Thermistor

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

• With NTC thermistors, resistance decreases as temperature rises; usually due to an increase in conduction electrons bumped up by thermal agitation from the valence 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 due to 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, 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 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.[5]

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

${\displaystyle \Delta R=k\,\Delta T,}$

where

${\displaystyle \Delta R}$, change in resistance,

${\displaystyle \Delta T}$, change in temperature,

${\displaystyle k}$, first-order temperature coefficient of resistance.

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

If ${\displaystyle k}$ is positive, the resistance increases with increasing temperature, and the device is called a positive temperature coefficient (PTC) thermistor, or posistor. If ${\displaystyle k}$ 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 ${\displaystyle k}$ 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 ${\displaystyle \alpha _{T}}$ ("alpha sub T") is used. It is defined as[6]

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

This ${\displaystyle \alpha _{T}}$ coefficient should not be confused with the ${\displaystyle a}$ parameter below.

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]

PTCs are usually prepared from barium (Ba), strontium, or lead titanates (e.g. PbTiO₃).[10][11]

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:

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

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 ${\displaystyle (\ln R)^{2}}$ 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.[12] To give resistance as a function of temperature, the above cubic equation in ${\displaystyle \ln R}$ can be solved, the real root of which is given by

${\displaystyle \ln R={\frac {b}{3c\,x^{1/3}}}-x^{1/3}}$

where

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

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:

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

NTC thermistors can also be characterised with the B (or β) parameter equation, which is essentially the Steinhart–Hart equation with ${\displaystyle a=1/T_{0}-(1/B)\ln R_{0}}$, ${\displaystyle b=1/B}$ and ${\displaystyle c=0}$,

${\displaystyle {\frac {1}{T}}={\frac {1}{T_{0}}}+{\frac {1}{B}}\ln {\frac {R}{R_{0}}},}$

where the temperatures and the B parameter are in kelvins, and R₀ is the resistance at temperature T₀ (25 °C = 298.15 K).[14] Solving for R yields

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

or, alternatively,

${\displaystyle R=r_{\infty }e^{B/T},}$

where ${\displaystyle r_{\infty }=R_{0}e^{-B/T_{0}}}$.

This can be solved for the temperature:

${\displaystyle T={\frac {B}{\ln(R/r_{\infty })}}.}$

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

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

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

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:

${\displaystyle P_{T}=K(T(R)-T_{0}),}$

where T(R) is the temperature of the thermistor as a function of its resistance R, ${\displaystyle T_{0}}$ 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:

${\displaystyle P_{E}=P_{T}.}$

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

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

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]

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.)[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 by Samuel Ruben in 1930.[32]

• Iron-hydrogen resistor
• Stretch sensor
• Thermocouple

Wikimedia Commons has media related to Thermistors.

• The thermistor at bucknell.edu
• Calculation of Steinhart-Hart Coefficients for Thermistors at sourceforge.net
• "Thermistors & Thermocouples:Matching the Tool to the Task in Thermal Validation" – Journal of Validation Technology