thought experiment - self-controlled voltage reference

[branadic]

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

Lets assume we have:

- a calibrated adc, we use a calibrated LTC2400, means, compensated for linearity etc.
- a calibrated high resolution dac with >20bit, means, compensated for linearity etc.
- three references (ref1, ref2 and ref3) with good short-term stability, we use three off-the-shelf LT1236* in LS8 for the first assumption, because they output 5V nominal
- an opto isolated µC that controls the adc, dac and the required switches
- in front of the adc input is a 2:1 divider (e.g. LTC1043) to measure at half of the full scale (2.5V nominal)

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).

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.

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.

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, means compensated when calculating the three differences. If one of the three references dies, you will notice by an extrem change in the calculated difference, it needs to be replaced and the system to be calibrated and adjusted.
Beside the additional power for driving ref2 and ref3, is this arrangement able to output a very, a high (not to say ultra) stabile output voltage of 1V? What are the traps I've overlooked in this is experiment?

Remember the magical number 3, suggesting ultra high stability (three legs are more stable than two or four --> see tripod, you need three sheets of granite grinding against each other to get high precision surface...). I'm curios about your opinion.

* The reference can be replaced by any other reference of you choise, I used it because it outputs 5V nominal.

[ddavidebor]

Mmmh it's late here but i don't know how and why it will improve something.

[branadic]

Improved stability because you can compensate for the drift?

[chickenHeadKnob]

I would question the need for the extra complication and error of the DAC. If you have N references, N > or = 3, then you can do all the tracking and adjusting in software, presumably you will be doing that anyway.

[branadic]

I'm not sure if I got you right, how do you want to adjust without having a dac? What do you mean by saying:

If you have N references, N > or = 3, then you can do all the tracking and adjusting in software, presumably you will be doing that anyway.

Sure I use three references, but after an initial calibrate and adjust cycle the system is monitoring it's own drift and able to adjust its reference output itself.

[chickenHeadKnob]

I'm not sure if I got you right, how do you want to adjust without having a dac? What do you mean by saying:

If you have N references, N > or = 3, then you can do all the tracking and adjusting in software, presumably you will be doing that anyway.

Sure I use three references, but after an initial calibrate and adjust cycle the system is monitoring it's own drift and able to adjust its reference output itself.

Yes I should have been more explicit, I mean I question the approach of always tweaking or adjusting your references with a circuit element which is less accurate than the rest of the system. Consider Hoffman's approach and his three + references. He sends one out to the cal lab on a rotational basis, to have the output monitored but not tweaked, so that he builds a cumulative history. I like this approach and I think I will emulate it. If you want a separate output at some prescribed standard voltage then i suppose you could build a buffered circuit that you can trim for convenience. If I have multiple references then I would leave all the averaging of multiple measurement and compensation calculations in software that way I avoid worrying about what errors are being introduced by any kind DAC feedback.

[madires]

Maybe I got it wrong but I think that you would just monitor the drift relations between all three references and the system will run away with time. It would be like placing three markers at random places around the world, measuring the distances between those and trying to figure which moves over time. You can tell how one moved in relation to the others but you can't tell if that one really moved or not, or the two other moved. To be able to do that you need a trustworthy observation point as a fixed reference.

[branadic]

Sending one ref periodical to a cal lab is one way, sure, but such a system is not self-monitoring. However, I don't like the idea to manually adjust the output to an ideal value, pots with tempco etc.
Also mentioned that the dac needs to be calibrated, maybe you remember the 32bit dac approach? I concealed the requirement for monitoring the ambient temperature to keep the thought-experiment simple and also the 1V ouput was only an example, not a fixed specification.

It's all about long-term stability, not absolut accuracy.

[branadic]

You can tell how one moved in relation to the others but you can't tell if that one really moved or not, or the two other moved.

Using three references you can do, not absolute but relative. Therefore I do an initial calibration (inital absolut value) and from there on I monitore the relative movement. It is improbably that all three references move in the same direction, with the same velocity and have correlated noise, so there will always be a difference between them.

[dfmischler]

Wouldn't you rather have a true, inherently accurate primary standard? 

[Andreas]

- in front of the adc input is a 2:1 divider (e.g. LTC1043) to measure at half of the full scale (2.5V nominal)

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).

We expect, all three references are uncorrelated, so their noise and drift is different.
 What are the traps I've overlooked in this is experiment?

The LTC1043 is unnecessary in this experiment since the LTC2400 has +/-12.5% overrange. (Ok you can use at maximum some 10 mV before the input protection diodes create non-linearities.

The noise of the ADC is nearly independant of the input voltage. But 10uVpp of a single measurement is 10ppm at 1V and only 2 ppm at 5V. Of course you can reduce noise by averaging many measurements.

