Dynamic Analysis of Switching-Mode DC/DC Converters

The most critical part of the modern switching-mode power supply is the regulated dc/dc converter. Its dynamic behavior directly determines or influences four of the important characteristics of the power supply: • Stability of the feedback loop • Rejection of input-voltage ripple and the closely-related transient re­ sponse to input-voltage perturbation • Output impedance and the closely-related transient response to load perturbation • Compatibility with the input EMI filter Due to the complexity of the operation of the converter, predicting its dynamic behavior has not been easy. Without accurate prediction, and depending only on building the circuit and tinkering with it until the operation is satisfactory, the engineering cost can easily escalate and schedules can be missed. The situation is not much better when the circuit is built in the computer, using a general-purpose circuit-simulation program such as SPICE. (At the end of this book is a form for obtaining information on a computer program especially well suited for dynamic analysis of switching-mode power converters: DYANA, an acronym for "DYnamic ANAlysis. " DYANA is based on the method given in this book. ) The main goal of this book is to help the power-supply designer in the prediction of the dynamic behavior by providing user-friendly analytical tools, concrete results of already-made analyses, tabulated for easy application by the reader, and examples of how to apply the tools provided in the book.

1. Survey of the Existing Analysis Methods.- 1. Introduction to the Injected-Absorbed-Current Method of Analysis.- 1-1 Theoretical Foundation.- 1-2 General, Low-Frequency, Small-Signal Model of a Switching Cell.- 1-3 Cell Transfer Functions.- 1-4 General Formulas for the Derivation of the Characteristic Coefficients.- 1-5 Summary and Conclusions.- References.- 2. Elementary Converters Operating at Constant Frequency with Duty Ratio as Controlled Quantity.- 2-1 Introduction.- 2-2 Buck Cell.- 2-3 Buck-Boost Cell.- 2-4 Boost Cell.- 2-5 Tabulation of Derived Transfer Functions, Comments.- 2-6 Influence of Capacitor Series Resistance.- 2-7 Characteristic Coefficients.- 2-8 Influence of the Inductor Resistance.- 2-9 Summary—General Expression of Regulator Input Impedance.- 2-10 Correspondence Between the Cell Model Using Characteristic Coefficients and Other Known Models.- 3. General Small-Signal, Low-Frequency Analysis of Switching Regulators.- 3-1 Introduction.- 3-2 Modulator Transfer Functions.- 3-3 Essential Parameters of a Closed-Loop Regulator: Input Impedance, Output Impedance, Input-to-Output Voltage Transfer Function.- References.- 4. State-Variables-Averaging Method.- 4-1 Introduction.- 4-2 Continuous-Conduction Mode.- 4-3 Discontinuous-Conduction Mode.- References.- 2. Multiple-Loop Switching Power Cells.- 5. Elementary Switching Power Cells with Inductor Current as Controlled Quantity.- 5-1 Introduction.- 5-2 Open-Loop Instability of Power Cells Using Constant-Frequency Peak-Current-Commanding Control.- 5-3 Characteristic Coefficients of Elementary Power Cells Using Constant-Frequency Peak-Current-Commanding Control and Linear Compensating Ramp.- 5-4 Output Characteristic Coefficients of the Buck Cell in Heavy Mode with Hysteretic, Constant Off Time, and PWM-Conductance Control.- 5-5 Practical Evaluation of Different Current-Mode Control Techniques.- References.- 6. Multiple-Loop Switching Cells Using Inductor Voltage in a Minor Feedback Loop.- 6-1 Introduction.- 6-2 Pole-Zero Cancellation in a Buck Cell in Heavy Mode Using an IVI Configuration.- 6-3 Transfer Functions of Different Functional Blocks.- 6-4 Complete Small-Signal, Low-Frequency Model of a Switching Regulator Using the IVI Configuration.- 6-5 IVI Configuration in Applications.- References.- 3. Special Configurations.- 7. ?uk and SEPIC Switching Cells.- 7-1 Introduction.