EC7107: SATELLITE COMMUNICATION SYSTEMS

Tutorial Sheet and Assignment Questions

1. Determine the orbital velocity of a satellite moving in a circular orbit at a height of 150 km above the
surface of the earth. G = 6.67 x 10-11 N-n2/kg2, ME = 5.98 x 1024 kg, radius of earth = 6370 km.
2. A satellite moving in an elliptical eccentric orbit has the semi-major axis of the orbit equal to 16,000 km. If
the difference between the apogee and the perigee in 30000 km, determine the orbit eccentricity.
3. Satellite – 1 in an elliptical orbit has the orbit semi-major axis equal to 18,0000 km and satellite – 2 in an
elliptical orbit has semi-major axis equal to 24,000 km. Determine the relationship between their orbital
periods.
4. Consider an earth satellite so positioned that it appears stationary to an observer on earth and serve the
purpose of a fixed relay station for intercontinental transmission of television and other communication.
What will be the height at which the satellite should be positioned and what would be the direction of its
motion? Given radius of earth to be 6400 km and acceleration due to gravity on the surface of the earth to
be 9.8 m/sec.
5. A remote sensing satellite of the earth revolves in a circular orbit at a height of 230 Km. above the earth’s
surface. What is the (a) orbital velocity (b) Period of revolution of the satellite? Radius of the earth is 6.4 x
106 m and acceleration due to gravity at the surface of the earth is 9.8 m/sec.
6. Explain what is meant by apogee height and perigee height. The Cosmos 1675 satellite has an apogee
height of 39,342 km and a perigee height of 613 km. Determine the semimajor axis and the eccentricity of
its orbit. Assume a mean earth radius of 6371 km.
7. A satellite makes a circle around the earth in 90 minutes. Calculate the height of a satellite above the
surface of the earth. Given the radius of earth is 6400 km.
8. The period of the moon around the earth in 27.3 days and the radius of the orbit is 3.9 x 10 5 km., if G =
6.67 x 10-11 Nm2 (kg)-2, find the mass of the earth.
9. An artificial satellite circles around the earth at distance of 3400 km., Calculate the period of revolution
and orbital velocity. Given radius of earth to be 6400 Km. and e.g. to be 98 Cm/Sec.2
10. A satellite moving in a highly eccentric Molniya orbit having the farthest and the closest points as 35,000
km. and 500 km. respectively from the surface of the earth. Determine the orbital time period and the
velocity at the apogee and perigee points. (Assume earth’s radius = 6360 km.)
11. Determine the magnitude of the velocity impulse needed to correct the inclination of 2o in the satellite orbit
35800 km. above the surface of the earth. Given that the radium of earth = 6364 Km. mass of earth = 5.98
x 1024 Kg. and Gravitational constant = 6.67 x 10-11 N-m2/Kg2.
12. Consider an earth station located at longitude QL = 80o West and latitude Ql = 40o north and a geostationary
satellite at longitude QS = 120o W. Calculate the azimuth angle A and elevation angle E.
13. A geosynchronous satellite moving in an equatorial circular orbit at a height of 35800 km. above the
surface of earth gets inclined at an angle of 2o due to some reason. Calculate the maximum deviation in
latitude and also the maximum deviation in longitude. Also determine maximum displacements in kms.
caused by latitude and longitude displacements. (RE=6364 kms).
14. A geostationary satellite moving in an equatorial circular orbit is at a height of 35786 km. from earth’s
surface. If the earth’s radius is 6378 km. determine the theoretical maximum coverage angle. Also
determine the maximum slant angle.
15. Show that the height of a geostationary orbit is 35,838 km. A non synchronous satellite orbits the earth
with a mean attitude of 1500 km. Determine how many times the satellite orbits the earth in one day.
16. Determine the maximum shadow angle that occurs at equinoxes for a satellite orbiting in a circular
equatorial orbit at a height of 13622 km. above the surface of the earth. Assume earth’s radius to be 6378
kms. Also determine the maximum daily eclipse duration.
17. Find the velocity of satellite at the perigee and apogee of its elliptical orbit in terms of the semi major axis
‘a’ and the eccentricity e.
18. For the inclination angle i = 28o, and the velocities of a satellite at the apogee and perigee as 1.61 km/s and
3.07 km/s respectively, calculate the value of the incremental velocity required to correct the orbit
inclination and to achieve orbit circularization.
19. (a) Find the maximum line of sight distance between two satellites at the same height H.
