32.768hKh tuning fork cut quartz crystal - stability question

[aurmer]

I am using this 32.768kHz Crystal, and my requirement is for long term accuracy while I don't care about stability between pulses. Can I actually assume that the error caused by instability has a Gaussian distribution around zero? In other words, is it realistic to ignore the (in)stability when determining the drift tolerance of the oscillator?

Assume that I correctly calibrated the accuracy against a reliable frequency reference. Each unit is calibrated in production using an inhibition compensation technique.

[guenthert]

Not quite sure, I understand the question.  If there is noise, then it might be Gaussian distributed, but you are already aware of the fact that in addition to noise, there is drift (presumably temperature and age related), to which I have difficulties attributing the term 'distribution' to.

[aurmer]

I suppose there is a more simple way to ask my question. Let's say that I calibrate my oscillator circuit in a controlled environment 25C, and all subsequent tests are done at the same temp, within a week so as to reduce the "aging" factor to negligible.

I understand that the XO has some instability and that no two oscillations of that circuit are guaranteed to have the same period. But if I measure 10^8 oscillations (this works out to almost a 24hr timespan), and I measure that number of pulses over and over again, should I expect that the error caused by frequency instability to be negligible? Will the frequency jitter average out to zero over long sampling periods?

-Another way to put it
 --- My Xtal's datasheet says it will perform within a 10ppm jitter tolerance, but if the jitter error averages out to be zero over a long period of time, then I can assume that there is no error due to that +/-10ppm jitter. Is this a reasonable assumption?

I am purely talking about error as it relates to jitter, not temp fluctuation and not aging.

I simply do not have the equipment at this time to conduct these tests quickly and with accuracy, so I am asking the theoretical question here.

[Dr. Frank]

I am using this 32.768kHz Crystal, and my requirement is for long term accuracy while I don't care about stability between pulses. Can I actually assume that the error caused by instability has a Gaussian distribution around zero? In other words, is it realistic to ignore the (in)stability when determining the drift tolerance of the oscillator?

Assume that I correctly calibrated the accuracy against a reliable frequency reference. Each unit is calibrated in production using an inhibition compensation technique.

There are several different noise or instability source which can be distinguished by different observation time scales, like tau = 0..1 sec, 1..100sec, > 1000sec, for example.

This concept is called Allan deviation, a graph which gives the instability figure for each time scale.

The short to midterm scales refer to "noise" instabilities, where you might also have non-Gaussian distribution.

The longterm scales more or less refer to drift terms, quasi ignoring or filtering these noise components.
In this sense, it's possible to measure the drift, isolated from noise.

I propose to visit some time-nuts sites where these statistics are visualized, like this fine one:
http://www.ko4bb.com/getsimple/index.php?id=timing-faq-1-measuring-oscillators-stability

Frank