The receiver antenna has a gain of 30dB and antenna noise temperature is 190 dB What is minimum require satellite transmitter power to achieve a 20 dB CNR at the output of the receiver. -

Marks: 10 M

Year: Dec 2012

$Given: Downlink Frequency(f)=2.2GHz$

$Equivalent noise temperature(T_e )=160K$

$Bandwidth(B)=1MHz$

$Gain of the receiver [G_RX]=30dB$

$Antenna noise temperature[T_ant]=190dB$

$[\frac{C}{N}]_D=20dB$

Geostationary satellite distance $(r)=42164Km$

To find: $[EIRP]:$

$System Noise temperature[T_S ]=[T_ant ]+10logT_e$

$=190+10log160$

$[T_S]=212.041dB$

Considering Losses as only frequency dependent loss i.e. $FSL$

$[FSL]=10log⁡(\frac{4πr}{λ})^2=10log⁡(\frac{4πrf}{c})^2=10log⁡(\frac{4π×42164×10^3×2.2×10^9}{3×10^8 })^2 [FSL]=191.789dB$

We Know

$[\frac{C}{N}]_D=[EIRP]+[\frac{G}{T_S}]_ES-10logk-10logB-[Losses]$

$[\frac{C}{N}]_D=[EIRP]+[G]_ES-[T_S]-10logk-10logB-[Losses]$

$20=[EIRP]+30-212.041-10 log⁡(1.38×10^{-23} )-10 log⁡(1×10^6 )-191.789$

$20=[EIRP]-205.23$

$[EIRP]=225.23dBW$