As madires already said: the measurements are not independant. Its like 3 boats on the sea orientated in the same direction. You can measure the distance between them from every boat. But the only thing that you can tell without seeing the polar star as fix point is which one of the boats is the fastest in forward direction. But this speed can be negative because all are drifting in backward direction.

So the only information that you really have is which one of the references is drifting fastest against the average. In reality by using equal devices from the same manufacturing process they will be more or less behave similar in direction.

Similar experiment in attachment.
3 MAX6250A and 1 AD586MNZ in plastic DIP measured with a ADC with a good aged AD586LQ over nearly 1 Year.
Without looking at the light blue line near 0 ppm which is the drift of the ADC against a LTZ1000A:
Could you really tell whether the ADC or the references drift?
Implicitly you would average the drift and blame the average value on the ADC making the references better.

And note: after a initial "independant" drift all references seem to drift into the same direction.
This implies that the ADC and the LTZ1000A are drifting the most. Funny?

With best regards

Andreas

[madires]

You can tell how one moved in relation to the others but you can't tell if that one really moved or not, or the two other moved.

Using three references you can do, not absolute but relative. Therefore I do an initial calibration (inital absolut value) and from there on I monitore the relative movement. It is improbably that all three references move in the same direction, with the same velocity and have correlated noise, so there will always be a difference between them.

The initial adjustment is the absolute starting point for ref#1 but as all three refs drift you can't detect how they drift away from the initial absolute adjustment if just the relative drifts between the three refs are measured. For example, assume you and two friends meet at a specific location in your town. Then everyone walks around and you try to estimate your distance to the starting point by monitoring the distance between all three friends. Does that work?

[branadic]

So the only information that you really have is which one of the references is drifting fastest against the average. In reality by using equal devices from the same manufacturing process they will be more or less behave similar in direction.

Similar experiment in attachment.
3 MAX6250A and 1 AD586MNZ in plastic DIP measured with a ADC with a good aged AD586LQ over nearly 1 Year.

Up to know I'm still unconvinced that the approach will fail. In your example the AD586 is the observer, a ref that itself is not long-term stable and drifts away over time, so no good oberserver at all, because the drift of him can't be compensated as you never know if some common-mode drift is due to hinmor the observed three references.
The way you measure the drift is not comparable with my approach, because ref1 measures the difference between 2 and 3, it's actual absolute value is not of interest in this moment. I don't need a fourth high stable observer, you do.

A drift of all three references in the same direction must have it's reason in some change in ambient condition, therefor a temperature and a humidity sensor is requiered.

I think I will setup a matlab emulation to check this.

[Andreas]

A drift of all three references in the same direction must have it's reason in some change in ambient condition, therefor a temperature and a humidity sensor is requiered.

In my experiment the temperature is controlled to 50+/- 0.2 degrees centigrade.
Room humidity is similar after 1 year.  winter 40-55 % summer 55-70%.

By the way: the relative accuracy of differences from 2 similar sources is better when you directly measure the difference and not the absolute value and then calculate the difference.

Example: your instrument has a uncertainity of 10ppm (reference voltage) + 6uV (thermocouples of setup)
At 5 V this would give +/-56uV for each measurement resulting in a statistical error of up to 79 uV.
If you measure the up to 5mV difference directly you will have only about 6.05 uV error.

With best regards

Andreas

[alm]

You can measure the difference very accurately, this is often done when comparing references, but what's the point if you don't know either value? In general one of the references you would be measuring would be a more accurate or recently calibrated one. You could average the references, although you might as well connect them in parallel instead of going through the elaborate scheme with an ADC. If drift was random, independent and identically distributed, then the drift of the mean would be a factor sqrt(3) better. It's not likely to be random, for example the LM399 will usually drift up and the LTZ1000 will often drift down. It that case, the improvement may be even less.

If abs(ref1-ref2) and abs(ref1-ref3) is smaller than abs(ref2-ref3), are ref2 and ref3 drifting less, or is their drift more closely correlated? Three references is way to little for any meaningful application of averaging.

[branadic]

Okay, let's sum up a few things.

Three references are simliar but never equal, they will have different noise and drift rate, so they will never behave exactly the same. This given but not yet faced fact is required for this experiement.

A shift of all three references by the same magnitude in the same direction is, in almost any case, caused by a change in ambient condition and not by mystical force. That means if I monitore the ambient conditions such as temperature,  humidity and pressure I can compansate for that.
For the upper given example of the boats this means, they were able to compensate for the drift by the sea if they would monitor the direction of the force of it. They don't have such a sensor, so they must use an absolut point (the polar star). It's also the same with the three friends. The don't need a fixed point unless they were able to monitor their relative forced movement.

Theoretical the approach is still possible, I haven't heard any argument that made it collapsing.

