Designing Control Loops for Linear and Switching Power Supplies : A Tutorial Guide

by Basso, Christophe

• ISBN13: 9781608075577
• ISBN10: 1608075575
• Format: Hardcover
• Copyright: 2012-09-30
• Publisher: Artech House

Summary

Loop control is an essential area of electronics engineering that today's professionals need to master. Rather than delving into extensive theory, this practical book focuses on what you really need to know for compensating or stabilizing a given control system. You can turn instantly to practical sections with numerous design examples and ready-made formulas to help you with your projects in the field. You also find coverage of the underpinnings and principles of control loops so you can gain a more complete understanding of the material. This authoritative volume explains how to conduct analysis of control systems and provides extensive details on practical compensators. It helps you measure your system, showing how to verify if a prototype is stable and features enough design margin. Moreover, you learn how to secure high-volume production by bench-verified safety margins.

Author Biography

Christophe Basso is a product engineering director at ON Semiconductor in Toulouse, France. He received his B.S.E.E. in electronics from Montpellier University and his M.S.E.E. in power electronics from the National Polytechnic Institute of Toulouse. A senior member of the IEEE, Mr. Basso is a recognized expert, patent holder, and author in the field.

Table of Contents

Foreword	p. xiii
Preface	p. xv
Acknowledgments	p. xvii
Basics of Loop Control	p. 1
Open-Loop Systems	p. 1
Perturbations	p. 3
The Necessity of Control-Closed-Loop Systems	p. 4
Notions of Time Constants	p. 6
Working with Time Constants	p. 7
The Proportional Term	p. 9
The Derivative Term	p. 10
The Integral Term	p. 11
Combining the Factors	p. 12
Performance of a Feedback Control System	p. 12
Transient or Steady State?	p. 13
The Step	p. 15
The Sinusoidal Sweep	p. 16
The Bode Plot	p. 17
Transfer Functions	p. 19
The Laplace Transform	p. 20
Excitation and Response Signals	p. 22
A Quick Example	p. 23
Combining Transfer Functions with Bode Plots	p. 25
Conclusion	p. 27
Selected Bibliography	p. 27
Transfer Functions	p. 29
Expressing Transfer Functions	p. 29
Writing Transfer Functions the Right Way	p. 31
The 0-db Crossover Pole	p. 32
Solving for the Roots	p. 32
Poles and Zeros Found by Inspection	p. 35
Poles, Zeros, and Time Constants	p. 36
Transient Response and Roots	p. 39
When the Roots Are Moving	p. 43
S-Plane and Transient Response	p. 49
Roots Trajectories in the Complex Plane	p. 54
Zeros in the Right Half Plane	p. 56
A Two-Step Conversion Process	p. 56
The Inductor Current Slew-Rate Is the Limit	p. 58
An Average Model to Visualize RHP Zero Effects	p. 60
The Right Half Plane Zero in the Boost Converter	p. 62
Conclusion	p. 66
References	p. 66
Determining a Bridge Input Impedance	p. 67
Reference	p. 69
Plotting Evans Loci with Mathcad	p. 70
Heaviside Expansion Formulas	p. 71
Reference	p. 74
Plotting a Right Half Plane Zero with SPICE	p. 74
Stability Criteria of a Control System	p. 77
Building An Oscillator	p. 77
Theory at Work	p. 79
Stability Criteria	p. 82
Gain Margin and Conditional Stability	p. 84
Minimum Versus Nonminimum-Phase Functions	p. 87
Nyquist Plots	p. 89
Extracting the Basic Information from the Nyquist Plot	p. 91
Modulus Margin	p. 93
Transient Response, Quality Factor, and Phase Margin	p. 97
A Second-Order System, the RLC Circuit	p. 97
Transient Response of a Second-Order System	p. 101
Phase Margin and Quality Factor	p. 110
Opening the Loop to Measure the Phase Margin	p. 117
The Phase Margin of a Switching Converter	p. 120
Considering a Delay in the Conversion Process	p. 122
The Delay in the Laplace Domain	p. 127
Delay Margin versus Phase Margin	p. 130
Selecting the Crossover Frequency	p. 133
