eFunda: Theory of Resistance Temperature Detectors Resistance Temperature Detector: Theory Design Home Sensors Sensor Home Instruments/Devices Methods/Principles Displacement Stress & Strain Pressure Fluid Flow Flowmeter Temperature Thermocouple Intro Thermocouple Theory RTD Intro RTD Theory Thermistors Intro Thermistors Theory Pyrometers Intro Pyrometers Theory Resources Bibliography  Login   Home Membership Magazines Forum Search Member Calculators  Materials  Design  Processes  Units  Formulas  Math 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 Relationshipfor 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
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