thought experiment - self-controlled voltage reference

[alm]

I'm still not confident that my approach won't work, because I was reading some more about correlation in context with noise measurements and an approach to compensate for the noise of the gear by correlation.

Yes, averaging helps against uncorrelated noise: the sqrt(n) best case improvement I have repeatedly stated.

How ever, up to now I haven't heard any argument that was able to stop me giving it a try.

I have no interest in keeping you from experimenting. I encourage you to convince us with results.

A real world simulation in my opinion isn't possible because you give them a behavior and a correlation they won't have, the references are uncorrelated.

The suggested simulation was for three uncorrelated random processes. Unless you question the quality of MATLAB's random generator for this purpose.

As long as the "world police" avoids starting nuclear w. w. and all people remember that we live in 21th century with no need for "cold war" and all that paranoia shown up in the last weeks I don't care about radioactivity. And if otherwise expected we get in such a situation I'm sure that I don't need this experiment anymore

And as long as the world police keeps from enforcing the laws of thermodynamics, we might even expect drift to be completely uncorrelated .

I would probably use a reed relay with gold plated contacts for these kinds of very low currents.

[madires]

Maybe lets get more practical. What relay would you suggest? A classical relay with gold plated contacts or one of those reed relais?

IMHO the reed ralay would be the right choice. It's more reliable, extremely good for switching low power signals, sealed and should have gold plated contacts anyway. Also the contact performance is more consistent.

[branadic]

Your opinion agrees with my thoughts, there are this Meder SMD-Reed-Relais available. They are everything but cheap but they will save space on the board. I have some samples of the rf version, pretty nice but not useful for real rf application when isolation is needed up to some GHz.

The suggested simulation was for three uncorrelated random processes. Unless you question the quality of MATLAB's random generator for this purpose.

I don't doubt the quality of Matlab (couldn't check your code because I use Octave and wasn't able to get it run) but your assumptions. The three references are uncorrelated be means uncorrelated drift, noise and aging rates. So together with the devide by two at the input I'll be able to also see the shift by 10mV of the reference in the same direction (upper example), wouldn't I?

[alm]

I don't doubt the quality of Matlab (couldn't check your code because I use Octave and wasn't able to get it run) but your assumptions. The three references are uncorrelated be means uncorrelated drift, noise and aging rates. So together with the devide by two at the input I'll be able to also see the shift by 10mV of the reference in the same direction (upper example), wouldn't I?

Changes to get it to run in Octave should be trivial. Uncorrelated does not mean the drift has to be different, just that they are as likely to drift in the same direction as they are to drift in the opposite direction. If all three references go up by 10 mV, then you don't detect anything. If two of them go up by 10 mV, then you can't tell whether two went up by 10 mV or the third went down by 10 mV (this is the same from the ADCs point of view). Note that time averaging works just as well to get rid of random noise. It's the not so random processes (eg. drift) that cause trouble.

[Andreas]

Maybe lets get more practical. What relay would you suggest? A classical relay with gold plated contacts or one of those reed relais?
I prefer a modular assembly,one board with the relais,the LTC1043 divider,the LTC2400 and the reference boards hucked up. For the first test I would use some LT1236LS8.

Hello branadic,

For my LTZ + LM399 references I am using 2-pole bistable signal relays with bifurcated gold contacts of type TQ2L2 (Matsushita / Panasonic).
The intention is that the thermal heating of the coil does not influence the thermocouples of the contacts.
The coils are only powered during switching, so that a 9V 200mAh block will power the multiplexer including processor for about one week switching.
With reed relays you will have a reliable contact over time but the wires will be most probably be of Kovar having
a 40uV/K thermocouple voltage against copper. So a good thermal design of the solder junction areas will be necessary.

Another approach would be a semiconductor multiplexer that I use for the 5V-ageing experiment. It consists of four simple CD4067 CMOS multiplexers switching either the 5V output or the GND signal of the Reference to the ADC.
The GND-signal is necessary since I have up to 60uV GND-shifts between the 32 references. I tried a differential multiplexer scheme but this was too noisy since I cannot use a battery supply with 32 references + heater for constant 50 degrees centigrade.

