Pulse-Width Modulated DC-DC Power Converters

Marian K. Kazimierczuk Wright State University, Dayton, Ohio, USA

About the Author xxi

Preface xxiii

Nomenclature xxv

1 Introduction 1

1.1 Classification of Power Supplies 1

1.2 Basic Functions of Voltage Regulators 3

1.3 Power Relationships in DC–DC Converters 4

1.4 DC Transfer Functions of DC–DC Converters 5

1.5 Static Characteristics of DC Voltage Regulators 6

1.6 Dynamic Characteristics of DC Voltage Regulators 9

1.7 Linear Voltage Regulators 12

1.7.1 Series Voltage Regulator 13

1.7.2 Shunt Voltage Regulator 14

1.8 Topologies of PWM DC–DC Converters 16

1.9 Relationships Among Current, Voltage, Energy, and Power 18

1.10 Summary 19

References 19

Review Questions 20

Problems 21

2 Buck PWM DC–DC Converter 22

2.1 Introduction 22

2.2 DC Analysis of PWM Buck Converter for CCM 22

2.2.1 Circuit Description 22

2.2.2 Assumptions 25

2.2.3 Time Interval: 0 < t ≤ DT 25

2.2.4 Time Interval: DT < t ≤ T 26

2.2.5 Device Stresses for CCM 27

2.2.6 DC Voltage Transfer Function for CCM 27

2.2.7 Boundary Between CCM and DCM 29

2.2.8 Capacitors 31

2.2.9 Ripple Voltage in Buck Converter for CCM 33

2.2.10 Switching Losses with Linear MOSFET Output Capacitance 39

2.2.11 Switching Losses with Nonlinear MOSFET Output Capacitance 40

2.2.12 Power Losses and Efficiency of Buck Converter for CCM 43

2.2.13 DC Voltage Transfer Function of Lossy Converter for CCM 48

2.2.14 MOSFET Gate-Drive Power 48

2.2.15 Gate Driver 49

2.2.16 Design of Buck Converter for CCM 50

2.3 DC Analysis of PWM Buck Converter for DCM 52

2.3.1 Time Interval: 0 < t ≤ DT 56

2.3.2 Time Interval: DT < t ≤ (D + D1)T 58

2.3.3 Time Interval: (D + D1)T < t ≤ T 58

2.3.4 Device Stresses for DCM 59

2.3.5 DC Voltage Transfer Function for DCM 59

2.3.6 Maximum Inductance for DCM 62

2.3.7 Power Losses and Efficiency of Buck Converter for DCM 63

2.3.8 Design of Buck Converter for DCM 65

2.4 Buck Converter with Input Filter 68

2.5 Buck Converter with Synchronous Rectifier 68

2.6 Buck Converter with Positive Common Rail 76

2.7 Quadratic Buck Converter 76

2.8 Tapped-Inductor Buck Converters 79

2.8.1 Tapped-Inductor Common-Diode Buck Converter 79

2.8.2 Tapped-Inductor Common-Transistor Buck Converter 81

2.8.3 Watkins–Johnson Converter 82

2.9 Multiphase Buck Converter 83

2.10 Switched-Inductor Buck Converter 85

2.11 Layout 85

2.12 Summary 85

References 87

Review Questions 88

Problems 88

3 Boost PWM DC–DC Converter 90

3.1 Introduction 90

3.2 DC Analysis of PWM Boost Converter for CCM 90

3.2.1 Circuit Description 90

3.2.2 Assumptions 91

3.2.3 Time Interval: 0 < t ≤ DT 93

3.2.4 Time Interval: DT < t ≤ T 94

3.2.5 DC Voltage Transfer Function for CCM 94

3.2.6 Boundary Between CCM and DCM 95

3.2.7 Ripple Voltage in Boost Converter for CCM 98

3.2.8 Power Losses and Efficiency of Boost Converter for CCM 100

3.2.9 DC Voltage Transfer Function of Lossy Boost Converter for CCM 102

3.2.10 Design of Boost Converter for CCM 103

3.3 DC Analysis of PWM Boost Converter for DCM 107

3.3.1 Time Interval: 0 < t ≤ DT 110

3.3.2 Time Interval: DT < t ≤ (D + D1)T 111

3.3.3 Time Interval: (D + D1)T < t ≤ T 112

