Analytical Winding Loss and Inductance Models for Gapped Inductors With Litz or Solid Wires

In gapped inductors, the fringing field of the air gaps causes additional eddy current losses in the windings and an increase of the inductance. Since this impact of the fringing field is very significant, calculating the additional eddy current losses and the inductance increase is important in the design of inductors. This article proposes analytical formulas to accurately calculate the inductance and the additional eddy current losses in gapped inductors with solid round wire and Litz wire windings. The analytical formulas are verified by measurements, showing that the proposed models are accurate over a wide-frequency range.