How are and what are the sources coupled to a 3-wire RTD leads?
This is a way I would do it, though I have no practical experience in implementing a circuit like this:







simulate this circuit &ndash; Schematic created using CircuitLab

This gives you two voltages: 

VM1 is measuring \$I1*(RL+R1+RL)\$ (and a bit of leakage though the second voltmeter, so for best results that should be disconnected) 

VM2 is measuring just \$I1*RL\$. (VM2 needs to be high impedance of course)

So to get V1 as voltage across the unknown resistor R1 you can then calculate \$V1 = VM1 - 2* VM2\$ With the known current I1 you can get to R1 simply by dividing \$R1 = \frac{V1}{I1}\$.

I think this method has the benefit that the measurements are all with respect to ground which is quite easy to implement. It probably has some downsides as well. Like I said, I haven't implemented one of these.



The thing with temperature measurements with a PT100 for example is, that you need to measure the resistance very well to get a precise temperature. If you measure 100.4 ohm instead of 100 ohm you think the temperature is 1 °C instead of 0 °C. If you connect two wires (the minimum you need) that leaves only 0.2 ohm for each wire to contribute to that error already. You don't need much wire to get into that region.

Typically you tend to ignore wire resistance and just assume a wire is a short. You can't do that in this case anymore.

So a naive approach would look like this:







simulate this circuit

But this is neglecting the wire resistance. Let's assume the wire has a resistance of 1 ohm. So your circuit really looks like this:







simulate this circuit

Now you would measure 102 ohm instead of 100 ohm and your temperature would be 5 °C.

So you need a way to get around that wire resistance. For this you add additional wires. The main idea is that those sense wires don't carry any current. In that case the resistance of them doesn't influence the voltage you are measuring.

A common way is the four wire measurement because you then have the voltage you want directly:







simulate this circuit

The benefit here is that you don't have anything to calculate, just measure the voltage (which does not depend on the wire resistance), divide by the know current and voilà you have the resistance of your sensor. But you need four wires, which cost more than three wires. So there is the variant as above.

The downside of the three wire method is that you need to do computations to get the desired value. And it might be a bit hard to get a good reading on the wire resistance because it is small, but with a good setup it is doable.