A Closed Expression for the Lightning Induced Voltage in Short Loops

This paper presents a closed expression for the lightning induced voltage in short loops, which considers the effect of the return stroke speed. It is shown that the traditional expression that provides the induced voltage as the product of the current time derivative by the mutual inductance is a particular case of the expression developed in this paper, which holds when the return stroke propagates with the speed of light. The comparison between the results of the traditional expression and the new one is carried out for different distances from the lightning flash and different stroke current waveforms. The effect of the return stroke speed is also investigated, showing that the higher the speed, the higher the induced voltage. The effect of loop length is investigated, showing that the loop can be considered as electrically short if its dimensions are smaller than one-tenth of the product between the current front time and the speed of light in free space.