I did prelim tests with a just a shorting bar and my results are as you demonstrated with yours: the PD were able to source its rated current, 2ADC, for my 3 units measured at at 6mV, 2mV, 3mV, as compared to when I measured current with the DMM. I then double checked the output voltage on the terminals with the DMM. These units are a 2020B x 2, and a 5020.
My 3030D Mastech, alas, still outputed 3A at ~800mV. Clearly, this was not designed as well as your version.
Nevertheless, its clear from the more meticulous checks you've made that the PD can output close to an ideal current source, that is its output is ~ independent of the voltage across the outputs, as whether its approaching zero volts up to its rated maximum output voltage, the rated current can be pumped out as you desire. Awesome!
As resistances is getting fairly small, the jacks or any other minor series resistance are starting to play bigger roles in the voltage drop measured. I think you can still push it to see what the theoretical minimum can be, but driving at 1-6mV output voltage at 1-3A is far from what any circuit I know can be powered! So, I think the point is very well made at this level.
In my units, the still uncleaned adjustment pots are likely playing large roles in not getting adjustment down further or improving the output stability. So, it should be interesting to revisit the tests when the units are spruced up.
So just to prove to myself that the short resistance is a big deal in CC testing I made a super short pictured here. .625 diameter tellurium copper with gold plated beryllium copper banana jacks.
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