3.3.4 Device Stresses for DCM 112

3.3.5 DC Voltage Transfer Function for DCM 112

3.3.6 Maximum Inductance for DCM 117

3.3.7 Power Losses and Efficiency of Boost Converter for DCM 117

3.3.8 Design of Boost Converter for DCM 120

3.4 Bidirectional Buck and Boost Converters 127

3.5 Synchronous Boost Converter 129

3.6 Tapped-Inductor Boost Converters 129

3.6.1 Tapped-Inductor Common-Diode Boost Converter 131

3.6.2 Tapped-Inductor Common-Load Boost Converter 132

3.7 Duality 133

3.8 Power Factor Correction 134

3.8.1 Power Factor 134

3.8.2 Boost Power Factor Corrector 138

3.8.3 Electronic Ballasts for Fluorescent Lamps 141

3.9 Summary 141

References 142

Review Questions 143

Problems 143

4 Buck–Boost PWM DC–DC Converter 145

4.1 Introduction 145

4.2 DC Analysis of PWM Buck–Boost Converter for CCM 145

4.2.1 Circuit Description 145

4.2.2 Assumptions 146

4.2.3 Time Interval: 0 < t ≤ DT 146

4.2.4 Time Interval: DT < t ≤ T 148

4.2.5 DC Voltage Transfer Function for CCM 149

4.2.6 Device Stresses for CCM 150

4.2.7 Boundary Between CCM and DCM 151

4.2.8 Ripple Voltage in Buck–Boost Converter for CCM 152

4.2.9 Power Losses and Efficiency of the Buck–Boost Converter for CCM 155

4.2.10 DC Voltage Transfer Function of Lossy Buck–Boost Converter for CCM 158

4.2.11 Design of Buck–Boost Converter for CCM 159

4.3 DC Analysis of PWM Buck–Boost Converter for DCM 162

4.3.1 Time Interval: 0 < t ≤ DT 165

4.3.2 Time Interval: DT < t ≤ (D + D1)T 166

4.3.3 Time Interval: (D + D1)T < t ≤ T 167

4.3.4 Device Stresses of the Buck–Boost Converter in DCM 167

4.3.5 DC Voltage Transfer Function of the Buck–Boost Converter for DCM 167

4.3.6 Maximum Inductance for DCM 170

4.3.7 Power Losses and Efficiency of the Buck–Boost Converter in DCM 172

4.3.8 Design of Buck–Boost Converter for DCM 174

4.4 Bidirectional Buck–Boost Converter 180

4.5 Synthesis of Buck–Boost Converter 181

4.6 Synthesis of Boost–Buck (ćuk) Converter 183

4.7 Noninverting Buck–Boost Converters 184

4.7.1 Cascaded Noninverting Buck–Boost Converters 184

4.7.2 Four-Transistor Noninverting Buck–Boost Converters 184

4.8 Tapped-Inductor Buck–Boost Converters 186

4.8.1 Tapped-Inductor Common-Diode Buck–Boost Converter 186

4.8.2 Tapped-Inductor Common-Transistor Buck–Boost Converter 187

4.8.3 Tapped-Inductor Common-Load Buck–Boost Converter 188

4.8.4 Tapped-Inductor Common-Source Buck–Boost Converter 191

4.9 Summary 192

References 192

Review Questions 193

Problems 193

5 Flyback PWM DC–DC Converter 195

5.1 Introduction 195

5.2 Transformers 196

5.3 DC Analysis of PWM Flyback Converter for CCM 197

5.3.1 Derivation of PWM Flyback Converter 197

5.3.2 Circuit Description 197

5.3.3 Assumptions 199

5.3.4 Time Interval: 0 < t ≤ DT 200

5.3.5 Time Interval: DT < t ≤ T 201

5.3.6 DC Voltage Transfer Function for CCM 203

5.3.7 Boundary Between CCM and DCM 204

5.3.8 Ripple Voltage in Flyback Converter for CCM 205

5.3.9 Power Losses and Efficiency of Flyback Converter for CCM 207

5.3.10 DC Voltage Transfer Function of Lossy Converter for CCM 210

5.3.11 Design of Flyback Converter for CCM 211

5.4 DC Analysis of PWM Flyback Converter for DCM 214

5.4.1 Time Interval: 0 < t ≤ DT 217

