Element Efficiency: A Unifying Concept for Array Antennas

The antenna-element efficiency parameter quantifies the effect of mutual coupling in array antennas. In general arrays, this efficiency varies from element to element. The average value of these element efficiencies is a significant summary parameter, and plays a prominent role in circumscribing array performance. A useful formula gives the minimum number of antennas necessary to realize a prescribed peak gain envelope. The important special case of an array of identical elements situated in identical array environments is termed an idempotent array. In particular, an infinite idempotent array models a large planar array. There, the unique element efficiency has been directly related to the rms value of the conventional active reflection coefficient as it varies when the beam is (phased) electronically steered. The element-efficiency formulation also provides a framework for the rigorous derivation of important theoretical results in the theory of phased arrays.

1. Introduction

The concept of the efficiency of a radiating element in an array of radiators was introduced in 1964 by Peter W. Hannan [1]. In those days, the disparate estimates for (an upper bound) on the broadside gain of a large planar array of similar radiating elements, resulting from two different intuitively reasonable calculations - based, on the one hand, on the sum of gains of the individual radiators and, on the other, the gain normally associated with the area occupied by a particular distribution of radiators - appeared to pose a paradox in need of resolution. The underlying explanation of the paradox was found to reside in the mutual coupling of the radiating elements neglected in the two 'Overly simplified approaches, In particular, Hannan demonstrated that in large regular arrays, a necessary amount 'Of mutual coupling must subsist among the elements 'Of the array. He introduced an element-effi-ciency parameter, which turned out to be a definite overall measure 'Of mutual coupling, and showed that the change in this efficiency as a function of element spacing resolved the apparent paradox.