Satellite Links Page 2, Figure 1 Satellite transponder input output power characteristic. the EIRP of the ground station carefully The goal is to obtain as much output power available. from the satellite while minimizing the signal distortion This usually means reducing or backing. off the input power so that the amplifier is operated just below compression This point gives. decent output power while producing manageable levels of distortion interference The saturated. input power density may be specified for a satellite as opposed to the saturated input power. In this example the output begins to compress at an input power of about 5 dBW Increasing the. input power beyond this point does not yield a linear increase in output power for example at. an input power of 10 dBW we would expect 40 dBW of output power and yet only are able to. achieve a power of 35 dBW The output is fully saturated at this point. A suitable input power level could be right before the saturated region is entered along with some. margin If the input power level was chosen to be 4 dBW we would say the the input power. back off IPBO is 6 dB since the power has been reduced 6 dB from the saturated power point. Correspondingly there is an output power back off OPBO which in this case is 2 5 dB that is. the output is 2 5 dB from being fully saturated, A common empirical formula that is used to model the input output characteristic described. Prof Sean Victor Hum Radio and Microwave Wireless Systems. Satellite Links Page 3, Wout 4Pin Psat, Wsat 1 Pin Psat 2. where Wsat is the saturated output power from the transponder Wout is the actual power power. produced at the output of the transponder Pin is the input power density to the transponder s. receiving antenna and Psat is the power density at the transponders receiving antenna that is. known to saturate the output of the transponder, 2 Link Budget. As discussed the link budgets on the uplink and downlink are treated separately since different. transmission distances may be involved and there is a significant different in frequency wavelength. On a per Hz basis the link budget equations are, EIRPG F SLU LU 228 6 units dB Hz 2. EIRPS F SLD LD 228 6 units dB Hz 3, where the subscripts U and D refer to the uplink and downlink respectively and the subscripts. S and G refer to the satellite and ground station respectively Note that the EIRP of the ground. station is selected so that the transponder is suitably backed off from saturation The terms LU. and LD refer to other losses on the uplink and downlink such as atmospheric absorption rain. attenuation etc, Free space loss forms the bulk of the loss in the link budget This is especially true for satellite. systems due to the huge distances involved which are typically tens of thousands of kilometres. from station to station Hence it is important to understand the orbit geometry of the satellite so. that the link distance and hence free space loss can be estimated accurately The calculation of. the link distance requires an understanding of orbital mechanics which is discussed in a separate. Knowing the link distance the free space loss can be calculated on the link being considered. uplink downlink The link losses on the uplink and downlink are not the same even if the. distance r is the same because the uplink and downlink frequencies are not the same In fact. usually the downlink is at lower frequencies This is done for multiple reasons. Atmospheric attenuation is less at lower frequencies. The ground station is not power limited like the satellite and hence is better equipped to. deal with attenuation on the uplink The maximum EIRP of the ground station is ultimately. limited by the satellite s transponder see the next section. The G T on the uplink is very poor since the satellite sees a warm earth Hence there. is little point in using a lower frequency with less attenuation since the SNR is going to be. relatively poor anyway, Improvements are thus best reserved for the downlink. Prof Sean Victor Hum Radio and Microwave Wireless Systems. Satellite Links Page 4, 3 Satellite Orbits, As discussed in a separate note on orbital mechanics the time T it takes the satellite to transit. through one orbit is determined knowing the gravitational force produced by the Earth and the. distance the satellite is from the centre of that mass a The orbital period is equal to. where mE G is the product of the Earth s mass me and the universal gravitation constant G. This results a constant 3 986 1014 N m2 kg which is known as Kepler s constant Knowing. the orbital altitude of the satellite H we can determine a Re H and find T The orbital. period for various different orbits and some well known satellites are summarized in Table 1. Table 1 Satellite orbits, Point of interest GEO orbit Geostationary orbit is a special case of a satellite orbit meeting. the following conditions, 1 The orbit is perfectly circular with an eccentricity of zero unlike LEO MEO and other. 