5.4.2 Time Interval: DT < t ≤ (D + D1)T 219

5.4.3 Time Interval: (D + D1)T < t ≤ T 220

5.4.4 DC Voltage Transfer Function for DCM 221

5.4.5 Maximum Magnetizing Inductance for DCM 222

5.4.6 Ripple Voltage in Flyback Converter for DCM 225

5.4.7 Power Losses and Efficiency of Flyback Converter for DCM 226

5.4.8 Design of Flyback Converter for DCM 228

5.5 Multiple-Output Flyback Converter 232

5.6 Bidirectional Flyback Converter 237

5.7 Ringing in Flyback Converter 237

5.8 Flyback Converter with Passive Dissipative Snubber 240

5.9 Flyback Converter with Zener Diode Voltage Clamp 240

5.10 Flyback Converter with Active Clamping 241

5.11 Two-Transistor Flyback Converter 241

5.12 Summary 243

References 244

Review Questions 244

Problems 245

6 Forward PWM DC–DC Converter 246

6.1 Introduction 246

6.2 DC Analysis of PWM Forward Converter for CCM 246

6.2.1 Derivation of Forward PWM Converter 246

6.2.2 Time Interval: 0 < t ≤ DT 248

6.2.3 Time Interval: DT < t ≤ DT + tm 251

6.2.4 Time Interval: DT + tm < t ≤ T 253

6.2.5 Maximum Duty Cycle 253

6.2.6 Device Stresses 254

6.2.7 DC Voltage Transfer Function for CCM 255

6.2.8 Boundary Between CCM and DCM 255

6.2.9 Ripple Voltage in Forward Converter for CCM 256

6.2.10 Power Losses and Efficiency of Forward Converter for CCM 258

6.2.11 DC Voltage Transfer Function of Lossy Converter for CCM 261

6.2.12 Design of Forward Converter for CCM 262

6.3 DC Analysis of PWM Forward Converter for DCM 269

6.3.1 Time Interval: 0 < t ≤ DT 269

6.3.2 Time Interval: DT < t ≤ DT + tm 272

6.3.3 Time Interval: DT + tm < t ≤ (D + D1)T 273

6.3.4 Time Interval: (D + D1)T < t ≤ T 273

6.3.5 DC Voltage Transfer Function for DCM 274

6.3.6 Maximum Inductance for DCM 277

6.3.7 Power Losses and Efficiency of Forward Converter for DCM 278

6.3.8 Design of Forward Converter for DCM 280

6.4 Multiple-Output Forward Converter 288

6.5 Forward Converter with Synchronous Rectifier 288

6.6 Forward Converters with Active Clamping 288

6.7 Two-Switch Forward Converter 290

6.8 Forward–Flyback Converter 291

6.9 Summary 292

References 293

Review Questions 293

Problems 294

7 Half-Bridge PWM DC–DC Converter 296

7.1 Introduction 296

7.2 DC Analysis of PWM Half-Bridge Converter for CCM 296

7.2.1 Circuit Description 296

7.2.2 Assumptions 299

7.2.3 Time Interval: 0 < t ≤ DT 299

7.2.4 Time Interval: DT < t ≤ T∕2 301

7.2.5 Time Interval: T∕2 < t ≤ T∕2 + DT 303

7.2.6 Time Interval: T∕2 + DT < t ≤ T 304

7.2.7 Device Stresses 304

7.2.8 DC Voltage Transfer Function of Lossless Half-Bridge Converter for CCM 304

7.2.9 Boundary Between CCM and DCM 305

7.2.10 Ripple Voltage in Half-Bridge Converter for CCM 306

7.2.11 Power Losses and Efficiency of Half-Bridge Converter for CCM 308

7.2.12 DC Voltage Transfer Function of Lossy Converter for CCM 311

7.2.13 Design of Half-Bridge Converter for CCM 312

7.3 DC Analysis of PWM Half-Bridge Converter for DCM 315

7.3.1 Time Interval: 0 < t ≤ DT 315

7.3.2 Time Interval: DT < t ≤ (D + D1)T 320

7.3.3 Time Interval: (D + D1)T < t ≤ T∕2 322

7.3.4 DC Voltage Transfer Function for DCM 322

7.3.5 Maximum Inductance for DCM 326

7.4 Summary 326

References 327

