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.(adsbygoogle = window.adsbygoogle || []).push({});

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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