# Temperature Measurement (Part 2)

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## Resistance Temperature Detectors

### In Part 1 of this series, George detailed the characteristics of common temperature sensors. In this article, he investigates temperature sensing by diodes, resistance temperature detectors (RTDs), thermistors, and touch on contactless detectors.

• How temperature sensing is done with diodes, RTDs and thermistors

• Temperature sensing in tough environments

• How thermistors work

• How to measure with silicon sensors

• A summary of contactless temperature sensors

• Resistor temperature detectors

• Thermistors

• Silicon sensors

• Contactless temperature sensors

Temperature measurement is an essential topic that all serious engineers should understand. Last month we discussed temperature sensing with thermocouples. Let’s continue by looking at a variety of other options, including resistor temperature detectors (RTDs) and thermistors.

##### RTDs

Another sensor commonly used in tough environments is the resistor temperature detector (RTD), whose resistance changes with temperature. RTDs are relatively pricey compared with other types of sensors, as the most are made of Platinum (Pt) wire. Less expensive RTDs may be made of Nickel (Ni) or Copper (Cu). RTDs can measure a wide temperature range, though not as high temperatures as the thermocouples. Typically, the range of –270°C to 900°C can be achieved. RTDs require an external stimulus (i.e., a current excitation) to function. The simplest configuration called a two-wire method comprises a constant current source feeding the RTD and measuring the voltage at the current source, such as shown in Figure 1a. Clearly, the resistance of the leads introduces an error.

If the lead resistance, for instance, should be 100 mΩ and the RTD resistance 100 Ω, roughly a 0.1% error would be introduced into the measurement. Using the so-called Kelvin topology shown in Figure 1b, the voltage drop across the lead resistance due to the excitation current is ignored. With a high impedance “voltmeter” circuit the sense current would be very small and the voltage drop across the sensing leads negligible.

RTDs are the most stable and accurate of all temperature sensing devices, but they suffer from a few drawbacks: nonlinearity, low sensitivity, and self-heating. The error caused by self-heating is calculated as follows: DT = RRTD × IEXCITATION × S, where S is the RTD characteristic in degrees Celsius per milliwatt.

The self-heating error becomes negligible when the RTD is used to measure high temperatures, such as those inside a jet engine, but it may become significant at low temperature measurements, where the RTD-generated heat could raise the actual temperature. Another concern is the RTD’s rather low sensitivity. Typically, it may be just a small fraction of an ohm per 1°C. That means very stable, low-noise, and low drift processing circuits must be used. A typical RTD such as PT100 varies less than 0.4 Ω/°C. With 100-µA excitation current this amounts to 40 µV/°C output change.

##### THERMISTORS

Similar to the RTDs, thermistors are also resistors that change value with temperature. Unlike the RTDs, thermistors’ resistance varies orders of magnitude through their operating range. Compared to thermocouples and RTDs, thermistors’ operating temperature range is much smaller, from only about –100°C to about 450°C.

Thermistors come in two types, NTC and PTC, and many ohmic values. NTC, or negative temperature coefficient thermistors’ resistance decreases with temperature. PTC, that is positive temperature coefficient thermistors’ resistance increases with temperature. While NTC thermistors are mostly used for temperature sensing, PTC thermistors are often used as current limiters, inrush current suppressors and fuses. Similar to RTDs, thermistors also require excitation resulting in self-heating. Consequently, the thermistor value and its excitation current must be carefully selected for a given application.

One concern with thermistors, just as with the thermocouples and the RTDs, is their nonlinearity. One way to compensate for this nonlinearity is by the use of a look-up table. In case you have a high-resolution analog-to-digital converter (ADC), you can determine the temperature by running an algorithm to solve the Steinhart-Hart equation for thermistors:

T is temperature in Kelvin. R is the thermistor resistance at temperature T. A, B, and C are constants provided by the thermistor manufacturer.

Before microcomputers with high-resolution ADCs became common, thermistors’ response had been frequently linearized within a specific operating range by a combination of resistors connected in series and parallel configuration with the thermistor. Such linearization, although not perfect throughout the entire range, would often be sufficient. Otherwise, a microprocessor with at least a 10 bit or a better ADC and a look-up table could provide more than satisfactory results.[1] When a microcontroller is not available, a limited linearization achieved by adding resistors results in an S-shaped temperature-to-voltage characteristic.

Figure 2 shows a linearized thermistor interface with an operational amplifier buffer. The resolution of thermistors is infinite, but for good results, the power supply stability must be at least an order of magnitude better than the desired precision of the temperature measurement. In many instances, while interfacing electronics with a resistive type sensor, it is advantageous to employ the Wheatstone bridge. This is illustrated by Figure 3. Resistors R1, R2, RP, and RS must be stable, so as not to influence the accuracy of the measurement. The output voltage, therefore, reflects the changing resistance Rand the stability of the excitation voltage.

