Analytical fringing field model for efficient winding loss calculation in gapped foil inductors

For optimizing gapped inductors, the magnetic fringing field surrounding the air gaps within the core is modeled. This modeling aims to calculate both the additional winding losses and the resulting inductance variation with frequency. The existing models solve a linear equation system, a process that is typically slow and cannot be strictly classified as analytical. This article introduces a novel approach to address the inherent issues within the underlying model, finally proposing a strictly analytical solution. Furthermore, an adaptive algorithm is proposed, leveraging the newly developed analytical solution to significantly reduce computation time without compromising the accuracy of the original model.