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Pulsewidth Modulated DC-to-DC Power Conversion Circuits, Dynamics, and Control Designs

by: Choi, Byungcho

Pulsewidth Modulated DC-to-DC Power Conversion Circuits, Dynamics, and Control Designs

by: Choi, Byungcho

ISBN 13:
9781118180631
ISBN 10:
1118180631
Edition: 1st
Format: Hardcover
Copyright: 07/22/2013
Publisher: Wiley-IEEE Press

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Pulsewidth Modulated DC-to-DC Power Conversion Circuits, Dynamics, and Control Designs > ISBN13: 9781118180631

Summary

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.

Author Biography

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*_m571

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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