Two dimensional field solutions for high frequency transformer windings

Analytical two-dimensional (2-D) field solutions produced by conductors located in magnetic cores are developed. The problem of arbitrarily placed rectangular conductors in the window of a ferrite core is solved by deriving analytical field solutions based on combining multiple sets of eigenfunctions in the window space and in each conductor into the 2-D Poisson equation with dynamic source terms. This technique extends classical, high frequency, one-dimensional (1-D) solutions and 2-D, DC solutions, to high frequency, two-dimensional problems. Results show higher accuracy over 1-D methods in computing AC resistance and fields. Improvements are significant due to the incorporation of various 2-D effects, not previously possible in 1-D solutions