An investigation into a slight-variation of the transformer effective permeability in LLC resonant converter

In the LLC resonant converter, the transformer core is usually gapped to realize the designed value of magnetizing inductance that allows for soft switching. The air gap length which is in a scale of millimeters may be affected by the humidity and long working hours of the ferrite material, resulting into a variation of the core permeability. Moreover, a slight variation of the transformer core permeability may be encountered with any possible change in the core temperature. In a proper transformer design, the transformer shall operate with an optimum value of effective permeability where the sum of both copper and core losses is minimal. In this paper, the transformer optimal design is presented. Moreover, the influence of the permeability on the transformer's copper and core losses is revealed. Furthermore, with the help of newly derived equations, the effect of the transformer's effective permeability on the LLC converter conduction turn-on and turn-off losses is reported. Along with the theoretical discussion, the analysis is supported with simulation and experimental results utilizing a 250W-200kHz prototype.