View source for Thermistor

{{short description|Type of resistor whose resistance varies with temperature}}
{{Infobox electronic component
| component = Thermistor
| image = [[File:NTC bead.jpg|200px]]
| caption = Negative temperature coefficient (NTC) thermistor, bead type, insulated wires
| type = [[Passivity (engineering)|Passive]]
| working_principle = [[Electric resistance]]
| symbol = [[File:Thermistor.svg]]
| symbol_caption = Thermistor symbol
}}
A '''thermistor''' is a type of [[resistor]] whose [[electrical resistance|resistance]] is dependent on [[temperature]], more so than in standard resistors. The word is a combination of ''[[heat|thermal]]'' and ''[[resistor]]''. Thermistors are widely used as [[inrush current limiter]]s, temperature [[sensors]] (negative temperature coefficient or '''NTC''' type typically), [[Resettable fuse|self-resetting overcurrent protectors]], and self-regulating [[heating element]]s (positive temperature coefficient or '''PTC''' type typically).

Thermistors are of two opposite fundamental types:
*With '''NTC''' thermistors, resistance '''''decreases''''' as temperature rises. 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. 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.<ref>{{Cite web |url=https://www.ei-sensor.com/what-is-a-thermistor/ |title=What is a Thermistor? How do thermistors work? |website=EI Sensor Technologies |language=en-US |access-date=2019-05-13}}</ref> With vastly improved formulas and techniques over the past 20 years, NTC thermistors can now achieve precision accuracies over wide temperature ranges such as ±0.1&nbsp;°C or ±0.2&nbsp;°C from 0&nbsp;°C to 70&nbsp;°C with excellent long-term stability. NTC thermistor elements come in many styles <ref>{{Cite web |url=https://www.ei-sensor.com/thermistors/ |title=Thermistors |website=EI Sensor Technologies |language=en-US |access-date=2019-05-13}}</ref> 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 rods and discs.  The typical operating temperature range of a thermistor is −55&nbsp;°C to +150&nbsp;°C, though some glass-body thermistors have a maximal operating temperature of +300&nbsp;°C. 

Thermistors differ from [[Resistance thermometer|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&nbsp;°C to 130&nbsp;°C.<ref>[http://www.microchiptechno.com/ntc_thermistors.php "NTC Thermistors"]. Micro-chip Technologies. 2010.</ref>

==Basic operation==
Assuming, as a first-order approximation, that the relationship between resistance and temperature is [[linear]], then
: <math>\Delta R = k\Delta T,</math>
where
: <math>\Delta R</math>, change in resistance,
: <math>\Delta T</math>, change in temperature,
: <math>k</math>, first-order [[Temperature coefficient|temperature coefficient of resistance]].

Thermistors can be classified into two types, depending on the sign of <math>k</math>.  If <math>k</math> is [[Positive number|positive]], the resistance increases with increasing temperature, and the device is called a [[Temperature coefficient#Positive temperature coefficient of resistance|positive temperature coefficient]] ('''PTC''') thermistor, or '''posistor'''.  If <math>k</math> is negative, the resistance decreases with increasing temperature, and the device is called a [[Temperature coefficient#Negative temperature coefficient|negative temperature coefficient]] ('''NTC''') thermistor. Resistors that are not thermistors are designed to have a <math>k</math>  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'' <math>\alpha_T</math> ("alpha sub T") is used. It is defined as<ref name="Thermistor Terminology">[http://www.ussensor.com/terminology.html Thermistor Terminology]. U.S. Sensor.</ref>
: <math>\alpha_T = \frac{1}{R(T)} \frac{dR}{dT}.</math>
This <math>\alpha_T</math> coefficient should not be confused with the <math>a</math> parameter below.

