Abstract
The directivity of a reflector antenna deteriorates as the feed moves away from the focal point for beam scanning. This deterioration can be substantially reduced if a cluster feed instead of a single feed is used to control a beam. A closed-form solution is presented for the cluster excitation to achieve the optimum directivity. For an offset <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">108 \lambda</tex> parabolic reflector scanning 10 beamwidths, the optimum-directivity achieved by a 19-element (seven-element) cluster is 12 dB (8 dB) higher than that of a single element. Comparison of the optimum-directivity design and the popular conjugate field matching design is made. When the cluster spacing <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</tex> is greater than <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1 \lambda</tex> , it is found that the optimum directivity is higher than that of conjugate field matching (CFM) scheme by an insignificant amount, although the excitations of two designs can be quite different. For <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d < 0.5 \lambda</tex> , the optimum design may exhibit the supergain phenomenon, namely, extremely high directivities achieved by an oscillatory cluster excitation.
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