# [time-nuts] three cornered comparison tools

Wed May 1 16:09:26 EDT 2013

```I recently made some measurements between 3 oscillators.  It wasn't a
true 'Three-Cornered Hat' measurement because the measurements were made
sequentially.  When I do the three-cornered hat calculation for the
hopefully 'better' oscillator, I end up trying to take the square root
of a negative number.  Is that a red flag that the data is invalid?  If
I ignore the minus sign, the results seem reasonable and I can
successfully calculate from the result for each oscillator back to the
measured results.

Ed

On 5/1/2013 12:08 PM, Tom Van Baak wrote:
>> 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.
>
> /tvb

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