Analytical Approximations for Fitting Magnetic Coupling Coefficients Between Adjacent Coils

This article presents a simple yet novel 2-D modeling approach for approximating the coupling coefficient between neighboring inductors as a function of coplanar separation and relative angular displacement. The approach uses simple geometric arguments to predict the effective magnetic flux between inductors. Two extreme coil geometry regimes are considered: planar coils (i.e., on printed circuit board) and solenoid coils, each with asymmetric ferrite cores about the central magnetic plane of the inductor. The proposed geometric approximation is used to predict the coupling coefficient between sensors as a function of separation distance and angular displacement, and the results are validated against 2-D finite element modeling results. The formulae approximations show excellent fit agreement with finite element (FE) simulated coupling coefficients, predicting comparable relationships with changing separation and angular displacement. When fit to 2-D FE and 3-D numerical coupling coefficient results, the approximated formulae exhibit a residual standard deviation of less than 0.5% for a planar coil design. The work demonstrates the validity of the analytical approximation for predicting coupling behavior between neighboring coils. This has practical uses for the automated estimation of the physical separation between coils, or the relative angles to determine curvature of surface coils are rested or adhered to.