Temperature Sensors Transmitters

Overview

Engineering reference data for Temperature Sensors Transmitters in process control.

Key Formulas

PID Controller

$u(t) = K_p e(t) + K_i \int e(t)dt + K_d \frac{de}{dt}$

Proportional-Integral-Derivative control.

Transfer Function

$G(s) = \frac{K}{\tau s + 1}$

First-order system.

Variables

Thermocouple Voltage-Temperature Relationship

The output voltage of a thermocouple is related to the temperature difference between its measurement (hot) and reference (cold) junctions. For a Type K thermocouple, this relationship is often approximated by a high-order polynomial:

$$V = a_0 + a_1T + a_2T^2 + a_3T^3 + ... + a_nT^n$$

Where $V$ is the voltage in microvolts (μV), and $T$ is the temperature in degrees Celsius (°C). The coefficients $a_n$ are specific to the thermocouple type and are determined by calibration standards (e.g., NIST ITS-90).

A simplified linear approximation for small temperature ranges is often useful:

$$V \approx S \cdot (T_{hot} - T_{cold})$$

Where $S$ is the Seebeck coefficient for the thermocouple material pair, measured in μV/°C.

Key Definitions

• Seebeck Effect: The phenomenon where a temperature difference between two dissimilar electrical conductors or semiconductors produces a voltage difference between the two substances.
• Seebeck Coefficient ($S$): The voltage generated per unit temperature difference between the hot and cold junctions of a thermocouple. It is not constant and varies with temperature.
• Cold Junction Compensation (CJC): The method used to automatically adjust the thermocouple's output voltage to account for the temperature at the reference (cold) junction, which is typically at the instrument or terminal block.

Common Thermocouple Types

While detailed properties may be in your References, this table summarizes key characteristics for common industrial thermocouples.

*Source: Engineering Toolbox, NIST ITS-90

References

• Original Source