The Complex Ground Return Plane a Simplified Model for Homogeneous and Multi-Layer Earth Return

For modelling current return in homogeneous ground, the paper introduces the concept of an ideal (superconducting) current return plane placed below the ground surface at a complex distance p equal to the complex penetration depth for plane waves. This "complex" plane appears as a mirroring surface, so that conductor images can be used to derive very simple formulae for self and mutual impedances under ground return conditions. Such equations, without proofs, were originally proposed by Dubanton and published by Gary.1 In this paper, plausibility arguments serve to initially justify the procedure, then the equations are analytically related to those of Carson and, finally, the errors, which in most cases are less than a few percent, are numerically evaluated. The ideal return plane at complex depth can also be used for multi-layer earth return.