This document outlines the course objectives and syllabus for a Measurements and Instrumentation course. The course aims to: [1] Familiarize students with measuring instrument characteristics and concepts of analog and digital instruments; [2] Teach students how to evaluate instrument performance using bridges, transducers, and different measurement techniques; and [3] Demonstrate various transducers and sensors used to measure physical quantities. The syllabus covers 5 units - science of measurements, analog instruments, digital instruments, comparative measurement methods, and transducers and data acquisition systems. Key topics include instrument elements, static and dynamic performance, error analysis, and an overview of common measurement devices.

1. DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING

2. 20EE403 - MEASUREMENTS AND
INSTRUMENTATION
 COURSE OBJECTIVES:
The students should be made to
 Know the characteristics of measuring instruments
 Understand the concept of analog and digital instruments
 Obtain the performance of bridges and transducers
 Compare various measurement techniques using different instruments
 Illustrate the various transducers and sensors to measure the quantity

3. SYLLABUS
 UNIT I SCIENCE OF MEASUREMENTS
Science of measurements: Importance of measurement - Methods of
measurement - Functional elements of an instrument - Static and dynamic
characteristics - Errors in measurement - Statistical evaluation of measurement data
- Standards and calibration.
 UNIT II ANALOG INSTRUMENTS
Introduction to analog measuring instruments - Construction, principle and
applications of Moving coil instruments - Moving iron instruments -
Dynamometer type instrument - Induction type instrument - Statistical analysis
of error data (Simple problems) - Error correction methods - Instrument
transformer - Measurements of power using CT and PT.
 UNIT Ill· DIGITAL INSTRUMENTS
Principle and it's applications - Digital voltmeter - Digital multi meter - Digital
frequency meter - Digital Storage Oscilloscope - LCR meter - Phase meter -
Harmonic analyser - Spectrum analyser - Concepts of smart meters.

4.  UNIT IV COMPARATIVE METHODS OF MEASUREMENTS
DC potentiometers, DC bridges (Wheatstone, Kelvin and Kelvin double bridge)
and AC bridges (Maxwell, Anderson and Schering bridges), Transformer ratio bridges,
Self-balancing bridges - Measurement of flux density - Measurement of iron loss -
Electrostatic and electromagnetic interference.
 UNIT V TRANSDUCERS AND DATA ACQUISITION SYSTEMS
Classification of transducers - Selection of transducers - Resistive, capacitive and
inductive transducers - Piezoelectric, hall effect, optical and digital transducers -
Elements of data acquisition system - Smart sensors – Data Loggers.

5. WHY M&I
 In electrical engineering we deal with voltage, current, energy, frequency,
resistance, inductance, capacitance, etc. To deal with these parameters we have to
first measure them. That’s where we need Instrumentation.
 Without Instrumentation one cannot be able to produce any instrument to
measure these parameters which includes oscilloscopes, multimeters, wattmeters,
etc.

6. Need for Measuring Instruments:
 Measurement is perhaps one of the most fundamental concepts in Engineering.
 Without the ability to measure, it would be difficult for scientists to conduct
experiments or form theories.
 Not only is measurement important in Engineering, it is also essential in farming,
construction, manufacturing, commerce, and numerous other occupations and
activities.
 The word “measurement” comes from the Greek word “metron,” which means
“limited proportion”.
 Measurements require tools and provide scientists with a quantity. A quantity
describes how much of something there is or how many there are.
 An Instrument is always needed to measure any quantity

7. UNIT – I
SCIENCE OF MEASUREMENTS
Science of measurements: Importance of measurement - Methods of
measurement - Functional elements of an instrument - Static and dynamic
characteristics - Errors in measurement - Statistical evaluation of measurement data
- Standards and calibration.

8. INTRODUCTION
 The measurement of a given quantity is essentially an act or
the result of comparison between the quantity (whose
magnitude is unknown) and a predefined standard.
Since two quantities are compared, the result is expressed in
numerical values.
In fact, measurement is the process by which one can
convert physical parameters to meaningful numbers.

