Thermistor is a portmanteau of the words thermal and resistor. A thermistor is a type of resistor used to measure temperature changes, relying on the change in its resistance with changing temperature. The temperature coefficient of a thermistor is defined as change in the resistance for 1 K change in temperature.

Semi conductors are classified as posistor and a thermistor based on their temperature coefficient of resistance. A posistor has a positive coefficient of temperature where as a thermistor has a negative coefficient of temperature. That is as the temperature increases the resistance decreases for a thermistor. Thermistors are semiconducting ceramics composed of mixtures of several metal oxides such as those of Cobalt, Magnesium, Manganese, Nickel, Tin, Titanium, Uranium, Zinc and Aluminum. Some NTC thermistors are crystallized from semiconducting material such as Silicon and Germanium.

Electrical circuitry is colder at start-up than after running for a length of time. NTC thermistors are used to take advantage of this to protect the circuitry from the surge in electrical flow that accompanies start-up. Because the resistance of NTC thermistors varies gradually with temperature, they are also used as temperature measuring devices.

The variation of resistance with temperature can be expressed linearly for a small change of temperature. However for higher temperatures, the resistance / temperature curve must be described in more detail. So, **Steinhart Hart equation** is widely used,

**1/T = a + b ln(R) + c (ln(R))^3** where T is the temperature and R is the resistance. Further a, b, c are Steinhart-Hart parameters which change from device to device.

The above equation can be approximated for a temperature T as **1/T = a + b ln(R)**. When T = T0 then R = R0, we get

**1/T - 1/T0 = B (ln(Rt) - ln(R0))**

This equation on simplification gives **Rt = R0 exp B (1/T - 1/T0)** where,

R0 - Resistance at T0 K in ohms

Rt - Resistance at T K in ohms

B - a constant depending on the material of the device

The value of B is given by **B = E/K** where,

E - energy gap in eV

K - Boltzmans constant (8.625 x 10^(-5) eV/K)

If T tends to infinity then R tends to A which is the thermistors resistance as temperature approaches infinity. Therefore, the temperature resistance relations can be written as **Rt = A exp B/T**.

The temperature coefficient of resistance is usually expressed as

**alpha = dR/dT (1/R)
= (A exp B/T) (-B/T^2) (1/A exp (B/T))
= -B/T^2**

where T is the absolute temperature in Kelvin.