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

Abstract

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 paper 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.

Eddy currents in rectangular conductors: Analytical 2D loss model in the context of magnetic component design

“…Because 1D models are not suited to model the fringing field impact [4], the verification section does not compare those models to the proposed model. It can be argued that with existing models for round conductors [11] it would be possible to identify a rectangular conductor as an equivalent round conductor with the same cross section and use these models instead. However, as shown in section III-A of this paper, the current induced magnetic field and corresponding losses (e.g., skin losses) are captured quite well with the proposed approach.…”

“…Typical state-of-the-art loss models for conductors with circular cross-section separate the problem of the 2 Computations times in the range of FEM simulations must be expected. field computation [10], [11] and the calculation of the losses caused by the magnetic field [12]. In order to use such approaches for conductors with rectangular crosssection, a model for the field inside the conductor is required, which can be linked to the external field by boundary conditions.…”

2-D Winding Losses Calculation for Round Conductor Coil

“…Core losses are not negligible for inductors, and they can be modeled based on complex permeability or the Steinmetz equation [19], [37], [38]. Steinmetz factors are valid for a limited frequency and flux density range, and TDK N87 ferrite's datasheet does not provide factors with that low flux density.…”

“…Albach [18] gave the exact solution of proximity effect losses under arbitrary field distribution, which needs to solve the exact external field distribution on each conductor's surface. Ewald and Biela [19], [20] derived field strength inside the core window of gapped inductors and calculated winding losses based on spatial r.m.s. field strength on a layer.…”