Deriving formulas for calculating the errors that occur in the measurement circu

[bibizyana]

Hello! I need to derive formulas for calculating the errors that occur in the measurement circuit with a two-wire and three-wire resistance thermometer connection scheme. But, unfortunately, I have almost no values except for α (temperature coefficient of the resistance converter), constants A, B and C, the nominal value of resistance R0 at a temperature of 0° C and table values of resistance for certain temperatures. Where can I find some information about it? I will be very grateful for any answer. Thanks in advance.

[Siwastaja]

Error occurs simply due to wire and connector resistance, so formula is simple, R_indicated = R_true + R_wire. If you have a table of resistances for certain temperatures, just add the wire resistance to those values and directly look up the indicated temperature. 3-wire differs from 2-wire such that you only add the difference of resistances between the two main wires and connectors.

The challenge is to know the wire and especially connector resistances. With wires, it's possible to look up to maybe some +/- 20% accuracy if you know the wire gauge, but connectors are worse, manufacturers only give worst case numbers, and connectors age and give different contact resistance on each insertion.

If you think about it, if it was easy to calculate the amount of error, there would be no need for 3- or 4-wire measurement - just calculate and remove the error. But 3- and 4-wire measurement is needed exactly because the error is unknown and cannot be calculated because of lack of knowledge into the wires and connectors used.

[jwet]

National Semi (now TI) had good app notes about applying RTD's and related with 2,3 and 4 wire type connections.  I think they went through some of this.  Its mostly just basic plug and chug kind of DC analysis and algebra taking all the parasitic wiring resistances, etc into account.  Sharp pencil, lots of paper and a red bull like sophomore circuits courses.  Go out after you finish and get blind drunk, you can relive the whole college experience...  Good luck.