Pulsed Vertical-Electric-Dipole Excited Voltages on Transmission Lines Over a Perfect Ground—A Closed-Form Analytical Description

Space-time analytical expressions for the vertical-electric-dipole excited load voltage response of a transmission line over a perfectly electrically conducting ground are derived. The problem is formulated with the aid of the electromagnetic reciprocity theorem of the time convolution type and subsequently solved analytically. It is demonstrated that the resulting closed-form formulas are readily applicable to calculating the lightning-induced voltages on overhead lines.