Question

Subject : Electrical and Electronics Engineering 2.(a).An earth station has a longitude of 99.5° west and latitude of 29.5° north. The satellite has a longitude of 143° west. Find the azimuth and elevation angle. (b).A single-phase, half-bridge inverters is feeding power into a load of resistance 10 ohms; d.c. input to the inverters is 400V.Determine the r.m.s. load voltage, load current power factor. (c).What are look angles? How do you determine? Explain with the help of neat diagrams.

Answer 1

a. Given that, For an earth station, Longitude, le = 99.99 west Latiude , Le = 29.5° North Longitude of satellite, is = 143° west Azimuth angle = ? Elevation angle = ? consider a geostationary satellite (1. e., Ls=0) Azimuth Angle. - As the given satellite is launched at the west of the earth, in northern hemisphere, the expression for the azimuth angle is given by - Az = 180°+2 - 11 where a is the intermediate angle and is calculated as,

d = tant' r tan lls-le) ] I sin le J = fant ſ tan (143*- 99.5°) 7 L sin (29.5°) J • fan' [1.929] d= 62596. Substituting d value in equation (1), we get Az = 180 + 62.596 = 242.596. 1. Azimuth angle; Az = 242.5961 Elevation The Angle expression for the elevation angle Elis given by 7. El = tan 6.6107345 - COS Y siny L central angle, which is obtained from where, y is the the expression, Cos Y = cos le cos (ls-le)

= cos (29.5") cos (143°- 99.50) = cos (29.80) cos (43.5°) = 0.8704 X 0.7254. COS Y = 0.6314 =) Y - cos"! (0.6319) => Y = 50.85 substituting y value in equation (2), we get El = tan! 6.6107345 - cos (50.85) 7 sin (50.85) 1-50.85 an' r 6.6107345 - 0.6314 1 - 50.85 0.7755 € 82.61 - 50.85 =) EL = 31.76 Ti Elevation angle = 31.760

Solution that to No LOAD set 27 A is single phase half- bridge inverter. Not VS12 -vs12 uslar - 15/28 182

1. The rms walue of Vocms) = m output voltage = 4009 - 2006 locms) = 400 , 20 A 2R 2x10 power delivered to the load - 200 x 20 = 4000 W when (Tu) is conducting uppen source ) and power to load is delivered by when 'Tz' is 'on' lower source deliver power to load. power delivered by each source = v Iscav) = 1 Ciscov)t lgucavs] heve 19 = ( min ) « stroni lasty 152 = (h) + he .: power delivered by each source = (W) x ( ) = 200 x 20 = 4000 W pf: power delivered to load supplied (VI 1 (unity power factor) :

Ans C. Look Angles: Look angles are the angles at which the communication between earth station and a satellite is possible by pointing the transmitting antenna towards is respective Satellite. These angles includes both Azimuth (A) and elevation angles. (E), which are measured with the help of latitudes and longitudes grid with respect to the earth station. Generally, these angles are set, such that effective communi cation is opted between the stations. Geostationary satellite refers to the satellites

having circular orbit along the earth's equator such that all points in orbit are equidistant from surface of earth Figure ou depicts the determination of look angles and the positions of the satellite and the earth station- Local vertical satellte → North projection of path onto focal TA EOS Horizontal plane Look Angles Determination Determination of Elevation Angle. Elevation angle is defined as the angle at which the axis of antenna Ps rotated vertically facing forwards the satellite in horizontal direction.

consider the flowe (2) Local horizontal satellite satellite Earth Station VE Earth calculating Elevation angle. From the frgcore (w), we can write, 90'+ E = 4 o E = 4 - 90 cos [E] = cos (4-90) o cos E] = sin 4 - 0 According to sine's law, --- (0) sin 4 = siny a - - - (3) NOW, Apply between satellite cosine rule the vectors and earth for figure (2) to get joining the centre station. the of relation the earth,

i.e. c = 0+b?- 2ab cos y similarly, d2= R?+ ? - BRYę cos y - RP [** 2 SY] Epe [1649 -2 * 057] doo [n 1-* 05 7]" — ) substitute equation (4) în equation (3), we get, cos [E] = sin for *)* 2 * 05772 In case of geostationary satelirte. (ideal), the cos y and siny values can be calculated from the point (line joining from the centre of the earth to the satellite), which is on the equator. 4

Determination of Animuth Angle. Azimuth angle CAD is defined as the angle at which the antenna pointing horizontally is rotated in clockwise direction Ground its axis vertically. 1. The calculation proceeds in finding the exact location of the point line., a line drawn from the centre of the earth to the satellite). Consider the following figure (3). Equatoy Geometry for Azimuth calculations The polar angle c is given by Ć - IA-18) where, LA - Latitude at point a LB = Latitude at point B. The angles at X vertex A and angle B y are at vertex related as

tan (o.5 V-x)] cot (0:50) sin {0.5(la-te)} sin [0.5 (la +16)] tan [015 V+ x)] = cot (0:50) cos {0.5(la-ls)} sin (0.5 (latle)} The Azimuth angle and elevation angle should be in range of o to 360 and above the minimum value respectively, for the visibility of satellite from the earth Station