Pulse-width Modulated DC-DC Power Converters

Pulse-width Modulated DC–DC Power Converters......Page 4
Contents......Page 10
Preface......Page 22
About the Author......Page 24
List of Symbols......Page 26
1.1 Classification of Power Supplies......Page 30
1.2 Basic Functions of Voltage Regulators......Page 32
1.4 DC Transfer Functions of DC–DC Converters......Page 34
1.5 Static Characteristics of DC Voltage Regulators......Page 35
1.6 Dynamic Characteristics of DC Voltage Regulators......Page 38
1.7 Linear Voltage Regulators......Page 41
1.7.1 Series Voltage Regulator......Page 42
1.7.2 Shunt Voltage Regulator......Page 43
1.8 Topologies of PWM DC–DC Converters......Page 46
1.9 Relationships among Current, Voltage, Energy, and Power......Page 47
1.10 Electromagnetic Compatibility......Page 48
1.12 References......Page 49
1.13 Review Questions......Page 50
1.14 Problems......Page 51
2.2.1 Circuit Description......Page 52
2.2.3 Time Interval 0 < t ≤ DT......Page 56
2.2.4 Time Interval DT < t ≤ T......Page 57
2.2.6 DC Voltage Transfer Function for CCM......Page 58
2.2.7 Boundary between CCM and DCM......Page 59
2.2.8 Ripple Voltage in Buck Converter for CCM......Page 61
2.2.9 Switching Losses with Linear MOSFET Output Capacitance......Page 66
2.2.10 Switching Losses with Nonlinear MOSFET Output Capacitance......Page 68
2.2.11 Power Losses and Ef.ciency of Buck Converter for CCM......Page 71
2.2.12 DC Voltage Transfer Function of Lossy Converter for CCM......Page 75
2.2.13 MOSFET Gate-drive Power......Page 76
2.2.14 Design of Buck Converter for CCM......Page 77
2.3 DC Analysis of PWM Buck Converter for DCM......Page 80
2.3.1 Time Interval 0 < t ≤ DT......Page 83
2.3.2 Time Interval DT < t ≤ (D + D1)T......Page 85
2.3.5 DC Voltage Transfer Function for DCM......Page 86
2.3.6 Maximum Inductance for DCM......Page 88
2.3.7 Power Losses and Efficiency of Buck Converter for DCM......Page 90
2.3.8 Design of Buck Converter for DCM......Page 92
2.5 Buck Converter with Synchronous Rectifier......Page 98
2.6 Buck Converter with Positive Common Rail......Page 101
2.7.1 Tapped-inductor Common-diode Buck Converter......Page 103
2.7.3 Watkins–Johnson Converter......Page 105
2.8 Multiphase Buck Converter......Page 106
2.9 Summary......Page 108
2.11 Review Questions......Page 110
2.12 Problems......Page 111
3.2.1 Circuit Description......Page 114
3.2.3 Time Interval 0 t ≤ DT......Page 117
3.2.4 Time Interval DT < t ≤ T......Page 118
3.2.5 DC Voltage Transfer Function for CCM......Page 119
3.2.6 Boundary between CCM and DCM......Page 120
3.2.7 Ripple Voltage in Boost Converter for CCM......Page 122
3.2.8 Power Losses and Efficiency of Boost Converter for CCM......Page 124
3.2.9 DC Voltage Transfer Function of Lossy Boost Converter for CCM......Page 126
3.2.10 Design of Boost Converter for CCM......Page 128
3.3 DC Analysis of PWM Boost Converter for DCM......Page 132
3.3.1 Time Interval 0 < t ≤ DT......Page 134
3.3.2 Time Interval DT < t ≤ (D + D1)T......Page 135
3.3.5 DC Voltage Transfer Function for DCM......Page 137
3.3.7 Power Losses and Efficiency of Boost Converter for DCM......Page 141
3.3.8 Design of Boost Converter for DCM......Page 144
3.4 Bidirectional Buck and Boost Converters......Page 151
3.5 Tapped-inductor Boost Converters......Page 153
3.5.2 Tapped-inductor Common-load Boost Converter......Page 155
3.6 Duality......Page 156
3.7.1 Power Factor......Page 158
3.7.2 Boost Power Factor Corrector......Page 161
3.8 Summary......Page 163
3.9 References......Page 164
3.11 Problems......Page 165
4.2.1 Circuit Description......Page 168
4.2.2 Assumptions......Page 169
4.2.4 Time Interval DT < t ≤ T......Page 171
4.2.5 DC Voltage Transfer Function for CCM......Page 172
4.2.6 Device Stresses for CCM......Page 173
4.2.7 Boundary between CCM and DCM......Page 174
4.2.8 Ripple Voltage in Buck-boost Converter for CCM......Page 175
