## Course Info

This course teaches how to design a feedback system to control a switching converter.

The equivalent circuit models derived in the previous courses are extended to model small-signal ac variations. These models are then solved, to find the important transfer functions of the converter and its regulator system.

Finally, the feedback loop is modeled, analyzed, and designed to meet requirements such as output regulation, bandwidth and transient response, and rejection of disturbances.

## Objective:

- Being able to design and analyze the feedback systems of switching regulators.

## Syllabus

### 7. AC Equivalent Circuit Modeling

How to extend the converter steady-state equivalent circuits, derived in the previous courses, to obtain small-signal ac equivalent circuits that model the important converter and regulator system dynamics.

- Introduction to AC Modeling
- Averaged AC Modeling
- Discussion of Averaging
- Perturbation and Linearization
- Construction of Equivalent Circuit
- Modeling the Pulse-Width Modulator
- The Canonical Model
- State-Space Averaging
- Homework assignment #1: switch realization

### 8.1 Converter Transfer Functions – Part 1

A review of the construction of Bode plots of the magnitude and phase of first-order, second-order, and higher-order transfer functions, with emphasis on techniques needed for design of regulator systems. Design-oriented analysis techniques to make approximations and gain insight into how to design ac systems having significant complexity.

- Introduction to Design-Oriented Analysis
- Review of Bode Diagrams: Pole
- Other Basic Terms
- Combinations
- Second-order Response: Resonance
- The Low-Q Approximation
- Analytical Factoring of Higher-Order Polynomials
- Homework Assignment #2: Transfer Functions

### 8.2 Converter Transfer Functions – Part 2

Design-oriented analysis techniques to make approximations and gain insight into how to design ac systems having significant complexity. Graphical construction techniques.

- Analysis of Converter Transfer Functions
- Transfer Functions of Basic Converters
- Graphical Construction of Impedances
- Graphical Construction of Parallel and More Complex Impedances
- Graphical Construction of Converter Transfer Functions
- Homework Assignment #3: Construction of Transfer Functions

### 9. Controller Design

Application of the material of Chapters 7 and 8 to design closed-loop regulators that employ switching converters. How to design a feedback system that accurately regulates its output while rejecting disturbances.

- Introduction
- Construction of Closed-loop Transfer Functions
- Stability
- Phase Margin vs. Closed-loop Q
- Regulator Design
- Design Example
- Op-amp Compensator Design
- Another Example: Point-of-Load Regulator
- Homework Assignment #4 (Part 1): Feedback
- Homework Assignment #4 (Part 2): Closed-Loop Simulation