Fundamentals of Power Electronics

R. W. Erickson

Table of Contents

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1. Introduction

Part I. Converters in Equilibrium

2. Principles of steady state converter analysis

3. Steady-state equivalent circuit modeling, losses, and efficiency 4. Switch realization

5. The discontinuous conduction mode

    5.1. Origin of the discontinuous conduction mode, and mode boundary
    5.2. Analysis of the conversion ratio M(D,K)
    5.3. Boost converter example
    5.4. Summary of results and key points

6. Converter circuits

    6.1. Circuit manipulations
      6.1.1. Inversion of source and load
      6.1.2. Cascade connection of converters
      6.1.3. Rotation of three-terminal cell
      6.1.4. Differential connection of the load

    6.2. A short list of converters

    6.3. Transformer isolation

      6.3.1. Full-bridge and half-bridge isolated buck converters
      6.3.2. Forward converter
      6.3.3. Push-pull isolated buck converter
      6.3.4. Flyback converter
      6.3.5. Boost-derived isolated converters
      6.3.6. Isolated versions of the SEPIC and the Cuk converter

    6.4. Converter evaluation and design

      6.4.1. Switch stress and utilization
      6.4.2. Design using computer spreadsheet

    6.5. Summary of key points

Part II. Converter Dynamics and Control

7. AC modeling

    7.1. Introduction

    7.2. The basic ac modeling approach

      7.2.1. Averaging the inductor waveforms
      7.2.2. Discussion of the averaging approximation
      7.2.3. Averaging the capacitor waveforms
      7.2.4. The average input current
      7.2.5. Perturbation and linearization
      7.2.6. Construction of the small-signal equivalent circuit model
      7.2.7. Results for several basic converters

    7.3. Example: A nonideal flyback converter

    7.4. State-space averaging

      7.4.1. The state equations of a network
      7.4.2. The basic state-space averaged model
      7.4.3. Discussion of the state-space averaging result
      7.4.4. Example: State-space averaging of a nonideal buck-boost converter

    7.5. Circuit averaging and averaged switch modeling

      7.5.1. Obtaining a time-invariant circuit
      7.5.2. Circuit averaging
      7.5.3. Perturbation and linearization
      7.5.4. Averaged switch modeling

    7.6. The canonical circuit model

      7.6.1. Development of the canonical circuit model
      7.6.2. Example: Manipulation of the buck-boost converter model into canonical form
      7.6.3. Canonical circuit parameter values for some common converters

    7.7. Modeling the pulse-width modulator

    7.8. Summary of key points

8. Converter transfer functions

    8.1. Review of Bode plots
      8.1.1. Single pole response
      8.1.2. Single zero response
      8.1.3. Right half-plane zero
      8.1.4. Frequency inversion
      8.1.5. Combinations
      8.1.6. Double pole response: resonance
      8.1.7. The low-Q approximation
      8.1.8. Approximate roots of an arbitrary-degree polynomial

    8.2. Analysis of converter transfer functions

      8.2.1. Example: Transfer functions of the boost converter
      8.2.2. Transfer functions of some basic dc-dc converters
      8.2.3. Physical origins of the RHP zero

    8.3. Graphical construction of converter transfer functions

      8.3.1. Series impedances: addition of asymptotes
      8.3.2. Parallel impedances: inverse addition
      8.3.3. Another example
      8.3.4. Voltage divider transfer functions: division of asymptotes

    8.4. Measurement of ac transfer functions and impedances

    8.5. Summary of key points

9. Controller design

    9.1. Introduction

    9.2. Effect of negative feedback on the network transfer functions

      9.2.1. Feedback reduces the transfer functions from disturbances to the output
      9.2.2. Feedback causes the transfer function from the reference input to the output to be insensitive to variations in the gains in the forward path of the loop

    9.3. Construction of the important quantities 1/(1+T) and T/(1+T) and the closed-loop transfer functions

    9.4. Stability

      9.4.1. The phase margin test
      9.4.2. The relation between phase margin and closed-loop damping factor
      9.4.3. Transient response vs. damping factor

