Tom Bishop, P.E.
EASA Senior Technical Support Specialist
What are thermistors?
Thermistors, derived from the term thermally sensitive resistors, are a very accurate and cost effective method for measuring temperature. Thermistors are usually two-terminal semiconductor devices made from semi-conductor materials that have an electrical resistance that varies non-linearly with temperature (see Figure 1). Some materials provide better stability while others have higher resistance ranges and are fabricated into smaller thermistors. Each specific thermistor has its own unique resistance versus temperature characteristic.
During the manufacture of thermistors, coarse resistance control is accomplished through the use of different metal oxides to form the semiconductor junction. It is common for several different material combinations to be used to arrive at the same nominal reference temperature (e.g., 25° C, typically designated as R25) resistance, and each combination results in a slightly different resistance versus temperature (R-T) characteristic. This variability of R-T characteristics is a primary factor that complicates thermistor identification and replacement.
Further, thermistors are manufactured in two types: NTC (negative temperature coefficient) and PTC (positive temperature coefficient). The NTC type thermistor is most commonly used to measure temperature. The NTC type has a resistance that decreases with increasing temperature; the PTC type has a resistance that increases with increasing temperature.
In contrast to the other type of detectors that utilize resistance change with temperature change, thermistors have a highly non-linear change in resistance, whereas resistance temperature detectors (RTDs) are nearly linear in resistance change versus temperature. Some reasons that thermistors are popular for measuring temperature are:
- Relatively high resistance change per degree of temperature provides high resolution
- High level of repeatability
- Small size results in fast response to temperature changes
- More economical
The type of thermistor that is selected for an application depends primarily on the required operating temperature range. Thermistor R-T curves, like those in Figures 2 and 3, are usually available from the thermistor manufacturer. Examination of the curves in these figures reinforces the statement made earlier: This variability of R-T characteristics is a primary factor that complicates thermistor identification and replacement.
Note: Because of their unique curves, thermistors must be matched with the controller in order to function properly.
Principle of operation
Thermistor resistance is determined by the manufacturer by applying a constant current through the thermistor and then measuring the voltage drop that occurs across the thermistor. By applying Ohm’s Law, R = V/I (resistance is equal to voltage divided by current), the resistance is determined. Then the Steinhart-Hart equation (see below) is used to calculate the temperature.
Although this approach is very flexible, limitations arise at both low and high temperatures. For example, with an NTC type, as the thermistor temperature decreases, its resistance increases and likewise, so does the voltage across it. The practical lower temperature limit is reached when the voltage exceeds the maximum input voltage of the analog to digital (A/D) converter. As the NTC thermistor temperature increases, its resistance decreases, and so does its sensitivity to temperature change. Since the system A/D converter has a fixed resolution, this means that temperature measurement resolution decreases with increasing temperature.
Steinhart-Hart equation
The Steinhart-Hart equation for thermistors is named for the two oceanographers with the Woods Hole Oceanographic Institute on Cape Cod, Massachusetts, who developed the equation and published it in a paper in 1968. The resistance versus temperature (R-T) characteristic, also known as an R/T curve, of the thermistor forms the "scale" that allows its use as a temperature sensor. This characteristic is a nonlinear, negative exponential function, and the most well-known expression of it is the Steinhart-Hart equation:
1/T = A + B(lnR) + C(lnR)3
where: T = temperature (kelvin)
R = resistance at temperature T
Note: The natural log “ln” is a mathematical function and is the logarithm to the base “e”; where “e” is a constant that is approximately equal to 2.718281828.
Coefficients A, B, and C are derived by calibrating at three temperature points and then solving the three simultaneous equations. The uncertainty associated with the use of the Steinhart-Hart equation is less than ±0.005° C for 50° C temperature spans within the 0° C-260° C range, so using the appropriate interpolation equation or lookup table in conjunction with a microprocessor can eliminate the potential nonlinearity problem. Table 1 provides the A, B and C coefficients for two different thermistors of one manufacturer. Note that the coefficients for thermistor 1k vary across three temperature ranges and that those of thermistor 10k vary across four temperature ranges. The 1k thermistor has a resistance of 1000 ohms at 25° C; and the 10k thermistor has a resistance of 10000 ohms at 25° C.
Example calculation for the 1k thermistor, for the temperature range 0 to 50° C:
1/T = A + B(lnR) + C(lnR)3 = 1.44054892093242E-03 + (2.69072584206089E-04 x 6.907755279) + (1.66192262189160E-07 x 329.617932) = 0.003554016
T = 298.15K
T = 25.0° C
Note: Temperature ° C = temperature K – 273.15
Temperature sensing capability
Generally, thermistors are operated at temperatures where they exhibit resistances of hundreds or thousands of ohms (see Figures 2 and 3). At these high resistances, simple two-wire resistance measurements are sufficient. Therefore thermistors are well suited for sensing temperature at remote locations via long two-wire cable because the resistance of the long wires is insignificant compared to the relatively high resistance of the thermistor.
Self-heating effect of thermistors
When the resistance of a thermistor is being measured there is a voltage across it and a current passing through it (from Ohm’s Law). Consequently, the power (W) in the thermistor is the product of the voltage (V) and current (I); that is, W = V x I. This power is dissipated in the thermistor, resulting in heating of the thermistor. The heating effect in turn causes the resistance of the thermistor to decrease (NTC) or increase (PTC). This power dissipation is known as self-heating of the thermistor. If the power levels are moderate (of the order of several milliwatts), the self-heating will not continue indefinitely, because the thermistor will reach thermal equilibrium with its environment.
However, when this steady-state is reached, the resistance of the thermistor will not accurately represent the temperature of its environment. Instead, the resistance of the thermistor will be lower (NTC) or higher (PTC) than expected, because of the self-heating effect.
To obtain a resistance reading from the thermistor that accurately represents the temperature of its environment, it is critical that the power levels (essentially the current levels) associated with the measurement are low enough not to cause appreciable self-heating.
The self-heating effect should be considered in basic resistance measurements using a digital multi-meter (DMM). Check the technical specifications for the meter, or contact the manufacturer, to determine the magnitudes of voltage and current associated with the applicable resistance measurement ranges. If the result will be more than a few milliwatts power level in the thermistor, a meter that uses less voltage and or current will be needed to obtain an accurate resistance measurement.
ANSI/EASA AR100
More information on this topic can be found in ANSI/EASA AR100- Section 3: Rewinding
- Section 4: Testing
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