Two-dimensional analysis of the edge effect field and losses in high-frequency transformer foils

In design of high-frequency magnetic devices, various approaches have been used to provide calculation tools that are able to predict winding losses, including skin effect and proximity effect, in their two-dimensional (2-D) aspects. Up to now, these approaches have been mainly focused on giving quantitative results for specific cases. Because the final purpose of designers is not to perform single calculations, but to obtain optimal designs, we have looked for a complementary approach providing more general 2-D guidelines and understanding of the phenomena. In this paper, we examine the case of a foil winding undergoing edge effect, a typical situation where classical one-dimensional theories underestimate the real losses. Using a 2-D closed-form formula we developed in a previous work and the associated database of 400 2-D numerical models, we systematically analyze the dependence of the 2-D field and the corresponding extra losses with the geometrical design variables describing the dimension and position of the winding.