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Thermistor

From Wikipedia, the free encyclopedia
Type of resistor whose resistance varies with temperature
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This article'slead sectionmay be too short to adequatelysummarize the key points. Please consider expanding the lead toprovide an accessible overview of all important aspects of the article.(February 2022)
Thermistor
Negative-temperature-coefficient (NTC) thermistor, bead type, insulated wires
Component typePassive
Working principle‍Electric resistance
Electronic symbol

Thermistor or varistor symbol[1]

Athermistor is a semiconductor type ofresistor in which the resistance is strongly dependent on temperature. The wordthermistor is aportmanteau ofthermal andresistor. 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 (NTC) thermistors haveless resistance athigher temperatures, whilepositive-temperature-coefficient (PTC) thermistors havemore resistance athigher temperatures.[2]

NTC thermistors are widely used asinrush current limiters and temperature sensors, while PTC thermistors are used as self-resettingovercurrent protectors andself-regulating heating elements. The operational temperature range of a thermistor is dependent on the probe type and is typically between −100 and 300 °C (−148 and 572 °F).

Types

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

  • WithNTC 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 aninrush current limiter.
  • WithPTC 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.[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 fromresistance 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

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

ΔR=kΔT,{\displaystyle \Delta R=k\,\Delta T,}

where

ΔR{\displaystyle \Delta R}, change in resistance,
ΔT{\displaystyle \Delta T}, change in temperature,
k{\displaystyle k}, first-ordertemperature coefficient of resistance.

Depending on type of the thermistor in question thek{\displaystyle k} may be either positive or negative.

Ifk{\displaystyle k} ispositive, the resistance increases with increasing temperature, and the device is called apositive-temperature-coefficient (PTC)thermistor, orposistor. There are two types of PTC resistor – switching thermistor andsilistor. Ifk{\displaystyle k} is negative, the resistance decreases with increasing temperature, and the device is called anegative-temperature-coefficient (NTC)thermistor. Resistors that are not thermistors are designed to have ak{\displaystyle k} as close to 0 as possible so that their resistance remains nearly constant over a wide temperature range.

Instead of the temperature coefficientk, sometimes thetemperature coefficient of resistanceαT{\displaystyle \alpha _{T}} ("alpha sub T") is used. It is defined as[6]

αT=1R(T)dRdT.{\displaystyle \alpha _{T}={\frac {1}{R(T)}}{\frac {dR}{dT}}.}

ThisαT{\displaystyle \alpha _{T}} coefficient should not be confused with thea{\displaystyle a} parameter below.

Construction and materials

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Thermistors are typically built by using metal oxides.[7] They're typically pressed into a bead, disk, or cylindrical shape and then encapsulated with an impermeable material such as epoxy or glass.[8]

NTC thermistors are manufactured from oxides of theiron group of metals: e.g. chromium (CrO,Cr2O3), manganese (e.g.MnO), cobalt (CoO), iron (iron oxides), and nickel (NiO,Ni2O3).[9][10] these oxides form a ceramic body with terminals composed of conductive metals such as silver, nickel, and tin.

PTC thermistors are usually prepared frombarium (Ba),strontium, orlead titanates (e.g. PbTiO3).[9][10]

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.[11]

Steinhart–Hart equation

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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–temperaturetransfer function provides a more faithful characterization of the performance. TheSteinhart–Hart equation is a widely used third-order approximation:

1T=a+bln⁡R+c(ln⁡R)3,{\displaystyle {\frac {1}{T}}=a+b\ln R+c\,(\ln R)^{3},}

wherea,b andc are called the Steinhart–Hart parameters and must be specified for each device.T is theabsolute temperature, andR 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(ln⁡R)2{\displaystyle (\ln R)^{2}} term. In practice, the equation gives good numerical results for resistances expressed in, for example,ohms (Ω) or kiloohms, but the coefficients a, b, and c must be stated with reference to that particular unit.[12] To give resistance as a function of temperature, the above cubic equation inln⁡R{\displaystyle \ln R} can be solved, the real root of which is given by

ln⁡R=b3cx1/3−x1/3{\displaystyle \ln R={\frac {b}{3c\,x^{1/3}}}-x^{1/3}}

where

y=12c(a−1T),x=y+(b3c)3+y2.{\displaystyle {\begin{aligned}y&={\frac {1}{2c}}\left(a-{\frac {1}{T}}\right),\\x&=y+{\sqrt {\left({\frac {b}{3c}}\right)^{3}+y^{2}}}.\end{aligned}}}

