Three wire method of connecting an RTD is popular as the calibration is relatively immune to the distance of the RTD from the signal conditioner (henceforth refrred to as SC). The method utilises the drop in one line to cancel the drop in another line. Consider that a two wire RTD is all that you have and is at a distance of 1 metre from the signal conditioner. Consider that it is excited by a current Iexc. (Bridge method is discussed later). Normal measurement will result in error due to the resistance of lead wires W1 from SC to Hi and W2 from SC to Lo of RTD. If you now have an additional wire W3 to the low end of the RTD, which is used to "return" the current Iexc (fed to RTD) at SC end, you have a three wire conifuration that yields two voltages at the SC end, from the RTD, viz, "elow" through W2 from the lo end of RTD, and "ehi" from the Hi end. If elow is fed to high impedance amplifier, there will be very little current in W2. This is how this three wire works!!.
The aim is to measure the voltage Vrtd across the RTD.
This is obtained as ehi - 2*elow. At the SC end twice elow is subtracted from ehi to get the voltage Vrtd across RTD without error. The assumption, a very valid one, is that resistance Rw3 of wire W3 is equal to resistance Rw1 of Wire W1.
Example: If Res of RTD is 175.8 ohms and Iexc is 1mA, Vrtd will be 175.8mV. If Rw1 = Rw3 = 1ohm, then elow will be 1mV being Iexc*Rw3. However
ehi = Iexc*Rw3 + Vrtd + Iexc*Rw1
since the excitation current flows thorugh W1 and returns through W3. The voltage returned by W2 is elow. This is same at both ends.
elow = Rw3*Iexc.
The operation at SC, ehi - 2*elow yields Vrtd if Rw1 = Rw3.
RTD end SC end
Loside = Rw3*Iexc elow = Rw3*Iexc
Hiside = Rw3*Iexc+Vrtd ehi = Rw1*Iexc +Vrtd+Rw3*Iexc
Note: If a bridge configuration is used, RTD forms one arm and a resistance say Rx is used at SC end to form an equivalent arm. In this case Rx should be connected to W2 at SC end while W3 "returns" the total current back from the RTD end. If each arm of bridge carries 1mA, current in W3 will be 2 mA. For zero error, Rw1 should equal Rw2 in this case. The bridge output after conditioning in SC remains unaffected by low (but equal) values of Rw1 and Rw2.
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