Accurate Small-Signal Modeling of Resonant Converter Based on Perturbation on the State Plane

Abstract

Resonant converters operate the switching frequency close to the resonant frequency to achieve soft switching. However, this also posts a great challenge on the small-signal modeling. Based on the fundamental approximation, E. Yang develops the first small-signal equivalent circuit model. Recently, the authors propose a simpler model based on the average concept on a rotating state plane. The assumptions of the two models are shown to be equivalent. This implies the two approaches are applicable only when there is an effective bandpass filter. However, the resonant tank in more popular resonant converters such as LLC converter does not behave like a good band-pass filter. Therefore, this paper aims at providing a more accurate small-signal modeling. It is based on perturbation on the state plane and describing function method. Using the series resonant converter (SRC) as an example, the model shows a perfect match to a simulation result. Based on the fact that the system poles can be captured by the natural response, a simplified, yet accurate, second-order model for an SRC is provided. All the small-signal dynamic are well-explained using the proposed model. The proposed modeling and simplification methods show a promising extension to model the LLC converter.