I'm using an Adafruit MAX31865 board to measure the resistance of a PT1000 RTD. The board comes with a 4300-Ohm resistor.
I'm trying to model the amount of noise (in degC/sqrt(Hz)) that I expect out of this circuit. But in order to do that, I'm trying to determine how the circuit does the measurement under the hood. One of the things that I don't understand is why the optimal reference resistor has a resistance 4x that of the RTD (e.g., 400 Ohm for a PT100, 4 kOhm for a PT1000). The MAX31865 datasheet says this (see also):
The reference resistor current also flows through the RTD. The voltage across the reference resistor is the reference voltage for the ADC. The voltage across the RTD is applied to the ADC’s differential inputs (RTDIN+ and RTDIN-). The ADC therefore produces a digital output that is equal to the ratio of the RTD resistance to the reference resistance. A reference resistor equal to four times the RTD’s 0 degC resistance is optimum for a platinum RTD. Therefore, a PT100 uses a 400 Ohm reference resistor, and a PT1000 uses a 4 kOhm reference resistor.
Can someone explain why "A reference resistor equal to four times the RTD's 0 degC resistance is the optimium for a platinum RTD"?