a question about microwave antenna
Generally, large antennas (30m+) are intended for deep space communication or radioastronomy, both ask for extremally low noise. In that cases the "spillover" introduce "too mutch noise". To reduce the spillover a large taper is used (typically -12 dB at the edge), this reduce the spillover to less than few K of noise temp. In other words with deep spece antennas the G/T ratio is maximized.
For smaller antennas (1m, 2m...), generally intended for terrestrial communications (evevation angle near to 0° over horrizont) the spillover noise is "already high" becasue the main beam is looking the ground (=300K). In this case what is maximized is the antenna efficiency, especially the illumination effciency, in other words the taper is in -3dB or -6dB.
A special mention require the small antennas used on DBS. In this case what is required is that the antenna is smaller than possible, due to cost and aesthetical considerations. Usually that type of antenna has an high F/D ratio (e.g. 0.6); this allow a more efficient capability of the horn to illuminate the dish.