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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.

(emphasis mine)

Can someone explain why "A reference resistor equal to four times the RTD's 0 degC resistance is the optimium for a platinum RTD"?

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For example, a PT1000 platinum RTD which has resistance = 1000Ω at 0°C has R=3900Ω at 850°C, and 850°C is the maximum temperature for platinum RTDs. 4X sufficiently covers that range for all types of platinum RTDs.

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It may be some ratio that they think works okay with their chip. To my judgement it represents far too high a measurement current. For example, with a PT100-DIN the measurement current is 4mA at 0°C and 3.1mA at 400°C (ignoring switch resistance and leadwires).

That represents self-heating of 1.6 to 2.4mW, which represents about 1°C error for in typical thin film element in air at 1m/s.

Typically we'd prefer about 1/10 that current (1/100 that dissipation, and 1/100 that error in the reading).

I would not use this chip for any application where accuracy is important unless you really understand the consequences in your setup. It is disturbing that they don't even mention it in the datasheet. Even in the olden days when getting low drift front ends was much more of a challenge, 1mA was considered about the limit for a PT100.

I suggest looking to other suppliers such as AD or TI.

P.S. In my example (0-400°C) about 36% of the ADC range is used (the span changes with the RTD temperature) so you get more like 13.5 bits resolution out of the ADC than 15.

Anyway, you are investigating noise. It's typical (!) 150uV RMS over Nyquist according to the datasheet. Near room temperature for a PT100 that's about 0.17°C RMS (so maybe 1°C p-p). At a more reasonable current, all that voltage noise would be a proportionally higher number of degrees, of course.

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I don't agree with that statement that "A reference resistor equal to four times the RTD's 0 degC resistance is the optimum for a platinum RTD."

In what follows, I assume that the reference resistor is in series with the RTD which, if I'm interpreting the diagrams correctly, is the way the circuit is wired.

First of all, you need to specify what your trying to optimize. Are you trying to provide temperature sensing over the widest possible temperature range? Or are you looking for the highest sensitivity (Vout vs temperature)?

If you're looking for the latter, then the optimum solution is to chose a reference resistor that is equal to the RTD resistance at the center of your temperature range of interest. This provides the greatest sensitivity, Vout vs RTD Resistance (temperature).

This can be shown by writing the equation for Vout, differentiate it with respect to RTD, and solve for RTD when that is set to zero.

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