General Multi-Frequency Small-Signal Model for Resonant Converters

Resonant converters are periodic time-varying system, one of whose distinctive features is the sideband effect. To be specific, when a small-signal perturbation is injected into the converter, a series of sideband frequency components will occur. The two sideband frequency components around the switching frequency determine the small-signal response of the resonant tank if it has sufficient band-pass filtering. Using complex Fourier series, the relationship between different frequency components can be described with a series of gains. This article derives all the necessary transfer functions between different frequencies for resonant converters. Combining them together forms a general small-signal model of resonant converters. There are multiple frequency components, i.e., the perturbation frequency and two sideband frequencies in this model, hence the name multifrequency model. Two kinds of inverters, i.e., the full-bridge and half-bridge structure, and three modulation methods, i.e., the switching frequency control, the duty-cycle control, and the input voltage control are considered in this article. The experimental results verify the validity of the proposed model.