Dear John & Magnus,
thank you very much for your detailed explanation. I realize
that the averaging topic is much more complex than I thought
- it certainly gives me something to think about :-) I never
thought in terms of noise bandwith in this application,
thanks for putting me on this track.
It seems that the simplest and safest way to get meaningfull
results is to hook up two mixers and a hand full of opamps
and comparators.
To learn more, I think the best way would be to put the
counter into its fast binary mode and acquire 1k time
interval samples per second. That would give me loads of
data to play with and it would be easy to try out how
different averaging schemes affect the result.
I´ll have to read and think some more :-)
Cheers,
Matthias
Am 19.08.2015 um 21:52 schrieb Magnus Danielson:
Dear Mathias,
On 08/19/2015 06:40 PM, Matthias Jelen wrote:
Hello,
I´ve got a question concerning ADEV-measurements.
I´m measuring the 15 MHz output of a KS-24361 with my
SR-620 with it´s
internal (Wenzel) OCXO using Timelab. For the first shot
I used the
counters frequency mode with 1s gatetime. ADEV at tau=1s
turned out to
be arounf 2E-11, which fits the 20 ps single shot
resolution of the
SR-620 nicely.
To overcome this limitation without setting up a DMTD
system, I used the
counter as TIC, feeding 1 kHz (derived from the counter´s
reference) to
the start channel, the 15 MHz to the stop channel and put
the counter
into average mode / 1k samples. This gives me one
averaged result per
second.
The idea was that this shouldn´t change the measurement
itself, because
like in frequency mode with 1s gate time I get the
averaged value over
one second, but I expected trigger noise etc. to be
averaged out to a
certain amount. I have to watch out for phase wraps, but
as the two
frequencys are quite equal, this is not a big issue here.
As expected, ADEV at tau=1s got much better, it is now in
the 4E-12
area, which sound reasonable.
What makes me wonder is the fact that result are
significantly better
now at longer taus (10..100s) also, despite of the fact
that also in
frequency mode these result were well aboce the noise
floor (2E-12 @ 10s
and so on...).
So, is it a good idea to use this kind of averaging, or
am I overlooking
something which turns the numbers better than they really
are? I´m
pretty sure I am not the first one to try this...
I´m looking forward to your comments.
OK, averaging or filtering of data before ADEV processing
is tricky, as it filters the data. Whenever you do that,
you actually convert your measurement from an ADEV measure
to something else. If you do proper post-processing, this
something else can have known properties and thus we can
relate the amplitude of the curve to amplitude of various
noise sources, as it will cause biasing from the ADEV
properties.
The reason you get better results is because the ADEV
response on white noise depends on the measurement system
bandwidth (see Allan deviation wikipedia page), and by
averaging you do reduce the bandwidth.
Sometimes when you do this, you loose the gain as you
increase the tau, since the dominant frequency will lower
and become more and more into the pass-band of the fixed
bandwidth filter you created. What you see is that it
flattens out to the length of the average before lowering
down, as if there was no filtering, so you have only
achieved a gain in skewed value for very short taus, but
then no gain at all for longer taus, so no real gain.
This was realized in 1980-1981 and in 1981 an article was
published in which they realized that they can change the
bandwidth along-side the change of tau, so that the gain
remains. This became the modified Allan deviation (MDEV),
and was inspired by the methods for improving frequency
measures for lasers as presented by J.J. Snyder in 1980
and 1981. J.J. Snyder was doing what you proposes,
averaging of blocks, and then extended this in software,
and this became a direct inspiration for the MDEV
development, which does a pre-averaging over tau before
processing through ADEV, and this combined is the MDEV.
Doing TIC averaging and then continue the processing with
MDEV processing should produce a proper MDEV curve, unless
my tired brain does not miss out on details. If you then
analyze it as a MDEV (rather than ADEV) then you use the
values properly. MDEV have the benefit that white phase
noise drops by tau^-1.5 rather than the ADEV tau^-1, and
starting with the SR-620 means you for fairly low taus hit
actual measurement noise. The averaging makes this trip
from tau0 of 1 ms in your setup.
So, you can go down this route, but you need to be careful
to ensure that you have done the processing correctly
enough that you get the results that can be interpreted
properly.
Oh, as you average, phase-unwrapping becomes
"interesting". :)
Cheers,
Magnus
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