A thermistor is a type of
resistorwith resistance varying according to its temperature. The word is a portmanteauof "thermal" and " resistor". Samuel Rubeninvented the thermistor in 1930, and was awarded [http://www.google.com/patents?id=0P19AAAAEBAJ&dq=2,021,491 U.S. Patent No. 2,021,491] .
Thermistors are widely used as inrush current limiters, temperature sensors, self-resetting overcurrent protectors, and self-regulating heating elements.
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 zero as possible, so that their resistance remains nearly constant over a wide temperature range.
Thermistors differ from
resistance temperature detectors (RTD) 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.
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 equationis 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::where: and 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
kelvinand R0 is the resistance at temperature T0 (usually 25 °C=298.15 K). Solving for "R" yields:
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.
Many NTC thermistors are made from a pressed disc or cast chip of a
semiconductorsuch 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 " conduction band". The more charge carriers that are available, the more current a material can conduct. This is described in the formula:
= electric current (ampere)
= density of charge carriers (count/m³)
= cross-sectional area of the material (m²)
= velocity of charge carriers (m/s)
= 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 with a range from about 0.01 kelvinto 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
ceramiccontaining barium titanate(BaTiO3) and other compounds. The dielectric constantof this ferroelectricmaterial varies with temperature. Below the Curie pointtemperature, the high dielectric constantprevents 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
polymerPTC, which is sold under brand names such as " Polyswitch" "Semifuse", and "Multifuse". This consists of a slice of plastic with carbongrains embedded in it. When the plasticis 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.
Though commonly used, "self-heating" is a misnomer. Thermistors are passive devices and thus cannot heat themselves. It is the external circuit that supplies the energy that causes the heating. "Resistive heating" is a more accurate term.
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
sailplanerate-of-climb instrument, the electronic variometer, or serve as a timerfor a relayas 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 °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 Lawwe 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.
* 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 ovencontrolling 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 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 the dashboard.
* Thermistors are also commonly used in modern digital thermostats and to monitor the temperature of battery packs while charging.
* [http://www.meas-spec.com/myMeas/MEAS_download/ApplicationNotes/Temperature/MEAS%20TPG%20TD002_Thermometry%20-%20.pdf Measurement Specialties thermistor technical data sheet: Temperature]
* [http://www.veriteq.com/download/whitepaper/Thermocouples-&-Thermistors_Matching-the-Tools-to-the-Task-in-Thermal-Validation.pdf Temperature Measurement Tools: Thermistors, Thermocouples]
Resistance temperature detector
* [http://www.emant.com/317004.page Thermistor App Note]
* [http://www.globu.net/pp/english/PP/ne555.htm Thermistor ADC using Parallel Port]
* [http://www.facstaff.bucknell.edu/mastascu/eLessonsHTML/Sensors/TempR.html The thermistor at bucknell.edu]
* [http://www.meas-spec.com/myMeas/sensors/MEAS_Temperature_TechnicalNotes.asp Measurement Specialties thermistor technical data sheets]
* [http://thermistor.sourceforge.net Thermistor calculation software at sourceforge.net]
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