A Novel Describing Function Small-Signal Modeling Approach for Passive Ripple Constant On-Time Controlled Converter with Exponentially Varying Slope

Passive ripple constant on-time (PRCOT) controlled converters have been widely used for mobile applications to improve light-load efficiency and transient response. An accurate small-signal model is inevitable for PRCOT control to estimate stability and design high loop gain bandwidth. The describing function (DF) method has been used to model the constant on-time control. However, previous research assumes a constant passive ripple slope, which is different at small RC time-constant conditions and causes inaccurate modeling results. In this paper, a new describing function modeling approach is proposed to handle exponentially varying slope. This paper takes a PRCOT controlled boost converter as an example to demonstrate the modeling approach. Simulation and experiment results verified the accuracy of the proposed model even beyond the switching frequency for both constant slope or exponentially varying slope passive ramp cases.