# Linearity in measuring devices

10/15/2010

Dear Control Engineering: Sometimes I see the term “linearity” used in reference to measuring devices. What does this mean?

Linearity reflects the ability of a sensor to respond to changes in a measured variable in the same way across the full range. If you’ve seen old pressure gages, they often have uneven scales where the divisions are larger at one end of the scale than the other. This compensates for non-linearities in the flexing of the bourdon tube. The same concepts apply to electronic devices, whether they are process instrments such a flowmeters, or discrete devices such as proximity sensors.

Let’s use a temperature sensor as an example. It has to convert a temperature to a voltage (thermocouple) or resistance (RTD, thermistor). As the temperature changes, the voltage or resistance has to change with it. If a device has high linearity, the amount of voltage or resistance change will be the same per change in temperature across the full range of the device.

In the case of a type K thermocouple, for example, when in roughly the middle of its measuring range (500 °C) a change of 10 °C will cause a change of 0.427 mV. If the device is truly linear, that change in voltage per degree will be the same over the entire measuring range. As a matter of fact, it isn’t. At the low extreme (-250 °C) a 10 °C change is 0.017 mV. At the opposite extreme of 1,370 °C, a 10 °C change is 0.340 mV.

Thermistors are generally regarded as non-linear. In an article The Challenges of Temperature Sensing, we included this graph of a typical thermistor response curve. What the graph shows is that at the low end of the range, a small change in temperature causes a large change in resistance. However the opposite is the case at the high end. The range of highest linearity for this device is roughly between -20 and 20 °C.

If you buy a temperature measuring device, or any other type of electronic sensor for that matter, the electronics in the transmitter will be designed to compensate for the non-linearities of the sensing element. You probably won’t even know that they’re there. The manufacturer will limit the effective range of the device such that it will cut off the worst areas at the extremes. If the behavior of the sensor is not predictable and repeatable beyond certain points, those areas should be excluded.

Peter Welander, pwelander@cfemedia.com

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