Why don't thermoelectric emfs cancel?

[jpb]

I am not questioning that thermoelectric voltages do affect the accuracy of Voltage measurement as per this Fluke paper as practical results are shown
https://us.flukecal.com/literature/electrical-calibration/watch-out-those-thermoelectric-voltages-cal-lab-journal-reprint

But the explanation seems a bit vague and only seems to consider a single junction in isolation. There are Two junctions (at least) involved in the measurement - the positive and negative - and if identical materials are used each side and the terminals on the meter are at equal temperature to each other and the terminals on the reference are at equal temperature then I'd expect the two junction emfs to be equal and opposite and so cancel out.

I'd only expect there to be a net effect if the two terminals are at different temperatures ( temperature gradient within the meter) which I'd expect to be much less than the temperature difference between the meter and the room.

Am I missing something obvious?

As an experiment I plan to add a zero volts (short circuit) reference to my voltage reference to see what the meter measures. Reversing the terminals did make a difference of 1 to 3 in the last digit but I suspect that there might be other effects going on.

[razvan784]

Yes, but in practice the materials are not exactly the same and the temperatures are not exactly the same - there is heat flow from inside the meter to its outside, and it can't be perfectly uniform; but it does compensate to a certain extent.
Also, watch out for thermal transients, which I think are much more important. I can see microvolt-level "tails" lasting multiple minutes after handling the banana plugs for instance; they do stabilize eventually. These are "low thermal emf" banana plugs.
See attached graph (y: volts, x: seconds), taken with a 34401a at 10PLC.

[helius]

The thermoelectric voltages do not cancel because the current paths through the two terminals are not identical at the microscopic level.
See my response to a similar question here.

The solution is to use a contact material with low thermoelectric power (ATP). The problem is not caused by dissimilar materials, despite much misinformation to the contrary.

[jpb]

Thanks for the prompt responses.

I can see that it is difficult to get uniform thermal effects.

I'm surprised that current paths matter that much where a voltage is being measured as the input impedance is of the order of Gohms on a Keithley or 10Mohms on standard DVMs so the current is only nano Amps possibly up to 1 micro Amp.

If current does affect it then  my plan of having a zero Voltage reference won't work well as it will be not passing current at least compared to the 10V case. The Fluke paper gives zero volts shorts as its example.

I think though, that given that the least significant digit is 10 microVolts on my 6 1/2 digit meter on 10V range, the value of the emfs involved is probably lower than this so perhaps I don't need to worry too much.

[Echo88]

Please elaborate on your hypothesis with the contact resistance helius.
Lets take a HP34420A or K2182 and assume 30pA of bias-current flows through the plating while measuring nanovolts: how high should the plating-resistance be to produce actually measurable amounts of heat and therefore introduce nV-errors?
I know that gold-plating is said to produce nV-errors compared to unplated copper-spades/posts, but ive never seen actual measurements or papers about it. Maybe someone has such a credible source apart from AN86?

[2N3055]

Please elaborate on your hypothesis with the contact resistance helius.
Lets take a HP34420A or K2182 and assume 30pA of bias-current flows through the plating while measuring nanovolts: how high should the plating-resistance be to produce actually measurable amounts of heat and therefore introduce nV-errors?
I know that gold-plating is said to produce nV-errors compared to unplated copper-spades/posts, but ive never seen actual measurements or papers about it. Maybe someone has such a credible source apart from AN86?

I agree. I would like an explanation and calculation on that. Usually it is like razvan784 said: it is very hard to achieve completely isothermal and symetrical system..
I understand that in a miliohmmeter with 1A current there would be both efects related to Thomson effect and Joule heat. But when measuring voltage even with 10MOhm input resistance, not even HighZ ? Not likely.

EDIT: Added bold text

[coppercone2]

something that comes to mind is trying to imagine the physical equilibrium differential point of the two materials.

