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

"Owen Duffy" wrote in message
...
"Joel Koltner" wrote in
:
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.

Well, correct *under a certain set of assumptions*. As with, e.g.,
manufacturer's data sheets and quiz/exam problems done in school, often these
assumptions are unstated.

In other words, I'm purposely not stating my assumptions to demonstrate how to
get yourself into trouble more readily. :-)

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

How does an antenna at 290K supply less? I mean, ignoring how well it works
as an antenna, shouldn't it still have kTB worth of noise generated just from
the resistance in its conductors?

(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.

I think that's rounding differences and my using T0=290K rather than 289K as a
reference.

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.

Sounds safe to me.

I find noise temperatures just as if not more intuitive than noise figures,
and (to me) it's more obvious what's going on when you have a string of
amplifiers.

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

Looks nice, thanks!

---Joel

"Joel Koltner" wrote in
:

"Owen Duffy" wrote in message
...
"Joel Koltner" wrote in
:
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.

Well, correct *under a certain set of assumptions*. As with, e.g.,
manufacturer's data sheets and quiz/exam problems done in school,
often these assumptions are unstated.

In other words, I'm purposely not stating my assumptions to
demonstrate how to get yourself into trouble more readily. :-)

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

How does an antenna at 290K supply less? I mean, ignoring how well it
works as an antenna, shouldn't it still have kTB worth of noise
generated just from the resistance in its conductors?

An antenna's feedpoint impedance comprises radiation resistance and loss
resistance.

Radiation resistance is a virtual resistance and does not contribute
thermal or Johnson noise.

It is a common mistake to consider that an antenna always includes 290K
due to kTB in its radiation resistance. If that were the case, we would
never have need for receivers with Teq much less than 290K! Mind you, if
a directive antenna points at hot earth, then external noise will never
be much less than 290K, so the requirements for terrestrial shots will be
different to space shots.

Attenuation gives rise to noise, and feed system loss is no exception.

An antenna does receive noise power from its environment, lets call it
external noise, and that needs to be factored into a receive system for
an overall figure of merit.

The ratio Gain/Temperature is antenna gain divided by total equivalent
noise temperature (internal and external) all referred to a common
reference point (usually the antenna connector or w/g flange). It is an
overall figure of merit, and if the power flux density (or field
strength) at the receive antenna is known, then S/N can be calculated
from that and G/T.

Hams tend to not use G/T.


I think that's rounding differences and my using T0=290K rather than
289K as a reference.

The 289 was not the reference, it was the result of using 3.00000dB NF (I
know you stated Noise Factor =2, but I used your rounded NF=3dB value).
....
I find noise temperatures just as if not more intuitive than noise
figures, and (to me) it's more obvious what's going on when you have a
string of amplifiers.

That was my point. Dealing with K is like dealing with power (P=kTB).


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

Looks nice, thanks!

Thanks.

There is a related calculator for deterimining the level of ambient noise
when receiver noise figure is known, see
http://www.vk1od.net/calc/anc.htm .

By and large, although lots of hams express an interest in weak signal
working, they aren't very interested in noise... which is a key parameter
determining whether a signal can be copied. I have asked scores of weak
signal enthusiasts their ambient noise level, and to date, only one has
answered (though not in absolute terms, but nevertheless had an
appreciation of the issue).

Owen

Owen Duffy wrote:
Radiation resistance is a virtual resistance and does not contribute
thermal or Johnson noise.

Sounds like what Walter Maxwell has been saying
for decades.
--
73, Cecil, IEEE, OOTC, http://www.w5dxp.com
"Government 'help' to business is just as disastrous as government
persecution..." Ayn Rand

"Owen Duffy" wrote in message
...
An antenna's feedpoint impedance comprises radiation resistance and loss
resistance.

OK.

Radiation resistance is a virtual resistance and does not contribute
thermal or Johnson noise.

Certainly, agreed.

But the loss resistance of the antenna itself is still contributing kTB,
right?

If I take a small loop of wire that has, say, a 100 milliohms of resistance,
it still generates kTB watts of thermal noise power. Why isn't this a
"problem?"

Hams tend to not use G/T.

