Neville Michie wrote: > Bruce, how does the three cornered hat scheme work? > > If I had two LPRO Rubidium oscillators and a TBOLT GPSDO, and I > divided each of them down to > 100KHz, then I could compare pairs of them with D latches and record > 3 different analogue > signals of phase difference. > One of the LPRO oscillators is in an oven to remove ambient > temperature influence. > If I ran them for several weeks and logged the signals every 10 minutes, > what could I expect to recover from the data and how would I apply > the 3 cornered hat scheme? > I ask this question because this is about where my building program > is taking me. > cheers, Neville Michie > > Neville
When the fluctuations of 3 quantities are independent then comparing 2 of them the individual variances of the add: VAR(1,2) = VAR(1) + VAR(2) VAR(1,3) = VAR(1) + VAR(3) VAR(2,3) = VAR(2)+ VAR(3) Where VAR(1,2) denotes the variance of the fluctuations in the difference between quantities 1 and 2. VAR(1,3) denotes the variance of the fluctuations in the difference between quantities 1 and 3. VAR(2,3) denotes the variance of the fluctuations in the difference between quantities 2 and 3. VAR(1) denotes the variance of the quantity 1. VAR(2) denotes the variance of the quantity 2. VAR(3) denotes the variance of the quantity 3. Thus VAR(1) = (VAR(1,2) + VAR(1,3) - VAR(2,3))/2 VAR(2) = (VAR(1,2) + VAR(2,3) - VAR(1,3))/2 VAR(3) = (VAR(1,3) + VAR(1,3) - VAR(1,2))/2 The same results hold for ADEV (used for characterising the stability of oscillators as variance of the phase is divergent for oscillators). ADEV(1,2) = ADEV(1) + ADEV(2) ADEV(1,3) = ADEV(1) + ADEV(3) ADEV(2,3) = ADEV(2) + ADEV(3) Where ADEV(1,2) denotes the Allen variance of the fluctuations in the phase difference between oscillators 1 and 2. ADEV(1,3) denotes the Allen variance of the fluctuations in the phase difference between oscillators 1 and 3. ADEV(2,3) denotes the Allen variance of the fluctuations in the phase difference between oscillators 2 and 3. ADEV(1) denotes the Allen variance of the phase fluctuations of oscillator 1. ADEV(2) denotes the Allen variance of the phase fluctuations of oscillator 2. ADEV(3) denotes the Allen variance of the phase fluctuations of oscillator 3. Thus ADEV(1) = (ADEV(1,2) + ADEV(1,3) - ADEV(2,3))/2 ADEV(2) = (ADEV(1,2) + ADEV(2,3) - ADEV(1,3))/2 ADEV(3) = (ADEV(1,3) + ADEV(1,3) - ADEV(1,2))/2 Note it is essential to measure the relative phase fluctuations between all 3 oscillator pairs simultaneously. The limitation is that the oscillators should all have similar ADEV. If the calculations assign negative values to one or more of the individual variances then the phase fluctuations for the individual oscillators may be correlated or at least one of the oscillators may be much quieter than the others. Eventually common environmental variations such as temperature pressure and humidity fluctuations introduce correlations invalidating the above simplified analysis. However in this case the theory has been extended to include the effect of correlations which are adjusted to ensure that the calculated individual variances are positive definite. Bruce _______________________________________________ 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.
