Advanced Modeling and Control of DC-DC Converters

Preface ix

1 Averaged-Switch Modeling and Simulation 1

1.1 Introductory Example (Synchronous Buck Converter) 1

1.2 Synchronous Buck Converter State Equations 4

1.3 Synchronous Buck Converter Averaging and Dynamic Modeling 7

1.4 Point of Load Application Example 11

1.5 Synchronous Buck Example Control-to-Output Transfer Function 12

1.6 Evaluating Frequency Responses Using MATLAB and Python 15

1.7 Review of Closed Loop Control Principles 19

1.8 Review of Feedback Loop Design Principles 23

1.9 Design Example Synchronous Buck POL Voltage Regulator 27

1.10 Introduction to LTspice Simulations 39

1.11 LTspice Simulation Example 41

1.12 LTspice Simulation Example Discussion 47

1.13 The PSIM and MATLAB Simulation Example 49

1.14 The Main Result 57

1.15 Derivation Part 1 62

1.16 Null-Double Injection 66

1.17 Derivation Part 2 68

1.18 Introduction 72

1.19 Solution Using the Feedback Theorem 74

1.20 Discussion 82

1.21 Introduction to Closed-Loop Voltage Regulator 88

1.22 Output Impedance 91

1.23 Summary 96

1.24 Introduction to Circuit Averaging and Averaged Switch Modelingm 97

1.25 Converter Analysis Using Averaged Switch Models 105

1.26 Simulations Using Averaged Switch Models 110

1.27 Design Verification 121

1.28 Including Losses in Averaged Switch Models 130

1.29 Alternative Averaged Switch Networks 137

1.30 Averaged Switch Modeling in DCM 139

1.31 Combined CCM/DCM Averaged Switch Model 146

1.32 Library of Spice Averaged Switch Models 154

1.33 Loop Gain Simulation in CCM/DCM 157

1.34 Small-Signal AC Modeling of DCM Converters 163

1.35 DCM Converter Transfer Functions 169

References 170

2 Techniques of Design-Oriented Analysis 171

2.1 Introduction to Extra Element Theorem 171

2.2 EET Questions and Answers 174

2.3 EET Derivation 175

2.4 Practical Applications of EET 180

2.5 EET Application-Effect of Capacitor ESR 182

2.6 Graphical Comparison of Impedances 186

2.7 Analysis of SEPIC Frequency Responses Using@EET 190

2.8 SEPIC Example ZN 195

2.9 SEPIC Example ZD 199

2.10 Derivation of ZD Using EET 201

2.11 SEPIC Example Undamped Frequency Response 204

2.12 SEPIC Example Impedance Interactions 208

2.13 Practical Design of Damping 214

2.14 Introduction to n-Extra Element Theorem (nEET) 221

2.15 nEET Application Example, Two-Section Filter 228

2.16 nEET Discussion 242

2.17 nEET Application Example, Damped Filter Transfer Function 242

2.18 nEET Frequency Inversion 255

2.19 nEET Application Example, Output Impedance 258

2.20 nEET Summary 262

References 263

3 Input Filter Design 265

3.1 Introduction to Electromagnetic Compatibility (EMC) and Interference (EMI) 265

3.2 Differential and Common-Mode EMI 270

3.3 EMI Measurement and Simulation Example 272

3.4 Addition of Input Filter to a Converter 286

3.5 Impedance Interactions 289

3.6 Approaches to Input Filter Design 294

3.7 Overview of MATLAB and Spice Examples 298

3.8 Control to Output Transfer Function with Input Filter 306

3.9 Determination of ZD and ZN 308

3.10 Input Filter Design Criteria 311

3.11 Corner Frequencies 316

3.12 Introduction to Input Filter Damping 317

3.13 Parallel RC Damping 319

3.14 Damping Networks 324

3.15 Optimum Damping 325

3.16 Optimum Damping Summary of Results 332

3.17 Multi-Stage Cascaded Filters 337

3.18 Cascaded Filter Design Example 340

3.19 Input Filter Design Summary 350

References 351

4 Current Mode Control 353

4.1 Introduction to Peak Current Mode Control 353

4.2 Simple Approximate Model 361

4.3 Small-Signal Model Based on Simple Approximation 367

4.4 Synchronous Buck POL Converter Design Example 373

> 0.5 384

4.6 Stabilization with Addition of an Artificial Ramp 392

4.7 Revisited Inclusion of Artificial Ramp Design Example 399

4.8 More Accurate Average Model 403

4.9 Average Spice CPM Sub-Circuit 408

4.10 Design Verification Using Average Circuit Simulations 416

4.11 Small-Signal AC Equivalent Circuit Models 427

4.12 Transfer Functions of CPM Controlled Converters 432

4.13 The CPM Controlled Boost Converter Analysis Example 443

4.14 Comparison of Frequency Responses of Duty-Cycle and Current-Mode Controlled Converters 454

4.15 Motivation for Modeling of High Frequency Effects 458

4.16 Pulse Width Modulator as a Sampler 462

4.17 Overview of Sampled Data Systems 464

4.18 Sampled Data Modeling of Switching Converters 475

4.19 Introduction to Sampled Data Modeling of PCM Controlled Converters 477

4.20 Development of Sampled Data Model 480

4.21 Frequency Responses of Sampled Data Models 486

4.22 The First-Order Approximation 489

4.23 The Second-Order Approximation 494

4.24 Summary and Conclusions 498

4.25 Introduction to Average Current Mode Control 499

4.26 Transfer Functions of Average Current Mode Controlled Converters 504

4.27 The ACM Controlled Boost DC-DC Converter Design Example 507

4.28 Design Verification by Average Circuit Simulations 518

4.29 Design of the Voltage Control Loop 524

4.30 The ACM Controlled Boost DC Voltage Regulator Design 528

References 538

Index 539