CONTENTS. Chapter 1. Introduction to Power Conversion 1. Basso_FM.qxd 11/20/07 8:39 PM Page v. Foreword xiii Preface xv Nomenclature

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1 Basso_FM.qxd 11/20/07 8:39 PM Page v Foreword xiii Preface xv Nomenclature xvii Chapter 1. Introduction to Power Conversion Do You Really Need to Simulate? / What You Will Find in the Following Pages / What You Will Not Find in this Book / Converting Power with Resistors / Associating Resistors / A Closed-Loop System / Deriving Useful Equations with the Linear Regulator / A Practical Working Example / Building a Simple Generic Linear Regulator / Conclusion on Linear Regulators / Converting Power with Switches / A Filter Is Needed / Current in the Inductance, Continuous or Discontinuous? / Charge and Flux Balance / Energy Storage / The Duty Cycle Factory / Voltage-Mode Operation / Current-Mode Operation / The Buck Converter / On-Time Event / Off-Time Event / Buck Waveforms CCM / Buck Waveforms DCM / Buck Transition Point DCM CCM / Buck CCM Output Ripple Voltage Calculation / Now with the ESR / Buck Ripple, the Numerical Application / The Boost Converter / On-Time Event / Off-Time Event / Boost Waveforms CCM / Boost Waveforms DCM / Boost Transition Point DCM CCM / Boost CCM Output Ripple Voltage Calculations / Now with the ESR / Boost Ripple, the Numerical Application / The Buck-Boost Converter / On-Time Event / Off-Time Event / 56 v

2 Basso_FM.qxd 11/20/07 8:39 PM Page vi vi Buck-Boost Waveforms CCM / Buck-Boost Waveforms DCM / Buck-Boost Transition Point DCM CCM / Buck-Boost CCM Output Ripple Voltage Calculation / Now with the ESR / Buck-Boost Ripple, the Numerical Application / Input Filtering / The RLC Filter / A More Comprehensive Representation / Creating a Simple Closed-Loop Current Source with SPICE / Understanding Overlapping Impedances / 72 Chapter 2. Small-Signal Modeling State-Space Averaging / SSA at Work for the Buck Converter First Step / The DC Transformer / Large-Signal Simulations / SSA at Work for the Buck Converter, the Linearization Second Step / SSA at Work for the Buck Converter, the Small-Signal Model Final Step / The PWM Switch Model the Voltage-Mode Case / Back to the Good Old Bipolars / An Invariant Internal Architecture / Waveform Averaging / Terminal Currents / Terminal Voltages / A Transformer Representation / Large-Signal Simulations / A More Complex Representation / A Small-Signal Model / Helping with Simulation / Discontinuous Mode Model / Deriving the d 2 Variable / Clamping Sources / Encapsulating the Model / The PWM Modulator Gain / Testing the Model / Mode Transition / The PWM Switch Model the Current-Mode Case / Current-Mode Instabilities / Preventing Instabilities / The Current-Mode Model in CCM / Upgrading the Model / The Current-Mode Model in DCM / Deriving the Duty Cycles d 1 and d 2 / Building the DCM Model / Testing the Model / Buck DCM, Instability in DC / Checking the Model in CCM / The PWM Switch Model Parasitic Elements Effects / A Variable Resistor / Ohmic Losses, Voltage Drops: The VM Case / Ohmic Losses, Voltage Drops: The CM Case / Testing the Lossy Model in Current Mode / Convergence Issues with the CM Model / PWM Switch Model in Borderline Conduction / Borderline Conduction the Voltage-Mode Case / Testing the Voltage-Mode BCM Model / 191

