AC winding loss in closed core thin film transformers accounting for two dimensional magnetic fields

Traditionally, Dow ell's one-dimensional method is used to calculate the AC winding loss factor for transformers with reasonable accuracy in most cases. However, for thin film transformers there can be significant two-dimensional fields which, if ignored will lead to erroneous results. The problem is exacerbated for transformers used in Flyback DC-DC converters which are exposed to arbitrary current waveforms. In this paper we derive the resistance matrix for a closed core transformer accounting for the two-dimensional fields present. The derived resistance matrix can then be used to analytically calculate AC winding loss for arbitrary current waveforms such as those found in Flyback converters.