# [time-nuts] theoretical Allan Variance question

Bob Camp kb8tq at n1k.org
Sat Oct 29 22:17:26 EDT 2016

```Hi

Well, situation one:

You have two perfect sources.
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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