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Thermistors and Resistance Temperature Detectors (RTDs)

One of the simplest classes of temperature sensor is one where temperature effects a change in electrical resistance. With this type of primary sensing element, a simple ohmmeter is able to function as a thermometer, interpreting the resistance as a temperature measurement:

Thermistors are devices made of metal oxide which either increase in resistance with increasing temperature (a positive temperature coefficient) or decrease in resistance with increasing temperature (a negative temperature coefficient). RTDs are devices made of pure metal (usually platinum or copper) which always increase in resistance with increasing temperature. The major difference between thermistors and RTDs is linearity: thermistors are highly sensitive and nonlinear, whereas RTDs are relatively insensitive but very linear. For this reason, thermistors are typically used where high accuracy is unimportant. Many consumer-grade devices use thermistors for temperature sensors.


Temperature coefficient of resistance (α)

Resistive Temperature Detectors (RTDs) relate resistance to temperature by the following formula:



   RT = Resistance of RTD at given temperature T (ohms)

   Rref = Resistance of RTD at the reference temperature Tref (ohms)

   α = Temperature coefficient of resistance (ohms per ohm/degree)


The following example shows how to use this formula to calculate the resistance of a “100 ohm” platinum RTD with a temperature coefficient value of 0.00392 at a temperature of 35 degrees Celsius:

Due to nonlinearities in the RTD’s behavior, this linear RTD formula is only an approximation. A better approximation is the Callendar-van Dusen formula, which introduces second, third, and fourth-degree terms for a better fit: RT = Rref (1 + AT + BT2 100CT3 + CT4) for temperatures ranging -200oC < T < 0oC and RT = Rref (1 + AT + BT2) for temperatures ranging 0o C < T < 661oC, both assuming Tref = 0oC.

Water’s melting/freezing point is the standard reference temperature for most RTDs. Here are some typical values of α for common metals:


  • Nickel = 0.00672 / oC

  • Tungsten = 0.0045 /oC

  • Silver = 0.0041 /oC

  • Gold = 0.0040 /oC

  • Platinum = 0.00392 /oC

  • Copper = 0.0038 /oC


As mentioned previously, platinum is a common wire material for industrial RTD construction. The alpha (α) value for platinum varies according to the alloying of the metal. For “reference grade” platinum wire, the most common alpha value is 0.003902. Industrial-grade platinum alloy RTD wire is commonly available in two different coefficient values: 0.00385 (the “European” alpha value) and 0.00392 (the “American” alpha value), of which the “European” value of 0.00385 is most commonly used (even in the United States!).

100  is a very common reference resistance (Rref at 0 degrees Celsius) for industrial RTDs. 1000  is another common reference resistance, and some industrial RTDs have reference resistances as low as 10 . Compared to thermistors with their tens or even hundreds of thousands of ohms’ nominal resistance, an RTD’s resistance is comparatively small. This can cause problems with measurement, since the wires connecting an RTD to its ohmmeter possess their own resistance, which will be a more substantial percentage of the total circuit resistance than for a thermistor.


Two-wire RTD circuits

The following schematic diagrams show the relative effects of 2 ohms total wire resistance on a thermistor circuit and on an RTD circuit:

Clearly, wire resistance is more problematic for low-resistance RTDs than for high-resistance thermistors. In the RTD circuit, wire resistance counts for 1.96% of the total circuit resistance. In the thermistor circuit, the same 2 ohms of wire resistance counts for only 0.004% of the total circuit resistance. The thermistor’s huge reference resistance value “swamps”1 the wire resistance to the point that the latter becomes insignificant by comparison.

In HVAC (Heating, Ventilation, and Air Conditioning) systems, where the temperature measurement range is relatively narrow, the nonlinearity of thermistors is not a serious concern and their relative immunity to wire resistance error is a definite advantage over RTDs. In industrial temperature measurement applications where the temperature ranges are usually much wider, the nonlinearity of thermistors becomes a significant problem, so we must find a way to use low-resistance RTDs and deal with the (lesser) problem of wire resistance.


Four-wire RTD circuits

A very old electrical technique known as the Kelvin or four-wire method is a practical solution for this problem. Commonly employed to make precise resistance measurements for scientific experiments in laboratory conditions, the four-wire technique uses four wires to connect the resistance under test (in this case, the RTD) to the measuring instrument:

Current is supplied to the RTD from a current source, whose job it is to precisely regulate current regardless of circuit resistance. A voltmeter measures the voltage dropped across the RTD, and Ohm’s Law is used to calculate the resistance of the RTD (R = V I).

None of the wire resistances are consequential in this circuit. The two wires carrying current to the RTD will drop some voltage along their length, but this is of no concern because the voltmeter only “sees” the voltage dropped across the RTD rather than the voltage drop across the current source. While the two wires connecting the voltmeter to the RTD do have resistance, they drop negligible voltage because the voltmeter draws so little current through them (remember an ideal voltmeters has infinite input impedance, and modern semiconductor-amplified voltmeters have impedances of several mega-ohms or more). Thus, the resistances of the current-carrying wires are of no effect because the voltmeter never senses their voltage drops, and the resistances of the voltmeter’s sensing wires are of no effect because they carry practically zero current.

