I believe that the problem is that the error in any one measurement is not uniformly distributed in exactly that way. If you are trying to count how many 10 MHz (100 ns interval) intervals occur between the 1 PPS edges in a period counter, you have to deal with the following?
* You might have any possible phase relationship between the two signals. If they are exactly related by a 10^7 ratio, it's possible for the 1 PPS edges to exactly coincide with the 10 MHz edges. Depending on the type of gating circuit, you will have jitter and possibly metastability resolving whether which edge occured first. The same thing happens on the end of the measured interval, but (depending on how it's set up) the propagation delays and metastability and jitter might be different. So you could get millions of sequential counts which were 1 count low, followed by millions of counts which were one count high, with no counts exactly at 10^7. * To stay away from such problems, most precision counters add a small amount of controlled jitter (phase modulation) to the clock. When averaged over many measurements the effects of the two edges (gate and clock) lining up exactly are greatly reduced, since you are sliding one back and forth across the other with the modulation and the chance of metastability is small (assuming the signal being measured doesn't happen to match the phase modulation frequency). * The metastability problem depends on how the edges are compared. Some traditional flip-flops and latches can be thought of as analog gain elements connected so that they tend to sit in state A or state B, which involve analog voltages and currents. If you graph the energy in the system, the energy is low in state A, rises to a peak halfway between A and B, and falls to a low value at state B. If the recognition of the timing edge occurs early enough the system remains in state A. If the timing is later the system is pushed toward the peak, but doesn't get over it and returns to state A. But if the timing is at the perfect location the system is balanced at the potential energy peak, and only random noise can push the system into a final state A or B over a significant length of time. Sorry if this is considered obvious or trivial. -- Bill Byrom N5BB ----- Original message ----- From: jimlux <jim...@earthlink.net> To: Discussion of precise time and frequency measurement <time-nuts@febo.com> Subject: Re: [time-nuts] uncertainty calculations Date: Fri, 14 Apr 2017 08:49:07 -0700 On 4/14/17 8:37 AM, jimlux wrote: > If one is counting an unknown 1pps source with a counter that > runs at 10 > MHz (e.g. the error in any one measurement is uniformly > distributed over > 1 ppm) and you collect 100 samples, > is the (1 sigma) measurement uncertainty 0.1ppm * sqrt(100)/sqrt(12) > > (standard deviation of a uniform distribution is 1/sqrt(12) ) > > (assuming for the moment that both sources have no underlying > variability - we're talking about the *measurement uncertainty*) > Oops.. 0.1 ppm * 1/sqrt(N) * 1/sqrt(12) That is, the standard deviation goes down as sqrt(N) _______________________________________________ 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.