Modeling Non-Quasi-Static Magnetic Coupling of Parallel Flat Inductors for Wireless Power Transfer Applications in Close Proximity to the Ground

Presented here is a novel rigorous analytical solution for investigation of the magnetic coupling of two parallel flat inductors located near conducting earth. The solution is derived by replacing the integrand of the double-integral expression for the flux linkage with its power series expansion and then carrying out analytical integration of each term of the resulting series of integrals. The mutual inductance is given as a combination of special functions, depending on the electromagnetic and geometrical parameters of the problem. The validity of the derived solution is assessed through comparison with the outcomes of conventional analytical and numerical algorithms. The results from the conducted simulations confirm that the proposed formulation offers advantages over the previous techniques in terms of both accuracy and efficiency.