Calculation and stability investigation of periodic steady states of the voltage controlled Buck DC-DC converter

A new method for investigating the complex dc-dc converters dynamics is suggested in this paper. The method is based on the formulation of a nonlinear difference equation with respect to the duty cycle. This equation embodies the nonlinear and discrete-time characteristics of dc-dc converters and allows both the calculation of normal and subharmonic steady states and their local stability analysis. The method is presented through the analysis of a voltage controlled Buck dc-dc converter.