Noise figure paradox

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?

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).

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.)

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?

Input appreciated,
---Joel Koltner



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Relevant Pages

  • Re: Noise figure paradox
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    (rec.radio.amateur.antenna)
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  • Re: Noise figure paradox
    ... The idea of a noise figure N is, simply enough, how much loss in SNR is seen ... Say I have an antenna that I know happens to provide an SNR ... and a noise factor of 2, at the output of the amplifier my SNR ... Like everyone else who has traveled this route, I quickly found that the very large values of noise figure and noise temperature, that are typical at HF, can conceal some approximations and even misconceptions. ...
    (rec.radio.amateur.antenna)