DMM Thought Experiment

[Crossphased]

I was doing some thinking today about how to economically increase DCV measurement capabilities from 6.5 to 7.5 digits, so I thought I'd ask the experts here their opinion.

Suppose you have two or 3 inexpensive HP34401 meters. Could you then use them together to increase your DCV precision/accuracy to 7.5 digits? I was thinking along the lines of something like this:


Suppose you then read the values from each meter over GPIB, and summed to a single value, and displayed separately. Could you confidently state this value is accurate to 7.5 digits? If so what qualifications would have to be made on the setup? For instance what if on the selected range of the meters, only 30% of the counts on each meter was being used... would you then only have an equivalent 6.5 digit result?

Extending the thought a bit further, would it be possible to stack ADCs to increase your precision beyond that of a single ADC, and to help combat INL. For instance:



I'm wondering if theres practical implementation details that would prevent reaching the desired results?

[TiN]

In short - no, that will not work. You cannot improve absolute accuracy even if you have ten 34401A's, you can only improve mean variation spread.
To simple terms - you have meter A and meter B to measure same voltage. Let's say Meter B shows +2ppm difference to meter A. But without knowing what is true voltage that you measured, you will never know what is more correct, meter A or meter B? Adding more meters will not add better uncertainty, unless you have known calibration error or history on at least one of these 34401A. Getting more clocks that show wrong time will not get you to measure time any more accurate, you need better clock.

Also accuracy to 7.5 digits on DCV without carefully characterized bank of expensive DC standards is nearly impossible (think many tens of $K). That is 0.1 ppm, which is almost equal to noise of the standard like Fluke 732. To perform ratio transfers at this level metrology labs use null-meters and compare between DC standards, like 732 or JJA. Even best 8.5d DMM stability like 3458A/HFL under 24 hours is already specified at 0.55 ppm, which is techincally 6.75 digits only

[schratterulrich]

Look at https://cdn.teledynelecroy.com/files/whitepapers/designcon-2017-understanding-vertical-resolution.pdf.

For lower bit resolutions it might work.
They use a similar concept in oscilloscopes.

[dietert1]

Many years ago we made a study on how to combine two DACs of a TI MSP430F2616. Those are 12 Bit DACs and we didn't combine them using statistics but using one of the DACs to apply small corrections to the other one. That chip also contains a temperature sensing diode, so the idea was: It's a stone and once you know the temperature behaviour it should make a high-resolution DAC as nice as any other. Of course the CPU needs to be off during DAC operation.
We used a HP 3457A bypassing its frontend to determine the calibration of the "more significant" DAC. We found an easy to understand error pattern and as far as i remember we were able to produce and reproduce true 19 or 20 Bits of resolution, which would roughly correspond to 1 or 2 ppm.
This is another example that there are smarter combinations of several ADCs and DACs than statistics to make one of higher resolution. Most stupid are those high-end audio DACs where they wire 16 or more rare 24 Bit audio DAC chips in parallel to get "perfect" sound.

Regards, Dieter

PS: If you get two precision DVMs from two different sources at ebay both with unknown calibration status and you find they agree within specs then that's luck, because most likely both of them are in good shape! If you got units of different make and age even better.

[razvan784]

I was doing some thinking today about how to economically increase DCV measurement capabilities from 6.5 to 7.5 digits [...]
Suppose you have two or 3 inexpensive HP34401 meters [...]

Sorry to be pedantic, but the 34401A is:
* already capable of 7 digit readings over serial/GPIB
* not accurate to 6 digits.
So you have to be careful what you mean by capability (resolution versus repeatability versus accuracy)

If I were to use multiple meters, I'd stick them in parallel, like Jim Williams does in the famous AN86.
Except maybe if I had to measure 30V, then I'd consider stacking them in series and using the better 10V range.

[Kleinstein]

Using more meters mainly helps with noise. Using the average of 4 meters would result in about half the noise. If works but is not very efficient because of the only square root like gain. Especially with equal meters the errors will tend to not cancel out. So there would be only little to no gain in accuracy.  The 34401 is not such a good starting point, as it is relatively high noise.

The series connection might help in some cases to get good accuracy for some 30 V, however it would need some extra HW, as the 10 K resistors shown would be too much loading to most source.

[Mr. Scram]

Sorry to be pedantic, but the 34401A is:
* already capable of 7 digit readings over serial/GPIB
* not accurate to 6 digits.
So you have to be careful what you mean by capability (resolution versus repeatability versus accuracy)

If I were to use multiple meters, I'd stick them in parallel, like Jim Williams does in the famous AN86.
Except maybe if I had to measure 30V, then I'd consider stacking them in series and using the better 10V range.

I don't think they're 7 actual digits, though. As far as I'm aware, it's just an internal reading before integration or noise elimination.

[razvan784]

I don't think they're 7 actual digits, though. As far as I'm aware, it's just an internal reading before integration or noise elimination.

They are "actual digits" in terms of resolution (but not accuracy). The readings obtained through the communication interface seem to go through the same process as those being displayed. I mean no further filtering is done AFAIK. For example, if you increase NPLC the readings come in slower and show less noise.
Hint: the (much more expensive) 34420A is sold as a 7 1/2 digit instrument and uses the exact same ADC (but a better front-end). The schematics are public.

