Scattering properties and mutual coupling of antennas with prescribed radiation pattern

An analysis is presented of the interrelations among the radiative, scattering, and coupling properties of arbitrary lossless antennas. The analysis is based on a well-known scattering representation of antennas in terms of spherical modes in free space. This scattering representation is given a network interpretation which brings into focus the degree of interdependence between scattering and radiation characteristics. The scattering matrix of a reciprocal antenna with one port and a prescribed radiation pattern is represented in a canonical form which exhibits explicitly the permissible range of adjustments in the antenna scattering characteristics. The significance of the canonical form is examined from several points of view, noting in particular its connection with the concept of resonant modes of a scatterer. The network interpretation also facilitates the evaluation of mutual coupling, and the mutual impedance between two antennas is expressed explicitly in terms of the radiative and scattering parameters of each antenna. It is shown that, generally, the mutual impedance may be expressed as a sum of two terms: a zeroth-order term, dependent exclusively on the radiation pattern, and a second term involving the scattering properties as well as the radiation patterns. Under certain conditions the mutual impedance may be approximated by the zeroth-order term alone. It is also shown that a similar zeroth-order approximation of the active impedance in an infinite planar phased array leads to a grating lobe series type of representation.