Combined analytical-numerical approach to the voltage of a cylindrical coil with pulsed current

This paper presents a combined analytical-numerical approach to solving the pulsed eddy current problem accurately and quickly. Considering the displacement current, the analytical solution to the voltage of a cylindrical coil above a laminated conductor in the complex-frequency domain is deduced by Laplace transform. The time-domain induction voltage values of a cylindrical coil with a pulsed current are calculated by the fourth-order integro-differential FFT-based numerical inversion of Laplace transform. At the same time, the time-domain analytical solution to the induced voltage of a cylindrical coil with a pulsed current above a half-infinite non-ferromagnetic conductor is derived, and has been verified by comparison with Finite Element Method (FEM) simulation results. The calculation results prove that the adopted numerical inversion method of applying Laplace transforms to the pulsed eddy current problem has a high accuracy and fast convergence. The transient voltages produced by a square-wave current excitation when considering the displacement current in the vacuum area are higher than those when ignoring the displacement current, by as much as 27.7% at certain times. The higher the lift-off is, the smaller the voltage peak is and the faster the voltage drops. As the application of this method, the induced voltages are computed in the measurements of metals thickness and metal coating thickness.