An introduction to switched-mode dc-dc converters. The first part of the course treats basic circuit operation, including steady-state converter modeling and analysis, switch realization, discontinuous conduction mode, and transformer-isolated converters. Next, converter control systems are covered, including ac modeling of converters using averaged methods, small-signal transfer functions, and classical feedback loop design. Finally, magnetics design for switched-mode applications is discussed, including: basic magnetics, the skin and proximity effects, inductor design, transformer design.

**
1. Introduction**

- Introduction to Power Processing
- Several Applications of Power Electronics
- Elements of Power Electronics

### I. Converters in Equilibrium

**2. Principles of Steady State Converter Analysis**

- Inductor Volt-Second Balance, Capacitor Charge Balance, and the Small-Ripple Approximation
- Boost Converter Example
- Cuk Converter Example
- Estimating the Output Voltage Ripple in Converters Containing Two-Pole Low-Pass Filters

**3. Steady-State Equivalent Circuit Modeling, Losses, and Efficiency**

- The DC Transformer Model
- Inclusion of Inductor Copper Loss
- Construction of Equivalent Circuit Model
- Example: Inclusion of Semiconductor Conduction Losses in the Boost Converter Model

**4. Switch Realization**

- Switch Applications
- Single-Quadrant Switches
- Current-Bidirectional Two-Quadrant Switches
- Voltage-Bidirectional Two-Quadrant Switches
- Four-Quadrant Switches
- Synchronous Rectifiers
- A Brief Survey of Power Semiconductor Devices
- Power Diodes
- Metal-Oxide-Semiconductor Field-Effect Transistor (MOSFET)
- Bipolar Junction Transistor (BJT)
- Insulated Gate Bipolar Transistor (IGBT)
- Wide bandgap devices
- Switching Loss
- Transistor Switching with Clamped Inductive Load
- Diode Recovered Charge
- Device Capacitances, and Leakage, Package, and Stray Inductances
- Efficiency vs. Switching Frequency

**5. The Discontinuous Conduction Mode**

- Origin of the Discontinuous Conduction Mode, and Mode Boundary
- Analysis of the Conversion Ratio M(D,K)
- Boost Converter Example

**6. Converter Circuits**

- Circuit Manipulations
- Inversion of Source and Load
- Cascade Connection of Converters
- Rotation of Three-Terminal Cell
- Differential Connection of the Load
- A Short List of Converters
- Transformer Isolation
- Full-Bridge and Half-Bridge Isolated Buck Converters
- Forward Converter
- Push-Pull Isolated Buck Converter
- Flyback Converter
- Boost-Derived Isolated Converters
- Isolated Versions of the SEPIC and the Cuk Converter
- Converter Evaluation and Design
- Switch Stress and Utilization
- Design Using Computer Spreadsheet

### II. Converter Dynamics and Control

**7. AC Equivalent Circuit Modeling**

- Introduction
- The Basic AC Modeling Approach
- Results for Several Basic Converters
- Example: A Nonideal Flyback Converter
- State-Space Averaging
- The Canonical Circuit Model
- Modeling the Pulse-Width Modulator

**8. Converter Transfer Functions**

- Review of Bode Plots
- Single pole/zero/RHP zero Responses
- Frequency Inversion
- Combinations
- Quadratic Pole Response: Resonance
- The Low-Q Approximation
- Approximate Roots of an Arbitrary-Degree Polynomial
- Analysis of Converter Transfer Functions
- Example: Transfer Functions of the Buck-Boost Converter
- Transfer Functions of Some Basic CCM Converters
- Physical Origins of the RHP Zero in Converters
- Graphical Construction of Impedances and Transfer Functions
- Series Impedances: Addition of Asymptotes
- Series Resonant Circuit Example
- Parallel Impedances: Inverse Addition of Asymptotes
- Parallel Resonant Circuit Example
- Voltage Divider Transfer Functions: Division of Asymptotes
- Graphical Construction of Converter Transfer Functions
- Measurement of AC Transfer Functions and Impedances

**9. Controller Design**

- Introduction
- Effect of Negative Feedback on the Network Transfer Functions
- Feedback Reduces the Transfer Functions from Disturbances to the Output
- 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
- Construction of the Important Quantities 1/(1 + T ) and T/(1 + T ) and the Closed-Loop Transfer Functions
- Stability
- The Phase Margin Test
- The Relationship Between Phase Margin and Closed-Loop Damping Factor
- Transient Response vs. Damping Factor
- Regulator Design
- Lead (PD) Compensator
- Lag (PI ) Compensator
- Combined (PID) Compensator
- Design Example
- Measurement of Loop Gains
- Voltage Injection
- Current Injection
- Measurement of Unstable Systems

### III. Magnetics

**13. Basic Magnetics Theory**

- Review of Basic Magnetics
- Transformer Modeling
- Loss Mechanisms in Magnetic Devices
- Core Loss
- Low-Frequency Copper Loss
- Eddy Currents in Winding Conductors
- Introduction to the Skin and Proximity Effects
- Leakage Flux in Windings
- Foil Windings and Layers
- Power Loss in a Layer
- Example: Power Loss in a Transformer Winding
- Interleaving the Windings
- PWM Waveform Harmonics
- Several Types of Magnetic Devices, Their B-H Loops, and Core vs. Copper Loss

**14. Inductor Design**

- Filter Inductor Design Constraints
- The Core Geometrical Constant Kg
- A Step-by-Step Procedure
- Multiple-Winding Magnetics Design via the Kg Method
- Window Area Allocation
- Coupled Inductor Design Constraints
- Design Procedure
- Example: Coupled Inductor for a Two-Output Forward Converter
- Example: CCM Flyback Transformer

**15. Transformer Design**

- Transformer Design: Basic Constraints
- Optimum Flux Density
- A Step-by-Step Transformer Design Procedure
- Example 1: Single-Output Isolated Cuk Converter
- Example 2: Multiple-Output Full-Bridge Buck Converter
- AC Inductor Design

**Layout and grounding principles** (1 lecture)

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

*RWE 8/11/15*