Integrals for the mutual coupling between dipoles or between slots: with or without complex conjugate?

Abstract

Derivations are given for two integral expressions that give the mutual impedance between dipoles, and a comparison is made. This leads to the conclusion that the expression without the complex conjugate, based on reciprocity, has to be preferred. The expression with complex conjugate, the induced-electromotive-force (EMF) method, is not exact. For practical purposes, however, both are often equivalent. For the mutual admittance between slots in a conducting ground plane, or magnetic currents, the conclusions are reversed: the induced-EMF method is the preferred one, while the reciprocity method is only valid for purely real slot excitations or current distributions.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>