The thermistor is a resistance thermometer. The relationship between its resistance and the temperature is highly nonlinear. Furthermore, the resistance changes negatively and sharply with a positive change in temperature, as shown schematically below.
Characteristics of Three Temperature Transducers
The thermistor resistance-temperature relationship can be approximated by,
The thermistor resistance can easily be measured, but the temperature is buried inside an exponential. Since all R and T are positive real numbers, we can apply a logarithm ln to both sides of the equation. Doing so allows us to solve for the temperature T,
Alternatively, some references use the negative temperature coefficient (NTC) a to describe the sensitivity of a thermistor,
Typically, the value of a falls between -2% ~ -8%.
With the above equations, the temperature can be directly obtained from the measured resistance. Note that the material constant b may vary slightly with temperature and is usually provided by vendors. One can also use several well known temperature conditions as check points, e.g., ice water at 0 °C (32 °F) and boiling water at 100 °C (212 °F), or use other pre-calibrated thermometers to calibrate/curve-fit the value of b.
However, b may vary considerably across the temperature range of interest. In this case, one should resort to a calibrated curve-fit of the R-T relationship and neglect the equations presented above. A suitable curve fit is suggested by,