Exact Analytical Solution of the Peak Gain for the LLC Resonant Converter

The peak gain is a fundamental value for an efficient design of resonant converters. In some cases, it is directly given by the maximum of the transferable power, which is likewise the peak of the gain curve for a given converter design and load resistance. As zero voltage switching (ZVS) is normally preferred for a MOSFET input bridge, there is a second limit for the maximal usable output power. It is the transition from the ZVS to the zero current switching (ZCS) region. This paper gives a survey over the solutions for both limits in continuous conduction mode (CCM) and discontinuous conduction mode (DCM) for the lossless LLC converter resulting in a very fast and accurate optimization process.