btw, how do we gauge usability of a last digit. is it using noise STDEV? say 10v range 12,345,678.9uV, what should STDEV look like so that the 9th is considered a usable reading?
and also what is the diff between RMS noise and STDEV?
RMS noise equals STDEV. You can recognize that directly from comparing the STDEV and the RMS formulae.
For the 3458A, averaging gives converging results, obviously, whereas the FLUKE 7510 may be worse at higher averages (it diverges).
I am not able to identify the reason for that, but it has something to do with the character of the internal noise sources.
Provided that the mid- to long-term stability (determined by variations of temperature, reference voltage and gain resistors over the measurement interval) are small enough, you may theoretically achieve 9 usable digits when averaging sufficiently.
The variance (or uncertainty) of a set of N measurements is given by stdv/ sqrt(N).
For the 10V range, you may average over about 50 measurements of NPLC 100 to have 1e-9 variance of the result.
4 averaged measurements of NPLC 1000 also give 1e-9.
I doubt that anything below 1e-8 is useful.
At first, the mentioned environmental parameters are worse, and second, the linearity of the A/D is 2e-8 'only'.
Therefore, any higher resolution is useless.
For classic analog references and DMM, an instability of 1e-8 is the absolute limit.
Below that, you need totally different working principles.
Together with our National Standards Office, PTB, a company named Supracon developed an AC quantum voltmeter, having about 1e-10 stability, see here:
http://www.supracon.com/en/ac_quantum_voltmeter.htmlFrank