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E-raamat: Designing Control Loops for Linear and Switching Power Supplies

  • Formaat: 590 pages
  • Ilmumisaeg: 31-Jan-2012
  • Kirjastus: Artech House Publishers
  • ISBN-13: 9781608075584
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  • Formaat: 590 pages
  • Ilmumisaeg: 31-Jan-2012
  • Kirjastus: Artech House Publishers
  • ISBN-13: 9781608075584
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Loop control is an essential area of electronics engineering that today's professionals need to master. A control system is a complex electronics architecture involving setpoints and targets. One simple example is the cruise control system of an automobile. Rather than delving into extensive theory, this practical book focuses on what power electronics engineers really need to know for compensating or stabilizing a given system. Engineers can turn instantly to practical sections with numerous design examples and ready-made formulas to help them with their projects in the field. Readers also find coverage of the underpinnings and principles of control loops so they 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 engineers measure their system, showing how to verify if a prototype is stable and features enough design margin. Moreover, professionals learn how to secure high-volume production by bench-verified safety margins.
Foreword xiii
Preface xv
Acknowledgments xvii
Chapter 1 Basics of Loop Control
1(28)
1.1 Open-Loop Systems
1(3)
1.1.1 Perturbations
3(1)
1.2 The Necessity of Control---Closed-Loop Systems
4(2)
1.3 Notions of Time Constants
6(6)
1.3.1 Working with Time Constants
7(2)
1.3.2 The Proportional Term
9(1)
1.3.3 The Derivative Term
10(1)
1.3.4 The Integral Term
11(1)
1.3.5 Combining the Factors
12(1)
1.4 Performance of a Feedback Control System
12(7)
1.4.1 Transient or Steady State?
13(2)
1.4.2 The Step
15(1)
1.4.3 The Sinusoidal Sweep
16(1)
1.4.4 The Bode Plot
17(2)
1.5 Transfer Functions
19(8)
1.5.1 The Laplace Transform
20(2)
1.5.2 Excitation and Response Signals
22(1)
1.5.3 A Quick Example
23(2)
1.5.4 Combining Transfer Functions with Bode Plots
25(2)
1.6 Conclusion
27(2)
Selected Bibliography
27(2)
Chapter 2 Transfer Functions
29(48)
2.1 Expressing Transfer Functions
29(3)
2.1.1 Writing Transfer Functions the Right Way
31(1)
2.1.2 The O-db Crossover Pole
32(1)
2.2 Solving for the Roots
32(7)
2.2.1 Poles and Zeros Found by Inspection
35(1)
2.2.2 Poles, Zeros, and Time Constants
36(3)
2.3 Transient Response and Roots
39(10)
2.3.1 When the Roots Are Moving
43(6)
2.4 S-Plane and Transient Response
49(7)
2.4.1 Roots Trajectories in the Complex Plane
54(2)
2.5 Zeros in the Right Half Plane
56(10)
2.5.1 A Two-Step Conversion Process
56(2)
2.5.2 The Inductor Current Slew-Rate Is the Limit
58(2)
2.5.3 An Average Model to Visualize RHP Zero Effects
60(2)
2.5.4 The Right Half Plane Zero in the Boost Converter
62(4)
2.6 Conclusion
66(11)
References
66(1)
Appendix 2A Determining a Bridge Input Impedance
67(2)
Reference
69(1)
Appendix 2B Plotting Evans Loci with Mathcad
70(1)
Appendix 2C Heaviside Expansion Formulas
71(3)
Reference
74(1)
Appendix 2D Plotting a Right Half Plane Zero with SPICE
74(3)
