Thermistor - Wikipedia https://en.wikipedia.

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Thermistor
A thermistor is a type of resistor whose resistance is dependent
on temperature, more so than in standard resistors. The word is a Thermistor
combination of thermal and resistor. Thermistors are widely used
as inrush current limiters, temperature sensors (negative
temperature coefficient or NTC type typically), self-resetting
overcurrent protectors, and self-regulating heating elements
(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. Negative temperature coefficient
(NTC) thermistor, bead type,
With PTC thermistors, resistance increases as temperature
rises. PTC thermistors are commonly installed in series with a insulated wires
circuit, and used to protect against overcurrent conditions, as Type Passive
resettable fuses.
Working Electric
Thermistors are generally produced using powdered metal principle resistance
oxides.[1] With vastly improved formulas and techniques over the Electronic symbol
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 Thermistor symbol
come in many styles [2] 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 °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.[3]

Contents
Basic operation
Steinhart–Hart equation
B or β parameter equation
Conduction model
NTC (negative temperature coefficient)
PTC (positive temperature coefficient)

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Self-heating effects
Applications
PTC
NTC
History
See also
References
External links

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

where

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

Thermistors can be classified into two types, depending on the sign of . If is positive, the resistance
increases with increasing temperature, and the device is called a positive temperature coefficient
(PTC) thermistor, or posistor. 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[4]

This coefficient should not be confused with the parameter below.

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:

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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 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.[5] As an example, typical values for a thermistor with a resistance of
3 kΩ at room temperature (25 °C = 298.15 K) 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 are in kelvins, and R0 is the resistance at temperature T0 (25 °C = 298.15 K).
Solving for R yields

or, alternatively,

where .

This can be solved for the temperature:

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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 it
promotes 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 A failed (blown) NTC thermistor that
titanium (Ti) doping an n-type semiconductor is formed and the worked as an inrush current limiter
charge carriers are electrons. In materials such as nickel oxide in a switched-mode power supply
(NiO) with lithium (Li) doping a p-type semiconductor is created,
where holes are the charge carriers.[6]

This is described in the formula

where

= 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).

The IEC standard symbol for a NTC thermistor includes a "−t°" under the rectangle.[7]

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

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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.[8]

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 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.[9]

The IEC standard symbol for a PTC thermistor includes a "+t°" under the rectangle.[10]

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 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:

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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.[4]

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 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

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heat diesel in cold climatic conditions before engine injection.

In temperature compensated synthesizer voltage controlled oscillators.[11]
In lithium battery protection circuits.[12]
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 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.[13]
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
ECU and to the dashboard.
To monitor the temperature of an incubator.
Thermistors are also commonly used in modern digital thermostats and to monitor the temperature
of battery packs while charging.
Thermistors are often used in the hot ends of 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.[14]
For measurement of temperature profile inside the sealed cavity of a convective (thermal) inertial
sensor.[15]
Thermistor Probe Assemblies [16] 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

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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.)[17]

Because early thermistors were difficult to produce and applications for the technology were limited,
commercial production of thermistors did not begin until the 1930s.[18] A commercially viable
thermistor was invented by Samuel Ruben in 1930.[19]

See also
Iron-hydrogen resistor
Stretch sensor
Thermocouple

References
1. "What is a Thermistor? How do thermistors work?" (https://www.ei-sensor.com/what-is-a-thermisto
r/). EI Sensor Technologies. Retrieved 2019-05-13.
2. "Thermistors" (https://www.ei-sensor.com/thermistors/). EI Sensor Technologies. Retrieved
2019-05-13.
3. "NTC Thermistors" (http://www.microchiptechno.com/ntc_thermistors.php). Micro-chip
Technologies. 2010.
4. Thermistor Terminology (http://www.ussensor.com/terminology.html). U.S. Sensor.
5. "Practical Temperature Measurements" (http://literature.cdn.keysight.com/litweb/pdf/5965-7822E.p
df). Agilent Application Note. Agilent Semiconductor.
6. L. W Turner, ed. (1976). Electronics Engineer's Reference Book (4 ed.). Butterworths. pp. 6-29 to
6-41. ISBN 0408001682.
7. "NTC thermistor » Resistor Guide" (http://www.resistorguide.com/ntc-thermistor/).
8. "PTC Thermistors and Silistors" (http://www.resistorguide.com/ptc-thermistor/) The Resistor Guide
9. Downie, Neil A., The Ultimate Book of Saturday Science (Princeton 2012) ISBN 0-691-14966-6
10. "PTC thermistor - Positive Temperature Coefficient" (http://www.resistorguide.com/ptc-thermistor/).
Resistor Guide.
11. Patchell, Jim. "Temperature Compensated VCO" (http://www.oldcrows.net/~patchell/synthmodules
/vco.html). www.oldcrows.net.
12. Patent CN 1273423A (China)
13. Inrush Current Limiting Power Thermistors (http://www.ussensor.com/inrush-current-limiting-power
-thermistors). U.S. Sensor
14. "PTC Thermistors Guide- "Publish By Analog Electronic Technologies" " (http://www.analogtechnol
ogies.com/thermistor.htm).
15. Mukherjee, Rahul; Basu, Joydeep; Mandal, Pradip; Guha, Prasanta Kumar. "A review of
micromachined thermal accelerometers" (http://stacks.iop.org/0960-1317/27/i=12/a=123002?key=
crossref.1e9a8280a933644098e54f005bcc2082). Journal of Micromechanics and
Microengineering. 27 (12). arXiv:1801.07297 (https://arxiv.org/abs/1801.07297).
Bibcode:2017JMiMi..27l3002M (https://ui.adsabs.harvard.edu/abs/2017JMiMi..27l3002M).
doi:10.1088/1361-6439/aa964d (https://doi.org/10.1088%2F1361-6439%2Faa964d).

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Thermistor - Wikipedia https://en.wikipedia.org/wiki/Thermistor

16. "Thermistor Probes" (https://www.ei-sensor.com/thermistor-probes/). EI Sensor Technologies.

Retrieved 2019-05-13.
17. "1833 - First Semiconductor Effect is Recorded" (http://www.computerhistory.org/semiconductor/ti
meline/1833-first.html). Computer History Museum. Retrieved 24 June 2014.
18. McGee, Thomas (1988). "Chapter 9". Principles and Methods of Temperature Measurement (http
s://books.google.com/books?id=qfmS7g4JzjwC&lpg=PP1&pg=PA203#v=onepage&q=thermistor&f
=false). John Wiley & Sons. p. 203.
19. Jones, Deric P., ed. (2009). Biomedical Sensors (https://books.google.com/books?id=7cI83YOIUT
kC&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). Momentum
Press. p. 12.

External links
The thermistor at bucknell.edu (https://web.archive.org/web/20041018121232/http://www.facstaff.b
ucknell.edu/mastascu/eLessonsHTML/Sensors/TempR.html)
Thermistor Calibration Online (https://sanjit1.github.io/Calibrator/webCalibrator.html)
Thermistor Calibration Java (https://www.github.com/Sanjit1/CalibratorJava)
Calculation of Steinhart-Hart Coefficients for Thermistors at sourceforge.net (http://thermistor.sourc
eforge.net)
"Thermistors & Thermocouples:Matching the Tool to the Task in Thermal Validation" (http://img.en2
5.com/Web/Vaisala/JVT%20KBull%20Article_final%20pdf.pdf) - Journal of Validation Technology

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