antenna look angles lec
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ANTENNA LOOK ANGLES
• The look angles for the ground station antenna are Azimuth and Elevation angles.
• They are required at the antenna so that it points directly at the satellite.
• Look angles are calculated by considering the elliptical orbit.
• These angles change in order to track the satellite.
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ANTENNA LOOK ANGLES
• For geostationary orbit, these angles values do not change as the satellites are stationary with respect to earth.
• Thus large earth stations are used for commercial communications, these antennas beam-width is very narrow and the tracking mechanism is required to compensate for the movement of the satellite.
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ANTENNA LOOK ANGLES
• For home antennas, antenna beam width is quite broad and hence and hence no tracking is essential, thus it leads to a fixed position for these antennas.
• Sub-Satellite Point:The point at which a line between the satellite and the centre of the Earth intersects the Earth’s surface is called the sub-satellite point.
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Figure 1: The geometry used in determining the look angles for Geostationary Satellites.
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Figure 2 : The spherical geometry related to figure 1
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With respect to the figure 1 and 2, the following information is needed to determine the look angles of geostationary orbit.
1. Earth Station Latitude: λE
2. Earth Station Longitude: ΦE
3. Sub-Satellite Point’s Longitude: ΦSS
4. ES: Position of Earth Station
5. SS: Sub-Satellite Point
6. S: Satellite
7. d: Range from ES to S
8. Ϭ: angle to be determined
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• Considering figure 2, it’s a spherical triangle. All sides are the arcs of a great circle. Three sides of this triangle are defined by the angles subtended by the centre of the earth.
• Side a: angle between North Pole and radius of the sub-satellite point.
• Side b: angle between radius of Earth and radius of the sub-satellite point.
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• Side c: angle between radius of Earth and the North Pole.
• a = 900 and such a spherical triangle is called quadrantal triangle.
• c = 900 – λE
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• Angle B is the angle between the plane containing c and the plane containing a.
Thus, B = ΦE-ΦSS
• Angle A is the angle between the plane containing b and the plane containing c.
• Angle C is the angle between the plane containing a and the plane containing b.
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• Thus, a = 900 • c = 900 – λE
• B = ΦE-ΦSS
Thus, • b = arcos (cos B cos λE) • A = arcsin (sin |B| / sin b)
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Figure 3 : A plane triangle obtained from figure 1
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• Applying the cosine rule for plane triangle to the triangle of figure 3 allows the range d to be found to a close approximation:
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• Applying the sine rule for plane triangles to the triangle of figure 3 allows the angle of elevation to be found:
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Polar Mount Antennas
• These antennas are pointing accurately only for one satellite .
• They have a single actuator which moves the antenna in a circular arc.
• Generally some pointing error is seen in these antennas.
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Polar Mount Antennas
• The dish of this antenna is mounted on an axis termed as polar axis such that the antenna bore sight is normal to this axis.
• The angle between polar mount and the local horizontal plane is set equal to the earth station latitude λE , making bore sight lie parallel to the equatorial plane.
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Polar Mount Antennas
• The axis is tilted at an angle, which is relative to the polar mount until the bore sight is pointing at a satellite position.
δ = 900 – El0 – λE
where El0 is the elevation required for the satellite position.
Thus cos El0 = (aGSO / d) sin λE
Hence δ = 900 – arcos [(aGSO / d) sin λE] - λE
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