"Joel Koltner" wrote in
:

Here something I've been thinking about lately...

The idea of a noise figure N is, simply enough, how much loss in SNR
is seen going through a network (typically an amplifier) -- N =
(Si/Ni)/(So/No), expressed in dB. Say I have an antenna that I know
happens to provide an SNR of 60dB... if I feed that antenna into an
amplifier with a power gain of 100 (20dB) and a noise factor of 2
(3dB), at the output of the amplifier my SNR will be 57dB. Easy
peasy, right?

But here's an interesting paradox: If I take that output with 57dB SNR
and feed it to another, identical amplifier, shouldn't the SNR at its
output now drop to 54dB?


Appealing, but wrong.

The amplifier has an equivalent noise temperature (Teq) of 289K.

To determine the effect of two cascaded stages of the same amplifier, Teq
of the combination =T1+T2/G1=289+289/100=318K which corresponds to NF=
3.2dB

Of course, most people know the answer is "no," but it's not
necessarily immediately obvious why this is.

The problem, to quote Wes Hayward, is that "the noise figure concept
has the drawback that it depends upon definition of a standard
temperature, usually 290K." In other words, the SNR at the output of
an amplifier degrades by the noise figure *only if one can assume that
the noise level going into the amplifier is equivalent to kTB*, where
T is usually taken to be 290K (...by the guy who built the amplifier).

If you were testing the amplifier with a standard signal generator at
room temperature, the generator does suppy 290K of noise.

An real antenna might supply much less through to much much more noise.


This assumption isn't correct in the two cascaded amplifier case.
Indeed, since the first amplifier has a gain of 20dB, in 1Hz the noise
power coming out of the amplifier is -174+20+3 = -154dBm. This is
equivalent to a noise temperature of 57533K! From this vantage point
it's pretty obvious that an amplifier with a noise figure of 3dB --
corresponding to noise temperature of 290K -- will have negligible
impact on the overall noise output. (If you run through the numbers,
the SNR at the output of the cascaded amplifiers is 56.94dB.)

I get 60-3.2=56.8dB.


Personally, I think that using noise temperatures tends to be "safer"
than using noise figures, as the later can easily lead one astray if
you're not careful to make sure you know what the "standard
temperature" used was. (After all, if someone just hands you a piece
of coax and says, "there's a 60dB SNR signal on line, please amplify
it by 20dB and insure that the output SNR is still 59dB," without
more information there's no way to determine how good of an amplifier
you need.) But I'd like to get other peoples' opinions on this
subject... how do you think about noise figures and temperatures?

It is not so much an issue of safer, is it use and mis-use, it is about
how you use NF with cascaded stages. Essentially, you convert them to T,
apply the gain effects, then T back to a NF for the combination. The
equation looks ugly, but if you work in T, you can do it in your head...
well until T becomes so large you want to use dBK.

You might find this little calculator interesting / helpful:
http://www.vk1od.net/calc/RxSensitivityCalc.htm .

Owen