Thermistor
A common temperature sensor is a Thermistor, which is a device with a temperature-dependent resistance Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle R(T)} and a negative temperature coefficient (NTC), i.e., the Resistance decreases with temperature, or Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\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:
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\frac {1}{T}}=a + b \ln R + c (\ln R)^{3} }
Usually, the coefficients Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\frac {1}{T}}=A+B\ln R}
or
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle R=R_0 e^{B({1\over T}-{1\over T_0})}} .