4.2.9 Power Losses and Efficiency of the Buck-boost Converter for CCM......Page 178
4.2.10 DC Voltage Transfer Function of Lossy Buck-boost Converter for CCM......Page 180
4.2.11 Design of Buck-boost Converter for CCM......Page 182
4.3 DC Analysis of PWM Buck-boost Converter for DCM......Page 188
4.3.1 Time Interval 0 < t ≤ DT......Page 189
4.3.4 Device Stresses of the Buck-boost Converter in DCM......Page 191
4.3.5 DC Voltage Transfer Function of the Buck-boost Converter for DCM......Page 192
4.3.7 Power Losses and Ef.ciency of the Buck-boost Converter in DCM......Page 195
4.3.8 Design of Buck-boost Converter for DCM......Page 197
4.4 Bidirectional Buck-boost Converter......Page 203
4.5 Synthesis of Buck-boost Converter......Page 204
4.6 Synthesis of Boost-buck ( ´ Cuk) Converter......Page 206
4.7.1 Cascaded Noninverting Buck-boost Converters......Page 207
4.7.2 Four-transistor Noninverting Buck-boost Converters......Page 208
4.8.1 Tapped-inductor Common-diode Buck-boost Converter......Page 210
4.8.2 Tapped-inductor Common-transistor Buck-boost Converter......Page 211
4.8.3 Tapped-inductor Common-load Buck-boost Converter......Page 212
4.8.4 Tapped-inductor Common-source Buck-boost Converter......Page 213
4.9 Summary......Page 214
4.10 References......Page 215
4.12 Problems......Page 216
5.1 Introduction......Page 218
5.2 Transformers......Page 219
5.3.1 Derivation of PWM Flyback Converter......Page 220
5.3.2 Circuit Description......Page 221
5.3.3 Assumptions......Page 222
5.3.4 Time Interval 0 < t ≤ DT......Page 224
5.3.5 Time Interval DT < t ≤ T......Page 225
5.3.6 DC Voltage Transfer Function for CCM......Page 226
5.3.7 Boundary between CCM and DCM......Page 227
5.3.8 Ripple Voltage in Flyback Converter for CCM......Page 228
5.3.9 Power Losses and Efficiency of Flyback Converter for CCM......Page 230
5.3.10 DC Voltage Transfer Function of Lossy Converter for CCM......Page 233
5.3.11 Design of Flyback Converter for CCM......Page 234
5.4 DC Analysis of PWM Flyback Converter for DCM......Page 240
5.4.1 Time Interval 0 < t ≤ DT......Page 241
5.4.2 Time Interval DT < t ≤ (D + D1)T......Page 242
5.4.4 DC Voltage Transfer Function for DCM......Page 243
5.4.6 Ripple Voltage in Flyback Converter for DCM......Page 247
5.4.7 Power Losses and Ef.ciency of Flyback Converter for DCM......Page 248
5.4.8 Design of Flyback Converter for DCM......Page 251
5.5 Multiple-output Flyback Converter......Page 257
5.7 Ringing in Flyback Converter......Page 258
5.8 Flyback Converter with Active Clamping......Page 261
5.9 Two-transistor Flyback Converter......Page 262
5.10 Summary......Page 263
5.11 References......Page 264
5.13 Problems......Page 265
6.2.1 Derivation of Forward PWM Converter......Page 268
6.2.2 Time Interval 0 < t ≤ DT......Page 270
6.2.3 Time Interval DT < t ≤ DT + tm......Page 272
6.2.4 Time Interval DT + tm < t ≤ T......Page 274
6.2.6 Device Stresses......Page 275
6.2.7 DC Voltage Transfer Function for CCM......Page 276
6.2.9 Ripple Voltage in Forward Converter for CCM......Page 277
6.2.10 Power Losses and Efficiency of Forward Converter for CCM......Page 279
6.2.11 DC Voltage Transfer Function of Lossy Converter for CCM......Page 282
6.2.12 Design of Forward Converter for CCM......Page 283
6.3.1 Time Interval 0 < t ≤ DT......Page 290
6.3.2 Time Interval DT < t ≤ DT + tm......Page 293
6.3.4 Time Interval (D + D1)T < t ≤ T......Page 294
6.3.5 DC Voltage Transfer Function for DCM......Page 295
6.3.7 Power Losses and Efficiency of Forward Converter for DCM......Page 299
6.3.8 Design of Forward Converter for DCM......Page 302
6.4 Multiple-output Forward Converter......Page 309
6.6 Forward Converters with Active Clamping......Page 310
6.8 Summary......Page 312
6.9 References......Page 313
6.10 Review Questions......Page 314
6.11 Problems......Page 315
7.2.1 Circuit Description......Page 318
