Mutual inductance calculations of non-identical n-sided planar coils with arbitrary geometry and spatial orientations

Planar coils are widely used in sensors, wireless chargers, robots, portable devices, medical implants, etc. An important factor in the performance of two magnetically coupled coils is the mutual inductance. However, the mutual inductance measurements between two arbitrarily positioned non-identical n-sided coils with lateral and angular misalignments have not been solved. In this paper, we calculated the mutual inductance between two arbitrarily positioned, non-identical n-sided planar spiral coils by the partial inductance method. The proposed model can adapt the calculations for any planar coil configurations including rectangle, pentagon, hexagon, or any other regular n-sided coils. Even the circular coils are approximated by multiple sides. In addition, measurements can cover lateral displacement, angular rotation, and both simultaneously. The theoretical calculation results are verified with the results of Ansys Maxwell simulations and previously published works in the literature. The relative errors of the presented method with simulation results are less than 0.1% in selected cases. Finally, the superiority of the proposed method over simulation in terms of time consumption is investigated. For the samples studied in this paper, more than 90% of the time could be saved compared to 3D finite element method simulations.