Modeling Current Distribution Within Conductors and Between Parallel Conductors in High Frequency Transformers

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, 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 and complex. 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 through a single matrix inversion to yield both the current distribution and the leakage inductance. Due to its simplicity, this method is easily applied to cases with a one-dimensional or two-dimensional distribution of current, as long as the net applied ampere-turns is zero (i.e., magnetizing current is negligible in the case of a two-winding transformer). We show that predicted results match both FEA simulations and experimental measurements very accurately for a variety of cases. This method can be used to rapidly analyze high frequency current distribution in transformers and can easily be integrated into numerical optimization algorithms.