Temperature measurements by means of NTC resistors and a two-parameter approximation curve

Table data for resistance-versus-temperature (R–T) dependence of negative temperature coefficient resistors (NTCRs), which have resistance RN = 10,000 Ω at a temperature of 25 °C and limits of error ±0.2 °C in the range from 0 °C to 70 °C [Fenwal Electronics Catalog: Thermistoren UNI Kurve; Typ: UUA41J1, UUA41J8 (10 kΩ at 25 °C, limits of error ±0.2 °C in the range from 0 °C to 70 °C); BetaTHERM Sensors, http://www.betatherm.com; BetaCURVE Thermistor Series III 10K3A1W2 (10 kΩ at 25 °C, limits of error ±0.2 °C in the range from 0 °C to 70 °C), http://www.betatherm.com/datasheets/datasheet.php?p_id=69#; Advanced Thermal Products, http://www.atpsensor.com/; coated chip thermistor A1004-C3 (10 kΩ at 25 °C, limits of error ±0.2 °C in the range from 0 °C to 70 °C), http://www.atpsensor.com/ntc/ntc_rvt_pdfs/rvt_pdf.html; Epcos, http://www.epcos.com; uni-curve NTC thermistor S 863/10k/F40 (10 kΩ at 25 °C, limits of error ±0.2 °C in the range from 0 °C to 70 °C), http://www.epcos.com/inf/50/db/ntc_02/00920093.pdf], are analysed. Determination of two approximation curves is described: a three-parameter one (abbreviated AC1) and a two-parameter one (AC2). These curves are compared with the three-parameter Steinhart–Hart equation (S&H) by using the table data of resistance for different NTCRs and calculating the following for all of them: unknown parameters by the least-squares method, approximated temperature using determined parameters, and the difference from the table data of temperature. The obtained results are presented, showing a very good agreement of curves, with their mutual differences within a few millikelvins, and the differences from the table data mostly within ±10 mK for the range from 0 °C to 70 °C (differences are larger only at a few points). Therefore, the presented two-parameter approximation curve AC2 can be very conveniently used with some NTCRs for the calculation of unknown temperature from the measured resistance.