How to Convert Resistance (Ω) to Temperature (°C) Using RTDs & Thermocouples in Industry
In the world of industrial automation and process control, accurate temperature measurement is vital. Two of the most widely used devices for this purpose are RTDs (Resistance Temperature Detectors) and thermocouples. However, these sensors output signals in different formats—RTDs as resistance in ohms (Ω) and thermocouples as millivolts (mV). Understanding how to convert resistance to temperature is crucial for integrating these devices into your control systems effectively.
This guide explores the conversion process from resistance to temperature for RTDs and thermocouples, including the relevant equations, standards, and application-specific considerations.
Understanding RTDs and Thermocouples
What Is an RTD?
An RTD works on the principle that the resistance of certain metals (commonly platinum) changes predictably with temperature. The most commonly used RTD is the Pt100, which has a resistance of 100 ohms at 0°C.
What Is a Thermocouple?
A thermocouple consists of two dissimilar metals joined at one end. It generates a voltage that varies with temperature, typically in millivolts. This voltage must be converted to temperature using a reference lookup table or polynomial formula.
RTD – Resistance to Temperature Conversion
The Callendar–Van Dusen Equation
For high-accuracy applications, RTDs use the Callendar–Van Dusen equation:
For temperatures between 0°C and 850°C:
(T) = R0 × (1 + A×T + B×T²)
Where:
- R(T) = resistance at temperature T (in °C)
- R0 = resistance at 0°C (typically 100 Ω for Pt100)
- A, B = constants derived from the material (Platinum: A = 3.9083×10⁻³, B = -5.775×10⁻⁷)
For temperatures below 0°C:
(T) = R0 × (1 + A×T + B×T² + C×(T - 100)×T³)
Note: Constant C = -4.183×10⁻¹² for standard platinum RTDs.
Example Calculation
Assume R(T) = 119.4 Ω, and R0 = 100 Ω.
To find T:
Use the inverse of the Callendar–Van Dusen equation or a pre-calibrated RTD table from standards like IEC 60751.
Thermocouple – Voltage to Temperature Conversion
Thermocouples do not use resistance but voltage output (mV). However, some systems may involve signal conditioning where RTD output is simulated via resistance.
Standard Thermocouple Types
| Type | Temp Range (°C) | Accuracy | Common Use |
|---|---|---|---|
| K | -200 to 1370 | ±2.2°C | General industrial use |
| J | -40 to 750 | ±2.2°C | Plastics industry |
| T | -200 to 370 | ±1.0°C | Cryogenics, labs |
| E | -200 to 900 | ±1.7°C | Low-temp sensitivity |
| N | -200 to 1300 | ±2.2°C | High stability |
NIST Polynomial Equation
The voltage-to-temperature relationship is defined by a polynomial:
(°C) = a0 + a1×V + a2×V² + ... + an×Vⁿ
Where V is the thermocouple voltage (in mV), and coefficients a0 through an are determined by the thermocouple type.
Cold Junction Compensation (CJC)
Always apply cold junction compensation—since thermocouple output is the temperature difference between the hot and reference junctions.
Using Converters, Transmitters, and Software
Modern industrial systems rarely do manual conversions. Instead, they use:
Temperature Transmitters
Transmitters (e.g., Rosemount 644, Siemens TH300) convert RTD or thermocouple signals into standardized outputs like 4–20 mA or HART digital.
PLCs and DCS Integration
Controllers from Siemens, Allen-Bradley, or Honeywell can accept analog/resistance signals and convert them using built-in scaling blocks or function modules.
| Sensor Type | Signal Type | Conversion Method |
|---|---|---|
| RTD (Pt100) | Resistance (Ω) | Lookup table or formula |
| Thermocouple | mV | Polynomial or lookup table |
| Transmitter | 4–20 mA | Linear scaling in PLC |
Best Practices for Industrial Applications
Use Standardized Tables
Rely on IEC 60751 for RTDs and NIST ITS-90 for thermocouples. These tables ensure consistency and are widely supported by most controllers and transmitters.
Avoid Long Lead Errors
For RTDs, use 3-wire or 4-wire configurations to eliminate lead wire resistance. This ensures accurate readings, especially in long cable runs.
Calibrate and Maintain
Perform routine calibration of temperature instruments using simulators to ensure accuracy. Clean and inspect thermowells or sensor sheaths for wear and fouling.
Conclusion
Accurate temperature measurement in industry hinges on understanding how to convert RTD resistance or thermocouple voltage into temperature. Whether using equations, tables, or transmitters, the key is selecting the right sensor, understanding its conversion method, and applying proper integration with your DCS or PLC.
By mastering these conversions and following best practices, you ensure precision, process safety, and operational efficiency in any industrial setup.