9.  The measuring process is one in which the property of an
object or system under consideration is compared to an
accepted standard unit, a standard defined for the particular
property.
Basic requirements:
1. The standard used for comparison purpose must be
accurately defined and should be commonly accepted.
2. The apparatus used and the method adopted must be
provable.

10. BASICS OF MEASUREMENT
 Measurements is a vast field which embraces detection,
acquisition control and analysis of data.
 It involves the measurement of physical, electrical,
mechanical, optical and chemical quantities and plays a very
significant role in every branch of scientific research and
engineering process which include control systems, process
Instrumentation and data reduction.
There are two major function of all branch of engineering
Design of equipment and processes and
 Proper operation control and maintenance of process.

11. METHODS OF MEASUREMENTS
The methods of measurements may be broadly classified into
two categories.
(i) Direct methods
The unknown quantity (also called the measurand) is directly
directly compared against a standard.
The result is expressed as a numerical number and a unit.
Direct methods are quite common for the measurement of
physical quantities like length, mass and time.

12. (ii) Indirect methods
Measurements by direct methods are not always possible,
feasible and practicable. These methods in most of the cases,
are inaccurate because they involve human factors.
They are also less sensitive.
Hence direct methods are not preferred and are less
commonly used.
A indirect measurement system consists of a transducing
element which converts the quantity to be measured into an
analogous signal.
The analogous signal is then processed by some
intermediate means and is then fed to the end devices which
present the results of the measurements.

13. PRIMARY, SECONDARY AND TERTIARY MEASUREMENTS
 Measurements may be classified as primary, secondary and
tertiary based upon whether direct or indirect methods are
used.
1. Primary Measurements
 A primary measurement is one that can be made by direct
observation without involving any conversion (translation) of
the measured quantity into length.
Typical examples of primary measurements are:
i) The matching of two lengths such as when determining the
length of an object with a meter rod.
ii) The matching of two colours, such as when judging the
colour of red hot metals.
iii) The counting of strokes of a clock chime to measure the
time.

14. 2. Secondary Measurement
 A secondary measurement involves only one translation
(conversion) to be done on the quantity under measurement
to convert it into a change of length.
 The measurement quantity may be pressure of gas, and
therefore, may not be observable.
Therefore, a secondary measurement requires,
i) An instrument which translates pressure changes into length
changes.
ii) A length scale or a standard which is calibrated in length
units equivalent to known changes in pressure.
 Therefore, in a pressure gauge, the primary signal (pressure)
is transmitted to a translator and the secondary signal (length)
is transmitted to observer’s eye.

15. 3. Tertiary Measurement
A tertiary measurement involves two translations. A typical
example of such a measurement of temperature of an object
by termo couple.
 The primary signal (temperature of object) is transmitted to
a translator which generates a voltage which is a function of
the temperature. Therefore, first translation is temperature to
voltage.
 The secondary translation is then voltage into length.
 The tertiary signal (length change) is transmitted to the
observer’s brain.

16. Functions of Measurement System
1. Indicating Function
 Instruments and systems use different kinds of methods for
supplying information concerning the variable quantity under
measurement.
 Most of the time this information is obtained as a deflection
of a pointer of a measuring instrument.
Example:
The deflection of pointer of a speedometer indicates the
speed of the automobile at that moment. A pressure gauge is
used for indicating pressure.

17. 2. Recording function
In many cases the instrument makes a written record, usually
usually on paper, of the value of the quantity under
measurement against time or against some other variables.
Thus the instrument performs a recording function.
Example:
A potentiometric type of recorder used for monitoring
temperature records the instantaneous values of temperature
on a strip chart recorder.
https://www.youtube.com/watch?v=RCa4nE6Z-SE

18. 3. Controlling function
This is one of the most important functions especially in the
field of industrial control pricesses. In this case, the
information is used by the instrument or the system to control
the original measured quantity.
The instruments whose functions are mainly indicating and
recording especially these instruments which are used for
engineering analysis purpose.
Example:
Controlling instruments are thermostats of temperature
control and floats for liquid level control.
https://www.youtube.com/watch?v=hgqCzz6QtqM&t=28s

19. MEASURING INSTRUMENT:
 It may be defined as a device for determining the value or magnitude of a quantity
or variable.

