University, Blacksburg, Virginia. Over the past twenty years, Dr. Choi has been teaching and doing research in the area of PWM DC-to-DC power conversion.
Preface vii
PART I CIRCUITS FOR DC-TO-DC
POWER CONVERTERS
1 PWM Dc-to-dc Power Conversion 3
1.1 Description of PWM Dc-to-dc Power Conversion 4
1.1.1 Dc-to-dc Power Conversion 4
1.1.2 PWM Technique 6
1.2 Dc-to-dc Power Conversion System 7
1.3 Features and Issues of PWM Dc-to-dc Converter 8
1.4 Chapter Highlights 10
References 12
2 Power Stage Components 13
2.1 Semiconductor Switches 13
2.1.1 MOSFETs 14
2.1.2 Diodes 15
2.1.3 Simple Switching Circuit 16
2.2 Energy Storage and Transfer Devices 17
2.2.1 Inductors 18
2.2.2 Capacitors 25
2.2.3 Transformers 31
2.3 Switching Circuits in Practice 38
2.3.1 Solenoid Drive Circuits 38
2.3.2 Capacitor Charging Circuit 44
2.4 Summary 50
References 51
Problems 51
3 Buck Converter 69
3.1 Ideal Step Down Dc-to-dc Power Conversion 70
3.2 Buck Converter: Step Down Dc-to-dc Converter 72
3.2.1 Evolution to Buck Converter 72
3.2.2 Frequency Domain Analysis 73
3.3 Buck Converter in Start Up Transient 76
3.3.1 Piecewise Linear Analysis 76
3.3.2 Startup Response 76
3.4 Buck Converter in Steady State 78
3.4.1 Circuit Analysis Techniques 78
3.4.2 Steady State Analysis 80
3.4.3 Estimation of -output Voltage Ripple 82
3.5 Buck Converter in Discontinuous Conduction Mode 87
3.5.1 Origin of Discontinuous Conduction Mode Operation 88
3.5.2 Conditions for DCM Operation 90
3.5.3 Steady State Operation in DCM 92
3.6 Closed-loop Control of Buck Converter 97
3.6.1 Closed-loop Feedback Controller 98
3.6.2 Responses of Closed-loop Controlled Buck Converter 102
3.7 Summary 107
References 108
Problems 108
4 Dc-to-dc Power Converter Circuits 123
4.1 Boost Converter 124
4.1.1 Evolution to Boost Converter 124
4.1.2 Steady State Analysis in CCM 126
4.1.3 Steady State Analysis in DCM 130
4.1.4 Effects of Parasitic Resistance on Voltage Gain 132
4.2 Buck/Boost Converter 135
4.2.1 Evolution to Buck/Boost Converter 135
4.2.2 Steady-state Analysis in CCM 138
4.2.3 Steady-state Analysis in DCM 141
4.3 Structure and Voltage Gain of Three Basic Converters 144
4.4 Flyback Converter: Transformer Isolated Buck/Boost Converter 145
4.4.1 Evolution to Flyback Converter 146
4.4.2 Steady-state Analysis in CCM 147
4.4.3 Steady-state Analysis in DCM 151
4.5 Bridge-Type Buck Derived Isolated Dc-to-dc Converters 154
4.5.1 Switch Network and Multi Winding Transformer 155
4.5.2 Full-Bridge Converter 158
4.5.3 Half-Bridge Converter 163
4.5.4 Push-Pull Converter 167
4.6 Forward Converters 167
4.6.1 Basic Operational Principles 167
4.6.2 Tertiary-Winding Reset Forward Converter 173
4.6.3 Two-Switch Forward Converter 177
4.7 Summary 180
References 181
Problems 181
PART II MODELING, DYNAMICS, AND DESIGN OF PWM DC-TO-DC CONVERTERS
5 Modeling PWM Dc-to-dc Converters 201
5.1 Overview of PWM Converter Modeling 202
5.2 Averaging Power Stage Dynamics 204
5.2.1 State-Space Averaging 206
5.2.2 Circuit Averaging 212
5.2.3 Generalization of Circuit Averaging Technique 221
5.2.4 Circuit Averaging and State Space Averaging 222
5.3 Linearizing Averaged Power Stage Dynamics 223
5.3.1 Linearization of Nonlinear Function and Small Signal Model 223
5.3.2 Small Signal Model for PWM Switch: PWM Switch Model 225
5.3.3 Small Signal Model of Converter Power Stage 227
5.4 Frequency Response of Converter Power Stage 230
5.4.1 Sinusoidal Response of Power Stage 230
5.4.2 Frequency Response and s-Domain Small signal Power Stage Model 232
5.5 Small signal Gain of PWM Block 235
5.6 Small signal Model for PWM Dc-to-dc Converters 236
