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Thermistor Equation

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,

where:  T is temperature (in kelvin),
  TRef is the reference temperature, usually at room temp. (25 °C; 77 °F; 298.15 K),
  R is the resistance of the thermistor (W),
  RRef is the resistance at TRef,
  b is a calibration constant depending on the thermistor material, usually between 3,000 and 5,000 K.

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,