# Accuracy and Linearity of Pressure Sensors

The performance of a pressure transmitter is affected by many factors, relating to various aspects of instrumentation and the type of application. However, it is possible to say that the three most relevant aspects include hysteresis, linearity and repeatability, of which the first is the major contributor to inaccurate readings.

While most pressure sensor manufacturers club these three together by including them under a single value which denotes the total accuracy of the transmitter, Viatran pressure transmitters have the value of linearity specified separately from the second value which represents the contribution of hysteresis and repeatability, towards the accuracy.

## Linearity

An accurate graphical representation of the electrical output of a transmitter should form a straight line plot, covering the range from zero to full-scale pressure. However, in reality this is rarely seen, with minor deviations over the range of inputs being the case in most cases. This is attributed to many factors, including the type of technology used in the sensors, the geometry of the diaphragm used within the transmitter, and fundamental flaws in the material of which the sensors are constructed.

The property of linearity is defined as the degree to which the actual output curve of a transmitter resembles the expected linear plot, and is quantified as the greatest deviation of the curve from a straight reference line.

There are various methods of quantification of linearity, the first one being the terminal line technique. A terminal line is that which joins the value of the zero output signal from a transmitter to the full-scale output signal, as shown in the accompanying figure. Linearity is then the maximum deviation occurring in the transmitter output line from the terminal line, and is described in terms of a percentage of the full-scale range of the transmitter.

A second technique is the Best Fit Straight Line (BFSL) method. This is now widely used in the field of pressure transmitters, and uses the mathematical linear regression model to fit a straight line into the various output data points of the given transmitter. The points that fall above and below this BFSL are weighted equally, and therefore linearity in this paradigm is defined as the greatest deviation of the transmitter output curve from the BFSL.

When these two are compared, the BFSL technique apparently gives a linearity value that is two-fold better than that derived using the terminal line method, as seen in the figure. However, this is because the former method passes a line between the two parallel lines that lie in closest proximity, while using a calibration curve to enclose all the output vs. measurement values. On the other hand the terminal line technique uses one line to connect the two points at the extremes of the transmitter output signals.

Viatran has adopted the BFSL technique as standard on its line of pressure transmitters because of its universal utilization in this field, providing a level playing field for comparison between Viatran units and other pressure transmitters.

The engineers at Viatran make use of uniquely designed diaphragm geometries and linear compensating analog correction techniques to compensate for nonlinearity, and improve sensor performance, besides choosing the best materials and technologies for each type of application and pressure range.

## Hysteresis

A hysteresis error is one which is due to the variation in outputs from a transmitter when the same specific pressure is applied. This variation depends on whether the pressure was increased or decreased to reach the preset point. In some situations, a transmitter which has significant hysteresis error gives a higher reading when the pressure is increased from 0 PSI to 50 PSI, than when it is reduced from 100 PSI to 50 PSI, as shown in the figure below. The difference between these two signal outputs is the hysteresis error. Viatran pressure sensing units show the hysteresis error as a percentage of the full-scale pressure.

## Repeatability

The property of repeatability refers to the capability of a pressure transmitter to provide the same output when the same pressure input is supplied in different rounds.

When a pressure transmitter has repeatability at zero pressure, it means simply that the output at zero pressure after two independent full-scale applications is measured and found to be the same both times. However, there may be a very small difference because of mechanical or electrical variations, which is called zero repeatability error.

Repeatability error may be quantified by looking at the variation between the outputs for both independent but equal pressure applications, and its value is given as a percentage of the full-scale pressure.

Both repeatability and hysteresis error measure the variability in output signals for a single pressure input, and it is for this reason that Viatran units state both these values in one quantity called “Hysteresis and Repeatability” in the product catalogs.

These two values are significantly affected by the mechanical and material properties of the diaphragm and the sensor. Thus Viatran pressure transmitters are engineered using carefully selected materials for both diaphragm and sensor, to offer maximum durability and minimal room for error due to these two properties.

This information has been sourced, reviewed and adapted from materials provided by Viatran.

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