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

"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

"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

I meant to flag this statement.

Does it provide enough information for you to apply it in the way you
have?

It says nothing of the absolute noise power or signal power. You seem to
assume the noise power KTB noise where T is 290K.

What if you were pointing at directive antenna at cold sky, and Tnoise
was say 10K. (As a complication, no antenna is perfect, and there would
also be some spillover noise from the hot earth, but the total might be
well under 100K.)

Alternatively, what if you were talking about a HF antenna and say Tnoise
was say, 30000K.

Owen

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 temperatu

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

""Joel Koltner" wrote in message
...
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?


Easy peasy, but wrong!!!


You may have a 60dB SNR but that says nothing about the actual level of
noise that is applied to the input of the amplifier from the antenna.

You may be better off thinking in terms of noise power (in Watts) rather
than NF.

For example, your amplifier will add a noise power of 3dB above thermal to
the path. If your input noise power from the antenna is 20dB above thermal
then when it is summed with the amplifier's noise contribution there will
only be a very very slight increase in the overall noise power. Hence the
noise figure will only increase very slightly, and your SNR will only
degrade very slightly. (It will not be 20+3dB!!!!)


The situation is the same when you add a second amplifier, you must take the
sum of the input noise from the antenna and the amplifier noise ( in watts),
multiplied by the amplifier gain (not in dB) to give you the noise power
that is at the input of the second amp. Then you must sum in the noise power
contribution of the second amplifier.

From the above it now becomes clear that if the gain of the first amp
dilutes the noise contribution of the second amp on the overall noise level.
(unless the gain is very low and the NF of the second amp is very high).

73
Jeff

Hello Ian,

Ian White GM3SEK wrote in
:

....
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.

I make the observation that hams *like* Noise Figure, the the roll up of
a system component's Noise Figure into whole of system impact is often
(very often) not done well.

I was explaining to a local EME enthusiast that a certain two stage 1296
LNA that represents NF=0.51dB when the FET specs give NF=0.78dB for the
first FET alone, is very creative. When the effects of input circuit loss
and roll up of the second stage noise is included, it is unlikely that
such a preamp would have a guaranteed NF better an 0.9dB.

In high performance systems, I perceive a preference to not use G/T as a
metric for receive system performance. Rather, hams will quote (brag) Sun
noise rise (Sun/ColdSky ratio) without statement of the solar flux at the
time, or the time (from which solar flux can be estimated from historical
records), or if they do quote solar flux, it will be the 10.7cm flux
which cannot be reliably extrapolated to the relevant ham band.

The 'science' is often obscured by shallow discussions about whether LNA
Noise Figure is more important than Gain.

Owen

So-- Which is the most relevant noise measurement? Noise Figure-
or Noise Temperature? If one is better than another at a given
frequency, than another, and then the other is better at greater freqs,
WHY? (and, keeping in mind the FIRST stage establishes the Noise
figure,IF it's gain is enough to overcome the next stage's noise
figure) , then why is this a consideration?
Finally, as temperature is free space must approach absolute zero,
but, considering space "noise from stars, ect", what is it REAL
absolute Noise Temp of the (cold) sky? Inquiring minds want to know!

Jim NN7K


Owen Duffy wrote:
Hello Ian,

Ian White GM3SEK wrote in
:

...
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.

I make the observation that hams *like* Noise Figure, the the roll up of
a system component's Noise Figure into whole of system impact is often
(very often) not done well.

I was explaining to a local EME enthusiast that a certain two stage 1296
LNA that represents NF=0.51dB when the FET specs give NF=0.78dB for the
first FET alone, is very creative. When the effects of input circuit loss
and roll up of the second stage noise is included, it is unlikely that
such a preamp would have a guaranteed NF better an 0.9dB.

In high performance systems, I perceive a preference to not use G/T as a
metric for receive system performance. Rather, hams will quote (brag) Sun
noise rise (Sun/ColdSky ratio) without statement of the solar flux at the
time, or the time (from which solar flux can be estimated from historical
records), or if they do quote solar flux, it will be the 10.7cm flux
which cannot be reliably extrapolated to the relevant ham band.