3 Basso_FM.qxd 11/20/07 8:39 PM Page vii vii Borderline Conduction the Current-Mode Case / Testing the Current-Mode BCM Model / The PWM Switch Model a Collection of Circuits / The Buck / The Tapped Buck / The Forward / The Buck-Boost / The Flyback / The Boost / The Tapped Boost / The Nonisolated SEPIC / The Isolated SEPIC / The Nonisolated C uk Converter / The Isolated C uk Converter / Other Averaged Models / Ridley Models / Small-Signal Current-Mode Models / Ridley Models at Work / CoPEC Models / CoPEC Models at Work / Ben-Yaakov Models / 220 What I Should Retain from Chap. 2 / 224 References / 224 Appendix 2A Basic Transfer Functions for Converters / 225 2A.1. Buck / 226 2A.2. Boost / 229 2A.3. Buck-Boost / 231 References / 235 Appendix 2B Poles, Zeros, and Complex Plane a Simple Introduction / 235 References / 240 Chapter 3. Feedback and Control Loops Observation Points / Stability Criteria / Phase Margin and Transient Response / Choosing the Crossover Frequency / Shaping the Compensation Loop / The Passive Pole / The Passive Zero / Right Half-Plane Zero / Type 1 Amplifier Active Integrator / Type 2 Amplifier Zero-Pole Pair / Type 2A Origin Pole Plus a Zero / Type 2B Proportional Plus a Pole / Type 3 Origin Pole Plus Two Coincident Zero-Pole Pairs / Selecting the Right Amplifier Type / An Easy Stabilization Tool the k Factor / Type 1 Derivation / Type 2 Derivation / Type 3 Derivation / Stabilizing a Voltage-Mode Buck Converter with the k Factor / Conditional Stability / Independent Pole-Zero Placement / Crossing Over Right at the Selected Frequency / The k Factor versus Manual Pole-Zero Placement / Stabilizing a Current-Mode Buck Converter with the k Factor / The Current-Mode Model and Transient Steps / 286

4 Basso_FM.qxd 11/20/07 8:39 PM Page viii viii 3.7. Feedback with the TL431 / A Type 2 Amplifier Design Example with the TL431 / A Type 3 Amplifier with the TL431 / Biasing the TL431 / The Resistive Divider / The Optocoupler / A Simplified Model / Extracting the Pole / Accounting for the Pole / Shunt Regulators / SPICE Model of the Shunt Regulator / Quickly Stabilizing a Converter Using the Shunt Regulator / Small-Signal Responses with PSIM and SIMPLIS / 316 What I Should Retain from Chap. 3 / 322 References / 322 Appendix 3A Automated Pole-Zero Placement / 323 Appendix 3B A TL431 Spice Model / 326 3B.1. A Behavioral TL431 Spice Model / 326 3B.2. Cathode Current versus Cathode Voltage / 328 3B.3. Output Impedance / 329 3B.4. Open-Loop Gain / 330 3B.5. Transient Test / 331 3B.6. Model Netlist / 331 Appendix 3C Type 2 Manual Pole-Zero Placement / 332 Appendix 3D Understanding the Virtual Ground in Closed-Loop Systems / 335 3D.1. Numerical Example / 336 3D.2. Loop Gain Is Unchanged / 337 Chapter 4. Basic Blocks and Generic Switched Models Generic Models for Faster Simulations / In-Line Equations / Operational Amplifiers / A More Realistic Model / A UC384X Error Amplifier / Sources with a Given Fan-Out / Voltage-Adjustable Passive Elements / The Resistor / The Capacitor / The Inductor / A Hysteresis Switch / An Undervoltage Lockout Block / Leading Edge Blanking / Comparator with Hysteresis / Logic Gates / Transformers / A Simple Saturable Core Model / Multioutput Transformers / Astable Generator / A Voltage-Controlled Oscillator / A Voltage-Controlled Oscillator Featuring Dead Time Control / Generic Controllers / Current-Mode Controllers / Current-Mode Model with a Buck / Current-Mode Instabilities / The Voltage-Mode Model / The Duty Cycle Generation / A Quick Example with a Forward Converter / 384

