Exact and Approximate Analytical Solutions for Lightning-Induced Voltage Calculations

In this paper, we thoroughly review all analytical solutions (both exact and approximate) presented to date in the literature for evaluation of voltages induced on a lossless horizontal conductor, placed over an infinite-conductivity ground, and excited by an external field produced by either a step function or a linearly rising current, moving unattenuated and undistorted along a vertical lightning channel. We also obtain the exact analytical solution for the step-function current case in the time domain via development in the s-domain. To date, there had been three attempts to obtain such solution, all of which yielding incorrect results.