Winding Resistance and Power Loss of Inductors With Litz and Solid-Round Wires

An analytical model based on the one-dimensional Dowell's equation for computing the ac-to-dc winding resistance ratio of the litz-wire windings independent of the porosity factor is derived. The model takes into account proximity effect within the bundle and between bundle layers, as well as the skin effect in each strand. Three frequency ranges for the winding resistance characteristics are considered: low-, medium-, and high-frequency range. In each range, the behavior of the ac-to-dc winding resistance ratio F
_R
is different. Moreover, an analytical optimization of the litz-wire winding strand diameter for litz-wire windings conducting sinusoidal and multiharmonic currents independent of the porosity factor is performed.