Pulse-width Modulated DC–DC Power Converters

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Pulse-width Modulated DC–DC Power Converters
MARIAN K. KAZIMIERCZUK
Wright State University
Dayton, Ohio, USA

Contents
Preface xix
About the Author xxi
List of Symbols xxiii
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 5
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 17
1.9 Relationships among Current, Voltage, Energy, and Power 18
1.10 Electromagnetic Compatibility 19
1.11 Summary 20
1.12 References 20
1.13 Review Questions 21
1.14 Problems 22
2 BuckPWMDC–DCConverter 23
2.1 Introduction 23
2.2 DC Analysis of PWM Buck Converter for CCM 23
2.2.1 Circuit Description 23
2.2.2 Assumptions 27
2.2.3 Time Interval 0 < t ≤ DT 27
2.2.4 Time Interval DT < t ≤ T 28
2.2.5 Device Stresses for CCM 29
2.2.6 DC Voltage Transfer Function for CCM 29
viii CONTENTS
2.2.7 Boundary between CCM and DCM 30
2.2.8 Ripple Voltage in Buck Converter for CCM 32
2.2.9 Switching Losses with Linear MOSFET Output
Capacitance 37
2.2.10 Switching Losses with Nonlinear MOSFET Output
Capacitance 39
2.2.11 Power Losses and Efficiency of Buck Converter for CCM 42
2.2.12 DC Voltage Transfer Function of Lossy Converter for
CCM 46
2.2.13 MOSFET Gate-drive Power 47
2.2.14 Design of Buck Converter for CCM 48
2.3 DC Analysis of PWM Buck Converter for DCM 51
2.3.1 Time Interval 0 < t ≤ DT 54
2.3.2 Time Interval DT < t ≤ (D + D1)T 56
2.3.3 Time Interval (D + D1)T < t ≤ T 57
2.3.4 Device Stresses for DCM 57
2.3.5 DC Voltage Transfer Function for DCM 57
2.3.6 Maximum Inductance for DCM 59
2.3.7 Power Losses and Efficiency of Buck Converter for DCM 61
2.3.8 Design of Buck Converter for DCM 63
2.4 Buck Converter with Input Filter 69
2.5 Buck Converter with Synchronous Rectifier 69
2.6 Buck Converter with Positive Common Rail 72
2.7 Tapped-inductor Buck Converters 74
2.7.1 Tapped-inductor Common-diode Buck Converter 74
2.7.2 Tapped-inductor Common-transistor Buck Converter 76
2.7.3 Watkins–Johnson Converter 76
2.8 Multiphase Buck Converter 77
2.9 Summary 79
2.10 References 81
2.11 Review Questions 81
2.12 Problems 82
3 Boost PWM DC–DC Converter 85
3.1 Introduction 85
3.2 DC Analysis of PWM Boost Converter for CCM 85
3.2.1 Circuit Description 85
3.2.2 Assumptions 88
3.2.3 Time Interval 0 < t ≤ DT 88
3.2.4 Time Interval DT < t ≤ T 89
3.2.5 DC Voltage Transfer Function for CCM 90
3.2.6 Boundary between CCM and DCM 91
3.2.7 Ripple Voltage in Boost Converter for CCM 93
3.2.8 Power Losses and Efficiency of Boost Converter for CCM 95
3.2.9 DC Voltage Transfer Function of Lossy Boost Converter
for CCM 97
3.2.10 Design of Boost Converter for CCM 99
3.3 DC Analysis of PWM Boost Converter for DCM 103
3.3.1 Time Interval 0 < t ≤ DT 105
CONTENTS ix
3.3.2 Time Interval DT < t ≤ (D + D1)T 106
3.3.3 Time Interval (D + D1)T < t ≤ T 108
3.3.4 Device Stresses for DCM 108
3.3.5 DC Voltage Transfer Function for DCM 108
3.3.6 Maximum Inductance for DCM 112
3.3.7 Power Losses and Efficiency of Boost Converter for DCM 112
3.3.8 Design of Boost Converter for DCM 115
3.4 Bidirectional Buck and Boost Converters 122
3.5 Tapped-inductor Boost Converters 124
3.5.1 Tapped-inductor Common-diode Boost Converter 126
3.5.2 Tapped-inductor Common-load Boost Converter 126
3.6 Duality 127
3.7 Power Factor Correction 129
3.7.1 Power Factor 129
3.7.2 Boost Power Factor Corrector 132
3.8 Summary 134
3.9 References 135
3.10 Review Questions 136
3.11 Problems 136
