![]() Precomputed calibration coefficients for various thermocouplesįor fitting nonlinear data, rational polynomial functions are more flexible, efficient and parsimonious than simple polynomial functions. The computationally more efficient rational function model uses fewer coefficients and provides an accuracy for most thermocouples of a few thousandths of a degree. ![]() Over the different types of thermocouples, the NIST models require ten terms in the polynomial to attain a temperature accuracy of ☐.05☌. By smoothing the quantization errors, as shown by the black line in the above graph, we can see that the model's residual errors are about ☐.002☌, much less than the NIST errors of about ☐.03☌. Most of the scatter in the above graph results from the quantization error – as revealed by the moiré patterns in the scattered points. Most importantly, the systematic nonlinear errors are much smaller than the quantization errors caused by NIST's rounding the voltage data to the nearest microvolt. From the viewpoint of computational efficiency, this model, using nine coefficients, provides significant less error than the ten-coefficient polynomial provided by NIST. In the graph the errors between model predictions and the actual temperature are plotted against temperature for a type K thermocouple. The data and calibration equation coefficients are taken from the NIST Thermocouple Database for type K thermocouples. For example, the following graph shows the temperature errors resulting from applying the NIST formula to the NIST data from a type K thermocouple. The thermocouple voltage is either referred to a cold junction at 0☌, or it is a compensated voltage as though it were referred to a cold junction at 0☌.īecause a single equation doesn't work very well over the full temperature range of a thermocouple, NIST breaks up that range into three or four smaller portions and publishes different sets of calibration coefficients for each sub-range.Įven so, the NIST polynomial equation doesn't quite compensate for all of a thermocouple's nonlinear response. Where the d i are calibration coefficients taken from the NIST database, T is the thermocouple temperature (in ☌), and V is the thermocouple voltage (in millivolts). The NIST polynomial equation is calibrated using ten terms, and is of the form, NIST also provide a polynomial formula you can use to compute temperature from a measured thermocouple voltage. A particularly useful source is the National Institute of Standards and Technology (NIST) database of thermocouple values. The rational polynomial coefficients provided here produce an order of magnitude lower errors than the NIST ITS-90 thermocouple coefficients for direct and inverse polynomials.Ĭomputing temperature using the NIST polynomial equationĬalibration tables of thermocouple voltage as a function of temperature are available for all common types of thermocouple. However, their polynomial curve fits exhibit errors much greater than that of the data fitted. NIST publishes a set of polynomials for converting thermocouple voltage to temperature. This is already done for you if you use the Thermocouple Wildcard's software drivers.įor those of you not using Mosaic's Thermocouple Wildcard, but looking for accurate equations for thermocouple measurement, we hope the thermocouple calibration coefficients on this page are helpful. ![]() Consequently, for accurate temperature measurement in your microcontroller project, you will need to apply a nonlinear calibration equation to a measured thermocouple potential to calculate the temperature. However, almost isn't usually good enough – in most microcontroller-based temperature measurement applications the deviations from linearity must be modeled to measure temperature accurately. The potential or voltage of thermocouples varies almost linearly with temperature. Why aren't rational polynomial functions used more?
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