The antenna gain formula (Eqn 2) applies to the main axis of main lobe of the antenna. Away from that axis a notional polar plot of satellite receiving antenna performance is given below.
Figure 7: Two different ways of presenting antenna radiation pattern data [Ref 2]
The approximate angular position of the first sidelobe null is given by:
The half power beamwidth of an antenna is given by
For a uniformly illuminated aperture k lies in the range 58 - 65. For a tapered aperture k = 70. More details on different aperture illumination designs are given in section 4.
The graph below shows the relationship between dish diameter, gain and beamwidth for typical antennas operating at 4, 6, 11 and 14 GHz.
Figure 8: Antenna gain and 3 dB beamwidth as a function of antenna diameter for practical antenna efficiencies [Ref 5].
At angles away from the axis of the main lobe the antenna response is determined by sidelobes. Antenna sidelobe performance has an important impact on interference received from adjacent satellites (and ground based signals operating on same bands) and it is also a major factor in determining antenna noise temperature. The angular position and amplitude of sidelobes can vary significantly between antennas, but in many cases exact data on antenna performance is not provided by manufacturers (it is expensive and time consuming to measure). To overcome this the ITU-R has published a generic receive antenna response mask which can be used in interference planning calculations.
Figure 9: Reference patterns for co-polar and cross-polar components for receiving antennas (source ITU-R Report 810-3).
One less obvious factor influencing antenna sidelobe performance is the LNC (or subreflector) and its supporting spars. In a prime focus dish the spars that support the LNC/LNA not only block some of the signal from the dish reducing the efficiency for on-axis gain they also reflect signals from directions other than that of the wanted satellite towards the feed causing interference to the wanted signal.
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