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ENGRstudent
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I think I've done this right, but I'm looking for some reassurance because I often make stupid mistakes when converting from dB to watts and back again.
Thank you in advance! I'm about to graduate in 2 weeks, and this forum has been AWESOME throughout my college career. Kudos to everyone who takes the time to help out.
The problem statement reads:
"A satellite in synchronous orbit outputs a 4 GHz signal with an EIRP of 100000 W. If the ground based receiver has a sensitivity of -75 dBm, what is the gain required of the receiving antenna?"
My equations:
(P_receiver) = (EIRP) x (G_free space) x (G_receiving antenna)
(G_free space) = [λ/(4*pi*d)]^2
P_receiver = receiving antenna power
G_free space = free space gain
G_receiving antenna = receiving antenna gain
λ = c/f
d = 35,800,000 meters (height of orbit for geosynchronous satellite courtesy of Wiki)
Converting receiver sensitivity to Watts:
-75 dBm = 30 + 10 * log[(P_receiver)] ==> P_receiver = 3.16 x 10^-11 W
Solving for G_free space:
(G_free space) = [(3.0 x 10^8)/(4 x 10^9)]/[(4*pi*35,800,000)]^2
= 2.78 x 10^-20
Solving for G_receiving antenna:
(G_receiving antenna) = (P_receiver)/[(EIRP)*(G_free space)]
(G_receiving antenna) = (3.16 x 10^-11)/[(100000)(2.78 x 10^-20)]
= 11367
= 10 * log(11367) = 40.56 dB
So my final answer is 40.56 dB. Yes? No? Maybe?
Thank you in advance! I'm about to graduate in 2 weeks, and this forum has been AWESOME throughout my college career. Kudos to everyone who takes the time to help out.
The problem statement reads:
"A satellite in synchronous orbit outputs a 4 GHz signal with an EIRP of 100000 W. If the ground based receiver has a sensitivity of -75 dBm, what is the gain required of the receiving antenna?"
My equations:
(P_receiver) = (EIRP) x (G_free space) x (G_receiving antenna)
(G_free space) = [λ/(4*pi*d)]^2
P_receiver = receiving antenna power
G_free space = free space gain
G_receiving antenna = receiving antenna gain
λ = c/f
d = 35,800,000 meters (height of orbit for geosynchronous satellite courtesy of Wiki)
Converting receiver sensitivity to Watts:
-75 dBm = 30 + 10 * log[(P_receiver)] ==> P_receiver = 3.16 x 10^-11 W
Solving for G_free space:
(G_free space) = [(3.0 x 10^8)/(4 x 10^9)]/[(4*pi*35,800,000)]^2
= 2.78 x 10^-20
Solving for G_receiving antenna:
(G_receiving antenna) = (P_receiver)/[(EIRP)*(G_free space)]
(G_receiving antenna) = (3.16 x 10^-11)/[(100000)(2.78 x 10^-20)]
= 11367
= 10 * log(11367) = 40.56 dB
So my final answer is 40.56 dB. Yes? No? Maybe?
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