(Solved): Question \#3 (50 points): A TV broadcasting GEO satellite (38,500km) equipped with 16 transponder ...

Question \#3 (50 points): A TV broadcasting GEO satellite $(38,500\mathrm{km})$ equipped with 16 transponders, each transponder has output power of $200\mathrm{W}$ and a bandwidth of $25\mathrm{MHz}$. The antenna on the satellite has a gain (on axis) of $34\mathrm{dB}$. The receiving terminals all use antennas with a circular aperture with a diameter of $0.5\mathrm{m}$ and an aperture efficiency of $65\%$. The noise i bandwidth of the digital TV receiver is $20\mathrm{MHz}$ a. What is the free space path loss and the receiving terminal antenna gain at frequency $f=$ $12.2\mathrm{GHz}$. b. What is the downlink power from the satellite to the earth station on the $3\mathrm{dB}$ contour (of-axis) of the satellite antenna beam. Consider that the satellite trinsmits a power of $180\mathrm{W}$ and atmospheric loss of $0.7\mathrm{dB}$. c. If the receiving station has a system noise temperature of $110\mathrm{K}$ in clear air. What is the noise power budget for the receiver using the receiver's noise bandwidth. d. Calculate the $\mathrm{C}/\mathrm{N}$ ratio for the receiver with a noise bandwidth of $20\mathrm{MHz}$. If the minimum allowed $\mathrm{C}/\mathrm{N}$ ratio is $10.0\mathrm{dB}$. What is the link margin? e. If heavy rain causes $2\mathrm{dB}$ excess path attenuation and the system noise temperature of the receiver increases to $210\mathrm{K}$. Calculate the $\mathrm{C}/\mathrm{N}$ under these rain conditions, and the link margin above the $\mathrm{C}/\mathrm{N}$ threshold of $10.0\mathrm{dB}$.