Jim Lux wrote in news:46D463CF.1080309
@jpl.nasa.gov:

Dave Oldridge wrote:
Owen Duffy wrote in news:Xns999955EE72868nonenowhere@
61.9.191.5:


Dave Oldridge wrote in
.159:


Near as I could measure it, the NF of the receiver after my mod was
1.2db. I had to resort to boiling and freezing water and a tiny
dummy
load to measure it at all.

snip


This

still demands high resolution measurement of noise power.


Yes, anything less than 4 digits is just about useless.

That would be necessary but not sufficient.
....

Just following through on the '4 digit' issue...

I have done two series of 250 measurements of audio noise voltage from a
SSB receiver using two different digital multimeters, the 9932 is a
modern digital multimeter that is NOT true RMS responding, and the 506 is
a modern digital multimeter that is true RMS responding with bandwidth
adequate to cover the receiver output response.

From observation with a stopwatch, I estimate that the 9932 updates 3
times per second, and the 506 updates 2 times per second. The integration
times are probably .33 and .5 seconds respectively.

I have measured the receiver equivalent noise bandwidth and it is 1600Hz.

95% of 250 readings were within 0.41dB for the 9932 and 0.31dB for the
506. These observations reconcile well with my Chi-squared based estimate
of the uncertainty that I referred to in an earlier post.

As for the number of digits, they are both 4 digit multimeters which
doesn't mean a lot. They were used to measure 200mV with 1mV resolution,
so the representational error is 0.04dB. The error due to the number of
digits in this downscale three digit application is insignificant
compared to the sampling error of 0.4dB and 0.3dB.

Graphically, the distributions are shown at
http://www.vk1od.net/nfm/temp.gif .

Different meters with different integration times, and different
receivers with different noise bandwidth will result in different
outcomes, but I argue that the uncertainty is predictable.

Owen

On Thu, 30 Aug 2007 10:11:22 GMT, Owen Duffy wrote:

they are both 4 digit multimeters which
doesn't mean a lot. They were used to measure 200mV with 1mV resolution,

Hi Owen,

The convention for decades has been to describe them as 3½ Digits, or
2000 count, not 4 digit unless they could represent 9999. Adding
digits does not generally add precision, resolution, monotonicity, or
accuracy. However, as it costs money to add a digit, the underlying
circuitry could usually support "some" of these attributes. Better
instruments perform rounding after the last digit.

73's
Richard Clark, KB7QHC

Richard Clark wrote in
:

On Thu, 30 Aug 2007 10:11:22 GMT, Owen Duffy wrote:

they are both 4 digit multimeters which
doesn't mean a lot. They were used to measure 200mV with 1mV
resolution,

Hi Owen,

The convention for decades has been to describe them as 3½ Digits, or
2000 count, not 4 digit unless they could represent 9999. Adding
digits does not generally add precision, resolution, monotonicity, or
accuracy. However, as it costs money to add a digit, the underlying
circuitry could usually support "some" of these attributes. Better
instruments perform rounding after the last digit.

Hi Richard,

It is interesting in marketing hype that reference is made to 2 digit and
3 digit instruments, which implies a log based metric (10*log
(MaxReading)) when you assume a 'full count', and the same hype refers to
the upper digit if it can only have values of 0 or 1 as half a digit,
whereas it probably has a weight of log(0.5) or 0.3... so in utility
terms, a 2 1/2 digit instrument is really a 2.3 digit instrument.

In my case, I was making the measurements straddling 200mV, so I needed a
bit of headroom for outliers, say 1dB or 225mV fsd, so it was effectively
2.35 digit instrument if you followed that argument.

Nevertheless, the error introduced by the resolution issue and instrument
accuracy does not explain the experimental results... something else is
happening, and one needs to look beyond the instrument itself to form a
realistic view of measurement uncertainty when measuring narrowband
noise.

Owen

On Thu, 30 Aug 2007 22:46:46 GMT, Owen Duffy wrote:

It is interesting in marketing hype that reference is made to 2 digit and
3 digit instruments, which implies a log based metric (10*log
(MaxReading)) when you assume a 'full count', and the same hype refers to
the upper digit if it can only have values of 0 or 1 as half a digit,
whereas it probably has a weight of log(0.5) or 0.3... so in utility
terms, a 2 1/2 digit instrument is really a 2.3 digit instrument.

