Frequency Approach in the Analysis of the Lightning Current Ground Reflection Coefficient

Traveling current source return stroke models, or current generation models, are a class of engineering models that take into account the reflection of current pulses from the striking point on the ground. The ground is represented as one homogeneous layer of soil with constant conductivity and permittivity. It is shown that, in electrical sense, the ground can be modelled with lumped elements, that is as a parallel connection of the grounding resistance and the capacitance. The analysis is done in the frequency domain. The bottom part of the channel and the ground are treated as two electrodes of a transmission line having a characteristic impedance. This transmission line has a specific structure: one electrode is represented by the conducting channel, which is straight and vertical over flat ground, while the other is the conducting ground. This physical model can be applied when the wavelength of the particular component in the channel current frequency spectrum is much greater than the distance between the elements of that transmission line. The bottom of the channel and the ground (the end of the transmission line) can be treated as if they were closed by a lumped element of certain impedance, provided that the wavelength of the corresponding component in the frequency spectrum is much greater than the skin depth of the current wave in the ground. Fortunately, the frequency spectrum of commonly observed channel-base currents more or less satisfies the afore- tated conditions, allowing the problem to be analyzed with lumped element model.