Thermistor

A thermistor is a semiconductor type of resistor in which the resistance is strongly dependent on temperature. The word thermistor is a portmanteau of thermal and resistor. The varying resistance with temperature allows these devices to be used as temperature sensors, or to control current as a function of temperature. Some thermistors have decreasing resistance with temperature, while other types have increasing resistance with temperature. This allows them to be used for limiting current to cold circuits, e.g. for inrush current protection, or for limiting current to hot circuits, e.g. to prevent thermal runaway.
Thermistors are categorized based on their conduction models. Negative-temperature-coefficient thermistors have less resistance at higher temperatures, while positive-temperature-coefficient thermistors have more resistance at higher temperatures.
NTC thermistors are widely used as inrush current limiters and temperature sensors, while PTC thermistors are used as self-resetting overcurrent protectors and self-regulating heating elements. The operational temperature range of a thermistor is dependent on the material and is typically between.

Types

Depending on materials used, thermistors are classified into two types:

With NTC thermistors, resistance decreases as temperature rises; usually because electrons are bumped up by thermal agitation from the valence band to the conduction band. An NTC is commonly used as a temperature sensor, or in series with a circuit as an inrush current limiter.
With PTC thermistors, resistance increases as temperature rises; usually because of increased thermal lattice agitations, particularly those of impurities and imperfections. PTC thermistors are commonly installed in series with a circuit, and used to protect against overcurrent conditions, as resettable fuses.

Thermistors are generally produced using powdered metal oxides. With vastly improved formulas and techniques over the past 20 years, NTC thermistors can now achieve accuracies over wide temperature ranges such as ±0.1 °C or ±0.2 °C from 0 °C to 70 °C with excellent long-term stability. NTC thermistor elements come in many styles, such as axial-leaded glass-encapsulated, glass-coated chips, epoxy-coated with bare or insulated lead wire and surface-mount, as well as thin film versions. The typical operating temperature range of a thermistor is −55 °C to +150 °C, though some glass-body thermistors have a maximal operating temperature of +300 °C.
Thermistors differ from resistance temperature detectors in that the material used in a thermistor is generally a ceramic or polymer, while RTDs use pure metals. The temperature response is also different; RTDs are useful over larger temperature ranges, while thermistors typically achieve a greater precision within a limited temperature range, typically −90 °C to 130 °C.

Basic operation

Assuming, as a first-order approximation, that the relationship between resistance and temperature is linear, then
where
Depending on type of the thermistor in question the may be either positive or negative.
If is positive, the resistance increases with increasing temperature, and the device is called a positive-temperature-coefficient ''thermistor, or posistor. There are two types of PTC resistorswitching thermistor and silistor. If is negative, the resistance decreases with increasing temperature, and the device is called a negative-temperature-coefficient thermistor. Resistors that are not thermistors are designed to have a as close to 0 as possible so that their resistance remains nearly constant over a wide temperature range.
Instead of the temperature coefficient k'', sometimes the temperature coefficient of resistance is used. It is defined as
This coefficient should not be confused with the parameter below.

Construction and materials

Thermistors are typically built by using metal oxides. They're typically pressed into a bead, disk, or cylindrical shape and then encapsulated with an impermeable material such as epoxy or glass.
NTC thermistors are manufactured from oxides of the iron group of metals: e.g. chromium, manganese, cobalt, iron, and nickel. these oxides form a ceramic body with terminals composed of conductive metals such as silver, nickel, and tin.
PTC thermistors are usually prepared from barium, strontium, or lead titanates.
Thermistors can also be produced by resonant acoustic mixing of the previously mentioned oxides, followed by a sintering process. This effort reduces production time and can eliminate the calcination step entirely.

