No problem the dual DMTD board looks pretty neat if it would work. I don't think I've seen a 4 channel one before. Although Corby said he had an 8 channel counter so anything is possible. Seems like you could use two of the original design though couldn't you? I assume Corby and others have done this for exactly the same reason. The way I understand it the two references need to be very close to each other in stability so the measured deviation can be corrected for by dividing by the square root of 2. Many of the videos I've watched the person used two identical/similar reference oscillators to test the DUT. Bill Wriley did say it could be extended to M clocks. I don't fully understand negative variances but it's supposed to be a sign the method is failing.
Bill
Yes you divide by sqrt(2) if the two DUTs are very similar to each other.
A bit simplified: you take a load of measurements and then you calculate the variance. The variance you get is the sum of the variance of both DUTs (remember, in the ideal case, the offset oscillator drops out).
I don't know how I can enter math here, so I write it like so: the variance of your measured data is
sigma
meas2 = sigma
12 + sigma
22where sigma
2 is the variance, and sigma
1 and sigma
2, respectively are the stabilities of your individual DUTs. Now if both DUTs are "the same", e.g. two LPRO-101 against each other, you have
sigma
1 = sigma
2 = sigma
12 = sigma
22 = sigma
dut2and therefore you can write
sigma
meas2 = sigma
12 + sigma
22 = 2 * sigma
dut2and now you don't want to know the variance, but the standard deviation AKA allan deviation, so take the square root
sigma
meas = sqrt(2 * sigma
dut2) = sqrt(2) * sigma
dutFor the three cornered hat, the methodology is very simple as well. This time you observe three oscillators, so you kind of have three measurements, each of which has its own variance (sigma
xy is the variance when DUTx is measured against DUTy):
sigma
122 = sigma
12 + sigma
22sigma
132 = sigma
12 + sigma
32sigma
232 = sigma
22 + sigma
32and now you can do the math and solve this equation system because you have three equations and three unknowns (the variance of each DUT). For example, take the first equation, subtract the second one and add the third one. You get
sigma
122 - sigma
132 + sigma
232 = sigma
22 - sigma
32 + sigma
22 + sigma
32 = 2 * sigma
22Note, on the right hand side, how all DUT variances have dropped out. All what remains is the variance of a single DUT, and on the left hand side, this is what you measured. So you can figure out the unknown variance of one DUT, provided you take at least three different measurements.
The problem with the negative variance arises from numerical problems. Because your measurement contains noise etc., your variances may not behave exactly as they should and the whole thing breaks apart. For instance, with the Riley DMTD, you can only measure two DUTs at a time against each other. So, if you want to do three cornered hat, you measure 1-2 on day 1, 1-3 on day 2 and 2-3 on day 3. However, the DUTs might change slightly during this time, you don't observe them at the same time and this is where the numerical problem may arise.
I would expect that if you had a multi-channel DMTD, where you can measure all three DUTs at the same time, the numerical problems will be less.