Thanks Tom for your quick and extensive reply. Indeed I confused Time Interval with Phase Difference…....
Corrected calc: 4/ [(Xi+2 - Xi+1) - (Xi+1 - Xi)]^2 = [(To + Ti+2) - 2(To + Ti+1) + (To + Ti)]^2 = [Ti+2 - 2Ti+1 + Ti]^2 = (Ti+2)^2 + 4(Ti+1)^2 + (Ti)^2 + 2(-2Ti+2*Ti+1 + Ti+2*Ti - 2Ti+1*Ti) 5/ <(Ti+1)^2> # <(Ti+1)^2> # < (Ti)^2> for large samples and <(Ti+a * Ti+b)> = 0 as Ti+1 and Ti are independent Then AVAR = (1/2Tau^2) * 6 < (Ti)^2> = (1/Tau^2) * 6 * SigmaTIC^2 6/ Hence ADEV = sqrt(3) * SigmaTIC / Tau So ADEV(Tau=1) = 1.73 * SigmaTIC (indeed…) By the way, it also seems that HDEV at Tau=1 is 2/sqrt(3) * Sigma = 1.15 SigmaTIC Best, Gilles. > Le 30 déc. 2018 à 07:14, Tom Van Baak <[email protected]> a écrit : > > Hi Gilles, > > Correct, the log-log slope will be -1. > > But I'm not sure about your ADEV and SigmaTIC claim. > > Assume the 53132A has 150 ps RMS resolution. The standard deviation is also > 150 ps. The Allan deviation at tau=1 would be 1.73 * 150 ps/s or 2.60e-10. > > Look at calc_adev() in http://leapsecond.com/tools/adev_lib.c and note the > three data[] terms. With multiple uncorrelated terms you simply sum the > variances. There are three terms so that's 3 * stdev. When you convert AVAR > to ADEV the 3 becomes sqrt(3), or 1.73. Make sense? > > For extra credit, note that MDEV at tau=1 is the same as ADEV. However, TDEV > at tau=1 is 1.50e-10, the same as stdev. In the same file, see that the > sqrt(3) factor is removed in calc_tdev(). > > ---- > > The best and largest pile of ADEV documentation is: > > "information about frequency stability analysis" > http://www.wriley.com/Freq%20Stab%20Analy%20Links.htm > > There is also a wikipedia page: > > https://en.wikipedia.org/wiki/Allan_variance > > For simpler introductions see: > > "Analysis of Time Domain Data" > https://tf.nist.gov/phase/Properties/four.htm > > "Clock Performance and Performance Measures" > https://tycho.usno.navy.mil/mclocks2.html > > "Fundamentals of Time and Frequency" > https://tf.nist.gov/general/pdf/1498.pdf > > ---- > > If you want to play with ADEV check out Stable32 [1] or TimeLab [2]. Both are > highly recommended and are also free. For questions like yours the Stable32 > noise generator feature is very useful to explore the shape(s) of ADEV for > given noise types. It was used to create: > > "Exploring Allan Deviation" > http://leapsecond.com/pages/allan/Exploring_Allan_Deviation_v2.pdf > > /tvb > > [1] http://www.stable32.com/ > [2] http://www.ke5fx.com/timelab/readme.htm > > > ----- Original Message ----- > From: "Club-Internet Clemgill" <[email protected]> > To: "Discussion of precise time and frequency measurement" > <[email protected]> > Sent: Saturday, December 29, 2018 2:28 PM > Subject: [time-nuts] TIC Characterization > > >> Hi, >> Looking to testing my HP53132A in TIC mode. >> I considered the Time Interval measurement technique: >> The start channel is connected to a 1 PPS signal, and to the stop channel >> though a coax cable (constant delay line). >> I found some references on the web, but no one with the associated maths. >> So I tried the following : >> >> 1/ AVAR = (1/2*Tau^2) * < [(Xi+2 - Xi+1) - (Xi+1 - Xi)]^2 > >> with (Xi+1 - Xi) = phase difference = time interval >> >> 2/ Phase difference = To + Ti >> where To is the constant delay between start and stop (coax line) >> and Ti is the counter's resolution at time i >> >> 3/ Assuming that Ti is a Central Gaussian distribution then: >> mean = < Ti > = 0 and variance = < Ti ^2> = SigmaTIC^2 >> >> 4/ [(Xi+2 - Xi+1) - (Xi+1 - Xi)]^2 = [(To + Ti+1) - (To + Ti)]^2 = (Ti+1 - >> Ti)^2 >> = (Ti+1)^2 + (Ti)^2 - 2(Ti+1 * Ti) >> >> 5/ <(Ti+1)^2> # < (Ti)^2> for large samples and >> <2(Ti+1 * Ti)> = 0 because Ti+1 and Ti are independent >> Then AVAR = (1/2Tau^2) * 2< (Ti)^2> = (1/Tau^2) * SigmaTIC^2 >> >> 6/ Hence ADEV = SigmaTIC / Tau >> >> So ADEV (log log) is a straight line with -1 slope >> And ADEV(Tau=1) provides the standard deviation = SigmaTIC of the Time >> Interval Counter's resolution >> >> Is this right ? >> Thanks to point me at related articles or web pages if you know any. >> >> Gilles. >> >> >> _______________________________________________ >> time-nuts mailing list -- [email protected] >> To unsubscribe, go to >> http://lists.febo.com/mailman/listinfo/time-nuts_lists.febo.com >> and follow the instructions there. > > > _______________________________________________ > time-nuts mailing list -- [email protected] > To unsubscribe, go to > http://lists.febo.com/mailman/listinfo/time-nuts_lists.febo.com > and follow the instructions there. _______________________________________________ time-nuts mailing list -- [email protected] To unsubscribe, go to http://lists.febo.com/mailman/listinfo/time-nuts_lists.febo.com and follow the instructions there.