[Andreas]

I don't need a fourth high stable observer, you do.

You will need it also:

To determine the drift of 3 references over time you will need 3 independent pairs of measurement values.
(3 unknown values can be determined with a set of 3 linear independent equations)

In your case you have your initial calibration value. (3 individual independent measurement values can be generated even when 2 of them are measured as difference).

Even when you are measuring in future 6 differences only 2 of the measurements are really independent.
The others you can calculate (except of the noise of the ADC-converter) from each other together with the absolute values of day one.

So you will need at least one measurement from a independent high stable observer ....

With best regards

Andreas

[branadic]

Don't mistake the initial calibration and adjustment for an independent high stable observer. All you do with this step is to set your system origin, so that it equals the origin of the rest of the world. You could also abdicate this step and define your value to be the new definition, your system will than be parallel translated to the rest of the world, that's it.

[madires]

Theoretical the approach is still possible, I haven't heard any argument that made it collapsing.

If somehow the voltage of all three refs is doubled your method woudn't be able to detect that, because the relations would stay the same. I think you should simulate or build your idea if you don't get the arguments. But don't complain later on if it doesn't work 

[branadic]

If somehow the voltage of all three refs is doubled your method woudn't be able to detect that, because the relations would stay the same.

An example that is far away from reality! And I claim that I would, because adc and dac would die by overvoltage. I could also observe the power rails and compare it to the ref-difference.

And by the way, you wouldn't even notice if for an observer watching our world the same happens to all JJ standard and references too.

[alm]

My argument is that the best you're going to get is an average of three independent random variables, and even then you only get an sqrt(3) reduction of the drift. If you have three balls move in random directions at random velocities, will the center of mass stay the same?

How about you post an example where it gives a more substantial improvement? You could try modeling the three references just as a 1D random walk, calculate the 'true' value via the method you're proposing, and compare the standard deviation of this true value to that of the individual references after say 1000 steps.

Something like:

Code: [Select]

nsteps=1000;
ref1 = zeros(nsteps,1);
ref2 = zeros(nsteps,1);
ref3 = zeros(nsteps,1);
true_value = zeros(nsteps,1);
for step = 2:nsteps
    ref1(step) = ref1(step-1) + randi(2)*2-3;
    ref2(step) = ref2(step-1) + randi(2)*2-3;
    ref3(step) = ref3(step-1) + randi(2)*2-3;
    true_value(step) = mean([ref1(step) ref2(step) ref3(step)]);
end
std(ref1)
std(ref2)
std(ref3)
std(true_value)


This ignores any systematic component to the drift (eg. a time-related aging process within the silicon), but at least gives us an impression of whether your method could work under ideal circumstances.

[ddavidebor]

If you have three balls move in random directions at random velocities, will the center of mass stay the same?

I think there is no more a lot to discuss

[madires]

If somehow the voltage of all three refs is doubled your method woudn't be able to detect that, because the relations would stay the same.

An example that is far away from reality! And I claim that I would, because adc and dac would die by overvoltage. I could also observe the power rails and compare it to the ref-difference.

A doubled voltage is extreme, I admit. I tried to point out the problem. If you like to have it more realistic let's take an increase or drop by 10mV which may be caused by radioactivity or whatever. Since all three refs are in the same box all will be effected at the same time. Yes, you could put everything in lead and add tons of sensors to mitigate things but the basic problem of the method is still the same. Monitoring the relations between all refs gives you a hint about they drift in relation to each other. It won't give you any hint how they drift away from the initial adjustment. If ref #1 drifts while you're measuring ref #2 with ref #1 as reference for the ADC how can you detect if ref #1 or ref #2 drifted. In the mean time ref #3 drifted also a little bit. Or maybe ref #1 and ref #2 drifted at the same time. What happens if the refs drift with varying speeds? Would your method be able to detect very slow drifts? Is it just a ADC glitch or did the voltage changed? Or didn't it change but the ref currently used as ADC ref did?

And by the way, you wouldn't even notice if for an observer watching our world the same happens to all JJ standard and references too.

If the observer wouldn't have his own uneffected reference he wouldn't notice it :-) The probabilty of three refs inside the same box being effected by something is much higher than the probabilty that all standards and references around the earth are effected at the same time, don't you agree?

[branadic]

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.
Because each reference can seperately be connected to adc_ref or adc_in it is also possible to connect two references to adc_ref and measure the third, what is close to the named correlation approach.

So we have the following measurements:

ADC-Ref     |   ADC-In

Ref1     |   Ref2

Ref1     |   Ref3

Ref2     |   Ref1

Ref2     |   Ref3

Ref3     |   Ref1

Ref3     |   Ref2

Ref1+2     |   Ref3

Ref1+3     |   Ref2

Ref2+3     |   Ref1

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

[branadic]

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.