Looking at slide #3 of the 5th lecture, I'm reminded of the concerns you might have measuring a high-side shunt in a high voltage/high power circuit.
If you're measuring with a scope or data logger, you need to use 2 single-ended channels, one on each side of the shunt, because a scope or data logger normally have a grounded (earthed) chassis. If you try connecting the ground clip of a single-ended scope channel to the low side of a shunt, you could destroy the instrument due to high currents flowing from the UUT through the instrument's chassis to earth.
If the instrument's channels are differential or if you have a differential probe, then you can measure the voltage across a shunt with one channel of the instrument.
Floating a scope or data logger's power source is a bad idea if you're attmempting to make a high side shunt measurement with a single channel because the instrument's chassis could be at a high and dangerous voltage with respect to earth. One brush against the instrument and you get a potentially lethal shock.
rswanson: using an op amp to square an analog signal is fairly easy--check app notes from any major analog vendor, it's a classic circuit configuration. I know some early but still valid app notes from ADI show how to do it.
To all: remember, when you talk with an experienced vendor, they will raise issues you may not have even thought you needed to be worried about--but hey, it's worth listening to what they say, even if it may not be a concern of yours in the end, in your situation.
rswanson: by analog, I meant a basic op amp scaled to transform the input signal x the resistor size--you don;t really need to do a true multiplication of two unknown analog signals. And I think vendor like Microchip do make power-measurement ICs which combine analog and digital blocks in one easy-to-apply device.
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