Platinum resistance thermometers: converting ohms to degrees Celsius Hans LIEDBERG

Overview If converting resistance to temperature by hand, remember: PRTs are not all that linear. If using a readout that calculates temperature for you, remember: PRTs come in different sensitivities.

Resistance-temperature relationship of a PRT PRTs are commonly characterised using two numbers, the resistance at the ice point (R(0 °C) = 100 Ω for all PRTs discussed in this paper) and the alpha value (alpha ranges from (0.00385 to 0.00393) Ω/Ω/°C for platinum of increasing purity). For example, “Pt100(385)” is used to describe a 100 Ω PRT with alpha = 0.00385 Ω/Ω/°C.

Resistance-temperature relationship of a PRT (cntd) Non-linearity: PRTs decrease in sensitivity with increasing temperature, a Pt100(385) from 0.397Ω/°C at -50°C to 0.385Ω/°C at 50°C and 0.345Ω/°C at 400°C.

Resistance-temperature relationship of a PRT (cntd) Decreasing sensitivity of a PRT with increasing temperature.

Resistance-temperature relationship of a PRT (cntd) Different sensitivities: The higher the purity of the platinum, the higher the alpha value of the PRT.

Errors arising from non-linearity Calibration data for a Pt100(385) sensor: To calculate temperature from measured resistance, the first reaction is to interpolate linearly between these data pairs.

Errors arising from non-linearity (cntd) Linear interpolation results in errors proportional to ΔT2:

Solutions to the non-linearity problem 1. Use a reference function that models the decreasing sensitivity of PRTs with increasing temperature well (e.g., ITS-90 or IEC 751). The deviations of a real PRT from such a reference function should be fairly linear. OR 2. Fit a 2nd order polynomial to the data (e.g., using Excel’s “Add trendline” function).

Errors arising from different sensitivities Calibration data for a Pt100(385) sensor: These data were measured with the readout using IEC 751 (which describes “385” PRTs) to calculate temperature.

Errors arising from different sensitivities (cntd) If the readout is mistakenly set to “‘Pt100(3916)” or “Pt100(3923)” during use, large errors will result:

Verifying the readout sensitivity setting Checking the PRT + readout system at the ice point only verifies that R(0°C) or R(0.01°C) is correct. To verify A, B and C coefficients, check the system at a temperature away from 0°C, using a simple fixed point (e.g., boiling point of water or sublimation point of carbon dioxide) or a PRT + readout system for which the correct resistance-to-temperature conversion method is not in doubt.

Conclusions PRTs capable of ±0.01°C accuracy are readily available. To achieve this, take care to use an appropriate method to interpolate between resistance-temperature data pairs or set your readout to the same function as was used during calibration. Cal lab and client should agree on the method of resistance-temperature conversion during contract review.