Evaluation of resistance–temperature calibration equations for NTC thermistors

The characteristics of thermistors for temperature measurement are the high sensitivity to yield a high resolution and the high accuracy in the narrow temperature range. This performance of this sensing element is affected by its calibration equation. Seven calibration equations were selected to evaluate the fitting agreement of the resistance–temperature data of four types of thermistors in this study. The parameters of these calibration equations are estimated using least squares method. The performance of these equations was compared with several statistics. The results of this study indicated that the basic equation and Steinhart and Hart equations were not the adequate calibration equation for four table data of thermistor. The Hoge-3 equation, 1/T=A0+A1ℓnRT+A2(ℓnRT)2+A3(ℓnRT)3+A4(ℓnRT)41/T=A0+A1ℓnRT+A2(ℓnRT)2+A3(ℓnRT)3+A4(ℓnRT)4, was the best equation for seven calibration equations. The form of this equation was a 4th4th-degree polynomial equation. It was easy to be incorporated into IC circuit to serve as a calculation equation to transform the measured resistance into the temperature value. The nonlinear least squares method and the criteria for comparison also could be applied to evaluate the fitting ability of calibration equations for other thermistors.