A Generalization of the Time-Domain Cooray–Rubinstein Formula

A compensation theorem and its approximation concerning EM fields generated by an impulsive vertical electric source above a nonperfectly conductive ground are introduced. The compensation EM fields with respect to an equivalent interface are first linearly interpolated between equivalent electric- and magnetic-current surface densities. These current densities are subsequently replaced by the known current densities corresponding to the perfectly electrically and magnetically conducting surfaces, thereby proposing an extension of the classic Cooray-Rubinstein formula. Illustrative numerical examples demonstrate its applicability.