Download - 01 Dee1012 Topic 1
TOPIC 1:
MEASUREMET AND ERROR
DEE1012- MEASUREMET
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Learning outcome:
1) Understand measurement process; primary sensing
element, variable manipulation element and data
presentation element.
2) Understand error in measurement; gross error,
systematic error, absolute error, relative error.
3) Understand Standards used in measurement;
international standard, primary standard, secondary
standard, working standard.
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INTRODUCTION
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INTRODUCTION
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INTRODUCTION
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INTRODUCTION
• Measuring is basically is used to monitor a process or
operation or as well as the controlling process
• For example thermometers, barometers, are used to
indicate the environmental conditions
• Similarly water, gas and electric meters are used to
keep track of the quantity of the commodity used,
and also special monitoring equipment used in
hospital
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DEFINITION OF MEASUREMENT
• The process of determining the amount, degree, or
capacity by comparison ( direct or indirect) with the
accepted standards of the system units being used.
(Electronic measurement, H.s Kalsi)
OR
• The process by which physical parameters can be
converted to meaningful numbers. (Bhavani and
Vasantha)
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DEFINITION OF MEASUREMENT
PROCESS,
MACHINE
OR SYSTEM
BEING
MEASURED
MEASUREMENT
SYSTEM
OUTPUT INPUT
True value
of
variable
Measured
value of
variable
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Before make a measurement, the
things that must be considered is:
• Measurement method
• Identify which parameter to be measured
• How much measurement should be taken
• Select the appropriate instrument
• Have the knowledge and experience of handling
equipment
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ELEMENT OF MEASUREMENT SYSTEM
• Any instrument or a measuring system can be described
in general by using block diagram.
• The block diagram indicates the necessary elements and
their functions in a general measuring system
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BLOCK DIAGRAM OF FUNCTIONAL
ELEMENTS OF AN INSTRUMENT
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Converted signal Amplified
signal
Human readable
form
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Example of element in measurement
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The various elements can be grouped
as: 1. Primary sensing element.
2. Variable conversion element.
3. Variable manipulation element.
4. Data transmission element
5. Data presentation element.
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i. Primary sensing element:
• An element of an instrument which makes first, the
contact with the quantity to be measured.
• In ammeter, coil carrying current to be measure is
primary sensing element.
• In most of the cases, a transducer follows primary
sensing element which converts the measured into
a corresponding electrical signal.
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ii. Variable Conversion Element (Data
Conditioning)
• The output of the primary sensing element is in electrical
form such as voltage, frequency or any other electrical
parameter.
• Such an output may not be suitable for the actual
measurement system.
• For example of the measurement system is digital then
the analog signal obtained from the primary sensing
element is not suitable for the digital system.
• Thus analog to digital converter is required which is
variable conversion element.
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iii. Variable Manipulation Element
(Data Conditioning)
• The level of the output from the previous stage may not
be enough to drive the next stage.
• Thus, variable manipulation element manipulates the
signal, preserving the original nature of the signal.
• For example an amplifier which just amplifies the
magnitude of the input, at its output, retaining the
original nature of the signal.
• It is not necessary that variable manipulation element
must be always after variable conversion element
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iv. Data transmission Element
• When the elements of the system are physically
separated, it is necessary to transmit the data from
one stage to other.
• This is achieved by the data transmission element.
• The transmitted data may be used by the system,
finally for monitoring, controlling or analyzing
purposes.
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vi Data presentation element:
• the person handling the instrument must get information in the proper form, according to the purpose for which it is intended.
• If the data is to be monitored, then visual display devices are used as data presentation element.
• If the signal is to be recorded for analysis purpose, then magnetic tapes, recorders, high speed cameras are used as data presentation elements.
• For control and analysis purpose, the microprocessors, computers and microcontrollers may be used as data presentation elements.
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Example: Analog meter
• Consider a simple analog meter used to measure current or voltage as shown in Figure 3.
• The moving coil is primary sensing element.
• The magnets and coil together act as data conditioning stage to convert current in a coil to a force.
