closed-form solutions for broad-band equivalent circuit of vertical rod buried in lossy grounds subjected to lightning strokes

In this paper, input impedance of a vertical rod under lightning stroke is first computed by applying the method of moments (mom) on the maxwell’s equations. the circuit model is then achieved through applying modified vector fitting (mvf) on the computed input impedance. after then the equivalent circuit is again extracted for a few values of ground conductivity and rod radius. finally using a new fuzzy-based model namely spatial membership functions, closed form solutions for all lumped elements of the equivalent circuit are achieved.