Hi The primer talks a lot about “averaging” of the samples. If you dig deep into the various papers on doing AVAR for frequency / time standards … you want to decimate / downsample the data rather than average. There are a *lot* of papers that make this distinction less than totally clear.
Bob > On Feb 21, 2020, at 9:58 AM, Chris Burford <cburfo...@austin.rr.com> wrote: > > 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 >> <mag...@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 >> >> >> _______________________________________________ >> time-nuts mailing list -- time-nuts@lists.febo.com >> To unsubscribe, go to >> http://lists.febo.com/mailman/listinfo/time-nuts_lists.febo.com >> and follow the instructions there. >> _______________________________________________ >> time-nuts mailing list -- time-nuts@lists.febo.com >> To unsubscribe, go to >> http://lists.febo.com/mailman/listinfo/time-nuts_lists.febo.com >> and follow the instructions there. > > _______________________________________________ > time-nuts mailing list -- time-nuts@lists.febo.com > To unsubscribe, go to > http://lists.febo.com/mailman/listinfo/time-nuts_lists.febo.com > and follow the instructions there. _______________________________________________ time-nuts mailing list -- time-nuts@lists.febo.com To unsubscribe, go to http://lists.febo.com/mailman/listinfo/time-nuts_lists.febo.com and follow the instructions there.
