Calculate Lna Gain of a system . Satelitte base station

I am struggling to find a solution for these 3 days ,although i have figured out one i cannot claim it is correct

I have computed that receive power is Pr = -108db.
Physical temperature at station is 20 C.
Bandwidth is B=72Mhz
I know that SNR after amplifier at right where is IF stage input is SNR =15db.

I want to find a minimum gain for tha LNA . And this is where i am stuck.


Could i say that

S/N= G * Pr / k*T*B
?

G would be total system gain and T using cascade ,should be after amplifier (Ta+Tline)*G1*GLna*G3*G4 + Tlna*Glna*G3*G4 + Tf*G3*G4 + Tamp*G4 ? There only uknown is Glna .

But i am not sure if this is the solution or it can be simpler.
Please help

Input Noise=4KTB, i.e.-128dBm

So input SNR=Pr/(Input Noise), i.e. 20dB.

Then system NF=Input_SNR/Output_SNR, i.e. 5dB

from system NF, you can easily find the Gain of LNA. the result is Gain=9dB.

Obviously your picture is lack of mixer and IF filter and IF amplifier. If add these components, the LNA gain should be 12dB. And the system noise is 4.2dB.

Can u explain this please? I am not getting it clearing in my mind. The role of IF filter and ampfr.

Thanks for answering.How did you find that input noise is -128dbm ?
Then knowing noise factor how can i easily find gain of LNA ? Because the only way i know is using cascade equation.

http://www.ijens.org/Vol_11_I_04/110...JECS-IJENS.pdf

This doesnt help. I know the theory.

The noise level is Noise=4KTB, i.e.-128dBm. I.e. Noise =4*(1.28E-23)*40*(70E+6), then log it , get -128dBm.
But,
Vfone,
I remember the noise is 4KTB, in your article, it is said to be KTB, which is right? I am also a little confused.

And Gain is caiculated by cascade method, you can use software to help you.

tony_lth thank you again. I used bandwidth 72E+6 . Hm i just dont understand why 4 is needed.Maybe that why i get different result there.

So T=(F-1)To and i can compute system temperature and solve that ?

Ts=Ta+ Tline +Tlna * L + To *L /Glna + ((F-1)To * L) / (Glna * G) ? here unknows is glna.. That is the solution ?

https://dl.dropbox.com/u/4499990/Pren.pdf here is what i get , total ****

Sorry, in my previous posts, the noise unit should be dBW, not dBm. i ignored it.
The sat telecomm noise is mainly thermal noise, and I searched and found that it should be 4KTB, not KTB, just like a resistor thermal noise. You can search the textbook.

Sat comm noise or atmospheric noise is thermal noise so 4kTB which is described in the last post. Similarly for shot noise we must take it as 4kTB only. Where as for flicker noise it should be kTB. This equation is known as Nyquist Equation of noise.