Closed‐form complex permeability expression for proximity‐effect homogenisation of litz‐wire windings

The eddy‐current losses in litz‐wire windings are mostly due to the proximity effect, which can be macroscopically modelled via a complex frequency‐dependent permeability. In this study, the authors propose a new closed‐form expression for this complex permeability. Results are compared with approximations found in the literature in a wide‐frequency range. For the sake of validation, a two‐dimensional)‐axisymmetric gapped transformer with litz‐wire primary and secondary coils is studied.