Frequency-Dependent Inductance and Winding Loss Model for Gapped Foil Inductors

For comprehensively optimizing high-frequency foil inductors, calculating the increased inductance and the additional eddy current losses due to a two-dimensional magnetic fringing field caused by air gaps in the center leg is mandatory. This article proposes an analytical model that accurately calculates the inductance and the additional eddy current losses in gapped inductors with foil windings. The analytical field expressions are combined into closed-form winding loss and inductance formulas and verified by measurements. Furthermore, the frequency dependency of the inductance due to the shielding effect of the foil conductors is being discussed.