Thermistor

A common temperature sensor is a Thermistor, which is a device with a temperature-dependent resistance $R(T)$ and a negative temperature coefficient (NTC), i.e., the Resistance decreases with temperature, or $\frac{\partial R(T)}{\partial T}<0$. Therefore, thermistors are sometime referenced as NTC sensors.

Their resistances can be described by a Steinhardt-Hart equation, which relates resistance R and absolute temperature T:

$\frac{1}{T}=a+b\ln R+c(\ln R{)}^3$

Usually, the coefficients $a,b,c$ are not specified in a data sheet of a device. More commonly, three things are quoted/specified:

• Reference temperature, typically 25 Celsius; sometimes this is not even mentioned explicitly
• Resistance R₀ at the reference temperature (typically 25 Celsius). Often, R₀=10kΩ.
• Characteristic of the exponential, the constant B=1/b in the above expression. Typically around 4000 Kelvin.

These parameters can be used with a simplified Steinhart-Hart equation, which assumes c=0 in the expression above. Then, the equation becomes

$\frac{1}{T}=A+B\ln R$

or

$R=R_0{e}^{B(\frac{1}{T}-\frac{1}{T_0})}$.

The absoute temperature then can be obtained by inverting the equation above:

$T={(\frac{1}{T_0}+\frac{1}{B}\ln \frac{R}{R_0})}^{-1}$