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A thermistor is a semiconductor type of resistor whose resistance is strongly dependent on temperature, more so than in standard resistors. The word thermistor is a portmanteau of thermal and resistor.

Thermistors are categorized based on their conduction models. Negative-temperature-coefficient (NTC) thermistors have less resistance at higher temperatures, while positive-temperature-coefficient (PTC) thermistors have more resistance at higher temperatures.[1]

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. An operational temperature range of a thermistor is dependent on the probe type and is typically between −100 °C and 300 °C (−148 °F and 572 °F).

Negative-temperature-coefficient (NTC) thermistor, bead type, insulated wires
Working principleElectric resistance
Electronic symbol

Thermistor or varistor symbol[2]


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

Thermistors are generally produced using powdered metal oxides.[3] With vastly improved formulas and techniques over the past 20 years[when?], 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 [4] such as axial-leaded glass-encapsulated (DO-35, DO-34 and DO-41 diodes), 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 (RTDs) 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.[5]

Basic operation

Assuming, as a first-order approximation, that the relationship between resistance and temperature is linear, then


, change in resistance,
, change in temperature,
, first-order temperature coefficient of resistance.

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 (PTC) thermistor, or posistor. There are two types of PTC resistor – switching thermistor and silistor. If 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 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 ("alpha sub T") is used. It is defined as[6]

This coefficient should not be confused with the parameter below.

Construction and materials

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Thermistors are typically built by using metal oxides.[7]

NTC thermistors are manufactured from oxides of the iron group of metals: e.g. chromium (CrO, Cr2O3), manganese (e.g. MnO), cobalt (CoO), iron (iron oxides), and nickel (NiO, Ni2O3).[8][9] these oxides form a ceramic body with terminals composed of conductive metals such as silver, nickel, and tin.

PTCs are usually prepared from barium (Ba), strontium, or lead titanates (e.g. PbTiO3).[8][9]

Steinhart–Hart equation

Main article: Steinhart–Hart equation

In practical devices, the linear approximation model (above) 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 ohms or kΩ, but the coefficients a, b, and c must be stated with reference to the unit.[10] To give resistance as a function of temperature, the above cubic equation in can be solved, the real root of which is given by


The error in the Steinhart–Hart equation is generally less than 0.02 °C in the measurement of temperature over a 200 °C range.[11] As an example, typical values for a thermistor with a resistance of 3 kΩ at room temperature (25 °C = 298.15 K, R in Ω) are:

B or β parameter equation

NTC thermistors can also be characterised with the B (or β) 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 (25 °C = 298.15 K).[12] 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)

A failed (blown) NTC thermistor that worked as an inrush current limiter in a switched-mode power supply

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 (Fe2O3) with titanium (Ti) doping an n-type semiconductor is formed and the charge carriers are electrons. In materials such as nickel oxide (NiO) with lithium (Li) doping a p-type semiconductor is created, where holes are the charge carriers.[13]

This is described in the formula


= electric current (amperes),
= density of charge carriers (count/m3),
= cross-sectional area of the material (m2),
= drift velocity of electrons (m/s),
= charge of an electron ( coulomb).

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 (−273.14 °C to 1,700 °C).[14]

The IEC standard symbol for a NTC thermistor includes a "−t°" under the rectangle.[15]

PTC (positive temperature coefficient)

Most PTC thermistors are made from doped polycrystalline ceramic (containing barium titanate (BaTiO3) and other compounds) 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 (a thermally sensitive silicon resistor). Silistors employ silicon as the semiconductive component material. Unlike ceramic PTC thermistors, silistors have an almost linear resistance-temperature characteristic.[16] 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.[17]

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 (and corresponding peak device temperature) 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 (and reduce the resulting current) 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.[18]

The IEC standard symbol for a PTC thermistor includes a "+t°" under the rectangle.[19]

Self-heating effects

When a current flows through a thermistor, it generates heat, which raises the temperature of the thermistor above that of its environment. If the thermistor is being used to measure the temperature of the environment, this electrical heating may introduce a significant error (an observer effect) if a correction is not made. Alternatively, this effect itself can be exploited. It can, for example, make a sensitive air-flow device employed in a sailplane rate-of-climb instrument, the electronic variometer, or serve as a timer for a relay as was formerly done in telephone exchanges.

The electrical power input to the thermistor is just

where I is current, and V is the voltage drop across the thermistor. This power is converted to heat, and this heat energy is transferred to the surrounding environment. The rate of transfer is well described by Newton's law of cooling:

where T(R) is the temperature of the thermistor as a function of its resistance R, is the temperature of the surroundings, and K is the dissipation constant, usually expressed in units of milliwatts per degree Celsius. At equilibrium, the two rates must be equal:

The current and voltage across the thermistor depend on the particular circuit configuration. As a simple example, if the voltage across the thermistor is held fixed, then by Ohm's law we have , and the equilibrium equation can be solved for the ambient temperature as a function of the measured resistance of the thermistor:

The dissipation constant is a measure of the thermal connection of the thermistor to its surroundings. It is generally given for the thermistor in still air and in well-stirred oil. Typical values for a small glass-bead thermistor are 1.5 mW/°C in still air and 6.0 mW/°C in stirred oil. If the temperature of the environment is known beforehand, then a thermistor may be used to measure the value of the dissipation constant. For example, the thermistor may be used as a flow-rate sensor, since the dissipation constant increases with the rate of flow of a fluid past the thermistor.

