Important qualities such as nonlinearity can have different values depending on how they are measured.
Setra Systems Inc.
Pressure transducers have begun to play a more important part in monitoring and controlling critical industrial processes. Applications as diverse as stack gas monitoring and laser interferometers now depend on accurate readings from capacitive pressure sensors. These devices, which incorporate a diaphragm that flexes slightly under pressure, are known for their high sensitivity and exhibit high accuracy, repeatability, and long-term stability.
It is important that designers working with these devices understand how critical specifications are derived. Key terms that include accuracy, nonlinearity, hysteresis, nonrepeatability, and long-term stability have definitions that depend on the technique used to calculate them.
Accuracy figures for capacitive pressure sensors generally are expressed as some percentage of a full scale measurement at a constant temperature. This accuracy reading is actually calculated by taking the square root of a sum-of-squares (root sum squares, or RSS). There are three squared terms in the equation: nonlinearity, hysteresis, and nonrepeatability. Thus, as an example, say a given capacitive pressure sensor had a nonlinearity of ±0.1%, hysteresis of ±0.05%, and nonrepeatability of ±0.02%. The calculated accuracy would be √((±0.1%)2+ (±0.05%)2+ (±0.02%)2)= √(0.01%+ 0.0025%+ 0.0004%)= √0.0129%= ±0.11% FS at constant temperature.
Nonlinearity can be defined in three ways. The best-fit-straight-line method gives readings that relate a calibration curve to a specified straight line. Deviations from the straight line are provided in terms of percentage of a full-scale reading. In contrast, nonlinearity specifications based on an end point method use a straight line that extends through the end points of the calibration curve. Finally, the terminal method of specifying nonlinearity gives the degree of deviation of a calibration curve from a specified straight line having end points at zero and full scale.
Several other specifications illuminate important qualities of pressure sensors. Hysteresis is the maximum difference in output at any pressure value within the specified range, when the value is approached with increasing and decreasing pressure. Nonrepeatability is the ability of a transducer to reproduce output readings when the same pressure value is applied to it consecutively, under the same conditions, and from the same direction. Long-term stability is how well a transducer can reproduce output readings obtained during its original calibration at room conditions for a specified period of time.
Zero output is factory set to within a certain percent of full scale. But a factor known as zero offset results in a shift up or down of the calibration curve. This offset does not degrade linearity or accuracy, however. Likewise, span output is factory set to within a certain percent of full scale. Span offset results in a change in the slope of the curve, but doesn’t worsen linearity or accuracy.
Temperature changes can change the zero and span output. The specifications that describe this behavior are thermal zero shift and thermal span shift. Both are specified as a maximum percentage of full-scale shift seen over a given temperature range, usually 100°F. These are then used to calculate the percent of full-scale shift expected for an application’s maximum temperature.
For example, say thermal zero shift and span shift for a given sensor were <±0.4% FS/100°F and<±0.3% FS/100°F respectively. If the compensated temperature range was –10 to 130°F for an application in question, the maximum temperature change from room temperature (70°F) would be 80°F.
The maximum thermal zero shift thus would be 80°F30.4%=0.32% FS. Similarly, the maximum thermal span shift would be 80°F30.3%=0.24% FS. Thus both zero and span shift from thermal effects over the anticipated temperature range would be less than these calculated maximums.
The total error band for a given capacitive pressure sensor would just be the sum of the various error terms over the anticipated temperature range. For the previous example, this would be the calculated thermal zero and span shifts (<±0.32% FS and <±0.24% FS respectively) summed with zero and span offsets, nonlinearity, hysteresis, and nonrepeatability errors. The long-term stability error generally is left out of these calculations.