[time-nuts] Re: Counter internal resolution error

[Dr. David Kirkby]

On Thu, 16 Mar 2023 at 19:06, Michael Wouters via time-nuts <
time-nuts at lists.febo.com> wrote:

> Dear time-nuts
>
> Counter specs often include an “internal resolution” error. For example,
> the SR620 specs say that it is 25 ps in single-shot, but this can be
> reduced to 4 ps with sufficient, repeated measurements. Can anyone    offer
> any enlightenment as to the origin of this error, and the statistical
> distribution it has? I mentioned the SR620 but information about the 53230A
> would be interesting too.
>
> Cheers
> Michael


I would have thought that if there were no systematic errors you could
reduce the average error to zero with an infinite amount of samples. But a
systematic error would prevent that. I don’t have an SR620, but it must
have a maximum amount of averaging.

I’m not a mathematician, but I if I had to take a guess, I would have
thought that the average error would reduce as the square root of the
number is samples. But (25/4)^2 is only 39, which is a lot less than the
maximum averaging the instrument can do. It would be interesting to either
find a formula, or even verify with a numerical simulation if I’m right
about the square root relationship.

I wonder if the 25 ps is based on a 95% (2 SD) confidence, 99.7% (3 SD)
confidence or some other metric.
-- 
Dr. David Kirkby,
Kirkby Microwave Ltd,
drkirkby at kirkbymicrowave.co.uk
https://www.kirkbymicrowave.co.uk/
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