This week, we needed to convert the resistances of some Chinese ”heraeus” Pt100 resistors to temperatures. It turned out that the Callendar–Van Dusen equation built-in in a LabVIEW function, from which I stole the previous iteration of my converter, works only for the temperatures above zero.
Aha!
said I, this is a perfect opportunity to test the Astro-MDX integration. And here we are.
The equations I used are as follows (JS):
// converting (t / °C) to (r / Ohm)
const R0 = 100;
const a = 3.9083e-3;
const b = -5.775e-7;
const c = -4.183e-12;
let r = 0;
if (t >= 0) {
r = R0 * (1 + a*t + b*Math.pow(t, 2));
} else {
r = R0 * (1 + a*t + b*Math.pow(t, 2) + c*Math.pow(t, 3)*(t - 100));
}
// converting (r / Ohm) to (t / °C)
if (r >= 100) {
t = 3383.809524 - .8658008658e-1*Math.sqrt(1758480889. - 2310000.*r);
} else {
t = .172184658699642e-7*Math.pow(r, 4) - .995479323918948e-5*Math.pow(r, 3) + .285795641832195e-2*Math.pow(r, 2) + 2.21610504733757*r - 241.959043339973;
}The t=f(r) equation above 0 °C (100 Ohm) is an exact solution of the corresponding r=f(t). Below zero, however, r=f(t) is an unsolveable 4th-order mess, so t=f(r) in this range was found by fitting the 4th order polynomial to the points calculated with r=f(t).
Strictly speaking, these equations are for the particular IEC-60751-compliant RTDs only, but your typical uncalibrated RTDs from Aliexpress are Class B at best, with an error around several tenth of K, so who cares.