# [time-nuts] Characterising frequency standards

Bruce Griffiths bruce.griffiths at xtra.co.nz
Wed Apr 8 12:11:17 UTC 2009

```Steve

It cant, it must be a matter of interpretation.
Perhaps it means something like:

1 tau means tau = 1x the interval between consecutive measurements.
2 tau means tau = 2x the interval between consecutive measurements

100000 tau means  tau = 100,000 x the interval between  consecutive
measurements

Bruce

Steve Rooke wrote:
> Bruce,
>
> But how does that explain the output of Tom's adev1 program which
> still seems to give a a good measurement at tau = 1s?
>
> 73,
> Steve
>
> 2009/4/8 Bruce Griffiths <bruce.griffiths at xtra.co.nz>:
>
>> Steve
>>
>> If you delete every second measurement then your effective minimum
>> sampling time is now 2s and you can no longer calculate ADEV for tau< 2s.
>> You can still calculate ADEV for tau = 100,000 sec.
>>
>> If you delete all but the first 200,000 lines then you can calculated
>> ADEV for tau=1sec and up to tau= 25,000 sec with reasonable accuracy.
>>
>> You shouldn't lose sight of the fact that ADEV and OADEV are both
>> estimates of the Allan deviation.
>>
>>
>> Bruce
>>
>> Steve Rooke wrote:
>>
>>> Tom,
>>>
>>> I understand fully the points that you have made but I have obviously
>>> not made my point clear to all and i apologise for my poor
>>> communication skills.
>>>
>>> This is what I'm getting at:
>>>
>>> Using your adev1.exe from http://www.leapsecond.com/tools/adev1.htm
>>> and processing various forms of gps.dat from
>>> http://www.leapsecond.com/pages/gpsdo-sim/gps.dat.gz.
>>>
>>> C:\Documents and Settings\Steve Rooke\Desktop>adev1.exe 1 <gps.dat
>>>
>>> ** Sampling period: 1 s
>>> ** Phase data scale factor: 1.000e+000
>>> ** Total phase samples: 400000
>>> ** Normal and Overlapping Allan deviation:
>>>
>>>        1 tau, 3.0127e-009 adev(n=399998),   3.0127e-009 oadev(n=399998)
>>>        2 tau, 1.5110e-009 adev(n=199998),   1.5119e-009 oadev(n=399996)
>>>        5 tau, 6.2107e-010 adev(n=79998),    6.1983e-010 oadev(n=399990)
>>>       10 tau, 3.1578e-010 adev(n=39998),    3.1549e-010 oadev(n=399980)
>>>       20 tau, 1.6531e-010 adev(n=19998),    1.6534e-010 oadev(n=399960)
>>>       50 tau, 7.2513e-011 adev(n=7998),     7.3531e-011 oadev(n=399900)
>>>      100 tau, 4.0029e-011 adev(n=3998),     4.0618e-011 oadev(n=399800)
>>>      200 tau, 2.1512e-011 adev(n=1998),     2.1633e-011 oadev(n=399600)
>>>      500 tau, 9.2193e-012 adev(n=798),      9.1630e-012 oadev(n=399000)
>>>     1000 tau, 4.9719e-012 adev(n=398),      4.7750e-012 oadev(n=398000)
>>>     2000 tau, 2.6742e-012 adev(n=198),      2.5214e-012 oadev(n=396000)
>>>     5000 tau, 1.0010e-012 adev(n=78),       1.1032e-012 oadev(n=390000)
>>>    10000 tau, 6.1333e-013 adev(n=38),       6.1039e-013 oadev(n=380000)
>>>    20000 tau, 3.8162e-013 adev(n=18),       3.2913e-013 oadev(n=360000)
>>>    50000 tau, 1.0228e-013 adev(n=6),        1.5074e-013 oadev(n=300000)
>>>   100000 tau, 5.8577e-014 adev(n=2),        6.7597e-014 oadev(n=200000)
>>>
>>> So far, so good. Now I delete every even line in the file which leaves
>>> me with 200000 lines of data (400000 lines in original gps.dat file).
