Advanced modeling and control topics in power electronics, and power factor corrected supplies. Averaged switch modeling of converters, computer simulation, ac modeling of the discontinuous conduction mode, the current programmed mode, null double injection techniques in linear circuits, input filter design, harmonics in power systems, low-harmonic rectifiers, and introduction to digital control.

Prerequisite: ECEN 5797Introduction to Power Electronics

Required Textbook: Erickson and Maksimovic,Fundamentals of Power Electronics, 2nd edition, Springer Science+Business (2000), ISBN 0-7923-7270-0. Can be ordered from the University of Colorado bookstore (same text as ECEN 5797).

Computer requirements: Access to web is required. A Spice simulator and MATLAB/Simulink are required. LTSpice and MATLAB/Simulink are available to on-campus students on Power Lab and Circuits Lab computers; contact the instructor if you need access to these labs. LTSpice can be downloaded by anybody for free using the link above. The student version of MATLAB/Simulink is sufficient; this can be purchased online or through the campus bookstore, if desired; if you are enrolled in this course then you are eligible to purchase student MATLAB. Use of a simple spreadsheet, such as Excel, may be helpful but is not required.

### Syllabus

Introduction

**Averaged switch modeling and simulation**

- Section 7.4 and Appendix B
- Deriving averaged small-signal models of converters by averaging only the switching elements
- Objectives of simulation
- Simulation of converter small-signal behavior using averaged switch models

**Techniques of Design-Oriented Analysis, with Application to Switching Converters**

- Middlebrook's Extra Element Theorem
- ( Appendix C)
- Use of null double injection techniques to find how addition of an element changes a transfer function.
- Input Filter Design
- Chapter 10
- How the addition of an input filter disrupts the loop gain of a switching regulator
- How to design an input filter having adequate damping, so that the input filter does not change the loop gain
- The n-Extra Element Theorem
- Supplementary notes posted on the web site. Also, Section 8.1.8 will be covered.
- An extension of the extra element theorem that allows exact expressions for complex transfer functions to be written "by inspection."
- Middlebrook's Feedback Theorem
- Supplementary notes posted on web site
- Analysis of feedback circuits using null double injection techniques

**Dynamic modeling and simulation of converters operating in discontinuous conduction mode**

- Chapter 11 and Appendix B
- Equivalent circuit modeling of converters operating in the discontinuous conduction mode, using averaged switch modeling
- How changing the operating mode leads to substantial changes in small-signal transfer functions

**Introduction to sampled-data modeling **

- Supplementary notes posted on web site
- Sampled-data small-signal modeling
- Pulse-width modulator as a sampler, equivalent hold
- Application of the sampled-data model to dicontinuous conduction mode

**Current Programmed Control**

- Chapter 12 and Appendix B
- Introduction to this very popular technique for controlling switching converters
- Basic circuitry and slope compensation
- Averaged switch modeling
- Sampled-data modeling of current programmed converters (Supplementary notes posted on the web site)
- Detailed small-signal analysis
- Simulation
- Effects of current mode control on basic transfer functions

**Introduction to Digital Control of Switching Converters **

- Supplementary notes posted on the web site
- Digital realization of the basic control loop
- Discrete-time converter model
- Examples of discrete-time compensator design

**Modern Rectifiers**

- Power and Harmonics in Nonsinusoidal Systems: Chapter 16
- Pulse-Width Modulated Rectfiers: Chapter 18
- Modeling, analysis, and control of low-harmonic rectifiers
- Boost, flyback, and other topologies for controlling the input current waveform of an ac-dc rectifier
- Average-current, peak-current-mode, critical conduction mode, and nonlinear carrier control techniques
- Determination of rms currents, and comparison of performances of popular topologies
- System considerations. Modelling losses. Simulation.

One midterm exam and one final exam. Ten to twelve one-week homework assignments.