4 Buck-boost PWM DC–DC Converter 139
4.1 Introduction 139
4.2 DC Analysis of PWM Buck-boost Converter for CCM 139
4.2.1 Circuit Description 139
4.2.2 Assumptions 140
4.2.3 Time Interval 0 < t ≤ DT 142
4.2.4 Time Interval DT < t ≤ T 142
4.2.5 DC Voltage Transfer Function for CCM 143
4.2.6 Device Stresses for CCM 144
4.2.7 Boundary between CCM and DCM 145
4.2.8 Ripple Voltage in Buck-boost Converter for CCM 146
4.2.9 Power Losses and Efficiency of the Buck-boost
Converter for CCM 149
4.2.10 DC Voltage Transfer Function of Lossy Buck-boost
Converter for CCM 151
4.2.11 Design of Buck-boost Converter for CCM 153
4.3 DC Analysis of PWM Buck-boost Converter for DCM 159
4.3.1 Time Interval 0 < t ≤ DT 160
4.3.2 Time Interval DT < t ≤ (D + D1)T 162
4.3.3 Time Interval (D + D1)T < t ≤ T 162
4.3.4 Device Stresses of the Buck-boost Converter in DCM 162
4.3.5 DC Voltage Transfer Function of the Buck-boost
Converter for DCM 163
4.3.6 Maximum Inductance for DCM 166
4.3.7 Power Losses and Efficiency of the Buck-boost Converter
in DCM 166
4.3.8 Design of Buck-boost Converter for DCM 168
4.4 Bidirectional Buck-boost Converter 174
4.5 Synthesis of Buck-boost Converter 175
x CONTENTS
4.6 Synthesis of Boost-buck (C&acute; uk) Converter 177
4.7 Noninverting Buck-boost Converters 178
4.7.1 Cascaded Noninverting Buck-boost Converters 178
4.7.2 Four-transistor Noninverting Buck-boost Converters 179
4.8 Tapped-inductor Buck-boost Converters 181
4.8.1 Tapped-inductor Common-diode Buck-boost Converter 181
4.8.2 Tapped-inductor Common-transistor Buck-boost
Converter 182
4.8.3 Tapped-inductor Common-load Buck-boost Converter 183
4.8.4 Tapped-inductor Common-source Buck-boost Converter 184
4.9 Summary 185
4.10 References 186
4.11 Review Questions 187
4.12 Problems 187
5 Flyback PWM DC–DC Converter 189
5.1 Introduction 189
5.2 Transformers 190
5.3 DC Analysis of PWM Flyback Converter for CCM 191
5.3.1 Derivation of PWM Flyback Converter 191
5.3.2 Circuit Description 192
5.3.3 Assumptions 193
5.3.4 Time Interval 0 < t ≤ DT 195
5.3.5 Time Interval DT < t ≤ T 196
5.3.6 DC Voltage Transfer Function for CCM 197
5.3.7 Boundary between CCM and DCM 198
5.3.8 Ripple Voltage in Flyback Converter for CCM 199
5.3.9 Power Losses and Efficiency of Flyback Converter for
CCM 201
5.3.10 DC Voltage Transfer Function of Lossy Converter for
CCM 204
5.3.11 Design of Flyback Converter for CCM 205
5.4 DC Analysis of PWM Flyback Converter for DCM 211
5.4.1 Time Interval 0 < t ≤ DT 212
5.4.2 Time Interval DT < t ≤ (D + D1)T 213
5.4.3 Time Interval (D + D1)T < t ≤ T 214
5.4.4 DC Voltage Transfer Function for DCM 214
5.4.5 Maximum Magnetizing Inductance for DCM 218
5.4.6 Ripple Voltage in Flyback Converter for DCM 218
5.4.7 Power Losses and Efficiency of Flyback Converter for
DCM 219
5.4.8 Design of Flyback Converter for DCM 222
5.5 Multiple-output Flyback Converter 228
5.6 Bidirectional Flyback Converter 229
5.7 Ringing in Flyback Converter 229
5.8 Flyback Converter with Active Clamping 232
5.9 Two-transistor Flyback Converter 233
5.10 Summary 234
5.11 References 235
CONTENTS xi
5.12 Review Questions 236
5.13 Problems 236
6 Forward PWM DC–DC Converter 239
6.1 Introduction 239
6.2 DC Analysis of PWM Forward Converter for CCM 239
6.2.1 Derivation of Forward PWM Converter 239
6.2.2 Time Interval 0 < t ≤ DT 241
6.2.3 Time Interval DT < t ≤ DT + tm 243
6.2.4 Time Interval DT + tm < t ≤ T 245
6.2.5 Maximum Duty Cycle 246
6.2.6 Device Stresses 246
