Planar slot array design to compromise optimum sum and difference patterns

Slot lengths and offsets are determined for a planar array of longitudinal shunt slots fed by rectangular waveguides for three cases: a) a desired sum pattern, accepting the corresponding plane and plane difference patterns; b) a desired plane difference pattern, accepting the corresponding sum and plane difference patterns; and c) a desired plane difference pattern, accepting the corresponding sum and plane difference patterns. All of this is done including the effects of external mutual coupling, and results in three sets of slot dimensions which are averaged to give a fourth set. The fourth set is found to produce patterns whose characteristics are a compromise among the three optimum (but mutually incompatible) prototype designs. The slot dimensions are affected by the choice of main-line/ branch-line coupling coefficients. These coupling coefficients should be chosen so that the slot dimensions are in their optimal dynamic range and so that the input admittance to each quadrant is matched. This is not feasible in all three modes (sum, plane difference, plane difference) in the presence of mutual coupling. However, compromises are possible. The method of steepest descent is efficacious in determining appropriate coupling coefficients, which are found not to possess quadrantal symmetry.