9½ Digit Multimeter, feasible?

[dietert1]

I think there will be a step forward as soon as somebody makes a low noise, completely ovenized meter, similar to the Z10. I mean with constant temperature, humidity and pressure.
Nowadays we have those nice integrated sensors that didn't exist when the 3458A was designed. E.g. the Bosch BME680 sensor is specified with RMS noise of 0.12 Pa, equiv. to 1.7 cm height change! And when using those sensors inside an oven, they perform really well. My latest setup delivers relative humidity readings predictable to +/- 0.1 % over several weeks.
Also Peltier elements became a mainstream product. So we can have cooling without moving air. Tremendous progress has also been made with low power, yet fast programmable logic (cellular phone technology). It may take some more time, but sooner or later people will come up with something much better than a 3458A.

Regards, Dieter

[iMo]

Creating a super stable controlled environment (like temperature, pressure, humidity, emi, radiation, etc) is an essential prerequisite, indeed, but will not help much, imho. You have to come with entirely new devices, based on ie. sub nanometer technology, or new material's physics, etc.

[dietert1]

Creating a super stable controlled environment (like temperature, pressure, humidity, emi, radiation, etc) is an essential prerequisite, indeed, but will not help much, imho. You have to come with entirely new devices, based on ie. sub nanometer technology, or new material's physics, etc.

I don't have to. In my opinion there has been enough new technology to try and do better.

[nimish]

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."

The Josephson effect is exact, so all you need is a precise enough time/frequency standard (easy). High speed serdes have made ultra stable time sources dirt cheap too.

[BrianHG]

8.5 digit meters already messes with my brain....
  9.5 digit?   What do you want me to do with that? 

It like trying to measure a 1k weight down down below the nano-gram, down to the pico-gram range.

I'm sure the moon orbiting above will mess with your measurements.

[Kleinstein]

.... 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."

The JJ is used for the definition and is thus exact. For evaluation before using it as the primary standard they still had to carefully check it against to old standards. Another test is checking 2 different JJ sources against each other. This was done with no detectable difference in the voltage, and they really looked hard. With a superconducting cicuit one can get very high accuracy, as there is not thermal EMF with superconductors. So no issue comparing mV voltages to the sub ppb level.

The actual use cases for a 9 digit DMM would be limited, mainly metrology and maybe a very few science experiments.  Anyway current 8 digit meters are not really accurate to the 8 th digit, it is just the noise and short time stabilty so that the 8the digit makes some sense. The stability and linearity are more good at the 7 th digit (or even worse with some types). One kind of needs the better noise to check the stability and linearity. The difficuly in making a much better meter is also more with the linearity and stability, not so much the noise.

[iMo]

Almost everybody plays with JJ these days.. 

[dietert1]

If 9.5 digits are realistic noise-wise and the voltmeter can be 0.01 ppm stable for a year, that would be a large improvement over the HP 3458A - a factor 100 or so. I'd guess linearity could then be handled numerically. The meter should include circuitry for linearity check and calibration (type of autocal).
As doctorandus wrote in another thread, the oven is a MCU plus some sensors and maybe 10 discretes. If you want a nice solution, add a W5500 web server. These things have become very easy nowadays and dirt cheap.

Regards, Dieter

[coromonadalix]

But in some labs, it was shown on the web ...    there was a 10 or 12 digit meter shown,  they where used in a lab to measure / generate mass by electricity etc ...

some kind of balance .. with equilibrium ...   they said it was more precise for mass reference than the called silicon sphere

sadly  can't recall the right name  i'm french ...

was something like this : https://radwag.blog/en/why-is-the-new-kilogram-better-on-the-revolution-in-the-international-si-system-of-units-and-the-redefinition-of-the-mass-standard--2021-08-24

[moerm]

I'm really excited about what one can learn here. For instance that 'x.y digits' has not to do with log(counts) but with digits! That's super-mega-cool because 7 segment LEDs (plus drivers) are dirt-cheap, cheaper by order of magnitude than the "famous standard HP3458".
Exciting proposition: Just glue 3 4.5 digit cheapo-meters to each other and have a 12 digits DMM (modest version), resp. a 13.5 digit one (marketing version)! Yay!
Or that a 1.2 mio counts meter actually is a 2.4 mio counts meter because it has the 1.2 mio counts twice, once positive and once negative Yeah, yeah, I know, you still get only 6 digits plus an imaginary 0.5 but let's not be picky. After all *no* '8.5 digits' DMM, not a single one I know of, actually has 300 mio (and a bit) counts and, in fact, the "famous standard HP3458" doesn't even have half of what real 8.5 digits would require.

