FEM Modelling of Dimensional-Resonant Inductors for LLC Converters in MHz Range

Due to decreasing switching losses of modern power semiconductors, the switching frequency is steadily increasing in order to shrink size and cost of passive components in power electronic devices. So, the focus of this paper is the design of magnetic components in the MHz-range. At such frequencies, the traditional core loss models are getting dubious, as additionally to magnetic hysteresis, eddy currents contribute significantly to the total core losses and change the field distribution due to dimensional resonance. In an open-source FEM implementation it is shown, how to consider these high-frequency effects in interaction with the material by directly employing thin core material measurements. Due to its local material implementation, the FEM simulation allows to model arbitrary core shapes and it can be used for classical loss optimal geometric designs. Differently, in this paper, the modelling approach is used to design a nearly dimensional-resonant inductor with a frequency-dependent inductance for a conceptual LLC single-phase battery charger with widely varying voltage ratios. A simulation study employing permittivity measurements identifies an exemplary non-gapped pot core to provide a relative inductance increase of approx. 20 % from 1 MHz to 2 MHz. With this frequency-dependent inductance, the maximal operation frequency of the exemplary LLC converter design can be reduced by from 2.4 MHz to 2.05 MHz. Due to the high losses, the maximal power for this design is limited below 1 kW. A comparable design with a distributed air gap yielding full 3.6 kW output power shows a reduced relative inductance increase of approx. 12 % in the same interval and a bandwidth reduction of about 100 kHz.