Review Questions 327

Problems 328

8 Full-Bridge PWM DC–DC Converter 330

8.1 Introduction 330

8.2 DC Analysis of PWM Full-Bridge Converter for CCM 330

8.2.1 Circuit Description 330

8.2.2 Assumptions 332

8.2.3 Time Interval: 0 < t ≤ DT 332

8.2.4 Time Interval: DT < t ≤ T∕2 334

8.2.5 Time Interval: T∕2 < t ≤ T∕2 + DT 336

8.2.6 Time Interval: T∕2 + DT < t ≤ T 336

8.2.7 Device Stresses 337

8.2.8 DC Voltage Transfer Function of Lossless Full-Wave Converter for CCM 337

8.2.9 Boundary Between CCM and DCM 338

8.2.10 Ripple Voltage in Full-Bridge Converter for CCM 339

8.2.11 Power Losses and Efficiency of Full-Bridge Converter for CCM 340

8.2.12 DC Voltage Transfer Function of Lossy Converter for CCM 344

8.2.13 Design of Full-Bridge Converter for CCM 345

8.3 DC Analysis of PWM Full-Bridge Converter for DCM 351

8.3.1 Time Interval: 0 < t ≤ DT 351

8.3.2 Time Interval: DT < t ≤ (D + D1)T 353

8.3.3 Time Interval: (D + D1)T < t ≤ T∕2 355

8.3.4 DC Voltage Transfer Function for DCM 356

8.3.5 Maximum Inductance for DCM 359

8.4 Phase-Controlled Full-Bridge Converter 361

8.5 Summary 362

References 362

Review Questions 362

Problems 363

9 Small-Signal Models of PWM Converters for CCM and DCM 365

9.1 Introduction 365

9.2 Assumptions 366

9.3 Averaged Model of Ideal Switching Network for CCM 366

9.4 Averaged Values of Switched Resistances 369

9.5 Model Reduction 375

9.6 Large-Signal Averaged Model for CCM 377

9.7 DC and Small-Signal Circuit Linear Models of Switching Network for CCM 381

9.7.1 Large-Signal Circuit Model of Switching Network for CCM 381

9.7.2 Linearization of Switching Network Model for CCM 384

9.8 Block Diagram of Small-signal Model of PWM DC–DC Converters 385

9.9 Family of PWM Converter Models for CCM 386

9.10 PWM Small-Signal Switch Model for CCM 389

9.11 Modeling of Ideal Switching Network for DCM 391

9.11.1 Relationships Among DC Components for DCM 391

9.11.2 Small-Signal Model of Ideal Switching Network for DCM 395

9.12 Averaged Parasitic Resistances for DCM 398

9.13 Summary 400

References 402

Review Questions 405

Problems 405

10 Small-Signal Characteristics of Buck Converter for CCM 407

10.1 Introduction 407

10.2 Small-Signal Model of the PWM Buck Converter 407

10.3 Open-Loop Transfer Functions 408

10.3.1 Open-Loop Control-to-Output Transfer Function 409

10.3.2 Delay in Control-to-Output Transfer Function 416

10.3.3 Open-Loop Input-to-Output Transfer Function 418

10.3.4 Open-Loop Input Impedance 420

10.3.5 Open-Loop Output Impedance 423

10.4 Open-Loop Step Responses 426

10.4.1 Open-Loop Response of Output Voltage to Step Change in Input Voltage 426

10.4.2 Open-Loop Response of Output Voltage to Step Change in Duty Cycle 431

10.4.3 Open-Loop Response of Output Voltage to Step Change in Load Current 433

10.5 Open-Loop DC Transfer Functions 434

10.6 Summary 436

References 436

Review Questions 437

Problems 438

11 Small-Signal Characteristics of Boost Converter for CCM 439

11.1 Introduction 439

11.2 DC Characteristics 439

11.3 Open-Loop Control-to-Output Transfer Function 440

11.4 Delay in Open-Loop Control-to-Output Transfer Function 449

11.5 Open-Loop Audio Susceptibility 451