And before anyone dares to talk about precision and accuracy, let me clearly state that those are not important. It's all about resolution, linearity, and ... wait a second and let me have a look at the HPilentsight marketing blabla ...

Now, yes, yes, I'll admit it, the word 'measuring' has (or once had?) a clear and concise meaning, and yes, that meaning was not "crudely guesstimate", but still, remember it's all about [insert HPilentsight marketing blurb like 'linearity']!

Whut? Precision and accuracy, pardon, of course I mean 'uncertainty', are 6.5 digits only (on a good day) at best? True, yes, but still: I call that heresy!

And now if you'll excuse me, someone needs to add some display digits to a 5.5 digit multimeter. After all, we'll need no less than a 10.5 digits DMM to verify that 9.5 digits DMM once it exists!

[Phil1977]

Just some metrology porn:

[RoGeorge]

The video description sais

Happy April 1st, 2023!

[Phil1977]

The video description sais

Happy April 1st, 2023!

Did you need to spoiler it for anyone else???

Okay, I didn't get it as a joke. It seemed quite legit that you can take a good instrument, reduce the noise, do more averaging and then get a stable display value for some time.

It definitely seemed more legit than the 6 digits on the FNIRSI-USB-Tester:

[moerm]

Okay, I didn't get it as a joke. It seemed quite legit that you can take a good instrument, reduce the noise, do more averaging and then get a stable display value for some time.

Absolutely! Who needs physics when we have statistics and marketing?

You see, the length of the potato peels I got when I peeled potatoes and measured the length of each with a crude ruler with 1 inch resolution turned out be 2.3134 inches, although, granted, not a single peel, when measured properly with 0.1 mm resolution) actually had that length.

Similarly, averaging plenty enough ADCs magically gain digits.

(Important note: no children were harmed during that test! In fact, the four year old daughter of my neighbour very much enjoyed painting lines on a wood stick that then served for the "measurements")

[Phil1977]

Each analogue measurement is only averaging.

But I get your point. Already 8 1/2 digits are much more than a healthy brain can imagine. And though it really works well to make an 8-bit ADC measure 12bit if you well define your analogue filters and do enough averaging, it just gets exponentially more complicated with every additional bit or digit.

Funny and hard to understand thing is that sometimes you have to add noise to increase measurement accuracy. Maths is strange sometimes...

[RoGeorge]

Not sometime, always must add noise.  Without noise, the averaging trick doesn't work at all.  And the noise has to be bigger than 1LSB.  And not any kind of noise, it has to be uniformly distributed, or else you'll get lying results.  Everything else has to remain perfectly constant, which in practice is not constant.

Even so, averaging does not increase accuracy, nor precision, only increases the resolution.

Accuracy, Precision and Resolution are 3 different aspects, they are not interchangeable words, and an instrument has to have all three to produce useful results.  Infinite resolution would be meaningless without corresponding accuracy and precision.


Now, since we are in the salad words realm, here's a reflection about metrology and the philosophical "Do we have free will?" (in the sense that the Universe is deterministic or not):

The short answer is yes, we do have free will because "metrology".

How's so?  Well, there are known math examples of chaotic functions, where the same function will have a wildly different outcome when even the slightest numerical deviation is plugged into the function as the initial conditions.  The fancy term is "Butterfly effect".

Now, if we switch from math to the real world, to get the initial condition it means to measure the current state.  And in metrology, a certain amount of error is inevitable.  Therefore, even if we were to know all the physics, we still can not measure the current state with zero error, so the Butterfly effect will still cram into our prediction, so we will still have an unpredictable result.

Even if the Universe were to be deterministic, our lives will still remain unpredictable because of metrological errors while measuring the initial conditions.

