[time-nuts] Allan Deviation Calulations

WarrenS warrensjmail-one at yahoo.com
Thu Sep 22 13:03:59 UTC 2011

A couple of things to consider

If you have two independent noise sources they add with their RMS sum
But for two noise readings that are close, the difference is more likely 
statistical variations than RMS adding, especially at your 100 sec time 

Assuming you have a system that is not limited by the SR620 25 ps noise 
floor (which is more like 1e-11 @ 1sec, or your limited data collection 
time, and that your data is correct,
You solve for X knowing that total noise =  [Square root of (X^2 + Y^2)]

The noise floor does not have to be factored in if the difference is much 
larger and you want an approximate answer.  The sum of two equal noise 
sources is times 1.4
Sum of two noise sources 10 to one apart give a 1% error.


Martyn Smith martyn at ptsyst.com


I'm trying to measure the Allan Deviation of an amplifier and need help with
the maths.

My measurement process uses the SR620 in time interval mode and I make one
measurement per second for about a day.

I then use Ulrichs excellent plotter to calculate the Allan Deviation.

The Allan Dev floor noise of the SR620 (without my amplifier) is as follows.

9.91E-13 (1 second)
1.59 E-13 (10 sec)
3.00 E-14 (100 sec)

I then add my amplifier into the measurement process.  I get the following
Allan Dev results

1.09E-12 (1 sec)
2.48E-13 (10 sec)
4.32E-14 (100 sec).

So the 1 sec Allan dev with my amp included, has gone up by 9.9E-14 for the
1 sec measurement.

How to I calculate the actual Allan Dev of my amp for the 1 sec period?

Best Regards


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