With the LTC1043 you have to notice that you cannot load the output directly by the ADC input. The input current of the LTC2400 will affect accuracy + linearity of the LTC1043. So you will have to use a buffer amplifier after the LTC1043. I currently use a LTC1050 with +14/-1.2V supply for this purpose. The LTC2400 has a linearity error nearly centered on mid-scale. If measuring the own 5V reference you will miss around 40uV reading something around 2.499960 instead of 2.500000V. So you will have to compensate for this according to AN86. And yes: the typical 4ppm linearity error of the LTC2400 seems to be in reality measured by the box method (+/-4 ppm around the best fit straight line and not the end points 0 + 5V) giving actually 40uV error at mid-scale.

The LTC1043 has a additional gain error of about +/-2-3 ppm depending whether you exchange input and output of the LTC1043 against the datasheet or not. So you should do a overall calibration of LTC2400 together with the LTC1043 for gain + linearity.

good luck + with best regards

Andreas

[madires]

With reed relays you will have a reliable contact over time but the wires will be most probably be of Kovar having
a 40uV/K thermocouple voltage against copper. So a good thermal design of the solder junction areas will be necessary.

Meder offers some reed relays with a thermocoupling voltage <1 µV/K.

[branadic]

Forgot to mention that, yes, the LTC1043 will get his buffer, both parts LTC1043 and LTC1050 are already here at the bench.

Meder offers some reed relays with a thermocoupling voltage <1 µV/K.

Really? I have to search for that. Thanks for this tip.

[Andreas]

With reed relays you will have a reliable contact over time but the wires will be most probably be of Kovar having
a 40uV/K thermocouple voltage against copper. So a good thermal design of the solder junction areas will be necessary.

Meder offers some reed relays with a thermocoupling voltage <1 µV/K.

If you think of the BT-type: It seems to be so that the circuit only works if using both contacts in a manner that the thermocouples are compensated against each other. (this is what I meant with carefully thermal design).

This assumes that the voltage references are all galvanically isolated against each other and the 2:1 divider.
And you will always have to use the whole contact pair for signal + return line.

With best regards

Andreas

[branadic]

This assumes that the voltage references are all galvanically isolated against each other and the 2:1 divider.
And you will always have to use the whole contact pair for signal + return line.

Something that won't be easy to realize when switching the references between input and reference pin of the adc.

[Dr. Frank]

Hello branadic,

you've constructed a very (too) complicated case, but it's a kind of Perpetuum Mobile only (Ultra Precision out of Thin Air), i.e. it does not work.
Such Perpetuum Mobile constructions are always difficult to unmask, but I will try to do it in a handy way.

To point out your error in reasoning, I have to sort your statements a little bit, and simply write down the calculation of the output of the ADC:

We now connect ref1 directly to the ref input of the adc and measure ref2, afterwards ref3 and save the difference ref2 - ref3.
We connect ref2 directly to the ref input of the adc and we measure ref1, afterwards ref3 and save the difference ref1 - ref3.
We connect ref3 directly to the ref input of the adc and measure ref1 and afterwards ref2 and save the difference ref1 - ref2.

The ADC will output digital readings, e.g. Mx=Refx/Ref1*K, and the calculation of the 3 differences Y1=M2-M3, Y2=.. and Y3=..  will be:

Y1 = (Ref2-Ref3)/Ref1 *K, Y2 = (Ref1-Ref3)/Ref2 *K, Y3 = (Ref1-Ref2)/Ref3 *K

Calibration Constant K is determined by the exact value of the 2:1 divider and the digtal length (~2^24) of the ADC, and can be measured / eliminated  by applying one of the Refs to Input and to Ref_in : M=Ref1/Ref1*K

This equation system:

Y1*Ref1/K = (Ref2-Ref3)
Y2*Ref2/K = (Ref1-Ref3)
Y3*Ref3/K = (Ref1-Ref2)

cannot be solved at all, because there are no independant variable on the left sides.
It is not even possible to determine the absolute values, not to mention any drifts.
If you try to elminiate two unknowns, you always end up with differences of them.
Simply speaking: you are already missing one independant, known reference at this point.