>>> (awk 'and(NR, 1) == 0 {print}' <gps.dat >gps1.dat)
>>>
>>> C:\Documents and Settings\Steve Rooke\Desktop>adev1.exe 1 <gps1.dat
>>>
>>> ** Sampling period: 1 s
>>> ** Phase data scale factor: 1.000e+000
>>> ** Total phase samples: 200000
>>> ** Normal and Overlapping Allan deviation:
>>>
>>>        1 tau, 3.0257e-009 adev(n=199998),   3.0257e-009 oadev(n=199998)
>>>        2 tau, 1.5373e-009 adev(n=99998),    1.5345e-009 oadev(n=199996)
>>>        5 tau, 6.3147e-010 adev(n=39998),    6.3057e-010 oadev(n=199990)
>>>       10 tau, 3.3140e-010 adev(n=19998),    3.3067e-010 oadev(n=199980)
>>>       20 tau, 1.7872e-010 adev(n=9998),     1.7810e-010 oadev(n=199960)
>>>       50 tau, 7.9428e-011 adev(n=3998),     8.1216e-011 oadev(n=199900)
>>>      100 tau, 4.2352e-011 adev(n=1998),     4.3265e-011 oadev(n=199800)
>>>      200 tau, 2.2001e-011 adev(n=998),      2.2593e-011 oadev(n=199600)
>>>      500 tau, 9.6853e-012 adev(n=398),      9.5441e-012 oadev(n=199000)
>>>     1000 tau, 5.0139e-012 adev(n=198),      5.0387e-012 oadev(n=198000)
>>>     2000 tau, 2.7994e-012 adev(n=98),       2.7090e-012 oadev(n=196000)
>>>     5000 tau, 1.4280e-012 adev(n=38),       1.2214e-012 oadev(n=190000)
>>>    10000 tau, 7.4881e-013 adev(n=18),       6.5814e-013 oadev(n=180000)
>>>    20000 tau, 7.6518e-013 adev(n=8),        3.7253e-013 oadev(n=160000)
>>>    50000 tau, 2.4698e-014 adev(n=2),        1.3539e-013 oadev(n=100000)
>>>
>>> Obviously we don't have enough data now for a measurement of 100000
>>> tau but the results for the other tau are quite close, especially when
>>> there are sufficient data points. Now this is discontinuous data,
>>> exactly what I was trying to allude to.
>>>
>>> OK, so now I take only the top 200000 lines of the gps.dat file (head
>>> -200000 gps.dat >gps2.dat)
>>>
>>> C:\Documents and Settings\Steve Rooke\Desktop>adev1.exe 1 <gps2.dat
>>>
>>> ** Sampling period: 1 s
>>> ** Phase data scale factor: 1.000e+000
>>> ** Total phase samples: 200000
>>> ** Normal and Overlapping Allan deviation:
>>>
>>>        1 tau, 3.0411e-009 adev(n=199998),   3.0411e-009 oadev(n=199998)
>>>        2 tau, 1.4985e-009 adev(n=99998),    1.4999e-009 oadev(n=199996)
>>>        5 tau, 6.1964e-010 adev(n=39998),    6.2010e-010 oadev(n=199990)
>>>       10 tau, 3.1315e-010 adev(n=19998),    3.1339e-010 oadev(n=199980)
>>>       20 tau, 1.6499e-010 adev(n=9998),     1.6495e-010 oadev(n=199960)
>>>       50 tau, 7.1425e-011 adev(n=3998),     7.3416e-011 oadev(n=199900)
>>>      100 tau, 3.9940e-011 adev(n=1998),     4.0730e-011 oadev(n=199800)
>>>      200 tau, 2.1488e-011 adev(n=998),      2.1558e-011 oadev(n=199600)
>>>      500 tau, 8.4809e-012 adev(n=398),      9.0886e-012 oadev(n=199000)
>>>     1000 tau, 4.9223e-012 adev(n=198),      4.7104e-012 oadev(n=198000)
>>>     2000 tau, 2.4335e-012 adev(n=98),       2.4515e-012 oadev(n=196000)
>>>     5000 tau, 1.0308e-012 adev(n=38),       1.0861e-012 oadev(n=190000)
>>>    10000 tau, 5.9504e-013 adev(n=18),       6.1031e-013 oadev(n=180000)
>>>    20000 tau, 3.6277e-013 adev(n=8),        3.1994e-013 oadev(n=160000)
>>>    50000 tau, 1.0630e-013 adev(n=2),        1.6715e-013 oadev(n=100000)
>>>
>>> Is there any Linux tools for calculating adev as I'm having to run
>>> Windows in a VMware session?
>>>
>>> 73,
>>> Steve
>>>
>>> 2009/4/8 Tom Van Baak <tvb at leapsecond.com>:
>>>
>>>
>>>> Steve,
>>>>
>>>> You've asked a couple of questions. Let me start with this.
>>>>
>>>> It is true that if one were only interested in the performance
>>>> of a pendulum (or quartz or atomic) clock for averaging times
>>>> of one day that all you would need is a series of time error
>>>> (aka phase) measurements made about the same time once
>>>> a day (doesn't have to be that exact). After one week, you'd
>>>> have 7 error measurements (=6 frequency =5 stability points)
>>>> and this is adequate to calculate the ADEV for tau 1 day.
>>>> This alone allows you to rank your clock among all the other
>>>> pendulum clocks out there. Note also you get time error and
>>>> rate error from these few data points too.
>>>>
>>>> As another example, suppose you have a nice HP 10811A
>>>> oscillator and want to measure its drift rate. In this case you
>>>> could spend just 100 seconds and measure its frequency
>>>> once a day, or even once every couple of days. Do this for
>>>> a month and you'd have several dozen points. If you plot
>>>> these frequency measurements you will likely see that they
>>>> approximately fall on a line; the slope of the is the frequency
>>>> drift rate of the 10811. The general shape of the points, or
>>>> the fit of the line is a rough indication of how consistent the
>>>> drift rate is or if it's increasing or decreasing.
>>>>
>>>> Neither of these examples require a lot of data. Both of these
>>>> are real-world examples.
>>>>
>>>> OK so far?
>>>>
>>>> /tvb
>>>>
>>>>
>>>>
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>>>>
>>>>
>>>>
>>>
>>>
>>>
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>
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>

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