7.2.2 Assumptions......Page 320
7.2.3 Time Interval 0 < t ≤ DT......Page 321
7.2.4 Time Interval DT < t ≤ T/2......Page 324
7.2.5 Time Interval T/2 < t ≤ T/2 + DT......Page 325
7.2.7 Device Stresses......Page 326
7.2.8 DC Voltage Transfer Function of Lossless Half-bridge Converter for CCM......Page 327
7.2.10 Ripple Voltage in Half-bridge Converter for CCM......Page 328
7.2.11 Power Losses and Efficiency of Half-bridge Converter for CCM......Page 330
7.2.12 DC Voltage Transfer Function of Lossy Converter for CCM......Page 333
7.2.13 Design of Half-bridge Converter for CCM......Page 334
7.3.1 Time Interval 0 < t ≤ DT......Page 341
7.3.2 Time Interval DT < t ≤ (D + D1)T......Page 343
7.3.3 Time Interval (D + D1)T < t ≤ T/2......Page 344
7.3.4 DC Voltage Transfer Function for DCM......Page 345
7.4 Summary......Page 349
7.5 References......Page 350
7.6 Review Questions......Page 351
7.7 Problems......Page 352
8.2.1 Circuit Description......Page 354
8.2.3 Time Interval 0 < t ≤ DT......Page 356
8.2.4 Time Interval DT < t ≤ T/2......Page 358
8.2.5 Time Interval T/2 < t ≤ T/2 + DT......Page 360
8.2.8 DC Voltage Transfer Function of Lossless Full-wave Converter for CCM......Page 361
8.2.9 Boundary between CCM and DCM......Page 362
8.2.10 Ripple Voltage in Full-bridge Converter for CCM......Page 364
8.2.11 Power Losses and Efficiency of Full-bridge Converter for CCM......Page 365
8.2.12 DC Voltage Transfer Function of Lossy Converter for CCM......Page 368
8.2.13 Design of Full-bridge Converter for CCM......Page 369
8.3.1 Time Interval 0 < t ≤ DT......Page 373
8.3.2 Time Interval DT < t ≤ (D + D1)T......Page 378
8.3.4 DC Voltage Transfer Function for DCM......Page 379
8.3.5 Maximum Inductance for DCM......Page 384
8.4 Phase-controlled Full-bridge Converter......Page 386
8.6 References......Page 387
8.7 Review Questions......Page 388
8.8 Problems......Page 389
9.2.1 Circuit Description......Page 392
9.2.3 Time Interval 0 < t ≤ DT......Page 394
9.2.5 Time Interval T/2 < t ≤ T/2 + DT......Page 397
9.2.6 Time Interval T/2 + DT < t ≤ T......Page 398
9.2.8 DC Voltage Transfer Function of Lossless Full-wave Converter for CCM......Page 399
9.2.9 Boundary between CCM and DCM......Page 400
9.2.10 Ripple Voltage in Push-pull Converter for CCM......Page 401
9.2.11 Power Losses and Efficiency of Push-pull Converter for CCM......Page 403
9.2.12 DC Voltage Transfer Function of Lossy Converter for CCM......Page 406
9.2.13 Design of Push-pull Converter for CCM......Page 407
9.3.1 Time Interval 0 < t ≤ DT......Page 413
9.3.2 Time Interval DT < t ≤ (D + D1)T......Page 415
9.3.4 DC Voltage Transfer Function for DCM......Page 417
9.3.5 Maximum Inductance for DCM......Page 421
9.6 References......Page 423
9.7 Review Questions......Page 424
9.8 Problems......Page 425
10.1 Introduction......Page 426
10.3 Averaged Model of Ideal Switching Network for CCM......Page 427
10.4 Averaged Values of Switched Resistances......Page 432
10.5 Model Reduction......Page 434
10.6 Large-signal Averaged Model for CCM......Page 436
10.7 DC and Small–signal Circuit Linear Models of Switching Network for CCM......Page 440
10.8 Family of PWM Converter Models for CCM......Page 447
10.9 PWM Small-signal Switch Model for CCM......Page 448
10.10.1 Relationships among DC Components for DCM......Page 450
10.10.2 Small-signal Model of Ideal Switching Network for DCM......Page 454
10.11 Averaged Parasitic Resistances for DCM......Page 457
10.12 Small-signal Models of PWM Converters for DCM......Page 459
10.13 Summary......Page 460
10.14 References......Page 462
10.15 Review Questions......Page 464
10.16 Problems......Page 465
11.2 DC Characteristics......Page 466
11.3 Open-loop Control-to-output Transfer Function......Page 469
11.4 Delay in Open-loop Control-to-output Transfer Function......Page 477
11.5 Open-loop Audio Susceptibility......Page 479
