Extension of Dowell and Semi-Analytical Homogenization Methods for Time-domain Analysis of Magnetic Devices

This paper extends the Dowell method and the semi-analytical homogenization method to analyze copper losses in a magnetic device in the time domain. The main contribution of this work is that the impedance provided by the Dowell method and the complex permeability resulting from the homogenization method are represented by the continued fractions and corresponding Cauer equivalent circuits, with which the time domain analysis can be effectively performed. The transient waveforms of the copper loss computed by the equivalent circuit in which the original leakage inductance is extended to a Cauer circuit are shown to be in good agreement with those computed by the finite element method. It is also shown that the Dowell method is valid only for the one-dimensional magnetic field over the winding region while the homogenization method is valid even when this assumption does not hold.