Re: Noise figure paradox

Joel Koltner wrote:
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,

Wes Hayward's articles in the 1970s completely transformed the way we think about the sensitivity and dynamic range of HF receivers. They mark the point where ideas such as "noise floor", "intermodulation intercept" and "blocking dynamic range" and "reciprocal mixing" entered mainstream amateur radio.

Inspired by those articles, I set out to apply those same concepts to VHF/UHF receivers... and ran into problems with the definitions of receiver sensitivity. 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.

The approximations will probably be unimportant in HF systems where the receiver has a high noise figure / noise temperature, and antenna noise is usually greater still. However, the misconceptions are always important, because they will give incorrect results for VHF/UHF receivers. The difference at VHF/UHF is that receiver noise and antenna noise are often quite similar, and both much lower than at HF.

I must emphasize that the fundamental concepts are the same at all frequencies. The differences are all due to the magnitudes of the numbers involved.

To cut the story short, noise temperature is the only concept that will always give correct results. As Owen points out, some of the numbers are large and ugly - but the important thing is that they are correct. The results can easily be converted back into a more comfortable format... and those results will likewise be correct.

For example, modern Noise Figure Analyzers have options to accept inputs and display results in any relevant engineering units; but the internal calculations are done entirely in terms of noise temperature because that concept will always give the correct results.


An important misconception is about the role of "290K" as a reference temperature. Contrary to what is stated above, this is *not* a designer option ("usually 290K", implying that some other value could be chosen). That number 290 is built into the IEEE standard definition relating noise factor to noise temperature:

F = T/290 + 1

That equation defines what the engineering world means by "noise factor". F and T are variables but the number 290 not; it is fixed by definition. (Noise factor F is a dimensionless ratio; the more commonly-seen Noise Figure is simply F converted into dB.)

What engineers do sometimes assume is that the *physical* temperature of their hardware is 290K, because that special case does allow some convenient simplifications. But that isn't the same as saying "my reference temperature is 290K". At best, it is loose language - fooling ourselves by saying something that we don't really mean. At worst, it is a perfect example of the way that a good approximation can hide a fundamental misconception.

An engineer working at HF wouldn't even notice what he has done. Because he is working with very high values of noise temperature, any errors will be negligible - in other words, he has made an excellent engineering approximation. But the misconceptions are still there... waiting. If that same engineer moves to work on low-noise UHF and microwave systems, he'll fall flat on his face.

Does this matter to he average radio amateur? Yes, it does, for many of us have multiband transceivers with coverage from HF through to UHF - exactly the range of applications where those pitfalls await the unwary. The engineers who design those radios need to have their concepts straight; so do the people who write equipment reviews; and if we want to make intelligent buying decisions, so do we all.



--

73 from Ian GM3SEK
.

Relevant Pages

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