Chapter 3 Stability Criteria of a Control System
77(76)
3.1 Building An Oscillator
77(5)
3.1.1 Theory at Work
79(3)
3.2 Stability Criteria
82(15)
3.2.1 Gain Margin and Conditional Stability
84(3)
3.2.2 Minimum Versus Nonminimum-Phase Functions
87(2)
3.2.3 Nyquist Plots
89(2)
3.2.4 Extracting the Basic Information from the Nyquist Plot
91(2)
3.2.5 Modulus Margin
93(4)
3.3 Transient Response, Quality Factor, and Phase Margin
97(36)
3.3.1 A Second-Order System, the RLC Circuit
97(4)
3.3.2 Transient Response of a Second-Order System
101(9)
3.3.3 Phase Margin and Quality Factor
110(7)
3.3.4 Opening the Loop to Measure the Phase Margin
117(3)
3.3.5 The Phase Margin of a Switching Converter
120(2)
3.3.6 Considering a Delay in the Conversion Process
122(5)
3.3.7 The Delay in the Laplace Domain
127(3)
3.3.8 Delay Margin versus Phase Margin
130(3)
3.4 Selecting the Crossover Frequency
133(17)
3.4.1 A Simplified Buck Converter
135(3)
3.4.2 The Output Impedance in Closed-Loop Conditions
138(4)
3.4.3 The Closed-Loop Output Impedance at Crossover
142(1)
3.4.4 Scaling the Reference to Obtain the Desired Output
143(6)
3.4.5 Increasing the Crossover Frequency Further
149(1)
3.5 Conclusion
150(3)
References
151(2)
Chapter 4 Compensation
153(100)
4.1 The PID Compensator
153(23)
4.1.1 The PID Expressions in the Laplace Domain
155(2)
4.1.2 Practical Implementation of a PID Compensator
157(4)
4.1.3 Practical Implementation of a PI Compensator
161(2)
4.1.4 The PID at Work in a Buck Converter
163(7)
4.1.5 The Buck Converter Transient Response with the PID Compensation
170(1)
4.1.6 The Setpoint Is Fixed: We Have a Regulator!
171(3)
4.1.7 A Peaky Output Impedance Plot
174(2)
4.2 Stabilizing the Converter with Poles-Zeros Placement
176(34)
4.2.1 A Simple Step-by-Step Technique
177(1)
4.2.2 The Plant Transfer Function
178(1)
4.2.3 Canceling the Static Error with an Integrator
179(3)
4.2.4 Adjusting the Gain with the Integrator: The Type 1
182(1)
4.2.5 Locally Boosting the Phase at Crossover
183(2)
4.2.6 Placing Poles and Zeros to Create Phase Boost
185(4)
4.2.7 Create Phase Boost up to 90° with a Single Pole/Zero Pair
189(2)
4.2.8 Mid-Band Gain Adjustment with the Single Pole/Zero Pair: The Type 2
191(1)
4.2.9 Design Example with a Type 2
192(2)
4.2.10 Create Phase Boost up to 180° with a Double Pole/Zero Pair
194(3)
4.2.11 Mid-Band Gain Adjustment with the Double Pole/Zero Pair: The Type 3
197(2)
4.2.12 Design Example with a Type 3
199(1)
4.2.13 Selecting the Right Compensator Type
200(1)
4.2.14 The Type 3 at Work with a Buck Converter
201(9)
4.3 Output Impedance Shaping
210(11)
4.3.1 Making the Output Impedance Resistive
212(9)
4.4 Conclusion
221(32)
References
222(1)
Appendix 4A The Buck Output Impedance with Fast Analytical Techniques
222(5)
References
227(1)
Appendix 4B The Quality Factor from a Bode Plot with Group Delay
227(3)
Appendix 4C The Phase Display in Simulators or Mathematical Solvers
230(2)
Calculating the Tangent
232(2)
Accounting for the Quadrant
234(2)
Improving the Arctangent Function
236(1)
Phase Display in a SPICE Simulator
237(5)
Conclusion
242(1)
Reference
243(1)
Appendix 4D Impact of Open-Loop Gain and Origin Pole on Op Amp-Based Transfer Functions
243(5)
The Integrator Case
