Small signal modeling of the hysteretic modulator with a current ripple synthesizer

In this paper, the synthetic ripple modulator for synchronous buck converter is modeled by the describing function approach. A detailed circuit configuration of the PWM modulator is introduced, including the hysteretic band control and the ripple synthesizer. The transfer function of the modulator is derived. By comparing the Bode plots for the open-loop hysteretic modulator and the closed-loop system, a good match is obtained between the analytical model and the SIMPLIS simulation results. The proposed model can be used in the design of the current ripple synthesizer to achieve fast transient response, and in the prediction of the system stability.