A one-parameter circular aperture distribution with narrow beamwidth and low sidelobes

Abstract

A one-parameter circular aperture distribution is developed which provides an optimum compromise between narrow beamwidth, low sidelobes, and low aperture <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</tex> . The pattern is a modified <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">J_{1}(x)/x</tex> , analogous to the Taylor one-parameter modified sin <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(x)/x</tex> line source distribution. Sidelobe envelope taper is essentially that of a uniformly excited circular aperture; hence the aperture is low <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</tex> . The aperture distribution which is rotationally symmetric is given by a modified Bessel function of zero order. Like all high efficiency distributions, it has a pedestal. All antenna quantities, sidelobe ratio, beamwidth, aperture efficiency, and edge taper, are uniquely related to the parameter <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</tex> . A table of these quantities is given for sidelobe ratios up to 50 dB. A typical pattern and several distributions are graphed. This new distribution allows tradeoff studies to be made against any design quantity, with all other quantities determined through the one-parameter.