[time-nuts] How to measure 1 sec tau

Bruce Griffiths bruce.griffiths at xtra.co.nz
Sat Sep 12 22:30:20 UTC 2009

WarrenS wrote:
> tau expert's advice sought
> Basically my question is that is the correct bandwidth to use when taking 1 sec and above tau data?
> What I want to know is how to record raw 1 second phase data to use for calculating 1 sec and above tau.
> Should I including in the data the results of every high freq noise source in the system?
> My limited understanding is that none of the high freq noise has any true effect on the 1 sec freq stability of the Osc.
> Would it not be better, when all I want to know is how much the Osc freq is changing from second to second
>  is to take the 'average' phase error over the previous 1 second period to use as each raw data point.  
> i.e oversample to get rid of the high freq noise.
> When I want to know how the Phase is changing between two high freq Osc,
> what I now use to get the highest accuracy and resolution possible, 
> is a 1 sec time interval average running at from 1 KHz to 10 MHz.
> By averaging 1000 to 10 million answers over a 1 second period the 
> phase shift noise is reduced and the resolution increased by 10 to 1000 times
> over what it would be if I just took a single sample each second.
> With this technique I'm able to get phase noise resolution down in the low fs. (< 0.01ps)
> Some have told me that this will give wrong false tau answer. 
> Maybe so, I do not know enough about what noise sources should be includes in tau.
> My though is, I am only interested in 1 second and above stability of my osc 
> and not the high freq noise of my Osc or test system, so this is the best way to get the correct answer
> My test have shown that this 1 sec averaging does not change the 1 sec 
> and above tau answers, it just lowers the noise floor.
> ws
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The attached equation is used to calculate AVAR from the phase noise
indicates that contribution of both flicker phase modulation (h_1 term)
and white phase modulation (h_2 term) depend on the AVAR measurement
system noise bandwidth.

Thus when the other terms in the phase noise spectrum dominate changing
the system noise bandwidth will have little effect.
However the range of Tau values for which both flicker PM and white PM
are insignificant varies from one source pair to the next.

Since both your oscillator pair and your detector system will have white
PM (for example) how can you be sure that the ocillator pair's white PM
contribution to AVAR isnt significant and is reduced along with the
system white PM contribution to AVAR as the cutoff frequency of the low
pass filter is reduced?

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