Determination of reflection coefficients at the top and bottom of elevated strike objects struck by lightning

[1] In this paper, we present an analysis of lightning return stroke currents along an elevated strike object. We derive closed form expressions, both in the frequency domain and in the time domain, to calculate the lightning current at any height along a strike object taking into account reflections at the top and at the bottom. The frequency dependence of reflection coefficients is taken into account. We also derive an expression to calculate the reflection coefficient as a function of frequency at the bottom of the lightning strike object from two currents measured at different heights along the strike object. We show that, if the current and its time derivative overlap with reflections at the top or bottom of the strike object, it is impossible to derive the reflection coefficient at the top of the strike object exactly from any number of simultaneous current measurements. We propose an extrapolation method to estimate this reflection coefficient. We propose a second method to calculate the top reflection coefficient from just one current derivative measurement if the current derivative and its reflections do not overlap significantly. We apply the proposed methodology to experimental data obtained on Peissenberg Tower (Germany) consisting of lightning currents measured at two heights. The results suggest that the reflection coefficient at ground level can be considered as practically constant in the frequency range 100 kHz to 800 kHz. Although the estimated ground and top reflection coefficients are in good overall agreement with values found in the literature, the estimated values for the top reflection coefficient from the extrapolation method are somewhat lower than those found employing the current derivative method; the differences are discussed.