Fate or not, you will appear to have free will anyway.  Because "metrology". 

[Kleinstein]

The noise can be intrinsic to the ADC or amplifier and one may not have to add it. This is especially the case if one aims for very high resolution.
One may not even need averaging because of quantization noise. A high numerical resolution and thus low quantization noise can be relatively easy with an integrating ADC. So numerical resolution well better than the other noise sources can make sense, as this can be one of the lower hanging fruits.

Even with some chopping / AZ switching there are usually low frequency fluctuations / 1/f noise. These limit how much averaging makes sense, as longer averaging also extends the frequency range to lower frequencies. So there is usually an optimum time for averaging or diminishing returns for even longer averaging. In the Allan variance curve this shows as a minimum or at least no longer falling curve.

Instead of long averaging for a single reading one may have to average over the whole experiment / reading sequence. With some experiments this can suppress the LF noise.

[dietert1]

In general, when looking at averaged results we also have the ensemble with all the samples. We can check the statistical quality of those data looking at distributions and correlations.
As far as i remember with data analysis there can be systematic uncertainties. They need to be assessed by modeling and simulation. In the end the rules are pretty simple - at least when enough samples are available. With very large ensembles ("cheap data") systematic errors will dominate.

Regards, Dieter

[moerm]

Prolog: Feel absolutely free to find me boring and old-school!

Each analogue measurement is only averaging.

(As philosopy has entered the thread ...) Nope.(a) A measurement is gathering/determining quantitative information at some point in time. No more, no less. (b1) Everything that we humans can (really) measure is necessarily analog because the world directly accessible to us is, (b2) if you allow a quick reminder, "digital" is just a simplifying "bundling" of analog; instead of dealing with an infinite set of numbers we simply say e.g. "everything below 0.8 V is zero anything above 2.3V is 1  and everything in between is undefined".

But I get your point. Already 8 1/2 digits are much more than a healthy brain can imagine. And though it really works well to make an 8-bit ADC measure 12bit if you well define your analogue filters and do enough averaging, it just gets exponentially more complicated with every additional bit or digit.

Funny and hard to understand thing is that sometimes you have to add noise to increase measurement accuracy. Maths is strange sometimes...

Uhm, quite frequently deal with numbers far beyond 8 (or even 80) digits in my job.
More importantly though, NO no amount of analog filtering 8 (or whatever) bits somehow gets you 12 (or whatever) bits. While, yes, that works in theoretical ponderings and is often used in science, measurements in electronics are, by their very nature, about physics. What filtering can do though is to get you more valid/"clean" bits in those your ADC got you. But if your ADC is 8 bits then you can't somehow magically get 12.

Not sometime, always must add noise.  Without noise, the averaging trick doesn't work at all.  And the noise has to be bigger than 1LSB.  And not any kind of noise, it has to be uniformly distributed, or else you'll get lying results.  Everything else has to remain perfectly constant, which in practice is not constant.

Nope, the noise must be random but I guess that's what you meant with "uniformly".
But no, at least in most cases on should not add noise because that's counter-productive. The goal of filtering out noise is to get a "cleaner" result and pretty much always there's already noise in the chain. Besides what does one get by adding (random) noise and then filters it out? In the best of cases one gets what one had before adding noise.

Even so, averaging does not increase accuracy, nor precision, only increases the resolution.

Accuracy, Precision and Resolution are 3 different aspects, they are not interchangeable words, and an instrument has to have all three to produce useful results.  Infinite resolution would be meaningless without corresponding accuracy and precision.

Yes and no. Yes they are different aspects and in particular, YES (hurray!) infinite, or let's say, much more resolution than accuracy and precision, is meaningless! (I'm very pleased to see that statement here).

But how much is "too much" or basically useless? My personal view is that I'm not interested in more then n+1 digits resolution when accuracy and precision is n digits.
Example: I don't care a flying fuck about an 8.5 digits multimeter with de facto 5.5 to, on a lucky day, 6 digits accuracy and precision (and that's the good ones.
But alas, companies are about profit which leads to marketing coming up with ever new BS. The sad state is that if one wants real 6 digits measurements one is bound to buy an "8.5 digits" DMM.

