Instrumentation and

Measurement (Lecture 2)
By
ADNAN FAZIL & AKHTAR HANIF

Department of Mechanical Engineering

Air University

Instrument Types
and
Performance Characteristics

Active and Passive Instruments

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.
An example of a passive instrument is the

pressure-measuring device shown in Figure

2.1.
An example of an active instrument is a float-

type petrol tank level indicator as sketched in

Figure 2.2.
The primary transducer float system is merely

modulating the value of the voltage from this

external power source.
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Active and Passive Instruments

One very important difference between active and

passive instruments is the level of measurement

resolution that can be obtained.
While it is possible to increase measurement resolution

by making the pointer longer, the scope for such

improvement is clearly restricted by the practical limit of
how long the pointer can conveniently be.
In an active instrument, however, adjustment of the

magnitude of the external energy input allows much

greater control over measurement resolution.
In terms of resolution: active instruments
In terms of cost: passive instruments

Balancing the measurement resolution requirements

against cost.
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NULL-TYPE AND DEFLECTION-TYPE

INSTRUMENTS
Null-type

and

deflection-type

instruments
Deadweight gauge shown in Figure

2.3, which is a null-type instrument.

Deflection

type depends on the

linearity and calibration of the spring,
whilst for the second it relies on the
calibration of the weights

Calibration of weights is much easier

Deflection type instrument is clearly

more convenient
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ANALOG 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 2.1) is a good example of
an analogue instrument.
A digital instrument has an output that varies in discrete steps and

so can only have a finite number of values. The revolution counter

sketched in Figure 2.4 is an example of a digital instrument

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DIGITAL INSTRUMENTS
A cam is attached to the revolving body whose motion is being

measured, and on each revolution the cam opens and closes a

switch. The switching operations are counted by an electronic
counter. This system can only count whole revolutions and
cannot discriminate any motion that is less than a full
revolution.

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ANALOGUE AND DIGITAL

INSTRUMENTS
Any digital computer system performs its computations in digital

form. An instrument whose output is in digital form is therefore

particularly advantageous in such applications, as it can be
interfaced directly to the control computer.
Analogue instruments must be interfaced to the microcomputer by

an analogue-to-digital (A/D) converter, which converts the

analogue output signal from the instrument into an equivalent
digital quantity that can be read into the computer.
A/D converter adds a significant cost to the system.
A finite time is involved in the process of converting an analogue

signal to a digital quantity, and this time can be critical in the

control of fast processes
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INDICATING INSTRUMENTS AND

INSTRUMENTS WITH A SIGNAL OUTPUT
The final way in which instruments can be divided is between

those that merely give an audio or visual indication of the

magnitude of the physical quantity measured and those that
give an output in the form of a measurement signal whose
magnitude is proportional to the measured quantity.
Indicating Instruments: can also be further divided into those

that have an analogue output and those that have a digital

display

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INDICATING INSTRUMENTS AND

INSTRUMENTS WITH A SIGNAL OUTPUT

One major drawback with indicating devices is that human

intervention is required to read and record a measurement.

Instruments that have a signal-type output are commonly used

as part of automatic control systems. In other circumstances,

they can also be found in measurement systems where the
output measurement signal is recorded in some way for later
use.

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STATIC CHARACTERISTICS OF
INSTRUMENTS
Accuracy and inaccuracy (measurement uncertainty)
Precision/repeatability/reproducibility
Tolerance
Range or span
Linearity

Sensitivity of measurement
Threshold
Resolution
Sensitivity to disturbance
Hysteresis effects
Dead space
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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.

If, for example, a pressure gauge of range 010 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.
Thus, if we were measuring pressures with expected values

between 0 and 1 bar, we would not use an instrument with a

range of 010 bar.
The term measurement uncertainty is frequently used in place of

inaccuracy.
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PRECISION/ REPEATABILITY/
REPRODUCIBILITY
Precision is a term that describes an instruments degree of

freedom from random errors.

If a large number of readings are taken of the same quantity by a

high precision instrument, then the spread of readings will be very

small.
Precision is often confused with accuracy.
High precision does not imply anything about measurement accuracy.
A high precision instrument may have a low accuracy.

Low accuracy measurements from a high precision instrument are

normally caused by a bias in the measurements, which is removable

by recalibration.

The terms repeatability and reproducibility mean approximately

the same but are applied in different contexts.

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PRECISION/ REPEATABILITY/
REPRODUCIBILITY
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 or time of measurement.

Both terms describe the spread of output readings for the same

input.
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PRECISION/ REPEATABILITY/
REPRODUCIBILITY

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TOLERANCE
Tolerance is a term that is closely related to accuracy and defines

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

Strictly speaking, Tolerance is not a static characteristic of

measuring instruments,
it is mentioned here because the accuracy of some instruments

is sometimes quoted as tolerance.

