Some Properties and Limitations of Electronically Steerable Phased Array Antennas*

Abstract

This paper is a treatment on linear and planar phased arrays of current sources, whose amplitudes are uniform and scan-invariant. By recognition that the radiation impedance of an array element is an analytic function of a complex scan variable, a powerful mathematical tool becomes available for the investigation of some important properties of the impedance as a function of scan. For example, it is proven that in a finite array the impedance seen by such a scan-invariant current source cannot be perfectly matched over a continuous scanning range using lossless, linear, passive and time-invariant elements. This result is extended to the infinite-array case by treating the latter as a periodic structure, and assuming that the Green's function of the unit cell is analytic with respect to the scan variable. The theory includes both linear and planar arrays. Among other results it is shown that the element impedance in an infinite array must be of a specific mathematical form. It is hoped that by recognizing the limitations imposed thereby, useful guidelines will be established for achieving optimal match of an array into space.