The evidence to support feasibility of using minimax approximation to calculate the parameters of thermistors’ thermometric characteristic models has been provided. Minimax approximation ensures the achievement of the minimum possible calibration error, while the least squares method minimizes the sum of squared errors. A rational expression has been proposed to describe the dependence of temperature on thermistor’s resistance. The effectiveness of the model in the form of a rational expression is illustrated with actual calibration results. This model provides higher accuracy in reproducing temperature compared to generalized Steinhart-Hart models.
- D.R. White, K. Hill, D. del Campo, C. Garcia Izquierdo, Guide on Secondary Thermometry – Thermistor Thermometry, BIPM, Consultative Committee for Thermometry (CCT), 2014.
- Hughes-Riley T., Lugoda P., Dias T., Trabi C.L., Morris R.H. A Study of thermistor performance within a textile structure. Sensors. 2017. Vol. 17, Iss. 8. Article number 1804. https://doi.org/10.3390/s17081804.
- K. Esenowo Jack, E. O. Nwangwu, I. Agwu Etu, E. U. Osuagwu, “A simple thermistor design for industrial temperature measurement,” IOSR J. Electr. Electron. Eng., 11, 05, 57–66, 2016. https://doi.org/10.9790/1676-1105035766.
- Li Ting, Wang Hongjun, Sun Jianping, Hao Xiaopeng, Wang Chengke, Yu Jiao. Exploration of Calibration Methods for Ocean NTC Thermistor Thermometers. J. Metrology Science and Technology, 2021, 65(5): 55-61. https://doi.org/10.12338/j.issn.2096-9015.2020.9027.
- Damir Ilić, Josip Butorac, Luka Ferković Temperature measurements by means of NTC resistors and a two- parameter approximation curve, Measurement. Vol. 41, no. 3, April 2008, pp. 294-299. https://doi.org/10.1016/ j.measurement.2006.11.007 .
- Steffen Rudtsch, Christoph von Rohden, “Calibration and self-validation of thermistors for high-precision temperature measurements,” Measurement: Journal of the International Measurement Confederation, 2015, 76, pp.1–6. https://doi.org/10.1016/j.measurement.2015.07.028 .
- Guang Liu, Liang Guo, Chunlong Liu, Qingwen Wu, Evaluation of different calibration equations for NTC thermistor applied to high-precision temperature measurement, Measurement, Vol. 120, 2018. pp. 21-27. https://doi.org/10.1016/j.measurement.2018.02.007.
- V. F. Mitin et al., "Nanocrystalline SiC Film thermistors for cryogenic applications," Review of Scientific Instruments. Vol. 89, no. 2, Feb 2018, pp. 025004-1–025004-5. https://doi.org/10.1063/1.5024505.
- D. J. Li, C. G. Xing, “Linearization of high precision human body temperature measurement circuit based on ntc thermistor,” Appl. Mech. Mater., 713–715, 381–384, 2015. https://doi.org/10.4028/www.scientific.net/AMM.713-715.381.
- X. Gong, X. Tang, Y. Li, M. Y. Zude Lin and J. Liu, "Investigation the Minimum Measurement Points for Calibration a High Precision NTC Thermistors in Cryogenic Field," 2021 IEEE 16th International Conference on Nano/Micro Engineered and Molecular Systems (NEMS), Xiamen, China, 2021, pp. 1088-1091, https://doi.org/10.1109/NEMS51815.2021.9451310.
- Lan, Y. , Yang, S. , Chen, G. and Yang, S. (2020) Characteristics of a Type of NTC Thermistors for Cryogenic Applications. Advances in Materials Physics and Chemistry, 10, 167-177. https://doi.org/10.4236/ ampc.2020.108012.
- Chiachung Chen Evaluation of resistance–temperature calibration equations for NTC thermistors. Measurement, Vol. 42. no. 7. 2009, pp. 1103-1111. https://doi.org/ 10.1016/j.measurement.2009.04.004.
- A. Li, H. Wang, L. Dong, Q. Han, M. Wen and X. Wen, "Research on the Adaptability of Thermistor Calibration Equations," in IEEE Instrumentation & Measurement Magazine, vol. 26, no. 2, pp. 13-18, April 2023, https://doi.org/10.1109/MIM.2023.10082999.
- R. P. Malachivskyi, R. A. Bun, O. V. Shevchuk, “Approximation of Thermometric Characteristics of Thermistors,” Computer Technologies of Printing, no. 2 (50), 2023. C. 87-97. https://doi.org/10.32403/2411-9210-2023-2-50-87-97, (in Ukrainian).
- Remez E. Ya. Fundamentals of the Numerical Methods of Chebyshev Approximation. Naukova Dumka, Kyiv (1969), (in Russian).
- V. A. Yatsuk and P. S. Malachivskyy, Methods to Improve Measurement Accuracy, Beskid Bit, Lviv (2008), (in Ukrainian).
- White, D. R. Interpolation Errors in Thermistor Calibration Equations. Int J Thermophys 38, 59 (2017). https://doi.org/10.1007/s10765-017-2194-x.
- P. S. Malachivskyy, Y. V Pizyur, R. P. Malachivskyi, “Chebyshev approximation by a rational expression for functions of many variables,” Cybernetics and Systems Analysis, Vol. 56. no. 5, 2020. рp. 811-819. https://doi.org/10.1007/s10559-020-00302-0.
- P. S. Malachivskyy, L. S. Melnychok, Y. V Pizyur, “Chebyshev Approximation of Multivariable Functions by a Constrained Rational Expression,” Cybernetics and Systems Analysis, Vol. 59. no. 1, 2023. pp. 146–159. https://doi.org/10.1007/s10559-023-00552-8.