Harmonic analysis of PWM switching power converter state variable in steady-state operation

A new method of analysis of the steady-state operation of PWM switching power converters is presented. The converter is modeled by a differential equation with periodical coefficients for the converter state variable. This differential equation is substituted by an equivalent system of linear differential equations with constant coefficients. Only the forced (steady-state) solutions are found for each equation of the obtained system. The final steady state solution for converter state variable is obtained as the sum of these forced solutions. A boost converter operating in discontinuous current mode is used as example to confirm the analytical results by numerical simulation.