A design procedure for matching volumetrically scanned waveguide arrays

The impedance of a phased array of waveguides arranged in a triangular lattice and fitted with H-plane corrugated plates is analyzed using a scattering matrix method. The principal result is a virtually exact equivalent network consisting of three interconnected three-ports, each derived in terms of physical dimensions and scan angles for any volume or plane of scan limited only by grating lobes. A typical design procedure is illustrated by the case of scanning anywhere within an octant of a sphere. The cause of surface wave impedance mismatches, and the circumvention of the difficulty are described. Very fine sampling of the impedance versus angle would be required to ensure good performance were it not for certain matching criteria which are developed from the network. To avoid conditions of complete mismatch, the element area must be reduced by 2 percent less than that spacing required for grating lobe suppression. The maximum VSWR is less than 3.0:1 and the average is close to 2.0:1 in this case.