• This force is transmitted to the pointer through mechanical linkages which act as data transmission element.
• The pointer and scale act as data presentation element.
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Example Analog meter
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TERMINOLOGY OF SCALE AND RANGE
• Scale
• A series of marks at regular intervals on an instrument
that is used for measuring. It is a part of the
instrument that shows the value of a parameter
measured. The scale is depending on the range.
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TERMINOLOGY OF SCALE AND RANGE
• Range
The minimum and maximum values of a quantity for
which an instrument is designed to measure is called
its range . E.g ammeter range : 0mA to 5 mA
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DEFINITION OF ERROR
• The deviation/ different between true values (computed) and measured values of
quantities
• Factors that affect the measurements are related to
the measuring instruments
the person using the instrument
• Error may be expressed either as absolute or as
percentage relative error
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1.ABSOLUTE ERROR
• The difference between the true value of the
variable and the measured value of the variable
• Can be expresses as,
𝑒 = 𝑌𝑛 − 𝑋𝑛
• Where;
• e = absolute error
• Yn = expected value (calculate)
• Xn= measure valued
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2. PERCENTAGE OF RELATIVE ERROR
Can be express as,
%𝑒 =𝑎𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝑒𝑟𝑟𝑜𝑟
𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒 𝑥 100%
%𝑒𝑟𝑟𝑜𝑟 =𝑒
𝑌𝑛 𝑥 100%
%𝑒𝑟𝑟𝑜𝑟 =𝑌𝑛−𝑋𝑛
𝑌𝑛 𝑥 100%
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𝐴𝑐𝑐𝑢𝑟𝑎𝑐𝑦 = 100% − %𝑒𝑟𝑟𝑜𝑟
EXAMPLE OF ABSOLUTE AND RELATIVE ERROR
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EXAMPLE 1
• A voltmeter reads 7.2 V and the true value of the
voltage is 7.5 V. Determine the absolute error and
percentage of relative error
• Solution:
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Yn = 7.2 V
Xn = 7.5 V
e = Yn -Xn= 7.5V-7.2 V=0.3V
% e = Yn – Xn X 100 = 7.5 V-7.2 V X100 =4%
Yn 7.5V
EXAMPLE 2
• A circuit below have 20V power supply connected
parallel to resistor R1 = 15k and R2 = 7k. A volt
meter connected to R1 resistor and give 19.5V
measured value. Calculate percentage relative error
of that meter.
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Solution:
R1 and R2 parallell with power supply 20V. So VR1 and
VR2 =20 V.
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Yn = 20 V
Xn = 19.5V
% e = Yn - Xn X 100 %
Yn
= 20 - 19.5 X 100%
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= 2.5 %
EXERCISE
1. A Voltmeter reads 111.5V. The error taken from an
error curve is 5.3%. Calculate the true value of the
voltage.
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Answer: 117.74V
%𝑒𝑟𝑟𝑜𝑟 =𝑌𝑛−𝑋𝑛
𝑌𝑛 𝑥 100%
%𝑒𝑟𝑟𝑜𝑟 =𝑌𝑛 − 111.5
𝑌𝑛 𝑥 100% = 5.3%
(𝑌𝑛−111.5
𝑌𝑛)𝑥100% =
5.3
100
𝑌𝑛 − 111.5 = 0.053𝑌𝑛 𝑌𝑛 − 0.053𝑌𝑛 = 111.5
𝑌𝑛 = 117.74V
MAIN TYPES OF ERRORS
• Classified by THREE:
1. Gross Errors
2. Systematic Errors
3. Random Errors
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1. GROSS ERROR
• These are mainly due to human mistakes :
carelessness or lack of experience of human being
mistakes in reading, recording observation and
calculating results
incorrect adjustment of instruments
Improper applications of instruments: Using a 0–100
V voltmeter to measure 0.1 V, etc.
