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

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.