There tends to be a lot of confusion around about how the measurement uncertainty of sensors is characterised and reported. Different manufacturers also tend to cite different measures of uncertainty, which can add to the difficulty: some will report the measure of error which looks the smallest (rather than the one which is most reflective of the uncertainty seen in service), as this makes the product appear more attractive.

There are a number of different types of error (of varying magnitude), and different measures of uncertainty include different combinations of them.

Zero drift

This is a very low-bandwidth, slow and random change in the signal returned by the sensor when it is subjected to zero input; this causes a simple linear shift in the measurements. There are a number of things which will cause zero drift: these are usually uncontrolled environmental factors, but may even in some cases be the aging of the sensor itself. The zero drift can be very large (typically 2% full-scale or more), but is easily corrected. This is done by applying zero input on the sensor and redefining the returned signal as ‘zero’. 

Zero drift is fairly normal and accepted in “comparator-type” instruments (like differential pressure sensors). It is not common for manufacturers to include zero-drift in the uncertainty cited: if they do, this will be “total error band” or TEB, and- for pressure sensors, at least- will typically be about 2% FS. Zero drift will dominate over all the other sources of error. Some data sheets will also cite “total error band after auto-zero” – which is the combined total error, excluding only the zero drift. For pressure sensors, this will typically be 0.2% FS to 1% FS, depending on the technology and manufacturer.

Residual temperature sensitivity

Many sensors will be sensitive not only to the primary measurand (like applied pressure) but will respond to other stimuli: because of its fundamental effect on material resistance, temperature will affect the output of most sensors. Many of the newer digital sensors will include a temperature sensing system and built-in temperature compensation: this means they have been factory-calibrated against both their primary measurand and against temperature, and can return the “correct” pressure at any applied temperature. There will usually be a finite ‘compensated temperature range’ (the range of temperatures over which the primary measurand has been calibrated).

The temperature correction, though, is not perfect. There will typically remain some residual temperature sensitivity. This is often the next largest component of total uncertainty (for pressure sensors, at least). If the error is measured at constant temperature after re-zeroing, both zero drift and residual temperature sensitivity are eliminated. This is often referred to as the “accuracy”, and for pressure sensors is typically 0.1% FS – 0.25% FS.

Calibration error

The next largest source of uncertainty (for most pressure sensors) is the calibration error, or the uncertainty of the calibration process itself; this is broadly equivalent to the uncertainty of the instruments providing the standard against which the sensor was calibrated.

Eliminating the calibration error from the uncertainty estimate is not a meaningful measure for factory-calibrated sensors, as this implies that the calibration test would take place after zeroing, at constant temperature, and after a high-order recalibration against a “perfect” reference. Eliminating calibration error from the uncertainty will yield a measure sometimes referred to as the “repeatability”: the maximum difference in signal between two measurements taken under the same applied conditions. For the case of pressure sensors, this repeatability would typically be 0.02% FS to 0.05% FS.

Minor sources of error

There are a number of other sources of error- for the specific case of pressure sensors, these will typically contribute a small but measurable amount of uncertainty (up to 0.05% FS)

Hysteresis: Hysteresis is an effect observed in many sensor types, and describes the uncertainty caused by a sensitivity to the sign of the gradient in the primary measurand (or, simply put, an electronic equivalent to mechanical backlash): measurements of the same pressure level tend to be higher if the pressure is increasing at the time of measurment, and lower if the pressure is decreasing.

Non-linearity: Pressure sensors are typically designed to have a linear response, so that the calibration curve is a straight line of fixed slope- and this response surface model is used in the internal data processing. In reality, the response is not perfectly linear- the difference between the ideal straight-line response assumed by the system and the true response is the non-linearity. For other sensors, the response may not be a straight line; in this case, the equivalent source of error would be the difference between the expected response (after which the calibration algorithm is modelled) and the actual response.

Gravity effects/orientation sensitivity: For some very sensitive pressure sensors (<1 kPa FS), the effect of gravity acting on the sensing membrane can be significant. Rotating the sensor so that the plane of the sensing membrane changes orientation relative to the gravity vector can therefore have a significant effect on the measured pressure. For the smallest range sensors available, this can be as much as 0.2% FS.

EMI/Noise: This is a measure of the sensitivity of the sensor to ambient electromagnetic interference, usually resulting in a very high frequency random signal superimposed on the output. Typically, for most modern digital sensors, this is very small (< 0.01% FS, or digital resolution-level) but can be large for the case of analogue sensors used in high-EMI environments (as in close proximity to switching power supplies, transformers or motor drives, for example). 

Digital resolution: For digital sensors, this is a measure of the smallest difference in the primary measurand which can be resolved by the analogue-to-digital converters. For an n-bit sensor, the digital resolution will be +/- 1/(2^n). For most advanced digital sensors, this is insignificant relative to other sources of uncertainty.