The error in the Steinhart–Hart equation is generally less than 0.02 °C in the measurement of temperature over a 200 °C range.[13] 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:

a=1.40×10−3,b=2.37×10−4,c=9.90×10−8.{\displaystyle {\begin{aligned}a&=1.40\times 10^{-3},\\b&=2.37\times 10^{-4},\\c&=9.90\times 10^{-8}.\end{aligned}}}

B orβ parameter equation

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NTC thermistors can also be characterised with theB (orβ) parameter equation, which is essentially theSteinhart–Hart equation witha=1/T0−(1/B)ln⁡R0{\displaystyle a=1/T_{0}-(1/B)\ln R_{0}},b=1/B{\displaystyle b=1/B} andc=0{\displaystyle c=0},

1T=1T0+1Bln⁡RR0,{\displaystyle {\frac {1}{T}}={\frac {1}{T_{0}}}+{\frac {1}{B}}\ln {\frac {R}{R_{0}}},}

where the temperatures and theB parameter are inkelvins, andR0 is the resistance of the thermistor at temperatureT0 (25 °C = 298.15 K).[14] Solving forR yields

R=R0eB(1T−1T0){\displaystyle R=R_{0}e^{B\left({\frac {1}{T}}-{\frac {1}{T_{0}}}\right)}}

or, alternatively,

R=r∞eB/T,{\displaystyle R=r_{\infty }e^{B/T},}

wherer∞=R0e−B/T0{\displaystyle r_{\infty }=R_{0}e^{-B/T_{0}}}.

This can be solved for the temperature:

T=Bln⁡(R/r∞)=T0∗BT0∗ln⁡(R/R0)+B.{\displaystyle T={\frac {B}{\ln(R/r_{\infty })}}={\frac {T_{0}*B}{T_{0}*\ln(R/R_{0})+B}}.}

TheB-parameter equation can also be written asln⁡R=B/T+ln⁡r∞{\displaystyle \ln R=B/T+\ln r_{\infty }}. This can be used to convert the function of resistance vs. temperature of a thermistor into a linear function ofln⁡R{\displaystyle \ln R} vs.1/T{\displaystyle 1/T}. The average slope of this function will then yield an estimate of the value of theB parameter.

Conduction model

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NTC (negative temperature coefficient)

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

Many NTC thermistors are made from a pressed disc, rod, plate, bead orcast chip ofsemiconducting material such assintered metaloxides. They work because raising the temperature of a semiconductor increases the number of activecharge carriers by promoting them into theconduction band. The more charge carriers that are available, the morecurrent a material can conduct. In certain materials like ferric oxide (Fe2O3) with titanium (Ti) doping ann-type semiconductor is formed and the charge carriers areelectrons. In materials such as nickel oxide (NiO) with lithium (Li) doping ap-type semiconductor is created, whereholes are the charge carriers.[15]

This is described in the formula

I=n⋅A⋅v⋅e,{\displaystyle I=n\cdot A\cdot v\cdot e,}

where

I{\displaystyle I} = electric current (amperes),
n{\displaystyle n} = density of charge carriers (count/m3),
A{\displaystyle A} = cross-sectional area of the material (m2),
v{\displaystyle v} = drift velocity of electrons (m/s),
e{\displaystyle e} = charge of an electron (e=1.602×10−19{\displaystyle e=1.602\times 10^{-19}} 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).[16]

TheIEC standard symbol for a NTC thermistor includes a "−t°" under the rectangle.[17]

PTC (positive temperature coefficient)

