Switching Power Supplies A to Z:This page intentionally left bank
Preface xi
Acknowledgements xvii
Chapter 1: The Principles of Switching Power Conversion 1
Introduction3
Overview and Basic Terminology 5
Understanding the Inductor22
Evolution of Switching Topologies 43
Chapter 2: DC-DC Converter Design and Magnetics61
DC Transfer Functions 64
The DC Level and the “Swing” of the Inductor Current Waveform 65
Defining the AC, DC, and Peak Currents 68
Understanding the AC, DC and Peak Currents 70
Defining the “Worst-case” Input Voltage72
The Current Ripple Ratio ‘r’ 75
Relating r to the Inductance 75
The Optimum Value of r 77
Do We Mean Inductor? Or Inductance? 79
How Inductance and Inductor Size Depend on Frequency 80
How Inductance and Inductor Size Depend on Load Current 80
How Vendors Specify the Current Rating of an Off-the-shelf Inductor and
How to Select It 81
What Is the Inductor Current Rating We Need to Consider for a Given Application? 82
The Spread and Tolerance of the Current Limit 85
Worked Example (1)88
Worked Examples (2, 3, and 4) 100
Worked Example (5) — When Not to Increase the Number of Turns 106
Worked Example (6) — Characterizing an Off-the-shelf Inductor in a
Specific Application 110
Calculating the “Other” Worst-case Stresses 118
Chapter 3: Off-line Converter Design and Magnetics 127
Flyback Converter Magnetics 130
Forward Converter Magnetics 152
Chapter 4: The Topology FAQ 177
Questions and Answers 179
Chapter 5: Conduction and Switching Losses 203
Switching a Resistive Load 206
Switching an Inductive Load 210
Switching Losses and Conduction Loss 213
A Simplified Model of the Mosfet for Studying Inductive Switching
Losses 215
The Parasitic Capacitances Expressed in an Alternate System 217
Gate Threshold Voltage 218
The Turn-on Transition 218
The Turn-off Transition 222
Gate Charge Factors 224
Worked Example 227
Applying the Switching Loss Analysis to Switching Topologies 231
Worst-case Input Voltage for Switching Losses 232
How Switching Losses Vary with the Parasitic Capacitances 233
Optimizing Driver Capability vis-à-vis Mosfet Characteristics 234
Chapter 6: Printed Circuit Board Layout 237
Introduction239
Trace Section Analysis 239
Some Points to Keep in Mind During Layout 240
Thermal Management Concerns 247
Chapter 7: Feedback Loop Analysis and Stability 249
Transfer Functions, Time Constant and the Forcing Function 251
Understanding ‘e’ and Plotting Curves on Log Scales 252
Time Domain and Frequency Domain Analysis 255
Complex Representation 256
Nonrepetitive Stimuli 258
The s-plane 258
Laplace Transform 260
Disturbances and the Role of Feedback262
Transfer Function of the RC Filter 264
The Integrator Op-amp (“pole-at-zero” filter) 267
Mathematics in the Log Plane 269
Transfer Function of the LC Filter 270
Summary of Transfer Functions of Passive Filters 273
Poles and Zeros 274
Interaction of Poles and Zeros 276
Closed and Open Loop Gain 277
The Voltage Divider 280
Pulse Width Modulator Transfer Function (gain) 281
Voltage Feedforward282
Power Stage Transfer Function 283
Plant Transfer Functions of All the Topologies 284
Boost Converter 286
Feedback Stage Transfer Functions 289
Closing the Loop 291
Criteria for Loop Stability 293
Plotting the Open-loop Gain and Phase with an Integrator 293
Canceling the Double Pole of the LC Filter 295
The ESR Zero 296
Designing a Type 3 Op-amp Compensation Network 297
Optimizing the Feedback Loop 301
Input Ripple Rejection 304
Load Transients 305
Type 1 and Type 2 Compensations 306
Transconductance Op-amp Compensation 308
Simpler Transconductance Op-amp Compensation311
Compensating with Current Mode Control 313
Chapter 8: EMI from the Ground up—Maxwell to CISPR 323
The Standards 326
Maxwell to EMI 328
Susceptibility/Immunity 333
Some Cost-related Rules-of-thumb 335
EMI for Subassemblies 335
CISPR 22 for Telecom Ports — Proposed Changes 336
Chapter 9: Measurements and Limits of Conducted EMI 339
Differential Mode and Common Mode Noise 341
How Conducted EMI Is Measured 344
The Conducted Emission Limits 348
Quasi-peak, Average, and Peak Measurements 351
Chapter 10: Practical EMI Line Filters 355
Safety Issues in EMI Filter Design 357
Practical Line Filters 359
Safety Restrictions on the Total Y-capacitance 367
Equivalent DM and CM Circuits 368
Some Notable Industry Experiences in EMI 371
Chapter 11: DM and CM Noise in Switching Power Supplies 373
Main Source of DM Noise 375
The Main Source of CM Noise 377
The Ground Choke 385
Chapter 12: Fixing EMI across the Board 387
The Role of the Transformer in EMI 389
EMI from Diodes 394
Beads, and an Industry Experience — the dV/dt of Schottky Diodes 397
Basic Layout Guidelines 398
Last-ditch Troubleshooting 399
Are We Going to Fail the Radiation Test? 402
Chapter 13: Input Capacitor and Stability Considerations in EMI Filters 403
Is the DM Choke Saturating? 405
Practical Line Filters in DC-DC Converter Modules 410
Chapter 14: The Math behind the Electromagnetic Puzzle417
Math Background — Fourier Series 419
The Rectangular Wave 420
Analysis of the Rectangular Wave 423
The Trapezoid 424
The EMI from a Trapezoid 426
The Road to Cost-effective Filter Design 427
Practical DM Filter Design 430
Practical CM Filter Design 433
viii
Appendix 1: Focusing on Some Real-world Issues 437
Sounds Like Worst-case, But There’s Danger Lurking in the Middle 439
Loop Design Sometimes Compensates for Lower-quality Switchers 440
Re-inventing the Wheel as a Square 442
The Mighty Zener 444
Better Do the Math: Ignore Transfer Functions at Your Own Peril 447
Aluminum Cap Multipliers — Why We Can’t Have Them and Eat Them Too 449
Limit Your Peak Current, Not Your Reliability 452
Reliability Is No Flash in the Pan 455
The Incredible Shrinking Core459
Plain Lucky We Don’t Live in a PSpice World! 462
Why Does the Efficiency of My Flyback Nose-dive? 465
It’s Not a Straight Line: Computing the Correct Drain to Source Resistance from
V-I Curves 468
Don’t Have a Scope? Use a DMM, Dummy! 470
Are We Making Light of Electronic Ballasts? 473
More on Designing Reliable Electronic Ballasts 476
The Organizational Side of Power Management: One Engineer’s Perspective 480
Appendix 2: Reference Design Table 485