An Equivalent Complex Permeability Model for Litz-Wire Windings

Previous methods for calculating power loss in litz-wire windings usually assume very fine strands such that the diameter of strands is much smaller than skin depth. In this paper, we present a method for calculating proximity-effect loss in litz-wire windings, using an equivalent complex permeability model of the winding. We first obtain a permeability model for litz-wire bundles, then use homogenization techniques to find the effective permeability of a winding. Permeability models are provided for bundles consisting of either rectangularly packed or hexagonally packed strands. The permeability model enables high-accuracy proximity-effect loss analysis and field analysis for litz-wire windings at high frequencies. It can also be used to find the leakage inductances in magnetic components.