Now, since we are in the salad words realm, here's a reflection about metrology and the philosophical "Do we have free will?" (in the sense that the Universe is deterministic or not):

The short answer is yes, we do have free will because "metrology".

How's so?  Well, there are known math examples of chaotic functions, where the same function will have a wildly different outcome when even the slightest numerical deviation is plugged into the function as the initial conditions.  The fancy term is "Butterfly effect".

Now, if we switch from math to the real world, to get the initial condition it means to measure the current state.  And in metrology, a certain amount of error is inevitable.  Therefore, even if we were to know all the physics, we still can not measure the current state with zero error, so the Butterfly effect will still cram into our prediction, so we will still have an unpredictable result.

Even if the Universe were to be deterministic, our lives will still remain unpredictable because of metrological errors while measuring the initial conditions.

Fate or not, you will appear to have free will anyway.  Because "metrology". 

Careful there! Philosophical excursions tend to look attractive but actually have plenty of spikes ...

So, just two quick remarks:

No, the fancy term is "avalanche effect". "butterfly effect" is the (frankly, idiotic IMO) hollywood term. And btw. functions with an avalanche effect are not (necessarily) "chaotic". In fact we usually try hard to have them be well deterministic - yet avalanche (e.g. in cryptography).

And the main reason for us not being capable to make zero error measurements is not really complex but the simple fact that there is pretty much always (at least) one element in between us, who measure and the target of the measurement and/those element(s) usually introduce errors (e.g. DMM. Another factor often encountered is accuracy and precision (e.g. parallax error).

Generally speaking statistics is not a friend of metrology. It tends to be useful though when dealing with large (measurement) result sets. And statistics *never* creates reality with one single (occasional) exceptions: humans.

[Kleinstein]

Statistics is also the area of mathematics that handles getting information out of uncertain / properbalistic data. For metrology it helps to know the statistics - ideally beyond the common normal distribution and uncorrelated noise case. It can provide quite some powerfull tools. Compared to quite some other parts of math it is also a relatively new area.

Averaging or digital filtering in general works well, if there is sufficient noise in the data to avoid sticky bits from the quatization. If there is not enough noise already, it can indeed help to add some analog "noise", to make the quantization effect more random. Ideally one would start with enough numerical resolution, so that one does not have to add noise, but if the resolution is limited one may need to add noise to get a better result after averaging / filtering. The added "noise" can be more than white noise and even contain a deterministic part. The wanted effect of the added noise is to make the quatization error (and to some degree the DNL error) more random, so that it also be filtered to a large part. It may be counter intuitive, but it works. As an extrem many SD converters start with 1 bit and do filtering for something like 16 Bit and even more.

For a DVM there are different limiting effects that set the useful resolution this are mainly: the numerical resolution / quantization limit, the noise, the stability (especially gain/ reference drift) and the linearity. With averaging / numerical scaling the numerical resolution is normally not the limiting point for the final result - this is more a thing for much lower resolution (e.g. 3.5 digits) meters. The quatization is more like one of many noise sources and at the high end usually one that is easy to take care of. With long scale meters the claimed resolution is usually the noise limit (e.g. RMS noise for 1 LSB step) - the quantization is often better and the stability and noise essentially always worse. 

With a slow high resolution instrument the noise and stability limit how good the linearity can be tested.  With a very fast ADC the classic histogram methods can get around this limitation by averaging enough. So one effectively gets extra resolution, at least for the noise and quantization part.  A high resolution DMM often already uses some internal averaging near to it's limits and additional gain from extra averaging is very limited. There are also just too many points to test and to low a data rate for much extra averaging (often not enough time for a complete test). So it is natural that one has larger uncertainties from INL and drift than from noise. It kind of has to be this way. One can't measure and let alone fix an INL error hidden in the noise.
To get 6 digit accuracy one indeed needs to by more like a 8 digit meter - even there the stabilty is hardly that good for even a moderate time.

[Echo88]

What are your propositions to improve on existing so called 8.5 digit DMMs like HPAK3458A/F8508A in regards to schematics/construction moerm?