Steinhart–Hart equation

In practical devices, the linear approximation model is accurate only over a limited temperature range. Over wider temperature ranges, a more complex resistance–temperature transfer function provides a more faithful characterization of the performance. 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 absolute temperature, and R is the resistance. The equation is not dimensionally correct, since a change in the units of R results in an equation with a different form, containing a term. In practice, the equation gives good numerical results for resistances expressed in, for example, ohms or kiloohms, but the coefficients a, b, and c must be stated with reference to that particular unit. To give resistance as a function of temperature, the above cubic equation in can be solved, the real root of which is given by
where
The error in the Steinhart–Hart equation is generally less than 0.02 °C in the measurement of temperature over a 200 °C range. As an example, typical values for a thermistor with a resistance of 3 kΩ at room temperature are:

''B'' or ''β'' parameter equation

NTC thermistors can also be characterised with the B parameter equation, which is essentially the Steinhart–Hart equation with, and,
where the temperatures and the B parameter are in kelvins, and R₀ is the resistance of the thermistor at temperature T₀. Solving for R yields
or, alternatively,
where.
This can be solved for the temperature:
The B-parameter equation can also be written as. This can be used to convert the function of resistance vs. temperature of a thermistor into a linear function of vs.. The average slope of this function will then yield an estimate of the value of the B parameter.

Conduction model

NTC (negative temperature coefficient)

Many NTC thermistors are made from a pressed disc, rod, plate, bead or cast chip of semiconducting material such as sintered metal oxides. They work because raising the temperature of a semiconductor increases the number of active charge carriers by promoting them into the conduction band. The more charge carriers that are available, the more current a material can conduct. In certain materials like ferric oxide with titanium doping an n-type semiconductor is formed and the charge carriers are electrons. In materials such as nickel oxide with lithium doping a p-type semiconductor is created, where holes are the charge carriers.
This is described in the formula
where
Over large changes in temperature, calibration is necessary. Over small changes in temperature, if the right semiconductor is used, the resistance of the material is linearly proportional to the temperature. There are many different semiconducting thermistors with a range from about 0.01 kelvin to 2,000 kelvins.
The IEC standard symbol for a NTC thermistor includes a "−t°" under the rectangle.

PTC (positive temperature coefficient)

Most PTC thermistors are made from doped polycrystalline ceramic which have the property that their resistance rises suddenly at a certain critical temperature. Barium titanate is ferroelectric and its dielectric constant varies with temperature. Below the Curie point temperature, the high dielectric constant prevents the formation of potential barriers between the crystal grains, leading to a low resistance. In this region the device has a small negative temperature coefficient. At the Curie point temperature, the dielectric constant drops sufficiently to allow the formation of potential barriers at the grain boundaries, and the resistance increases sharply with temperature. At even higher temperatures, the material reverts to NTC behaviour.
Another type of thermistor is a silistor. Silistors employ silicon as the semiconductive component material. Unlike ceramic PTC thermistors, silistors have an almost linear resistance-temperature characteristic. Silicon PTC thermistors have a much smaller drift than an NTC thermistor. They are stable devices which are hermetically sealed in an axial leaded glass encapsulated package.
Barium titanate thermistors can be used as self-controlled heaters; for a given voltage, the ceramic will heat to a certain temperature, but the power used will depend on the heat loss from the ceramic.
The dynamics of PTC thermistors being powered lends to a wide range of applications. When first connected to a voltage source, a large current corresponding to the low, cold, resistance flows, but as the thermistor self-heats, the current is reduced until a limiting current is reached. The current-limiting effect can replace fuses. In the degaussing circuits of many CRT monitors and televisions an appropriately chosen thermistor is connected in series with the degaussing coil. This results in a smooth current decrease for an improved degaussing effect. Some of these degaussing circuits have auxiliary heating elements to heat the thermistor further.
Another type of PTC thermistor is the polymer PTC, which is sold under brand names such as "Polyswitch" "Semifuse", and "Multifuse". This consists of plastic with carbon grains embedded in it. When the plastic is cool, the carbon grains are all in contact with each other, forming a conductive path through the device. When the plastic heats up, it expands, forcing the carbon grains apart, and causing the resistance of the device to rise, which then causes increased heating and rapid resistance increase. Like the BaTiO₃ thermistor, this device has a highly nonlinear resistance/temperature response useful for thermal or circuit control, not for temperature measurement. Besides circuit elements used to limit current, self-limiting heaters can be made in the form of wires or strips, useful for heat tracing. PTC thermistors "latch" into a hot / high resistance state: once hot, they stay in that high resistance state, until cooled.
The effect can be used as a primitive latch/memory circuit, the effect being enhanced by using two PTC thermistors in series, with one thermistor cool, and the other thermistor hot.
The IEC standard symbol for a PTC thermistor includes a "+t°" under the rectangle.