Mutual inductance calculation between two coaxial planar spiral coils with an arbitrary number of sides

In this paper, we present a full derivation of a new model based on the partial inductance method to calculate the mutual inductance between two planar spiral coils with an arbitrary number of sides. The planar spiral coils are approximated by regular concentric polygons and then each polygon is decomposed to its sides. The mutual inductance between each side of the primary and secondary polygons is analyzed considering geometrical properties of the sides with respect to each other. The method developed in the present study is general and straightforward in comparison with those available in the literature as it includes only required sequential steps to calculate the mutual inductance between the independent segments of the coils. We validated the results of the proposed method with those available in the literature, simulation and measurement results. Moreover, the developed method was implemented for the percent error analysis to assess the error of the approximation of the circular coils with n-sided polygons.