Directivity optimization of a reflector antenna with cluster feeds: A closed-form solution

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
108 \lambda
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
d
is greater than
1 \lambda
, 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
d < 0.5 \lambda
, the optimum design may exhibit the supergain phenomenon, namely, extremely high directivities achieved by an oscillatory cluster excitation.