How important is DMM linearity for drift measurements?

[e61_phil]

Hi,

I'm currently developing a high voltage measurement system for drift measurements in the ppm range.  I wonder how important the linearity of the system is at the end? It is obvious to me, that a decrease in slope (gain) of the measurement would bring errors into the measurement, because 100ppm difference at 1kV could be "another 100ppm" at 5kV if the system isn't linear. But the error of even 1% non linearity (over say 10kV) looks, vey small for my purposes (100ppm drift at different voltages).

Am I wrong?

Thanks Philipp

[ap]

Your question cannot be answered this way. You should specify what accuracy requirements you have absolute, what voltage you measure, and any known test system parameters, if they exist yet.
Any system has zero, gain and linearity inaccuracies and drifts. The measurement accuracy is always a combination of these. They usually should be combined according to GUM rules.
If you let us know more the group can certainly help.

[e61_phil]

The goal is measuring drift in the single digit ppm range. The absolute values doesn't matter (1% is enough) but it must be rock stable over a couple of hours. The voltages are between 4kV and 10kV.

[Kleinstein]

There is not just one measure of nonlinearity. The more important one are INL and DNL. With a drift measurement one does not care very much about good INL values, but the DNL should be reasonably good.

[doktor pyta]

Probably You already know this but...

If You are measuring high voltages (DC, I assume) and You want to obtain nonlinearity in ppm region it is crucial to have well designed voltage divider. Typical HV resistors have typically 1...10 ppm/V voltage coefficient and using them at say 10kV can give few percent of nonlinearity error. Even famous Vishay Z201 have " <0.1 ppm/V". Also error due to self heating will be important.

I own two Fluke HV dividers for 10kV and for 30kV. First one is built using many 500k precision low tempco wirewound resistors. The second is also made using PWW resistors but the whole divider is inside big oil tank with stabilized temperature.

In other words this seems to be a difficult task.

P.S. I forgot about effect of corona and importance of guarding to prevent leakage.

[ap]

So if i undertstand correctly, you want to measure say 6.5kV with a relative uncertainty of say 5ppm.
So the combined drift of all parameters involved shall not be below 5ppm.
The applicable drift/uncertainty parameters would then be:
Zero drift and gain drift of a/d
Dnl and inl of a/d
Drift of reference
Drift of voltage divider (thermal, voltage-induced, aging neglectable)
Drift of any other circuitry involved ( opamp stages...)
You need to determine these individually for the required time span of a few hours, and calculate results, some data may not be readily available, you may have to determine it. Certainly inl and dnl are of relevance for this, to answer your original question. Say your voltage drifts by 200V, within this range you could theoretically see the full inl of your converter used. It is critical that you do a propper error budget analysis.
It will be pretty hard to achieve this accuracy, but possible i should say. The voltage divider also needs attention, you cannot just add a series ladder of resistors as dr pyta points out, but since your voltage is somewhat stable, it is of help. The fluke 752 manual may give you some advice here.

[tggzzz]

Without understanding your application in detail... If there is no drift, the linearity is, of course, irrelevant.

If you are only interested in drift of a single value, then I would presume that resolution, stabiliity and (if appropriate) repeatability are all going to be more important than linearity.

If you are doing differential measurements, then linearity may be more important, e.g. one half might have a positive tempco, the other half a negative tempco, so the difference would be double the tempco.

[ap]

Without understanding your application in detail... If there is no drift, the linearity is, of course, irrelevant.

If you are only interested in drift of a single value, then I would presume that resolution, stabiliity and (if appropriate) repeatability are all going to be more important than linearity.

If you are doing differential measurements, then linearity may be more important, e.g. one half might have a positive tempco, the other half a negative tempco, so the difference would be double the tempco.

Well, i think this is misleading and not a very scientific view of things. First of, in a single measurement, you always measure one paramter. In this case it is the voltage. it is always an absolute value, even though only the relative change is of relevance (2 measurements a few hours apart). For these measurements, there are contributors of uncertainty. these multiple contributors of error need to be analyzed and added. If the measurement is based on a differential measurement or not just causes a different error propagation calculation. As soon as there is a difference in the measurements, inl and dnl have to be taken into account, to the degree required mathematically.

[tggzzz]

Without understanding your application in detail... If there is no drift, the linearity is, of course, irrelevant.

If you are only interested in drift of a single value, then I would presume that resolution, stabiliity and (if appropriate) repeatability are all going to be more important than linearity.

If you are doing differential measurements, then linearity may be more important, e.g. one half might have a positive tempco, the other half a negative tempco, so the difference would be double the tempco.

Well, i think this is misleading and not a very scientific view of things. First of, in a single measurement, you always measure one paramter. In this case it is the voltage. it is always an absolute value, even though only the relative change is of relevance (2 measurements a few hours apart). For these measurements, there are contributors of uncertainty. these multiple contributors of error need to be analyzed and added. If the measurement is based on a differential measurement or not just causes a different error propagation calculation. As soon as there is a difference in the measurements, inl and dnl have to be taken into account, to the degree required mathematically.

It was a poor choice of words on my part, and intended merely top alert the OP to some issues. It was not intended as a definitive statement.

