A graphical technique for determining optimal array antenna geometry

A new graphical technique is presented for determining the optimal face tilt and element packing geometry for planar, phased-array antennas with scan limits specified in earth's coordinates. The technique, although very simple to implement, is instructive in that it clearly shows, on one graph, the relationships between required azimuth and elevation scan limits, the element packing geometry, the grating lobe locations, grating lobe scan boundaries, the maximum off-axis scan angle, and the array face tilt angle. The technique can be used to design the array to either minimize the maximum scan off-axis scan requirement or to minimize the total number of elements in the array. Examples are presented that clearly show the two designs are not the same. It is shown that the grating lobe scan boundary (GLB) for a particular array geometry can easily be constructed in sine-space by drawing unit circles centered at six grating lobe locations nearest to the origin of the sine-space plane. Equations are presented for drawing the required scan boundary (RSB) in earth's coordinates for the array with its face tilted back from the vertical. The ability to simply construct the RSB and GLB on the same sine-space plot makes it very simple to choose the tilt angle and element geometry that either minimizes the area in the GLB or the maximum off-axis scan requirement for a given RSB.