A Novel Approach to Accurate Small Signal Modeling of Resonant Converters

Due to advent of high switching frequency devices such as Sillion Carbide (SiC) and Gallium nitride (GaN) switches, the resonant converters have become a popular choice for modern switched mode power supply applications. The application of the resonant converters extend from high power EV charging to low power consumer electronics. The high efficiency and compact design of resonant converters are made possible by the resonance phenomenon, which also presents design and control challenges. There have been attempts to ascertain the small signal control to output dynamics for resonant converters, but they have either involved intricate mathematical calculations or have resulted in numerical solutions that don't offer much insight. This paper models the various stages of a series resonant converter using the Fundamental Harmonic Approximation (FHA). The perturbations in the inductor current envelope, that is caused by the small signal perturbations in the control variable (switching frequency), is analyzed in laplace domain. The control-to-output transfer function of a series resonant converter is then derived analytically using the current envelop. The validity of the model is then verified using simulation and experimental results.