Accurate Loop Gain Model of Ripple-Based Constant on-time Controlled Buck Converters

Ripple based constant on-time (RBCOT) control has been widely used in dc–dc buck converters over past years. However, there has been no accurate loop gain model to link the property of RBCOT controlled buck converter to existing knowledge about basic feedback control principles like crossover frequency (Fc) and phase margin so far. The previously reported stability criterion for the output capacitor's equivalent series-resistor, i.e., Ton/(2C), is insufficient to avoid subharmonic oscillations over all duty cycle values. This article presents a new accurate loop gain model for the RBCOT control. Without simplification, the proposed model can accurately predict the system response even beyond the switching frequency. The proposed modeling approach has been extended to two types of external ramp compensation schemes (for solving the subharmonic oscillation issue) and optimum ranges of ramp compensation amplitudes have been derived accordingly. The modeling results are verified by the SIMPLIS simulations and experimental results.