6.2.7 DC Voltage Transfer Function for CCM 247
6.2.8 Boundary between CCM and DCM 248
6.2.9 Ripple Voltage in Forward Converter for CCM 248
6.2.10 Power Losses and Efficiency of Forward Converter for
CCM 250
6.2.11 DC Voltage Transfer Function of Lossy Converter for
CCM 253
6.2.12 Design of Forward Converter for CCM 254
6.3 DC Analysis of PWM Forward Converter for DCM 261
6.3.1 Time Interval 0 < t ≤ DT 261
6.3.2 Time Interval DT < t ≤ DT + tm 264
6.3.3 Time Interval DT + tm < t ≤ (D + D1)T 265
6.3.4 Time Interval (D + D1)T < t ≤ T 265
6.3.5 DC Voltage Transfer Function for DCM 266
6.3.6 Maximum Inductance for DCM 270
6.3.7 Power Losses and Efficiency of Forward Converter for
DCM 270
6.3.8 Design of Forward Converter for DCM 273
6.4 Multiple-output Forward Converter 280
6.5 Forward Converter with Synchronous Rectifier 281
6.6 Forward Converters with Active Clamping 281
6.7 Two-switch Forward Converter 283
6.8 Summary 283
6.9 References 284
6.10 Review Questions 285
6.11 Problems 286
7 Half-bridge PWM DC–DC Converter 289
7.1 Introduction 289
7.2 DC Analysis of PWM Half-bridge Converter for CCM 289
7.2.1 Circuit Description 289
7.2.2 Assumptions 291
7.2.3 Time Interval 0 < t ≤ DT 292
7.2.4 Time Interval DT < t ≤ T/2 295
7.2.5 Time Interval T/2 < t ≤ T/2 + DT 296
7.2.6 Time Interval T/2 + DT < t ≤ T 297
xii CONTENTS
7.2.7 Device Stresses 297
7.2.8 DC Voltage Transfer Function of Lossless Half-bridge
Converter for CCM 298
7.2.9 Boundary between CCM and DCM 299
7.2.10 Ripple Voltage in Half-bridge Converter for CCM 299
7.2.11 Power Losses and Efficiency of Half-bridge Converter for
CCM 301
7.2.12 DC Voltage Transfer Function of Lossy Converter for
CCM 304
7.2.13 Design of Half-bridge Converter for CCM 305
7.3 DC Analysis of PWM Half-bridge Converter for DCM 312
7.3.1 Time Interval 0 < t ≤ DT 312
7.3.2 Time Interval DT < t ≤ (D + D1)T 314
7.3.3 Time Interval (D + D1)T < t ≤ T/2 315
7.3.4 DC Voltage Transfer Function for DCM 316
7.3.5 Maximum Inductance for DCM 320
7.4 Summary 320
7.5 References 321
7.6 Review Questions 322
7.7 Problems 323
8 Full-bridge PWM DC–DC Converter 325
8.1 Introduction 325
8.2 DC Analysis of PWM Full-bridge Converter for CCM 325
8.2.1 Circuit Description 325
8.2.2 Assumptions 327
8.2.3 Time Interval 0 < t ≤ DT 327
8.2.4 Time Interval DT < t ≤ T/2 329
8.2.5 Time Interval T/2 < t ≤ T/2 + DT 331
8.2.6 Time Interval T/2 + DT < t ≤ T 332
8.2.7 Device Stresses 332
8.2.8 DC Voltage Transfer Function of Lossless Full-wave
Converter for CCM 332
8.2.9 Boundary between CCM and DCM 333
8.2.10 Ripple Voltage in Full-bridge Converter for CCM 335
8.2.11 Power Losses and Efficiency of Full-bridge Converter for
CCM 336
8.2.12 DC Voltage Transfer Function of Lossy Converter for
CCM 339
8.2.13 Design of Full-bridge Converter for CCM 340
8.3 DC Analysis of PWM Full-bridge Converter for DCM 344
8.3.1 Time Interval 0 < t ≤ DT 344
8.3.2 Time Interval DT < t ≤ (D + D1)T 349
8.3.3 Time Interval (D + D1)T < t ≤ T/2 350
8.3.4 DC Voltage Transfer Function for DCM 350
8.3.5 Maximum Inductance for DCM 355
8.4 Phase-controlled Full-bridge Converter 357
8.5 Summary 358
8.6 References 358
CONTENTS xiii
8.7 Review Questions 359
8.8 Problems 360
9 Push-pull PWM DC–DC Converter 363
9.1 Introduction 363
9.2 DC Analysis of PWM Push-pull Converter for CCM 363
9.2.1 Circuit Description 363
9.2.2 Assumptions 365
9.2.3 Time Interval 0 < t ≤ DT 365
9.2.4 Time Interval DT < t ≤ T/2 368
9.2.5 Time Interval T/2 < t ≤ T/2 + DT 368
