What is 3 corner hat measurement?

[3roomlab]

I read from this interesting post

https://www.eevblog.com/forum/metrology/volt-nut-meeting-2019-in-stuttgartgermany/msg4401343/#msg4401343

specifically this
"Three corner hat measurements - W. Oelschlegel"

There isnt anything useful on google to read.
Would anyone kindly explain?

[Vgkid]

It is the comparison of 3 references to each other a,b,c
So a-b b-c c-a.
Usually you tend to hear about it with the time nuts list.
http://www.wriley.com/3-CornHat.htm

[miro123]

The classical one 3- corner has limitation in Voltnut area.
The general method is described for higher order - not only 3.
the combination are N=n*(n-1)/2     
where N- number of combination
n - number of references

They are many improved versions of this algorithm nowadays - e.g. applying dynamic filtering/AI or MI.
They improve the performance in Vref measurement area.






 

[edpalmer42]

Normally, you have a master reference and compare various devices to the master to determine their performance.  The master reference has to be much better (whatever 'better' means) than the device under test.  In the Time-Nuts area, this is typically to measure Allan Deviation which is a specialized offshoot of Standard Deviation.  Standard Deviation doesn't work for oscillators, but that's a huge topic that I won't get into.

But what if you don't have a master?  That's where the 3-cornered hat method comes in.  It allows you to compare three seperate devices and derive the actual performance of each device.  The trick is you make all the measurements *simultaneously*.  You then use matrix math to determine the actual performance of each of the 3 devices.   If the measurements aren't made simultaneously, the math won't work and you'll end up with zeros and infinities in the results.  Ideally, you'd compare three units that were all the same model so they'd likely have similar performance.  If one device is much better or worse than the other two, the calculation results might be of poor quality.

This has nothing to do with the idea of establishing a pool of devices to provide a master reference of frequency or voltage.  It's a trick to allow the measurement of device performance in the absence of a master reference.  If there are any other applications for this technique, I'm not aware of them.

[3roomlab]

Normally, you have a master reference and compare various devices to the master to determine their performance.  The master reference has to be much better (whatever 'better' means) than the device under test.  In the Time-Nuts area, this is typically to measure Allan Deviation which is a specialized offshoot of Standard Deviation.  Standard Deviation doesn't work for oscillators, but that's a huge topic that I won't get into.

But what if you don't have a master?  That's where the 3-cornered hat method comes in.  It allows you to compare three seperate devices and derive the actual performance of each device.  The trick is you make all the measurements *simultaneously*.  You then use matrix math to determine the actual performance of each of the 3 devices.   If the measurements aren't made simultaneously, the math won't work and you'll end up with zeros and infinities in the results.  Ideally, you'd compare three units that were all the same model so they'd likely have similar performance.  If one device is much better or worse than the other two, the calculation results might be of poor quality.

This has nothing to do with the idea of establishing a pool of devices to provide a master reference of frequency or voltage.  It's a trick to allow the measurement of device performance in the absence of a master reference.  If there are any other applications for this technique, I'm not aware of them.

I am interested to know what to do without the master reference
do you by any chance have an example of how this calculation works? (or how it is done?)

[edpalmer42]

I am interested to know what to do without the master reference
do you by any chance have an example of how this calculation works? (or how it is done?)

I don't have an example.

You need three time interval counters that are connected to a computer to collect the data.  Depending on the counter, the connection can be via GPIB, serial, ethernet, or whatever allows you to gather the data.  As mentioned earlier, you measure A-B, B-C, and C-A.  In each case, you're measuring the time delay between the rising edge of the signal on Channel 1 and the rising edge of the signal on Channel 2.  Depending on how good your three oscillators are, you might be able to just connect them directly to the counters.  For high performance oscillators, it might be necessary to provide various complexities of pre-processing of the input signals to enhance the small differences and bring them out of the noise.  Converting a sine wave input to a square wave is a likely first step.  Ultimately, you'd have to go to a DMTD system configured for 3-cornered hat operation.

You'll probably need to write a program that queries the counters and logs the data.

Once you've got the data, you import it into Stable32 or Timelab to do the analysis.  They're both freeware.  They process the data and produce nice graphs that show you the performance of each oscillator.

Of course, there are many details that have to be considered to get usable results.  This isn't a simple or plug-and-play operation.

[MegaVolt]

I am interested to know what to do without the master reference
do you by any chance have an example of how this calculation works? (or how it is done?)

You measure the noise variance with three instruments simultaneously. A-B, B-C, C-D. Then apply the formula to get the variance of each source.

[alm]

If I understood the talk correctly, the Allan deviation as a function of time for a reference is considered to be constant over time (he provided data on this), and the noise of the detector (Keithley 2182A) negligible. Then from measurements of differences between voltage references, the Allan deviation of each individual voltage reference can be calculated using this three corner hat method.

Then a new reference can be measured relative to a reference with known Allan deviation, and from this one series the Allan deviation of the new reference can be calculated.

Wulf measured a couple of the Fluke 7000 references against his Fluke 732B (with known Allan deviation) during MM2022.

[armandine2]

specifically this
"Three corner hat measurements - W. Oelschlegel"

There isnt anything useful on google to read.

Don't forget to try Google Scholar - I find for the esoteric stuff it usually has something.