[time-nuts] three cornered comparison tools

Tom Van Baak tvb at LeapSecond.com
Wed May 1 14:08:21 EDT 2013

> Folks,
> I asked about 3 cornered comparisons some time ago, and now have plenty 
> of data to start exploring, and way more than the 3 oscillators I had 
> when I asked six months ago.
> Apart from Stable32, which I do not have access to, are there any free 
> tools which will allow me to perform 3 cornered comparisons between my 
> oscillators?
> Thanks,
> david

I use Excel on the { tau, ADEV } pairs when I want to get fancy, or just a calculator for something quick. You can sometimes simply eyeball it on a composite log-log adev plot.

I'll give the formula is below, but to understand, first consider this backwards example:

Suppose for some tau the ADEV of three oscillators is 6e-12, 8e-12, and 10e-12, respectively. But -- you don't know that yet -- because all you have is pairwise measurements. The assumption is that noise is rms additive. Let's do the numbers:

When you measure A vs. B you should get 1.00e-11, since that is sqrt( 6e-12 ^ 2 + 8e-12 ^ 2 ).

When you measure B vs. C you should get 1.28e-11, since that is sqrt( 8e-12 ^ 2 + 10e-12 ^ 2 ).

When you measure C vs. A you should get 1.17e-11, since that is sqrt( 10e-12 ^ 2 + 6e-12 ^ 2 ).

So given your three ADEV measurement pairs (AB=1.00e-11, BC=1.28e-11, AC=1.17e-11) you just work backwards to compute ADEV for A, B, and C, as in:

    A = 0.707 * sqrt(+ AB*AB - BC*BC + AC*AC)
    B = 0.707 * sqrt(+ AB*AB + BC*BC - AC*AC)
    C = 0.707 * sqrt(- AB*AB + BC*BC + AC*AC)

Depending on how clean your measurement system is, and how well-behaved and modestly different the oscillators are, the 3-hat technique can work pretty well.


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