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.
