Table Of ContentSwitch-Mode Power Converters
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Switch-Mode Power Converters
Design and Analysis
Keng C. Wu
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Wu,KengC.,1948-
Switch-modepowerconverters/KengC.Wu.
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ISBN0-12-088795-9(alk.paper)
1. Electriccurrentconverters.2. Switchingpowersupplies.I.Title.
TK7872.C8W8532006
621.31’7–dc22
2005014319
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To
My wife, Shwu
My daughter, Stephanie
My mother, Tai
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Table of Contents
Preface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
1. IsolatedStep-Down(Buck)Converter 1
1.1. CCMOpen-LoopOutputandDutyCycle
Determination. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2. DCMOpen-LoopOutputandDutyCycle
Determination. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3. CCMtoDCMTransition,CriticalInductance. . . . . . . . . . 6
1.4. GainFormulaforNonidealOperationalAmplifiers . . . . . . 7
1.5. FeedbackunderVoltage-ModeControl. . . . . . . . . . . . . . . 9
1.6. Voltage-ModeCCMClosedLoop . . . . . . . . . . . . . . . . . . 11
1.7. Voltage-ModeDCMClosedLoop . . . . . . . . . . . . . . . . . . 13
1.8. Voltage-ModeCCMSmall-SignalStability . . . . . . . . . . . . 14
1.9. Current-ModeControl. . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.10. CCMCurrent-ModeControlinaClosed-Loop
SteadyState . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.11. CCMCurrent-ModeControlSmall-SignalStability. . . . . . . 24
1.12. OutputCapacitorSizeandAcceleratedSteady-State
Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
1.13. ACompleteExample . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
1.14. StateTransitionTechnique . . . . . . . . . . . . . . . . . . . . . . . 45
2. Push–PullConverterwithCurrent-ModeControlandSlope
Compensation 49
2.1. PowerStageofaCenter-TappedPush–PullConverter. . . . . 50
2.2. DiscontinuousConduction-ModeOperation . . . . . . . . . . . 51
2.3. ContinuousConduction-ModeOperation . . . . . . . . . . . . . 61
3. NonisolatedForwardConverterwithAverageCurrent-Mode
Control 67
3.1. AverageCurrentFeedback . . . . . . . . . . . . . . . . . . . . . . . 67
3.2. DutyCycleDetermination . . . . . . . . . . . . . . . . . . . . . . . 71
vii
viii CONTENTS
3.3. Steady-StateClosedLoop . . . . . . . . . . . . . . . . . . . . . . . . 72
3.4. Closed-LoopRegulationandOutputSensitivity. . . . . . . . . . 73
3.5. Small-SignalLoopGainandStability. . . . . . . . . . . . . . . . . 74
3.6. Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
3.7. StateTransitionTechnique. . . . . . . . . . . . . . . . . . . . . . . . 76
4. Phase-ShiftedFull-BridgeConverter 83
4.1. Power-StageOperation . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.2. CurrentDoubler. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.3. Steady-StateDutyCycle. . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.4. Steady-StateOutputWaveforms . . . . . . . . . . . . . . . . . . . . 87
4.5. Steady-StateOutputWaveformsExample. . . . . . . . . . . . . . 93
5. Current-FedPush–PullConverters 95
5.1. OverlappingContinuous-ConductionMode . . . . . . . . . . . . 97
5.2. OverlappingContinuousConduction,SteadyState. . . . . . . . 101
5.3. OverlappingContinuousConduction,Example . . . . . . . . . . 105
5.4. NonoverlappingContinuous-ConductionMode. . . . . . . . . . 105
5.5. LoadCurrentSharingandParallelOperation . . . . . . . . . . . 108
5.6. ACSmall-SignalStudiesUsingState-SpaceAveraging . . . . . 113
5.7. State-TransitionTechnique. . . . . . . . . . . . . . . . . . . . . . . . 116
6. IsolatedFlybackConverters 119
6.1. DCMDuty-CycleDetermination,AnotherApproach. . . . . . 120
6.2. CCMDuty-CycleDetermination. . . . . . . . . . . . . . . . . . . . 121
6.3. CriticalInductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
6.4. Voltage-ModeDCMClosedLoop. . . . . . . . . . . . . . . . . . . 123
6.5. Voltage-ModeDCMSmall-SignalStability. . . . . . . . . . . . . 124
6.6. Voltage-ModeCCMClosedLoop. . . . . . . . . . . . . . . . . . . 125
6.7. Voltage-ModeCCMSmall-SignalStability . . . . . . . . . . . . . 126
6.8. PeakCurrent-ModeDCMClosedLoop. . . . . . . . . . . . . . . 126
6.9. PeakCurrent-ModeDCMSmall-SignalStability. . . . . . . . . 128
6.10. PeakCurrent-ModeCCMClosedLoop . . . . . . . . . . . . . . . 129
6.11. PeakCurrent-ModeCCMSmall-SignalStability . . . . . . . . . 130
6.12. OutputCapacitor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
6.13. AcceleratedSteady-StateOutput . . . . . . . . . . . . . . . . . . . . 133
6.14. ACompleteDCMExample . . . . . . . . . . . . . . . . . . . . . . . 136
7. NonisolatedBoostConverter 149
7.1. Duty-CycleDetermination . . . . . . . . . . . . . . . . . . . . . . . . 149
7.2. CriticalInductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
CONTENTS ix
7.3. PeakCurrent-ModeClosed-LoopSteadyState
inCCM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