11.6 Open-Loop Input Impedance 455

11.7 Open-Loop Output Impedance 457

11.8 Open-Loop Step Responses 461

11.8.1 Open-Loop Response of Output Voltage to Step Change in Input Voltage 461

11.8.2 Open-Loop Response of Output Voltage to Step Change in Duty Cycle 464

11.8.3 Open-Loop Response of Output Voltage to Step Change in Load Current 465

11.9 Summary 467

References 467

Review Questions 468

Problems 468

12 Voltage-Mode Control of PWM Buck Converter 470

12.1 Introduction 470

12.2 Properties of Negative Feedback 471

12.3 Stability 474

12.4 Single-Loop Control of PWM Buck Converter 475

12.5 Closed-Loop Small-Signal Model of Buck Converter 478

12.6 Pulse-Width Modulator 478

12.7 Feedback Network 483

12.8 Transfer Function of Buck Converter with Modulator and Feedback Network 486

12.9 Control Circuits 489

12.9.1 Error Amplifier 489

12.9.2 Proportional Controller 490

12.9.3 Integral Controller 492

12.9.4 Proportional-Integral Controller 493

12.9.5 Integral-Single-Lead Controller 497

12.9.6 Loop Gain 504

12.9.7 Closed-Loop Control-to-Output Voltage Transfer Function 504

12.9.8 Closed-Loop Input-to-Output Transfer Function 506

12.9.9 Closed-Loop Input Impedance 508

12.9.10 Closed-Loop Output Impedance 509

12.10 Closed-Loop Step Responses 511

12.10.1 Response to Step Change in Input Voltage 511

12.10.2 Response to Step Change in Reference Voltage 513

12.10.3 Closed-Loop Response to Step Change in Load Current 515

12.10.4 Closed-Loop DC Transfer Functions 515

12.11 Summary 518

References 519

Review Questions 519

Problems 520

13 Voltage-Mode Control of Boost Converter 521

13.1 Introduction 521

13.2 Circuit of Boost Converter with Voltage-Mode Control 521

13.3 Transfer Function of Modulator, Boost Converter Power Stage, and Feedback Network 523

13.4 Integral-Double-Lead Controller 527

13.5 Design of Integral-Double-Lead Controller 532

13.6 Loop Gain 536

13.7 Closed-Loop Control-to-Output Voltage Transfer Function 537

13.8 Closed-Loop Audio Susceptibility 539

13.9 Closed-Loop Input Impedance 539

13.10 Closed-Loop Output Impedance 542

13.11 Closed-Loop Step Responses 544

13.11.1 Closed-Loop Response to Step Change in Input Voltage 544

13.11.2 Closed-Loop Response to Step Change in Reference Voltage 547

13.11.3 Closed-Loop Response to Step Change in Load Current 548

13.12 Closed-Loop DC Transfer Functions 549

13.13 Summary 552

References 552

Review Questions 552

Problems 553

14 Current-Mode Control 554

14.1 Introduction 554

14.2 Principle of Operation of PWM Converters with Peak CMC 555

14.3 Relationship Between Duty Cycle and Inductor-Current Slopes 559

14.4 Instability of Closed-Current Loop 560

14.5 Slope Compensation 564

14.5.1 Analysis of Slope Compensation in Time Domain 564

14.5.2 Boundary of Slope Compensation for Buck and Buck–Boost Converters 569

14.5.3 Boundary Slope Compensation for Boost Converter 570

14.6 Sample-and-Hold Effect on Current Loop 570

14.6.1 Natural Response of Inductor Current to Small Perturbation in Closed-Current Loop 572

14.6.2 Forced Response of Inductor Current to Step Change in Control Voltage in Closed-Current Loop 575

