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Temperature Sensors

Reference data and engineering information about temperature sensors for process control applications.

temperaturesensors

Overview

Engineering reference data for Temperature Sensors in process control.

Key Formulas

PID Controller

u(t)=Kpe(t)+Ki∫e(t)dt+Kddedtu(t) = K_p e(t) + K_i \int e(t)dt + K_d \frac{de}{dt}

Proportional-Integral-Derivative control.

Transfer Function

G(s)=Kτs+1G(s) = \frac{K}{\tau s + 1}

First-order system.

Variables

SymbolDescriptionUnit
KpK_pProportional gain—
KiK_iIntegral gain1/s
KdK_dDerivative gains
τ\tauTime constants

Comparison of Temperature Sensors

While the existing content covers key formulas, a direct comparison of common sensor types helps in selection. The following table outlines their general characteristics.

Sensor TypePrincipleTypical Range (°C)AccuracyResponse TimeNotes
RTD (Pt100)Resistance change in pure metal-200 to 850HighModerateStable, linear, requires excitation current
ThermocoupleSeebeck effect (junction voltage)-270 to 2300ModerateFastWide range, self-powered, requires reference junction
Thermistor (NTC)Large resistance change in semiconductor-50 to 300High (over limited range)Very fastHighly nonlinear, sensitive, low cost

Key Operating Principles

Resistance Temperature Detectors (RTDs)

The resistance of a pure metal (e.g., platinum) increases with temperature. The relationship is often approximated by the Callendar-Van Dusen equation: R(T)=R0(1+AT+BT2+C(T−100)T3)R(T) = R_0(1 + AT + BT^2 + C(T-100)T^3) where for T>0°CT > 0°C, C=0C = 0.

Thermocouples

When two dissimilar metals are joined, a voltage (the Seebeck voltage) is produced that is proportional to the temperature difference between the measurement junction and the reference (cold) junction. V=SAB(Tmeas−Tref)V = S_{AB}(T_{meas} - T_{ref}) where SABS_{AB} is the Seebeck coefficient of the couple.

Selection Criteria

Choosing a sensor depends on application requirements:

  • Range: Thermocouples excel for high temperatures.
  • Accuracy/Stability: RTDs generally offer the best long-term stability and accuracy.
  • Response Time: Thermistors and fine-wire thermocouples respond fastest.
  • Cost & Complexity: Thermistors are simple and cheap; RTDs and thermocouples may require linearization and signal conditioning.

References

Source: engineeringtoolbox.com