Hi Owen,

There are also 3000 count meters.

In my case, I was making the measurements straddling 200mV, so I needed a
bit of headroom for outliers, say 1dB or 225mV fsd, so it was effectively
2.35 digit instrument if you followed that argument.

Certainly, but I abandoned multimeters to general utility long ago and
went straight to my own designs for known precision. The common sound
card will give you 65000 count readings; and there is a world of
higher ADCs up to at least 16 million count readings.

Nevertheless, the error introduced by the resolution issue and instrument
accuracy does not explain the experimental results... something else is
happening, and one needs to look beyond the instrument itself to form a
realistic view of measurement uncertainty when measuring narrowband
noise.

You get non-monotonicity, quantization error, sample hold time errors,
codec error, issues of conversion errors through flash, successive
approximation, or single/dual-slope methods.

It would be simpler to handle the noise power in the linear domain,
and do the conversion to digital late in the chain (if at all).
Getting out into the hundredths of dB resolution (outside of the
standard 1KHz product lines) drives you into building your own
solution.

Linear circuits in the AF arena have long managed 6, 7 and sometimes 8
place resolution. You might have to twist as many knobs to get the
reading, but you also control the variables. Bolometery solves a lot
of complexities (but that is where this topic started - after a
fashion; and in that regard, optical pyrometry might be summoned up).

73's
Richard Clark, KB7QHC

Dear Crew: I am delighted with the content, care, and thought contained in
this thread. The continual issue of all measurements comprising at least
two numbers (estimate of the quantity measured and an estimate of the
uncertainty of the former) needs always to be dealt with. While the
law-of-large-numbers suggests that a normal distribution is a good
assumption to start with, experience shows that sometimes normal is not
normal. The famous paper by Costa (Dec 1959, Proc. of the (wonderful) IRE)
about communication in the presence of noise and other signals notes that a
Poisson distribution is the appropriate distribution ("Poisson, Shannon, and
the radio amateur").

I had the opportunity at Ohio State to craft a system that measured very
wide BW noise that changed slowly and to add statistical measures to what
was measured. Today, the task would be trivial - a sound card would run
circles around what I did with a voltage to frequency converter,
accumulator, counter-made-into-a-sidereal-clock, punched paper tape, and an
IBM 1620.

It is not enough just to put a number on something. We must remember
the early speed-of-light measurements that had a mean that turned out to be
outside of latter measurement's uncertainty band. An investigation of the
old log books found that not all of the data had been used! When all of the
data was used, the mean was within the more modern measurement's span.

73, Mac N8TT
--
J. Mc Laughlin; Michigan U.S.A.
Home:
"Richard Clark" wrote in message
...
On Thu, 30 Aug 2007 22:46:46 GMT, Owen Duffy wrote:

On Fri, 31 Aug 2007 20:43:42 -0400, "J. Mc Laughlin"
wrote:

I had the opportunity at Ohio State to craft a system that measured very
wide BW noise that changed slowly and to add statistical measures to what
was measured. Today, the task would be trivial - a sound card would run
circles around what I did with a voltage to frequency converter,
accumulator, counter-made-into-a-sidereal-clock, punched paper tape, and an
IBM 1620.

Hi Mac,

Last night at dinner, I had a conversation with a former HP exec and
we rambled on over glasses of Burgundy about how kids had lost access
to "flipping bits" on the computer, and instead played on them. What
this has in regard to the quote above is that newer technology may
have made everything simpler, but the laborious route you took drew
together many issues and gave you a visceral connection to the
process, building an instinct so to speak.

For instance, your allusion to counter-made-into-a-sidereal-clock may
not be fully appreciated for its "sidereal" quality which is a specie
of time with a continuous slip against civil time. This would be a
source of constant irritation for one being tugged away from their
Cesium Beam Standard. (At a rate of something roughly at 4 minutes a
day?)

So in some sense the solution becoming "trivial" removes intuition
from the problem.

