Dynamic modeling of self-oscillating resonant converters

This paper describes a novel modeling approach for self-oscillating resonant power converters operating under a variable structure system (VSS) control method. Using a fundamental harmonic approximation, the link between control and switching frequency in steady-state is found to be accurately described by an affine function that depends on the load. In addition, the control-to-switching frequency dynamics are shown to present advantageous phase leading characteristics at high frequencies. The resulting control-to-switching frequency dynamics can be appended to the well-known transfer functions for frequency modulation, in order to obtain a complete control-to-output model. With the new model, the advantages of the VSS controller become apparent: reduced DC gain tolerance for uncertain loads, extended bandwidth and improved phase margin at high frequencies. While results for both the series and parallel resonant converters are provided, the proposed approach has been illustrated in the case of modeling the control-to-output voltage transfer function of a parallel resonant converter. Numerical simulations and experimental results confirm and verify the analytical derivations.