High-frequency response of a hemispherical grounding electrode

The lightning discharge current is characterized by a high-frequency spectrum extending from DC to about 10 MHz. The calculation of the grounding impedance is one of the most important aspects of designing lightning protection systems. The search for analytical expressions for the calculation of the grounding impedance for simple structures has been of interest for almost a century. However, solutions only exist for simple structures such as rod-like structures. In this paper, we present, to the best of our knowledge, the first analytical solution for the impedance and the step voltage associated with a hemispherical grounding electrode. The derived analytical solutions can have different applications such as (i) providing a benchmark for testing numerical solvers, and (ii) analysing lightning flashes to non-grounded structures.