20. A satellite is in a circular orbit at an attitude H = 10,000 km. Find the maximum eclipse time.
21. Find the coverage angle of a satellite for which it is visible of a minimum elevation angle. E min = 10o for the
following circular orbits. RE = 6378.155 km.
 a. geostationary b. H = 10,00 km. c. H = 20,000 km.
22. A satellite at a distance of 40,000 km. from a point on the earth’s surface radiates a power of 2W from an
antenna with a gain of 17 dB in the direction of the observer. Find the flux density at the receiving point,
and the power received by an antenna with an effective area of 10 m2.
23. If this satellite operates at a frequency of 11 GHz, and if the receiving antenna has a gain of 52.3 dB. , find
the received power.
24. A 4-GHz receiver has the following gains and arise temperatures:
Tin = 50 K GRF = 23 dB
TRF = 50 K Gm = 0 dB
Ton = 500 K GIF = 30 dB
TIF = 1000 K
25. For a satellite transponder with a receiver antenna gain of 22 dB, and 2NA gain of 10 dB and an equivalent
noise temperature of 22o K, determine the G/T figure of merit.
26. A satellite earth station having an antenna of diameter 30 m and overall efficiency of 68% works at signal
frequency of 4150 MHz. At this frequency the system noise temperature is 70 o K when antenna points at
the satellite at an elevation angle of 28o. Calculate the G/T ratio of the earth station. In case the noise
temperature rises to 88oK, what would be the new G/T ratio?
27. A microwave communication link is to be designed for the 6.4 – 6.9 GHz band using a synchronous
satellite a distance of 24,600 miles from the transmitter site. For excellent reception, it is desirable to
achieve at the satellite a signal-to-noise ratio of at least 100. Calculate the transmitter power and antenna
requirements for this purpose.
28. For the complete link of a satellite, prove that
(C/N)T-1 = (C/N)U-1 + (C/N)D-1
where C/N is the signal to noise power spectral density ratio. The suffix T, U and D stands for total, uplink
and downlink respectively.
29. Consider a Ku band fu = 14.25-fd = 11.95 GHz satellite system with following system parameters.
Noise band width = 36 MHz
GU/Tu = 1.6 dB/K (Antenna gain to noise temp. ratio)
Satellite saturation EIRPs = 44 dBW
Antenna diameter (earth station) = 7 m.
Transmit antenna gain at 14.25 GHz (GT) = 57.6 dB
Receive antenna gain at 11.95 GHz (G) = 56.3 dB
Carrier power into antenna (Pt) = 174 W
Maximum uplink and downlink slant range (u & dd) = 37506 km.
Tracking losses 1.2 dB (Lu) and 0.9 dB (Ld)
System noise temp (T) = 160 K.
Based on the above parameters, calculate carrier to noise ratio for uplink, for downlink and total.
i. If a purely resistive attenuator is inserted into a receiver system such that a loss of faster
2 occurs in the power available between input and output, then prove that i) Teff = Ts (2 – 1)
Where Teff is the effective temperature of a noise source Ts is the system noise temperature.
30. Calculate the effective area of a 10-ft parabolic reflector antenna at a frequency of (a) 4GHz (b) 12GHz.
31. An antenna has a gain of 46 dB at 12 GHz. Calculate its effective area. Calculate the gain of a 3 m reflector
antenna at (a) 6 GHz and (b) 14 GHz.
32. Find the gain and beamwidh of an antenna of diameter 2 m operating at 14 GHz. Assume an aperture
efficiency of 60 %.
33. An INTELSAT V transponder using a global beam achieves a 17.8 dB (C/N) i at an earth station. The
transponder carries 972 channels on a single carrier, the FDM/FM signal fully occupies a 36-MHz
bandwidth in the transponder. If the weighted (S/N) on the top baseband channel is 51.0 dB, find the rms
test-tone deviation and the rms multicarrier deviation that must be used. Compare these with the tabulated
values.
34. A single carrier that will occupy (when modulated) 9 MHz of an INTELSAT V transponder can produce a
(C/N)i of 14.7 dB at a standard earth station using the satellite’s global beam. Assuming an 8000-p Wp
space segment noise allocation, how many telephone channels can the transponder carry?
35. In a TDMA network the reference burst and the preamble each requires 560 bits, and the nominal guard
interval between bursts is equivalent to 120 bits. Given that there are eight traffic bursts and one reference
burst per frame and total frame length is equivalent to 40,800 bits, calculate the frame efficiency.