==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:
: <math>\frac{1}{T} = a + b \ln R + c\, (\ln R)^3,</math>
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.  To give resistance as a function of temperature, the above can be rearranged into
:<math>R = \exp\left[(x - y)^{1/3} - (x + y)^{1/3}\right],</math>
where
:<math>\begin{align}
  y &= \frac{1}{2c} \left(a - \frac{1}{T}\right), \\
  x &= \sqrt{\left(\frac{b}{3c}\right)^3 + y^2}.
\end{align}</math>

The error in the Steinhart–Hart equation is generally less than 0.02&nbsp;°C in the measurement of temperature over a 200&nbsp;°C range.<ref>[http://literature.cdn.keysight.com/litweb/pdf/5965-7822E.pdf "Practical Temperature Measurements"]. Agilent Application Note. Agilent Semiconductor.</ref> As an example, typical values for a thermistor with a resistance of 3&nbsp;kΩ at room temperature (25&nbsp;°C = 298.15&nbsp;K) are:
:<math>\begin{align}
  a &= 1.40 \times 10^{-3}, \\
  b &= 2.37 \times 10^{-4}, \\
  c &= 9.90 \times 10^{-8}.
\end{align}</math>

==''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 <math>a = 1/T_0 - (1/B) \ln R_0</math>, <math>b = 1/B</math> and <math>c = 0</math>,

: <math>\frac{1}{T} = \frac{1}{T_0} + \frac{1}{B} \ln \frac{R}{R_0},</math>

where the temperatures are in [[kelvin]]s<!-- lower-case and pluralized! See Kelvin#Usage_conventions -->, and ''R''<sub>0</sub> is the resistance at temperature ''T''<sub>0</sub> (25&nbsp;°C&nbsp;= 298.15&nbsp;K). Solving for ''R'' yields

: <math>R = R_0 e^{B\left(\frac{1}{T} - \frac{1}{T_0}\right)}</math>

or, alternatively,

: <math>R = r_\infty e^{B/T},</math>

where <math>r_\infty = R_0 e^{-B/T_0}</math>.

This can be solved for the temperature:

: <math>T = \frac{B}{\ln(R / r_\infty)}.</math>

The ''B''-parameter equation can also be written as <math>\ln R = B/T + \ln r_\infty</math>. This can be used to convert the function of resistance vs. temperature of a thermistor into a linear function of <math>\ln R</math> vs. <math>1/T</math>. The average slope of this function will then yield an estimate of the value of the ''B'' parameter.

==Conduction model==

===NTC (negative temperature coefficient)===
[[Image:Failed NTC thermistor.png|thumb|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 [[casting|cast]] chip of [[semiconductor|semiconducting]] material such as [[sintering|sintered]] metal [[oxides]].  They work because raising the temperature of a semiconductor increases the number of active [[charge carrier]]s{{snf}} it promotes them into the ''[[conduction band]]''. The more charge carriers that are available, the more [[current (electricity)|current]] a material can conduct. In certain materials like ferric oxide (Fe<sub>2</sub>O<sub>3</sub>) with titanium (Ti) doping an ''n-type'' semiconductor is formed and the charge carriers are [[electron]]s. In materials such as nickel oxide (NiO) with lithium (Li) doping a ''p-type'' semiconductor is created, where [[Electron hole|holes]] are the charge carriers.<ref name=EERB>{{cite book |title=Electronics Engineer's Reference Book |year=1976 |publisher=Butterworths |isbn=0408001682 |pages=6-29 to 6-41 |edition=4 |editor=L. W  Turner}}</ref>

This is described in the formula
: <math>
I = n \cdot A \cdot v \cdot e,
</math>
where
: <math>I</math> = electric current (amperes),
: <math>n</math> = density of charge carriers (count/m<sup>3</sup>),
: <math>A</math> = cross-sectional area of the material (m<sup>2</sup>),
: <math>v</math> = drift velocity of electrons (m/s),
: <math>e</math> = charge of an electron (<math>e = 1.602 \times 10^{-19}</math> 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&nbsp;[[kelvin]] to 2,000&nbsp;kelvins (−273.14&nbsp;°C to 1,700&nbsp;°C).{{Citation needed|date=May 2013}}

The [[International Electrotechnical Commission|IEC]] standard symbol for a NTC thermistor includes a "−t°" under the rectangle.<ref>{{cite web |url=http://www.resistorguide.com/ntc-thermistor/ |title=NTC thermistor » Resistor Guide |publisher=}}</ref>

===PTC (positive temperature coefficient)===
Most PTC thermistors are made from doped polycrystalline [[ceramic]] (containing [[barium titanate]] (BaTiO<sub>3</sub>) 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.<ref>[http://www.resistorguide.com/ptc-thermistor/ "PTC Thermistors and Silistors"] The Resistor Guide</ref>

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 also is extremely useful. 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 [[electrical conductor|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 BaTiO<sub>3</sub> 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 [[Flip-flop (electronics)|latch/memory circuit]], the effect being enhanced by using two PTC thermistors in series, with one thermistor cool, and the other thermistor hot.<ref>Downie, Neil A., ''The Ultimate Book of Saturday Science'' (Princeton 2012) {{ISBN|0-691-14966-6}}</ref>

The [[International Electrotechnical Commission|IEC]] standard symbol for a PTC thermistor includes a "+t°" under the rectangle.<ref>
{{cite web
 | title= PTC thermistor - Positive Temperature Coefficient
 | website= Resistor Guide
 | url= http://www.resistorguide.com/ptc-thermistor/
}}</ref>

==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 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 exchange]]s.

