Modeling of a Transfer Function for Frequency Controlled Resonant Inverters

A linear transfer function for the output current control of frequency-controlled resonant inverters is proposed in this paper. The circuit of resonant inverters can be transformed into two coupled circuits through the complex phasor transform. The circuits consist of cross-coupled power sources and passive elements. The circuits are used to induce the state space equation, which is transformed into the $4^{th}$ order cross-coupled transfer function. The $4^{th}$ order cross-coupled transfer function is modeled into a $2^{nd}$ order linear transfer function based on a behavior analysis of the pole and zero locations that facilitate a simple and intuitive linear transfer function. The feasibility and validity of the proposed linear transfer function were verified by simulation and experiment.