# Static Characteristics Of Transducers

Wednesday, November 29th, 2017 - Transducer/Sensor

## Static Characteristics Of Transducers

Static characteristics describe the device performance at room conditions (i.e. at a temperature of 25 ± 10 degrees Celsius, a relative humidity of 90% or less and a barometric pressure of 880-1080 mbar) , with very slow changes in the measurand and in the absence of any mechanical shock (unless this latter happens to be the measurand). Static characteristics include: linearity, accuracy, stability, precision, sensitivity and resolution.

### Linearity Of Transducer

Linearity–can be defined as the variation in the constant of proportionality between the input physical quantity and the output electrical signal. A sensor or a transducer is therefore said to be linear when the constant of proportionality has the same value within the whole measurand range (i.e. when the graph relating input to output is a straight line). The linearity error is expressed as a percentage of the maximum electrical output value. For example, in Figure 1.1 the dotted line shows the theoretical straight line of maximum linearity within the measurand range. Curve ‘a’ shows the output characteristic for a device which is linear up to 70% of the measurand range and then exibits increasing deviation from straight line linearity. This behaviour is often known as ‘output saturation’ and affects most transducers, particularly optical ones.

Curve ‘b’ shows the output characteristic of a transducer with a marked non-linear behaviour throughout the measurand range. The linearity error for device ‘b’ would therefore be +8.6%, -3.4% FSO (full-scale output) with respect to the terminal linearity curve. In fact it is meaningless to quote a linearity error without stating what sort of straight line it uses as reference. The choice of this straight line depends on the device output curve and its applications; as shown in Figures 1.2-1.5 there are four main types of curve used for linearity calculations:

(a) Theoretical slope

The straight line between the theoretical end points. Usually 0-100% for both FSO and range-in which case it is called the ‘terminal line’ (see dotted line in Figure 1.2)-or it can purposely be offset to suit certain applications (see broken line).

(b) End-point line

The straight line between the end points, namely the output values at the upper and lower measurand range limits obtained during anyone calibration (see broken line in Figure 1.3).

(c) Best straight line A line midway between the two parallel straight lines which are closest together and envelop all the output values obtained during calibration  (see broken line in Figure 1.4).

### Precision Of Transducers

Precision–can be defined as the tolerance within which a measurement can be repeated (e.g. the ability of a device to give the same output value

when the same input value is applied to it). Precision is normally expressed as a percentage of FSO and is sometimes referred to as repeatability. Note that the measurement must be carried out always in the same way to avoid hysteresis problems. See Figure 1.6.

### Hysteresis Of Transducers Hysteresis–can be defined as the maximum difference in the output values obtained by covering the measurand range first in the increasing direction  (i.e. from zero to 100%) and then in the decreasing direction (i.e. from 100% to zero). See Figure 1.7.

### Sensitivity Of Transducers

Sensitivity-can be defined as the relationship between the variations in the output electrical quantity and the corresponding variations in the input physical quantity.

### Resolution Of Transducer Resolution-can be defined as the magnitude of the output step changes produced by a continuously varying measurand. Normally expressed as a percentage of FSO. For digital output devices resolution is given by the number of bits in the output data word(s) or, in the case of incremental position transducers, by the number of states obtained per unit measurand change. Figure 1.8 shows the output for a wirewound potentiometer with a very poor resolution of 2.5% FSO.