The electrical power input to the thermistor is just

: <math>P_E = IV,</math>

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]]:

: <math>P_T = K(T(R) - T_0),</math>

where ''T''(''R'') is the temperature of the thermistor as a function of its resistance ''R'', <math>T_0</math> 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:

: <math>P_E = P_T.</math>

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 <math>I = V/R</math>, and the equilibrium equation can be solved for the ambient temperature as a function of the measured resistance of the thermistor:

: <math>T_0 = T(R) - \frac{V^2}{KR}.</math>

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&nbsp;mW/°C in still air and 6.0&nbsp;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.<ref name="Thermistor Terminology"/>

==Applications==

===PTC===
* As current-limiting devices for circuit protection, as replacements for fuses. Current through the device causes a small amount of resistive heating. If the current is large enough to generate more heat than the device can lose to its surroundings, the device heats up, causing its resistance to increase. This creates a self-reinforcing effect that drives the resistance upwards, therefore limiting the current.
* As timers in the [[degauss|degaussing coil]] circuit of most CRT displays.  When the display unit is initially switched on, current flows through the thermistor and degaussing coil.  The coil and thermistor are intentionally sized so that the current flow will heat the thermistor to the point that the degaussing coil shuts off in under a second.  For effective degaussing, it is necessary that the magnitude of the alternating magnetic field produced by the degaussing coil decreases smoothly and continuously, rather than sharply switching off or decreasing in steps; the PTC thermistor accomplishes this naturally as it heats up.  A degaussing circuit using a PTC thermistor is simple, reliable (for its simplicity), and inexpensive.
* As heater in automotive industry to provide additional heat inside cabin with diesel engine or to heat diesel in cold climatic conditions before engine injection.
* In temperature compensated [[synthesizer]] voltage controlled oscillators.<ref>{{cite web|url=http://www.oldcrows.net/~patchell/synthmodules/vco.html|title=Temperature Compensated VCO|first=Jim|last=Patchell|website=www.oldcrows.net}}</ref>
* In [[lithium battery]] protection circuits.<ref>Patent CN 1273423A (China)</ref>
* In an electrically actuated [[Wax motor]] to provide the heat necessary to expand the wax.
* Many electric motors and dry type power transformers incorporate PTC thermistors in their windings. When used in conjunction with a monitoring relay they provide overtemperature protection to prevent insulation damage. The equipment manufacturer selects a thermistor with a highly non-linear response curve where resistance increases dramatically at the maximum allowable winding temperature, causing the relay to operate.

