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. This method uses an equivalent complex permeability model of the winding to describe the proximity effect. We first obtain a permeability model for litz-wire bundles, then use homogenization techniques to find the average permeability of a winding. Permeability models are provided for bundles consisting 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.