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Ground conductivity plays an important role both in the evaluation of the electromagnetic (EM) fields due to a lightning event and in the calculation of the line parameters, which are, in turn, fundamental in the analysis of the lightning-induced voltages on overhead lines. The exact formulation of the EM fields over a lossy ground involves the numerical evaluation of the Sommerfeld integrals, which are slowly converging and can only be computed in the frequency domain. For this reason, a great effort has been devoted in the derivation of approximate formulas that can provide accurate results with low computational costs. The most popular one is the Cooray-Rubinstein formula, which has been proposed in the frequency domain. Here, its time-domain counterpart is mathematically derived, and an efficient algorithm for its implementation is presented together with some comparisons with the exact approach.