A thermistor is a type of resistor used to measure temperature changes, relying on the change in its resistance with changing temperature.
A thermistor is a type of resistor used to measure temperature changes, relying on the change in its resistance with changing temperature. The word is a combination of thermal and resistor. Samuel Ruben invented the thermistor in 1930, and was awarded U.S. Patent No. 2,021,491.
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 sulphide 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.
Assuming, as a first-order approximation, that the relationship between resistance and temperature is linear, then:
- ΔR = kΔT
- ΔR = change in resistance
- ΔT = change in temperature
- k = first-order temperature coefficient of resistance
Thermistors can be classified into two types depending on the sign of k. If k is positive, the resistance increases with increasing temperature, and the device is called a positive temperature coefficient (PTC) thermistor, or posistor. If 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 the smallest possible k, so that their resistance remains nearly constant over a wide temperature range.
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.
In practice, the linear approximation (above) 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 kelvins and R is the resistance in ohms. To give resistance as a function of temperature, the above can be rearranged into:
The error in the Steinhart-Hart equation is generally less than
0.02°C in the measurement of temperature. As an example, typical values
for a thermistor with a resistance of 3000 Ω at room temperature (25°C
= 298.15 K) are:
B parameter equation
NTC thermistors can also be characterised with the B parameter equation, which is essentially the Steinhart Hart equation with c=0.
where the temperatures are in kelvin. Using the expansion only to the first order yields:
- R0 is the resistance at temperature T0 (usually 25 °C=298.15 K)
Many NTC thermistors are made from a pressed disc 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 electrons able to move about and carry charge - it promotes them into the conducting band. The more charge carriers that are available, the more current a material can conduct. This is described in the formula:
I = electric current (ampere)
n = density of charge carriers (count/m³)
A = cross-sectional area of the material (m²)
v = velocity of charge carriers (m/s)
e = charge of an electron ( coulomb)
The current is measured using an ammeter.
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 sizes ranging from
about 0.01 kelvin to 2,000 kelvins (-273.14°C to 1,700°C).
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 (BaTiO3) 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. The equations used for modeling this behaviour were
derived by W. Heywang and G. H. Jonker in the 1960s.
Another type of PTC thermistor is the polymer PTC, which is sold under brand names such as "Polyfuse", "Polyswitch" and "Multiswitch". 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.
Yet another type of thermistor is a Silistor, a thermally
sensitive silicon resistor. Silistors are similarly constructed and
operate on the same principles as other thermistors, but employ silicon
as the semiconductive component material.
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 self-heating effect will introduce an error if
a correction is not made.
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, T0 is the temperature of the surroundings, and K is the dissipation constant, usually expressed in units of milliwatts per °C. 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 I = V / R
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.
- 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, and therefore causing even more heating. This
creates a self-reinforcing effect that drives the resistance upwards,
reducing the current and voltage available to the device.
- PTC thermistors can be used as heating elements in small
temperature-controlled ovens. As the temperature rises, resistance
increases, decreasing the current and the heating. The result is a
steady state. A typical application is a crystal oven
controlling the temperature of the crystal of a high-precision crystal
oscillator. Crystal ovens are usually set at the upper limit of the
equipment's temperature specification, so they can maintain the
temperature by heating.
- 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 purpose designed for this application.
- Thermistors are also commonly used in modern digital thermostats and to monitor the temperature of battery packs while charging.
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