The electrical resistance and thermal conductivity of the two materials is different. You make an exact bend and put it in a exact flame. If the physical bend is in the center of your flame, heat is being carried out at different rates by both wires because the alloys are different.

[David Hess]

I agree with razvan784.  The thermometric potentials of the paired junctions should cancel but the materials are not identical and the temperatures are not identical.  Precision DC circuits make some effort to match both of these things.

These problems also show up with thermocouple measurements and thermocouple extension cables.  Higher accuracy thermocouple cables use higher purity materials and connectors with better isothermal performance.

Another trick which can be used is to chop the excitation and signal which cancels the thermocouple errors.  Precision low resistance measurements often do this.

[helius]

I apologize that I am not able to provide calculations without some additional research, which will not be forthcoming soon. Sorry to disappoint.
When considering the thermoelectric effects we must consider not only the Seebeck effect and the temperature coefficient of resistance, but also dynamic charge movement caused by the surface scattering and the phonon formation. This is a complicated topic.

[SilverSolder]

Is there some simple experiment that we can try at the bench that demonstrates thermal effects NOT cancelling?

For example, would this be expected to demonstrate the problem:  measure an external voltage reference with your DMM to 6 digits.  Then, reverse the cables at both ends (at the DMM and at the reference).  Let the temperatures settle for a little while.
Would we expect to see a difference at the uV level from doing this?

[jpb]

Is there some simple experiment that we can try at the bench that demonstrates thermal effects NOT cancelling?

For example, would this be expected to demonstrate the problem:  measure an external voltage reference with your DMM to 6 digits.  Then, reverse the cables at both ends (at the DMM and at the reference).  Let the temperatures settle for a little while.
Would we expect to see a difference at the uV level from doing this?

The reversal idea is in the Fluke paper. I tried it with mine and go a difference of 1 digit on my Keithley 2000 and 3 digits (or rather a change of 3 in the last digit - but you know what I mean) on my Keithley 2015 but I suspect that it is not down to emf alone.
I'm planning to add a second set of terminals to my reference in parallel but it would also allow me to measure a short and see how close to zero it is - this would at least indicate if there is an issue or not at the 10 uV level (the resolution of my 6 1/2 digit meters at 10V scale).

[razvan784]

Exchanging the leads should not produce much of a difference in thermal emf, as the leads should be almost identical, as should be the binding posts / banana jacks. The leads and jacks however form one or more thermal junctions, e.g. in the case of my 34401A: Cu jacks -> CuBe banana spring -> CuTe or brass banana body -> Cu wire. With higher-end meters, you would probably get something like Cu internal wiring -> CuTe binding post -> Cu spade -> Cu external wire -- better but still not perfect.
More to the point, if you exchanged the two leads, you'd have to wait around 5 minutes for the thermal transients to stabilize, as shown in the graph I posted earlier. In those 5 minutes, the meter/vref may drift slightly, corrupting your measurement. Or you may affect the natural airflow around the instrument.
As a related example, my meter offset takes 3 to 4 hours to stabilize from a cold turn-on. Then, I can see a slight jump when opening the window. This is with a copper wire shorting the inputs, so these are probably internal thermal offsets which do not fully cancel out and which are outside the autozero loop - front/rear switch, protection components maybe. They can be compensated through calibration of course, but there is a limit to this - maybe this is why the 34401A is only specified (24h) at 30 ppm of the 100mV range, as opposed to 6 ppm of the 1V range. I'd bet it's not the amplifier, it's the parasitic emfs.

[Conrad Hoffman]

My advice has always been to get some untinned copper "bell wire", or pull wires out of old multiconductor phone cable you find in the ceiling, do fresh end strips and screw it down directly in the banana jacks. Don't introduce any more junctions than absolutely necessary. It gets more complicated on circuit boards where you have Kovar leads and such. The late Jim Williams had some suggestions there but I'm not sure perfection is possible for any of these situations. OTOH, you can usually reduce the problem to a manageable or even negligible artifact.