The power dissipated in a thermistor is typically maintained at a very low level to ensure insignificant temperature measurement error due to self-heating. However, some thermistor applications depend upon significant "self-heating" to raise the body temperature of the thermistor well above the ambient temperature, so the sensor then detects even subtle changes in the thermal conductivity of the environment. Some of these applications include liquid-level detection, liquid-flow measurement and air-flow measurement.[6]





The first NTC thermistor was discovered in 1833 by Michael Faraday, who reported on the semiconducting behavior of silver sulfide. Faraday noticed that the resistance of silver sulfide decreased dramatically as temperature increased. (This was also the first documented observation of a semiconducting material.)[28]

Because early thermistors were difficult to produce and applications for the technology were limited, commercial production of thermistors did not begin until the 1930s.[29] A commercially viable thermistor was invented by Samuel Ruben in 1930.[30]

See also


  1. ^ "PTC thermistor vs. NTC thermistor for measuring the temperature of a liquid". Electrical Engineering Stack Exchange. Retrieved 24 April 2022.
  2. ^ "Standards for Resistor Symbols". EePower. EETech Media. Retrieved September 13, 2021.
  3. ^ "What is a Thermistor? How do thermistors work?". EI Sensor Technologies. Retrieved 2019-05-13.
  4. ^ "Thermistors". EI Sensor Technologies. Retrieved 2019-05-13.
  5. ^ "NTC Thermistors" Archived 2017-09-22 at the Wayback Machine. Micro-chip Technologies. 2010.
  6. ^ a b Thermistor Terminology. Littlefuse Technical Resources.
  7. ^ Industrial ventilation design guidebook. Howard D. Goodfellow, Esko Tähti. San Diego, Calif.: Academic. 2001. ISBN 978-0-12-289676-7. OCLC 162128694.((cite book)): CS1 maint: others (link)
  8. ^ a b Morris, Alan S. (2020). "Chapter 14 - Temperature measurement". Measurement and instrumentation theory and application. Reza Langari (Third ed.). Amsterdam. ISBN 978-0-12-817142-4. OCLC 1196195913.((cite book)): CS1 maint: location missing publisher (link)
  9. ^ a b Fatigue testing and analysis : theory and practice. Yung-Li Lee. Burlington, Mass.: Elsevier Butterworth-Heinemann. 2005. ISBN 978-0-08-047769-5. OCLC 56731934.((cite book)): CS1 maint: others (link)
  10. ^ Matus, Michael (2011). "Temperature measurement in dimensional metrology - Why the Steinhart-Hart equation works so well". MacroScale.
  11. ^ "Practical Temperature Measurements". Agilent Application Note. Agilent Semiconductor.
  12. ^ Becker, J. A. (1947). "Properties and Uses of Thermistors-Thermally Sensitive Resistors". Bell System Technical Journal. 26: 170–212. doi:10.1002/j.1538-7305.1947.tb01314.x. Retrieved 22 April 2022.
  13. ^ L. W Turner, ed. (1976). Electronics Engineer's Reference Book (4 ed.). Butterworths. pp. 6-29 to 6-41. ISBN 0408001682.
  14. ^ "Thermal-FluidsPedia | Temperature measurements and instrumentation | Thermal-Fluids Central".
  15. ^ "NTC thermistor » Resistor Guide".
  16. ^ "PTC Thermistors and Silistors" The Resistor Guide
  17. ^ "What is a Thermistor? How do thermistors work?".
  18. ^ Downie, Neil A., The Ultimate Book of Saturday Science (Princeton 2012) ISBN 0-691-14966-6
  19. ^ "PTC thermistor – Positive Temperature Coefficient". Resistor Guide.
  20. ^ Patchell, Jim. "Temperature Compensated VCO".
  21. ^ Patent CN 1273423A (China)
  22. ^ "ED35S PTC Thermistors".
  23. ^ Inrush Current Limiting Power Thermistors. U.S. Sensor
  24. ^ "PTC Thermistors Guide- "Publish By Analog Electronic Technologies"".
  25. ^ Mukherjee, Rahul; Basu, Joydeep; Mandal, Pradip; Guha, Prasanta Kumar (2017). "A review of micromachined thermal accelerometers". Journal of Micromechanics and Microengineering. 27 (12): 123002. arXiv:1801.07297. Bibcode:2017JMiMi..27l3002M. doi:10.1088/1361-6439/aa964d. S2CID 116232359.
  26. ^ "Thermistor Probes". EI Sensor Technologies. Retrieved 2019-05-13.
  27. ^ "ED35U UL Recognized Glass Encapsulated NTC Thermistors".
  28. ^ "1833 - First Semiconductor Effect is Recorded". Computer History Museum. Retrieved 24 June 2014.
  29. ^ McGee, Thomas (1988). "Chapter 9". Principles and Methods of Temperature Measurement. John Wiley & Sons. p. 203. ISBN 9780471627678.
  30. ^ Jones, Deric P., ed. (2009). Biomedical Sensors. Momentum Press. p. 12. ISBN 9781606500569.