[time-nuts] Re: Counter internal resolution error

[Bob Camp]

Hi

The random errors have a standard deviation. The “one sigma” is often what is 
used to characterize them rather than the average. If they spec 10 ps resolution
and that’s limited by the random stuff, they are talking about 10 ps one sigma .

Bob

> On Mar 19, 2023, at 9:27 AM, Dr. David Kirkby via time-nuts <time-nuts at lists.febo.com> wrote:
> 
> 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/
> Telephone 01621-680100./ +44 1621 680100
> 
> Registered in England & Wales, company number 08914892.
> Registered office:
> Stokes Hall Lodge, Burnham Rd, Althorne, Chelmsford, Essex, CM3 6DT, United
> Kingdom
> _______________________________________________
> time-nuts mailing list -- time-nuts at lists.febo.com
> To unsubscribe send an email to time-nuts-leave at lists.febo.com