Design-Oriented Equivalent Circuit Model for Resonant Converters

Resonant converters are popular for their inherent soft-switching capability. Small-signal models for those converters are critical for an optimal controller design. The equivalent circuit models available so far are based on the fundamental harmonic approximation. This requires the resonant tanks to behave as good band-pass filters. Consequently, the models work well for series resonant converter (SRC) but not LLC converter. Moreover, the resulting models are too complicated to be useful and the corresponding simplified versions further sacrifice the accuracy. The recent modeling breakthrough is based on the describing function method. The accurate analytical models for both SRC and LLC are presented for the first time. Not surprisingly, the exact models are shown to be infinite-order systems. In most of the applications, the frequency range of interest is below the switching frequency, meaning the models can be simplified into a proper reduced-order form. This paper proposes a methodology to simplify the complicated results from the describing function method, and the corresponding equivalent circuit models is developed. For example, the proposed third-order model for the LLC converter is accurate at half switching frequency. In addition to the accuracy, the simplified models provide significant insights on the small-signal dynamics of resonant converters.