ENGINEERING

MEASUREMENTS

Prof. Dr. Emin Korkut

1
 Measuring Instrument Types
and Performance Characteristics
1. Review of instrument types
1.1 Active and Passive Instruments

Instruments can be subdivided into separate classes according to

several criteria. These classifications are made considering accuracy,
cost and general applicability to different applications.

Instruments are divided into: active or passive ones

According to whether the instrument output is entirely produced by

the quantity being measured or whether the quantity being
measured simply modulates the magnitude of some external power
source. 2
 An example of a passive instrument is the pressure-
measuring device shown in Figure 1.

Figure 1. Passive pressure gauge.

The pressure of the fluid is translated into a movement of a pointer

against a scale.
An example of an active instrument is a float-type petrol tank
level indicator as sketched in Figure 2.

Figure 2 Petrol-tank level indicator

(active instrument).

Here, the change in petrol level moves a potentiometer arm, and the
output signal consists of a proportion of the external voltage source
applied across the two ends of the potentiometer.
 1.2 Null-type and deflection-type instruments
• The pressure gauge just mentioned is a good example of a
deflection type of instrument, where the value of the quantity
being measured is displayed in terms of the amount of
movement of a pointer

An alternative type of pressure gauge is the deadweight gauge

shown in Figure 3, which is a null-type instrument.

Figure 3: Dead-weight pressure gauge.

1.3 Analogue and Digital Instruments
An analogue instrument gives an output that varies continuously as the
quantity being measured changes. The output can have an infinite number of
values within the range that the instrument is designed to measure. The
deflection-type of pressure gauge described earlier in this chapter (Figure 1) is
a good example of an analogue instrument. As the input value changes, the
pointer moves with a smooth continuous motion. Whilst the pointer can
therefore be in an infinite number of positions within its range of movement,
the number of different positions that the eye can discriminate between
is strictly limited, this discrimination being dependent upon how large the
scale is and how finely it is divided.

Figure 1. Passive
pressure gauge.
A digital instrument has an output that varies in discrete
steps and so can only have a finite number of values.

The rev counter sketched in Figure 4 is an example

of a digital instrument.

Figure 4
Rev counter
1.4 Indicating instruments and instruments with a
signal output

• Instruments merely give an audio or visual indication of

the magnitude of the physical quantity measured.

• Instruments that give an output in the form of a measurement

signal whose magnitude is proportional to the measured quantity.
1.5 Smart and non-smart instruments

• The advent of the microprocessor has created a new

division in instruments between those that do incorporate a
microprocessor (smart) and those that don’t.
 1.2 Static characteristics of instruments

If we have a thermometer in a room and its reading shows a

temperature of 20°C, then it does not really matter whether the
true temperature of the room is 19.5°C or 20.5°C. Such small
variations around 20°C are too small to affect whether we feel
warm enough or not. Our bodies cannot discriminate between
such close levels of temperature and therefore a thermometer
with an inaccuracy of ±0.5°C is perfectly adequate.
1.2.1 Accuracy and inaccuracy (measurement uncertainty)

• The accuracy of an instrument is a measure of how

close the output reading of the instrument is to the
correct value.

• In practice, it is more usual to quote the inaccuracy figure

rather than the accuracy figure for an instrument.

• Inaccuracy is the extent to which a reading might be wrong,

and is often quoted as a percentage of the full-scale (f.s.)
reading of an instrument.
• For example, a pressure gauge of range 0–10 bar has a
quoted inaccuracy of ±1.0% f.s. (±1% of full-scale
reading), then the maximum error to be expected in any
reading is 0.1 bar.

This means that when the instrument is reading 1.0 bar, the
possible error is 10% of this value.
 1.2.2 Precision/repeatability/reproducibility

Precision is a term that describes an instrument’s degree of

freedom from random errors.

Repeatability describes the closeness of output readings when

the same input is applied repetitively over a short period of time,
with the same measurement conditions, same instrument and
observer, same location and same conditions of use maintained
throughout.

Reproducibility describes the closeness of output readings for the

same input when there are changes in the method of measurement,
observer, measuring instrument, location, conditions of use and time
of measurement.
• The degree of repeatability
or reproducibility in
measurements from an
instrument is an alternative
way of expressing its
precision. Figure 5
illustrates this more clearly.

The figure shows the results of

tests on three industrial robots
that were programmed to
place components at a
particular point on a table.

Figure 5: Comparison of accuracy and

precision.
 1.2.3 Tolerance and Range or span

Tolerance is a term that is closely related to accuracy and

defines the maximum error that is to be expected in some value.

 For example one resistor chosen at random from a batch having a

nominal value 1000W and tolerance 5% might have an actual value
anywhere between 950W and 1050 W.

