NTC precision and understanding basic datasheets

[thexeno]

Hi all,

I've started to play again with NTCs, while the last time I have used the NTCLE100E3 series, which provides a very helpful datasheet, from where I learned and verified quite a bit of stuff, specially in terms of worst case error and also thankfully to the forum.

Now, I was playing with hotplate of 3D printers and realized the need to buy one. Many of them are sold with a NTC, but it is without any datahseet, with a given Beta factor and a given resistance at 25°C. So I started to dig around on what is it possible to achieve with such limited data. But this led me to another, more fondamental problem.

Explaining better. In a measurement environment, neglecting any error related to a voltage divider and an ADC acquisition and focusing only on the NTC resistance itself and the temperature, I learned that I can obtain easily the temperature error from the Beta characterization, i.e. beta and its tolerance and the error on R due to such Beta, where all of such data is given in the datasheet:

and the final temperature error is defined from:

So that I can estimate the worst case scenario for my given range, with no calibration and have the sensor replaceable, since I defined the worst case tolerance.

But then I discovered other NTCs, like the NTCS0402E3 serie or other similar. They are providing the resistance error and the Beta error, with no TCR (Alpha, the punctual temperature coefficient). I have couple of problems: how to define the resistor error due to the beta error, and how to devise the TCR from the Beta curve, so that in the end I can find the worst case error.

Hope my problem makes sense to any of you. The only thing that I found where they mentions how to use the Beta tolerance is in this application note https://www.vishay.com/docs/29053/ntcintro.pdf, where is mentioning something here:

But when I try calculations with data of the complete NTCLE100E3 datasheet, it does not make any sense what I am obtain. Actually it is not even the TCR, but the tolerance of TCR. If this is true, the "only" steps missing are the conversion of the TCR tolerance to a temperature/resistor reading and their relative tolerances.