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Most PTC thermistors are made from doped polycrystallineceramic (containingbarium titanate (BaTiO3) and other compounds) which have the property that their resistance rises suddenly at a certain critical temperature. Barium titanate isferroelectric and itsdielectric constant varies with temperature. Below theCurie point temperature, the highdielectric 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 asilistor (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.[18] 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.[19]

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 thedegaussing circuits of manyCRT 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 thepolymer PTC, which is sold under brand names such as "Polyswitch" "Semifuse", and "Multifuse". This consists of plastic withcarbon grains embedded in it. When theplastic is cool, the carbon grains are all in contact with each other, forming aconductive 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 forheat 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 primitivelatch/memory circuit, the effect being enhanced by using two PTC thermistors in series, with one thermistor cool, and the other thermistor hot.[20]

TheIEC standard symbol for a PTC thermistor includes a "+t°" under the rectangle.[21]

Self-heating effects

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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 (anobserver 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 asailplane rate-of-climb instrument, the electronicvariometer, or serve as atimer for arelay as was formerly done intelephone exchanges.

The electrical power input to the thermistor is just

PE=IV,{\displaystyle P_{E}=IV,}

whereI is current, andV 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 byNewton's law of cooling:

PT=K(T(R)−T0),{\displaystyle P_{T}=K(T(R)-T_{0}),}

whereT(R) is the temperature of the thermistor as a function of its resistanceR,T0{\displaystyle T_{0}} is the temperature of the surroundings, andK is thedissipation constant, usually expressed in units of milliwatts per degree Celsius. At equilibrium, the two rates must be equal:

PE=PT.{\displaystyle P_{E}=P_{T}.}

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 byOhm's law we haveI=V/R{\displaystyle I=V/R}, and the equilibrium equation can be solved for the ambient temperature as a function of the measured resistance of the thermistor:

T0=T(R)−V2KR.{\displaystyle T_{0}=T(R)-{\frac {V^{2}}{KR}}.}

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]

Applications

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PTC

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  • 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 heat more quickly than the device can lose it 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 thedegaussing 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 heaters, in the automotive industry, to provide cabin heating (in addition to heating provided by a heat pump or the waste heat of an internal combustion engine), or to heat diesel fuel in cold conditions before engine injection.
  • In temperature-compensated voltage-controlled oscillators insynthesizers.[22]
  • Inlithium battery protection circuits.[23]
  • In an electrically actuatedwax 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.
  • To preventthermal runaway in electronic circuits. Many electronic devices, for examplebipolar transistors, draw more power as they get hotter. Commonly, such circuits contain ordinary resistors to limit the current available and prevent the device from overheating. However, in some applications, PTC thermistors allow better performance than resistors.
  • To preventcurrent hogging in electronic circuits. Current hogging can occur when electronic devices are connected in parallel. In severe cases, current hogging can cause cascading failure of all the devices. A PTC thermistor attached in series with each device can assure the current is divided reasonably evenly between the devices.
  • In crystal oscillators for temperature compensation, medical equipment temperature control, and industrial automation, silicon PTC thermistors display a nearly linear positive temperature coefficient (0.7%/°C). A linearization resistor can be added if further linearization is needed.[24]

NTC

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  • As a 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.[25]
  • 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 theECU and to the dashboard.
  • To monitor the temperature of an incubator.
  • Thermistors are also commonly used in moderndigital thermostats and to monitor the temperature of battery packs while charging.
  • Thermistors are often used in the hot ends of3D 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 preventfoodborne 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.[26]
  • For measurement of temperature profile inside the sealed cavity of a convective (thermal)inertial sensor.[27]
  • Thermistor Probe Assemblies[28] 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.
  • UL Recognized NTC thermistors in the XGPU2 category helps save equipment manufacturers time and money when applying for safety approvals for their end product. DO-35 hermetically sealed glass encapsulated thermistors[29] can operate up to 250 °C which gives them an advantage in many applications when UL is requested for a sensing element.

