# Simple Equivalent Circuit Model of a Series Resonant Converter

This nugget simplifies the original equivalent circuit model, and proposes a simple equivalent circuit model of a series resonant converter. Shown in Fig. 2, the proposed equivalent circuit model is a third-order circuit. The components C

_{e}and L

_{e}forms a beat frequency double pole and R

_{e}is responsible for the damping. When switching frequency f

_{s}is far away from resonant frequency f

_{o}, R

_{e}is large. The quality factor of the beat frequency double pole is large, thereby enabling its observation. In this case, the circuit is a third order with a beat frequency double pole and a low frequency single pole caused by the output filter. When switching frequency f

_{s}is close to resonant frequency f

_{o}, R

_{e}is small causing the beat frequency double pole to split. In this case, no beat frequency double pole is observed. Instead, L

_{e}will resonant with output capacitor C

_{f}to form a low frequency double pole. With the analytical model, the beat frequency dynamics can be explained, and the region where the beat frequency double pole is observed can be determined analytically. Furthermore, for the first time, analytical expressions of the transfer functions are derived. The equivalent circuit model and analytical transfer functions are valuable tools to design the feedback control appropriately.