Harmonic analysis of PWM converters

A nonlinear vector differential equation of periodically time-variant system is applied to the harmonic analysis of pulsewidth modulation (PWM) converters. The differential equation is solved by a combination of harmonic balance and small parameter methods. This results in an equivalent system of algebraic equations from which a steady-state solution required for the harmonic analysis is obtained. The first three equations of this system usually suffice for the practical analysis of PWM converters. The analysis may be formalized and simplified if the first equation is used to obtain dc components, and the inductor current and capacitor voltage harmonic content are obtained from two subsequent equations. An example (three-switch converter) is given.