An Approximate Time-Domain Formula for the Calculation of the Horizontal Electric Field from Lightning

This paper presents an approximate formula to calculate the horizontal electric field from lightning, considering finitely conducting earth. The formula is represented by an analytical expression in the time domain, which is useful for the calculation of lightning-induced voltages on power and telecommunication lines, without the need of domain transformations. The paper also compares the results of the formula with the results obtained from frequency-domain techniques, namely the numerical calculation of Sommerfeld's integrals and the Cooray-Rubinstein's formula. The comparison is favorable for a wide range of distances from the lightning channel and values of earth's conductivity. The horizontal electric field calculated by the formula is composed of two components of opposed polarities, one due to the return stroke charge and the other due to the return stroke current, resulting in an electric field with a bipolar wave shape. The charge component prevails in the region close to the lightning channel, while the current component prevails in the region far from it.