If you would relate your measurements to a fourth Ref4, which absolute value you know in first instance, you could resolve this equation system, and would get the absolute values of Ref1, Ref2, Ref3, but the drift of this forth reference would always go into the drift determinations.

To say it short: To measure absolute drift, which is needed to compensate for that, you always need to compare against one fixed (ultrastable) reference, e.g. an JJ standard.

If you measure relative drifts, it is necessary only to measure against one reference, i.e. always the same known reference.

If the differences between Ref1, Ref2, Ref3 are low, the uncertainty and stability of the ADC refence is not important, if you measure their differences directly.
(E.g: you can measure small differences with 3 1/2 or 4 1/2 digits panels)

In this case, you get the relative drifts of Ref1 compared to Ref2 to Ref3, and this gives you an idea, how stable those are, as an ensemble.
The more different references of one kind you have , the smaller is the possibility that they all drift in the same direction.
The max. spread of drift of the differences is then a measure of their individual stabilities, i.e. you can really estimate their absolute drifts.

Of course it's possible to determine outliers, i.e. references with much bigger drift rates than the others..

That's the classical metrological problem, to determine the stability of standards, if there is nothing "better" than those, or:

"A man with one clock always knows the Time. A man with two clocks is never sure. A man with three clocks is able to decide."


The following I also do not understand, how it will give results, or improve your construction

I just want to share and discuss an idea with you.

Lets assume we have:

Ref1 is connected to the dac that outputs let's say for the moment 1V, that is measured against a Josephson standard and adjusted to the exact value of 1.000000V. The correction factor is saved (initial calibration and adjustment).
Now the drift value for each reference is calulated and saved and the ouput of the dac with ref1 connected to it is corrected to the new value for 1.000000V based on the drift info.

You could only determine the absolute value of the refernces once, if you apply those 1.00000V to the ADCs input.
 
Later measurements or corrections are always done on a drifty reference, therefore the correction drifts also, and there is again no fixpoint

We expect, all three references are uncorrelated, so their noise and drift is different. After the initial calibration the system is monitoring itself. Any difference in trace length is static and therefore systematic,

No that's not true! (What do you mean with trace length??)

The differences are NOT static, and are unsystematic, as the drifts are independant and not determined.

Anyhow, all measurements are self-related, and therefore you cannot eliminate the absolute values, nor the drift.


Conclusion: There is no free lunch.
Otherwise: If your perpetuum idea would work, others would have realized it already, wouldn't they?

Frank
 

[chickenHeadKnob]

Hello branadic,

you've constructed a very (too) complicated case, but it's a kind of Perpetuum Mobile only (Ultra Precision out of Thin Air), i.e. it does not work.
Such Perpetuum Mobile constructions are always difficult to unmask, but I will try to do it in a handy way.

The criticism that branadic's approach is  a perpetuum mobile  because of its circularity is a bit to simple.

In this case, you get the relative drifts of Ref1 compared to Ref2 to Ref3, and this gives you an idea, how stable those are, as an ensemble.
The more different references of one kind you have , the smaller is the possibility that they all drift in the same direction.
The max. spread of drift of the differences is then a measure of their individual stabilities, i.e. you can really estimate their absolute drifts.

Of course it's possible to determine outliers, i.e. references with much bigger drift rates than the others..

Yes! this is key.

Dr. Frank goes on to say:

That's the classical metrological problem, to determine the stability of standards, if there is nothing "better" than those, or:




Conclusion: There is no free lunch.
Otherwise: If your perpetuum idea would work, others would have realized it already, wouldn't they?

Frank

But others have realized it!

