A Hybrid Analytical-Numerical Approach to the Evaluation of the Flux Linkage of Misaligned Coils Above a Stratified Earth

This work presents a hybrid analytical-numerical procedure that allows the efficient computation of the flux linkage of two misaligned circular coils placed above a stratified ground, which may include non-magnetic as well as magnetic materials. After deriving the Hankel transform describing the flux linkage, the semi-infinite integration interval is continued to the negative real axis. Next, the part of the integrand that exhibits branch point singularities is expressed in pole-residue form. This task is accomplished through the use of a well-established rational function fitting algorithm. Finally, the integration contour is deformed in the complex plane, so as to surround the pole singularities produced by the fitting algorithm. This makes it possible to apply the residue theorem, which leads to converting the integral representation for the flux into the sum of residues at the poles of the integrand. The derived solution has value in practical applications like wireless power transfer systems for battery electric vehicles charging.