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