248(4)
Appendix 4E Summary of Compensator Configurations
252(1)
Chapter 5 Operational Amplifiers-Based Compensators
253(104)
5.1 Type 1: An Origin Pole
253(2)
5.1.1 A Design Example
255(2)
5.2 Type 2: An Origin Pole, plus a Pole/Zero Pair
257(3)
5.2.1 A Design Example
260(2)
5.3 Type 2a: An Origin Pole plus a Zero
262(1)
5.3.1 A Design Example
263(1)
5.4 Type 2b: Some Static Gain plus a Pole
264(2)
5.4.1 A Design Example
266(1)
5.5 Type 2: Isolation with an Optocoupler
267(2)
5.5.1 Optocoupler and Op Amp: the Direct Connection, Common Emitter
269(2)
5.5.2 A Design Example
271(2)
5.5.3 Optocoupler and Op Amp: The Direct Connection, Common Collector
273(2)
5.5.4 Optocoupler and Op Amp: The Direct Connection Common Emitter and UC384X
275(1)
5.5.5 Optocoupler and Op Amp: Pull Down with Fast Lane
276(3)
5.5.6 A Design Example
279(1)
5.5.7 Optocoupler and Op Amp: Pull-Down with Fast Lane, Common Emitter, and UC384X
280(3)
5.5.8 Optocoupler and Op Amp: Pull Down Without Fast Lane
283(2)
5.5.9 A Design Example
285(3)
5.5.10 Optocoupler and Op Amp: A Dual-Loop Approach in CC-CV Applications
288(5)
5.5.11 A Design Example
293(6)
5.6 The Type 2: Pole and Zero are Coincident to Create an Isolated Type 1
299(2)
5.6.1 A Design Example
301(2)
5.7 The Type 2: A Slightly Different Arrangement
303(5)
5.8 The Type 3: An Origin Pole, a Pole/Zero Pair
308(5)
5.8.1 A Design Example
313(2)
5.9 The Type 3: Isolation with an Optocoupler
315(1)
5.9.1 Optocoupler and Op Amp: The Direct Connection, Common Collector
315(2)
5.9.2 A Design Example
317(2)
5.9.3 Optocoupler and Op Amp: The Direct Connection, Common Emitter
319(2)
5.9.4 Optocoupler and Op Amp: The Direct Connection, Common Emitter, and UC384X
321(1)
5.9.5 Optocoupler and Op Amp: Pull-Down with Fast Lane
322(4)
5.9.6 A Design Example
326(2)
5.9.7 Optocoupler and Op Amp: Pull Down without Fast Lane
328(4)
5.9.8 A Design Example
332(3)
5.10 Conclusion
335(22)
References
335(1)
Appendix 5A Summary Pictures
335(5)
Appendix 5B Automating Components Calculations with k Factor
340(1)
Type 1
340(1)
Type 2
341(1)
Type 3
342(2)
Reference
344(2)
Appendix 5C The Optocoupler
346(1)
Transmitting Light
346(1)
Current Transfer Ratio
347(1)
The Optocoupler Pole
348(2)
Extracting the Optocoupler Pole
350(1)
Watch for the LED Dynamic Resistance
351(3)
Good Design Practices
354(1)
References
355(2)
Chapter 6 Operational Transconductance Amplifier-Based Compensators
357(26)
6.1 The Type 1: An Origin Pole
358(1)
6.1.1 A Design Example
359(1)
6.2 The Type 2: An Origin Pole plus a Pole/Zero Pair
360(4)
6.2.1 A Design Example
364(1)
6.3 Optocoupler and OTA: A Buffered Connection
365(15)
6.3.1 A Design Example
368(2)
6.4 The Type 3: An Origin Pole and a Pole/Zero Pair
370(7)
6.4.1 A Design Example
377(3)
6.5 Conclusion
380(3)
Appendix 6A Summary Pictures
380(1)
References
381(2)
Chapter 7 TL431-Based Compensators
383(72)
7.1 A Bandgap-Based Component
383(7)
7.1.1 The Reference Voltage
385(2)
7.1.2 The Need for Bias Current
387(3)
7.2 Biasing the TL431: The Impact on the Gain
390(2)
7.3 Biasing the TL431: A Different Arrangement
392(3)
7.4 Biasing the TL431: Component Limits
395(1)
7.5 The Fast Lane Is the Problem
396(1)
7.6 Disabling the Fast Lane
397(34)
