A technique for the synthesis of shaped-beam radiation patterns with approximately equal-percentage ripple

Abstract

A new pattern synthesis technique which leads to shaped-beam patterns of approximately equal percentage or dB ripple is discussed. The method is based on the controlled location of the zeros of the pattern function in the complex pattern plane with the relative displacement of these zeros from the real <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\sin \theta</tex> axis determining the magnitude of ripple obtained with the synthesized pattern. In applying the technique, the locations are approximately constrained by starting with a fan or sector pattern having known zero locations. The sector pattern is then warped or perturbed to the pattern of desired shape by deterministic perturbations of the zeros. It is found that the design ripple of the sector pattern is approximately maintained during this process. A trade-off exists between ripple magnitude and maximum normalized slope of the approximating pattern function. Independent control of ripple level within the shaped-beam region and of sidelobe level without is achieved. Several examples of shaped-beam patterns (including <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\csc^{2} \theta</tex> patterns) are presented and discussed.