A Simplified Buck Converter	p. 135
The Output Impedance in Closed-Loop Conditions	p. 138
The Closed-Loop Output Impedance at Crossover	p. 142
Scaling the Reference to Obtain the Desired Output	p. 143
Increasing the Crossover Frequency Further	p. 149
Conclusion	p. 150
References	p. 151
Compensation	p. 153
The PID Compensator	p. 153
The Pip Expressions in the Laplace Domain	p. 155
Practical Implementation of a PID Compensator	p. 157
Practical Implementation of a PI Compensator	p. 161
The PID at Work in a Buck Convener	p. 163
The Buck Converter Transient Response with the PID Compensation	p. 170
The Setpoint Is Fixed: We Have a Regulator!	p. 171
A Peaky Output Impedance Plot	p. 174
Stabilizing the Converter with Poles-Zeros Placement	p. 176
A Simple Step-by-Step Technique	p. 177
The Plant Transfer Function	p. 178
Canceling the Static Error with an Integrator	p. 179
Adjusting the Gain with the Integrator: The Type 1	p. 182
Locally Boosting the Phase at Crossover	p. 183
Placing Poles and Zeros to Create Phase Boost	p. 185
Create Phase Boost up to 90° with a Single Pole/Zero Pair	p. 189
Mid-Band Gain Adjustment with the Single Pole/Zero Pair: The Type 2	p. 191
Design Example with a Type 2	p. 192
Create Phase Boost up to 180° with a Double Pole/Zero Pair	p. 194
Mid-Band Gain Adjustment with the Double Pole/Zero Pair: The Type 3	p. 197
Design Example with a Type 3	p. 199
Selecting the Right Compensator Type	p. 200
The Type 3 at Work with a Buck Converter	p. 201
Output Impedance Shaping	p. 210
Making the Output Impedance Resistive	p. 212
Conclusion	p. 221
References	p. 222
The Buck Output Impedance with Fast Analytical Techniques	p. 222
Reference	p. 227
The Quality Factor from a Bode Plot with Group Delay	p. 227
The Phase Display in Simulators or Mathematical Solvers	p. 230
Calculating the Tangent	p. 232
Accounting for the Quadrant	p. 234
Improving the Arctangent Function	p. 236
Phase Display in a SPICE Simulator	p. 237
Conclusion	p. 242
Reference	p. 243
Impact of Open-Loop Gain and Origin Pole on Op Amp-Based Transfer Functions	p. 243
The Integrator Case	p. 248
Summary of Compensator Configurations	p. 252
Operational Amplifiers-Based Compensators	p. 253
Type 1: An Origin Pole	p. 253
A Design Example	p. 255
Type 2: An Origin Pole, plus a Pole/Zero Pair	p. 257
A Design Example	p. 260
Type 2a: An Origin Pole plus a Zero	p. 262
A Design Example	p. 263
Type 2b: Some Static Gain plus a Pole	p. 264
A Design Example	p. 266
Type 2: Isolation with an Optocoupler	p. 267
Optocoupler and Op Amp: the Direct Connection, Common Emitter	p. 269
A Design Example	p. 271
Optocoupler and Op Amp: The Direct Connection, Common Collector	p. 273
Optocoupler and Op Amp: The Direct Connection Common Emitter and UC384X	p. 275
Optocoupler and Op Amp: Pull Down with Fast Lane	p. 276
A Design Example	p. 279
Optocoupler and Op Amp: Pull-Down with Fast Lane, Common Emitter, and UC384X	p. 280
Optocoupler and Op Amp: Pull Down Without Fast Lane	p. 283
A Design Example	p. 285
Optocoupler and Op Amp: A Dual-Loop Approach in CC-CV Applications	p. 288
A Design Example	p. 293
The Type 2: Pole and Zero are Coincident to Create an Isolated Type 1	p. 299
A Design Example	p. 301
The Type 2: A Slightly Different Arrangement	p. 303
The Type 3: An Origin Pole, a Pole/Zero Pair	p. 308
A Design Example	p. 313
The Type 3: Isolation with an Optocoupler	p. 315
Optocoupler and Op Amp: The Direct Connection, Common Collector	p. 315
A Design Example	p. 317
Optocoupler and Op Amp: The Direct Connection, Common Emitter	p. 319
Optocoupler and Op Amp: The Direct Connection, Common Emitter, and UC384X	p. 321
Optocoupler and Op Amp: Pull-Down with Fast Lane	p. 322
A Design Example	p. 326
Optocoupler and Op Amp: Pull Down without Fast Lane	p. 328
A Design Example	p. 332
Conclusion	p. 335
References	p. 335
Summary Pictures	p. 335