===NTC===
* As a [[resistance thermometer]] for low-temperature measurements of the order of 10&nbsp;K.
* As an [[inrush current limiter]] device in power supply circuits, they present a higher resistance initially, which prevents large currents from flowing at turn-on, and then heat up and become much lower resistance to allow higher current flow during normal operation. These thermistors are usually much larger than measuring type thermistors, and are purposely designed for this application.<ref>[http://www.ussensor.com/inrush-current-limiting-power-thermistors Inrush Current Limiting Power Thermistors]. U.S. Sensor</ref>
* As sensors in automotive applications to monitor fluid temperatures like the engine coolant, cabin air, external air or engine oil temperature, and feed the relative readings to control units like the [[Electronic control unit|ECU]] and to the dashboard.
* To monitor the temperature of an incubator.
* Thermistors are also commonly used in modern [[Thermostat#Digital|digital thermostats]] and to monitor the temperature of battery packs while charging.
* Thermistors are often used in the hot ends of [[3D printing|3D printers]]; they monitor the heat produced and allow the printer's control circuitry to keep a constant temperature for melting the plastic filament.
* In the food handling and processing industry, especially for food storage systems and food preparation. Maintaining the correct temperature is critical to prevent [[foodborne illness]].
* Throughout the consumer appliance industry for measuring temperature.  Toasters, coffee makers, refrigerators, freezers, hair dryers, etc. all rely on thermistors for proper temperature control.
* NTC thermistors come in bare and lugged forms, the former is for point sensing to achieve high accuracy for specific points, such as laser diode die, etc.<ref>{{Cite web|url=http://www.analogtechnologies.com/thermistor.htm |title=PTC Thermistors Guide- "Publish By Analog Electronic Technologies".}}</ref>
* For measurement of temperature profile inside the sealed cavity of a convective (thermal) [[inertial sensor]]<ref>{{Cite journal|last=Mukherjee|first=Rahul|last2=Basu|first2=Joydeep|last3=Mandal|first3=Pradip|last4=Guha|first4=Prasanta Kumar|title=A review of micromachined thermal accelerometers|url=http://stacks.iop.org/0960-1317/27/i=12/a=123002?key=crossref.1e9a8280a933644098e54f005bcc2082|journal=Journal of Micromechanics and Microengineering|volume=27|issue=12|doi=10.1088/1361-6439/aa964d|arxiv=1801.07297|bibcode=2017JMiMi..27l3002M}}</ref>.
*Thermistor Probe Assemblies <ref>{{Cite web|url=https://www.ei-sensor.com/thermistor-probes/|title=Thermistor Probes|website=EI Sensor Technologies|language=en-US|access-date=2019-05-13}}</ref> offer protection of the sensor in harsh environments.  The thermistor sensing element can be packaged into a variety of enclosures for use in industries such as HVAC/R, Building Automation, Pool/Spa, Energy and Industrial Electronics. Enclosures can be made out of stainless steel, aluminum, copper brass or plastic and configurations include threaded (NPT, etc), flanged (with mounting holes for ease of installation) and straight (flat tip, pointed tip, radius tip, etc.). Thermistor probe assemblies are very rugged and are highly customizable to fit the application needs. Probe assemblies have gained in popularity over the years as improvements in research, engineering and manufacturing techniques have been made.

==History==
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.)<ref name=CHM-semicon>{{cite web|title=1833 - First Semiconductor Effect is Recorded|url=http://www.computerhistory.org/semiconductor/timeline/1833-first.html|website=Computer History Museum|accessdate=24 June 2014}}</ref>

Because early thermistors were difficult to produce and applications for the technology were limited, commercial production of thermistors did not begin until the 1930s.<ref>{{cite book |first=Thomas |last=McGee |year=1988 |title=Principles and Methods of Temperature Measurement |chapter=Chapter 9 |page=203 |publisher=John Wiley & Sons |url=https://books.google.com/books?id=qfmS7g4JzjwC&lpg=PP1&pg=PA203#v=onepage&q=thermistor&f=false}}</ref> A commercially viable thermistor was invented by [[Samuel Ruben]] in 1930.<ref>{{cite book |title=Biomedical Sensors |editor=Jones, Deric P. |year=2009 |publisher=Momentum Press |page=12| url=https://books.google.com/books?id=7cI83YOIUTkC&pg=PA12&dq=Samuel+Ruben+and+Thermistor&hl=en&ei=gHVyTpyUG5Cltwfkp-SFCg&sa=X&oi=book_result&ct=result&resnum=2&ved=0CDEQ6AEwAQ#v=onepage&q&f=false}}</ref>

==See also==
* [[Iron-hydrogen resistor]]
* [[Stretch sensor]]
* [[Thermocouple]]

== References ==
{{reflist|30em}}

==External links==
{{Commons category|Thermistors}}
<!--PLEASE DO NOT USE THIS SECTION AS A LINK FARM FOR YOUR WEBSITE OR ARBITRARY FACTS-->
*[https://web.archive.org/web/20041018121232/http://www.facstaff.bucknell.edu/mastascu/eLessonsHTML/Sensors/TempR.html The thermistor at bucknell.edu]
*[https://sanjit1.github.io/Calibrator/webCalibrator.html Thermistor Calibration Online]
*[http://www.github.com/Sanjit1/CalibratorJava Thermistor Calibration Java]
*[http://img.en25.com/Web/Vaisala/JVT%20KBull%20Article_final%20pdf.pdf "Thermistors & Thermocouples:Matching the Tool to the Task in Thermal Validation"] - Journal of Validation Technology

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