When used correctly, tolerance describes the maximum deviation

of a manufactured component from some specified value

One resistor chosen at random from a batch having a nominal

value 1000 and tolerance 5% might have an actual value

anywhere between 950 and 1050 .
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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.

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LINEARITY
It is normally desirable that the output

reading of an instrument is linearly

proportional to the quantity being measured.
The Figure show a plot of the typical output

readings of an instrument when a sequence of

input quantities are applied to it.
Normal procedure is to draw a good fit straight

line through the Xs

This can often be done with reasonable

accuracy by eye yet it is always preferable to

apply a mathematical least-squares line-fitting
techniques

The non-linearity is then defined as the

maximum deviation of any of the output

readings from this straight line.
Non-linearity is usually expressed as a

percentage of full-scale reading.

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SENSITIVITY OF MEASUREMENT

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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 30C, the change in resistance is 7. Hence
the measurement sensitivity = 7/30 = 0.233 /C.
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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.
Manufacturers vary in the way that they specify threshold for

instruments.
Some quote absolute values,

others quote threshold as a percentage of full-scale readings.

As an illustration, a car speedometer typically has a threshold of about

15 km/h.
This means that, if the vehicle starts from rest and accelerates, no output

reading is observed on the speedometer until the speed reaches 15 km/h.

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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.

One of the major factors influencing the resolution of an

instrument is how finely its output scale is divided into

subdivisions.
Using a car speedometer as an example again,
This has subdivisions of typically 20 km/h.
This means that when the needle is between the scale markings, we

cannot estimate speed more accurately than to the nearest 5 km/h.

This figure of 5 km/h thus represents the resolution of the instrument.
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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, and 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 is sometimes known
by the alternative term, bias.

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SENSITIVITY TO DISTURBANCE

Zero drift or bias

describes the effect where the zero reading of an instrument is

modified by a change in ambient conditions.

Zero drift is normally removable by calibration.

Sensitivity drift (also known as scale factor drift)

defines the amount by which an instruments sensitivity of

measurement varies as ambient conditions change.

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SENSITIVITY TO DISTURBANCE

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HYSTERESIS EFFECTS
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

Devices like the mechanical flyball (a device for measuring

rotational velocity) suffer hysteresis from both of the above

sources because they have friction in moving parts and also
contain a spring.
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HYSTERESIS EFFECTS

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DEAD SPACE
Dead space is defined as the range of different input values

over which there is no change in output value.

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QUIZ 1
A spring balance is calibrated in an environment at a temperature of

20C and has the following deflection/load characteristic.

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

following deflection/load characteristic is measured.

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

temperature.
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SIGNALS AND DYNAMIC

CHARACTERISTICS OF INSTRUMENTS
Important type of signals
Step signal
Ramp signal
Sinusoidal signal
Dynamic characteristics of instruments
Zero order instruments
First order instruments
Second order instruments

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STEP SIGNAL

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RAMP SIGNAL

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SINUSOIDAL SIGNAL

x(t)=cos(t)

x(t)=sin(t)

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DYNAMIC CHARACTERISTICS OF
INSTRUMENTS
The static characteristics of measuring instruments are
concerned only with the steady state reading that the instrument
settles down to, such as the accuracy of the reading etc.
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.

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DYNAMIC CHARACTERISTICS OF
INSTRUMENTS
For an LTI system following relation can be written between input and output for

time t greater than zero.

Where
qi is the measured quantity,
q0 is the output reading and
a0 . . . an, b0 . . . bm are constants.
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DYNAMIC CHARACTERISTICS OF
INSTRUMENTS

If we limit consideration to that of step changes in the measured quantity only

then equation reduces to:

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ZERO ORDER INSTRUMENT

If all the coefficients a1 . . . an other than a0 in equation (2.2) are assumed

zero, then:

Any instrument that behaves according to equation (2.3) is said to be of zero

order type.

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ZERO ORDER INSTRUMENT

Following a step change in the measured quantity at time t, the instrument

output moves immediately to a new value at the same time instant t, as shown
in Figure

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ZERO ORDER INSTRUMENT

A potentiometer, which measures motion, is a good example of such

an instrument,
The output voltage changes instantaneously as the slider is displaced

along the potentiometer track.

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FIRST ORDER INSTRUMENT

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

equation then:

Any instrument that behaves according to the above equation is known as a

first order instrument.

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FIRST ORDER INSTRUMENT

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SECOND ORDER INSTRUMENT

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

zero, then we get:

K (static sensitivity),
(un-damped natural frequency) and
(damping ratio)

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RESPONSE CHARACTERISTICS OF
SECOND ORDER INSTRUMENTS

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