Properties of Phased Arrays

This paper discusses in some detail the scanning properties of planar and linear phased arrays consisting of a large number of equispaced radiators, either omnidirectional or directive. Assuming that a suitable beam shape and sidelobe level in the broadside direction have been attained, it is shown how scanning of the array through introduction of a phase delay into the wave front distorts this pattern and introduces new sidelobes. The study uses contour maps of the antenna pattern in "sin ¿-space," which is a projection of the unit sphere on the plane of the array. In this space the antenna pattem remains invariant with scan angle and merely undergoes a translation proportional to the phase delay between adjacent radiators. Using a parallel projection of the unit sphere onto the plane of the array, the actual antenna pattems are then readily obtained in conventional spherical coordinates. This method also permits ready evaluation of the influence of the directivity of the radiating elements, including a slight shift of the beam maximum with respect to that of an array of isotropic radiators. Furthermore, a pictorial representation of the coverage of a tilted planar array of given scanning properties can be obtained in terms of an earth-fixed coordinate systerr. Finally, it is shown how the beam-pointing error in a phased array is related to systematic errors in the phase delay.