- 7-2 Characteristic Coefficients of the ?uk Converter in Heavy Mode.- 7-3 Extensions of the ?uk Converter.- 7-4 Comments.- 7-5 The SEPIC Converter as a Derivative of the ?uk Converter.- References.- 8. Analysis of Power Cells with Duty-Ratio Control at Variable Frequency.- 8-1 Introduction.- 8-2 Porter Switching Cell.- 8-3 Switching Cells with Constant Off Time or Constant On Time Control.- 8-4 Buck Cell in Heavy Mode with Frequency Control and Feedforward of Input Voltage.- References.- 9. Free-Running Hysteretic Regulator.- 9-1 Introduction.- 9-2 Exact Steady-State Analysis.- 9-3 Approximate Steady-State Analysis.- 9-4 Design Example.- 9-5 Transient Analysis.- References.- 4. Applications of Linear Analysis Method.- 10. Interconnection of a Power Source and a Switching Regulator.- 10-1 Introduction.- 10-2 Switching Regulator with Capacitive Input Filter.- 10-3 Analysis of the Switching Regulator with General Input Filter.- 10-4 Influence of Input Filter on Regulator Parameters.- 10-5 Simplified Approach.- 10-6 Regulator Employing a Buck Cell Operating at Constant Frequency, in Heavy Mode, with Duty Ratio Control, Preceded by an Input LC Filter.- 10-7 Final Remarks.- References.- 11. Feedforward in Switching Regulators.- 11-1 Introduction.- 11-2 A Combined Input Voltage and Output Current Feedforward in Regulators Using Switching Cells with Inductor Current as the Controlled Quantity.- 11-3 Feedforward Concept in Configurations with an Input Filter.- 11-4 Feedforward of Major Perturbations.- References.- 12. Parallel Operation of Switching Regulators.- 12-1 Introduction.- 12-2 Paralleled Autonomous Sources with Feedback-Controlled Current-Sharing.- 12-3 Conclusions.- References.- 5. Selected Analytic Approaches and Applications and Future Advances in Analysis Methods.- 13. Selected Analysis Examples.- 13-1 Introduction.- 13-2 Small-Signal Analysis of a Regulator Using a Buck Cell at Constant Frequency, in Heavy Mode, and with a Fast Voltage-Feedback Path.- 13-3 Small-Signal Analysis of a Regulator Using a Buck Cell at Constant Frequency, in Heavy Mode, and with Combined Fast Voltage and Output-Current Feedback.- 13-4 State-Plane Analysis of a Boost Cell.- References.- 14. High-Frequency Extension of the Linear Cell Model.- 14-1 Introduction.- 14-2 Inclusion of the Discrete (Sampled) Injected-Current Waveform into the Cell Model.- 14-3 Derivation of the Discrete Characteristic Coefficients of a Boost Cell in Heavy Mode, at Constant Switching Frequency, and with Duty Ratio as Controlled Quantity.- 14-4 Comparison of the Transfer Functions Obtained by Different Approaches.- 14-5 Discrete Characteristic Coefficients of the Elementary Switching Cells in Heavy and Light Modes, at Constant Switching Frequency, and with Duty Ratio as Controlled Quantity.- 14-6 Discrete Characteristic Coefficients of the Elementary Switching Cells in Heavy Mode, at Constant Switching Frequency, with Maximum Inductor Current as Controlled Quantity, and with Linear Compensating Ramp.- 14-7 Conclusions.- References.- Appendixes.- Appendix 1. Additional Information for Chapter 5.- A1-1 Derivation of Time Delay Between Control and Injected Current for Constant Off Time Current-Mode Control.- A1-2 Control-to-Output Voltage Functions of CurrentMode-Controlled Buck Converter with Three Different Control Methods.- Appendix 2. Graphical-Analytical Representation of Transfer Functions.- A2-1 Introduction.- A2-2 Transfer Functions of Passive Networks.- References.- Appendix 3. Examples and Problems.- A3-1 Introduction.- A3-2 Appendix to Chapter 2—Regulators Employing Elementary Cells, Operating at Constant Switching Frequency, and with Duty Ratio as the Controlled Quantity.- A3-3 Appendix to Chapter 14—Successive Approximations of the Cell Controlled-Quantity-to-Output-Voltage Transfer Function.- Appendix 4. Sources of Technical Information.- A4-1 Conferences.- A4-2 Periodicals.- A4-3 Compendia.- A4-4 Textbooks.