14.6.3 Relationship Between s-Domain and z-Domain 577

14.6.4 Transfer Function of Closed-Current Loop in z-Domain 578

14.7 Closed-Loop Control Voltage-to-Inductor Current Transfer Function in s-Domain 580

14.7.1 Approximation of Hicl by Rational Transfer Function 582

14.7.2 Step Responses of Closed-Inner Loop 588

14.8 Loop Gain of Current Loop 588

14.8.1 Loop Gain of Inner Loop in z-Domain 588

14.8.2 Loop Gain of Inner Loop in s-Domain 590

14.9 Gain-Crossover Frequency of Inner Loop 595

14.10 Phase Margin of Inner Loop 596

14.11 Maximum Duty Cycle for Converters without Slope Compensation 598

14.12 Maximum Duty Cycle for Converters with Slope Compensation 600

14.13 Minimum Slope Compensation for Buck and Buck–Boost Converter 605

14.14 Minimum Slope Compensation for Boost Converter 607

14.15 Error Voltage-to-Duty Cycle Transfer Function 610

14.16 Closed-Loop Control Voltage-to-Duty Cycle Transfer Function of Current Loop 614

14.17 Alternative Representation of Current Loop 618

14.18 Current Loop with Disturbances 618

14.18.1 Modified Approximation of Current Loop 619

14.19 Voltage Loop of PWM Converters with Current-Mode Control 624

14.19.1 Control-to-Output Transfer Function for Buck Converter 624

14.19.2 Block Diagram of Power Stages of PWM Converters 627

14.19.3 Closed-Voltage Loop Transfer Function of PWM Converters with Current-Mode Control 628

14.19.4 Closed-Loop Audio Susceptibility of PWM Converters with Current-Mode Control 628

14.19.5 Closed-Loop Output Impedance of PWM Converters with Current-Mode Control 630

14.20 Feedforward Gains in PWM Converters with Current-Mode Control without Slope Compensation 631

14.21 Feedforward Gains in PWM Converters with Current-Mode Control and Slope Compensation 634

14.22 Control-to-Output Voltage Transfer Function of Inner Loop with Feedforward Gains 636

14.23 Audio-Susceptibility of Inner Loop with Feedforward Gains 637

14.24 Closed-Loop Transfer Functions with Feedforward Gains 638

14.25 Slope Compensation by Adding a Ramp to Inductor Current Waveform 638

14.26 Relationships for Constant-Frequency Current-Mode On-Time Control 639

14.27 Summary 639

References 640

Review Questions 644

Problems 644

14.28 Appendix: Sample-and-Hold Modeling 645

14.28.1 Sampler of the Control Voltage 645

14.28.2 Zero-Order Hold of Inductor Current 648

14.28.3 Approximations of esTs 650

15 Current-Mode Control of Boost Converter 653

15.1 Introduction 653

15.2 Open-Loop Small-Signal Transfer Functions 653

15.2.1 Open-Loop Duty Cycle-to-Inductor Current Transfer Function 653

15.2.2 High-Frequency Open-Loop Duty Cycle-to-Inductor Current Transfer Function 659

15.2.3 Open-Loop Input Voltage-to-Inductor Current Transfer Function 660

15.2.4 Open-Loop Inductor-to-Output Current Transfer Function 665

15.3 Open-Loop Step Responses of Inductor Current 667

15.3.1 Open-Loop Response of Inductor Current to Step Change in Input Voltage 667

15.3.2 Open-Loop Response of the Inductor Current to Step Change in the Duty Cycle 670

15.3.3 Open-Loop Response of Inductor Current to Step Change in Load Current 672

15.4 Closed-Current-Loop Transfer Functions 675

15.4.1 Forward Gain 675

