Mutual inductance calculation for rectangular and circular coils with parallel axes

Simple and practical methods have been provided for the mutual inductance between rectangular and circular coils with parallel axes. The 2D Integral solution is given for the coils without the axial overlap. To improve the efficacy of the proposed approach for the partial or full axial overlap, the series solution derived by the truncated region eigenfunction expansion (TREE) is provided. Both integral and TREE expressions show very high accuracy through comparison with the finite element method simulation and experiment results. Numerical comparisons reveal that the TREE solution is the most efficient while keeping sufficient accuracy, and it is also applicable to all sorts of coil positions. Analytical and truncated region eigenfunction expansion (TREE) methods have been provided for calculating mutual inductance between circular and rectangular coils. Accurate and fast computation is verified by FEM and experiments.