Linearisation for Thermocouples and RTDs

Linearisation is a greater challenge for thermocouples than for resistance temperature detectors (RTDs). Thermocouples have a non-linear relationship between their thermoelectric output (EMF) and temperature—except over very narrow ranges. For this reason, the EMF-to-temperature response must be corrected to produce accurate measurements.

The IEC 60584-1 standard provides comprehensive EMF vs. temperature tables for all standard thermocouple types, assuming a 0°C reference junction. It also outlines mathematical approximations of these relationships. For example, the Type K thermocouple uses an eight-term power series plus an exponential term, with constants given to 11 significant figures. Type R is similar but even more complex—covering the range from -50°C to 1767.6°C requires four different polynomial equations, ranging from third to seventh order.

RTDs, in contrast, have a much more predictable resistance-to-temperature response. Standard platinum RTDs follow a relatively simple quadratic equation, defined in IEC 60751. In most cases, this can be modelled using a second-order polynomial; at most, a third-order term may be required. Other RTD materials, such as copper, exhibit an almost linear resistance change over their operating range, making linearisation even simpler.

However, RTDs can still be affected by non-linearities—not from the sensor itself, but from the measurement system. If the RTD is measured using a null-balance bridge or a potentiometric system, there is no added error. But in fixed bridge circuits, some non-linearity can result due to the constant power draw of the bridge. If the system uses a high-impedance amplifier or digital readout, this is generally not an issue. But where low-impedance devices like galvanometers are used, these effects must be corrected.

Today, most linearisation is handled digitally using microprocessor-based systems. The typical approach involves curve fitting—breaking the EMF or resistance relationship into small linear segments stored in a look-up table. These segments are continuous at their boundaries but differ in slope, and accuracy improves with the number of segments. Since modern digital instruments have ample memory and processing power, this method can closely match the official reference tables for thermocouples and RTDs. Many instruments support multiple sensor types, switching between different ROM segments to match the linearisation requirements.

Alternatively, linearisation can be performed as a continuous function using analogue electronics. These circuits combine logarithmic, exponential, power, and root modules to simulate the sensor characteristic. However, their accuracy is usually limited to around ±0.2% over a few hundred degrees.

In practice, most modern digital instruments use real-time digital linearisation immediately after analogue-to-digital conversion. These systems model the thermocouple or RTD response using coefficients stored in memory, eliminating the discontinuities of segmented approaches and enabling very high measurement accuracy.