Re: [time-nuts] TIC Characterization
In message , Magnus D anielson writes: >> measure (start=house_std, stop=siggen) and (start=siggen, stop=house_std) for >> as many siggen phase settings as you have patience for. > >Well, this was the second setup I was talking about. To disclose the >full non-linearity you want to tweak it to 9.999 MHz rather than 10 MHz. Yes, that is a fall-back if your siggen cannot control the phase. Of course if you both set 9.999 MHz *and* sweep the phase, you will be able to separte the effects of the siggen and counter even better. -- Poul-Henning Kamp | UNIX since Zilog Zeus 3.20 p...@freebsd.org | TCP/IP since RFC 956 FreeBSD committer | BSD since 4.3-tahoe Never attribute to malice what can adequately be explained by incompetence. ___ 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.
Re: [time-nuts] TIC Characterization
> Thanks Tom for your quick and extensive reply. > Indeed I confused Time Interval with Phase Difference… ... > By the way, it also seems that HDEV at Tau=1 is 2/sqrt(3) * Sigma = 1.15 > SigmaTIC > I don't believe that HDEV result. For many large runs of simulated normalized white phase noise input I get: adev(1) = 1.732, mdev(1) = 1.732, tdev(1) = 1.000, hdev(1) = 1.825 See: https://en.wikipedia.org/wiki/Sum_of_normally_distributed_random_variables or google for topics like: sums of independent random variables normal sum distribution linear combinations of normal random variables Then look at both calc_adev() and calc_hdev() in http://leapsecond.com/tools/adev_lib.c Assuming you have white phase noise input with mean=0, stdev=1 and using tau=1, then, 1) The key lines for ADEV are: v = data[i + 2*tau] - 2 * data[i + tau] + data[i]; sum /= 2.0; So you would expect sqrt( (1 + 4 + 1) / 2 ) = sqrt(6/2) = 1.7321 2) The key lines for HDEV are: v = data[i + 3*tau] - 3 * data[i + 2*tau] + 3 * data[i + tau] - data[i]; sum /= 6.0; So you would expect sqrt( (1 + 9 + 9 + 1) / 6 ) = sqrt(20/6) = 1.8257 3) MDEV is the same as ADEV for tau = 1 so that's why it is also 1.7321. 4) TDEV is MDEV / sqrt(3) so that why it gives 1.. For testing counter resolution TDEV is often more instructive than ADEV: a) TDEV doesn't have that misleading, distracting, prolonged -1 slope that ADEV plots often show. b) TDEV has the nice property of reporting 1 when given 1 RMS data. c) The units for TDEV are seconds, which is appropriate for a TIC (time interval counter). d) The units for ADEV are fractional frequency, which is natural for frequency standards. e) Unless there are design flaws, instrument drift, or environmental issues, TDEV should be flat from tau 1 to forever. f) Subtle, unwanted variations are much easier to observe in a flat line (TDEV) than a -1 line (ADEV). /tvb - Original Message - From: "Club-Internet Clemgill" To: "Tom Van Baak" ; "Discussion of precise time and frequency measurement" Sent: Sunday, December 30, 2018 1:07 AM Subject: Re: [time-nuts] TIC Characterization 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 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.co
Re: [time-nuts] TIC Characterization
In message , Magnus D anielson writes: >Hi Gilles, > >On 12/29/18 11:28 PM, Club-Internet Clemgill wrote: >> 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). > >Fair enough setup. This is a static test setup which works as long as >you do not lock the counter up to a 10 MHz of the same source as the >PPS, and for all maters not accurate enough, so it's best for the test >for it to be free-running. Here is another test-setup, which is very revealing about non-white noise in TIC counters: You need a signal generator which can be locked to an external frequency and control the phase of the output signal relative to that external frequency. The HP3336 is a good cancidate. Lock both the counter under investigation and the siggen to the same house standard. Set the siggen to output same frequency as house standard. measure (start=house_std, stop=siggen) and (start=siggen, stop=house_std) for as many siggen phase settings as you have patience for. Plot results, and wonder why you don't get a straight line... -- Poul-Henning Kamp | UNIX since Zilog Zeus 3.20 p...@freebsd.org | TCP/IP since RFC 956 FreeBSD committer | BSD since 4.3-tahoe Never attribute to malice what can adequately be explained by incompetence. ___ 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.
Re: [time-nuts] TIC Characterization
Hi Gilles, On 12/29/18 11:28 PM, Club-Internet Clemgill wrote: > 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). Fair enough setup. This is a static test setup which works as long as you do not lock the counter up to a 10 MHz of the same source as the PPS, and for all maters not accurate enough, so it's best for the test for it to be free-running. When you lock it up, you get a very static behavior of the systematic noise of quantization resolution, and you will be hitting essentially the same bin all the time, and well, you are not that lucky on real-life signals since the phase relationship glides ever so slightly that you want to make sure you do that. So, either you use the time-base offset to cause the quantization of the counter glide relative to the PPS reference or you use an offset oscillator for your signal, both achieve the same goal. The difference lies in wither you have both start and stop channels glide, as for internal reference offset, or you have only the stop channel glide, as you do with an offset oscillator but have time-base and start channel being synchronous. The jitter for the later one is expected lower, because it will have the start-channel banging the same bin more or less each time since the time-base of the counter, steering the phase of the quantization is synchronous to the start-channel, thus essentially removing the noise of the start-channel. While you get an ADEV slope of -1 and it looks like white phase modulation noise, the counters resolution is a very systematic noise and you should not forget that, rather, you can use this fact in your tests to learn more about it. You will find that it is not perfectly linear slope either, so for an average performance you want to average over the full set of phase-relationships between time-base and start/stop channels. > I found some references on the web, but no one with the associated maths. The counter resolution and slope is somewhat of a white spot. It is "known" but not very well researched. I did one presentation on it with associated paper, but I need to redo that one because it does not present it properly. > 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 It will not be completely true, but a dominant feature. Turns out that the quantization staircase is a very systematic property, but then offset by the white phase modulation and flicker phase modulation that you can expect. However, the staircase quantization will dominate for these short taus and it is only for longer taus you go into the flicker part. > 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. You do indeed get an ADEV -1 slope for the counter quantization, I've done essentially the same analysis. I've then done a paper showing how noise and quantization interacts and somewhat shifts this around in, ehm, interesting ways. Unfortunately the paper as presented was not all that good, but I should do work on that, because there is some further insights to present more thoroughly as well as making the real point go through better. I have only seen an Agilent app-note which addresses some of this, but then with the focus on frequency measurements. Others seems to have treated the subject as a fact of life and moved on. So, thank you for reminding me about this property, it is indeed somewhat of a white spot. 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.
Re: [time-nuts] TIC Characterization
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" To: "Discussion of precise time and frequency measurement" 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 -- 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.
