Improving NTC Thermistor interpolation in wide temperature range using scaled resistance and nonlinear least-squares fitting

Negative Temperature Coefficient (NTC) thermistors are widely used for temperature measurements due to their fast response and high sensitivity. A basic interpolation method for NTC thermistors relies on a linear relationship between 1/ T and ln( R / R 0 ). ( T : temperature in kelvin, R : thermistor resistance, and R 0 : an arbitrary reference resistance) However, this linear model is only valid within a limited temperature range. For broader ranges, higher-order terms of ln( R / R 0 ) have been added to the interpolation equations, leading to polynomial fitting. A major limitation of the existing method is that higher-order terms tend to dominate for certain choices of R 0 , causing numerical instability. This is especially problematic because rounding errors in higher-order terms may lead to significant temperature estimation errors. Additionally, this method minimizes errors in 1/ T , not in T , which results in uneven weighting of calibration points, especially in wide temperature ranges. This study proposes two improvements to overcome these issues. First, a scaled resistance parameter, r = ( R / R 0 ) p , is introduced, where R 0 is the geometric mean of the maximum and minimum resistances in the calibration range, and p is 2 · [ln( R max / R min )] −1 . This normalization improves numerical stability. Second, nonlinear fitting is used to minimize temperature errors rather than errors in 1/ T . While a simpler weighted least-squares method addresses the second issue, it does not solve the first. The proposed approach ensures reliable interpolation across wide temperature ranges and offers a robust alternative to the existing method, demonstrated using calibration data on real thermistors.