Warren
Calculating an integral using a sampled data system when the Nyquist
criterion is met is exactly equivalent to filtering albeit using just
the right coefficients.
Using rectangular approximation to the integral of the underlying
continuous function is also equivalent to a filter albeit a very simple one.
Unfortunately rectangular integration (which you use) isnt particularly
accurate, using trapezoidal integration is far more accurate in most cases.
Since this isnt a control system the instability associated with
trapezoidal integration and higher order integration algorithms in
feedback systems isnt an issue.
Whittaker-Shannon-Kotelnikov interpolation allows an exact
reconstruction (when the Nyquist sampling criterion is met) of the
underlying continuous function from the samples.
The result can then be integrated term by term to produce a set of
weights/filter coefficients for the data samples.
In other words in a sampled data system integration is equivalent to
using a filter.
Near enough is never good enough if you cant estimate the errors
involved in the various approximations.
This is particularly true when one is attempting to evaluate the
deviation of an approximate method from that achieved using the correct
method.
Bruce
WarrenS wrote:
Bruce
So why are you saying I need millions of samples?
Is it that this method of integration may give the wrong answer one
out a million times?
And you will not let up until you find that one in a million times
that it may error?
I don't think you're going to find it, but if you want we can go with
that.
BTW It does NOT need ANY scale factors, special or otherwise to give
the right answers.
It uses the same scale factor of ONE for ALL noise sources.
If you can't give me an example of a data log that it may fail on,
that I can run thru excel to prove otherwise, then
We're done here until next time.
ws
***************
*************
The results have so far only been shown to be useful when white phase
noise dominates.
When the phase noise is white almost anything can be made to produce a
result that differs from ADEV by at scale factor.
In practice its sometimes difficult to know over what range of Tau that
the phase noise is in fact white.
The various tests and comparisons that have been made or are underway
are necessary but not sufficient proof of the usefulness of this
technique.
The phase noise frequency response of the technique is also required so
that its limitations can be delineated.
1000 samples of a divergent noise process are insufficient, spreadsheet
analysis of the millions of samples that are probably necessary is
impossible/impractical.
Using something like Matlab is probably necessary to achieve meaningful
results.
Bruce
*******************
WarrenS wrote:
OK, So, It is not perfect, but its simple and does give answers that
are GOOD enough.
At least you now understand if the integrator works then the tester
works.
So that we do not go down hill again after all this progress,
If you would like to send me a data file of say 1000 + samples of any
noise type of your choice
I'll send you back an excel spread sheet to show the insignificant
error that this integration method produces.
ws
****************
You cannot approximate the sinc function frequency response of an ideal
integrator with an arbitrary low pass filter.
Your scheme will tend to misbehave (in that it will produce anomalous
ADEV estimates) when flicker phase noise is significant.
You actually need to use an analog low pass filter (or its equivalent)
and an integrator to produce useful ADEV measures
Bruce
***************
WarrenS wrote:
(My apologies to all, this is a game Bruce and I play every time I
bring up my simple tester.)
Bruce wrote:
"So you now actually integrate/average the frequency over the sampling
interval (Tau) after rejecting the need to do this for months?"
Yes, I integrate/average just the same as I have always done it from
day one.
Did you finally understand how the integration works using most any
ADC?
Hint: it's done with oversampling the tau zero time.
(and a LP filter set to a value above the tau zero but below the
oversamping rate)
The VERY SAME thing I have been trying to tell you from day one,
something that you have chosen to ignore.
The very original Block diagram that I posted shows it, if you need
more information.
ws
*******************
Warren
So you now actually integrate/average the frequency over the sampling
interval (Tau) after rejecting the need to do this for months?
Bruce
*****************
WarrenS wrote:
Bruce
Before we go around again and discuses what my simple tester can and
can not do and why,
It would be helpful if you would take the time to better understand
how it works and why it works the way I have done it.
You really should try one yourself if you can't see why it works.
You are going to be surprised and embarrassed at how good it works.
Why you're at it, try the "swing test" with anything you have. Let me
know how that goes.
I'm not saying that may tester will match someone's Latest ever
changing NEW idea of what the "correct AVAR" should be,
After all it just Logs correct, integrated, Freq difference data of
ANY noise type
and does it without adding any dead time or aliasing all by using
pretty much using ANY ADC capability of over sampling at the tau Zero
rate.
If one then uses the data log with something like the classic Stable
32 S/W or Ulrich's Plotter,
it gives is the exact same results as other methods costing much much
more, over the whole tau range.
This is limited only be its reference oscillator (Same way that all
others are limited of course, Doesn't get much better than that).
If that is not good enough for you, them you need to discuss the
results with Symmetricon and others that give the same answer as mine,
not me.