    9.5. Regulator design

      9.5.1. Lead (PD) compensator
      9.5.2. Lag (PI) compensator
      9.5.3. Combined (PID) compensator
      9.5.4. Design example

    9.6. Measurement of loop gains

      9.6.1. Voltage injection
      9.6.2. Current injection
      9.6.3. Measurement of unstable systems

    9.7. Summary of key points

10. Ac and dc equivalent circuit modeling of the discontinuous conduction mode

    10.1. DCM averaged switch model

    10.2. Small-signal ac modeling of the DCM switch network

    10.3. Generalized switch averaging

      10.3.1. DCM buck converter example
      10.3.2. Proof of generalized averaged switch modeling

    10.4. Summary of key points

11. Current programmed control

    11.1. Oscillation for D > 0.5

    11.2. A simple first-order model

      11.2.1. Simple model via algebraic approach: buck-boost example
      11.2.2. Averaged switch modeling

    11.3. A more accurate model

      11.3.1. Current programmed controller model
      11.3.2. Example: analysis of CPM buck converter

    11.4. Discontinuous conduction mode

    11.5. Summary of key points

Part III. Magnetics

12. Basic magnetics theory

    12.1. Review of basic magnetics
      12.1.1. Basic relations
      12.1.2. Magnetic circuits

    12.2. Transformer modeling

      12.2.1. The ideal transformer
      12.2.2. The magnetizing inductance
      12.2.3. Leakage inductances

    12.3. Loss mechanisms in magnetic devices

      12.3.1. Core loss
      12.3.2. Low-frequency copper loss

    12.4. Eddy currents in winding conductors

      12.4.1. The skin effect
      12.4.2. The proximity effect
      12.4.3. Magnetic fields in the vicinity of winding conductors: MMF diagrams
      12.4.4. Power loss in a layer
      12.4.5. Example: power loss in a transformer winding
      12.4.6. PWM waveform harmonics

    12.5. Summary of key points

13. Filter inductor design

    13.1. Several types of magnetic devices, their B-H loops, and core vs. copper loss

    13.2. Filter inductor design constraints

      13.2.1. Maximum flux density
      13.2.2. Inductance
      13.2.3. Winding area
      13.2.4. Winding resistance

    13.3. The core geometrical constant Kg

    13.4. A step-by-step procedure

    13.5. Summary of key points

14. Transformer design

    14.1. Winding area optimization

    14.2. Transformer design: basic constraints

      14.2.1. Core loss
      14.2.2. Flux density
      14.2.3. Copper loss
      14.2.4. Total power loss vs. Bmax
      14.2.5. Optimum flux density

    14.3. A step-by-step transformer design procedure

    14.4. Examples

      14.4.1. Example 1: single-output isolated Cuk converter
      14.4.2. Example 2: multiple-output full-bridge buck converter

    14.5. Ac inductor design
      14.5.1. Outline of derivation
      14.5.2. Step-by-step ac inductor design procedure

    14.6. Summary

Part IV. Modern Rectifiers, and Power System Harmonics

15. Power and harmonics in nonsinusoidal systems

    15.1. Average power

    15.2. Root-mean-square (rms) value of a waveform

    15.3. Power factor

      15.3.1. Linear resistive load, nonsinusoidal voltage
      15.3.2. Nonlinear dynamic load, sinusoidal voltage

    15.4. Power phasors in sinusoidal systems

    15.5. Harmonic currents in three-phase systems

      15.5.1. Harmonic currents in three-phase four-wire networks
      15.5.2. Harmonic currents in three-phase three-wire networks
      15.5.3. Harmonic current flow in power factor correction capacitors

    15.6. AC line current harmonic standards

      15.6.1. US MIL STD 461B
      15.6.2. International Electrotechnical Commission standard 555
      15.6.3. IEEE/ANSI standard 519