5.6.1 Voltage Feedback Circuit 236
5.6.2 Small signal Model for PWM Converters 238
5.7 Summary 240
References 241
Problems 241
6 Power Stage Transfer Functions 247
6.1 Bode Plot for Transfer Functions 247
6.1.1 Basic Definitions 248
6.1.2 Bode Plots for Multiplication Factors 250
6.1.3 Bode Plot Construction for Transfer Functions 259
6.1.4 Identification of Transfer Function from Bode Plot 264
6.2 Power Stage Transfer Functions of Buck Converter 266
6.2.1 Input-to-output Transfer Function 266
6.2.2 Duty Ratio-to-output Transfer Function 270
6.2.3 Load Current-to-output Transfer Function 273
6.3 Power Stage Transfer Functions of Boost Converter 274
6.3.1 Input-to-output Transfer Function 274
6.3.2 Duty Ratio-to-output Transfer Function and RHP Zero 276
6.3.3 Load Current-to-output Transfer Function 280
6.3.4 Physical Origin of RHP Zero 280
6.4 Power Stage Transfer Functions of Buck/Boost Converter 284
6.5 Empirical Methods in Small signal Analysis 286
6.6 Summary 289
References 289
Problems 291
7 Dynamic Performance of PWM Dc-to-dc Converters 299
7.1 Stability 300
7.2 Frequency-Domain Performance Criteria 303
7.2.1 Loop Gain 303
7.2.2 Audio-Susceptibility 304
7.2.3 -output Impedance 305
7.3 Time-Domain Performance Criteria 307
7.3.1 Step Load Response 307
7.3.2 Step Input Response 308
7.4 Stability of Dc-to-dc Converters 309
7.4.1 Stability of Linear Time-Invariant Systems 309
7.4.2 Small signal Stability of Dc-to-dc Converters 310
7.5 Nyquist Criterion 311
7.6 Relative Stability: Gain Margin and Phase Margin 318
7.7 Summary 325
References 325
Problems 326
8 Closed-loop Performance and Feedback Compensation 333
8.1 Asymptotic Analysis Method 334
8.1.1 Concept of Asymptotic Analysis Method 334
8.1.2 Examples of Asymptotic Analysis Method 336
8.2 Frequency-Domain Performance 341
8.2.1 Audio-Susceptibility 342
8.2.2 -output Impedance 345
8.3 Voltage Feedback Compensation and Loop Gain 346
8.3.1 Problems of Single Integrator 347
8.3.2 Voltage Feedback Compensation Structure 349
8.3.3 Circuit Implementation of Voltage Feedback Compensation 351
8.4 Compensation Design and Closed-loop Performance 351
8.4.1 Voltage Feedback Compensation and Loop Gain 352
8.4.2 Feedback Compensation Design Guidelines 354
8.4.3 Voltage Feedback Compensation and Closed-loop
Performance 355
8.4.4 Phase Margin and Closed-loop Performance 369
8.4.5 Compensation Zero and Speed of Transient Responses 374
8.4.6 Step Load Response 378
8.4.7 Non-Minimum Phase System Case: Boost and Buck/boost Converters 380
8.5 Summary 385
References 387
Problems 387
9 Practical Considerations in Modeling, Analysis, and Design of PWM Converters 409
9.1 Generalization of PWM Converter Model 410
9.1.1 Converter Modeling with Parasitic Resistances 410
9.1.2 Modeling and Analysis of PWM Converters in DCM Operation 417
9.1.3 Modeling of Isolated PWM Converters 427
9.2 Design and Analysis of Dc-to-Dc Converters with Practical Source System 433
9.2.1 Audio-Susceptibility Analysis 435
9.2.2 Stability Analysis 436
9.2.3 Input Impedance of Regulated Dc-to-Dc Converter 443
9.2.4 Origin of Instability 448
9.2.5 Control Design with Source Impedance 450
9.2.6 Impacts of Source Impedance on Loop Gain and -output Impedance 450
9.3 Consideration for Non-Resistive Load 452
9.4 Summary 453
References 456
Problems 456
PART III CURRENT MODE CONTROL
10 Current Mode Control – Functional Basics and Classical Analysis 467
10.1 Current Mode Control Basics 469
10.1.1 Evolution to Peak Current Mode Control 469
10.1.2 Benefits and Issues of Peak Current Mode Control 476
10.1.3 Average Current Mode Control and Charge Control 478
