Element pattern bounds in uniform phased arrays

Abstract

Limits are delineated within which the radiation pattern of a single excited element in an infinite regular array of terminated elements may be modified through a uniform feed or matching network. In the absence of grating lobes the element pattern of a planar array is limited by the universal <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">cos \theta</tex> bound. When the array spacing admits grating lobes, it will be shown that the bound is effectively reduced by a factor dependent on the radiating elements employed in the array. This factor, and therefore the limits on performance of the army of specified elements attainable through any feed network, may be computed from any one element pattern. The pattern of a single excited element of the unmatched array in the open-circuited array environment, the element pattern in the short-circuited array environment of the matched array, or any of the element patterns in the terminated array environment may be used. These results lead to a classification of the conditions resulting in "blindness" of an array. Certain instances of "blindness" are necessary in the sense that they cannot even in principle be removed by an adjustment of the feed network, while others can, in principle, be tuned out. These results are applicable generally, and are in no way restricted to idealized or single mode radiating elements. Detailed analysis of an array of slits covered by a dielectric slab is presented as an illustration of the general theory.