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# Chapter 4 solution to problems

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satellite communication by william Stallings

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### Chapter 4 solution to problems

1. 1. Chapter 4 Solution to ProblemsQuestion #1.A C-band earth station has an antenna with a transmit gain of 54 dB. The transmitter outputpower is set to 100 W at a frequency of 6.100 GHz. The signal is received by a satellite at adistance of 37,500 km by an antenna with a gain of 26 dB. The signal is then routed to atransponder with a noise temperature of 500 K, a bandwidth of 36 MHz, and a gain of 110 dB. a. Calculate the path loss at 6.1 GHz. Wavelength is 0.04918 m.Answer: Path loss = 20 log ( 4 R / ) = 20 log ( 4 37,500 103 / 0.04918) dBLp = 199.6 dBb. Calculate the power at the output port (sometimes called the output waveguide flange) of thesatellite antenna, in dBW.Answer: Uplink power budget givesPr = Pt + Gt + Gr - Lp dBW= 20 + 54 + 26 – 199.6 = -99.6 dBWc. Calculate the noise power at the transponder input, in dBW, in a bandwidth of 36 MHz.Answer: N = k Ts BN = -228.6 + 27 + 75.6 = -126.0 dBWd. Calculate the C/N ratio, in dB, in the transponder.Answer: C/N = Pr – N = -99.6 + 126.0 = 26.4 dBe. Calculate the carrier power, in dBW and in watts, at the transponder output.Answer: The gain of the transponder is 110 dB. Output power isPt = Pr + G = -99.6 + 110 = 10.4 dBW or 101.04 = 11.0 W.2. The satellite in Question #1 above serves the 48 contiguous states of the US. The antennaon the satellite transmits at a frequency of 3875 MHz to an earth station at a distance of 39,000km. The antenna has a 6o E-W beamwidth and a 3o N-S beamwidth. The receiving earth stationhas an antenna with a gain of 53 dB and a system noise temperature of 100 K and is located at4-2the edge of the coverage zone of the satellite antenna. (Assume antenna gain is 3 dB lower thanin the center of the beam)Ignore your result for transponder output power in Question 1 above. Assume thetransponder carrier power is 10 W at the input port of the transmit antenna on the satellite. a. Calculate the gain of the satellite antenna in the direction of the receiving earth station.[Use the approximate formula G = 33,000/(product of beamwidths).]Answer: G = 33,000 / ( 6 x 3) = 1833 or 32.6 dB on axis.Hence satellite antenna gain towards earth station is 32.6 – 3 = 29.6 dB.
2. 2. b. Calculate the carrier power received by the earth station, in dBW.Answer: Calculate the path loss at 3.875GHz. Wavelength is 0.07742 m.Path loss = 20 log ( 4 R / ) = 20 log ( 4 39,000 103 / 0.07742) dBLp = 196.0 dBDownlink power budget givesPr = Pt + Gt + Gr - Lp dBW= 10 + 29.6 + 53 – 196.0 = -103.4 dBWc. Calculate the noise power of the earth station in 36 MHz bandwidth.Answer: N = k Ts BN = -228.6 + 20 + 75.6 = -133.0 dBWd. Hence find the C/N in dB for the earth station.Answer: C/N = Pr – N = -103.4 + 133.0 = 29.6 dB