7.7 The Type 1: An Origin Pole, Common-Emitter Configuration
399(3)
7.7.1 A Design Example
402(1)
7.8 The Type 1: Common-Collector Configuration
403(1)
7.9 The Type 2: An Origin Pole plus a Pole/Zero Pair
403(4)
7.9.1 A Design Example
407(1)
7.10 The Type 2: Common-Emitter Configuration and UC384X
408(3)
7.11 The Type 2: Common-Collector Configuration and UC384X
411(1)
7.12 The Type 2: Disabling the Fast Lane
411(2)
7.12.1 A Design Example
413(2)
7.13 The Type 3: An Origin Pole plus a Double Pole/Zero Pair
415(8)
7.13.1 A Design Example
423(1)
7.14 The Type 3: An Origin Pole plus a Double Pole/Zero Pair---No Fast Lane
424(5)
7.14.1 A Design Example
429(2)
7.15 Testing the Ac Responses on a Bench
431(3)
7.16 Isolated Zener-Based Compensator
434(7)
7.16.1 A Design Example
436(5)
7.17 Nonisolated Zener-Based Compensator
441(2)
7.18 Nonisolated Zener-Based Compensator: A Lower Cost Version
443(2)
7.19 Conclusion
445(10)
References
445(1)
Appendix 7A Summary Pictures
445(3)
Appendix 7B Second Stage LC Filter
448(1)
A Simplified Approach
449(1)
Simulation at Work
450(4)
References
454(1)
Chapter 8 Shunt Regulator-Based Compensators
455(32)
8.1 The Type 2: An Origin Pole plus a Pole/Zero Pair
456(4)
8.1.1 A Design Example
460(6)
8.2 The Type 3: An Origin Pole plus a Double Pole/Zero Pair
466(2)
8.2.1 A Design Example
468(3)
8.3 The Type 3: An Origin Pole plus a Double Pole/Zero Pair---No Fast Lane
471(3)
8.3.1 A Design Example
474(2)
8.4 Isolated Zener-Based Compensator
476(7)
8.4.1 A Design Example
480(3)
8.5 Conclusion
483(4)
References
483(1)
Appendix 8A Summary Pictures
484(3)
Chapter 9 Measurements and Design Examples
487(78)
9.1 Measuring the Control System Transfer Function
487(75)
9.1.1 Opening the Loop with Bias Point Loss
488(4)
9.1.2 Power Stage Transfer Function without Bias Point Loss
492(1)
9.1.3 Opening the Loop in ac Only
493(3)
9.1.4 Voltage Variations at the Injection Points
496(8)
9.1.5 Impedances at the Injection Points
504(1)
9.1.6 Buffering the Data
505(4)
9.2 Design Example 1: A Forward dc-dc Converter
509(1)
9.2.1 Moving Parameters
509(2)
9.2.2 The Electrical Schematic
511(3)
9.2.3 Extracting the Power Stage Transfer Response
514(1)
9.2.4 Compensating the Converter
515(4)
9.3 Design Example 2: A Linear Regulator
519(1)
9.3.1 Extracting the Power Stage Transfer Function
520(1)
9.3.2 Crossover Frequency Selection and Compensation
521(6)
9.3.3 Testing the Transient Response
527(1)
9.4 Design Example 3: A CCM Voltage-Mode Boost Converter
528(1)
9.4.1 The Power Stage Transfer Function
529(4)
9.4.2 Compensating the Converter
533(2)
Strategy 1
535(1)
Strategy 2
535(2)
9.4.3 Plotting the Loop Gain
537(2)
9.5 Design Example 4: A Primary-Regulated Flyback Converter
539(1)
9.5.1 Deriving the Transfer Function
540(4)
9.5.2 Verifying the Equations
544(1)
9.5.3 Stabilizing the Converter
545(7)
9.6 Design Example 5: Input Filter Compensation
552(1)
9.6.1 A Negative Incremental Resistance
553(1)
9.6.2 Building an Oscillator
554(2)
9.6.3 Taming the Oscillations
556(6)
9.7 Conclusion
562(3)
References
562(3)
Conclusion 565(2)
Appendix 567(4)
About the Author 571
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 recognized expert, patent holder, and author in the field.