9.2.6 Time Interval T/2 + DT < t ≤ T 369
9.2.7 Device Stresses 370
9.2.8 DC Voltage Transfer Function of Lossless Full-wave
Converter for CCM 370
9.2.9 Boundary between CCM and DCM 371
9.2.10 Ripple Voltage in Push-pull Converter for CCM 372
9.2.11 Power Losses and Efficiency of Push-pull Converter for
CCM 374
9.2.12 DC Voltage Transfer Function of Lossy Converter for
CCM 377
9.2.13 Design of Push-pull Converter for CCM 378
9.3 DC Analysis of PWM Push-pull Converter for DCM 384
9.3.1 Time Interval 0 < t ≤ DT 384
9.3.2 Time Interval DT < t ≤ (D + D1)T 386
9.3.3 Time Interval (D + D1)T < t ≤ T/2 388
9.3.4 DC Voltage Transfer Function for DCM 388
9.3.5 Maximum Inductance for DCM 392
9.4 Comparison of PWM DC–DC Converters 394
9.5 Summary 394
9.6 References 394
9.7 Review Questions 395
9.8 Problems 396
10 Small-signal Models of PWM Converters for CCM
and DCM 397
10.1 Introduction 397
10.2 Assumptions 398
10.3 Averaged Model of Ideal Switching Network for CCM 398
10.4 Averaged Values of Switched Resistances 403
10.5 Model Reduction 405
10.6 Large-signal Averaged Model for CCM 407
10.7 DC and Small–signal Circuit Linear Models of Switching
Network for CCM 411
10.8 Family of PWM Converter Models for CCM 418
10.9 PWM Small-signal Switch Model for CCM 419
10.10 Modeling of the Ideal Switching Network for DCM 421
10.10.1 Relationships among DC Components for DCM 421
xiv CONTENTS
10.10.2 Small-signal Model of Ideal Switching Network for DCM 425
10.11 Averaged Parasitic Resistances for DCM 428
10.12 Small-signal Models of PWM Converters for DCM 430
10.13 Summary 431
10.14 References 433
10.15 Review Questions 435
10.16 Problems 436
11 Open-loop Small-signal Characteristics of Boost
Converter for CCM 437
11.1 Introduction 437
11.2 DC Characteristics 437
11.3 Open-loop Control-to-output Transfer Function 440
11.4 Delay in Open-loop Control-to-output Transfer Function 448
11.5 Open-loop Audio Susceptibility 450
11.6 Open-loop Input Impedance 453
11.7 Open-loop Output Impedance 455
11.8 Open-loop Step Responses 458
11.8.1 Open-loop Response of Output Voltage to Step Change in
Input Voltage 458
11.8.2 Open-loop Response of Output Voltage to Step Change in
Duty Cycle 461
11.8.3 Open-loop Response of Output Voltage to Step Change in
Load Current 462
11.9 Summary 464
11.10 References 465
11.11 Review Questions 465
11.12 Problems 466
12 Voltage-mode Control of Boost Converter 469
12.1 Introduction 469
12.2 Circuit of Boost Converter with Voltage-mode Control 469
12.3 Pulse-width Modulator 471
12.4 Transfer Function of Modulator, Boost Converter Power Stage,
and Feedback Network 474
12.5 Error Amplifier 478
12.6 Integral-single-lead Controller 480
12.7 Integral-double-lead Controller 485
12.7.1 Analysis of Integral-double-lead Controller 485
12.7.2 Design of Integral-double-lead Controller 488
12.8 Loop Gain 492
12.9 Closed-loop Control-to-output Voltage Transfer Function 493
12.10 Closed-loop Audio Susceptibility 495
12.11 Closed-loop Input Impedance 496
12.12 Closed-loop Output Impedance 500
12.13 Closed-loop Step Responses 502
12.13.1 Closed-loop Response to Step Change in Input Voltage 502
CONTENTS xv
12.13.2 Closed-loop Response to Step Change in Reference
Voltage 503
12.13.3 Closed-loop Response to Step Change in Load Current 505
12.14 Closed-loop DC Transfer Functions 506
12.15 Summary 507
12.16 References 508
12.17 Review Questions 508
12.18 Problems 509
13 Current-mode Control 511
13.1 Introduction 511
