Mathematical Model
Polynomial formulas relate the electrical resistance of a thermistor to its absolute temperature with high precision. The steinhart hart equation uses the natural logarithm of the resistance to calculate the temperature in Kelvin. It is the standard method for converting NTC thermistor readings in high-accuracy applications.
Curve Fitting
Three coefficients are typically required to define the relationship over a specific range. Applying the steinhart hart equation allows for a fit that is superior to the simpler Beta model.
Metrological Accuracy
Residual errors using this method are often less than 0.01 degrees Celsius. Calibration for the steinhart hart equation involves using stable temperature baths and high-resolution ohmmeters.
Algorithm Implementation
Firmware in a data logger or controller calculates the temperature using the stored coefficients. A steinhart hart equation calculation is computationally more intensive than a look-up table but offers superior resolution. Periodic verification of the thermistor resistance confirms that the coefficients remain valid.
The coefficients are designated as A, B and C in the third-order version of the formula. Finding these values requires at least three calibration points that span the entire measurement range. Verification of the model involves checking the calculated temperature against a reference at an intermediate point not used for the curve fit.
This process ensures that the interpolation error remains within the expected limits for the instrument.
