A thermistor is a type of resistor whose resistance varies significantly with temperature, more
so than in standard resistors. The word is a portmanteau of thermal and resistor. Thermistors
are widely used as inrush current limiters, temperature sensors, self-resetting overcurrent
protectors, and self-regulating heating elements. Thermistors differ from resistance temperature
detectors 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 higher precision within a limited
temperature range, typically −90 °C to 130 °C.
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 classification of . If is
positive, the resistance increases with increasing temperature, and the device is called a positive
temperature coefficient thermistor, or posistor. If is negative, the resistance decreases with
increasing temperature, and the device is called a negative temperature coefficient
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
is used. It is defined as
This coefficient should not be confused with the parameter below.
Steinhart–Hart equation In practice, the linear approximation works
only over a small temperature range. For accurate temperature measurements, the resistance/temperature
curve of the device must be described in more detail. 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 temperature in kelvin and R is the resistance in ohms. To give resistance
as a function of temperature, the above can be rearranged into:
where and
The error in the Steinhart–Hart equation is generally less than 0.02 °C in the measurement
of temperature over a 200 °C range. As an example, typical values for a thermistor with
a resistance of 3000 Ω at room temperature are:
B or β parameter equation NTC thermistors can also be characterised
with the B parameter equation, which is essentially the Steinhart–Hart equation with , and ,
Where the temperatures are in kelvin and R0 is the resistance at temperature T0. 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
Many NTC thermistors are made from a pressed disc, rod, plate, bead or cast chip of a semiconductor
such as a sintered metal oxide. 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 with titanium doping a n-type semiconductor is formed and
the charge carriers are electrons. In materials such as nickel oxide with lithium doping a
p-type semiconductor is created where holes are the charge carriers.
This is described in the formula:
= electric current = density of charge carriers = cross-sectional area of the material = velocity
of charge carriers = charge of an electron 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.
PTC Most PTC thermistors are of the "switching"
type, which means that their resistance rises suddenly at a certain critical temperature.
The devices are made of a doped polycrystalline ceramic containing barium titanate and other
compounds. The dielectric constant of this ferroelectric material 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. 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. In contrary to the "switching" type thermistor, silistors have an almost linear
resistance-temperature characteristic. The degaussing coils in many CRT monitors
were controlled by thermistors bonded to a small heating element. The thermistor would
be connected in series with the coil across the AC input, with the heater also directly
connected to the AC input. When cold the thermistor would allow a large current to flow through
but would be quickly heated by the heating element and the current would trail to zero.
This would degauss the screen every time the power is removed for long enough for the device
to cool. Another device similar in function to PTC
thermistor is the polymer PTC, which is sold under brand names such as "Polyswitch" "Semifuse",
and "Multifuse". This consists of a slice 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 rapidly. Like the BaTiO3
thermistor, this device has a highly nonlinear resistance/temperature response and is used
for switching, not for proportional temperature measurement.
Self-heating effects When a current flows through a thermistor,
it will generate heat which will raise 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:
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 will 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.
Applications PTC thermistors can be used 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. PTC thermistors were used 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, and inexpensive.
PTC thermistors were used 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. NTC thermistors are used as resistance thermometers
in low-temperature measurements of the order of 10 K.
NTC thermistors can be used as inrush-current limiting devices 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.
NTC thermistors are regularly used in automotive applications. For example, they monitor things
like coolant temperature and/or oil temperature inside the engine and provide data to the
ECU and, indirectly, to the dashboard. NTC thermistors can be also used 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. NTC thermistors are used in the Food Handling
and Processing industry, especially for food storage systems and food preparation. Maintaining
the correct temperature is critical to prevent food borne illness.
NTC thermistors are used 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. 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.
Because early thermistors were difficult to produce and applications for the technology
were limited, commercial production of thermistors did not begin until the 1930s. A commercially
viable thermistor was invented by Samuel Ruben in 1930.
See also Iron-hydrogen resistor
Thermocouple References
External links The thermistor at bucknell.edu
Software for thermistor calculation at Sourceforge "Thermistors & Thermocouples:Matching the
Tool to the Task in Thermal Validation" - Journal of Validation Technology