13.2 Principle of Operation of PWM Converters with
Peak-current-mode Control 512
13.3 Relationship between Duty Cycle and Inductor-current Slopes 516
13.4 Instability of Closed-current Loop 518
13.5 Slope Compensation 521
13.6 Sample-and-hold Effect on Current Loop 526
13.6.1 Natural Response of Inductor Current to Small
Perturbation in Closed-current Loop 526
13.6.2 Forced Response of Inductor Current to Step Change in
Control Voltage in Closed-current Loop 528
13.6.3 Transfer Function of Closed-current Loop in z-Domain 530
13.7 Current Loop in s-Domain 531
13.7.1 Control Voltage-to-inductor Current Transfer Function 531
13.7.2 Error Voltage-to-duty Cycle Transfer Function 534
13.7.3 Loop Gain of Current Loop 537
13.7.4 Closed-loop Transfer Function of Current Loop 543
13.7.5 Alternative Representation of Current Loop 546
13.7.6 Current Loop with Disturbances 546
13.7.7 Modified Approximation of Current Loop 547
13.8 Voltage Loop of PWM Converters with Current-mode Control 550
13.8.1 Closed-voltage Loop Transfer Function 552
13.8.2 Closed-loop Audio Susceptibility 552
13.8.3 Closed-loop Output Impedance 553
13.9 Feedforward Gains in PWM Converters with Current-mode
Control without Slope Compensation 554
13.10 Feedforward Gains in PWM Converters with Current-mode
Control and Slope Compensation 557
13.11 Closed-loop Transfer Functions with Feedforward Gains 559
13.12 Slope Compensation by Adding a Ramp to Inductor Current 560
13.13 Relationships for Constant-frequency Current-mode On-time
Control 561
13.14 Summary 561
13.15 References 562
13.16 Review Questions 565
13.17 Problems 565
13.18 Appendix: Sample-and-hold Modeling 566
13.18.1 Sampler 566
xvi CONTENTS
14 Current-mode Control of Boost Converter 571
14.1 Introduction 571
14.2 Open-loop Small-signal Transfer Functions 571
14.2.1 Open-loop Duty Cycle-to-inductor Current Transfer
Function 571
14.2.2 Open-loop Input Voltage-to-inductor Current Transfer
Function 578
14.2.3 Open-loop Inductor-to-output Current Transfer Function 581
14.3 Open-loop Step Responses of Inductor Current 585
14.3.1 Open-loop Response of Inductor Current to Step Change
in Input Voltage 585
14.3.2 Open-loop Response of Inductor Current to Step Change
in Duty Cycle 588
14.3.3 Open-loop Response of Inductor Current to Step Change
in Load Current 590
14.4 Closed-current-loop Transfer Functions 592
14.4.1 Input Voltage-to-duty Cycle Transfer Function 599
14.4.2 Load Current-to-duty Cycle Transfer Function 604
14.4.3 Output Impedance of Closed-current Loop 604
14.5 Closed-voltage-loop Transfer Functions 608
14.5.1 Control Voltage-to-feedback Voltage Function 608
14.5.2 Loop Gain of Voltage Loop 611
14.5.3 Closed-loop Gain of Voltage Loop 614
14.5.4 Closed-loop Audio Susceptibility with Integral
Controller 616
14.5.5 Closed-loop Output Impedance with Integral Controller 619
14.6 Closed-loop Step Responses 620
14.6.1 Closed-loop Response of Output Voltage to Step Change
in Input Voltage 620
14.6.2 Closed-loop Response of Output Voltage to Step Change
in Load Current 620
14.6.3 Closed-loop Response of Output Voltage to Step Change
in Reference Voltage 622
14.7 Closed-loop DC Transfer Functions 623
14.8 Summary 624
14.9 References 624
14.10 Review Questions 625
14.11 Problems 626
15 Silicon and Silicon Carbide Power Diodes 627
15.1 Introduction 627
15.2 Electronic Power Switches 627
15.3 Intrinsic Semiconductors 628
15.4 Extrinsic Semiconductors 630