15.4.2 Loop Gain of Current Loop 675

15.4.3 Closed-Loop Gain of Current Loop 675

15.4.4 Control-to-Output Transfer Function 677

15.4.5 Input Voltage-to-Duty Cycle Transfer Function 684

15.4.6 Load Current-to-Duty Cycle Transfer Function 688

15.4.7 Output Impedance of Closed-Current Loop 690

15.5 Closed-Voltage-Loop Transfer Functions 695

15.5.1 Control-to-Output Transfer Function 695

15.5.2 Control Voltage-to-Feedback Voltage Transfer Function 695

15.5.3 Loop Gain of Voltage Loop 697

15.5.4 Closed-Loop Gain of Voltage Loop 701

15.5.5 Closed-Loop Audio Susceptibility with Integral Controller 703

15.5.6 Closed-Loop Output Impedance with Integral Controller 704

15.6 Closed-Loop Step Responses 706

15.6.1 Closed-Loop Response of Output Voltage to Step Change in Input Voltage 706

15.6.2 Closed-Loop Response of Output Voltage to Step Change in Load Current 708

15.6.3 Closed-Loop Response of Output Voltage to Step Change in Reference Voltage 708

15.7 Closed-Loop DC Transfer Functions 710

15.8 Summary 711

References 711

Review Questions 712

Problems 712

16 Open-Loop Small-Signal Characteristics of PWM Boost Converter for DCM 713

16.1 Introduction 713

16.2 Small-Signal Model of Boost Converter for DCM 713

16.3 Open-Loop Control-to-Output Transfer Function 716

16.4 Open-Loop Input-to-Output Voltage Transfer Function 719

16.5 Open-Loop Input Impedance 724

16.6 Open-Loop Output Impedance 725

16.7 Step Responses of Output Voltage of Boost Converter for DCM 728

16.7.1 Response of Output Voltage to Step Change in Input Voltage 728

16.7.2 Response of Output Voltage to Step Change in Duty Cycle 730

16.7.3 Response of Output Voltage to Step Change in Load Current 730

16.8 Open-Loop Duty Cycle-to-Inductor Current Transfer Function 731

16.9 Open-Loop Input Voltage-to-Inductor Current Transfer Function 735

16.10 Open-Loop Output Current-to-Inductor Current Transfer Function 735

16.11 Step Responses of Inductor Current of Boost Converter for DCM 738

16.11.1 Step Response of Inductor Current to Step Change in Input Voltage 738

16.11.2 Step Response of Inductor Current to Step Change in Duty Cycle 740

16.11.3 Step Response of Inductor Current to Step Change in Load Current 741

16.12 DC Characteristics of Boost Converter for DCM 742

16.12.1 DC-to-DC Voltage Transfer Function of Lossless Boost Converter for DCM 742

16.12.2 DC-to-DC Voltage Transfer Function of Lossy Boost Converter for DCM 743

16.12.3 Efficiency of Boost Converter for DCM 745

16.13 Summary 745

References 745

Review Questions 746

Problems 746

17 Silicon and Silicon-Carbide Power Diodes 747

17.1 Introduction 747

17.2 Electronic Power Switches 747

17.3 Atom 748

17.4 Electron and Hole Effective Mass 749

17.5 Semiconductors 750

17.6 Intrinsic Semiconductors 751

17.7 Extrinsic Semiconductors 756

17.7.1 n-Type Semiconductor 756

17.7.2 p-Type Semiconductor 759

17.7.3 Maximum Operating Temperature 761

17.8 Wide Band Gap Semiconductors 762

17.9 Physical Structure of Junction Diodes 764

17.9.1 Formation of Depletion Layer 765

17.9.2 Charge Transport 767

17.10 Static I–V Diode Characteristic 768

17.11 Breakdown Voltage of Junction Diodes 772