The 'science' is often obscured by shallow discussions about whether LNA
Noise Figure is more important than Gain.

Owen

Jim-NN7K . wrote in
:



So-- Which is the most relevant noise measurement? Noise Figure-
or Noise Temperature? If one is better than another at a given

As both Ian and I mentioned, Noise Figure is based on the degradation in
S/N ratio assuming that the source contributes 290K thermal or Johnson
noise (KTB noise) from the equivalent source resistance.

This if fine for describing the operation of a receiver when driven by a
standard signal generator.

The radiation resistance component of the equivalent source impedance of
an antenna is not a source of KTB noise, but is a source of received
noise power from various sources, and the level varies with many factors
including frequency and time.

Expressing a receive system performance as a Noise Figure assumes an
external or 'ambient' noise component that is of little application
relevance.

Expressing a receive system performance as an equivalent Noise
Temperature expresses only the receiver's internal noise, which is a
limited perspective from an application point of view. However,
comparison of the system's internal noise with the external noise gives
insight into the S/N degradation due to the system.

Both measures contain sufficient information, just that you have to
transform NF to obtain Teq which is the more direct input to calculation
of system S/N, or exploration of cascaded stages for example. Because of
this, NF is sometimes misinterpreted as to its direct signifcance.

frequency, than another, and then the other is better at greater
freqs, WHY? (and, keeping in mind the FIRST stage establishes the
Noise
figure,IF it's gain is enough to overcome the next stage's noise
figure) , then why is this a consideration?

The first stage is very important in determining system noise
temperature, but in high performance stations, so are the losses in the
feed system, switching etc. The contribution of later stages should not
be considered insignificant until calculated.

Often, the LNA runs with so much gain that the transceiver AGC reduces
gain sufficiently to degrade transceiver noise temperature to perhaps
30,000K (NF=20dB). Consider a 0.5dB NF 35dB gain LNA (T=35K, Gain=3,000),
then it rolls 30,000/3000=10K into the system noise temperature which may
be significant depending on the external noise level.

Even worse is the scenario where an OM installs a 20dB attenuator between
LNA and transceiver to 'correct' S meter readings. In that case, a 5dB NF
receiver with 20dB attenuator has NF=25dB, T=90,000K, so it rolls
90,000/3000=30K into the otherwise same system... but this is done!

Finally, as temperature is free space must approach absolute zero,
but, considering space "noise from stars, ect", what is it REAL
absolute Noise Temp of the (cold) sky? Inquiring minds want to know!

IIRC the coldest part of the sky in the 5 - 10GHz region is around 4K. As
I mentioned in an earlier post, practical antennas capture significant
energy in their sidelobes, so the total noise input power might be well
in excess of 4K.

The more interesting question is the background when pointing in the
desired direction (eg the moon for EME), and how much sidelobe noise is
received.

Owen

"Jim-NN7K" . wrote in message
...


So-- Which is the most relevant noise measurement? Noise Figure-
or Noise Temperature? If one is better than another at a given
frequency, than another, and then the other is better at greater freqs,
WHY?

In my experience, the community seems to dictate the terminology. (If you
buy a big, long sandwich for lunch, is it a "hero," a "sub" or a "hoagie"?)

More to the point, when selecting an LNA for C-band satellite, you will
almost always see the noise temperature in the specs. However, for Ku-band,
the LNA noise figure is usually spec'ed.

As was pointed out, they are directly convertible. Go a little less than
halfway downpage at
http://www.microwaves101.com/encyclo...oisefigure.cfm
and see the graph of noise temperature versus noise figure. (This web page
also provides illustrations of what's already been presented here.)

The noise figure of the first stage strongly influences the total system
noise figure, hence the oft-seen placement of a low noise preamp close to
the antenna.

Richard Clark wrote in
:

On Fri, 20 Mar 2009 19:46:53 -0700, "Joel Koltner"
wrote:

Say I have an antenna that I know happens to provide an SNR
of 60dB...

I've been following this saga for a while now, and I note no one seems
nonplused by the statement above. For as much that has been unsaid,
there must be a flood of presumptions that flowed from this detail.

Indeed. I addressed some in my second posting, perhaps you missed it?

Owen