10.2 Classical Analysis and Control Design Procedures 480
10.2.1 Small signal Model for Peak Current Mode Control 482
10.2.2 Loop Gain Analysis 488
10.2.3 Stability Analysis 491
10.2.4 Voltage Feedback Compensation 494
10.2.5 Control Design Procedures 499
10.2.6 Analysis of Converter Dynamics in DCM 508
10.3 Closed-loop Performance of Peak Current Mode Control 511
10.3.1 Audio-Susceptibility Analysis 512
10.3.2 -output Impedance Analysis 519
10.3.3 Step Load Response Analysis 523
10.4 Current Mode Control for Boost and Buck/Boost Converters 535
10.4.1 Stability Analysis and Control Design 535
10.4.2 Loop Gain Analysis 546
10.5 Summary 551
References 553
Problems 553
11 Current Mode Control – Sampling Effects and New Control Design Procedures 561
11.1 Sampling Effects of Current Mode Control 562
11.1.1 Origin and Consequence of Sampling Effects 562
11.1.2 Modeling Methodology for Sampling Effects 565
11.1.3 Feedforward Gains 566
11.1.4 Complete s-Domain Model for Current Mode Control 567
11.1.5 Two Prevalent s-Domain Models for Current Mode Control 567
11.2 Expressions for s-Domain Model for Current Mode Control 569
11.2.1 Modified Small signal Model 570
11.2.2 Modulator Gain F*m 571
11.2.3 He(s): s-Domain Representation of Sampling Effects 572
11.2.4 Feedforward Gains 582
11.3 New Control Design Procedures for Current Mode Control 586
11.3.1 New Power Stage Model 586
11.3.2 Control-to-output Transfer Function with Current-Loop Closed 588
11.3.3 Control Design Procedures 593
11.3.4 Correlation between New and Classical Design Procedures 609
11.4 Current Mode Control for Off-Line Flyback Converter with Optocoupler-Isolated Feedback 615
11.4.1 Off-Line Power Supplies 615
11.4.2 Current Mode Control for Flyback Converter with Optocoupler Feedback 616
11.5 Summary 630
References 633
Problems 633
Index 637
Preface vii
PART I CIRCUITS FOR DC-TO-DC
POWER CONVERTERS
1 PWM Dc-to-dc Power Conversion 3
1.1 Description of PWM Dc-to-dc Power Conversion 4
1.1.1 Dc-to-dc Power Conversion 4
1.1.2 PWM Technique 6
1.2 Dc-to-dc Power Conversion System 7
1.3 Features and Issues of PWM Dc-to-dc Converter 8
1.4 Chapter Highlights 10
References 12
2 Power Stage Components 13
2.1 Semiconductor Switches 13
2.1.1 MOSFETs 14
2.1.2 Diodes 15
2.1.3 Simple Switching Circuit 16
2.2 Energy Storage and Transfer Devices 17
2.2.1 Inductors 18
2.2.2 Capacitors 25
2.2.3 Transformers 31
2.3 Switching Circuits in Practice 38
2.3.1 Solenoid Drive Circuits 38
2.3.2 Capacitor Charging Circuit 44
2.4 Summary 50
References 51
Problems 51
3 Buck Converter 69
3.1 Ideal Step Down Dc-to-dc Power Conversion 70
3.2 Buck Converter: Step Down Dc-to-dc Converter 72
3.2.1 Evolution to Buck Converter 72
3.2.2 Frequency Domain Analysis 73
3.3 Buck Converter in Start Up Transient 76
3.3.1 Piecewise Linear Analysis 76
3.3.2 Startup Response 76
3.4 Buck Converter in Steady State 78
3.4.1 Circuit Analysis Techniques 78
3.4.2 Steady State Analysis 80
3.4.3 Estimation of -output Voltage Ripple 82
3.5 Buck Converter in Discontinuous Conduction Mode 87
3.5.1 Origin of Discontinuous Conduction Mode Operation 88
3.5.2 Conditions for DCM Operation 90
3.5.3 Steady State Operation in DCM 92
3.6 Closed-loop Control of Buck Converter 97
3.6.1 Closed-loop Feedback Controller 98
3.6.2 Responses of Closed-loop Controlled Buck Converter 102
3.7 Summary 107
References 108
Problems 108
4 Dc-to-dc Power Converter Circuits 123
4.1 Boost Converter 124
4.1.1 Evolution to Boost Converter 124
4.1.2 Steady State Analysis in CCM 126
4.1.3 Steady State Analysis in DCM 130
