# [time-nuts] theoretical Allan Variance question

Michael Wouters michaeljwouters at gmail.com
Sun Oct 30 00:04:09 EDT 2016

```Dear Stewart

FWIW, if you do the experiment I suggested (TI measurement on
identical 10 MHZ etc) on a HP53132A counter, you get ADEV = 2.0x10^-10
at 1 second.

The manual says the LSD is 150 ps; when you include trigger errors, it
specifies a resolution of 300 ps. The 200 ps implied by the
measurement above is somewhere in between. The specs may be
conservative though.

As Bob Camp said, in Situation 2, you see the noise of the measurement system.

Cheers
Michael

On Sun, Oct 30, 2016 at 1:17 PM, Bob Camp <kb8tq at n1k.org> wrote:
> Hi
>
> Well, situation one:
>
> You have two perfect sources.
> Your measuring device is noiseless
> If your devices are in perfect sync, you get a series of zeros
>
> Situation two:
>
> Same sources
> Noisy measuring device
> You get the standard deviation of the difference in measurements
> Your ADEV is simply a measure of the noise of the measuring device
>
> Situation three:
>
> Your sources are much worse than 1x10^-9 at 1 second
>
> Situation four:
>
> The real world, you have a bit of each and you really donâ€™t know
> what is what.
>
> Lots of possibilities and no single answer.
>
> Bob
>
>> On Oct 29, 2016, at 7:38 PM, Stewart Cobb <stewart.cobb at gmail.com> wrote:
>>
>> What's the expected value of ADEV at tau = 1 s for time-interval
>> measurements quantized at 1 ns?
>>
>> This question can probably be answered from pure theory (by someone more
>> mathematical than me), but it arises from a very practical situation. I
>> have several HP5334B counters comparing PPS pulses from various devices.
>> The HP5334B readout is quantized at 1 ns, and the spec sheet (IIRC) also
>> gives the instrument accuracy as 1 ns.
>>
>> The devices under test are relatively stable. Their PPS pulses are all
>> within a few microseconds of each other but uncorrelated.  They are stable
>> enough that the dominant error source on the ADEV plot out to several
>> hundred seconds is the 1 ns quantization of the counter. The plots all
>> start near 1 ns and follow a -1 slope down to the point where the
>> individual device characteristics start to dominate the counter
>> quantization error.
>>
>> One might expect that the actual ADEV value in this situation would be
>> exactly 1 ns at tau = 1 second.  Values of 0.5 ns or sqrt(2)/2 ns might not
>> be surprising. My actual measured value is about 0.65 ns, which does not
>> seem to have an obvious explanation.  This brings to mind various questions:
>>
>> What is the theoretical ADEV value of a perfect time-interval measurement
>> quantized at 1 ns? What's the effect of an imperfect measurement
>> (instrument errors)? Can one use this technique in reverse to sort
>> instruments by their error contributions, or to tune up an instrument
>> calibration?
>>
>> I'd be grateful for answers to any of these questions.
>>
>> BTW, thanks to whichever time-nuts recommended the HP5334B, back in the
>> archives; they're perfect for what I'm doing. And thanks to fellow time-nut
>> Rick Karlquist for his part in designing them.
>>
>> Cheers!
>> --Stu
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