History

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The first NTC thermistor was discovered in 1833 byMichael Faraday, who reported on the semiconducting behavior ofsilver sulfide. Faraday noticed that the resistance of silver sulfide decreased dramatically as temperature increased. This was also the first documented observation of asemiconducting material.[30]

Because early thermistors were difficult to produce and applications for the technology were limited, commercial production of thermistors did not begin until the 1930s.[31] A commercially viable thermistor was invented bySamuel Ruben in 1930.[32]

See also

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References

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  1. ^"Standards for Resistor Symbols".EePower. EETech Media. RetrievedSeptember 13, 2021.
  2. ^"PTC thermistor vs. NTC thermistor for measuring the temperature of a liquid".Electrical Engineering Stack Exchange. Retrieved24 April 2022.
  3. ^"What is a Thermistor? How do thermistors work?".EI Sensor Technologies. Retrieved2019-05-13.
  4. ^"Thermistors".EI Sensor Technologies. 19 February 2019. Retrieved2019-05-13.
  5. ^"NTC Thermistors"Archived 2017-09-22 at theWayback Machine. Micro-chip Technologies. 2010.
  6. ^abThermistor 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. ^"Thermistor Basics".Wavelength Electronics. Wavelength Electronics, Inc. Retrieved8 July 2024.
  9. ^abMorris, 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)
  10. ^abFatigue 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)
  11. ^Yüksel Price, Berat; Kennedy, Stuart R. (2022-05-01)."Resonant acoustic-mixing technology as a novel method for production of negative-temperature coefficient thermistors".Journal of Materials Science: Materials in Electronics.33 (14):11380–11391.doi:10.1007/s10854-022-08110-2.ISSN 1573-482X.
  12. ^Matus, Michael (2011)."Temperature measurement in dimensional metrology - Why the Steinhart-Hart equation works so well"(PDF).MacroScale. Archived fromthe original(PDF) on 2024-06-03.
  13. ^"Practical Temperature Measurements". Agilent Application Note. Agilent Semiconductor.
  14. ^Becker, J. A. (1947)."Properties and Uses of Thermistors-Thermally Sensitive Resistors".Bell System Technical Journal.26:170–212.Bibcode:1947BSTJ...26..170B.doi:10.1002/j.1538-7305.1947.tb01314.x. Retrieved22 April 2022.
  15. ^L. W Turner, ed. (1976).Electronics Engineer's Reference Book (4 ed.). Butterworths. pp. 6-29 to 6-41.ISBN 0408001682.
  16. ^"Thermal-FluidsPedia | Temperature measurements and instrumentation | Thermal-Fluids Central".
  17. ^"NTC thermistor » Resistor Guide".
  18. ^"PTC Thermistors and Silistors" The Resistor Guide
  19. ^"What is a Thermistor? How do thermistors work?". 21 August 2024.
  20. ^Downie, Neil A.,The Ultimate Book of Saturday Science (Princeton 2012)ISBN 0-691-14966-6
  21. ^"PTC thermistor – Positive Temperature Coefficient".Resistor Guide.
  22. ^Patchell, Jim."Temperature Compensated VCO".www.oldcrows.net.
  23. ^Patent CN 1273423A (China)
  24. ^"ED35S PTC Thermistors". 28 September 2020.
  25. ^Inrush Current Limiting Power Thermistors. U.S. Sensor
  26. ^"PTC Thermistors Guide- "Publish By Analog Electronic Technologies"".
  27. ^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.
  28. ^"Thermistor Probes".EI Sensor Technologies. 19 February 2019. Retrieved2019-05-13.
  29. ^"ED35U UL Recognized Glass Encapsulated NTC Thermistors". 21 October 2021.
  30. ^"1833 - First Semiconductor Effect is Recorded".Computer History Museum. Retrieved24 June 2014.
  31. ^McGee, Thomas (1988)."Chapter 9".Principles and Methods of Temperature Measurement. John Wiley & Sons. p. 203.ISBN 9780471627678.
  32. ^Jones, Deric P., ed. (2009).Biomedical Sensors. Momentum Press. p. 12.ISBN 9781606500569.

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