17.11.1 Depletion-Layer Width 773

17.11.2 Electric Field Intensity Distribution 775

17.11.3 Avalanche Breakdown Voltage 779

17.11.4 Punch-Through Breakdown Voltage 781

17.11.5 Edge Terminations 782

17.12 Capacitances of Junction Diodes 784

17.12.1 Junction Capacitance 784

17.12.2 Diffusion Capacitance 787

17.13 Reverse Recovery of pn Junction Diodes 789

17.13.1 Qualitative Description 789

17.13.2 Reverse Recovery in Resistive Circuits 790

17.13.3 Charge-Continuity Equation 793

17.13.4 Reverse Recovery in Inductive Circuits 796

17.14 Schottky Diodes 798

17.14.1 Static I–V Characteristic of Schottky Diodes 801

17.14.2 Breakdown Voltages of Schottky Diodes 802

17.14.3 Junction Capacitance of Schottky Diodes 802

17.14.4 Switching Characteristics of Schottky Diodes 802

17.15 Solar Cells 806

17.16 Light-Emitting Diodes 809

17.17 SPICE Model of Diodes 810

17.18 Summary 811

References 815

Review Questions 816

Problems 817

18 Silicon and Silicon-Carbide Power MOSFETs 819

18.1 Introduction 819

18.2 Integrated MOSFETs 819

18.3 Physical Structure of Power MOSFETs 819

18.4 Principle of Operation of Power MOSFETs 824

18.4.1 Cutoff Region 824

18.4.2 Formation of MOSFET Channel 824

18.4.3 Linear Region 824

18.4.4 Saturation Region 825

18.4.5 Antiparallel Diode 825

18.5 Derivation of Power MOSFET Characteristics 826

18.5.1 Ohmic Region 826

18.5.2 Pinch-off Region 829

18.5.3 Channel-Length Modulation 830

18.6 Power MOSFET Characteristics 831

18.7 Mobility of Charge Carriers 833

18.7.1 Effect of Doping Concentration on Mobility 834

18.7.2 Effect of Temperature on Mobility 836

18.7.3 Effect of Electric Field on Mobility 840

18.8 Short-Channel Effects 846

18.8.1 Ohmic Region 846

18.8.2 Pinch-off Region 847

18.9 Aspect Ratio of Power MOSFETs 848

18.10 Breakdown Voltage of Power MOSFETs 850

18.11 Gate Oxide Breakdown Voltage of Power MOSFETs 852

18.12 Specific On-Resistance 852

18.13 Figures-of-Merit of Semiconductors 855

18.14 On-Resistance of Power MOSFETs 857

18.14.1 Channel Resistance 857

18.14.2 Accumulation Region Resistance 857

18.14.3 Neck Region Resistance 858

18.14.4 Drift Region Resistance 859

18.15 Capacitances of Power MOSFETs 862

18.15.1 Gate-to-Source Capacitance 862

18.15.2 Drain-to-Source Capacitance 864

18.15.3 Gate-to-Drain Capacitance 864

18.16 Switching Waveforms 875

18.17 SPICE Model of Power MOSFETs 877

18.18 IGBTs 879

18.19 Heat Sinks 880

18.20 Summary 886

References 888

Review Questions 888

Problems 889

19 Electromagnetic Compatibility 891

19.1 Introduction 891

19.2 Definition of EMI 891

19.3 Definition of EMC 892

19.4 EMI Immunity 892

19.5 EMI Susceptibility 893

19.6 Classification of EMI 893

19.7 Sources of EMI 895

19.8 Safety Standards 896

19.9 EMC Standards 896

19.10 Near Field and Far Field 897

19.11 Techniques of EMI Reduction 897

19.12 Insertion Loss 898

19.13 EMI Filters 898

19.14 Feed-Through Capacitors 900

19.15 EMI Shielding 900

19.16 Interconnections 902

19.17 Summary 903

References 903

Review Questions 903

Problem 904

A Introduction to SPICE 907

B Introduction to MATLAB® 910

C Physical Constants 915

Answers to Problems 917

Index 925