Mutual Inductance Calculation of Rectangular Coils with Convex Torus Finite Magnetic Shields in Wireless Power Transfer

Mutual inductance is one of the critical parameters of wireless power transfer systems, and the accurate calculation of mutual inductance is considered an essential theoretical basis for designing and optimizing wireless power transfer systems. However, the problem of calculating the mutual inductance of a bilateral bounded magnetically shielded rectangular coil with a convex toroid still needs to be solved. Therefore, this article proposes a spatial boundary separation analysis method and derives vector magnetic potential expressions for each region with convex toroidal magnetic shielding structure using the double Fourier transform and Maxwell's equations. The mutual inductance calculation formula under the spatial position are obtained using boundary conditions and spatial geometric relaionships. In contrast to traditional approximation methods, the mutual inductance calculation method of this article permits an accurate numerical solution for the mutual inductance between rectangular coils. The 4.69% difference between calculated and experimental mutual inductance values confirms the accuracy of the computational method in this research. The proposed model of this article matches the transmission efficiency of the conventional rectangular disc coil at over 97% for the same specifications and reduces material usage by 11.12%.