# Temperature measurements: theoretical aspects

thermal resistors application

Resistive temperature detectors (RTD) operating principle is based on dependence of conductivity on temperature. This dependence is represented by temperature resistance coefficient. Sensors based on metals have positive temperature resistance coefficient, while sensors based on semiconductors and oxides normally have negative temperature resistance coefficient. For instance, platinum RTD has the following resistance dependence on temperature:

where t — is temperature °С, R_{0} — sensor temperature at 0°С.

At 0°С detector’s resistance is 100 Ohm, at 200°С detector’s resistance is 175,84 Ohm.

For copper RTD temperature characteristics is as follows:

There are different methods to measure resistance. One of the most widely spread methods is to power up the sensor by DC and to measure reistor’s voltage decrease. To enhance the precision and to avoid ambient noise impact it is desirable to use high power. On the other hand, high power level leads to considerable power dissipation on the resistor, which can lead to measured temperature values distortion. For instance, if 175,84 Ohm resistor is powered up by 5 mA current, the power decrease is 789,2 mV. 0,1 °С temperature change corresponds to 0,2 mV power decrease. In order to detect 0,2 mV change, the voltage meter should have resolution 0,05 — 0,1 mV or higher. Zero drift of the power meter should not exceed 0,1 mV. If the power meter is ADC-based, then the digits number should be 14-16 bits.

Thermistors with negative temperature resistance ratio have non-linear resistance dependence on temperature, which can be approximated by several equations, for instance:

where t — temperature in Kelvin degrees, t_{0} — calibration temperature, R_{0} — resistance at calibration temperature, β — material’s characteristic temperature (in the range 3000 – 10000 K).

For thermistor resistance impedance measurements one can use the same measuring scheme as is used for resistive temperature detector. In this case it is necessary to use 16-digit analog-to-digital converter.