I have recently added metal working to my list of hobbies, and one of the  precision wonders required is a surface plate, or even better- optical flats. As you have vastly more education in physics than myself  I won't presume to tell you how they are made, I just give my understanding which is that you start with three crude articles (blanks) and grind them one on the other, flipping and exchanging the blanks in rotation. With patience and ever finer grinding media you can derive ever finer planarity and level. This is how amateur astronomers routinely gain optical quality surfaces with cave man equipment. Either implicitly or explicitly I believe this process to be the inspiration for branadic's contraption.

Now I still see problems with Branadics attempt, as the high points (outlier references) do not necessarily stay high points as they would with surface plates (between rubbings), also there are many more points of potential contact with surface plates, which means you would need a huge sea of reference zeners. I also find the DAC suspect as it has its own error characteristic and it does not average like grinding media.

The idea that you might be able to bootstrap into the next higher level of precision fascinates me, for the intrinsic possibility of getting something for nothing, and because unlike the other volt-nutters who have access to 3458's I am existing in precision poverty.

[alm]

The crucial difference in my opinion between the construction of an optical flat in the way you describe and branadic's approach is that drift and noise of voltage references is a stochastic (random) process, unlike the flatness and bumps of a solid surface which is for most intents and purposes constant. The difference between two random processes is just another random process. Its variance might be slightly lower, but only if they have a known and perfect correlation will subtraction result in substantial cancellation of errors. A substantial and unknown correlation is even worse, however, since you might actually be amplifying errors.

I share Dr. Frank's criticism that it seems overcomplicated: a bunch of subtraction, switching etc that to me seem to serve no purpose, which is why I suggested simulations to reduce it to the simplest system possible. The problem with experimental validation is that to quantify drift, you need a reference with a substantially lower drift than a single reference. So you might actually need that 3458a to design the low cost reference. And the 3458a is not particularly great for long term drift (maybe a factor of two better than a single LM399), which is why the real volt nut will use a voltage transfer standard -- or even a JJ -- as reference for the 3458a .

Starting with crappy references to prove the concept might actually be the simplest solution: if you can get 0.01% stability (something that you should be able to measure with a decent 4.5+ digit DMM) from a crappy reference that shows 1% drift over some reasonable time period (you don't want to measure for a year), then it shows that your method can substantially improve the stability. Of course more effects (like the noise of the DAC) come into play as you go to even higher stability, but something crappy like zeners might be a good way to show a proof of concept. It may for example turn out that drift in those crappy reference is dominated by the highly correlated change in ambient temperature, something that will play much less of a role in better references.

[Dr. Frank]

The criticism that branadic's approach is  a perpetuum mobile  because of its circularity is a bit to simple.

Sorry, but it IS REALLY as simple as this... it was my intention to clarify this as easy as possible.

Alternatively, if it's still too complicated to see it clearly, one could write down the complete set of six equations M1 ... M6 for the ADC output, and then try to solve it, also with no result:
3 of those 6 equations are inverse versions, and the fourth equation can be calculated from the other two.

So you have 2 independant equations  for 3 variables only.
That's sufficient for determining all ratios between those 3 references, but neither their absolute values, nor their absolute drifts.
 

But others have realized it!

Sorry: WHO has created an ultrastable Artefact Standard from 3 drifty ones, as described by branadic? (E.g. Zener Refs, Weston cells, kilogram standard of Sèvres, etc...)

I don't know anybody.  Please show me where I can find that.

I have recently added metal working to my list of hobbies, and one of the  precision wonders required is a surface plate, or even better- optical flats. As you have vastly more education in physics than myself  I won't presume to tell you how they are made, I just give my understanding which is that you start with three crude articles (blanks) and grind them one on the other, flipping and exchanging the blanks in rotation. With patience and ever finer grinding media you can derive ever finer planarity and level. This is how amateur astronomers routinely gain optical quality surfaces with cave man equipment. Either implicitly or explicitly I believe this process to be the inspiration for branadic's contraption.

A near perfect flat surface has nothing to do with such artefact standards for SI units.
You have used a very, very inappropriate comparison.

