Optimum scannable planar arrays with an invariant sidelobe level

This paper presents two alternative methods for determining the current distribution in the elements of a scanning rectangular array which is optimum in the sense that its radiation pattern has a constant sidelobe level and a narrowest beamwidth in all directions. Exact formulas for both even and odd numbers of elements are given. The dependence of the main-lobe beamwidth on the total number of elements, the element spacing, the sidelobe level, and the scan angle is studied in detail. The minimum required number of controlled elements in a square array with electronic beam scanning over a specified sector for a guaranteed upper limit on beamwidth without grating lobes is determined. Numerical results are included, which illustrate many interesting features of the new design technique.