RTD's resistance to temperature

Question

What is the formula for finding temprature from resistance? I want to use it with PT 100 / 500 / 1000 .

Answer 1

If you're not concerned about the utmost in accuracy, you can use the Callendar-Van Duesen equation, but that gives you resistance as as function of temperature, which is not what you asked for.

It's possible to directly use the Callendar-Van Duesen equation by performing a binary search to find the inverse. You get one binary bit of accuracy for each evaluation, so to get 20 bits you'd have to evaluate the equation 20 times.

There are different standards for RTDs, and you'll need the correct coefficients for the type you are using. The US standard for years was \$\alpha= 0.00392\$, but now most use the DIN standard \$\alpha= 0.00385\$ (the resistance of a DIN standard RTD that is 100 ohms at 0°C is 138.5 ohms at 100°C).

In general the resistance of a given type of RTD is just proportional to the value at a reference temperature, so the resistance of a "500 ohm" RTD at a given temperature is just 1/5 of the value of a similar type of "100 ohm" sensor. So you only need one set of equations or one curve for Pt100, Pt500 and Pt1000 sensors.

Under IPTS-68 and later standards the Callendar-Van Duesen equation was replaced by polynomials, which gives a tiny bit more accuracy, but unless you're doing metrology type work, the probe tolerance will likely dominate, even for relatively high-grade sensors.

In my work with temperature measurement and control, I would typically fit my own polynomial to the curve, optimized for the exact range involved. This is pretty trivial to do these days, using MATLAB or one of the free clones. Since instrument specifications are based on something like maximum absolute error at any given point in the range, I would minimize that rather than the more typical least-squares optimization.

In fact, a lookup table with linear interpolation would work pretty well too. RTDs deviate only slightly from linearity over a fairly wide range. Particularly if you are covering a narrow range like -50 to 70°C.

There are also simple analog methods to provide a first order correction to the RTD nonlinearity (you increase the current slightly at higher temperatures) so you end up with an "S" shaped error curve (rather than a much larger parabolic error term) with only very small deviations if the temperature range is small (as for comfort heating).

Answer 2

There is a nice discussion of resistance probes here.

These probes use a length of fine metal wound into a coil or formed onto a ceramic piece. These use the well known characteristic of the metal to change resistance over a temperature range. The PT type probes use platinum that is very fine and the probes are relatively expensive and fragile. None the less they are prized for their stability, accuracy and repeatability.

The probes leverage the significant characteristic in that the metal resistance is a linear change with temperature over a usable range for a particular sensor. The resistance versus temperature characteristic of a particular probe will be determined as the ratio as follows:

Given:

R0 = resistance at 0°C

R100 = resistance at 100°C

Then:

Alpha = (R100 - R0) / (100 * R0)

The Alpha value for pure platinum has a value of .003925 ohm/ohm/°C. The Alpha value for the probes that you would procure would be specified by the manufacturer. They will vary because the chemical composition of the platinum is carefully adjusted to give the probe a certain resistance at a given temperature. Knowing the Alpha for your probe and the resistance at a particular temperature it is possible to determine the temperature of the probe at a measured resistance by using the formula above.

Note that in reality nothing is ever so perfect and so it is normally necessary to apply calibration process with each probe to capture the resistance at two or more temperature points. This data can then be stored in a non-volatile way and then later retrieved to compute temperature when a resistance reading is made. This will lead to the highest accuracy readings. If more than two calibration points are used to increase accuracy the equivalent Alpha is computed for each span range between the calibration points and measured resistance is matched to the proper range before computing the actual temperature. There are times of course where the ultimate accuracy is not needed and the published Alpha value for the sensor is used without calibration.

Answer 3

The RTD resistors have a value set to a nominal temperature, eg 100 ohms at 25 ° C. From this value, follow a linear variation of temperature with positive coefficient. This regime of variation, provided by the manufacturer's technical specification sheet.

Here you can find more information and some useful data.