On 4 June 2010 08:32, Charles P. Steinmetz <[email protected]> wrote: > If I may be allowed to summarize, it appears that Warren and Bruce agree > that integration is necessary to produce true ADEV results. Warren asserts > that the low-pass filtering his method uses is "close enough" to integration > to provide a useful approximation to ADEV, while Bruce disagrees. So, the > remaining points of contention seem to be: > > 1. How close can a LPF implementation come to integration in ADEV > calculations, and
Well, Warren uses two stages of integration. There has already been talk of the simple R/C filter in the feedback loop. Unless my education in electronics was completely wrong, the series R/C circuit forms a simple LPF and is an integrator (assuming that the resistor is in series with the input and the capacitor is in parallel with the output). See http://en.wikipedia.org/wiki/Integrator_circuit, http://en.wikipedia.org/wiki/RC_filter. Sorry these are not academic papers but if you spot something wrong please feel free to edit them appropriately. This first stage of integration is set at a much wider frequency than tau0 and forms the PLL-loop filter allowing it to track the FAST changes of a noisy unknown oscillator. That last bit is very important and something some previous attempts at this method failed to resolve. Now there is a noisy control voltage on the reference oscillator and it is absolutely no good trying to make a single measurement at tau0 because the settling time of the filter has not been constrained to it so it will not give an integrated mean value. This where the second stage of integration comes in which is the oversampling which takes a number of readings during tau0 (please correct me if I have the terminology wrong here) which are then averaged to give a mean, integrated, value of the control voltage for tau0. So why two stages, look closely above, until the idea of oversampling was tried, the PLL-loop filter had to have a settling time, IE. cutoff frequency, equal to tau0 so that the measurement at tau0 reflected the mean, average, integrated, value for that tau0 period. But if a filter with that sort of cutoff is used then the reference oscillator is not able to track noise on the unknown oscillator at all and it would give results for things like flicker noise, random walk, etc, which were lower than the actual values. Now have a look at the top end of John's graphs where there is a divergence. > 2. How close to true ADEV is "good enough"? well, considering we have integrated frequency measurements at tau0 intervals, there is little wonder that it correlates closely to ADEV because that's exactly what it is. > I humbly submit that trading insults has become too dreary for words, and > that neither Warren nor Bruce will ever convince the other on the latter > point. Well, I've been on this list long enough to know that Bruce will always resort to that sort of behaviour when he is boxed into a corner or cannot get his point of view accepted. Anyone who speaks up against him is usually put in their place. This saga has come about because someone dared to challenge him so we have been subjected to his tantrums. > I thus humbly suggest (nay, plead) that the discussion be re-focused on the > two points above in a "just the facts, ma'am" manner. One can certainly > characterize mathematically the differences between integration and LP > filtering, and predict the differential effect of various LPF > implementations given various statistical noise distributions. If one is > willing to agree that certain models of noise distributions characterize > reasonably accurately the performance of the oscillators that interest us, > one can calculate the expected magnitudes of the departures from true ADEV > exhibited by the LPF method. Each person can then conclude for him- or > herself whether this is "good enough" for his or her purposes. Indeed, > careful analysis of this sort should assist in minimizing the departures by > suggesting optimal LPF implementations. Ask yourself what is the difference between a simple R/C LPF and integration, what is integration in fact. What is the difference between an electronic LPF and an integrator designed in electronics. I think we are getting hung up between the mathematical term integration and the electrical term. Although I should say that of course ADEV is a mathematical derivation taking frequency data and finding the averages of various positional averages. Whether the frequency data is provided as the inverse of the measured period of the unknown oscillator or the voltage reading of a fancy VCO (ref osc), makes no difference, providing that each data point is accurately represented. In terms of "optimal LPF implementations" as I see mentioned here, this is the trap that previous people trying to use the tight-PLL method have fallen into. An "optimal" LPF will give a very accurate average value of the frequency for each tau0 point but only at the fundamental. It will get the effects of noise wrong unless its bandwidth is sufficient to encompass that but then the LPF will not be "optimal" and the resulting frequency data will be incorrect. Best regards, Steve > Best regards, > > Charles > > > > _______________________________________________ > time-nuts mailing list -- [email protected] > To unsubscribe, go to > https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts > and follow the instructions there. > -- Steve Rooke - ZL3TUV & G8KVD The only reason for time is so that everything doesn't happen at once. - Einstein _______________________________________________ time-nuts mailing list -- [email protected] To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there.
