9½ Digit Multimeter, feasible?

[laichh]

Saw this post on StackExchange.com, how would you answer?

https://electronics.stackexchange.com/questions/450454/why-isnt-there-any-9-5-digit-multimeter-or-higher

The real puzzle could be: "How far away are we from the 9½ digit multimeter?"

That's 10 nV resolution on 10 V range!

[Kleinstein]

For the noise it is a question one how long one averages / waits and how stable the zero is. With care the stability / LF noise may be kept low for a reasonable time, though this is not easy. One may can get the ADC close to the 100 nV per square root of Hz level. This would mean averaging/integration over some 100 seconds to get an RMS noise down to the 10 nV level.

For my DIY solution, that is really low noise (e.g. slightly below 3458 for the ADC noise, but still a poor reference), I get an RMS noise just below 500 nV for 25 SPS for a +-25 V full scale. With a little averaging (e.g. 2 seconds) the 100 nV digit is OK, though the Allan variance hardly goes below 30 nV. An thus 250 milion counts or just a little more than what is normally called 8 1/2 digits - maybe 8 3/4 with a little stretch. Given enough time maybe a SNR  corresponding to 9 digits.
However for a good meter there is more than the noise, when looking at a short.

Already the 8 digit meters are somewhat limited by the low frequency reference noise. E.g. a single LTZ1000 ref. hardly gets below the 50 nV level for the Allan deviation. The reference limitation at least is not that bad if one measures a relatively small voltage, like just a littler over 10% and thus just at the edge where the next lower range does not work. So the extra ADC resolution can still be of some use. Also some tests can use the same reference.

Another limitation is linearity. It gets already tricky to get much better than some 0.1 ppm and especially to test that the linearity is really that good. This starts with the problem that there is just not enough time to test at every possible reading, so no 100% testing possible.

For a high end lab and use as a differential voltmeter, a JJA can give more than 9 digit stable resolution. It just is expensive and a bit tricky to use with the protection. Such high resolution also only makes sense if the signal source is also that stable. At the high end it is not just the meter, but also the source noise and drift.

[Phil1977]

Just use a binary display - then good ADCs give you 24 digits!

Beside the technical reasons that Kleinstein has explained: If you need more than 8 digits of resolution, then you need to buy or build a whole customized measurement system. I suppose 8 1/2 digits are the upper limit that is reasonable in a multimeter - and even in these multimeters only some ranges can really make use of this resolution.

If you look for frequency counters or for timers you easily get more than 10 digits of resolution. You can buy interferometers for distance measurements that go down to 100nm at 100m range - that equals 9 digits. It depends on the application - but I just don't know a standard application for a voltmeter that requires more than 8 digits.

[macaba]

Actual digits: no, physics & reality pushes back.
Marketing digits: yes, DMM vendors are known to place their products in an entire digit category above what they could truly be pragmatically considered to be.

[m k]

25V over 50ohms is 500mA, 100nV less is 2nA difference.

What kind of a practical happening creates 2nA?

If HP 34401A is idling and human touches its bumper the voltage reading goes sky high.

[EC8010]

Marketing digits: yes, DMM vendors are known to place their products in an entire digit category above what they could truly be pragmatically considered to be.

Yes. My Agilent 34410A claims to be a 6 1/2 digit meter, but 12 is the largest number it can display before changing range, strictly making it a 6.08 digit meter. And the last digit is generally dubious, making it a reliable 5 digit meter. But that doesn't sound so impressive.

[Dr. Frank]

We discussed this subject on the recent Metrology Meeting 2024 in Stuttgart:

The StD or the Allan Deviation is used in DCV metrology (as communicated by Mr. Luis Palafox from PTB) as the decisive parameter of stability.
At first, you need a very quiet DCV source, e.g. a 10V JJ array, which would give about 2nv rms  @ 10V, or 2*10^-10 noise, about 10 "digits".

The HP3458A already displays 9 digits, if you read via GPIB with OFORMAT DREAL, or if you use Statistics Mean and Standard Deviation.

The performance with usual LTZ, LTFLU based references then is about 100 .. 200nV rms noise, i.e. 0.02ppm or a bit less than 8 Digits.
This is a convolution (quadratic sum) of the source noise and the noise of the DMM.
I regularly achieve such noise figures, and 9 Digits,  by taking 16 measurements of NPLC 100 with statistics on the DREAL data with Welfords Algorithm.

Measuring an ADR1000 based reference often gives noise figures below 100nV, i.e. 0.01ppm or  full 8 digits.
Mostly the flicker or popcorn noise of the internal LTZ1000A reference kicks in.

Therefore, a more silent reference like the ADR1000 inside the 3458A, and several less noisy OpAmps on the ADC board would improve its noise performance, but you would again need a much less noisy DUT for judgement.

ChuckB, aka Chuck Beuning demonstrated on the MM2024 both:

He presented his new analog ultra low noise DCV reference Z10, having an StD / Allan Deviation near the level of a JJ array, i.e. 4..5nV @ 10V.

