Hi There are entire (big and heavy) books written on quantization errors…..
In a counter, there are a number of different sub-systems contributing to the error. Depending on the design, each may ( or may not) be a bit better than absolutely needed. Toss in things like 10 MHz reference feedthrough (which is decidedly weird statistically) and you have a real mess. The simple answer is that there is no single answer for a full blown counter. For an ADC sampling system, there may indeed be a somewhat more tractable answer to the question (unless feed through is an issue with your setup …). Bob > On Oct 30, 2016, at 8:32 AM, jimlux <jim...@earthlink.net> wrote: > > On 10/29/16 10:14 PM, Tom Van Baak wrote: >>> One might expect that the actual ADEV value in this situation would be >>> exactly 1 ns at tau = 1 second. Values of 0.5 ns or sqrt(2)/2 ns might not >>> be surprising. My actual measured value is about 0.65 ns, which does not >>> seem to have an obvious explanation. This brings to mind various questions: >>> >>> What is the theoretical ADEV value of a perfect time-interval measurement >>> quantized at 1 ns? What's the effect of an imperfect measurement >>> (instrument errors)? Can one use this technique in reverse to sort >>> instruments by their error contributions, or to tune up an instrument >>> calibration? >> >> Hi Stu, >> >> If you have white phase noise with standard deviation of 1 then the ADEV >> will be sqrt(3). This is because each term in the ADEV formula is based on >> the addition/subtraction of 3 phase samples. And the variance of normally >> distributed random variables is the sum of the variances. So if your >> standard deviation is 0.5 ns, then the AVAR should be 1.5 ns and the ADEV >> should be 0.87 ns, which is sqrt(3)/2 ns. You can check this with a quick >> simulation [1]. >> >> Note this assumes that 1 ns quantization error has a normal distribution >> with standard deviation of +/- 0.5 ns. Someone who's actually measured the >> hp 5334B quantization noise can correct this assumption. >> > > isn't the distribution of quantization more like a rectangular distribution > (e.g. like an ADC). so variance of 1/12th? > > > > > > _______________________________________________ > time-nuts mailing list -- time-nuts@febo.com > To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts > and follow the instructions there. _______________________________________________ time-nuts mailing list -- time-nuts@febo.com To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there.
