I don't understand why it won't work with a 12.5k reference resistor and a 10k resistor under test. A LTC2440 (And others ADCs from the same family) accept 0...5V differential on the reference pins. Only the input is limited to -Vref/2 to +Vref/2.
In this case yes. But the other way round or when you have nearly equally resistors (with one resistor changing by +/-10 ppm) it would not work. (The measured value is limited to 2500mV).
This simple circuit will not fully compensate for the wire resistance. So it may work for an RTD but not for very precise measurements.
Thats what I have overlooked on the first view.
The only annoying wire resistance comes from the wire between the reference resistor and the resistor under test. The others are fully compensated if you connect the IN and Ref pins close enough to the resistors.
I have to keep the reference resistor on constant temperature and the DUT on variable temperature.
With 12K5 resistors the voltage drop between reference and resistor under test is 0.12 mV.
(With 1K0 resistors its even more).
0.12 mV against 2500 mV over the resistor is around 50 ppm.
Copper wire has around 3850 ppm/K. With a temperature difference of 30 deg C
I would have up to 6ppm error by the wiring T.C.
-> 4 wire measurement is absolutely necessary.
With best regards
Andreas