[dietert1]

An extra digit for an integrating voltmeter is cheap data. And systematic errors tend to be small when comparing measurements taken within a short time span. So for certain experiments (like a linearity check) that can be finished within some hours, the criterion cannot be the one year stability (or the lack of). You want some reserve digits in order to have digitization noise below analog noise level. Then you can average and make the statistical uncertainty small in comparison to systematic errors. One of the systematic limits of precision voltage measurement is thermal EMF. I think banana plugs and binding posts won't work for measurements at 9 digits below 10 V = 10 nV level.

Regards, Dieter

[moerm]

Kleinstein I largely agree with you plus I respect you too much to engage in a debate over details I see differently.

So I restrain myself to one point only: NO, no amount of statistics creates or changes physical reality - and that's what measuring is about. It does however, as I indicated, sometimes create a (pseudo) reality in peoples minds.
As I said, random noise in the digits one *really* has/gets can be (to a large degree) filtered out, e.g. by averaging. If in repeated, carefully executed, and properly verified experiments someone with a good knowledge level (like you) manages to get more precision and/or accuracy out of an ADC I'll accept that.
But generally speaking statistics is useful (mainly if not only) in "post-processing" large amounts of (e.g. measurement) data.

What you wrote about isn't what triggers me. What triggers me is (a) the fairy tale that one somehow can get more digits out of an ADC than it has, and (b) the bloody BS and the great lengths companies go in order to sell, often overpriced at that.

(maybe also see the next part of this comment)

What are your propositions to improve on existing so called 8.5 digit DMMs like HPAK3458A/F8508A in regards to schematics/construction moerm?

None. My approach is entirely different: how about designing, building and selling 6.5 digit multimeters as such, as 6.5 digit multimeters instead of adding some basically worthless digits and calling - and brazenly selling it as - an "8.5 digit multimeter" - aka acting honesty, which granted sadly has become a rarity nowadays, especially in anything related to money.

Why would I not even try to design and build an 8.5 digit multimeter? Because I see and accept boundaries and it seems to me that nature has put a boundary at about 1 ppm. Yes, we *sometimes* can cross that boundary and I'm not saying that one shouldn't try although I myself certainly won't.

Also note that we currently do *not have* 8.5 digit multimeters. We only have multimeters with about 6 *valid* digits with a label that says "8.5 digits" and a matching price.

I get it, "more! better!" seems to be hardwired in humans and I lusted for a F8508 too but found back to rationality and realized that I just lusted for it but don't really need it. My contempt for basically cheating companies and marketing liars was helpful in that.
So, I certainly understand people who strive to get a "top class DMM".

[Phil1977]

Uhm, quite frequently deal with numbers far beyond 8 (or even 80) digits in my job.
More importantly though, NO no amount of analog filtering 8 (or whatever) bits somehow gets you 12 (or whatever) bits. While, yes, that works in theoretical ponderings and is often used in science, measurements in electronics are, by their very nature, about physics. What filtering can do though is to get you more valid/"clean" bits in those your ADC got you. But if your ADC is 8 bits then you can't somehow magically get 12.

But to talk in examples that can be followed by a larger part of the readers: If you have a 1MHz 8-bit ADC available and need a 100Hz 12-bit then you don't need to go shopping. Normal distributed noise is reduced by sqrt(n) if n is the number of averaged measurements. That means if the ADC delivers 6 effective bits then you gain sqrt(10 000)=100 approx= 2^6.5 so your averaged result should theoretically have 12.5 effective bits. If your target are 12 data bits of which 10 should be effective then this method can work without any problem.

Of course I agree you can't have any magic algorithm that creates a usable 12-bit signal out of a 8-bit ADC without drastically reducing its sample rate. "Garbage in garbage out" stays always valid.

[dietert1]

Contributor moerm is trolling this thread.
There is nothing like a 1 ppm physical limit. Zener references with a stability of 0.02 ppm over several months have been demonstrated before. One can find the reports in this forum. And integrating ADCs stable to that level are commercially available.
The 1 ppm limit is something created by the calibration lab market. If Fluke or Keysight labs with quantum standards don't certify to better than 1 ppm it's their choice. Quantum voltage standards are known to be good for about 0.0001 ppm, ten times better than necessary for a 9½ digit meter.

Regards, Dieter