WiderstandsTemperaturBeziehung

Widerstands-Temperaturkoeffizient, often abbreviated as TCR, describes how the electrical resistance of a material changes with temperature. It is defined as α = (1/R0)(dR/dT) at a reference temperature T0 and is typically expressed in per degree Celsius. For many metals, α is positive, meaning resistance increases with temperature; for most semiconductors and carbon-based resistors, α is negative, so resistance decreases as temperature rises. The common linear approximation R(T) ≈ R0[1 + α(T − T0)] applies over limited ranges, but real materials may show non-linear behavior requiring higher-order terms or a temperature-dependent α.

Applications include temperature compensation in electronic circuits, calibration of resistive sensors, and the design of precision resistors. Materials with small, stable α, such as platinum, are used in resistance temperature detectors (RTDs) and other industrial sensors, while materials with large |α|, such as certain thermistors, provide high sensitivity but exhibit non-linearity.

Measurement and standards: international standards define reference values and tolerances for RTDs; for example, IEC 60751 specifies the characteristics of platinum resistance thermometers and their α values at standard temperatures. Temperature drift due to TCR is a major consideration in resistor networks and in analog-to-digital conversions.

Limitations: the TCR depends on temperature, aging, mechanical stress, and impurities, so designers account for these factors and may require calibration. The concept underpins the selection and use of resistors in temperature-compensated circuits, sensors, metrology, and instrumentation across electronics.