11.6 Open-loop Input Impedance......Page 482
11.7 Open-loop Output Impedance......Page 484
11.8.1 Open-loop Response of Output Voltage to Step Change in Input Voltage......Page 487
11.8.2 Open-loop Response of Output Voltage to Step Change in Duty Cycle......Page 490
11.8.3 Open-loop Response of Output Voltage to Step Change in Load Current......Page 491
11.9 Summary......Page 493
11.11 Review Questions......Page 494
11.12 Problems......Page 495
12.2 Circuit of Boost Converter with Voltage-mode Control......Page 498
12.3 Pulse-width Modulator......Page 500
12.4 Transfer Function of Modulator, Boost Converter Power Stage, and Feedback Network......Page 503
12.5 Error Amplifier......Page 507
12.6 Integral-single-lead Controller......Page 509
12.7.1 Analysis of Integral-double-lead Controller......Page 514
12.7.2 Design of Integral-double-lead Controller......Page 517
12.8 Loop Gain......Page 521
12.9 Closed-loop Control-to-output Voltage Transfer Function......Page 522
12.10 Closed-loop Audio Susceptibility......Page 524
12.11 Closed-loop Input Impedance......Page 525
12.12 Closed-loop Output Impedance......Page 529
12.13.1 Closed-loop Response to Step Change in Input Voltage......Page 531
12.13.2 Closed-loop Response to Step Change in Reference Voltage......Page 532
12.13.3 Closed-loop Response to Step Change in Load Current......Page 534
12.14 Closed-loop DC Transfer Functions......Page 535
12.15 Summary......Page 536
12.17 Review Questions......Page 537
12.18 Problems......Page 538
13.1 Introduction......Page 540
13.2 Principle of Operation of PWM Converters with Peak-current-mode Control......Page 541
13.3 Relationship between Duty Cycle and Inductor-current Slopes......Page 545
13.4 Instability of Closed-current Loop......Page 547
13.5 Slope Compensation......Page 550
13.6.1 Natural Response of Inductor Current to Small Perturbation in Closed-current Loop......Page 555
13.6.2 Forced Response of Inductor Current to Step Change in Control Voltage in Closed-current Loop......Page 557
13.6.3 Transfer Function of Closed-current Loop in z-Domain......Page 559
13.7.1 Control Voltage-to-inductor Current Transfer Function......Page 560
13.7.2 Error Voltage-to-duty Cycle Transfer Function......Page 563
13.7.3 Loop Gain of Current Loop......Page 566
13.7.4 Closed-loop Transfer Function of Current Loop......Page 572
13.7.6 Current Loop with Disturbances......Page 575
13.7.7 Modified Approximation of Current Loop......Page 576
13.8 Voltage Loop of PWM Converters with Current-mode Control......Page 579
13.8.2 Closed-loop Audio Susceptibility......Page 581
13.8.3 Closed-loop Output Impedance......Page 582
13.9 Feedforward Gains in PWM Converters with Current-mode Control without Slope Compensation......Page 583
13.10 Feedforward Gains in PWM Converters with Current-mode Control and Slope Compensation......Page 586
13.11 Closed-loop Transfer Functions with Feedforward Gains......Page 588
13.12 Slope Compensation by Adding a Ramp to Inductor Current......Page 589
13.14 Summary......Page 590
13.15 References......Page 591
13.17 Problems......Page 594
13.18.1 Sampler......Page 595
14.2.1 Open-loop Duty Cycle-to-inductor Current Transfer Function......Page 600
14.2.2 Open-loop Input Voltage-to-inductor Current Transfer Function......Page 607
14.2.3 Open-loop Inductor-to-output Current Transfer Function......Page 610
14.3.1 Open-loop Response of Inductor Current to Step Change in Input Voltage......Page 614
14.3.2 Open-loop Response of Inductor Current to Step Change in Duty Cycle......Page 617
14.3.3 Open-loop Response of Inductor Current to Step Change in Load Current......Page 619
14.4 Closed-current-loop Transfer Functions......Page 621
14.4.1 Input Voltage-to-duty Cycle Transfer Function......Page 628
14.4.3 Output Impedance of Closed-current Loop......Page 633
14.5.1 Control Voltage-to-feedback Voltage Function......Page 637