The analogon to your flat mirror in volt metrology is perhaps the Hammon type divider or the Kelvin-Varley divider, which create ultra - precise volt RATIOs by self-calibration only, without the aid of another hyper-standard (and currently there is nothing better in metrology, if you do not use  a quantum standard, i.e. the JJ array.)

The idea that you might be able to bootstrap into the next higher level of precision fascinates me, for the intrinsic possibility of getting something for nothing, and because unlike the other volt-nutters who have access to 3458's I am existing in precision poverty.

This "bootstrapping" really exists, but in a different meaning!

This is routinely used for stability determination, i.e. it's a common "metrological practice" to compare two or more stable standards against each other (the more, the better), and then from their relative drifts to ESTIMATE their individual absolute drifts.

How do you think the Cesium beam clocks have been qualified, i.e. the statement " A Cs clock is precise to 1 sec in 30 million years" ??

Very easy, there are two ways:

Theoretically, you calculate all known external influences on the stability, try to mitigate them and calculate the worst case deviation / stability figures  theoretically.

Practically, necessary as a proof of the theory: you compare all Cs clocks of all state institutes (NIST, PTB, BIPM, etc.) against each other via dual view satellite connection.
You will get the relative drift rates, which are very low, on the order of 10e-16/yr, and then do some statistics to estimate their individual drifts.
Here again, you cannot measure the absolute drift rates directly, because up to recently, there did not exist more stable clocks.



I have explained that technique in my article about the LTZ1000 reference, where I compare 4 independant ultra-refs, and estimate their individual drifts to < 1ppm/yr.
I cannot improve their individual stabilities either, but it was solely a great thing (call it a metrological trick) to measure their relative drifts and estimate their absolute drifts WITHOUT using a JJ array standard.

And indeed, that's possible with branadic's attempt also (if he removes all that unnecessary complications), not less, but also not more.

Frank

[chickenHeadKnob]

The criticism that branadic's approach is  a perpetuum mobile  because of its circularity is a bit to simple.

Sorry, but it IS REALLY as simple as this... it was my intention to clarify this as easy as possible.

Alternatively, if it's still too complicated to see it clearly, one could write down the complete set of six equations M1 ... M6 for the ADC output, and then try to solve it, also with no result:
3 of those 6 equations are inverse versions, and the fourth equation can be calculated from the other two.

So you have 2 independant equations  for 3 variables only.
That's sufficient for determining all ratios between those 3 references, but neither their absolute values, nor their absolute drifts.

I hope we don't get into a misunderstanding with each other as I learn from your posts and enjoy them. I was almost in  full agreement with your previous post but reacted to the phrase " perpetual mobile" as it invokes the laws of thermodynamics and would lead the discussion into a cul de sac. Which I worsened by using the phrase "too simple" when I meant to convey the meaning: the mere presence of circularity was insufficient to be a flaw.

And while I do have I simple mind I did follow your original argument with the equations and agree with it. You can't get there from here, if there is an accepted standard value and here is three drifty unknowns.  My small disagreement was with the notion that any circular (self referential) process axiomatically meant you were stuck with the originating level of precision.

 The mental model I was operating under was that of a mathematician who needs to prove an infinite series set before him converges to a finite result. Just like in metrology there are dual burdens, first prove the series converges to a (any) finite result, that is, is it increasingly  precise. Second if it converges, does it converge to a known value,  that is, is it accurate. Please correct me if I have reversed the definitions of Accuracy and precision. For what it is worth I never thought Branadic's putative machine achieves improvement in either accuracy or precision. But what if someone comes up with a system which iteratively evolves greater precision in its intermediate results, up to some physical limit. That is in my mathematical analogy does it converge to some value + epsilon? This is why I gave the example of amateur lens grinders. I think the laws of nature do not a priori prohibit such a process they just may make it difficult, again please correct me if I am wrong.

Sorry: WHO has created an ultrastable Artefact Standard from 3 drifty ones, as described by branadic? (E.g. Zener Refs, Weston cells, kilogram standard of Sèvres, etc...)

I don't know anybody.  Please show me where I can find that.