73's
Richard Clark, KB7QHC

Owen Duffy wrote:
Jim Lux wrote in news:46D463CF.1080309
@jpl.nasa.gov:


Dave Oldridge wrote:

Owen Duffy wrote in news:Xns999955EE72868nonenowhere@
61.9.191.5:



Dave Oldridge wrote in
5.159:



Near as I could measure it, the NF of the receiver after my mod was
1.2db. I had to resort to boiling and freezing water and a tiny

dummy

load to measure it at all.

snip

This


still demands high resolution measurement of noise power.


Yes, anything less than 4 digits is just about useless.

That would be necessary but not sufficient.

...

Just following through on the '4 digit' issue...

I have done two series of 250 measurements of audio noise voltage from a
SSB receiver using two different digital multimeters, the 9932 is a
modern digital multimeter that is NOT true RMS responding, and the 506 is
a modern digital multimeter that is true RMS responding with bandwidth
adequate to cover the receiver output response.

From observation with a stopwatch, I estimate that the 9932 updates 3
times per second, and the 506 updates 2 times per second. The integration
times are probably .33 and .5 seconds respectively.

I have measured the receiver equivalent noise bandwidth and it is 1600Hz.

95% of 250 readings were within 0.41dB for the 9932 and 0.31dB for the
506. These observations reconcile well with my Chi-squared based estimate
of the uncertainty that I referred to in an earlier post.

As for the number of digits, they are both 4 digit multimeters which
doesn't mean a lot. They were used to measure 200mV with 1mV resolution,
so the representational error is 0.04dB.


Gotta be a bit careful there, because quantization error has a uniform
distribution, so the variance is 1/12 of the span. This is different
than the (presumably) normally distributed actual measurands.

When giving an uncertainty (sampling error), one should also say whether
it's a one sigma, two sigma, or 3 sigma number. *Standard uncertainty*
is 1 sigma... *expanded uncertainty*, often given as a +/- number is
usually the 95% percent confidence interval, which, for normal
distributions, is 2 sigma


given your statistics above, you would be giving the expanded
uncertainty as 0.41dB

By the way, unless your device actually directly measures dB (e.g. it
has a log detector) or the errors are inherently ratios, it's probably
better to give the value in a linear scale (milliwatts?) with the
uncertainty in the same units. That gets you around the "ratio" problem
where log(1+delta) -log(1-delta)

http://physics.nist.gov/cuu/Uncertainty/index.html has the simple
explanation, and the technical note (TN1297) , and references to the ISO
Guide to Expression of Uncertainty in Measurment (aka the GUM)


The error due to the number of
digits in this downscale three digit application is insignificant
compared to the sampling error of 0.4dB and 0.3dB.

Graphically, the distributions are shown at
http://www.vk1od.net/nfm/temp.gif .

Different meters with different integration times, and different
receivers with different noise bandwidth will result in different
outcomes, but I argue that the uncertainty is predictable.

Indeed, it is.


Owen

Jim Lux wrote in
:

Owen Duffy wrote:

...

Just following through on the '4 digit' issue...

I have done two series of 250 measurements of audio noise voltage
from a SSB receiver using two different digital multimeters, the 9932
is a modern digital multimeter that is NOT true RMS responding, and
the 506 is a modern digital multimeter that is true RMS responding
with bandwidth adequate to cover the receiver output response.

From observation with a stopwatch, I estimate that the 9932 updates 3
times per second, and the 506 updates 2 times per second. The
integration times are probably .33 and .5 seconds respectively.

I have measured the receiver equivalent noise bandwidth and it is
1600Hz.

95% of 250 readings were within 0.41dB for the 9932 and 0.31dB for
the 506. These observations reconcile well with my Chi-squared based
estimate of the uncertainty that I referred to in an earlier post.

As for the number of digits, they are both 4 digit multimeters which
doesn't mean a lot. They were used to measure 200mV with 1mV
resolution, so the representational error is 0.04dB.


Gotta be a bit careful there, because quantization error has a uniform
distribution, so the variance is 1/12 of the span. This is different
than the (presumably) normally distributed actual measurands.

