14 Temperature measurement

 

14.3 Varying resistance devices

Varying resistance devices rely on the physical principle of the variation of resistance with temperature. The devices are known as either resistance thermometers or thermistors according to whether the material used for their construction is a metal or a semiconductor, and both are common measuring devices. The normal method of measuring resistance is to use a d.c. bridge. The excitation voltage of the bridge has to be chosen very carefully because, although a high value is desirable for achieving high measurement sensitivity, the self-heating effect of high currents flowing in the temperature transducer creates an error by increasing the temperature of the device and so changing the resistance value.

 

14.3.1 Resistance thermometers (resistance temperature devices)

Resistance thermometers, which are alternatively known as resistance temperature devices (or RTDs), rely on the principle that the resistance of a metal varies with temperature according to the relationship:

                  R = R₀ ( 1 + a₁T + a₂T² + a₃T³ +…+ a_nTⁿ)                   (14.7)

This equation is non-linear and so is inconvenient for measurement purposes. The equation becomes linear if all the terms in a₂T² and higher powers of T are negligible such that the resistance and temperature are related according to:

                                           R  R₀ (1 + a₁T)

This equation is approximately true over a limited temperature range for some metals, notably platinum, copper and nickel, whose characteristics are summarized in Figure 14.8. Platinum has the most linear resistance–temperature characteristic, and it also has good chemical inertness, making it the preferred type of resistance thermometer in most applications. Its resistance–temperature relationship is linear within ±0.4% over the temperature range between -200°C and +40°C. Even at +1000°C, the quoted inaccuracy figure is only ±1.2%. Platinum thermometers are made in two forms, as a coil wound on a mandrel and as a film deposited on a ceramic substrate. The nominal resistance at 0°C is typically 100 Ω or 1000 Ω, though 200 Ω and 500 Ω versions also exist. Sensitivity is 0.385 Ω /°C (100 Ω type) or 3.85 Ω /°C (1000 Ω type). A high nominal resistance is advantageous in terms of higher measurement sensitivity, and the resistance of connecting leads has less effect on measurement accuracy. However, cost goes up as the nominal resistance increases.

Besides having a less linear characteristic, both nickel and copper are inferior to platinum in terms of their greater susceptibility to oxidation and corrosion. This seriously limits their accuracy and longevity. However, because platinum is very expensive compared with nickel and copper, the latter are used in resistance thermometers when cost is important. Another metal, tungsten, is also used in resistance thermometers in some circumstances, particularly for high temperature measurements. The working range of each of these four types of resistance thermometer is as shown below:

Platinum: -270°C to +1000°C (though use above 650°C is uncommon)

Copper: -200°C to +260°C

Nickel: -200°C to +430°C

Tungsten: -270°C to +1100°C

In the case of non-corrosive and non-conducting environments, resistance thermometers are used without protection. In all other applications, they are protected inside a sheath. As in the case of thermocouples, such protection reduces the speed of response of the system to rapid changes in temperature. A typical time constant for a sheathed platinum resistance thermometer is 0.4 seconds. Moisture build-up within the sheath can also impair measurement accuracy.

14.3.2 Thermistors

Thermistors are manufactured from beads of semiconductor material prepared from oxides of the iron group of metals such as chromium, cobalt, iron, manganese and nickel. Normally, thermistors have a negative temperature coefficient, i.e. the resistance decreases as the temperature increases, according to:

                                   R = R₀e^{[ (1/T-1/T0)]}                                 (14.8)

This relationship is illustrated in Figure 14.9. However, alternative forms of heavily doped thermistors are now available (at greater cost) that have a positive temperature coefficient. The form of equation (14.8) is such that it is not possible to make a linear approximation to the curve over even a small temperature range, and hence the thermistor is very definitely a non-linear sensor. However, the major advantages of thermistors are their relatively low cost and their small size. This size advantage means that the time constant of thermistors operated in sheaths is small, although the size reduction also decreases its heat dissipation capability and so makes the self[1]heating effect greater. In consequence, thermistors have to be operated at generally

lower current levels than resistance thermometers and so the measurement sensitivity is less.

 

14.4 Semiconductor devices

Semiconductor devices, consisting of either diodes or integrated circuit transistors, have only been commonly used in industrial applications for a few years, but they were first invented several decades ago. They have the advantage of being relatively inexpensive, but one difficulty that affects their use is the need to provide an external power supply to the sensor.

Integrated circuit transistors produce an output proportional to the absolute temperature. Different types are configured to give an output in the form of either a varying current (typically 1 µA/K) or varying voltage (typically 10 mV/K). Current forms are normally used with a digital voltmeter that detects the current output in terms of the voltage drop across a 10 kΩ resistor. Although the devices have a very low cost (typically a few pounds) and a better linearity than either thermocouples or resistance thermometers, they only have a limited measurement range from -50°C to +150°C. Their inaccuracy is typically ±3%, which limits their range of application. However, they are widely used to monitor pipes and cables, where their low cost means that it is feasible to mount multiple sensors along the length of the pipe/cable to detect hot spots.

In diodes, the forward voltage across the device varies with temperature. Output from a typical diode package is in the micro amp range. Diodes have a small size, with good output linearity and typical inaccuracy of only ±0.5%. Silicon diodes cover the temperature range from -50 to +200°C and germanium ones from -270 to +40°C.