20. FUNCTIONAL ELEMENTS OF AN
INSTRUMENT:
Most of the measurement systems contain three main functional elements. They are:
i) Primary sensing element
ii) Variable conversion element
iii) Data presentation element.

21. Primary sensing element:
 The quantity under measurement makes its first contact with the primary sensing
element of a measurement system. i.e., the measurand- (the unknown quantity
which is to be measured) is first detected by primary sensor which gives the output
in a different analogous form.
 This output is then converted into an e electrical signal by a transducer - (which
converts energy from one form to another).
 The first stage of a measurement system is known as a detector transducer stage’.

22. Variable conversion element:
 The output of the primary sensing element may be electrical signal of any form , it
may be voltage, a frequency or some other electrical parameter
 For the instrument to perform the desired function, it may be necessary to convert
this output to some other suitable form.

23. Variable manipulation element:
 The function of this element is to manipulate the signal presented to it preserving
the original nature of the signal.
 It is involved in signal conditioning.
 NOTE: When the elements of an instrument are actually physically separated,
it becomes necessary to transmit data from one to another. The element that
performs this function i s called a data transmission element’.

24. Data presentation element:
 The information about the quantity under measurement has to be conveyed to the
personnel handling the instrument or the system for monitoring, control, or
analysis purposes. This function is done by data presentation element.
 https://www.youtube.com/watch?v=oAdNKL8SgNY

25. STATIC& DYNAMIC PERFORMANCE
CHARACTERISTICS OF AN INSTRUMENT
The performance characteristics of an instrument are mainly divided into two
categories:
i) Static characteristics
ii) Dynamic characteristics

26. Static characteristics:
 The set of criteria defined for the instruments, which are used to measure the
quantities which are slowly varying with time or mostly constant, i.e., do not vary
with time, is called ‘static characteristics’.

27. i) Accuracy
ii) Precision
iii) Sensitivity
iv) Linearity
v) Reproducibility
vi) Repeatability
vii) Resolution
viii) Threshold
ix) Drift
x) Stability
xi) Tolerance
xii) Range or span

28. Accuracy:
It is the degree of closeness with which the reading approaches the true value of the quantity
to be measured.
The accuracy can be expressed in following ways:
a) Point accuracy:
Such an accuracy is specified at only one particular point of scale.
It does not give any information about the accuracy at any other point on the scale.
b) Accuracy as percentage of scale of span:
When an instrument as uniform scale, its accuracy may be expressed in terms of scale range.
c) Accuracy as percentage of true value:
The best way to conceive the idea of accuracy is to specify it in terms of the true value of the
quantity being measured.

29. Precision:
 It is the measure of reproducibility i.e., given a fixed value of a quantity, precision is a
measure of the degree of agreement within a group of measurements. The precision is
composed of two characteristics:
a) Conformity:
Consider a resistor having true value as 2385692 , which is being measured by an
ohmmeter. But the reader can read consistently, a value as 2.4 M due to the non
availability of proper scale. The error created due to the limitation of the scale reading is a
precision error.
b) Number of significant figures:
The precision of the measurement is obtained from the number of significant figures, in
which the reading is expressed. The significant figures convey the actual information about
the magnitude & the measurement precision of the quantity.

31. Sensitivity:
The sensitivity denotes the
smallest change in the measured
variable to which the instrument
responds. It is defined as the
ratio of the changes in the
output of an instrument to a
change in the value of the
quantity to be measured.

