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What is the Purpose of CI capacitor? The datasheet does not mention anything for it except its recommended value. My guess is that it is used to suppress RF noise on the PT100/PT1000 cable. But It mentions different value capacitor for PT100 and different value for PT1000 resistor used. I would expect the value to be the same no matter the PT resistor used if the purpose was to remove noise. And so I am not sure the purpose of this capacitor. I will test using different value capacitor on my PCB and see if it measures temperature correctly, but I wanted a second opinion on that. MAX31865 CI

Background: It came to my mind to ask about this capacitor since one of our devices uses a heatbed with AC mains+ Thyristor to control the heating on the heatbed and this MAX31865 IC would stop refreshing its temperature (aka stuck on transmitting one specific temperature but once the AC control stops, it would start refreshing again), probably due to noise coupled on the PT100 cables from the ON/OFF of the AC voltage control. (The temperature freezes after the heating/AC control cuts off the AC voltage on more than ~17%, aka when the noise generated from AC control is string enough to interfere with the AC). One can see the unshielded PT100 cables are close to the unshielded main's cables:
AC mains wires with PT100/1000 mores mixed up

We basically sabotaged our own device. I hope using capacitors on the PT100's Cables will help the noise go back on the chassis/earth:

MAX31865 noise reduction

But I would like to know what to do with CI as well.

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According to the datasheet:

For operation in noisy environments, a filter capacitor may be placed across the RTDIN+ and RTDIN- inputs

They are looking for a LPF pole at around 16kHz at nominal resistance so the value of the capacitor will change inversely proportional to the source impedance (which is the RTD resistance since it's connected to a current source with very high impedance).

Since the RTD resistance changes with temperature, the pole frequency will move lower as the sensor temperature increases, for example to 11kHz at 100°C and about 6.4kHz at 400°C.

Adding capacitors randomly may cause other issues and/or increase noise sensitivity depending on exactly what is going on. Shielding the wires to the sensor and using CI would be my first move if you can't use something more resistant to EMI than that chip for budgetary reasons or whatever.

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