2

Instrument types and

performance characteristics
2.1 Review of instrument types
• Instruments can be subdivided into separate
classes according to several criteria.
• These subclassifications are useful in broadly
establishing several attributes of particular
instruments such as accuracy, cost, and
general applicability to different applications.
2.1.1 Active and passive instruments
• An example of a passive instrument is the
pressure-measuring device shown in Figure
2.1. The pressure of the fluid is translated into
a movement of a pointer against a scale.
passive instruments
• An example of an active instrument is a float-
type petrol tank level indicator as sketched in
Figure 2.2. 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.
Active instruments
2.1.2 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 2.3, which
is a null-type instrument.
Null-type instrument
2.1.3 Analogue and digital
instruments
• An analogue instrument gives an output that
varies continuously as the quantity being
measured changes (Figure 2.1).

• 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 2.4 is an example of a digital
instrument.
Digital instruments
2.1.4 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.
2.1.5 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.
2.2 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.
• If we had to measure the temperature of certain
chemical processes, however, a variation of
0.5°C might have a significant effect on the
rate of reaction or even the products of a
process. A measurement inaccuracy much less
than ±0.5°C is therefore clearly required.
• Accuracy of measurement is thus one
consideration in the choice of instrument for a
particular application.
• Other parameters such as sensitivity, linearity
and the reaction to ambient temperature
changes are further considerations.
2.2.1 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.
• If, 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.
2.2.2 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 2.5 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.
2.2.3 Tolerance
• 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.
2.2.4 Range or span

• The range or span of an instrument defines the

minimum and maximum values of a quantity
that the instrument is designed to measure.
2.2.5 Linearity
• It is normally desirable that the output reading
of an instrument is linearly proportional to the
quantity being measured.
2.2.6 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:

scale deflection
value of measurand producing deflection
• 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.

Resistance (Ω) Temperature (°C)

307 200
314 230
321 260
328 290
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.
2.2.7 Threshold
• 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.
2.2.8 Resolution
• 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.
2.2.9 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 temperature
etc., 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.
• Example
A spring balance is calibrated in an
environment at a temperature of 20°C and has
the following deflection/load characteristic.

Load (kg) 0 1 2 3
Deflection (mm) 0 20 40 60
• It is then used in an environment at a
temperature of 30°C and the following
deflection/load characteristic is measured.

Load (kg): 0 1 2 3
Deflection (mm) 5 27 49 71

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
2.2.10 Hysteresis effects
• Figure 2.8 illustrates the output characteristic
of an instrument that exhibits 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 2.8.
2.2.11 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 2.8.
2.3 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.

• If we limit consideration to that of step

changes in the measured quantity only, then
equation reduces to:
2.3.1 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 as defined earlier.
2.3.2 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 2.11.
 𝑎1 𝑑𝑞0 𝑏0
+ 𝑞0 = 𝑞𝑖
𝑎0 𝑑𝑡 𝑎0

Defining K = b0/a0 as the static sensitivity and

 = a1/a0 as the time constant of the system,
equation becomes:

𝑑𝑞0
 + 𝑞0 = 𝐾 𝑞𝑖
𝑑𝑡
2.3.3 Second order instrument
• If all coefficients a3 . . . an other than a0, a1
and a2 in equation are assumed zero, then we
get:
 𝑎2 𝑑 2 𝑞0 𝑎1 𝑑𝑞0 𝑏0
2
+ + 𝑞0 = 𝑞𝑖
𝑎0 𝑑𝑡 𝑎0 𝑑𝑡 𝑎0
It is convenient to re-express the variables a0,
a1, a2 and b0 in equation in terms of three
parameters K (static sensitivity), ω (undamped
natural frequency) and  (damping ratio),
where:

1 𝑑 2 𝑞0 2 𝑑𝑞0
2 2
+ + 𝑞0 = 𝐾𝑞𝑖
𝜔 𝑑𝑡 𝜔 𝑑𝑡

𝑏0 2
𝑎0 𝑎1 𝜔
𝐾= , 𝜔 = , =
𝑎0 𝑎2 2𝑎0
• 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 Figure 2.12.