# [time-nuts] Characterising frequency standards

Magnus Danielson magnus at rubidium.dyndns.org
Mon Apr 13 12:09:57 UTC 2009

```Steve,

Steve Rooke wrote:
> Bruce,
>
> 2009/4/12 Bruce Griffiths <bruce.griffiths at xtra.co.nz>:
>> Steve
>>
>> Steve Rooke wrote:
>>> If I take two sequential phase readings from an input source and place
>>> this into one data set and aniother two readings from the same source
>>> but spaced by one cycle and put this in a second data set. From the
>>> first data set I can calculate ADEV for tau = 1s and can calculate
>>> ADEV for tau = 2 sec from the second data set. If I now pre-process
>>> the data in the second set to remove all the effects of drift (given
>>> that I have already determined this), I now have two 1 sec samples
>>> which show a statistical difference and can be fed to ADEV with a tau0
>>> = 1 sec producing a result for tau = 1 sec. The results from this
>>> second calculation should show equal accuracy as that using the first
>>> data set (given the limited size of the data set).
>>>
>>>
>> You need to give far more detail as its unclear exactly what you are
>> doing with what samples.
>> Label all the phase samples and then show which samples belong to which
>> data set.
>> Also need to show clearly what you mean by skipping a cycle.
>
> Say I have a 1Hz input source and my counter measures the period of
> the first cycle and assigns this to A1. At the end of the first cycle
> the counter is able to be rest and re-triggered to capture the second
> cycle and assign this to A2. So far 2 sec have passed and I have two
> readings in data set A.
Strange counter. Traditionally counters rests after the stop event have
occured, since they cannot know anything else.The Gate time gives a hint
on the first point in time it can trigger, the gate just arms the stop
event. There is no real end point. It can however rest and retrigger the
start event ASAP when gate times are sufficiently large. It's just a
smart rearrangement of what to do when to achieve zero dead-time for
period/frequency measurements.

You could also use a counter which is pseudo zero dead time in that it
can time-stamp three values, two differences without deadtime but has
deadtime after that. Essentially two counters where the stop event of
the first is the start event of the next.
> I now repeat the experiment and assign the measurement of the first
> period to B1. The counter I am using this time is unable to stop at
> the end of the first measurement and retrigger immediately so I'm
> unable to measure the second cycle but is left in the armed position.
> When the third cycle starts, the counter triggers and completes the
> measurement of the third cycle which is now assigned to B2.
This is what most normal counters do.
> For the purposes of my original text, the first data set refers to A1
> & A2. Similarly the second data set refers to B1 & B2. Reference to
> pre-processing of the second data set refers to mathematically
> removing the effects of drift from B1 & B2 to produce a third data set
> which is used as the data input for an ADEV calculation where tau0 = 1
> sec with output of tau = 1 sec.
You would need to use bias adjustments, but the B1 & B2 period/frequency
samples is badly tainted data and should not be used.having a deadtime
at the size of tau0 is serious bussness. Removing the phase drift over
the dead time does not aid you since if you remove the phase ramp of the
evolving clock, that of f*t or v*t (depending on which normalisation you
prefer), you have the background phase noise. What we want to do is to
characterize this phase noise. Taking two samples of it back-to-back and
taking two samples with a (equalent sized length) gap becomes two
different filters. Maybe some ascii art may aid:
__
__   |  |__
|__|

y1 y2 y3
A1 A2

A2-A1 = y2-y1

vs.
__
__    __|  |__
|__|

y1  y2   y3
B1        B2

B2-B1 = y3-y1

Consider now the case when frequency samples has twice the tau of the
above examples
_____
__      |     |__
|_____|

y1    y2
y2-y1

These examples where all based on sequences of frequency measurements,
just as you indicate in your caes.

As you see on the differences, the nominal frequency cancels and the
nominal phase error has also cancled out, so there is nothing to
compensate there. Drift rate would however not be canceled, but for most
of our sources, the noise is higher than the drift rate for shorter taus.