If for some reason you want to set one up wrong so that it matches the
results of some other special instrument, I'd be glad to tell you how
to have it add back in the dead time or aliasing artifact problems or
whatever else you would like it to do wrong, that it presently does
correctly.
ws
******************
Bruce wrote
As long as one is aware that your method (as implemented by you)
doesn't
actually measure Allan variance, it may be useful for comparing the
relative stability some sources for small Tau (unfortunately the range
of Tau for which the method may produce useful results depends on the
phase noise characteristics of the sources being compared).
To measure AVAR the technique has to have the same response to all
phase
noise spectral components as does AVAR.
Since you do not integrate/average the frequency measures the phase
noise response of the method is not identical to that used in
calculating AVAR.
This technique probably works best when white phase noise dominates
the
phase noise spectral region of interest (usually for small Tau).
For those who can follow the theory, the following paper shows how the
above method is affected by aliasing etc:
http://hal.archives-ouvertes.fr/docs/00/37/63/05/PDF/alaa_p1_v4a.pdf
The paper also shows how the required integration (needed to actually
measure AVAR) can be approximated from the discrete sample sequence.
Alternatively one could avoid the numerical integration by replacing
the
ADC with a zero deadtime (ie not a dual slope converter. A multislope
algorithm like that used in the 34401A (but not the 3458A) should work
as the signal is integrated continuously) integrating ADC. One
possibility is to use a VFC as NIST did when they used this technique
some decades ago.
Of course, the classical DMTD setup undersamples the phase noise
spectrum and thus may suffer from aliasing artifacts.
Such aliasing artifacts have no significant effect when the phase
noise
spectrum is flat.
Bruce
*********************
WarrenS wrote:
For the Really cheap time nuts,
It sounds like Bert Kehren has done a great Job building a Dual Mixer
tester.
There are other simpler, less standard ways to get good data for
Allan
Variance and small frequency differences.
My VERY simple $10.00 analog tight PLL Tester BB (Previously posted)
pretty much accomplishes the same goals as his,
and it can do 1e-13 in a second, and 1e-11 in 10ms (limited of
course
by the single reference Oscillator used)
A simple test that most can do at home, and still challenges the best
high end testers out there is Tom's the swinging Oscillator test.
http://www.leapsecond.com/pages/10811-g/
(The results from my PLL tester is attached)
ws
******************
----- Original Message ----- From: <EWKehren at aol.com>
To: <time-nuts at febo.com>
Sent: Tuesday, May 11, 2010 7:02 AM
Subject: [time-nuts] Dual Mixer
The Dual Mixer project is nearing completion.
Let me refresh every ones memory as to my goals.
a) Total cost less than $ 200
b) 1 E-13 with a one second offset
c) use parts attainable by every one
d) easy to assemble only a few surface mount parts
e) a five channel counter that yields 1 E 15 resolution and
interfaces
directly to a PC via RS232 or USB
f) A counter that also gives you instant frequency difference at
the
sample rate, not only Allan Variance
g) Modular so one can use only the Dual Mixer
h) Modular so one can use multiple units to do simultaneous
comparison of
more than two oscillators.
i) Isolation between D/M and counter so that the counter can be
powered
by the PC USB port
I am happy to report that all goals have been accomplished, attached
is a
picture of the D/M, limitation of the file size does not allow me to
attach
an actual board picture, but if you contact me direct I will send
you one,
the final board is actually nicer since the first layout had to
accommodate
several variances.
The D/M part leans heavy on the original NIST unit with a few
substitutions
and recommendations from Bob Camp. Also beside Opto Couplers
SN65LVDS1's
have been included for those that want to use other counting
methods.
Selection of filter capacitors allow the use at other offset
frequencies such as
10 and 100 Hz. The D/M fits in a standard 74 X 111 X 20 mm Euro
case
and
the counter can be stacked below or next to it using the Opto
Isolators as
the inter connect. The SYPD-1's fit right on the board but
connections are
included to use the HP 10514 A. As a matter of fact removing the HP
mixer
board from its housing fits it nicely on the board and every thing
is still
inside the housing.
The counter will handle 1 an 10 Hz offset with a 1 E 14 resolution
at 10
Hz. Thanks to Richard Mc Corkle we have great drawings and code,
available to
every one.
Code, drawings, list of material and PC board layouts and its file,
will
be available to every one once the project is completed.
I need help in the following areas
a) help me create a nice set of drawings that are computer
generated
something I am not able to do
b) create the computer program that takes the output of the counter
board
and allows Allan Variance plots, frequency difference and dual
temperature
readings and plots using RS232 and USB.
c) an independent test by a third party.
As I said previously, I am not getting in the business of supplying
parts
but will work with people that will help achieve the three points
listed
above. Presently I have boards on order and will have two
uncommitted board
sets and probably also component kits.
Please contact me directly.
Again thank you Corby Dawson, Richard Mc Corkle and Bob Camp.
Bert Kehren Miami
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