7.4. PeakCurrent-ModeSmall-SignalStabilityinCCM. . . . . . 152
7.5. PeakCurrent-ModeClosed-LoopSteadyStateinDCM . . 153
7.6. PeakCurrent-ModeSmall-SignalStabilityinDCM . . . . . 154
7.7. DCMOutputCapacitorSize . . . . . . . . . . . . . . . . . . . . . 155
7.8. CCMOutputCapacitorSize . . . . . . . . . . . . . . . . . . . . . 156
8. Quasi-ResonantConverters 157
8.1. HowDoesItWork?. . . . . . . . . . . . . . . . . . . . . . . . . . . 158
8.2. MathematicalAnalysis . . . . . . . . . . . . . . . . . . . . . . . . . 159
8.3. Steady-StateClosedLoopandStability. . . . . . . . . . . . . . 165
8.4. DesignIssues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
8.5. ExampleandDilemma . . . . . . . . . . . . . . . . . . . . . . . . . 168
9. Class-EResonantConverter 171
9.1. StartingStatesoftheSteadyState . . . . . . . . . . . . . . . . . 175
9.2. Time-DomainSteady-StateSolutions . . . . . . . . . . . . . . . 182
9.3. Closed-LoopDCAnalysis. . . . . . . . . . . . . . . . . . . . . . . 184
9.4. Closed-LoopACAnalysis. . . . . . . . . . . . . . . . . . . . . . . 187
9.5. TypeIIAmplifier. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
9.6. Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
9.7. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
10. AC–DCPower-FactorCorrectionSupplies 203
10.1. FundamentalDefinition . . . . . . . . . . . . . . . . . . . . . . . . 204
10.2. Single-PhaseSingle-StageNonisolatedBoostPFC. . . . . . . 206
10.3. OutputCapacitorSize. . . . . . . . . . . . . . . . . . . . . . . . . . 207
10.4. DCMBoostInductorSelection . . . . . . . . . . . . . . . . . . . 210
10.5. CCMBoostInductorSelection . . . . . . . . . . . . . . . . . . . 214
10.6. High-PowerPFCandLoadSharing . . . . . . . . . . . . . . . . 217
10.7. SurgeProtection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
10.8. LoadShort-CircuitProtection . . . . . . . . . . . . . . . . . . . . 222
10.9. Three-PhasePFC . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
11. ErrorAmplifiers 237
11.1. AmplifierCategory. . . . . . . . . . . . . . . . . . . . . . . . . . . . 238
11.2. InnatePhaseoftheControlLoop . . . . . . . . . . . . . . . . . 242
11.3. TypeIIAmplifierImplementation . . . . . . . . . . . . . . . . . 243
11.4. TypeIIIAmplifierImplementation . . . . . . . . . . . . . . . . 245
11.5. ExampleforTypeIIAmplifierImplementation . . . . . . . . 247
x CONTENTS
12. SupportingCircuits 249
12.1. BipolarSwitchDrivers . . . . . . . . . . . . . . . . . . . . . . . . . 249
12.2. MOSFETSwitchDrivers . . . . . . . . . . . . . . . . . . . . . . . 255
12.3. DissipativeSnubber . . . . . . . . . . . . . . . . . . . . . . . . . . . 259
12.4. LosslessSnubber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260
12.5. IsolatedFeedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
12.6. SoftStart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263
12.7. Negative-ChargePump. . . . . . . . . . . . . . . . . . . . . . . . . 264
12.8. Single-PhaseFull-WaveRectifierwithRCFilter. . . . . . . . 267
12.9. Duty-CycleClamping. . . . . . . . . . . . . . . . . . . . . . . . . . 273
13. State-SpaceAveragingandtheCukConverter 279
13.1. State-SpaceAveraging . . . . . . . . . . . . . . . . . . . . . . . . . 279
13.2. GeneralProcedure. . . . . . . . . . . . . . . . . . . . . . . . . . . . 282
13.3. Example:CukConverter. . . . . . . . . . . . . . . . . . . . . . . . 282
14. Simulation 291
14.1. DynamicEquationsforaForwardConverterwith
Voltage-ModeControl . . . . . . . . . . . . . . . . . . . . . . . . . 292
14.2. Turn-onForwardConverterwithVoltage-Mode
Control. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298
14.3. Steady-StateForwardConverterwithVoltage-Mode
Control. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298
14.4. SteadyState,ZoomedIn. . . . . . . . . . . . . . . . . . . . . . . . 298
14.5. Load-TransientForwardConverterwith
Voltage-ModeControl . . . . . . . . . . . . . . . . . . . . . . . . . 303
14.6. DynamicEquationsforaForwardConverterwith
PeakCurrent-ModeControl . . . . . . . . . . . . . . . . . . . . . 306
14.7. Simulation,ForwardConverterwithPeakCurrent-Mode
Control. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310
14.8. StateTransitionTechnique:AcceleratedSteadyState . . . . 313
15. PowerQualityandIntegrity 327
15.1. ToleranceofComponents,Devices,andOperating
Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329
15.2. DCOutputRegulationandWorstCaseAnalysis . . . . . . . 330
15.3. SupplyOutputRippleandNoise . . . . . . . . . . . . . . . . . . 332
15.4. SupplyOutputTransientResponses . . . . . . . . . . . . . . . . 333
15.5. TheConceptsofFrequencyandHarmonicContent . . . . . 335
15.6. Control-LoopBandwidth . . . . . . . . . . . . . . . . . . . . . . . 339
15.7. StepResponseTest . . . . . . . . . . . . . . . . . . . . . . . . . . . 342
Description:Electric current converters. 2. Switching power supplies. I. Title. TK7872.C8W853
2006. 621.31'7–dc22. 2005014319. British Library Cataloguing in Publication
