2:1 Converter Charge Vector Analysis

Dickson Charge Vector Analysis

Charge Vector Analysis in FSL

DISCRETE TIME MODELING

Converter Analysis

PWM(small ripple)

Resonant(AC link)

Switched CapacitorHybrid SwitchedCapacitor

QSW & QRConverters

Multilevel

Resonant SC

MMC Z source, matrix,others

Averaging(waveform, switch, state space Charge)

State Plane

SinusoidalAnalysis

Switched Circuits

Historical PerspectiveRobert D MiddlebrookPhD, Standford, 1955CalTech Professor, 1955 1998

Slobodan CúkPhD CalTech, 1976

CalTech Prof, 1977 1999

A. R. Brown and R. D. Middlebrook, “Sampled data Modeling of Switching Regulators” PESC 1981

Model a switched system as anaveraged, time invariant system with

where

Large Signal Modeling of SMPS: Averaging

Linear Circuit Modeling Using State Space

Switching Signals(t)

0

1

Converting to Linear System

Approximate Steady State Waveforms

Approximate Steady State Waveforms

Approximate Steady State Waveforms

The Averaging Approximation

The Averaged System

Buck State Space Averaging

Buck Averaged Model