[golden_labels]

You would need identical resistors to make this work (impossible) or at least know precisely their resistance and thermal coefficients (expensive).

Extending and correcting what Kleinstein has said above about noise:

If the number of the meters/ADCs needed would increase quadratically, the situation would still be quite optimistic. Unfortunately it is increasing exponentially. What’s the difference? See the attachment.
To extend the resolution by 1 decimal digit, you would need at least 16 DMMs (not 10, because you can’t extract fractional bits). And this is resolution, not accuracy. This is why flash ADC is not used in any higher-resolution converter: for a 24-bit ADC you would need 16.7 million comparators in a chip. Oh, and a 16.7-million-lines-to-24-lines priority encoder.

However, for constant voltage you may spread your measurements not in space, but in time. As long as the signal is stable (ignoring noise), 16 consecutive measurements will give you 1 more digit of resolution. Assuming infinitely high precision or precision being affected only by random noise . And of course accuracy is as bad as it was. But yes, this works as a way of fighting noise.

[dietert1]

As far as i understand, in Gaussian statistics averaging 16 measurements the average has a factor 4 less sigma than the single measurement. So that means two more bits. In order to get 10 times lower sigma, you need to average 100 measurements. Anyway, there are systematic errors that propagate through averaging. Usually those DMMs are designed to have a balance between noise resp. systematic drift  and resolution, so you can't really win that much by averaging.
Maybe somebody can explain a little about noise reduction by median method (nonlinear).
Redundancy also doesn't help much for precision but it helps detecting technical problems. We have two very stable HP 3456A and it's nice to see that the distance between the two results stays the same within +/- 1 ppm when running a precision measurement . Even a much jounger precision DMM can develop a problem or drift at any time.

Regards, Dieter

[golden_labels]

As a clarification: I was speaking only about resolution. I wasn’t touching statistics¹: we know nothing about variance in this case, and people usually care only about point estimation.
____
¹ Strictly speaking it relies on LLN, but calling that “statistics” would be as appropriate as if I would call looking at a speedometer “mathematics”.

[Kleinstein]

With most modern DMMs like the 34401 at not too fast a data rate there is usually enough nominal resolution (before noise). It is the noise that set the practically useful resolution. So in the 34401 the possible values can be fine enough spaced to get 7 digit resolution, as available via GPIB, but the noise is often so high that the 7 th digit is not really stable unless averaging is used. So there are 2 resolution limits and often the noise limit is relevant:
1) the nominal resolution that often depends linear on the integration time, and thus could be limiting for fast conversions (e.g. 1 ms)
2) the noise limit, that often scales with about the square root of the integration time. To very long times averaging tends to get more effective as 1/f noise can otherwise dominate.
Resolution is not just a single fixed number, but depends on the speed.

Another point to keep in mind is that when measuring a voltage not close to zero, the noise from the reference can be limiting. So it is not only the ADC that matters, but also the reference. Using several meters would also use multiple reference and would thus also reduce reference noise.

The balance between noise and accuracy can vary quite a bit between meters. I would consider the 34401 relatively noisy but with good linearity. Newer meters like the keysight 34465 tend to be lower noise (from the ADC), but often not better in linearity and the reference in 6 digit DMMs is still usually a LM399.

@golden_labels: there is no need to divide the voltage equally between the meters. So there is no need for accurate resistors - a different ratio would only reduce the gain in noise (the reference noise part) a little. But who cares about 1% more or less noise.

[e61_phil]

First of all: We have to differentiate between accuracy and resolution. Tricks like a second DAC combined with another one normally only increases resolution, but don't overcome the accuracy of the master DAC.

I did some "simulations" some time ago to figure out how accurate "the volt" is in our company measured by different instruments.
https://www.eevblog.com/forum/metrology/combination-of-uncertainties/

Increasing accuracy with more meters (or other artifacts) is only possible if the path to the volt is completely independent or the root uncertainty is really low and doesn't contribute to the overall uncertainty. Using 100 34401A from the same cal lab doesn't help here, because they are normally all calibrated against the same calibrator which is a big contributor to the uncertainty. The only thing what is reduced is noise and short time stability of the 34401A and that is already really good.

By the way: Three meters showing the same doesn't mean that the reading is correct. Depending on the accuracy it isn't unlikely that all meters are wrong in the same direction.

[dietert1]

That's what i wrote: Running multiple meters parallel does not help for accuracy. It helps detecting problems in the DMMs and this matters if you prefer using old DMMs for whatever reason.
By the way: One of our two HP 3456A is an early model (SN 3xxx) and it runs with a fan. It takes some minutes to settle to 1 ppm.
The other one is a later model (SN 19xxx) without fan and a slightly different reference board. It needs an hour to settle.
They came to us from different labs. If those two units go parallel with less than 3 ppm drift over 10 years  i think it means the datasheet specs were very conservative and that a regular calibration may not be necessary, at least not every year. Anyway, i will try and check that soon at a metrology meeting.

Regards, Dieter