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A thermistor is a type of resistor used to measure temperature changes, relying on the change in its resistance with changing temperature.

If we assume that the relationship between resistance and temperature is linear (i.e. we make a first-order approximation), then we can say that:

ΔR = change in resistance
ΔT = change in temperature
k = first-order temperature coefficient of resistance

Thermistors can be classified into two types depending on the sign of k. If k is positive, the resistance increases with increasing temperature, and the device is called a positive temperature coefficient (PTC) thermistor, or posistor. If k is negative, the resistance decreases with increasing temperature, and the device is called a negative temperature coefficient (NTC) thermistor. Resistors that are not thermistors are designed to have the smallest possible k, so that their resistance remains almost constant over a wide temperature range.

Table of contents
1 Steinhart Hart equation
2 Conduction model
3 Applications
4 References

Steinhart Hart equation

In practice, the linear approximation (above) works only over a small temperature range. For accurate temperature measurements, the resistance/temperature curve of the device must be described in more detail. The Steinhart-Hart equation is a widely used third-order approximation:
where a, b and c are called the Steinhart-Hart parameters, and must be specified for each device. T is the temperature in
kelvin and R is the resistance in ohms. To give resistance as a function of temperature, the above can be rearranged into:

Conduction model

Many NTC thermistors are made from a thin coil of
semiconducting material such as a sintered metal oxide. They work because raising the temperature of a semiconductor increases the number of electrons able to move about and carry charge - it promotes them into the conducting band. The more charge carriers that are available, the more current a material can conduct. This is described in the formula:


Where i is current, n is the number of charge carriers, A is area of the material, v is voltage and e is the charge on an electron.

The current is measured using an ammeter. Over large changes in temperature, callibration is necessary. However, this is unnecessary if the right semiconductor is used, because over small changes in temperature the resistance of the material is linearly proportional to the temperature. There are many different semiconducting thermistors and their range goes from about 0.01 kelvin to 2000 kelvin (approx. 1700°C)



I.S. Steinhart & S.R. Hart in "Deep Sea Research" vol. 15 p. 497 (1968) - in which the Steinhart-Hart equation was first published.