## 1. How do thermistors work?

Thermistors are a type of temperature sensitive resistive device in which the resistive element is a semiconducting metal oxide. This sets them apart from RTDs which contain a pure metal resistive element. Thermistors are categorized as having either positive or negative temperature coefficients (known as PTC and NTC respectively). A positive temperature coefficient means that resistance increases with rising temperature whereas a negative temperature coefficient means that resistance decreases. NTCs are most appropriate for temperature measurement because they enable temperature to be determined more accurately from measured resistance. Thermistors are available in many resistance ratings, the magnitude of which affects their performance (see purchasing tips). Any two NTC thermistors with the same resistance and temperature range are normally interchangeable. Thermistors are available either bare or protected by a metal sheath. Bare thermistors are fragile and generally unsuitable for immersion in liquids. Sheath protected thermistors are therefore more common in industry, despite their higher cost.

The resistance of the thermistor can be measured by placing it in series with a fixed resistor of known resistance and applying a known voltage. Such a circuit is known as a voltage divider and causes the potential difference across the thermistor to shift as a function of its resistance. This enables resistance to be calculated from the measured voltage. In practice a Wheatstone bridge circuit is the preferred method for detecting the resistance of a thermistor. The Wheatstone bridge performs a similar function to a voltage divider but provides improved sensitivity. Note that the Wheatstone bridge measures the sensor’s lead resistance as if it were part of the thermistor resistance. Although the resistance can be cancelled out during post processing, its effect can also be reduced by using a high resistance thermistor.

The equation for calculating thermistor resistance, including cancellation of lead wire resistance, is displayed above. Once resistance is known, the Steinhart-Hart Equation (below) can be used to determine the temperature of any NTC resistor. The coefficients A, B and C are properties of the sensor. They are identical for any 2 thermistors of identical reference resistance and temperature range, but it is worth double checking with the manufacturer. The coefficients can also be calculated by carrying out calibration. The table below shows the A, B and C coefficients for a 10,000 ohm NTC thermistor. See the additional links section for Steinhart-Hart equation calculators. Note that occasionally the Steinhart-Hart equation includes an additional term not shown here. However, it is normally emitted because of its small size.

Steinhart-hart equation coefficients

## 2. General characteristics of thermistors

Thermistors are low cost temperature sensitive devices used for measuring temperature (among other uses). They possess high accuracy, high sensitivity and excellent long term stability. However, they suffer from a small temperature measurement range and a nonlinear output which complicates the process of determining temperature from resistance. Thermistors are active sensors, meaning that they require a voltage supply and are therefore also susceptible to self-heating. Their output is in Volts, from which the thermistor resistance and therefore the temperature can be determined. They are available either bare (in which case they are fragile and typically not suitable for immersion in liquids) or enclosed in a protective metal sheath.

## 3. Input and output signals

Thermistors are active sensors and therefore require a supply voltage for their Wheatstone bridge circuit. The Wheatstone bridge outputs a voltage as a function of thermistor resistance, from which temperature can be determined. Thermistors rarely contain built in electronics and therefore require external electronics to implement the Wheatstone bridge. The external electronics will also amplify the bridge output and convert it into a standard output signal (e.g. 0-10 V) that is proportional to temperature.

## 4. Applications of thermistors

The most common application of thermistors is probably not for measuring temperature but rather for limiting current and providing over heating protection in electronic circuits. Thermistors are generally less popular than thermocouples and RTDs, in part due to their low maximum temperature. However, they do see extensive use in a number of temperature measurement applications due to their high accuracy, low cost and small size. These applications include use within automotive engine cooling systems, HVAC digital thermostats and for cold junction temperature measurement in thermocouple amplifiers.

## 5. Typical specification

• NTC vs PTC: Thermistors have either negative or positive temperature coefficients (NTC or PTC respectively). The resistance of an NTC thermistor decreases with increasing temperature whereas the resistance of a PTC increases with increasing temperature. We recommend purchasing only NTCs for temperature measurement applications because they enable more accurate determination of temperature from measured resistance. There is a niche type of PTC made of silicon which provides a highly linear output. However, their sensitivity is about 1/5th that of a metal oxide PTC or NPC.
• Reference resistance: The reference resistance is the thermistor’s resistance at its reference temperature, normally 25 °C. Common resistances include 100, 1,000, 3,000 , 5,000 and 10,000 ohms. High resistance thermistors are less sensitive to errors caused by lead wire resistance and less prone to self-heating because the higher resistance reduces current. However, the lower current makes higher resistance thermistors more sensitive to electrical noise.
• Response time: Due to their thermal mass, thermistors require a finite time to arrive at the temperature of the fluid. Response time is much faster for bare thermistors than for those in protective sheaths but also depends on the fluid thermal conductivity and velocity, e.g. response times in water are shorter than in air. Response times are defined in terms of time constants. The time constant is the time taken for the temperature difference between the thermocouple and the fluid to decay by 63.2% (e.g. from 100 °C to 46.8 °C). The 2nd time constant is the time taken for temperature to decay by a further 63.2%, i.e. from 63.2% to 86.5%. Notably, the time taken for the temperature difference to decay from 0% to 63.2% is equal to the time taken from 63.2% to 86.5%. The first 5 time constants are illustrated in the graph below.
• Sheath length and diameter: Thermistor sheaths are typically 3-8 mm in diameter and 25-500 mm long, though other sizes are available.

Thermistors:

• Are very low cost temperature sensors.
• Achieve extremely high accuracies.
• Have a much higher sensitivity than thermocouples and RTDs, resulting in a higher practical resolution.
• Have excellent long term stability.
• Have reasonably fast response times (generally faster than RTDs but slower than exposed thermocouples).

Thermistors:

• Have a small temperature measurement range.
• May suffer from self-heating, which reduces accuracy.
• Have a non-linear output, making determination of temperature more difficult.

## 9. Application tips

• Calibration for improved accuracy: The accuracy of thermistors can be improved by calibrating them every 12 months, to account for long term temperature drift. However, due to their excellent long term stability, calibration is less important than for thermocouples and RTDs.
• Avoid thermal shunting: Thermal shunting occurs when the presence of the thermistor effects the measured temperature by absorbing heat. The susceptibility to thermal shunting is application dependent. Due to their small size, bare thermistors are unlikely to cause thermal shunting. However, thermistors enclosed in protective sheaths can cause thermal shunting.
• Self-heating: The current passing through the thermistor generates heat which potentially increases its temperature, causing measurement error. Self-heating can be reduced by using a high resistance thermistor so that the current is minimized. The heating power is equal to the thermistor resistance multiplied by the current squared and has the unit of Watts. Many manufacturers provide the heat dissipation capability of the thermistor (units of Watts/°C). If for example, a thermistor generates 0.1 Watt of heat due to self-heating and dissipates only 0.02 Watts/°C, its temperature will rise by 5 °C. In practice the extent of self-heating is much smaller than this.
• Thermowells: A thermowell is type of protective sheath which performs the same function as a regular thermistor sheath but is not permanently attached to the sensor. It enables the thermistor to be removed from a pipe or vessel without any down time or leakage of fluid because the thermowell remains in place providing a reliable fluid tight seal.

Physical principal of thermistor operation

Steinhart-Hart temperature calculator

Steinhart-Hart coefficient calculator / thermistor calibrator