A near perfect flat surface has nothing to do with such artefact standards for SI units.
You have used a very, very inappropriate comparison.

The analogon to your flat mirror in volt metrology is perhaps the Hammon type divider or the Kelvin-Varley divider, which create ultra - precise volt RATIOs by self-calibration only, without the aid of another hyper-standard (and currently there is nothing better in metrology, if you do not use  a quantum standard, i.e. the JJ array.)

Frank

It was not my claim or intention to convey that you could achieve a standard kilogram by rubbing three rocks together. Hammon, KV dividers, null meter, torsion  balances and other instruments of precision do have many useful applications even if you do not have access to a known standard. Here in my wilderness,  I consider it a partial victory if I have a machine or process which can make precise measurements even if I can not trace the result back to a known standard.

best regards

[branadic]

1. Comparing a thought experiment about a self-controlled reference that is powered by mains or battery with a perpetual motion machine harvesting free energy out of nothing only be applying a portion of energy to it for one time is farcical. I really tried to manage a factual discussion, but the perpetual motion machine statement is far beyond that.

2. Believing that a few linear equations are adequate to explain a complex nonlinear construct is farcical too.

3. Telling people that they are wrong because others would have already realized a soultion for a given problem is ignorant and nonscientific. If everything would have been realized I were unemployed in my job as r&d engineer.

Nothing personal against you Frank, but you don't know it all.

BTW.: Your holy JJ is everything but absolut stable too.

[Dr. Frank]

1. Comparing a thought experiment about a self-controlled reference that is powered by mains or battery with a perpetual motion machine harvesting free energy out of nothing only be applying a portion of energy to it for one time is farcical. I really tried to manage a factual discussion, but the perpetual motion machine statement is far beyond that.

2. Believing that a few linear equations are adequate to explain a complex nonlinear construct is farcical too.

3. Telling people that they are wrong because others would have already realized a soultion for a given problem is ignorant and nonscientific. If everything would have been realized I were unemployed in my job as r&d engineer.

Nothing personal against you Frank, but you don't know it all.

BTW.: Your holy JJ is everything but absolut stable too.

1. Yes it's right, I used this comparison with Perpetual Mobiles (more energy from less energy) because I really doubt that your construction is capable of creating more stability out of less stability.
Sorry, it was not intended to insult you, I just wanted to pin point the problem, I have with your construction. And I am not the only one, obviously.

2. As long as your relatively simple construction is a linear system, I think it's adequate to use linear equations only.
I did not find nonlinear relationships in your description. Also, their existence would not prove your statement automatically right, I think.

You are an engineer?

Fine, then you should be able to express your theoretical  construct in mathematical expressions, let them be linear or non-linear either. I'm really curios, where in your construct the non linear behavior is buried, which I have obviously overlooked.
 

I really would appreciate, if you prove me wrong, and yourself right by presenting your calculations.

3.  You are right, I do not know everything, and I did never claim that.
Honestly, I tried really hard to understand your puzzled description, and I failed, obviously. 

As far as I have understood it, your construct was far too simple, that nobody else should have had this idea already - if it really works.

So, please help me, and explain your idea in another, more understandable way.

Best would be to do it mathematically, because that's the most scientific way, and what engineers and scientists understand best.


"Btw.:"  What do you want to tell me with that sentence?
I did not state that either, and no, it is not "my holy JJ", what do you think?

Stay objective, please.

Frank

[Andreas]

Hello,

to come back closer to the original theme some of my thoughts:

- the minimum quality what can be expected when bringing 3 references together is that the resulting drift of the whole system can be brought to that what the average value of the 3 references is.
- further you can do some statistic functions (standard deviation, x-r card...) to find out if one of the references behaves unusual or has the largest drift with respect to the average value. So this unusual reference can be excluded for further measurements.
Of course for statistics it would be better to have many references and not only 3. But if the system excludes the right of the references it may be more stable than just a system with 3 averaging devices.

