After some more research, I think I've answered some of my own questions -

Tellurium copper is used for binding posts, not because it has any special thermal or EMF mojo, but because it machines much better than pure copper. And, I suppose, because it sounds like it's extra special.

The Seebeck coefficients (uV/C, relative to Cu) of some relevant materials:
Cu 0.0
Ag .2
Au .5
Yellow brass 1.5
Phosphor bronze 2.0
63/37 solder 3.0
Sn 3.1
Stainless steel 3.1
Beryllium copper 5.0
Fe -12.3
Ni  22.3
Te -49.25

Based on the extreme Seebeck coefficient of pure tellurium vs. copper, I'd expect that there might be some coefficient between Cu and CuTe (0.5% Te), but I could find no reference. The relatively large number for CuBe is interesting, since that's a common material for banana plug springs, where one might expect the greatest temperature differential to occur in such a connection (between the thermal masses of the binding post/jack and the bulk of the banana plug). Heat has to flow a considerable distance through the springs, very much more than when it flows through a surface plating.

The Pomona (Fluke) EM5295-48-0# uses CuBe (gold plated) for the spring contacts. It seems there might be an improvement to be had by using the older style pin plugs, where a solid pin was partially sliced into 4 sections which were then spread apart a bit to create tension. That could eliminate relatively large thermocouples at a thermal gradient, and might also be expected to have less thermal resistance, allowing the connection to settle quicker.

But maybe not - I'm still not clear on how plated conductors behave in this situation. For a high impedance voltage measurement where almost no current flows, the gold plating may carry the signal, so there is no real thermocouple (or more correctly, it's entirely contained within the connector). But if that's the case, why fool around with special copper connectors when common brass ones would be easier/cheaper? For current or resistance, the signal would also flow through the base metal, so does this have an effect (especially for tinned copper test leads, where there may be a larger temperature difference between the ends???

Nickle is avoided as a contact material largely because it is subject to fretting corrosion. Tests done by AMP (http://www.te.com/documentation/whitepapers/pdf/p154-74.pdf) show that a Ni to Ni contact can increase from 8 mOhm to 5 Ohms (sic!) in a short time due to this, while Ag and Au plated contacts exhibit negligible changes.

Cu (with Be for better machining) seems to be used as the base material for jacks/plugs to get thermal EMF cancellation to the wiring on both sides (i.e. use copper everywhere except where there is a minimal thermal gradient, like platings).

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