Concerning the derivation of exact solutions to inductive circuit problems for eddy current testing

A novel strategy, which enables the derivation of exact solutions describing all electromagnetic interactions arising in inductively coupled circuits, is developed. Differential circuit equations are formulated in terms of the magnetic fields arising in inductive systems, using Faraday׳s law and convolution, and solved using the Fourier transform. The approach is valid for systems containing any number of driving and receiving coils, and may be extended to include nearby conducting and ferromagnetic structures. Furthermore, arbitrary excitation waveforms, such as a sinusoid or a square wave for applications in conventional and transient eddy current, respectively, may be considered. In this first work, the general theory is presented and subsequently applied to the simple case of a coaxial driver and receiver coil configuration. Theoretical expressions for the self- and mutual inductance coefficients are shown to fall out of the theory naturally. Experimental results, obtained for a square wave function excitation, are found to be in excellent agreement with the analytical predictions.