Christian: Created page with "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 ${\partial R(T) \over \partial T} < 0$ . 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: ${\frac {1}{..."$

2024-12-30T10:40:59Z

Created page with "A common temperature sensor is a Thermistor, which is a device with a temperature-dependent resistance <math>R(T)</math> and a negative temperature coefficient (NTC), i.e., the Resistance decreases with temperature, or <math>{\partial R(T) \over \partial T} < 0 </math>. 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: <math> {\frac {1}{..."

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A common temperature sensor is a Thermistor, which is a device with a temperature-dependent resistance <math>R(T)</math> and a negative temperature coefficient (NTC), i.e., the Resistance decreases with temperature, or <math>{\partial R(T) \over \partial T} < 0 </math>. 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:

<math> {\frac {1}{T}}=a + b \ln R + c (\ln R)^{3} </math>

Usually, the coefficients <math>a,b,c</math> 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 R<sub>0</sub> at the reference temperature (typically 25 Celsius). Often, R<sub>0</sub>=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

<math> {\frac {1}{T}}=A+B\ln R</math>

or

<math>R=R_0 e^{B({1\over T}-{1\over T_0})}</math>.

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

<math>T = \left( {1\over T_0} + {1\over B} \ln {R\over R_0} \right) ^{-1}</math>

Thermistor - Revision history