Electromagnetic field coupling to a line of finite length: theory and fast iterative solutions in frequency and time domains

A system of integral-differential equations for evaluating currents and voltages induced by external electromagnetic fields on a finite-length horizontal wire above a perfectly conducting ground is derived under the thin wire approximation. Based on perturbation theory, an iterative procedure is proposed to solve the derived coupling equations, where the zeroth iteration term is determined by using the transmission line (TL) approximation. The method can be applied both in the frequency and in the time domains. The proposed iterative procedure converges rapidly to the exact analytical solution for the case of an infinite line, and to the NEC solution for a line of finite length. Moreover, with only one iteration, an excellent approximation to the exact solution can be obtained. The method is applied to assess the validity of the TL approximation for plane wave coupling to an overhead line of finite length. It is shown that the resulting errors for the early-time response are generally higher than those corresponding to infinite lines.