4.1.4 Effects of Parasitic Resistance on Voltage Gain 132
4.2 Buck/Boost Converter 135
4.2.1 Evolution to Buck/Boost Converter 135
4.2.2 Steady-state Analysis in CCM 138
4.2.3 Steady-state Analysis in DCM 141
4.3 Structure and Voltage Gain of Three Basic Converters 144
4.4 Flyback Converter: Transformer Isolated Buck/Boost Converter 145
4.4.1 Evolution to Flyback Converter 146
4.4.2 Steady-state Analysis in CCM 147
4.4.3 Steady-state Analysis in DCM 151
4.5 Bridge-Type Buck Derived Isolated Dc-to-dc Converters 154
4.5.1 Switch Network and Multi Winding Transformer 155
4.5.2 Full-Bridge Converter 158
4.5.3 Half-Bridge Converter 163
4.5.4 Push-Pull Converter 167
4.6 Forward Converters 167
4.6.1 Basic Operational Principles 167
4.6.2 Tertiary-Winding Reset Forward Converter 173
4.6.3 Two-Switch Forward Converter 177
4.7 Summary 180
References 181
Problems 181
PART II MODELING, DYNAMICS, AND DESIGN OF PWM DC-TO-DC CONVERTERS
5 Modeling PWM Dc-to-dc Converters 201
5.1 Overview of PWM Converter Modeling 202
5.2 Averaging Power Stage Dynamics 204
5.2.1 State-Space Averaging 206
5.2.2 Circuit Averaging 212
5.2.3 Generalization of Circuit Averaging Technique 221
5.2.4 Circuit Averaging and State Space Averaging 222
5.3 Linearizing Averaged Power Stage Dynamics 223
5.3.1 Linearization of Nonlinear Function and Small Signal Model 223
5.3.2 Small Signal Model for PWM Switch: PWM Switch Model 225
5.3.3 Small Signal Model of Converter Power Stage 227
5.4 Frequency Response of Converter Power Stage 230
5.4.1 Sinusoidal Response of Power Stage 230
5.4.2 Frequency Response and s-Domain Small signal Power Stage Model 232
5.5 Small signal Gain of PWM Block 235
5.6 Small signal Model for PWM Dc-to-dc Converters 236
5.6.1 Voltage Feedback Circuit 236
5.6.2 Small signal Model for PWM Converters 238
5.7 Summary 240
References 241
Problems 241
6 Power Stage Transfer Functions 247
6.1 Bode Plot for Transfer Functions 247
6.1.1 Basic Definitions 248
6.1.2 Bode Plots for Multiplication Factors 250
6.1.3 Bode Plot Construction for Transfer Functions 259
6.1.4 Identification of Transfer Function from Bode Plot 264
6.2 Power Stage Transfer Functions of Buck Converter 266
6.2.1 Input-to-output Transfer Function 266
6.2.2 Duty Ratio-to-output Transfer Function 270
6.2.3 Load Current-to-output Transfer Function 273
6.3 Power Stage Transfer Functions of Boost Converter 274
6.3.1 Input-to-output Transfer Function 274
6.3.2 Duty Ratio-to-output Transfer Function and RHP Zero 276
6.3.3 Load Current-to-output Transfer Function 280
6.3.4 Physical Origin of RHP Zero 280
6.4 Power Stage Transfer Functions of Buck/Boost Converter 284
6.5 Empirical Methods in Small signal Analysis 286
6.6 Summary 289
References 289
Problems 291
7 Dynamic Performance of PWM Dc-to-dc Converters 299
7.1 Stability 300
7.2 Frequency-Domain Performance Criteria 303
7.2.1 Loop Gain 303
7.2.2 Audio-Susceptibility 304
7.2.3 -output Impedance 305
7.3 Time-Domain Performance Criteria 307
7.3.1 Step Load Response 307
7.3.2 Step Input Response 308
7.4 Stability of Dc-to-dc Converters 309
7.4.1 Stability of Linear Time-Invariant Systems 309
7.4.2 Small signal Stability of Dc-to-dc Converters 310
7.5 Nyquist Criterion 311
7.6 Relative Stability: Gain Margin and Phase Margin 318
7.7 Summary 325
References 325
Problems 326
8 Closed-loop Performance and Feedback Compensation 333
8.1 Asymptotic Analysis Method 334
8.1.1 Concept of Asymptotic Analysis Method 334
8.1.2 Examples of Asymptotic Analysis Method 336
8.2 Frequency-Domain Performance 341
8.2.1 Audio-Susceptibility 342
8.2.2 -output Impedance 345
8.3 Voltage Feedback Compensation and Loop Gain 346