[jpb]

I've now done some experiments.

I added a second set of terminals - see photos - which are on opposite sides in case there is some sort of temperature gradient.

I connected and allowed an hour or so for stabilisation which gave 10.00002 and 9.99998. I then connected the negative to the other positive (i.e. a zero volts difference) and got all zeros.
I then reversed the connections and got quite a big difference but perhaps I should have left it some time to settle. I then replaced the original connection and got the same readings.
See photos.
The fact that I read 0s for the 0V case implies to me that there isn't a significant emf effect at the resolution of my meters. The difference in the reversed case is probably something else.

The maximum difference seems to be about 5ppm and the 1day spec is something like 15ppm I think so the closeness to 10V is quite impressive in itself.

EDIT: I should have added, I've not calibrated or set the zero - the meters are just as they've been since I got them (second hand) about 4 or 5 years ago.

[jpb]

photos continued...

[SilverSolder]

Can we trust the average DMM to read exactly the same voltage in the Positive and Negative direction even with no thermal EMF on the outside connections?

[jpb]

I left the -ve case going for a while (a couple of hours) to see what it settled at and it seems that it is around 3-4 less in LSD in magnitude - two photos, one of the negative voltage and one of the positive voltage after reconnecting and you can see it returns to the previous values.

The differences though are only of the same order of magnitude as the general drift with temperature/warming up. I suspect that it is not emf otherwise it should show up on the 0V case and it doesn't.

[Conrad Hoffman]

Can we trust the average DMM to read exactly the same voltage in the Positive and Negative direction even with no thermal EMF on the outside connections?

One of my old HP3455s is nearly perfect. The other is off a few ppm and I've never figured out how to fix it.

[guenthert]

Can we trust the average DMM to read exactly the same voltage in the Positive and Negative direction even with no thermal EMF on the outside connections?

Don't want to make this an trust issue, but can we expect a given DMM to behave like that?  Well, if auto-zero is working as intended, i.e. there is no offset at 0V, then it's a question of how large the error in linearity is.  For some DMM, e.g. HP3458, HP3456, Datron 1271/1281 it is specified (for at least one function and range).  For the HP34410A it is specified as at most 2ppm of reading + 1ppm of range in the 10VDC range.  I just swapped the cables (regular banana, not low EMF ones) at the DMM, while the other end was connected to a 1N829 (might be NOS) and there was no difference in the absolute value (at 10NLC integration time and auto-zero on -- I didn't attempt to use statistics to get into the sub-ppm range).  YMMV.

[jpb]

Can we trust the average DMM to read exactly the same voltage in the Positive and Negative direction even with no thermal EMF on the outside connections?

Don't want to make this an trust issue, but can we expect a given DMM to behave like that?  Well, if auto-zero is working as intended, i.e. there is no offset at 0V, then it's a question of how large the error in linearity is.  For some DMM, e.g. HP3458, HP3456, Datron 1271/1281 it is specified (for at least one function and range).  For the HP34410A it is specified as at most 2ppm of reading + 1ppm of range in the 10VDC range.  I just swapped the cables (regular banana, not low EMF ones) at the DMM, while the other end was connected to a 1N829 (might be NOS) and there was no difference in the absolute value (at 10NLC integration time and auto-zero on -- I didn't attempt to use statistics to get into the sub-ppm range).  YMMV.

If it is a matter of linearity then this implies that the 10V range is 10V to -10V with 0V at the centre? For some reason I assumed that to maximize resolution they would design some sort of switching arrangement for negative voltages so that the ADC range would be something like -0.1V to 10.1V or whatever overrange is allowed.

[SilverSolder]

The circuitry in some of my DMMs (Fluke 8505a) switches the reference to the opposite polarity when the voltage is < 0.  Only when this circuitry is accurately adjusted (and nobody breathes within 20') do the positive and negative readings match within one ppm on that particular instrument, even though it is easily within spec on both sides of zero.