Time domain analytical modeling of finite length thin wire embedded in homogeneous lossy medium

This paper deals with the analytical solution of the time domain integro-differential Pocklington equation for a straight, finite length, thin wire, embedded in a homogeneous lossy medium. The analytical solution is obtained approximating the integral part of the Pocklington equation and handling the differential operator by the aid of Laplace transform. The resulting space-time dependent equation follows up from the inverse Laplace transform performed via Cauchy residue theorem. The excitation, in a form of electromagnetic pulse (EMP), is treated via analytical convolution. The obtained analytical results are compared to those calculated using the frequency domain numerical solution of Pocklington equation combined with inverse fast Fourier transform (IFFT).