8.3.1 Problems of Single Integrator 347
8.3.2 Voltage Feedback Compensation Structure 349
8.3.3 Circuit Implementation of Voltage Feedback Compensation 351
8.4 Compensation Design and Closed-loop Performance 351
8.4.1 Voltage Feedback Compensation and Loop Gain 352
8.4.2 Feedback Compensation Design Guidelines 354
8.4.3 Voltage Feedback Compensation and Closed-loop
Performance 355
8.4.4 Phase Margin and Closed-loop Performance 369
8.4.5 Compensation Zero and Speed of Transient Responses 374
8.4.6 Step Load Response 378
8.4.7 Non-Minimum Phase System Case: Boost and Buck/boost Converters 380
8.5 Summary 385
References 387
Problems 387
9 Practical Considerations in Modeling, Analysis, and Design of PWM Converters 409
9.1 Generalization of PWM Converter Model 410
9.1.1 Converter Modeling with Parasitic Resistances 410
9.1.2 Modeling and Analysis of PWM Converters in DCM Operation 417
9.1.3 Modeling of Isolated PWM Converters 427
9.2 Design and Analysis of Dc-to-Dc Converters with Practical Source System 433
9.2.1 Audio-Susceptibility Analysis 435
9.2.2 Stability Analysis 436
9.2.3 Input Impedance of Regulated Dc-to-Dc Converter 443
9.2.4 Origin of Instability 448
9.2.5 Control Design with Source Impedance 450
9.2.6 Impacts of Source Impedance on Loop Gain and -output Impedance 450
9.3 Consideration for Non-Resistive Load 452
9.4 Summary 453
References 456
Problems 456
PART III CURRENT MODE CONTROL
10 Current Mode Control – Functional Basics and Classical Analysis 467
10.1 Current Mode Control Basics 469
10.1.1 Evolution to Peak Current Mode Control 469
10.1.2 Benefits and Issues of Peak Current Mode Control 476
10.1.3 Average Current Mode Control and Charge Control 478
10.2 Classical Analysis and Control Design Procedures 480
10.2.1 Small signal Model for Peak Current Mode Control 482
10.2.2 Loop Gain Analysis 488
10.2.3 Stability Analysis 491
10.2.4 Voltage Feedback Compensation 494
10.2.5 Control Design Procedures 499
10.2.6 Analysis of Converter Dynamics in DCM 508
10.3 Closed-loop Performance of Peak Current Mode Control 511
10.3.1 Audio-Susceptibility Analysis 512
10.3.2 -output Impedance Analysis 519
10.3.3 Step Load Response Analysis 523
10.4 Current Mode Control for Boost and Buck/Boost Converters 535
10.4.1 Stability Analysis and Control Design 535
10.4.2 Loop Gain Analysis 546
10.5 Summary 551
References 553
Problems 553
11 Current Mode Control – Sampling Effects and New Control Design Procedures 561
11.1 Sampling Effects of Current Mode Control 562
11.1.1 Origin and Consequence of Sampling Effects 562
11.1.2 Modeling Methodology for Sampling Effects 565
11.1.3 Feedforward Gains 566
11.1.4 Complete s-Domain Model for Current Mode Control 567
11.1.5 Two Prevalent s-Domain Models for Current Mode Control 567
11.2 Expressions for s-Domain Model for Current Mode Control 569
11.2.1 Modified Small signal Model 570
11.2.2 Modulator Gain F*m 571
11.2.3 He(s): s-Domain Representation of Sampling Effects 572
11.2.4 Feedforward Gains 582
11.3 New Control Design Procedures for Current Mode Control 586
11.3.1 New Power Stage Model 586
11.3.2 Control-to-output Transfer Function with Current-Loop Closed 588
11.3.3 Control Design Procedures 593
11.3.4 Correlation between New and Classical Design Procedures 609
11.4 Current Mode Control for Off-Line Flyback Converter with Optocoupler-Isolated Feedback 615
11.4.1 Off-Line Power Supplies 615
11.4.2 Current Mode Control for Flyback Converter with Optocoupler Feedback 616
11.5 Summary 630
References 633
Problems 633
Index 637
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