Modeling a hysteretic modulator's PFM and PWM modes

In this paper, the describing function approach is used to extend the modeling of hysteretic mode control from the PWM mode to the PWM/PFM dual mode. A detailed circuit configuration of the PFM modulator and derivation of the model are introduced. Based on the derived model, a single zero transfer function is presented and several engineering approximations are applied to represent the dynamic characteristics of the PWM/PFM hysteretic modulator. A closed loop analysis is performed to assist the system designer with understanding the modulator.