On high-frequency circuit equivalents of a vertical ground rod

Vertical ground rods have been used extensively from the early days of electrical engineering for earth termination of electrical and lightning protection systems. They are usually represented with equivalent circuits with lumped and distributed parameters based on quasistatic approximation, which limits the upper frequency of their validity domain. However, lightning-related studies often require modeling in the megahertz frequency range. Also, emerging technologies, such as power-line communications, require analysis in frequency ranges even up to a few tens of megahertz. The rigorous electromagnetic (EM) field theory approach may be used for such frequency ranges, but equivalent circuits are needed for the usual network analysis methods. In this paper, we look at possibilities to construct simple equivalent circuits that can approximate or match results from the EM model. In particular, we compare a usual homogenous distributed parameter circuit with a nonhomogenous one determined by curve matching with results from the EM model. The analysis is illustrated using numerical simulations.