Macromodeling of Mutual Inductance for Displaced Coils Based on Laplace’s Equation

Abstract

Magnetic coupling is applied in a vast of different applications like sensors or medical imaging. Especially for inductive position sensors, magnetic coupling is a main aspect. Hereby, the position information is coded in the mutual inductance between a coil and a target. Consequently, the change of mutual inductance according to the relative position of coupled coils is of special interest in such applications. In this contribution, a new generalized method is presented which can be used to derive a macro model describing the mutual inductance with respect to a relative position of a pair of coils. In contrast to the known procedures, the presented method can be applied for complex coil geometries since no analytic solution of the mutual inductance is necessary. For this purpose, it is utilized that the mutual inductance for a pair of coils can be treated as a potential function that obeys Laplace’s equation. By solving Laplace’s equation, a physics-based approach for a macro model is derived, which explicitly describes the behavior of the mutual inductance based on the relative position of the coils. With this macro model, further analysis can be performed in circuit design or performance analysis of the sensor for example. For evaluation, the accuracy of the procedure is presented for different coil geometries, which are applied in industrial and biomedical applications to emphasize the broad applicability of the presented method.