Winding resistance and power loss for inductors with litz and solid-round wires

An analytical model based on one dimensional 1-D Dowell's equation for computing ac-to-dc winding resistance ratio FR of litz wire is presented. The model takes into account proximity effect within the bundle and between bundle layers as well as the skin effect. Model describes three frequency ranges: low-, medium-, and high-frequency range. In each of ranges, the behavior of the ac-to-dc winding resistance ratio FR is different. Moreover, an analytical optimization of the litz-wire winding strand diameter is performed. The boundary frequency between the low-frequency and the medium-frequency ranges, are given for both solid-round-wire and litz-wire windings. Hence, useful frequency range of both windings can be determined and compared.