Time-differences allows us to skip every other cycle thought.
>>> I now collect a large data set but with a single cycle skipped between
>>> each sample. I feed this into ADEV using tau0 = 2 sec to produce tau
>>> results >= 2 sec. I then pre-process the data to remove any drift and
>>> feed this to ADEV with a tau0 = 1 sec to produce just the tau = 1 sec
>>> result. I now have a complete set of results for tau >= 1 sec. Agreed,
>>> there is the issue of modulation at 1/2 input f but ignoring this for
>>> the moment, this should give a valid result.
>>>
>>>
>> Again you need to give more detail.
>
> In this case the data set is constructed from the measurement of the
> cycle periods of a 1Hz input source where even cycles are skipped,
> hence each data point is a measurement of the period of each odd (1,
> 3, 5, 7...) cycle of the incoming waveform. In this case the time
> between each measurement is 2 sec so ADEV is calculated with tau = 2
> sec for tau >= 2 sec. This data set is then mathematically processed
> to remove the effects of drift, bearing in mind the 2 sec spacing of
> each data point, and ADEV is then calculated with tau0 = 1 sec for tau
> = 1 sec.
How did you establish the effect of drift?
>> What noise from what source?
>
> PN - White noise phase WPM, Flicker noise phase FPM, White noise
> frequency WFM, Flicker noise frequency FFM and Random walk frequency
> RWFM.
These are just the names for the various 1/f power noises. They enter
through a myriad of places, white phase noise and 1/f is common to
amplifiers, 1/f^5 is thermal noise onto the same amplifiers. 1/f^2 is
oscillator shaped white phase noise and 1/f^3 is oscillator shaped 1/f
noise. Rubiola spends quite some time on that subject, both in his
excelent book and in various papers.
>> Noise in such measurements can originate in the measuring instrument or
>> the source.
>
> Indeed, and this is an important aspect to consider as we have been
> discussing the effects of induced jitter/PN to a frequency standard
> when it is buffered and divided down. Ideally measurements of ADEV
> would be made on the raw frequency standard source (eg. 10MHz) rather
> than, say, a divided 1Hz signal.
Yes and no. There are benefits in dividing it down, you can identify
cycle slips easier and adjust for them, where as one 10 MHz cycle to
1 s using a 1 Hz signal is not optimum thought. A slightly higher rate
will allow for quicker gathering of high statistical freedom and thus
improved statistical stability as allowed through the overlapping Allan
Deviation estimator as compared to use the non-overlapping Allan
Deviation estimator on the same time-stretch of samples. When running
long runs, sufficient freedom may be achieved even using the
non-overlapping estimator.

A divide down does not have to make significant change to phase-noise,
its effect can be minimized as we have discussed before.

The 1 PPS signal is also quite historical artifact which is still quite
handy. It allows direct comparision of non-equalent frequencies as the
division ration is adjusted. It is also what comes out of a majority of
GPS receivers. Few GPS receivers evaluate their time offset at a faster
rate than 1 Hz anyway, but 2, 5, 10 and 20 Hz is available. The L1 C/A
signal would allow for a rate of 1 kHz but it would require really good
signal conditions.

For high resolution work, the PPS is not that good, since beating two 10
MHz would give you some 5-7 decades of better resolution if you can
handle the problems with slow slopes.
>> For short measurement times quantisation noise and instrumental noise
>> may mask the noise from the source but they are still present.
>
> Well, these form the noise floor of our measurement system.
Some of them we can control, though better triggering devices, as
learned the hard way and investigated by many.

Other ways to handle it is to use cross-correlation techniques where two
independent system noises sees the same signal, in which case only the
input source noise correlate and the system noise effect can be
partially canceled out.

There are systematic noise problems also, such as lack of zero dead
time, resolution, interpolator distorsion etc.

Cheers,
Magnus

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