[time-nuts] Frequency standards for different tau in Allen Dev measurement

Fri Feb 21 14:58:44 UTC 2020

Here is a good article for Allan deviation that you can file with other 
reference material. It is well written and somewhat high level.

https://www.phidgets.com/docs/Allan_Deviation_Primer 
<https://www.phidgets.com/docs/Allan_Deviation_Primer>

Chris

On 02/20/20 21:45:58, Taka Kamiya via time-nuts wrote:
> I was in electronics in big ways in 70s.  Then had a long break and came back to it in last few years.  Back then, if I wanted 1s resolution, the gate time had to be 1s.  So measuring ns and ps was pretty much impossible.  As I understand it, HP53132A (my main counter) takes thousands of samples (I assume t samples) to arrive at most likely real frequency.  That was something I had hard time wrapping my head around.
>
> I understand most of what you said, but I've never taken statistics, so I am guessing on some part.  I can see how adev goes down as tau gets longer.  Basically, averaging is taking place.  But I am still not sure why at some point, it goes back up.  I understand noise will start to take effect, but the same noise has been there all along while adev was going down.  Then, why is this inflection point where sign of slope suddenly changes?
>
> Also, to reach adev(tau=10), it takes longer than 10 seconds.  Manual for TimeLab basically says more samples are taken than just 10, but does not elaborate further.  Say it takes 50 seconds to get there, and say that's the lowest point of adev, does that mean it is the best to set gate time to 10 second or 50 second?  (or even, take whatever gate time and repeat the measurement until accumulated gate time equals tau?
>
> ---------------------------------------
> (Mr.) Taka Kamiya
> KB4EMF / ex JF2DKG
>   
>
>      On Thursday, February 20, 2020, 7:54:22 PM EST, Magnus Danielson <magnus at rubidium.se> wrote:
>   
>   Hi Taka,
>
> On 2020-02-20 19:40, Taka Kamiya via time-nuts wrote:
>> I have a question concerning frequency standard and their Allen deviation.  (to measure Allen Dev in frequency mode using TimeLab)
>>
>> It is commonly said that for shorter tau measurement, I'd need OCXO because it's short tau jitter is superior to just about anything else.  Also, it is said that for longer tau measurement, I'd need something like Rb or Cs which has superior stability over longer term.
> Seems reasonably correct.
>> Here's the question part.  A frequency counter that measures DUT basically puts out a reading every second during the measurement.  When TimeLab is well into 1000s or so, it is still reading every second; it does not change the gate time to say, 1000s.
>> That being the case, why this consensus of what time source to use for what tau?
>> I recall reading on TICC, in time interval mode, anything that's reasonably good is good enough.  I'm aware TI mode and Freq mode is entirely different, but it is the same in fact that measurement is made for very short time span AT A TIME.
>> I'm still trying to wrap my small head around this.
> OK.
>
> I can understand that this is confusing. You are not alone being
> confused about it, so don't worry.
>
> As you measure frequency, you "count" a number of cycles over some time,
> hence the name frequency counter. The number of periods (sometimes
> called events) over the observation time (also known as time-base or
> tau) can be used to estimate frequency like this:
>
> f = events / time
>
> while it is practical that average period time becomes
>
> t = time / events
>
> In modern counters (that is starting from early 70thies) we can
> interpolate time to achieve better time-resolution for the integer
> number of events.
>
> This is all nice and dandy, but now consider that the start and stop
> events is rather represented by time-stamps in some clock x, such that
> for the measurements we have
>
> time = x_stop - x_start
>
> This does not really change anything for the measurements, but it helps
> to bridge over to the measurement of Allan deviation for multiple tau.
> It turns out that trying to build a standard deviation for the estimated
> frequency becomes hard, so that is why a more indirect method had to be
> applied, but the Allan deviation fills the role of the standard
> deviation for the frequency estimation of two phase-samples being the
> time-base time tau inbetween. As we now combine the counters noise-floor
> with that of the reference, the Allan deviation plots provide a slopes
> of different directions due to different noises. At the lowest point on
> the curve, is where the least deviation of frequency measurement occurs.
> Due to the characteristics of a crystal oscillator to that of the
> rubidium, cesium or hydrogen maser, the lowest point occurs at different
> taus, and provide different values. Lowest value is better, so there is
> where I should select the time-base for my frequency measurement. So,
> this may be at 10 s, 100 s or 1000 s, which means that the frequency
> measurement should be using start and stop measurements with that
> distance. OK, fine. So what about TimeLab in all this. Well, as we
> measure with a TIC we collect a bunch of phase-samples at some base
> rate, such as 10 Hz or whatever. TimeLab and other tools can then use
> this to calculate Allan Deviation for a number of different taus simply
> by using three samples, these being tau in between and algoritmically do
> that for different taus. One then collects a number of such measurements
> to form an average, the more, the better confidence interval we can but
> on the Allan Deviation estimation, but it does not improve our frequency
> estimation, just our estimation of uncertainty for that frequency
> estimation for that tau. Once you have that Allan Deviation plot, you
> can establish the lowest point and then only need two phase samples to
> estimate frequency.
>
> So, the measurement per second thing is more collection of data rather
> than frequency estimation in itself.
>
> Cheers,
> Magnus
>
>
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