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1. GROSS ERROR
• The complete elimination of gross error is not
possible, but can minimize them by:
taking reading (at least 3seperate reading),
recording and calculating properly
Make sure know use the meter or instrument
• This error cannot be treated mathematically
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2. SYSTEMATIC ERROR
• Occur due to shortcomings of the instruments, such as defective or worn parts, ageing effects and environmental effects.
• 3 types of systematic errors :
1. Instrumental error- friction, magnetic and zero & full scale adjustment.
2. Environmental error – due to surrounding external condition such as temperature, pressure, humidity, stray magnetic and electrostatics fields
3. Observation error- parallax error
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2. SYSTEMATIC ERROR
• Way to minimize :
Calibrate meter ( instruments)
Choose suitable meter ( instuments)for measurement.
Reduce effects caused by temperature change,
humidity, magnetic and electrostatic by using
magnetic
cleaning the instruments, and housing the instruments
properly depending on the application and type of
the instrument.
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3. RANDOM ERROR
• These are errors that remain after gross and
systematic errors have been substantially reduced.
• These errors are due to unknown causes.
• Way to minimize:
increase number of observation
using the statistical methods to obtain best
approximation reading
• This error can be treated mathematically
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CHARACTERISTICS OF MEASUREMENT
1. Accuracy – Closeness with which an instrument
reading approaches the true value of the variable
being measured.
2. Precision –A measure of consistency or
repeatability of measurement.
If the readings are taken repeatedly does not
change, the instrument have high precision.
Accurate instruments, precision must be high. But
precision does not guarantee accuracy
Digital instruments are more precise than analog instruments
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CHARACTERISTICS OF MEASUREMENT
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CHARACTERISTICS OF MEASUREMENT
3. Resolution – The smallest change in the measured
value to which the instrument can respond. It is the
smallest change the instrument can measure.
4. Significant Figure - Significant figures convey actual
information regarding the magnitude and the
measurement precision of a quantity. The more
significant figures , the greater the precision of
measurement.
Example 68Ω, 69Ω- two significant figures.
68.0Ω, 67.9Ω- three significant figures
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Country significant figures
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Number Significant Figures
52 2
520 3
5.14 3
5.014 4
5.1250 5
0.0034 2
21000 5
0.0213 3
1.000 4
1000.0 5
STANDARD IN THE MEASUREMENT
• Measurement Standard is a measurement devices or
measurement system that define, create and
protect the quantity value for comparison with other
measurement devices.
• It is consists of 4 categories as follows:
1.International Standards
2.Primary Standards
3. Secondary Standards (Reference standard)
4. Working Standards
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1.International Standards
• Define by international agreement. They represent
certain units of measurement to the closest possibly
accuracy that production and measurement
technology allow.
• Example BSI(British Standard Institution),
IEC(international Electro technical commission) and
ISO (International Organization for Standard)
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1.International Standards
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1.International Standards
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2.Primary Standards
• Maintain by national standards laboratories in
different parts of the world.
• The main function is the calibration and verification
of secondary standards
• Example, Makmal Metrologi Kebangsaan Malaysia
SIRIM.
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Makmal Metrologi kebangsaan (NML)
(dibwh sirim) merupakan badan yang bertanggungjawab ke atas piawaian
pengukuran unit SI yang kita gunakan
sehingga kini.
3. Secondary Standards (Reference
standard) • It is basic reference standards used in industrial
measurement laboratories.
• Each industry has its own secondary standard.
• Example: SIRIM, Timbang & Sukat kem. Perdagangan
& perindustrian, Pusat penyelidikan pertahanan,
local universiti and industries
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4. Working Standards
• Working standard is the principle tools of a
measurement laboratory and the lowest level of
standards.
• They are used to check and calibrate general
laboratory instruments for accuracy.
• Example : The resistor manufacturing industry
maintains a standard resistor in the laboratory for
checking the values of the manufactured resistors.
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STANDARD IN THE MEASUREMENT
• International Standards (defined based on
international agreement )
• Primary Standards (maintained by national
standards laboratories)
• Secondary Standards ( used by industrial
measurement laboratories)
• Working Standards ( used in general laboratory)
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