Theory of mutual coupling among minimum-scattering antennas

A novel and rigorou formulation for mutual impedance among a class of idealized but realizable antennas is presented. Unlike past treatments of mutual coupling, which have proceeded from structurally specified antennas, the present treatment deals with a class of antennas, all the electromagnetic properties of which are rigorously expressed explicitly in terms of their radiation patterns alone. Employing a network formulation based on a scattering representation of electromagnetic fields in terms of spherical (or cylindrical) modes, the mutual impedances between such antennas are computed exactly. Several alternate representations for the mutual impedance are derived, one of which is an integral representation involving the power pattern function for both real and complex angles. In special cases, these exact results agree with published results obtained by applying well-known approximate techniques to structurally specified antennas. An important and illuminating example is provided by an infinite planar array of antennas radiating into a half-space for which the present formulation yields the well-known grating-lobe series representation of the active impedance without an explicit reference to structural properties of the radiating elements.