32. Thus, if the calibration curve is linear, as shown, the sensitivity of the instrument is the slope of
The calibration curve.
If the calibration curve is not linear as shown, then the sensitivity varies with the input.
Inverse sensitivity or deflection factor is defined as the reciprocal of sensitivity.
Inverse sensitivity or deflection factor = 1/ sensitivity

33. Linearity:
The linearity is defined as the
ability to reproduce the input
characteristics symmetrically &
linearly.
The curve shows the actual
calibration curve & idealized
straight line.

34. Reproducibility:
It is the degree of closeness with which a given value may be repeatedly measured.
It is specified in terms of scale readings over a given period of time.
Repeatability:
It is defined as the variation of scale reading & random in nature.

35. Drift:
Drift may be classified into three categories:
a) zero drift:
If the whole calibration gradually shifts due
to slippage, permanent set, or due to undue
warming up of electronic tube circuits, zero
drift sets in.
b) span drift or sensitivity drift
If there is proportional change in the
indication all along the upward scale, the
drifts is called span drift or sensitivity drift.
c) Zonal drift:
In case the drift occurs only a portion of
span of an instrument, it is called zonal drift.

36. Resolution:
If the input is slowly increased from some arbitrary input value, it will again be found that output
does not change at all until a certain increment is exceeded. This increment is called resolution. The
smallest increment an instrument can detect and display.
Threshold:
If the instrument input is increased very gradually from zero there will be some minimum value
below which no output change can be detected. This minimum value defines the threshold of the
instrument.
Stability:
It is the ability of an instrument to retain its performance throughout is specified operating life.
Tolerance:
The maximum allowable error in the measurement is specified in terms of some value which is
called tolerance.
Range or span:
The minimum & maximum values of a quantity for which an instrument is designed to measure is
called its range or span.

37. Dynamic characteristics:
The set of criteria defined for the instruments, which are changes rapidly with time, is
called ‘dynamic characteristics’.
The various static characteristics are:
i) Speed of response
ii) Measuring lag
iii) Fidelity
iv) Dynamic error

38. Speed of response:
It is defined as the rapidity with which a measurement system responds to changes in the
measured quantity.
Measuring lag:
It is the retardation or delay in the response of a measurement system to changes in the
measured quantity. The measuring lags are of two types:
a) Retardation type:
In this case the response of the measurement system begins immediately after the change in
measured quantity has occurred.
b) Time delay lag:
In this case the response of the measurement system begins after a dead time after the
application of the input.

39. Fidelity:
It is defined as the degree to which a measurement system indicates changes in the
measurand quantity without dynamic error.
Dynamic error:
It is the difference between the true value of the quantity changing with time & the
value indicated by the measurement system if no static error is assumed. It is also
called measurement error.

40.  The measurement of an amount is based on some international standards
which are completely accurate compared with others.
 Generally, measurement of any quantity is done by comparing it with derived
standards with which they are not completely accurate.
 Thus, the errors in measurement are not only due to error in methods, but are
also due to derivation being not done perfectly well.
 So, 100% measurement error is not possible with any methods.
Error in measurement

41. Types of Error

42.  Gross errors are caused by mistake in using instruments or meters,
calculating measurement and recording data results
 The best example of these errors is a person or operator reading
pressure gage 1.01N/m2 as 1.10N/m2.
 It may be due to the person’s habit of not properly remembering data at
the time of taking, writing and calculating.
 This may be the reason for gross errors in the reported data, and such
errors may end up in calculation of the final results, thus deviating
results.
Gross Errors

43.  Blunders are final source of errors and these errors are caused by faulty
recording or due to a wrong value while recording a measurement, or
forgetting a digit while reading a scale.
 These blunders should stick out like sore thumbs if one person checks
the work of another person.
 It should not be comprised in the analysis of data.
Blunders

44.  The measurement error is the result of the variation of a measurement
of the true value.
 Usually, Measurement error consists of a random error and systematic
error.
 The best example of the measurement error is, if electronic scales are
loaded with 1kg standard weight and the reading is 10002grams, then
The measurement error is = (1002grams-1000grams) =2grams
Measurement Error

