Contents I. Introduction
Dc–dc converters, in general, can be divided into two categories: pulsewidth modulation (PWM) converters, and resonant converters. As most of the applications involve a regulated output voltage, a feedback loop is incorporated into the control system to stabilize the output voltage. For optimal design purpose, small-signal equivalent circuit models are indispensable. For PWM converters, equivalent circuit models are available to engineers for most of the control methods. First, for single loop (voltage mode) control, averaging concept is widely used. This concept was first proposed by Wester and Middlebrook [1] and then represented in state-space approach by Middlebrook and Cuk [2]. To provide more insights on circuit level, three-terminal switch model was proposed by Tymerski et al. [3] and Vorperian [4]. Second, for current mode control, the inductor current has sideband effect and it causes subharmonic problem in some cases (D > 0.5 for peak current mode) [5]. In this case, average concept breaks down as the switching frequency components are neglected. A more advanced modeling methodology describing function method is successfully applied to all kinds of current mode controls by Li and Lee [5] and analytical transfer functions are derived. To provide more physical insights, unified three-terminal switch models are developed by Yan et al. [6] and Tian et al. [7]. Third, for V2 control or ripple-based control methods, both the capacitor voltage and inductor current have the sideband effects [11]. Analytical small-signal models are derived based on describing function method by Li and Lee [8] and further analyzed by Tian et al. [9], [10]. To provide more physical insights, a unified equivalent circuit model for V2 control is developed in [11] and optimal design guidelines are proposed for point-of-load applications employing ceramic caps. Therefore, for PWM converters, feedback design is straightforward with the help of all these research efforts.