If doesn't seem like "receiver factor" (input intercept point/noise figure)
has caught on much either.

By and large, although lots of hams express an interest in weak signal
working, they aren't very interested in noise... which is a key parameter
determining whether a signal can be copied.

I realized awhile back that noise is the primary factor that limits how far
you can transmit a signal and still recovery it successfully. (Granted, these
days it's often phase noise in oscillators rather than the noise figures in
amplifiers that determines this, but still.)

A discussion of noise sounds like a good topic for a ham fair... technically
there's little more complex than algebra (i.e., it's accessible to pretty much
everyone), but plenty of room for misapplication.

I'm learning a lot here...

---Joel

Joel Koltner wrote:
Radiation resistance is a virtual resistance and does not contribute
thermal or Johnson noise.

Certainly, agreed.

But the loss resistance of the antenna itself is still contributing
kTB, right?

If I take a small loop of wire that has, say, a 100 milliohms of
resistance, it still generates kTB watts of thermal noise power. Why
isn't this a "problem?"


Because that noise power has a source impedance of 100 milliohms, which
is dramatically mismatched to the input impedance of a normal receiver.
This is explained in Wes Hayward's full-length textbook, 'Introduction
to Radio Frequency Design' (now re-published by ARRL).


--

73 from Ian GM3SEK 'In Practice' columnist for RadCom (RSGB)
http://www.ifwtech.co.uk/g3sek

"Joel Koltner" wrote in
:

....
But the loss resistance of the antenna itself is still contributing
kTB, right?

Yes... but summing the contributions isn't trivial.

An alternative view is to consider the contribution of conductor loss and
other losses in the antenna structure and feed, and treat the system as
an ideal (lossless antenna) with a specified 'feed loss'.

My observation is that convention is the use the antenna connector or w/g
flange as a reference point for such calcs. It may even be laid down in
standards... but I am not sure. Someone else may know?

Notwithstanding that convention, I note the VK3UM tools seem to make
their reference point a point on the space side of the antenna. That
would give rise to a slighly different G/T figure.


If I take a small loop of wire that has, say, a 100 milliohms of
resistance, it still generates kTB watts of thermal noise power. Why
isn't this a "problem?"

I don't know what you mean by "problem". I have explained above that it
should be accounted for, and a method.
....
A discussion of noise sounds like a good topic for a ham fair...
technically there's little more complex than algebra (i.e., it's
accessible to pretty much everyone), but plenty of room for
misapplication.

I haven't been to ham fairs in your country, but here there are mostly
focussed on exhanging junk (selling the junk bought at the last fair, and
buying some different junk to sell at the next fair).

Noise is dealt with pretty well in text books, but text books aren't as
popular as mags.

Complicating this in the real world is that receivers aren't perfectly
linear, and measurements in a shielded room often have limited relevance
to real life performance where the 'noise' due to intermodulation
distortion is a significant issue... especially with a trend to avoiding
front end loss (noise) by ditching front end selectivity.

Noise is an interesting topic.

I have just discovered an Agilent AN which discusses uncertainty in noise
measurement. I am about to compare it to my proposition of a statistical
estimate of noise measurement (sampling) uncertainty, see
http://www.vk1od.net/measurement/noise/nmu.htm .

Owen

On Mon, 23 Mar 2009 15:28:51 -0700, "Joel Koltner"
wrote:

I realized awhile back that noise is the primary factor that limits how far
you can transmit a signal and still recovery it successfully. (Granted, these
days it's often phase noise in oscillators rather than the noise figures in
amplifiers that determines this, but still.)

Hi Joel,

This is an antiquated consideration limited to amplitude modulation,
the same specie as noise. I suppose there are noise products that
fall into the phase/frequency category that lay claim to "primary
factor," but that is a rather limited appeal.

Deep space communications proceeds many dB below the noise floor
enabled through technology that has become ubiquitous in cell phones -
Spread Spectrum. I have developed pulsed measurement applications for
which any single pulse has a poor S+N/N, but through repetition
improves S+N/N response with the square root increase of samples
taken.

73's
Richard Clark, KB7QHC

"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