Automating Components Calculations with k Factor	p. 340
	p. 340
	p. 341
	p. 342
Reference	p. 344
The Optocoupler	p. 346
Transmitting Light	p. 346
Current Transfer Ratio	p. 347
The Optocoupler Pole	p. 348
Extracting the Optocoupler Pole	p. 350
Watch for the LED Dynamic Resistance	p. 351
Good Design Practices	p. 354
References	p. 355
Operational Transconductance Amplifier-Based Compensators	p. 357
The Type 1: An Origin Pole	p. 358
A Design Example	p. 359
The Type 2: An Origin Pole plus a Pole/Zero Pair	p. 360
A Design Example	p. 364
Optocoupler and OTA: A Buffered Connection	p. 365
A Design Example	p. 368
The Type 3: An Origin Pole and a Pole/Zero Pair	p. 370
A Design Example	p. 377
Conclusion	p. 380
Summary Pictures	p. 380
References	p. 381
TL431-Based Compensators	p. 383
A Bandgap-Based Component	p. 383
The Reference Voltage	p. 385
The Need for Bias Current	p. 387
Biasing the TL431: The Impact on the Gain	p. 390
Biasing the TL431: A Different Arrangement	p. 392
Biasing the TL431: Component Limits	p. 395
The Fast Lane Is the Problem	p. 396
Disabling the Fast Lane	p. 397
The Type 1: An Origin Pole, Common-Emitter Configuration	p. 399
A Design Example	p. 402
The Type 1: Common-Collector Configuration	p. 403
The Type 2: An Origin Pole plus a Pole/Zero Pair	p. 403
A Design Example	p. 407
The Type 2: Common-Emitter Configuration and UC384X	p. 408
The Type 2: Common-Collector Configuration and UC384X	p. 411
The Type 2: Disabling the Fast Lane	p. 411
A Design Example	p. 413
The Type 3: An Origin Pole plus a Double Pole/Zero Pair	p. 415
A Design Example	p. 423
The Type 3: An Origin Pole plus a Double Pole/Zero Pair-No Fast Lane	p. 424
A Design Example	p. 429
Testing the Ac Responses on a Bench	p. 431
Isolated Zener-Based Compensator	p. 434
A Design Example	p. 436
Nonisolated Zener-Based Compensator	p. 441
Nonisolated Zener-Based Compensator: A Lower Cost Version	p. 443
Conclusion	p. 445
References	p. 445
Summary Pictures	p. 445
Second Stage LC Filter	p. 448
A Simplified Approach	p. 449
Simulation at Work	p. 450
References	p. 454
Shunt Regulator-Based Compensators	p. 455
The Type 2: An Origin Pole plus a Pole/Zero Pair	p. 456
A Design Example	p. 460
The Type 3: An Origin Pole plus a Double Pole/Zero Pair	p. 466
A Design Example	p. 468
The Type 3: An Origin Pole plus a Double Pole/Zero Pair-No Fast Lane	p. 471
A Design Example	p. 474
Isolated Zener-Based Compensator	p. 476
A Design Example	p. 480
Conclusion	p. 483
References	p. 483
Summary Pictures	p. 484
Measurements and Design Examples	p. 487
Measuring the Control System Transfer Function	p. 487
Opening the Loop with Bias Point Loss	p. 488
Power Stage Transfer Function without Bias Point Loss	p. 492
Opening the Loop in ac Only	p. 493
Voltage Variations at the Injection Points	p. 496
Impedances at the Injection Points	p. 504
Buffering the Data	p. 505
Design Example 1: A Forward dc-dc Converter	p. 509
Moving Parameters	p. 509
The Electrical Schematic	p. 511
Extracting the Power Stage Transfer Response	p. 514
Compensating the Converter	p. 515
Design Example 2: A Linear Regulator	p. 519
Extracting the Power Stage Transfer Function	p. 520
Crossover Frequency Selection and Compensation	p. 521
Testing the Transient Response	p. 527
Design Example 3: A CCM Voltage-Mode Boost Converter	p. 528
The Power Stage Transfer Function	p. 529
Compensating the Converter	p. 533
	p. 535
	p. 535
Plotting the Loop Gain	p. 537
Design Example 4: A Primary-Regulated Flyback Converter	p. 539
Deriving the Transfer Function	p. 540
Verifying the Equations	p. 544
Stabilizing the Converter	p. 545
Design Example 5: Input Filter Compensation	p. 552
A Negative Incremental Resistance	p. 553
Building an Oscillator	p. 554
Taming the Oscillations	p. 556
Conclusion	p. 562
References	p. 562
Conclusion	p. 565
Appendix	p. 567
About the Author	p. 571
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