Noise figure on cascade system. Calculating SNR between stages

[ffddoo]

Hi


I'm calculating SNR on a system and I'm not sure if I'm understanding NF concept.
I've include calculations here:



The problem is: I can easily calculate signal at any block output as (in dB) G=So-Si, then S1=S0+G1 and S2=S1+G2 and S2=S0+G1+G2
With NF the expression is F=SNRi/SNRo and as a result, in dB NF=SNRi-SNRo ........ or maybe not?

because total NF=F1+(F2-1)/G1 so I can calculate NFtotal, and im sure cal is well done, and I think then SNR2=SNR1-NFtotal but what for SNR1? because if i calc SNR1=SNR0-NF1 then i could do SNR2=SNR1-NF2 and then SNR2=SNR0-NF1-NF2 wich is different of the result from NFtotal.


help please.

 

[chuckey]

As I understand it, the NF is the thermal noise at the output of an amp compared with just loading the input with its terminating impedance. Now the problem I have with your calculations is that there is no reference to the actual amplitude of the signal compared to that of the thermal noise. For example your figure 40 dbmicroV is the signal,with a S/N of 28 dB, so the noise is in the micro volts and the added noise of the first stage will add to it. If you input signal was 1V with a S/N of 28 dB, then the noise would be in the 10's of millivolts and the noise of the first stage would not add to it.
????Frank

 

[ffddoo]

As I understand it, the NF is the thermal noise at the output of an amp compared with just loading the input with its terminating impedance. Now the problem I have with your calculations is that there is no reference to the actual amplitude of the signal compared to that of the thermal noise. For example your figure 40 dbmicroV is the signal,with a S/N of 28 dB, so the noise is in the micro volts and the added noise of the first stage will add to it. If you input signal was 1V with a S/N of 28 dB, then the noise would be in the 10's of millivolts and the noise of the first stage would not add to it.
????Frank

You mean F=SNRi/SNRo but just at certain level of noise?

 

[albbg]

You mean F=SNRi/SNRo but just at certain level of noise?

Yes, let's suppose we have a noisy amplifier having gain G. At the input we'll place a resistor having value equal to the input impedance of the amplifier. This resistor will generates a noise power given by N=k*T*B where k is the Boltzmann constant, T the temperature and B the considered bandwidth. Passing through the amplifier, this noise will be amplified by G, but also some noise will be added. Referring this last to the output and calling it "Na" we'll have:

No=G*Ni+Na

since a superimposed signal having power Si will be at the otuput So=G*Si then:

SNRi=Si/Ni and SNRo=G*Si/(G*Ni+Na)

by definition the noise figure is F=SNRi/SNRo=(G*Ni+Na)/(G*Ni)=1+Na/(G*Ni)

So the noise figure is valid only if referred to a given temperature T that have to be the same on the resistor and on the amplifier.

If the input noise of your chain is equivalent to that generated by a resistor, as said before, then SNR1=28-2=26 dB. Otherwise it means other blocks are present before the first you draw, then the friis formula has to be applied.