5 Basso_FM.qxd 11/20/07 8:39 PM Page ix ix Dead Time Generation / List of Generic Models / Convergence Options / 388 What I Should Retain from Chap. 4 / 391 References / 392 Appendix 4A An Incomplete Review of the Terminology Used in Magnetic Designs / 392 4A.1. Introduction / 392 4A.2. Field Definition / 393 4A.3. Permeability / 393 4A.4. Founding Laws / 396 4A.5. Inductance / 396 4A.6. Avoiding Saturation / 397 References / 398 Appendix 4B Feeding Transformer Models with Physical Values / 398 4B.1. Understanding the Equivalent Inductor Model / 398 4B.2. Determining the Physical Values of the Two-Winding T Model / 400 4B.3. The Three-Winding T Model / 401 References / 405 Chapter 5. Simulations and Practical Designs of Nonisolated Converters The Buck Converter / A 12 V, 4 A Voltage-Mode Buck from a 28 V Source / AC Analysis / Transient Analysis / The Power Switch / The Diode / Output Ripple and Transient Response / Input Ripple / A 5 V, 10 A Current-Mode Buck from a Car Battery / AC Analysis / Transient Analysis / A Synchronous Buck Converter / A Low-Cost Floating Buck Converter / Component Constraints for the Buck Converter / The Boost Converter / A Voltage-Mode 48 V, 2 A Boost from a Car Battery / AC Analysis / Transient Analysis / A Current-Mode 5 V, 1 A Boost from a Li-Ion Battery / AC Analysis / Transient Analysis / Input Filter / Component Constraints for the Boost Converter / The Buck-Boost Converter / A Voltage-Mode 12 V, 2 A Buck-Boost Converter Powered from a Car Battery / AC Analysis / Transient Analysis / A Discontinuous Current-Mode 12 V, 2 A Buck-Boost Converter Operating from a Car Battery / AC Analysis / Transient Analysis / Component Constraints for the Buck-Boost Converter / 486 References / 486 Appendix 5A The Boost in Discontinuous Mode, Design Equations / 487 5A.1. Input Current / 487 5A.2. Output Ripple Voltage / 489

6 Basso_FM.qxd 11/20/07 8:39 PM Page x x Chapter 6. Simulations and Practical Designs of Off-Line Converters The Front End The Rectifier Bridge / Capacitor Selection / Diode Conduction Time / RMS Current in the Capacitor / Current in the Diodes / Input Power Factor / A 100-W Rectifier Operated on Universal Mains / Hold-Up Time / Waveforms and Line Impedance / In-Rush Current / Voltage Doubler / Power Factor Correction / Definition of Power Factor / Nonsinusoidal Signals / A Link to the Distortion / Why Power Factor Correction? / Harmonic Limits / A Need for Storage / Passive PFC / Improving the Harmonic Content / The Valley-Fill Passive Corrector / Active Power Factor Correction / Different Techniques / Constant On-Time Borderline Operation / Frequency Variations in BCM / Averaged Modeling of the BCM Boost / Fixed-Frequency Average Current-Mode Control / Shaping the Current / Fixed-Frequency Peak Current-Mode Control / Compensating the Peak Current-Mode Control PFC / Average Modeling of the Peak Current-Mode PFC / Hysteretic Power Factor Correction / Fixed-Frequency DCM Boost / Flyback Converter / Testing the Flyback PFC / Designing a BCM Boost PFC / Average Simulations / Reducing the Simulation Time / Cycle-by-Cycle Simulation / The Follow-Boost Technique / 574 What I Should Retain from Chap. 6 / 575 References / 576 Chapter 7. Simulations and Practical Designs of Flyback Converters An Isolated Buck-Boost / Flyback Waveforms, No Parasitic Elements / Flyback Waveforms with Parasitic Elements / Observing the Drain Signal, No Clamping Action / Clamping the Drain Excursion / DCM, Looking for Valleys / Designing the Clamping Network / The RCD Configuration / Selecting k c / Curing the Leakage Ringing / 605

