Beamwidth
The angular width of the beam radiated by high-gain antennas is measured by the half-power beam width (HPBW), which is the angular separation between the points on the antenna radiation pattern at which the power drops to one-half (-3 dB) its maximum value. For parabolic antennas, the HPBW θ is given by:
where k is a factor which varies slightly depending on the shape of the reflector and the feed illumination pattern. For a "typical" parabolic antenna k = 70 when θ is in degrees.
For a typical 2 meter satellite dish operating on C band (4 GHz), like the one shown here, this formula gives a beamwidth of about 2.6°. For the Arecibo antenna at 2.4 GHz the beamwidth is 0.028°. It can be seen that parabolic antennas can produce very narrow beams, and aiming them can be a problem. Some parabolic dishes are equipped with a boresight so they can be aimed accurately at the other antenna.
It can be seen there is an inverse relation between gain and beam width. By combining the beamwidth equation with the gain equation, the relation is:
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