14.5.2 Loop Gain of Voltage Loop......Page 640
14.5.3 Closed-loop Gain of Voltage Loop......Page 643
14.5.4 Closed-loop Audio Susceptibility with Integral Controller......Page 645
14.5.5 Closed-loop Output Impedance with Integral Controller......Page 648
14.6.2 Closed-loop Response of Output Voltage to Step Change in Load Current......Page 649
14.6.3 Closed-loop Response of Output Voltage to Step Change in Reference Voltage......Page 651
14.7 Closed-loop DC Transfer Functions......Page 652
14.9 References......Page 653
14.10 Review Questions......Page 654
14.11 Problems......Page 655
15.2 Electronic Power Switches......Page 656
15.3 Intrinsic Semiconductors......Page 657
15.4 Extrinsic Semiconductors......Page 659
15.5 Silicon and Silicon Carbide......Page 660
15.6 Physical Structure of Junction Diodes......Page 661
15.7 Static I –V Diode Characteristic......Page 663
15.8 Breakdown Voltage of Junction Diodes......Page 666
15.8.1 Width of Depletion Region......Page 667
15.8.2 Electric Field Distribution......Page 668
15.8.4 Punch-through Breakdown Voltage......Page 671
15.8.5 Edge Terminations......Page 673
15.9 Capacitances of Junction Diodes......Page 674
15.9.1 Junction Capacitance......Page 675
15.9.2 Diffusion Capacitance......Page 677
15.10.1 Qualitative Description......Page 679
15.10.2 Reverse Recovery in Resistive Circuits......Page 680
15.10.3 Charge-continuity Equation......Page 683
15.10.4 Reverse Recovery in Inductive Circuits......Page 686
15.11 Schottky Diodes......Page 688
15.11.1 Static I –V Characteristic of Schottky Diodes......Page 690
15.11.2 Junction Capacitance of Schottky Diodes......Page 691
15.11.3 Switching Characteristics of Schottky Diodes......Page 692
15.12 SPICE Model of Diodes......Page 695
15.13 Summary......Page 696
15.14 References......Page 698
15.16 Problems......Page 699
16.2 Physical Structure of Power MOSFETs......Page 702
16.3.2 Formation of Channel......Page 706
16.3.4 Saturation Region......Page 707
16.4.1 Ohmic Region......Page 708
16.4.3 Channel-length Modulation......Page 712
16.5 Power MOSFET Characteristics......Page 713
16.6 Mobility of Charge Carriers......Page 715
16.6.1 Effect of Doping Concentration on Mobility......Page 716
16.6.2 Effect of Temperature on Mobility......Page 718
16.6.3 Effect of Electric Field on Mobility......Page 721
16.7 Short-channel Effects......Page 726
16.8 Aspect Ratio of Power MOSFETs......Page 727
16.9 Breakdown Voltage of Power MOSFETs......Page 728
16.11 Resistance of Drift Region......Page 730
16.12 Figures-of-merit......Page 733
16.13.1 Channel Resistance......Page 734
16.13.3 Neck Region Resistance......Page 736
16.13.4 Drift Region Resistance......Page 737
16.14.1 Gate-to-source Capacitance......Page 739
16.14.3 Gate-to-drain Capacitance......Page 741
16.15 Switching Waveforms......Page 752
16.16 SPICE Model of Power MOSFETs......Page 753
16.17 Insulated Gate Bipolar Transistors......Page 755
16.18 Heat Sinks......Page 757
16.19 Summary......Page 759
16.21 Review Questions......Page 761
16.22 Problems......Page 762
17.1 Introduction......Page 764
17.3.1 Waveforms......Page 765
17.3.2 DC Voltage Transfer Function......Page 770
17.3.3 Voltage and Current Stresses......Page 771
17.4.1 Waveforms......Page 774
17.4.2 DC Voltage Transfer Function......Page 777
17.4.3 Current and Voltage Stresses......Page 778
17.5 Zero-current-switching DC–DC Converters......Page 780
17.6.1 Waveforms......Page 782
17.6.2 Voltage Transfer Function......Page 785
17.6.3 Current and Voltage Stresses......Page 786
17.7 Multiresonant Converters......Page 788
17.8 Summary......Page 790
17.9 References......Page 791
17.10 Review Questions......Page 792
17.11 Problems......Page 793
Appendix A Introduction to SPICE......Page 794
Appendix B Introduction to MATLAB......Page 798
Answers to Problems......Page 802
Index......Page 808