45.  The Systematic errors that occur due to fault in the measuring device
are known as systematic errors.
 These errors can be detached by correcting the measurement device.
These errors may be classified into different categories.
 Instrumental Errors
 Environmental Errors
 Observational Errors
 Theoretical
Systematic Errors

46.  Instrumental errors occur due to wrong construction of the measuring
instruments.
 These types of errors include loading effect and misuse of the
instruments.
 In order to reduce these errors in measurement, different correction
factors must be applied and in the extreme condition instrument must be
recalibrated carefully.
Instrumental Errors

47.  The environmental errors occur due to some external conditions of the
instrument.
 External conditions mainly include pressure, temperature, humidity or
due to magnetic fields. In order to reduce the environmental errors
 Try to maintain the humidity and temperature constant in the laboratory
by making some arrangements.
 Ensure that there shall not be any external electrostatic or magnetic field
around the instrument.
Environmental Errors

48.  As the name suggests, these types of errors occurs due to wrong
observations or reading in the instruments particularly in case of energy
meter reading.
 The wrong observations may be due to PARALLAX.
 In order to reduce the PARALLAX error highly accurate meters are
needed: meters provided with mirror scales.
Observational Errors
 Theoretical errors are caused by simplification of the model system.
 For example, a theory states that the temperature of the system
surrounding will not change the readings taken when it actually does,
then this factor will begin a source of error in measurement.
Theoretical Errors

49.  Random errors are caused by the sudden change in experimental
conditions and noise and tiredness in the working persons.
 These errors are either positive or negative. An example of the random
errors is during changes in humidity, unexpected change in temperature
and fluctuation in voltage.
 These errors may be reduced by taking the average of a large number
of readings.
 https://www.youtube.com/watch?v=7S3z8We8r84
Random Errors

50. STATISTICAL EVALUATION OF
MEASUREMENT DATA
 Out of the various possible errors, the random errors cannot be determined in the
ordinary process of measurements. Such errors are treated mathematically.
 The mathematical analysis of the various measurements is called statistical analysis of
the data.
 For such statistical analysis, the same reading is taken number of times, generally using
different observers, different instruments & by different ways of measurement. The
statistical analysis helps to determine analytically the uncertainty of the final test results.

51. Arithmetic mean &median:
When the number of readings of the same
measurement are taken, the most likely
value from the set of measured value is the
arithmetic mean of the number of readings
taken.
The arithmetic mean value can be
mathematically obtained as,

52. Median
A median value is obtained which is a close approximation to the arithmetic mean
value. For a set of measurements X1, X2, X3.Xn written down in the ascending
order of magnitudes, the median value is given by,

53. Find the mean, median, mode, and range for the following list of values:
13, 18, 13, 14, 13, 16, 14, 21, 13
Solution:
Given data: 13, 18, 13, 14, 13, 16, 14, 21, 13
The mean is the usual average.
Mean = {13 + 18 + 13 + 14 + 13 + 16 + 14 + 21 + 13} / {9} = 15
The median is the middle value, so to rewrite the list in ascending order as given below:
13, 13, 13, 13, 14, 14, 16, 18, 21
There are nine numbers in the list, so the middle one will be
{9 + 1} / {2} = {10} / {2} = 5
= 5th number
Hence, the median is 14.
The mode is the number that is repeated more often than any other, so 13 is the mode.
The largest value in the list is 21, and the smallest is 13, so the range is 21 – 13 = 8.
Mean = 15
Median = 14
Mode = 13
Range = 8

54. The deviation tells us about the departure of a given reading from the arithmetic mean of
the data set
The average deviation is defined as the sum of the absolute values of deviations divided
by the number of readings. This is also called mean deviation
Average deviation:

55. STANDARD DEVIATION
σ =
𝑑12+𝑑22+ …….+𝑑𝑛2
𝑛
,
=
Σ𝑑2
𝑛
n-1 for n < 20
• The amount by which the n
measurement values are
spread about the mean is
expressed by standard
deviation.
• It is also called root mean
square deviation.
• SD is defined as the square
root of the sum of the
individual deviations squared,
divided by the number of
readings.
• It is denoted by σ.

