The mutual inductance between the primary and secondary coils is an important parameter in the wireless power transfer system, and the mutual inductance calculation of coils in many complicated circumstances has been studied. However, the mutual inductance calculation of two circular coils in arbitrary relative position with magnetic tiles have not been solved. In this study, an analytical formula of the mutual inductance with respect to the parameters of the system such as arbitrary relative position, geometry, and the properties of the magnetic tiles is proposed. The proposed formula is derived from the proposed parameter vector method, and the proposed parameter vector method can not only be used to explore the tendencies of the mutual inductance in arbitrary relative position, but also provide a fairly concise and general method for mutual inductance calculation. The finite-element analysis and experimental results validated the reliability and accuracy of the proposed formula, and an accuracy of a few parts in a thousand can be readily attainable.

中文翻译：

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无线输电系统中任意放置有磁砖的圆形线圈的互感计算

初级线圈和次级线圈之间的互感是无线电力传输系统中的重要参数，并且已经研究了许多复杂情况下线圈的互感计算。然而，尚未解决两个任意位置的圆形线圈与磁瓦的互感计算问题。在这项研究中，提出了关于系统参数（例如任意相对位置，几何形状和磁砖特性）的互感的解析公式。所提出的公式是从所提出的参数向量法推导而来的，所提出的参数向量法不仅可以用于探索任意相对位置处互感的趋势，同时也提供了一种相当简洁通用的互感计算方法。有限元分析和实验结果验证了所提公式的可靠性和准确性，可以很容易地达到千分之几的精度。