[volt-nuts] Best way to measure micro Ohms

[ed breya]

I just noticed this discussion recently, so I'm late to the party, but 
that never stops me from adding my one-cent's worth.

David, regardless of the aluminum and other material issues, I think 
your initial idea of using a lock-in analyzer is definitely the way to 
go. I'm very fond of LIAs, although I seldom need or use them, so my 
opinion is somewhat biased. I have five - two Ithaco 391A orange-band, a 
PAR 5204, an SR830 and SR850.

If you use an audio power amplifier for driving the experiment, you can 
rig it up so that the LIA can be used to measure the drive current as 
well as the resulting voltage drop. Let's say the amplifier is for 8 
ohms, so you put a few ohms in series with the output, then from there 
into a precision one-ohm sampling resistor, then into the RUT, forming a 
voltage divider. The RUT is expected to be in the micro-ohm region, 
which is many thousands of times smaller than the sampling R, so its 
tiny voltage drop will be negligible, allowing the sample voltage to be 
a good representation of the test current. You could also just treat the 
whole thing as a voltage divider and calculate the "exact" results.

The voltage on the RUT is measured at whatever gain is needed. The 
voltage on the sample resistor will be plentiful at 1V/A, and both 
signals will have very low source R, and minimal noise. Since both 
signals can be measured by the LIA, the uncertainties in assessing each 
part with different equipment are much reduced.

The reference frequency should be as low as possible, limited by the 
amplifier's low-end capability, and selected so it and its harmonics 
land as far as possible from the power line frequency and its harmonics, 
for say up to n=15, or whatever is practical. This will help to reduce 
line interference from nearby sources, and ground loops, and from the 
amplifier. Especially at low frequencies, the amplifier may show a lot 
of line harmonics when driven to high levels - the filter capacitors in 
its power supply can only do so much, and audio PAs are likely not all 
that great in terms of PSRR. Turning on the LIA's line notch filter will 
also help, at least with the fundamental.

The frequency needs to be very low in order to minimize the parasitic 
currents that will cause errors, especially considering that this setup 
is dividing on the order of a million in a single stage. If this appears 
to cause problems, you can reduce the large division ratio by using a 
much smaller sample resistor, and treating it as a divider for 
calculation purposes. Alternatively, adding some appropriate shielding, 
or splitting the division into isolated sections can greatly reduce the 
effects. To avoid signal ground loops, measuring the drive current and 
the RUT voltage should be separate operations, each carried on its own 
BNC cable to the LIA, while the other is completely disconnected and out 
of the way - having no common-grounding or cable bundling or fancy 
signal routing/switching is best. The weakest link ground-loop-wise may 
be the necessity of carrying the reference drive between the LIA and 
power amplifier input, likely sharing the same ground as the output. 
This could force you to set it up for differential measurement of the 
RUT signal. The special audio PA that I have for such purposes has its 
ins and outs transformer-coupled, which helps a lot.

This could be fun and interesting. There are plenty of pieces and 
variables involved to experiment with to optimize the measurement, and 
lots of other tricks available to enhance it if necessary.

Ed