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Resistance-Temperature Relationship

The resistance-temperature (R-T) relationship plays a central role in resistance temperature detectors (RTDs). The R-T relationship of some common RTD materials are illustratrated in the following schematic where the y-axis is the normalized resistance with respect to resistance at 0 °C (32 °F), x-axis is the temperature.

Resistance-Temperature Relationship
for some RTD materials

For a given material, the resistance at any temperature can be obtained by curve-fitting the R-T curve. Suppose that a nth degree polynomial least-square curve-fit is used. The temperature function will then be,

Some references suggest to express the resistance as a function of temperature (rather than temperature as a function of resistance), i.e.,

Although such a relationship is mathematically correct, its usefulness is limited. After all, we are interested in determining temperature from a resistance measurement.

A Simplified Case

Some materials have an almost linear R-T relationship within a certain temperature range, T1 < T < T2. Such a linear function would take the form,

Rearranging to bring temperature out gives,

where a is the average temperature coefficient of resistance in the (T1,T2) temperature range, i.e., a is the slope of the R-T line.

Both the measured temperature and the reference temparature should be within the (T1,T2) temperature range,

T1 < {T, TRef} < T2