## Other Characteristics of Measurement Systems Linearity and Resolution

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Accuracy, precision, and sensitivity are the characteristics that sufficiently describe the static behavior of a sensor. But sometimes other characteristics
are added or substituted for them when it is necessary to describe alternative behavi...

Accuracy, precision, and sensitivity are the characteristics that sufficiently describe the static behavior of a sensor. But sometimes other characteristics
are added or substituted for them when it is necessary to describe alternative behavior or behavior that is of particular interest for a given case; likewise
characteristics can be added that are complementary to describe the suitability of a measurement system for a specific application. The linearity describes the closeness between the calibration curve and a specified straight line. Depending on which straight line is considered, several definitions apply.

Independent Linearity. The straight line is defined by the least squares criterion. With this system the maximal positive error and the minimal negative error are equal. This is the method that usually gives the "best" quality.

• Zero-Based Linearity. The straight line is also defined by the least squares criterion but with the additional restriction of passing through zero.
Terminal-Based Linearity. The straight line is defined by the output corresponding to the lower input and the theoretical output when the
higher input is applied.
End-Points Linearity. The straight line is defined by the real output when the input is the minimum of the measurement range and the output when the input is the maximum.
Theoretical Linearity. The straight line is defined by the theoretical predictions when designing the sensor.

Figure 1.6 shows these different straight lines for a sensor with a given calibration curve. In sum, the linearity of a curve indicates to what extent a
sensor's sensitivity is constant. Nevertheless, for a sensor to be acceptable, it does not need to have a high linearity. The interest of linearity is that when
sensitivity is constant, ii is easier to make the conversion from reading to measured value. It is only necessary to multiply the reading by a constant
value in order to know the input. In linear instruments the nonlinearity equals the inaccuracy.

Today, with microprocessors capable of being incorporated in measurement systems, there is more interest in repeatability than in linearity because we can produce a look-up table giving input values corresponding to measured values. By using interpolation. it is possible to reduce the size of that
table to a reasonable dimension.

The main factors that influence linearity are resolution, threshold, and hysteresis.

The resolution (or discrimination) is the minimal change of the input necessary to produce a detectable change at the output. When the input
increment is from zero, then it is called the threshold.

The hysteresrs refers to the difference between two output values that correspond to the same input, depending on the direction (increasing or
decreasing) of successive input values. That is, in a way similar to the magnetization in ferromagnetic materials, it can happen that the output corresponding to a given input depends on whether the previous input was higher or lower than the present one.

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