Chuck, in cooperation with xdevs, they developed a 4 fold ADR1000 reference for the 3458A, and replaced 3 OpAmps for the +/-12V and 5V reference of the ADC.

Chuck presented the Allan Deviation of the altered 3458A, measuring his Z10 reference, or a zero input on the 10V range, like in xdevs former DMM noise comparison campaign.

For the Z10, he achieved about 40nV rms, i.e. 0.004ppm, and for the short 15nv rms, i.e. 0.0015ppm.

Therefore, the 3458A is capable of delivering near 9 digits stable results with these changes.

Frank

[EC8010]

Fascinating stuff. Were any of the Stuttgart presentations documented for subsequent download?

[Dr. Frank]

Fascinating stuff. Were any of the Stuttgart presentations documented for subsequent download?

Yes, the presentations were made accessible to all the participants.
Frank

[EC8010]

But not to those who weren't able to attend.

[Sensorcat]

Yes. My Agilent 34410A claims to be a 6 1/2 digit meter, but 12 is the largest number it can display before changing range, strictly making it a 6.08 digit meter. And the last digit is generally dubious, making it a reliable 5 digit meter. But that doesn't sound so impressive.

My result is 6.38 digits for your meter, with log(N) the number of digits for N counts. You have: 0.000 000 to 1.199 999 and -0.000 001 to -1.199 999; so N=2,399,999.

[2N3055]

Yes. My Agilent 34410A claims to be a 6 1/2 digit meter, but 12 is the largest number it can display before changing range, strictly making it a 6.08 digit meter. And the last digit is generally dubious, making it a reliable 5 digit meter. But that doesn't sound so impressive.

My result is 6.38 digits for your meter, with log(N) the number of digits for N counts. You have: 0.000 000 to 1.199 999 and -0.000 001 to -1.199 999; so N=2,399,999.

6 1/2 digit nomenclature has got nothing to do with logarithms. And it is not about full scale range but display digits number.

In this particular case it is full 6 digits on the right (0-9) plus first left digit that has only two states (0 or 1).
20% over 1,000 000 is reserve range.

Some meters (like R&S®HMC8012) claim 5¾-digit display (with 480 000 counts).. 0-4 range for first digit would actually make it what I would call 5 1/2 digit and 34410A would be 6 1/10 digits, but hey..
It is marketing crap.

Therefore I highly prefer counts nomenclature ... 480 000 counts or 1 999 999 counts. ± is implied.

[guenthert]

Noise is an obvious challenge, another is linearity.  E.g. the old Datron 1271/1281 use only run-of-the-mill components and a conceptually simple ADC, but they put quite some effort into improving linearity of its integrator.  Even just verifying the linearity of a long-scale DMM is a major undertaking.  I'm afraid, for enthusiasts and small companies, best one can do is compare to a HP 3458A.

[Dr. Frank]

Noise is an obvious challenge, another is linearity.  E.g. the old Datron 1271/1281 use only run-of-the-mill components and a conceptually simple ADC, but they put quite some effort into improving linearity of its integrator.  Even just verifying the linearity of a long-scale DMM is a major undertaking.  I'm afraid, for enthusiasts and small companies, best one can do is compare to a HP 3458A.

.. it's INL would be good for 2*10^-8 or 8 Digits only.

The initial question about a 9 1/2 digit DMM is kind of incomplete, or unspecific.

The discussion therefore went into the direction of 'resolution', instead of stability and uncertainty of DCV measurements.
I have answered the aspect of stability, which would give a lower limit for relative comparisons (transfer) between different DCV references, ignoring the INL error (between e.g. 7.15V vs. 10V references).

In practice, if I make transfer measurements between my 11..12 references, within 30..40 minutes, I'm able to achieve about 0.05 ... 0.1ppm transfer uncertainty, due to mid term drifts of the references, and room temperature changes of about 0.3°C during this period of time. This time-frame already goes beyond the 10min. transfer specification of the 3458A, the Datron 1281 and the Fluke 8508/58/88A transfer specification looks nicer.

Although the StD of each individual measurement is always at 0.01 .. 0.02 ppm, that means a 5 times higher uncertainty of my transfer and repeatability measurements.

Therefore, relative DCV measurements with analogue circuits are mostly limited by the Zener references themselves. Maybe others can give some hints, how differential measurements (e.g. 3-cornered-hat) on a 10V : 10V level might improve these transfer uncertainties.

Using a JJ array would virtually improve INL and noise / stability in the transfer process, but the uncertainty of any Zener Reference, even the Z10, will still stay at the 0.1ppm level, I guess.
That means, that an 8 digit DMM is currently optimum for the actual reference technology, and 9 1/2 digits make no practical sense at all.

If somebody would invent a quantum reference @ room temperature, that would change the game.

Frank

[mendip_discovery]

I have wondered why they haven't upgraded, to 9.5 or even more. But my experience with any thing high precision is you are never that far away from the last few digits being a random number generator and no real use to anyone.

