Approximate Discrete-Time Modeling of DC–DC Converters With Consideration of the Effects of Pulse Width Modulation

Abstract

For dc–dc converters with pulsating output current, such as boost and buck–boost converters, the use of leading-edge or trailing-edge pulse width modulation (PWM) can result in distinctly different behavior. This phenomenon is not readily captured by the usual averaged model but can be predicted with a discrete-time model. However, the discrete-time model, which tracks the dynamics of state variables over a switching period, is usually more complex and less convenient to apply for the design of the feedback control. Based on the low-pass characteristics of dc–dc converters, an approximate discrete-time model is proposed in this paper, and upon transforming to the s -domain, the model results in transfer functions that can be conveniently used for deriving practical closed-loop parameters. With the proposed model, the loop gain, the input and output impedances are derived and analyzed. The effects of applying different types of PWM on the stability of a single dc–dc converter and a system of cascaded dc–dc converters are discussed. Finally, prototypes of a buck converter, a boost converter, and a cascaded system of buck and boost converters are constructed to verify the effectiveness of the approximate discrete-time model.