Ok, point taken. I think more correctly, the maximum error would be 20
*log(1+1/200/2) or 0.0217dB.

The expected error due to representation in three digits does not account
for the variation in measurements.


When giving an uncertainty (sampling error), one should also say
whether it's a one sigma, two sigma, or 3 sigma number. *Standard
uncertainty* is 1 sigma... *expanded uncertainty*, often given as a
+/- number is usually the 95% percent confidence interval, which, for
normal distributions, is 2 sigma

Whilst it might be reasonable to assume that the combined error in
measurement of a high S/N sine wave voltage might be normally
distributed, and that might also be true of measurement of noise voltage
in some circumstances, I propose that measurement of noise power in
narrow bandwidth with short integration times is distributed as Chi-
squared and the number of samples becomes relevant in determining the
number of degrees of freedom for the distribution. For this reason, I
have talked about a confidence level rather than sigma (which is more
applicable to normally distributed data).

Just for interest, in the case of the 9932 measurement set:

Average=0.201, sigma=0.0046, 1sigma based uncertainty estimate=0.20dB,
2sigma based uncertainty estimate=0.41dB, 3sigma based uncertainty
estimate=0.62dB.



given your statistics above, you would be giving the expanded
uncertainty as 0.41dB

I stated it as 95% of obs within 0.41, I should have said 95% of obs
within +/-0.41, I was explicit about the implied confidence, the 95%
doesn't equate to either the 1sigma or 3sigma confidence, it is very
close to the 2sigma confidence (95.45%), and it is at the high confidence
end of the scale.


By the way, unless your device actually directly measures dB (e.g. it
has a log detector) or the errors are inherently ratios, it's probably
better to give the value in a linear scale (milliwatts?) with the
uncertainty in the same units. That gets you around the "ratio"
problem where log(1+delta) -log(1-delta)

I understand what you mean in your last sentence.

I did record the voltage, and converted the values to dB for analysis.
The interval was calculated by taking the average of the 2.5 percentile
and 97.5 percentile, which is an approximation, but as such small values
is pretty close.

I have converted results to dB to make it easier to see the relevance of
the error or uncertainty, but in so doing, another (small in this case)
error is introduced.


http://physics.nist.gov/cuu/Uncertainty/index.html has the simple
explanation, and the technical note (TN1297) , and references to the
ISO Guide to Expression of Uncertainty in Measurment (aka the GUM)

In terms of the above, I am proposing that measurements of narrowband
noise with short integration time is not strictly normally distributed,
and an estimate of its uncertainty to a given confidence level can be
obtained from the Chi-square distribution.

One could not estimate the results of the test from knowledge of the
instrument accuracy (inherent and representational error) alone.

I think the experiment supports the proposition that digital multimeters
with typically short integration times do not deliver high resolution
measurement of narrow band (eg SSB telephony) noise.

The error due to the number of
digits in this downscale three digit application is insignificant
compared to the sampling error of 0.4dB and 0.3dB.

Graphically, the distributions are shown at
http://www.vk1od.net/nfm/temp.gif .

Different meters with different integration times, and different
receivers with different noise bandwidth will result in different
outcomes, but I argue that the uncertainty is predictable.

Indeed, it is.

Thanks, appreciate the comments.

Owen

Owen Duffy wrote:
Jim Lux wrote in
:


Whilst it might be reasonable to assume that the combined error in
measurement of a high S/N sine wave voltage might be normally
distributed, and that might also be true of measurement of noise voltage
in some circumstances, I propose that measurement of noise power in
narrow bandwidth with short integration times is distributed as Chi-
squared and the number of samples becomes relevant in determining the
number of degrees of freedom for the distribution. For this reason, I
have talked about a confidence level rather than sigma (which is more
applicable to normally distributed data).

I would agree..

My question would be whether the original measurement (before averaging)
is normally distributed. I suspect it is, being essentially integrated
noise.

Owen Duffy wrote in
:

....
Graphically, the distributions are shown at
http://www.vk1od.net/nfm/temp.gif .

The graphic has a different URL, and is now incorporated in a write up of
the experiment, draft at http://www.vk1od.net/nfm/multimeter.htm .

Owen