The downlink C/N₀ ratio in a direct broadcast satellite (DBS) system is estimated to be 85dB-Hz. The specifications of the link are:

Satellite ELRP                                                                                = 57dBW

Downlink carrier frequency                                                        = 12.5 GHz

Data rate                                                                                        = 10 Mb/s

Required E/N0 at the receiving earth terminal                        = 10 dB

Distance of the satellite from the receiving earth terminal   = 41,000 km

Calculate the minimum diameter of the dish antenna needed to provide a satisfactory TV reception, assuming that the dish has an efficiency of 55 percent and it is located alongside the home where the temperature is 310K. For this calculation, assume that the operation of the DBS system is essentially downlink-limited.