An accurate closed-form approximation for ground return impedance calculations

Abstract

The calculation of ground return impedances generally requires the evaluation of an infinite complex integral. Algebraic series expressions that usually converge to the value of this integral have been known for about 50 years. Several approximate "closed-form" expressions for the integral have been proposed in recent years. Under most conditions, these approximate models give values within 15 percent of the correct value. This letter presents an improved "closed-form" approximation which gives values within 2.5 percent of the correct ones in all cases tested. It does so without any convergence difficulties. Furthermore, the results obtained are better than the ones obtained from series expression approximations if premature truncation takes place.