Sub-ppm voltage measure.

[Dr. Frank]

I'm trying to understand how it is possible to measure voltages below 1ppm and so far I see only one method: compare two very close voltages using a null meter.

I have compiled a table for comparing different devices.

From it we can draw conclusions:
1. The best null meter is a nanovoltmeter.
2. The best nanovoltmeter is the HP 34420a (for good reason it is used in the set of Johnson standard )
3. Ordinary null meters approach nanovoltmeters only if the difference between the compared voltages is less than 1ppm.

Tell me what other methods are there to get the best accuracy?

In the table, you can change the values ​​of the compared voltages and the difference between them. Lines that do not fit the range are automatically crossed out.

The table does not include temperature.

Sorry, you pose the wrong questions, or in other words, you are not fully aware about what you want to achieve, in terms of 'Resolution', 'Stability' and 'Uncertainty'.
The term 'Accuracy' is also too unspecific, to get the correct understanding about this problem.

At first, regarding 'Resolution', it's quite easy to 'measure' voltages at sub-ppm levels.

Simply use a 7 1/2 or  8 1/2 digit DMM, and you can resolve 0.1ppm or even 0.01ppm at 10V or any other voltage level. Even most 6 1/2 digit DMMs offer one more digit over the instrumentation bus, which might be partly usable at sub-ppm levels.

Using a differential method, you might compare two nearly equal voltages @ 10V with even lower resolution, down to about 10^-10, or 0.0001 ppm.
That's the level of resolution, National Standards Institutes are today transferring the S.I. volt from a Josephson Junction Array to real analogue world.

As you proposed, they use something like the HP34420A, Keithley 2182A, or other special Null-Meters to achieve ~ 1 nV differential resolution.. involving some statistics.
Therefore, 1nV / 10V ~ 10^-10. You'll find this 1nV value also on the NIST, NPL, PTB sites, or for commercial JJA systems.
Sophisticated DMMs (not the specialized nV meters) achieve around 10nV resolution.

If you want to compare two different voltages, you need a scaling device, like a 720A Kelvin-Varley-Divider, or a 752A Hamon-Divider, or highly linear A/Ds, like inside the long-scale DMMs.
All of them also allow for sub-ppm resolution, either in differential, or in direct modes.

Second, let's talk about 'Stability', or how 'useful' these high resolutions might be.
This depends on the noise of the involved objects, as being voltage source 1, voltage source 2 and comparison device, the time-scale of observation, and environmental conditions.

For example, if you measure the output of a 7.15V or 10V voltage standard (LTZ1000, 732B, or else) by means of a HP3458A, you usually can achieve a stability (i.e. noise or Standard Deviation) of 0.02 .. 0.05 ppm over 1 minute, which is mostly the quadratic sum of the noise effects of the zener references inside the standard, and the LTZ1000 inside the 3458A, and of the OpAmps involved.
These stability figures can be achieved for equal and different voltage comparisons, and also with other scaling and null devices.

For longer times, temperature and ageing effects will add.

As zener based elements are the best / most stable references we currently have at room temperature level, these mostly limit the stability figures.


The third aspect is the uncertainty of voltage measurements.
JJAs  have zero uncertainty, per definition of the new S.I.
It has been proven, that the difference between two different JJAs is lower than 10^-19.

Transferring this zero uncertainty from cryo/quantum to the macroscopic world, like zener based references, this is possible with these 10^-10 of resolution.
But as soon as you'd disconnect them from the JJA system, the noise and timely / environmental parameters chime in, and you might assign an uncertainty of a few tenths of ppm to the reference at most, using some monitoring and statistical techniques.
This 'real' uncertainty for a reference has to be evaluated from case to case.. you won't find that in the specifications.. only 'Stability' is given.

Scaling to other voltages than the usual 10V will add another few tenths of ppm, like using the 752A adds 0.2ppm @ 100V, and 0.5ppm at 1000V.

So, here you have it.. there exist a couple of methods to achieve sub-ppm in voltage metrology.. but you always should be aware of what you are talking about.

Frank

[alm]

For measuring a Fluke 732A/B based on a Fluke-characterized Fluke 732A/B, Fluke has the Direct Voltage Maintenance Program. They talk about typically achieving a transfer uncertainty of 0.05 ppm. Can you quote a lower uncertainty achieved without a Josephson Junction Array?

Also be careful that the quoted uncertainties for nanovolt meters do not cover uncertainty due to noise in your reference and thermal EMF. I imagine that will limit the accuracy of a transfer between any (non-JJA) real-life voltage references to well above 0.002 ppm.

Has anyone found the instructions for the Fluke DVMP transfer procedure? I imagine they ship a characterized 732B + nanovolt meter + cables + a transfer switch, but I haven't seen any technical details beyond the paper I linked.

[MegaVolt]

Sorry, you pose the wrong questions, or in other words, you are not fully aware about what you want to achieve, in terms of 'Resolution', 'Stability' and 'Uncertainty'.
The term 'Accuracy' is also too unspecific, to get the correct understanding about this problem.

I think most of the misunderstanding is made by Google translator

But I thought that the numbers in the Excel table are something that do not need translation. And in them I tried not to make mistakes.

Let's try to figure out the example of numbers.

For example, I want to find out how much my homemade LTZ1000 drifts relative to, for example, 732a.

And I use for this 7 1/2 DMM Keithley 7510.
Judging by its specification, the accuracy with which I can estimate the discrepancy between the two sources is 900 nV. Those. I can believe values ​​that are more than 0.1 ppm. And it doesn’t matter that on the screen I can see numbers with a resolution of 10 nV.

Those. with this device I cannot separate the LTZ1000 drift less than 0,1ppm due to the fact that I can not distinguish it from the device drift.

Am I reasoning right?