Impedance of a coil above a planar conductor with an arbitrary continuous conductivity depth profile

Abstract

An exact method is presented for calculating the impedance of a coil above a planar conductor with a conductivity profile that varies with depth. The method can be applied to arbitrary continuous profiles and in terms of accuracy or scope it is advantageous over the existing approaches, namely the analytical approach involving the solution of the relevant differential equation in terms of higher transcendental functions and the numerical approach involving the piecewise approximation of the continuous conductivity profile. The method is also very fast and in the context of eddy current nondestructive evaluation it can be readily applied to invert conductivity profiles from coil impedance measurements.