Frequency-Dependent Tower Impedence above Imperfectly Conducting Earth

Abstract

Impedance, admittance and surge impedance formulas of a vertical conductor with a circular cross-section above an imperfectly conducting earth have been derived applying a complex penetration depth of the earth and Neumann's formula.
It becomes clear that the frequency- and time-dependence of the characteristic impedance due to an imperfectly conducting earth is not significant, and thus it can be neglected, i. e. a perfectly conducting earth can be assumed in an evaluation of a tower surge impendance. The propagation velocity is nearly equal to the light velocity in free space, or about 90% of the light velocity. However, the frequency-dependence of the resistance and the attenuation constant of a tower can not be neglected. The surge impendance formula developed in the paper agrees well with various measured results, and is expected to be very useful in a surge analysis.