15.5 Silicon and Silicon Carbide 631
15.6 Physical Structure of Junction Diodes 632
15.7 Static I –V Diode Characteristic 634
15.8 Breakdown Voltage of Junction Diodes 637
CONTENTS xvii
15.8.1 Width of Depletion Region 638
15.8.2 Electric Field Distribution 639
15.8.3 Avalanche Breakdown Voltage 642
15.8.4 Punch-through Breakdown Voltage 642
15.8.5 Edge Terminations 644
15.9 Capacitances of Junction Diodes 645
15.9.1 Junction Capacitance 646
15.9.2 Diffusion Capacitance 648
15.10 Reverse Recovery of pn Junction Diodes 650
15.10.1 Qualitative Description 650
15.10.2 Reverse Recovery in Resistive Circuits 651
15.10.3 Charge-continuity Equation 654
15.10.4 Reverse Recovery in Inductive Circuits 657
15.11 Schottky Diodes 659
15.11.1 Static I –V Characteristic of Schottky Diodes 661
15.11.2 Junction Capacitance of Schottky Diodes 662
15.11.3 Switching Characteristics of Schottky Diodes 663
15.12 SPICE Model of Diodes 666
15.13 Summary 667
15.14 References 669
15.15 Review Questions 670
15.16 Problems 670
16 Silicon and Silicon Carbide Power MOSFETs 673
16.1 Introduction 673
16.2 Physical Structure of Power MOSFETs 673
16.3 Principle of Operation of Power MOSFETs 677
16.3.1 Cutoff Region 677
16.3.2 Formation of Channel 677
16.3.3 Linear Region 678
16.3.4 Saturation Region 678
16.3.5 Antiparallel Diode 679
16.3.6 Integrated MOSFETs 679
16.4 Derivation of Power MOSFET Characteristics 679
16.4.1 Ohmic Region 679
16.4.2 Pinch-off Region 683
16.4.3 Channel-length Modulation 683
16.5 Power MOSFET Characteristics 684
16.6 Mobility of Charge Carriers 686
16.6.1 Effect of Doping Concentration on Mobility 687
16.6.2 Effect of Temperature on Mobility 689
16.6.3 Effect of Electric Field on Mobility 692
16.7 Short-channel Effects 697
16.8 Aspect Ratio of Power MOSFETs 698
16.9 Breakdown Voltage of Power MOSFETs 699
16.10 Gate Oxide Breakdown Voltage of Power MOSFETs 701
16.11 Resistance of Drift Region 701
16.12 Figures-of-merit 704
16.13 On-resistance of Power MOSFETs 705
xviii CONTENTS
16.13.1 Channel Resistance 705
16.13.2 Accumulation Region Resistance 707
16.13.3 Neck Region Resistance 707
16.13.4 Drift Region Resistance 708
16.14 Capacitances of Power MOSFETs 710
16.14.1 Gate-to-source Capacitance 710
16.14.2 Drain-to-source Capacitance 712
16.14.3 Gate-to-drain Capacitance 712
16.15 Switching Waveforms 723
16.16 SPICE Model of Power MOSFETs 724
16.17 Insulated Gate Bipolar Transistors 726
16.18 Heat Sinks 728
16.19 Summary 730
16.20 References 732
16.21 Review Questions 732
16.22 Problems 733
17 Soft-switching DC–DC Converters 735
17.1 Introduction 735
17.2 Zero-voltage-switching DC–DC Converters 736
17.3 Buck ZVS Quasi-resonant DC–DC Converter 736
17.3.1 Waveforms 736
17.3.2 DC Voltage Transfer Function 741
17.3.3 Voltage and Current Stresses 742
17.4 Boost ZVS Quasi-resonant DC–DC Converter 745
17.4.1 Waveforms 745
17.4.2 DC Voltage Transfer Function 748
17.4.3 Current and Voltage Stresses 749
17.4.4 Generalization 751
17.5 Zero-current-switching DC–DC Converters 751
17.6 Boost ZCS Quasi-resonant DC–DC Converter 753
17.6.1 Waveforms 753
17.6.2 Voltage Transfer Function 756
17.6.3 Current and Voltage Stresses 757
17.6.4 Generalization 759
17.7 Multiresonant Converters 759
17.8 Summary 761
17.9 References 762
17.10 Review Questions 763
17.11 Problems 764
Appendix A Introduction to SPICE 765
Appendix B Introduction to MATLAB 769
Answers to Problems 773
Index 779

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