@branadic: what do you mean when writing Ref1+Ref2 do you want to add the voltages to around 14V or do you mean the average value of the both references Ref1+Ref2.

When measuring small differences or drifts between 2 devices it may be better to measure directly the difference of the 2 voltage references instead of calculating the difference between the 2 absolute values.
In my daily measurement of LTZ and LM399 references I do both. Measurement of the absolute value and the difference.
If calculating the standard deviation in uV out of 50 succeding days for the measured difference and the calculated difference each I get the following values:

meas. diff         calc. diff
1.04                 1.36       first 50 days
0.85                 1.03       2nd 50 days
0.53                 0.85
1.12                 1.30
1.05                 1.19
1.15                 1.27
0.90                 1.23
0.70                 0.80
0.66                 0.80      last 50 days

So you can see that the standard deviation of the calculated differences is regularly higher than the direct measurement.
The reason is that with the direct measurement the noise of the adc counts only once. Whereas with the difference measurement the noise is included 2 times (or 4 times when regarding the offset nulling) into the result.

With best regards

Andreas

[alm]

- the minimum quality what can be expected when bringing 3 references together is that the resulting drift of the whole system can be brought to that what the average value of the 3 references is.

You should be able to do better than the average. If you have ten references with a random drift that is identical in magnitude, then the average should be more stable than each individual reference. sqrt(10) times better in the ideal case.

- further you can do some statistic functions (standard deviation, x-r card...) to find out if one of the references behaves unusual or has the largest drift with respect to the average value. So this unusual reference can be excluded for further measurements.
Of course for statistics it would be better to have many references and not only 3. But if the system excludes the right of the references it may be more stable than just a system with 3 averaging devices.

Or it could just pick the two which drift in the same direction (there are only two directions to choose from), and make matters worse. Three is not enough for something as random as drift in my opinion, unless one reference is really an order of magnitude worse then the others. Plus I don't see the point of building such an elaborate setup for that, just do what Agilent et al. do and run them for a few thousand hours, measure the drift over time, and picking the best. Of course this brings you back to the question of how to measure drift .

All this is a far from the (close to) 'absolute stability' that was the original claim.

[quantumvolt]

- the minimum quality what can be expected when bringing 3 references together is that the resulting drift of the whole system can be brought to that what the average value of the 3 references is.

You should be able to do better than the average. If you have ten references with a random drift that is identical in magnitude, then the average should be more stable than each individual reference. sqrt(10) times better in the ideal case.

Do better than the average? I am all ears. Please define the term and present me with a method that obtains this. Or do you just misunderstand "the resulting drift of the whole system can be brought to that what the average value of the 3 references is" which is exactly what you say. Whether it is for square root of 3, 10 or some other positive integer n is immaterial for the "standard error of the mean" principle.

[quantumvolt]

...
If you have ten references with a random drift that is identical in magnitude, then the average should be more stable than each individual reference. sqrt(10) times better in the ideal case.
...

It is unnecessary for the references to have drift that is is "identical in magnitude" to obtain the effect. The stability of the average will be more stable than the worst reference.

Another question is that one will normally only average references that are of similar stability so that the worst one doesn't contribute negatively to the resultant stability ...

[quantumvolt]

...

That sentence is ambiguous in my opinion.

...

(for identical drift, hence my ideal case statement)

...

If you want other posters to increase the level of precision in their language, I suggest that you avoid formulations like identical drift. References with identical drift track each other and are meaningless to average. One might think that you mean "identical drift parameters" ...

I am sorry I find your post difficult to read. If I need to consult formulas, I prefer a decent "wiki" or academic source. Finally, as I cannot see that you answer my question or bring anything new into the theory of "The Standard error of the Mean" based on "The Central Limit Theorem" (which everyone can search and find good resources for on the web), I prefer to not pursue the theme further. Over and out ... 

[branadic]

@branadic: what do you mean when writing Ref1+Ref2 do you want to add the voltages to around 14V or do you mean the average value of the both references Ref1+Ref2.