16. Line-commutated rectifiers

    16.1. The single-phase full wave rectifier
      16.1.1. Continuous conduction mode
      16.1.2. Discontinuous conduction mode
      16.1.3. Behavior when C is large
      16.1.4. Minimizing THD when C is small

    16.2. The three-phase bridge rectifier

      16.2.1. Continuous conduction mode
      16.2.2. Discontinuous conduction mode

    16.3. Phase control

      16.3.1. Inverter mode
      16.3.2. Harmonics and power factor
      16.3.3. Commutation

    16.4. Harmonic trap filters

    16.5. Transformer connections

    16.6. Summary

17. The ideal rectifier

    17.1. Properties of the ideal rectifier

    17.2. Realization of a near-ideal rectifier

    17.3. Single-phase converter systems incorporating ideal rectifiers

    17.4. RMS values of rectifier waveforms

      17.4.1. Boost rectifier example
      17.4.2. Comparison of single-phase rectifier topologies

    17.5. Ideal three-phase rectifiers

      17.5.1. Three-phase rectifiers operating in CCM
      17.5.2. Some other approaches to three-phase rectification

    17.6. Summary of key points

18. Low harmonic rectifier modeling and control

    18.1. Modeling losses and efficiency in CCM high-quality rectifiers
      18.1.1. Expression for controller duty cycle d(t)
      18.1.2. Expression for the dc load current
      18.1.3. Solution for converter efficiency
      18.1.4. Design example

    18.2. Controller schemes

      18.2.1. Average current control
      18.2.2. Feedforward
      18.2.3. Current programmed control
      18.2.4. Hysteretic control
      18.2.5. Nonlinear carrier control

    18.3. Control system modeling

      18.3.1. Modeling the outer low-bandwidth control system
      18.3.2. Modeling the inner wide-bandwidth average current controller

    18.4. Summary of key points

Part V. Resonant converters

19. Resonant Conversion

    19.1. Sinusoidal analysis of resonant converters
      19.1.1. Controlled switch network model
      19.1.2. Modeling the rectifier and capacitive filter networks
      19.1.3. Resonant tank network
      19.1.4. Solution of converter voltage conversion ratio M = V/Vg

    19.2. Examples

      19.2.1. Series resonant dc-dc converter example
      19.2.2. Subharmonic modes of the series resonant converter
      19.2.3. Parallel resonant dc-dc converter example

    19.3. Exact characteristics of the series and parallel resonant converters

      19.3.1. Series resonant converter
      19.3.2. Parallel resonant converter

    19.4. Soft switching

      19.4.1. Operation of the full bridge below resonance: zero-current switching
      19.4.2. Operation of the full bridge above resonance: zero-voltage switching
      19.4.3. The zero voltage transition converter

    19.5. Load-dependent properties of resonant converters

      19.5.1. Inverter output characteristics
      19.5.2. Dependence of transistor current on load
      19.5.3. Dependence of the ZVS/ZCS boundary on load resistance

    19.6. Summary of key points

20. Quasi-resonant converters

    20.1. The zero-current-switching quasi-resonant switch cell
      20.1.1. Waveforms of the half-wave ZCS quasi-resonant switch cell
      20.1.2. The average terminal waveforms
      20.1.3. The full-wave ZCS quasi-resonant switch cell

    20.2. Resonant switch topologies

      20.2.1. The zero-voltage-switching quasi-resonant switch
      20.2.2. The zero-voltage-switching multi-resonant switch
      20.2.3. Quasi-square-wave resonant switches

    20.3. Ac modeling of quasi-resonant converters

    20.4. Summary of key points

Appendices

Appendix 1. RMS values of commonly-observed converter waveforms

    A1.1. Some common waveforms
    A1.2. General piecewise waveform

Appendix 2. Magnetics design tables

    A2.1. Pot core data
    A2.2. EE core data
    A2.3. EC core data
    A2.4. ETD core data
    A2.5. PQ core data
    A2.6. American wire gauge data

Appendix 3. Averaged switch modeling of a CCM SEPIC

Index