A generic and accurate frequency-domain model for buck, boost and buck-boost converters

Due to the PWM comparator and the switching components, PWM converters are inherent nonlinear in nature. The widely used average model is a simplified linear model and is precise mainly in low frequency range. To better understand the nonlinearity nature and accurately design high bandwidth PWM converters to improve the dynamic performance, a converter model that is accurate up to high-frequency region is required. In this paper, we rebuild the model of the three basic converters: buck, boost and buck-boost converters. Firstly, both trailing-edge and leading-edge PWM comparators are accurately modeled. Then, with the help of time varying system theory, an accurate transfer function of duty-cycle-to-output is derived. Finally, a generic non-linear frequency-domain model for buck, boost and buck-boost converters is proposed. Since the only precondition in the derivation is the small-signal assumption, therefore, the model is an accurate small-signal model. A buck and a boost converter prototypes are fabricated in the lab, and the closed loop gains are measured with a network analyzer. Experimental result verifies the accuracy of the new model.