Advertisement

Interpolation Errors in Thermistor Calibration Equations

TEMPMEKO 2016
Part of the following topical collections:
  1. TEMPMEKO 2016: Selected Papers of the 12th International Symposium on Temperature, Humidity, Moisture and Thermal Measurements in Industry and Science

Abstract

Thermistors are widely used temperature sensors capable of measurement uncertainties approaching those of standard platinum resistance thermometers. However, the extreme nonlinearity of thermistors means that complicated calibration equations are required to minimize the effects of interpolation errors and achieve low uncertainties. This study investigates the magnitude of interpolation errors as a function of temperature range and the number of terms in the calibration equation. Approximation theory is used to derive an expression for the interpolation error and indicates that the temperature range and the number of terms in the calibration equation are the key influence variables. Numerical experiments based on published resistance–temperature data confirm these conclusions and additionally give guidelines on the maximum and minimum interpolation error likely to occur for a given temperature range and number of terms in the calibration equation.

Keywords

Calibration Calibration equation Interpolation error Steinhart–Hart equation Thermistors 

References

  1. 1.
    D.R. White, K. Hill, D. del Campo, C. Garcia Izquierdo, Guide on Secondary Thermometry: Thermistor Thermometry (BIPM, Paris, 2014). http://www.bipm.org/utils/common/pdf/ITS-90/Guide-SecTh-Thermistor-thermometry.pdf
  2. 2.
    P.R.N. Childs, Practical Temperature Measurement (Butterworth-Heinemann, Boston, 2001)Google Scholar
  3. 3.
    J. Fraden, Handbook of Modern Sensors: Physics, Designs, and Applications (Springer, New York, 2010)CrossRefGoogle Scholar
  4. 4.
    T.W. Kerlin, R.L. Shepard, Industrial Temperature Measurement (Research Triangle Park NC, ISA, 1982)Google Scholar
  5. 5.
    J.S. Steinhart, S.R. Hart, Calibration curves for thermistors. Deep Sea Res. 15, 497–503 (1968)Google Scholar
  6. 6.
    A.S. Bennett, The calibration of thermistors over the range 0 \(^{\,\circ }\text{ C }\)–30 \(^{\,\circ }\text{ C }\). Deep Sea Res. 19, 157–163 (1971)Google Scholar
  7. 7.
    H.J. Hoge, Useful procedure in least squares, and tests of some equations for thermistors. Rev. Sci. Inst. 59, 975–979 (1988)ADSCrossRefGoogle Scholar
  8. 8.
    C.-C. Chen, Evaluation of resistance–temperature calibration equations for NTC thermistors. Measurement 42, 1103–1111 (2009)CrossRefGoogle Scholar
  9. 9.
    E.W. Cheney, Introduction to Approximation Theory (American Mathematical Society, Providence, 1982)MATHGoogle Scholar
  10. 10.
    D.R. White, P. Saunders, Propagation of uncertainty with calibration equations. Meas. Sci. Technol. 18, 2157–2169 (2007)ADSCrossRefGoogle Scholar
  11. 11.
    S.M. Sze, Physics of Semiconductor Devices, 2nd edn. (Wiley, New York, 1981)Google Scholar
  12. 12.
    D.R. White, Some mathematical properties of the ITS-90 scale, in Temperature: Its Measurement and Control in Science and Industry, vol. 8, ed. by Christopher W. Meyer (AIP, Melville, 2013), pp. 81–88Google Scholar
  13. 13.
    D.R. White, Errors in linearizing resistance networks for thermistors. Int. J. Thermophys. 36, 3404–3420 (2015)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Measurement Standards LaboratoryLower HuttNew Zealand

Personalised recommendations