Note how wire colors (white and red) are used to indicate which wires are common pairs at the RTD. Often, these wire colors will be the technician’s only guide to properly connecting a 4-wire RTD to a sensing instrument.

The only disadvantage of the four-wire method is the sheer number of wires necessary. Four wires per RTD can add up to a sizeable wire count when many different RTDs are installed in a process area. Wires cost money, and occupy expensive conduit, so there are situations where the four-wire method is a burden.


Three-wire RTD circuits

A compromise between two-wire and four-wire RTD connections is the three-wire connection, which looks like this:

In a three-wire RTD circuit, voltmeter “A” measures the voltage dropped across the RTD (plus the voltage dropped across the bottom current-carrying wire). Voltmeter “B” measures just the voltage dropped across the top current-carrying wire. Assuming both current-carrying wires will have (very nearly) the same resistance, subtracting the indication of voltmeter “B” from the indication given by voltmeter “A” yields the voltage dropped across the RTD:

If the resistances of the two current-carrying wires are precisely identical (and this includes the electrical resistance of any connections within those current-carrying paths, such as terminal blocks), the calculated RTD voltage will be the same as the true RTD voltage, and no wire-resistance error will appear. If, however, one of those current-carrying wires happens to exhibit more resistance than the other, the calculated RTD voltage will not be the same as the actual RTD voltage, and a measurement error will result.

Thus, we see that the three-wire RTD circuit saves us wire cost over a four-wire circuit, but at the “expense” of a potential measurement error. The beauty of the four-wire design was that wire resistances were completely irrelevant: a true determination of RTD voltage (and therefore RTD resistance) could be made regardless of how much resistance each wire had, or even if the wire resistances were different from each other. The error-canceling property of the three-wire circuit, by contrast, hinges on the assumption that the two current-carrying wires have exactly the same resistance, which may or may not actually be true.

It should be understood that real three-wire RTD instruments do not employ direct-indicating voltmeters. Actual RTD instruments use either analog or digital “conditioning” circuits to measure the voltage drops and perform the necessary calculations to compensate for wire resistance. The voltmeters shown in the four-wire and three-wire diagrams serve only to illustrate the basic concepts, not to showcase a practical instrument design.

A photograph of a modern temperature transmitter capable of receiving input from 2-wire, 3- wire, or 4-wire RTDs (as well as thermocouples, another type of temperature sensor entirely) shows the connection points and the labeling:


The rectangle symbol shown on the label represents the resistive element of the RTD. The symbol with the “+” and “” marks represents a thermocouple junction, and may be ignored for the purposes of this discussion. As shown by the diagram, a two-wire RTD would connect between terminals 2 and 3. Likewise, a three-wire RTD would connect to terminals 1, 2, and 3 (with terminals 1 and 2 being the points of connection for the two common wires of the RTD). Finally, a four-wire RTD would connect to terminals 1, 2, 3, and 4 (terminals 1 and 2 being common, and terminals 3 and 4 being common, at the RTD).

Once the RTD has been connected to the appropriate terminals of the temperature transmitter, the transmitter needs to be electronically configured for that type of RTD. In the case of this particular temperature transmitter, the configuration is performed using a “smart” communicator device using the HART digital protocol to access the transmitter’s microprocessor-based settings. Here, the technician would configure the transmitter for 2-wire, 3-wire, or 4-wire RTD connection.


Self-heating error

One problem inherent to both thermistors and RTDs is self-heating. In order to measure the resistance of either device, we must pass an electric current through it. Unfortunately, this results in the generation of heat at the resistance according to Joule’s Law:

This dissipated power causes the thermistor or RTD to increase in temperature beyond its surrounding environment, introducing a positive measurement error. The effect may be minimized by limiting excitation current to a bare minimum, but this results in less voltage dropped across the device. The smaller the developed voltage, the more sensitive the voltage-measuring instrument must be to accurately sense the condition of the resistive element. Furthermore, a decreased signal voltage means we will have a decreased signal-to-noise ratio, for any given amount of noise induced in the circuit from external sources.

One clever way to circumvent the self-heating problem without diminishing excitation current to the point of uselessness is to pulse current through the resistive sensor and digitally sample the voltage only during those brief time periods while the thermistor or RTD is powered. This technique works well when we are able to tolerate slow sample rates from our temperature instrument, which is often the case because most temperature measurement applications are slow-changing by nature. The pulsed-current technique enjoys the further advantage of reducing power consumption for the instrument, an important factor in battery-powered temperature measurement applications.


1“Swamping” is the term given to the overshadowing of one effect by another. Here, the normal resistance of the high-value RTD greatly overshadows any wire resistance, such that wire resistance becomes negligible.

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