Modeling Current Distribution Within Conductors and Between Parallel Conductors in High-Frequency Magnetics

In both planar and wire-wound transformers, large copper cross-sections and parallel windings are often used to increase conduction area and decrease copper loss. However, at high frequency, current is not guaranteed to spread out maximally over the cross-section of a single conductor or to split evenly between parallel conductors. Finite element analysis (FEA) and SPICE-based systems have been used to analyze current distribution within magnetic components, but these methods are computationally intensive. In this paper, we show that Maxwell's equations, in the high frequency limit, yield a set of linear algebraic equations that are rapidly solvable to yield both the current and magnetic field distribution and hence can be used to predict loss and leakage inductance. Due to its simplicity, this method is easily applied to cases with a one-dimensional or two-dimensional distribution of current. We show that predicted results match both FEA simulations and experimental measurements very accurately for a variety of cases. This paper is accompanied by several software implementations of the method. This method can be used to rapidly analyze high frequency current distribution in transformers and can easily be integrated into numerical optimization algorithms.