Thermistors’ self-heating characteristic can be taken advantage of in measurement of air or a liquid flow. Thermistor specification sheets contain a dissipation factor δ (Greek letter delta), which is usually based on 25°C still air. Flowing air or liquid dissipates the heat more efficiently and the subsequent drop in the thermistor temperature can be calibrated in the appropriate substance rate of flow.

Some sources recommend to calculate the values of the linearization resistors as follows:

RT is the resistance value of the thermistor at the mean temperature T in Kelvin. B is the constant supplied by the manufacturer. Because the linearization resistors RP and RT are in parallel, the sensitivity of the thermistor is decreased. The rate of output change versus temperature of the linearized R/T characteristic is:

##### SILICON SENSORS

Another category, silicon sensors, are formed by a P-N junction (i.e., a diode), whose forward voltage VF changes with temperature TJ. This is the basis for temperature sensors often implemented within integrated circuits where they are used for external as well as internal temperature sensing, circuits’ temperature compensation, or a thermocouple reference.

Diode’s temperature sensitivity is determined by the change of its forward voltage VF when operated at two different currents, typically in 10:1 ratio.

k stands for the Boltzman’s constant. q is the charge of an electron.

m is determined experimentally for a particular diode by measurement:

Equations 4, 5, and 6 are linear. Typically, VF changes by approximately –2.3 mV/°C, depending on the P-N junction structure.

There are many integrated circuits for temperature measurement using the P-N junction temperature dependency. Many of them already contain an amplifier with conditioning circuits, such as the LTC2983 or the ubiquitous three-pin LM35 calibrated to output 10 mV/°C or LM34 with 10 mV/°F. Some sensors have analog, others digital outputs, such as SPI or I2C with differing precisions. Visiting National Semiconductor, Linear Technology, and other websites will produce many temperature sensors and their suggested conditioning circuits. Using some of the ICs may be tricky, so read the specifications carefully. LM35, for instance, doesn’t like capacitive loads. Just a few feet of a shielded cable (about 50 pF) connected to its output can turn it into a saw tooth oscillator. Manufacturers generally recommend interface methods in their application notes.

##### CONTACTLESS TEMPERATURE SENSORS

We should not forget about contactless temperature sensors, which are in a separate class by themselves. I shall address them specifically in the third part of this series. The ones we’re most familiar with work in far infrared radiation region, usually in the 7-to-14-µm wavelengths. Pyroelectric sensors are omnipresent due to their performance and low cost. They are typically used in passive infrared (PIR) intrusion detectors and motion sensors controlling light fixtures. The sensors work within a defined area of view, which can be a composition of one or more view cones created by optics. These can be refractive (lenses) or reflective (mirrors). Refractive optics are prevalent due to their low cost of manufacture as compared with curved, faceted mirrors. The lenses are usually Fresnel lenses, injection molded from plastics, such as polyethylene, which is transparent to IR radiation. (Refer to my article series, “Fundamental Optics,” in Circuit Cellar issues 305, 306, and 307.– see RESOURCES below for links.)

Hand-held contactless thermometers for home use have been available for years in hardware stores for less than \$50. Unlike motion sensors, they measure absolute temperature. They need good narrow field of view optics and stable processing circuitry. For experimenting, note that Adafruit sells contact-less infrared thermopile sensor breakout board that features a Texas Instruments thermopile sensor TMP006 and has temperature detection range of 0° to 60°C (www.adafruit.com/products/1296). Sensors are made for specific temperature range and absolute or relative temperature change, something we shall discuss in the next issue.

##### CONTACTLESS TEMP MEASUREMENT

This ends our excursion into the realm of contact temperature measurement and detection. I did not mention some less common, specialized methods, such as the fiber-optic temperature sensor containing a crystal of undoped GaAs, capable of biological implantation. Those who are interested can find information on the ‘Net. In the next part of this series, we’ll consider contactless temperature measurement.

REFERENCE
[1] M. Biegert, “Linearize Thermistors with New Formula,” 2014, www.edn.com/design/sensors/4429105/Linearize-thermistors-with-new-formula.

RESOURCES
Linear Technology, “LTC2983—Multi-Sensor High Accuracy Digital Temperature Measurement System,” www.linear.com/product/LTC2983.
G. Novacek, “Fundamental Optics-Part 1,” Circuit Cellar 305, 2015
G. Novacek, “Fundamental Optics-Part 2,” Circuit Cellar 306, 2016.
G. Novacek, “Fundamental Optics-Part 3,” Circuit Cellar 307, 2016.

PUBLISHED IN CIRCUIT CELLAR MAGAZINE • JULY 2016 #312  – Get a PDF of the issue

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