3.An Improved Calculation of Proximity-Effect Loss in

      Abstract—The two best-known methods for calculating highfrequency winding loss in round-wire windings—the Dowell method and the Ferreira method—give significantly different results at high frequency. We apply 2-D finite-element method (FEM) simulations to evaluate the accuracy of each method for predicting proximity-effect losses. We find that both methods can have substantial errors, exceeding 60%. The Ferreira method, which is based on the exact Bessel-function solution for the eddy current in an isolated conducting cylinder subjected to a timevarying magnetic field, is found to be most accurate for loosely packed windings, whereas the Dowell method, which approximates winding layers comprising multiple turns of round wire with a rectangular conducting sheet, is most accurate for closely-packed windings.

      To achieve higher accuracy than is possible with either method alone, we introduce a new formula, based on modifying the Dowell method. Parameters in the new formula are chosen based on fitting

our FEM simulation data. By expressing the results in terms of normalized parameters, we construct a model that can be used to determine proximity-effect loss for any round-wire winding with error under 2%.

Index Terms—proximity effect, winding loss