Mutual Inductance Calculation Method of Circular Coils for an Arbitrary Position With Double‐Sided Toroidal Magnetic Medium

ABSTRACT Mutual inductance serves as a critical factor governing the power transfer capacity and efficiency in wireless power transfer systems. Accurate calculation of mutual inductance is critical for system design. However, the problem of calculating mutual inductance for arbitrarily positioned circular coils with double‐sided bounded toroidal magnetic media has not yet been resolved. To tackle this problem, a fully analytical bilateral mirror method is introduced in this paper. In this approach, the influence of the magnetic medium on both the transmitter and receiver sides is replaced by three equivalent image current coils. By employing the criterion of magnetic flux uniqueness before and after the equivalence, the current coefficients of the image coils are individually determined, leading to an analytical formula for the mutual inductance when the receiver coil is in an arbitrary position. The mutual inductance calculation error between arbitrarily positioned coils was verified through finite element simulations and experimental platform testing to not exceed 4.46%; the effectiveness of the proposed method was thereby demonstrated. Moreover, this method was employed to design the optimal parameters of the toroidal magnetic medium.