56. VARIANCE
 V= 𝜎2 =
𝑑12+𝑑22+ …….+𝑑𝑛2
𝑛
,
N-1 for n < 20.
Variance means square
deviation, so it is the square
of the standard deviation.
It is denoted as V.

57. Problem
 By using a micrometer screw, the following readings were taken of a certain length:
1.34, 1.38, 1.56, 1.47, 1.42, 1.44, 1.53, 1.48, 1.40, 1.59 mm. Calculate the following:
A. Arithmetic mean
B. Mean deviation
C. Standard deviation
D. Variance

58. STANDARD & CALIBRATION
Standard
All the instruments are calibrated at the time of manufacturer against measurement standards.
A standard of measurement is a physical representation of a unit of measurement.
A standard means known accurate measure of physical quantity.
The different size of standards of measurement are classified as
i) International standards
ii) Primary standards
iii) Secondary standards
iv) Working standards

59.  International standards are defined as the international agreement.
 These standards , as mentioned above are maintained at the international bureau
of weights and measures and are periodically evaluated and checked by absolute
measurements in term s of fundamental units of physics.
 These international standards are not available to the ordinary users for the
calibration purpose.
International standards

60. Primary standards
 These are highly accurate absolute standards, which can be used as ultimate
reference standards. These primary standards are maintained at national standard
laboratories in different countries.
 These standards representing fundamental units as well as some electrical and
mechanical derived units are calibrated independently by absolute measurements
at each of the national laboratories.
 These are not available for use, outside the national laboratories.
 The main function of the primary standards is the calibration and verification of
secondary standards.

61. Secondary standards
 As mentioned above, the primary standards are not available for use outside the
national laboratories.
 The various industries need some reference standards.
 So, to protect highly accurate primary standards the secondary standards are
maintained, which are designed and constructed from the absolute standards.
 These are used by the measurement and calibration laboratories in industries and
are maintained by the particular industry to which they belong. Each industry has
its own standards.

62. These are the basic tools of a measurement laboratory and
are used to check an d calibrate the instruments used in
laboratory for accuracy and the performance.
Working standards

63. CALIBRATION
 Calibration is the process of making an adjustment or marking a scale so that the
readings of an instrument agree with the accepted & the certified standard.
 In other words, it is the procedure for determining the correct values of measurand
by comparison with the measured or standard ones.
 The calibration offers a guarantee to the device or instrument that it is operating
with required accuracy, under stipulated environmental conditions.
 The calibration procedure involves the steps like visual inspection for various
defects, installation according to the specifications, zero adjustment etc.,
 The calibration is the procedure for determining the correct values of measurand
by comparison with standard ones.
 The standard of device with which comparison is made is called a standard
instrument. The instrument which is unknown & is to be calibrated is called test
instrument. Thus in calibration, test instrument is compared with standard
instrument.

64. Types of calibration methodologies:
i) Direct comparisons
ii) Indirect comparisons

65. Direct comparisons:
 In a direct comparison, a source or generator
applies a known input to the meter under
test. The ratio of what meter is indicating &
the known generator values gives the meter’s
error. In such case the meter is the test
instrument while the generator is the
standard instrument. The deviation of meter
from the standard value is compared with the
allowable performance limit.
 With the help of direct comparison a
generator or source also can be calibrated.
Indirect comparisons:
 In the indirect comparison, the test instrument
is compared with the response standard
instrument of same type i .e., if test
instrument is meter, standard instrument is
also meter, if test instrument is generator; the
standard instrument is also generator & so
on.
 If the test instrument is a meter then the same
input is applied to the test meter as well a
standard meter.
 In case of generator calibration, the output of
the generator tester as well as standard, or set
to same nominal levels.
 Then the transfer meter is used which
measures the outputs of both standard and
test generator.