7 Basso_FM.qxd 11/20/07 8:39 PM Page xi xi Which Diode to Select? / Beware of Voltage Variations / TVS Clamp / Two-Switch Flyback / Active Clamp / Design Example / Simulation Circuit / Small-Signal Response of the Flyback Topology / DCM Voltage Mode / CCM Voltage Mode / DCM Current Mode / CCM Current Mode / Practical Considerations about the Flyback / Start-Up of the Controller / Start-Up Resistor Design Example / Half-Wave Connection / Good Riddance, Start-up Resistor! / High-Voltage Current Source / The Auxiliary Winding / Short-Circuit Protection / Observing the Feedback Pin / Compensating the Propagation Delay / Sensing the Secondary Side Current / Improving the Drive Capability / Overvoltage Protection / Standby Power of Converters / What Is Standby Power? / The Origins of Losses / Skipping Unwanted Cycles / Skipping Cycles with a UC384X / Frequency Foldback / A 20-W, Single-Output Power Supply / A 90-W, Single-Output Power Supply / A 35-W, Multioutput Power Supply / Component Constraints for the Flyback Converter / 725 What I Should Retain from Chap. 7 / 726 References / 727 Appendix 7A Reading the Waveforms to Extract the Transformer Parameters / 727 Appendix 7B The Stress / 729 7B.1. Voltage / 730 7B.2. Current / 731 Appendix 7C Transformer Design for the 90 W Adapter / 732 7C.1. Core Selection / 732 7C.2. Determining the Primary and Secondary Turns / 733 7C.3. Choosing the Primary and Secondary Wire Sizes / 734 7C.4. Choosing the Material, Based on the Desired Inductance, or Gapping the Core If Necessary / 735 7C.5. Designs Using Intusoft Magnetic Designer / 735 Chapter 8. Simulations and Practical Designs of Forward Converters An Isolated Buck Converter / Need for a Complete Core Reset / Reset Solution 1, a Third Winding / Leakage Inductance and Overlap / Reset Solution 2, a Two-Switch Configuration / Two-Switch Forward and Half-Bridge Driver / Reset Solution 3, the Resonant Demagnetization / 762

8 Basso_FM.qxd 11/20/07 8:39 PM Page xii xii 8.5. Reset Solution 4, the RCD Clamp / Reset Solution 5, the Active Clamp / Synchronous Rectification / Multioutput Forward Converters / Magnetic Amplifiers / Synchronous Postregulation / Coupled Inductors / Small-Signal Response of the Forward Converter / Voltage Mode / Current Mode / Multioutput Forward / A Single-Output 12-V, 250-W Forward Design Example / MOSFET Selection / Installing a Snubber / Diode Selection / Small-Signal Analysis / Transient Results / Short-Circuit Protection / Component Constraints for the Forward Converter / 849 What I Should Retain from Chap. 8 / 849 References / 850 Appendix 8A Half-Bridge Drivers Using the Bootstrap Technique / 851 Appendix 8B Impedance Reflections / 855 Appendix 8C Transformer and Inductor Designs for the 250-W Adapter / 859 8C.1. Transformer Variables / 859 8C.2. Transformer Core Selection / 859 8C.3. Determining the Primary and Secondary Turns / 860 8C.4. Choosing the Primary and Secondary Wire Sizes / 861 8C.5. Gapping the Core / 861 8C.6. Designs Using Intusoft Magnetic Designer / 862 8C.7. Inductor Design / 865 8C.8. Core Selection / 866 8C.9. Choosing the Wire Size and Checking the DC Resistive Loss / 867 8C.10. Checking the Core Loss / 867 8C.11. Estimating the Temperature Rise / 867 Appendix 8D CD-ROM Content / 868 Conclusion 869 Index 871

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