2 The altitude of the satellite is such that the orbital period of the satellite is 23 hours 56. minutes and 4 1 seconds which is one sidereal day which is the time it takes for the Earth. to rotate about its axis exactly once, Prof Sean Victor Hum Radio and Microwave Wireless Systems. Satellite Links Page 5, 3 The satellite s orbital plane must coincide with the the plane of the equator. Under these conditions the satellite appears perfectly stationary with respect to an stationary. station on the Earth s surface This makes this orbit highly coveted for telecommunications and. broadcast applications such as television The geostationary orbital altitude is from Table 1 H. 35 786 km It follows knowing that Re 6 378 2 km that the ratio ReR H e. 0 151 1 6 61, Another way of remembering this is that the geosynchronous orbit altitude is approximately 6 6. Earth radii, 4 Orbital Geometry, Satellites generally orbit the Earth along an elliptical path and this ellipse is actually inclined. relative to the equatorial plane of the Earth Satellites also orbit the Earth at different speeds. since the orbital periods depend on the orbital altitude of the satellite Generally to locate a. satellite at an instant in time requires knowledge of the geometry of the ellipse relative the the. Earth as well as times that the satellite passes reference points along the ellipse The parameters. are known as the Keplerian elements of the satellite and are precisely known by satellite operators. The relation of these elements to the elliptical geometry we have described here is beyond the. scope of this document but it suffices to say that in general the distance from a ground station to. the satellite depends on time and that the satellite may not always be visible above the horizon. nadir direction, zenith direction, sub satellite point. Figure 2 The sub satellite point, From the perspective of a ground station what matters is the location of the sub satellite point. on the Earth s surface which is a point on the ground in the nadir downward pointing direction. of the satellite This point is shown in Figure 2 This point can be described by its latitude and. longitude The Earth station also can be located by its own latitude and longitude Combined. these parameters are, Le the Earth station latitude the number of degrees the station is north of the equator. e the Earth station longitude the number of degrees the station is west of the prime. Prof Sean Victor Hum Radio and Microwave Wireless Systems. Satellite Links Page 6, Ls the latitude of the sub satellite point and. s the longitude of the sub satellite point, Consider the link between a ground station and orbiting satellite shown in Figure 3. Figure 3 Orbit geometry, The angle is related to the coordinates of the Earth station and the sub satellite point according. cos cos Le cos Ls cos s e sin Le sin Ls 5, The remaining angles shown in the diagram are easily related by applying the law of sines to the. triangle formed by the orbit geometry Hence, sin sin 90 sin. Since sin 90 cos, is the elevation angle angle above the horizon that the Earth station antenna needs to be. pointed to to make contact with the satellite Therefore knowing the coordinates of the Earth. station and the sub satellite point the appropriate elevation angle can be found An additional. angle the azimuth angle is also needed but is not discussed here. Knowing the angle we can find the total distance r the satellite is from the ground station. Using the law of cosines, r2 Re H 2 Re2 2Re Re H cos 8. r Re H 1 2 cos 9, Prof Sean Victor Hum Radio and Microwave Wireless Systems. Satellite Links Page 7, The elevation angle can then be found knowing sin 90 cos so. Re H sin sin, cos 1 2 10, If instead we wish to determine for a given elevation angle in advance we can use the fact. that 90 sin cos and, cos cos 11, The satellite is only visible from an earth station is the elevation angle to be above some. minimum value which is at least 0 From Figure 3 this requires. For a nominal GEO orbit 81 3 for the satellite to be visible. Prof Sean Victor Hum Radio and Microwave Wireless Systems. Satellite Links Page 6 L s the latitude of the sub satellite point and s the longitude of the sub satellite point Consider the link between a ground station and orbiting satellite shown in Figure 3 Figure 3 Orbit geometry The angle is related to the coordinates of the Earth station and the sub satellite point according

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