Patterns and polarizations of simultaneously excited planar arrays on a conformal surface

A conformal array on a surface of small curvature can be approximated by a number of planar arrays, several of which may be excited simultaneously so as to achieve a performance similar to that of a conformal array. Since the main beam of a planar array can be steered to any direction in the visible Space, several arrays, each oriented in a different direction, can be steered cooperatively to form a single beam in a desired direction. A general formulation of the radiation field of such an array of arrays is developed with the aid of vector recomposition formulas between two orthogonal co-ordinate systems. This formulation does not involve the integration of the current source but is solely dependent upon the knowledge of the far-field expressions of elementary radiators. Using this formulation, it can be shown that within each array, the conventional row and column phase setting can be used, although each array requires an additional phase shift to compensate for the phase difference caused by its position on the curved surface. As examples, the radiation patterns and polarizations of multiple arrays of short dipoles are studied using the present formulation. A comparison of the multiple planar arrays with the conventional conformal array is also presented.