A new method of analysis for PWM switching power converters

A new method of analysis for pulse-width modulation (PWM) switching power converters is presented. It allows one to find an approximate periodic solution for the converter vector state variable. The converter is modelled by a differential equation with periodic coefficients. This equation is substituted by an equivalent system of linear differential equations with constant coefficients. Only the forced (steady-state) solutions should be found for each equation of this system. The equations are solved in sequence. The final steady-state solution of the PWM differential equation is obtained as the sum of these forced solutions. The method allows one to find the converter de transfer function and efficiency, to evaluate their frequency dependences, and to find the critical frequency and ripple. The first three equations of the equivalent system are usually adequate for practical purposes, and these equations are obtained by an easy formal procedure. One can also obtain the dynamic equation of the state variable de component, and calculate the converter line to output and duty cycle to output transfer functions. A boost converter is used as an example to confirm the analytical results by numerical simulation.