Hi!
From: "Magnus Danielson" <[email protected]>
ADEV assumes brick-wall filtering up to the Nyquist frequency as result
of the sample-rate. When you filter the data as you do a Linear
Regression / Least Square estimation, the actual bandwidth will be much
less, so the ADEV measures will be biased for lower taus, but for higher
taus less of the kernel of the ADEV will be affected by the filter and
thus the bias will reduce.
Thanks for clarification. Bob already pointed me to problem and after some
reading *DEV theme seems to be clearer.
Does the ADEV plots I got looks reasonable for the used "mid range"
OCXOs (see the second plot for the long run test)?
You probably want to find the source of the wavy response as the orange
and red trace.
I have already found the problem. It is HW problem related to poor isolation
between reference OCXO signal and counter input signal clock line (it is
also possible there are some grounding or power supply decoupling problems -
the HW is made in "ugly construction" style). When the input clock frequency
is very close (0.3..0.4Hz difference) to the OCXO subharmonic this problem
become visible (it is not FW problem discussed before, cause counter
reference is not a harmonic of the OCXO anymore). It looks like some
commercial counters suffers from that problem too. After I connected OCXO
and input feed lines with short pieces of the coax this effect greatly
decreased, but not disappeared. The "large N" plots were measured with the
input signal 1.4Hz (0.3ppm) higher then 1/2 subharmonic of the OCXO
frequency, with such frequency difference that problem completely
disappears. I will check for this problem again when I will move the HW to
the normal PCB.
If fact, you can do a Omega-style counter you can use for PDEV, you just
need to use the right approach to be able to decimate the data. Oh,
there's a draft paper on that:
https://arxiv.org/abs/1604.01004
Thanks for the document. It needs some time to study and maybe I will add
the features to the counter to calculate correct PDEV.
If ADEV is needed, the averaging
interval can be reduced and several measurements (more then eight) can
be combined into one point (creating the new weighting function which
resembles the usual Pi one, as shown in the [1] p.54), it should be
possible to calculate usual ADEV using such data. As far as I
understand, the filter which is formed by the resulting weighting
function will have wider bandwidth, so the impact on ADEV will be
smaller and it can be computed correctly. Am I missing something?
Well, you can reduce averaging interval to 1 and then you compute the
ADEV, but it does not behave as the MDEV any longer.
With no averaging it will be a simple reciprocal counter with time
resolution of only 2.5ns. The idea was to use trapezoidal weighting, so the
counter will become somewhere "between" Pi and Delta counters. When the
upper base of the weighting function trapezium is 0 length (triangular
weighting) it is usual Delta counter, if it is infinitely long the result
should converge to usual Pi counter. Prof. Rubiola claims if the ratio of
upper to lower base is more than 8/9 the ADEV plots made from such data
should be sufficiently close to usual ADEV. Of cause the gain from the
averaging will be at least 3 times less than from the usual Delta averaging.
Maybe I need to find or make "not so good" signal source and measure its
ADEV using above method and compare with the traditional. It should be
interesting experiment.
What you can do is that you can calculate MDEV or PDEV, and then apply
the suitable bias function to convert the level to that of ADEV.
That can be done if the statistics is calculated inside the counter, but it
will not make the exported data suitable for post processing with the
TimeLab or other software that is not aware of what is going on inside the
counter.
Yes, they give relatively close values of deviation, where PDEV goes
somewhat lower, indicating that there is a slight advantage of the LR/LS
frequency estimation measure over that of the Delta counter, as given by
it's MDEV.
Here is another question - how to correctly calculate averaging length in
Delta counter? I have 5e6 timestamps in one second, so Pi and Omega counters
process 5e6 samples totally and one measurement have also 5e6 samples, but
the Delta one processes 10e6 totally with each of the averaged measurement
having 5e6 samples. Delta counter actually used two times more data. What
should be equal when comparing different counter types - the number of
samples in one measurement (gating time) or the total number of samples
processed?
Thanks!
Oleg
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