From a non technical pov what is the gain of extra digits. For hardware developers there isn't a massive desire for it, there are researchers out there but how much are the asking for more digits.

I would say we are hitting a wall slightly as we are getting to the point where the purity of copper the connections, the humidity, temperature and even the presence of people have an effect on the results. Though I am not an expert.

[iMo]

It does not matter whether 9 or 11 digits are of any practical use, we human species will always strive to go more faster, more deeper, more higher, more accurate.. It is encoded in our DNA..

[Sensorcat]

Yes. My Agilent 34410A claims to be a 6 1/2 digit meter, but 12 is the largest number it can display before changing range, strictly making it a 6.08 digit meter. And the last digit is generally dubious, making it a reliable 5 digit meter. But that doesn't sound so impressive.

My result is 6.38 digits for your meter, with log(N) the number of digits for N counts. You have: 0.000 000 to 1.199 999 and -0.000 001 to -1.199 999; so N=2,399,999.

6 1/2 digit nomenclature has got nothing to do with logarithms. And it is not about full scale range but display digits number.

May I ask what makes you so sure about that? Is there a standard that defines it? A law maybe? If yes, please post your source. If not, everybody can decide himself what it has to do with. And the logarithm makes sense, since each digit represents one order of magnitude in counts of the display: log(1000)=3, log(10,000)=4, ...

In this particular case it is full 6 digits on the right (0-9) plus first left digit that has only two states (0 or 1).
20% over 1,000 000 is reserve range.

The first digit has three states: -1, 0, +1.
What is reserve and what is range is completely arbitrary.

[2N3055]

Yes. My Agilent 34410A claims to be a 6 1/2 digit meter, but 12 is the largest number it can display before changing range, strictly making it a 6.08 digit meter. And the last digit is generally dubious, making it a reliable 5 digit meter. But that doesn't sound so impressive.

My result is 6.38 digits for your meter, with log(N) the number of digits for N counts. You have: 0.000 000 to 1.199 999 and -0.000 001 to -1.199 999; so N=2,399,999.

6 1/2 digit nomenclature has got nothing to do with logarithms. And it is not about full scale range but display digits number.

May I ask what makes you so sure about that? Is there a standard that defines it? A law maybe? If yes, please post your source. If not, everybody can decide himself what it has to do with. And the logarithm makes sense, since each digit represents one order of magnitude in counts of the display: log(1000)=3, log(10,000)=4, ...

In this particular case it is full 6 digits on the right (0-9) plus first left digit that has only two states (0 or 1).
20% over 1,000 000 is reserve range.

The first digit has three states: -1, 0, +1.
What is reserve and what is range is completely arbitrary.

You are creating science where there isn't any. My source are old datasheets and manuals and many discussions how that nomenclature was "invented" by marketing and has nothing to do with science or exact math.
There are old HP magazines where in one of those there were details about how 34401A  was designed, there is discussion about x and x digits and how range is 1 000 000 with 20% overrange to comfortably measure around 10V etc..
Whatever I said, take it as such, information was shared with you in good faith.

If you want to make a science project of it and search for peer review, referenced sources and such, you are welcome to waste your time. You'll get nowhere. But hey have fun...

[miro123]

Can we keep to the main subject "9½ Digit Multimeter, feasible?"  You are free to start new tread
Thanks.
Back to the question -  9½ Digit Multimeter, feasible?. I have many question
  - do you need 9 1/2 digit  linearity
  - do you need 9 1/2 short term stabilitty
  - what is the definition of short term stability - lowest in alan dev or strictly specified time - e.g. 24h   or 6h
  - do you need 9 1/2 digit DMM or only cat 3 DC voltmeter or nanovoltmeter or single lets asy +-10V range
  - last but not least. what about the noise?

As soon as you have simple A4 specs of what you want to achieve we can discus the requirement feasibility and details.

[coromonadalix]

if it was easily doable   we would have seen some ....   

[coromonadalix]

@miro123  what are your intent(s)  reacting like this ....

and 2n3055 answers are valid ...

[ivo]

As soon as they package up a programmable Josephson Junction source in a portable black box, we might get one

[dobsonr741]

How far away are we from the 9½ digit multimeter?

Twice as far of what you think. You also need a stable voltage source under test to measure. For-profit businesses will not create an instrument just to measure a treasured voltage reference all day.

[Rax]

You also need a stable voltage source under test to measure.

Which... exists (a JJ). I always wondered what exact measuring system gets employed to evaluate a JJ. Or maybe it's always the physics behind it warranting the output and the data never "flows in that direction."

[mendip_discovery]

Feasible, Yes.

The question is why would you want to?

I don't think it's happened partly as there is little interest in it. With the SI units they have been working hard to fix problems such as the meter getting shorter and he kg getting lighter that the the money and effort has gone to that. Then when it comes to the next levels of research I personally believe they are looking at what industry is looking for as that is where the money for going to come from.

Without some new tech (better precision and accuracy) in other areas the we are stagnating and until the next chapter is here we can only just wait for it to happen. Chicken and the Egg.