Phased-array radiator reflection coefficient extraction from computer waveguide simulator data when grating lobes are present

Commercially available finite-element software that solves Maxwell's equations for arbitrary three-dimensional bounded structures has enabled phase-array radiator designers to perform waveguide simulator modeling of phased-array radiating elements on the computer very efficiently. Published work on waveguide simulator design has concentrated on array performance in the absence of grating lobes, a requirement for many radar applications. For such simulators, the reflection coefficient of each propagating mode at the waveguide simulator port gives the radiator reflection coefficient at a discrete scan angle. However, the design of limited scan arrays can lead to selection of an array element spacing that allows grating lobes in real space. When a waveguide simulator is modeled on the computer, and a grating lobe is present, the two waveguide modes representing the main lobe and the grating lobe will propagate in the waveguide simulator and they will be coupled together. The simulator port-reflection coefficient of either mode is not the true reflection coefficient seen by the radiating element. We describe a method for extracting the reflection coefficient of the radiating element from the waveguide simulator data when one or more grating lobes are present.