Low-frequency characterization of switched DC-DC converters

Averaging techniques are developed here to represent buck, boost, and buck-boost types of switched dc-dc converters by approximate continuous models. Simple analytical expressions in terms of the circuit components are derived for the characteristic transient and frequency responses of timeaveraged (continuous) power-stage models for use in designing and understanding the behavior of corresponding switched power stages. Novel conclusions include the dependence of effective circuit component values upon switch duty ratio and the existence of a real positive zero in certain transfer functions. Responses from analog computer simulations of the switched and averaged power stages agree well and, in turn, confirm the analytic predictions. High-order systems can be analyzed by the averaging technique without a commensurate increase in complexity.