Having said that, the "you always measure one parameter" and "voltage is always absolute" isn't necessarily correct.

I was (too) briefly alluding to cases where you are only interested in the voltage difference between two nodes, but cannot place one of the probes on one of the nodes. In such cases you measure the voltage on one node V1 w.r.t. (say) 0V, and on the other node V2 also w.r.t. 0V. The parameter of interest V_diff = V1-V2, and the common mode voltage V_cm= (V1+V2)/2 is irrelevant. For small changes in V1 and V2, the INL and DNL are less important than stability, resolution and repeatability.

But ultimately it is up to the OP to understand what he needs; I suspect some simple arithmetical examples will help him.

[e61_phil]

I will try to clarify some things:

The absolute ratio doesn't matter so much for me. So if the real voltage is 3456V for example it is ok if my measurement systems says 3400V. But this reading have to be very stable. At the end I have to measuare the stabilty of this 3400V within single digit ppm. I don't excpect more drift than about 100ppm at absolute maximum. If my assumption is correct the linearity (the INL to bei more precise) doesn't matter for my application. However, the DNL can cause some issues.

[tggzzz]

I will try to clarify some things:

The absolute ratio doesn't matter so much for me. So if the real voltage is 3456V for example it is ok if my measurement systems says 3400V. But this reading have to be very stable. At the end I have to measuare the stabilty of this 3400V within single digit ppm. I don't excpect more drift than about 100ppm at absolute maximum. If my assumption is correct the linearity (the INL to bei more precise) doesn't matter for my application. However, the DNL can cause some issues.

I know of other applications with similar constraints. A company I once worked for made an attenuation measuring set with a stability and repeatability of 0.001dB - but an accuracy of 0.1dB. It was used to see how the attenuation varied during the course of a 7-day long experiment.

[zlymex]

Here is one of my suggestion.
1. Use a modern 7.5 or 8.5 digits DMM(such as 3458A), this will ensure the drift in ppm level for several hours time.
2. Find nine 10 Meg resistors of the same type as the voltage divider of the meter.  It's a Vishay for 3458A
3. Air wire those nine resistor in series, connect them to the voltage to be measured and the DMM which set to 1000V DC range
The 90 Meg resistor and internal 10 Meg resistor form a divider, with good power coefficient, voltage coefficient, temperature coefficient and low leakage.

[ap]

If your max variation is only 100 ppm, inl is probably not your concern but dnl is more. This may vary from the a/d used though. Some a/d's have a behaviour that they have pretty unequal distributed inl nonlinearities, so depends a little. You can fix this by selecting a suitable a/d.
Re. Accuracy, if you demand say 5 ppm, you need to have a much less than 5ppm/K temp coefficient obviously, unless you can keep your environment extremely stable and wait until selfheating is stabilized. Hard to achieve. The 3458a input resistor most likely does not support this ( do not have the data handy), in case a 3458 is an option for you. You will need e.g. Vishay z- foil resistors with less than 1 ppm/K tempco all over the place.

[e61_phil]

I will use Caddock USF270 with 2ppm/K (max not typical like Vishay). The resistors are also heated.

I don't want to use the 3458A for these measurements to keep it free for other things. Furthermore, I think the 3458A isn't sufficient for that purpose. The 1000V Range TC is about 2ppm/K and the input 10Meg isn't specified.

[zlymex]

Here is another suggestion of mine for high stability.
1. >4kV cannot be measured directly, a divider is a must.
2. The best high voltage divider is made up with many identical resistors for not only the best TCR match, but also for low power coefficient and low voltage coefficient
3. Since the voltage to be measured is not fixed, the divider could be variable, or the measurement unit will
4. A voltage reference(could be variable) plus a null detector can be used to measure the divided voltage. There is no worry about the linearity of the DMM any more because the linearity of the divider(such as a KVD is guaranteed)
5. In case a DMM to be used instead of a null detector, a very small range such as 100mV or 10mV can be selected to reduce the none idea characteristics such as none linearity by 100 or 1000 times. However, a bias current cancellation circuit should be used to in such case.
This idea is actually from old differential voltmeters such as Fluke 887.

[e61_phil]

Hi zlymex,

this is exact the concept I try to implement. I build a very stable 100Meg Resistor out of many USF270 (0.02ppm/V and 500V per resistor @10kV input) this resistor chain ends at the input of a TIA. On the other side is a AD5781 (20bit DAC with LTZ1000 Reference) sending a compensation current to the TIA (via VHP101 resistor). The TIA output is showing the current unbalance. At measurement start the unbalance is nulled.

Therefore, I'm interested in the linearity of the whole measurement setup. My requirements to the ADC aren't very high.

[zlymex]

I didn't know you have such high requirement at first. It seems to me now the scheme is quite nice. There will be no noticeable none linearity issues at low voltage side since the ADC is only responsible for the unbalance current which is a faction of the whole current just like the role of a null detector. May be the weak point of the system lies in the 100 Meg resistor string that is prone for leakage and interference, and 50mW per resistor also make them a bit warm(which will be more ambient sensitive).