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The half power BeamWidth [1] is the angular separation between the
half power points on the antenna radiation pattern, where the gain is
one half the maximum value. For a reflector antenna it may be
expressed
HPBW = a = k l / D
where k is a factor that depends on the shape of the reflector and
the method of illumination. For a typical antenna, k = 70° (1.22 if
a is in radians). Thus the half power beamwidth decreases with
decreasing wavelength and increasing diameter.
For example, in the case of the 2 meter antenna, the half power
beamwidth at 6 GHz is approximately 1.75° . At 14 GHz, the half
power beamwidth is approximately 0.75° . As an extreme example, the
half power beamwidth of the Deep Space Network 64 meter antenna in
Goldstone, California is only 0.04 ° at X-band (8.4 GHz).
The gain may be expressed directly in terms of the half power
beamwidth by eliminating the factor D/l . Thus,
G = h (p k / a )2
Inserting the typical values h = 0.55 and k = 70° , one obtains
G = 27,000/ (a° )2
where a° is expressed in degrees. This is a well known engineering
approximation for the gain (expressed as a numeric). It shows directly
how the size of the beam automatically determines the gain. Although
this relation was derived specifically for a reflector antenna with a
circular beam, similar relations can be obtained for other antenna
types and beam shapes. The value of the numerator will be somewhat
different in each case.
For example, for a satellite antenna with a circular spot beam of
diameter 1° , the gain is 27,000 or 44.3 dB. For a Ku-band downlink
at 12 GHz, the required antenna diameter determined from either the
gain or the half power beamwidth is 1.75 m.
A horn antenna would be used to provide full earth coverage from
geostationary orbit, where the angular diameter of the earth is
17.4° . Thus, the required gain is 89.2 or 19.5 dB. Assuming an
efficiency of 0.70, the horn diameter for a C-band downlink frequency
of 4 GHz would be 27 cm.
Taken From ATI Space and Communications [2]
Links:
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[1] http://melbournewireless.org.au/?BeamWidth
[2] http://www.aticourses.com/antennas_tutorial.htm
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