No, what I mean by that is that the reference voltage for the adc is the average of both. Using cross-correlation algorithm it is possible to eleminate the influence of the test gear. The idea is based on the published articels:

Two-channel amplifer for high-sensitivity voltage noise measurements
Three-channel amplifier for high-sensitivity voltage noise measurements
Cross-correlation-based trans-impedance amplifier for current noise measurements
etc.

[branadic]

I have started to type in some code in Octave (Matlab).

Code: [Select]

close all;
clear all;

% t=1000h
t=0:1:1000;

% Electrical Characteristics LT1236
% Output Voltage [V]
Vout_min=4.9975;
Vout_typ=5;
Vout_max=5.0025;
% Long-Term Stability
LTS=20e-6;
% typ. Output Voltage Noise of LT1236LS8 [V]
Vpp=3e-6;

% Random Initial Output Voltage for each reference
Vout1_ini=(Vout_max-Vout_min)*rand(1,1)+Vout_min;
Vout2_ini=(Vout_max-Vout_min)*rand(1,1)+Vout_min;
Vout3_ini=(Vout_max-Vout_min)*rand(1,1)+Vout_min;

% Random Long-Term Stability for each reference
LTS1=LTS*rand(1,1);
a1=exp(log(length(t)-1)/(LTS1*1e6));
LTSx=log(t)/log(a1)/1e6;

LTS2=LTS*rand(1,1);
a2=exp(log(length(t)-1)/(LTS2*1e6));
LTSy=log(t)/log(a2)/1e6;

LTS3=LTS*rand(1,1);
a3=exp(log(length(t)-1)/(LTS3*1e6));
LTSz=log(t)/log(a3)/1e6;

% Noise for each reference
noise1=Vpp*(rand(1,length(t))-0.5);
noise2=Vpp*(rand(1,length(t))-0.5);
noise3=Vpp*(rand(1,length(t))-0.5);

% Output Voltage over time
for i=2:length(t)
Vdrift1(1,i)=Vout1_ini.*LTSx(1,i);
Vdrift2(1,i)=Vout2_ini.*LTSy(1,i);
Vdrift3(1,i)=Vout3_ini.*LTSz(1,i);
end
Vout1=Vout1_ini+Vdrift1+noise1;
Vout2=Vout2_ini+Vdrift2+noise2;
Vout3=Vout3_ini+Vdrift3+noise3;

% Data Acquisition with calibrated ADC
in1_ref2=round(Vout2./(Vout1/2)*2^24);
in1_ref3=round(Vout3./(Vout1/2)*2^24);
in2_ref1=round(Vout1./(Vout2/2)*2^24);
in2_ref3=round(Vout3./(Vout2/2)*2^24);
in3_ref1=round(Vout1./(Vout3/2)*2^24);
in3_ref2=round(Vout2./(Vout3/2)*2^24);

in1_ref2_ref3=round(((Vout2+Vout3)/2)./(Vout1/2)*2^24);
in2_ref1_ref3=round(((Vout1+Vout3)/2)./(Vout2/2)*2^24);
in3_ref1_ref2=round(((Vout1+Vout2)/2)./(Vout3/2)*2^24);


[alm]

A few quick remarks:
- Long term drift can only have a positive sign, so references won't drift down?
- The drift (LTSx) is very regular and predictable. Compare this to for example the long term stability graph from the LTZ1000 datasheet (note that this is voltage over time, not dV/dt over time).
- No ADC error or noise?

[branadic]

A few quick remarks:
- Long term drift can only have a positive sign, so references won't drift down?
- The drift (LTSx) is very regular and predictable. Compare this to for example the long term stability graph from the LTZ1000 datasheet (note that this is voltage over time, not dV/dt over time).
- No ADC error or noise?

Let's assume the drift to be positive for all three references, I don't think this is a big deal.
The drift is not regular, I use a random drift value in ppm after 1000h and then calcuate the logarithm drift behaviour over time. My considerations are based on the datasheet of the LT1236LS8.
Noise is included, but the adc is assumed to be calibrated with a parabolic function, something I was shown live by Andreas.