Solve Link Budget: EIRP 100000 W, -75 dBm Receiver Sensitivity

AI Thread Summary
The discussion revolves around calculating the required gain of a receiving antenna for a satellite signal with an EIRP of 100,000 W and a receiver sensitivity of -75 dBm. The original poster converted the receiver sensitivity to watts and calculated the free space gain, arriving at a final gain requirement of 40.56 dB for the receiving antenna. However, there was confusion regarding the calculations, particularly the free space loss and the necessary gain to meet the receiver's minimum sensitivity. Another user suggested converting all values to dB for easier calculations and provided an alternative method, concluding that a gain of approximately 41.2 dBi is needed. The thread emphasizes the importance of careful unit conversion and verification in link budget calculations.
ENGRstudent
Messages
26
Reaction score
0
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?
 
Last edited:
Engineering news on Phys.org
i get -128.5dBm without an antenna on the ground, thing is I'm stumped on how to calculate needed gain for the antenna.

so i just added the arrl antenna book to my wish list, hopefully this should be covered.

edit: shouldn't it be -75-(-128.5)=53.5dB of gain to meet the receiver minimum? :blushing:
 
Last edited:
Thanks for taking the time to look over the problem. Where did you get -128.5 from?

I just worked it again and found an error in my last step, and the new value I got for the gain is 40.56 dB.

I have attached my work as a PDF to make it more clear. Please review it to see where I may have made a mistake?

Thanks again!

EDIT: I made a mistake in my correction, 40.56 dB is still my final answer.
 

Attachments

Last edited:
the equations are a little different in my book, they want a ratio for both antenna gains which i left at 1.

Pr=Pt*Gt*Gr*λ^2/16*pi^2*d^2
 
Don't know if its too late to answer this but here it goes. 1st convert everything to dB, adding and subtracting is way easier then multiplying and dividing. So 100000 Watts EIRP = 80 dBm. Free space loss of 4 GHz at 35,800 Km is 196.2 db. So 80 - 196.2 = -116.2 dbm. Your receiver needs -75 so you need a -75 - -116.2 = 41.2 dBi antenna. (dBi because transmit power was in EIRP)

Equations:
Free space loss in dB: P(dBm) = 32.43 + 20LogD(km) + 20LogF(MHz)
watts to dbm: dBm = (10 log (power watts)) + 30
 
I used to be an HVAC technician. One time I had a service call in which there was no power to the thermostat. The thermostat did not have power because the fuse in the air handler was blown. The fuse in the air handler was blown because there was a low voltage short. The rubber coating on one of the thermostat wires was chewed off by a rodent. The exposed metal in the thermostat wire was touching the metal cabinet of the air handler. This was a low voltage short. This low voltage...
Hey guys. I have a question related to electricity and alternating current. Say an alien fictional society developed electricity, and settled on a standard like 73V AC current at 46 Hz. How would appliances be designed, and what impact would the lower frequency and voltage have on transformers, wiring, TVs, computers, LEDs, motors, and heating, assuming the laws of physics and technology are the same as on Earth?
Thread 'How Does Jaguar's 1980s V12 Dual Coil Ignition System Enhance Spark Strength?'
I have come across a dual coil ignition system as used by Jaguar on their V12 in the 1980's. It uses two ignition coils with their primary windings wired in parallel. The primary coil has its secondary winding wired to the distributor and then to the spark plugs as is standard practice. However, the auxiliary coil has it secondary winding output sealed off. The purpose of the system was to provide a stronger spark to the plugs, always a difficult task with the very short dwell time of a...

Similar threads

Back
Top