Analytical eddy current loss model for foil conductors in gapped cores

For modelling and optimizing gapped high-frequency inductors, the calculation of eddy current losses in foil windings due to the two-dimensional fringing field caused by air gaps in the core is important. The winding loss models must offer a high accuracy when calculating the 2D field distribution and must be computationally efficient in order to enable several thousand calculations required during the optimization. This article proposes an analytical model based on the magnetic vector potential formulation that can predict the eddy current losses in foil windings due to the fringing field of an arbitrary number of air gaps. The analytical model is combined into a closed-form loss formula and verified by FEA simulations.