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If we assume that the relationship between resistance and temperature is linear (i.e. we make a first-order approximation), then we can say that:
where
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 the smallest possible ', so that their resistance remains almost constant over a wide 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 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
Many NTC thermistors are made from a thin coil of semiconducting material 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:
= number of charge carriers
= area of the material (m²)
= voltage (volt)
= charge of an electron ( (coulomb))
The current is measured using an ammeter. Over large changes in temperature, callibration 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 and their range goes from about 0.01 kelvin to 2000 kelvin (approx. 1700°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 pointIn physics, the Curie point or Curie temperature is the temperature above which a ferromagnet loses its ferromagnetic ability to possess a net spontaneous magnetization in the absence of an external magnetic field. At temperatures below the Curie point, m 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 modelling this behaviour were worked by W. Heywang and G. H. Jonker in the 1960sCenturies: 19th century 20th century 21st century Decades: 1900s 1910s 1920s 1930s 1940s 1950s 1960s 1970s 1980s 1990s 2000s 2010s Years: 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 Events and trends The 1960s was a turbulent decade of change around.
Another type of PTC thermistor is the polymerA polymer is a long, repeating chain of atoms, formed through the linkage of many molecules called monomers. The monomers can be identical, or in complex polymers such as proteins the monomers have one or more substituted chemical groups, this gives them PTC, which is sold under brand names such as "Polyfuse", "Polyswitch" and "Multiswitch". This consists of a slice of plastic with carbonAlternative meaning: Carbon (computing Carbon is a chemical element in the periodic table that has the symbol C and atomic number 6. An abundant nonmetallic, tetravalent element, carbon has several allotropic forms: diamonds (hardest known mineral). Bindi 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.