The range or span of an instrument defines the minimum and

maximum values of a quantity that the instrument is designed to
measure.
1.2.4 Linearity

 It is normally desirable that the output reading of an

instrument is linearly proportional to the quantity being
measured.

Figure 6: Instrument output characteristic.

 1.2.5 Sensitivity of measurement

• The sensitivity of measurement is a measure of the change in

instrument output that occurs when the quantity being measured
changes by a given amount. Thus, sensitivity is the ratio:
Example
The following resistance values of a platinum resistance
thermometer were measured at a range of temperatures.
Determine the measurement sensitivity of the instrument in
ohms/°C.

Solution
If these values are plotted on a graph, the straight-line relationship
between resistance change and temperature change is obvious. For a
change in temperature of 30°C, the change in resistance is 7. Hence
the measurement sensitivity = 7/30 = 0.233Ω/°C.
1.2.6 Threshold and Resolution

If the input to an instrument is gradually increased from zero,

the input will have to reach a certain minimum level before
the change in the instrument output reading is of a large
enough magnitude to be detectable. This minimum level of
input is known as the threshold of the instrument.

When an instrument is showing a particular output reading, there is

a lower limit on the magnitude of the change in the input measured
quantity that produces an observable change in the instrument
output. Like threshold, resolution is sometimes specified as an
absolute value and sometimes as a percentage of f.s. deflection.
 1.2.7 Sensitivity to disturbance

• All calibrations and specifications of an instrument are only

valid under controlled conditions of temperature, pressure etc.

• These standard ambient conditions are usually defined in the

instrument specification.

• As variations occur in the ambient temperatureetc., certain

static instrument characteristics change.

• The sensitivity to disturbance is a measure of the magnitude of this

change.

• Such environmental changes affect instruments in two main ways,

known as zero drift and sensitivity drift.
• Zero drift or bias describes the effect where the zero
reading of an instrument is modified by a change in
ambient conditions.

• Sensitivity drift (also known as scale factor drift)

defines the amount by which an instrument’s
sensitivity of measurement varies as ambient
conditions change.
Figure 7: Effects of disturbance: (a) zero drift, (b) sensitivity
drift, and (c) zero drift plus sensitivity drift.
Example
A spring balance is calibrated in an environment at a temperature
of 20°C and has the following deflection/load characteristics.

• It is then used in an environment at a temperature of 30°C and the

following deflection/load characteristic are measured.

Determine the zero drift and sensitivity drift per °C change in

ambient temperature.
Solution
At 20°C, deflection/load characteristic is a straight line.
Sensitivity = 20 mm/kg.

At 30°C, deflection/load characteristic is still a straight

line. Sensitivity = 22 mm/kg.

•Bias (zero drift) = 5mm (the no-load deflection)

•Sensitivity drift = 2 mm/kg

•Zero drift/°C = 5/10 = 0.5 mm/°C

•Sensitivity drift/°C = 2/10 = 0.2 (mm per kg)/°C

1.2.8 Hysteresis effects

Figure 8 illustrates the output characteristic of an instrument

that exhibits hysteresis.

Figure 8: Instrument characteristic with hysteresis.

• If the input measured quantity to the instrument is
steadily increased from a negative value, the output
reading varies in the manner shown in curve (a). If the
input variable is then steadily decreased, the output
varies in the manner shown in curve (b).

• The non-coincidence between these loading and

unloading curves is known as hysteresis.

• Two quantities are defined, maximum input hysteresis

and maximum output hysteresis, as shown in Figure 8.
1.2.9 Dead space
•Dead space is defined as the range of different input values
over which there is no change in output value.
•Any instrument that exhibits hysteresis also displays dead
space, as marked on Figure 8.

Figure 9: Instrument characteristic with dead space.

 1.3 Dynamic characteristics of instruments

The dynamic characteristics of a measuring instrument

describe its behavior between the time a measured quantity
changes value and the time when the instrument output attains
a steady value in response.

where qi is the measured quantity, q0 is the output reading and

a0 . . . an, b0 . . . bm are constants.
1.3.1 Zero order instrument
If all the coefficients a1 . . . an other than a0 in equation are
assumed zero, then:

where K is a constant known as the instrument sensitivity

Figure 10: Zero-order instrument characteristic.

1.3.2 First order instrument

If all the coefficients a2 . . . an except for a0 and a1 are

assumed zero in equation then:

If equation is solved analytically, the output quantity q0 in

response to a step change in qi at time t varies with time in the
manner shown in Figure 11.
Figure 11: First-order instrument characteristic.
Defining K = b0/a0 as the static sensitivity and as
the time constant of the system, equation becomes:
 1.3.3 Second order instrument

If all coefficients a3 . . . an other than a0, a1 and a2 in equation

are assumed zero, then we get:
The output responses of a second order instrument for
various values of following a step change in the value of the
measured quantity at time t are shown in Figure12.

Figure 12: Response characteristics of second-order instruments.