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UNIT 1
BASIC MEASUREMENT CONCEPTS
Measurement systems
Static and dynamic characteristics
Units and standards of measurements
Error analysis
Moving coil meters
Moving iron meters
Multimeters
Bridge measurements
Maxwell
Hay
Schering
Anderson
Wien bridge.
R.JhansiRani AP/ECE
SIGNIFICANCE OF MEASUREMENT
Importance of Measurement is simply and
eloquently expressed in the following statement
of famous physicist Lord Kelvin:
“I often say that when you can measure what
you are speaking about and can express it in
numbers, you know something about it; when
you cannot express in it numbers your
knowledge is of meager and unsatisfactory
kind”
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R.JhansiRani AP/ECE
INTRODUCTION Measurement means, to monitor a process or a operation
and using an instrument, express the parameter, quantity or a variable in terms of meaningful numbers.
Measurement of a given parameter or quantity is the act or result of a quantitative comparison between a predefined standard and an unknown quantity to be measured.
There are 2 basic requirements:
The comparison standard is accurately defined and commonly accepted , and
The procedure and the instrument used for obtaining the comparison must be provable.
R.JhansiRani AP/ECE
EVOLUTION OF INSTRUMENTS.
a) Mechanical
b) Electrical
c) Electronic Instruments.
MECHANICAL:
These instruments are very reliable for static and stable conditions. But their disadvantage is that they are unable to respond rapidly to measurements of dynamic and transient conditions.
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CONTD
ELECTRICAL:
It is faster than mechanical, indicating the output are
rapid than mechanical methods. But it depends on the
mechanical movement of the meters. The response is 0.5
to 24 seconds.
ELECTRONIC:
It is more reliable than other system. It uses
semiconductor devices and weak signal can also be
detected.
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R.JhansiRani AP/ECE
Measuring instrument:
It is defined as the device for determining the value or
magnitude of a quantity or variable.
Electronic measurement:
It is the one which is based on electronic or electrical principles
for its measurement function.
R.JhansiRani AP/ECE
ADVANTAGES OF ELECTRONIC MEASUREMENT Most of the quantities can be converted by transducers
into the electrical or electronic signals.
Electronic signals can be amplified, filtered, multiplexed, sampled and measured.
Measured signals can be transmitted over long distance through cables or radio links, without any loss of information.
Many measurements can be done simultaneously or in rapid succession.
Electronic circuits can measure the events of very short duration
Higher sensitivity, low power consumption and a higher degree of reliability are the important features of electronic instruments and measurements.
R.JhansiRani AP/ECE
FUNCTIONAL ELEMENTS OF AN INSTRUMENT
Primary
Sensing
element
Variable
Conversion
element
Variable
manipulation
element
Data
Transmission
element
Data
presentation
element
Data Storage
&playback
element
Quantity
To be measured
observer
Data conditioning element
R.JhansiRani AP/ECE
Primary Sensing Element:
An element of an instrument which makes first
contact with the quantity to be measured. In most cases a
Transducer follows primary sensing element which
converts the measurand into a corresponding electrical
signal.
Variable Conversion Element:
output of the primary sensing element is in electrical
form such as Voltage, Frequency….such an o/pt may not
be suitable for the actual measurement system. (Ex: A/D
converter)
R.JhansiRani AP/ECE
Variable Manipulation Element:
The level of the o/pt 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.
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.
Data Presentation Element:
The data is monitored, for analyzing purpose using data
presentation element.(Ex: Visual display)
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EXAMPLE
Moving coil senses current
Magnets & coil convert current in coil to force
Force is transmitted to pointer through mechanical links
Pointer and scale presents the current value
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PERFORMANCE CHARACTERISTICS
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, ie., do not vary with time is called static characteristics
Dynamic characteristics: when the quantity under measurement changes rapidly with time, it is necessary to study the dynamic relations existing b/w i/pt and o/pt which is expressed as differential equations
The set of criteria defined based on such dynamic differential equation is called dynamic characteristics
R.JhansiRani AP/ECE
CALIBRATION
Calibration is the process of making an adjustment
or making a scale so that the reading of an
instrument agree with the accepted and certified
standard.
Note: if the device is repaired, aged or modified
then recalibration is carried out.
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STATIC CHARACTERSTICS
Accuracy
Precision
Resolution
Error
Sensitivity
Threshold
Reproducibility
Zero drift
Stability
Linearity
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ACCURACY: DEGREE OF CLOSENESS WHICH THE INSTRUMENT READING
APPROACHES THE TRUE VALUE OF THE QUANTITY TO BE MEASURED. IT
INDICATES THE ABILITY OF AN INSTRUMENT TO INDICATE TRUE VALUE OF
THE QUANTITY.
A) ACCURACY AS “% OF FULL SCALE READING”: IF THE INSTRUMENT HAVE UNIFORM SCALE, THEN ACCURACY IS EXPRESSED AS
% OF FULL SCALE READING.
ACCURACY IS 0.1% FOR FULL SCALE OF 50 UNITS MEANS 0.05 UNITS ERROR
IS PRESENT IN ANY MEASUREMENT.
ACCURACY IS 0.2% FOR FULL SCALE OF 25 UNITS MEANS 0.05 UNITS ERROR
THUS AS READING DECREASES ERROR IS MORE AND LEADS
MISLEADING. R.JhansiRani AP/ECE
B) ACCURACY AS “% OF TRUE VALUE”:
Best method for specifying accuracy. It is specified in terms of true value of the quantity being measured. Eg: ±0.1% of true value.
As the reading gets smaller error also gets reduced. Hence accuracy is better.
C) Accuracy as “% of scale span”: Maximum point on scale -Minimum point on scale is scale
span.
For range 25-225,
Scale span is 200
If accuracy is 0.2% of span then, error is 0.4 units in any measurement.
D) Point Accuracy It is specified at only one point of scale.
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PRECISION: It is the measure of consistency or repeatability
of measurement.
It denotes the closeness with which individual
measurements are departed or distributed about
the average of numbers of measured values.
High precision may not have high accurate
Types: conformity
Number of significant figures.
R.JhansiRani AP/ECE
Conformity: Error created due to limitation of scale reading is a
precision error.
Ex: resistor of value 2385692Ω is read as 2.4MΩ.
Significant figures: Precision is obtained from number of significant figures.
Ex: 110 ohms can be specified as 109 or 111 thus 3 significant figures.
If it is specified as 110.0 then it may be 110.1 or 109.9
Thus there are 4 significant figures.
Greater the significant figure greater is the precision.
R.JhansiRani AP/ECE
Error:
The algebraic difference between the indicated value
and the true value of the quantity to be measured is called
an error.
Error of 1 ut is negligible when measure in order of 1000 ut
Error of 1 ut is significant when measure in order of 5 ut
e = At – Am , where
e – error (or) absolute error
Am – measured value of quantity
At – true value of quantity
Note: instead of specifying absolute error, the relative or
percentage of error is specified.
R.JhansiRani AP/ECE
Sensitivity:
The ratio of the change in output of an instrument to
a change in the value of the quantity to be measured.
Note: if the calibration curve is linear, then sensitivity of the
instrument is the slope of the calibration curve.
R.JhansiRani AP/ECE
For manufactures
Reciprocal of sensitivity is called inverse sensitivity or deflection factor.
unit: sensitivity – mm/µA, mm/Ω, counts/V etc;
Deflection meter - µA/mm, Ω/mm, V/counts etc;
Sensitivity should be high, to achieve this the range of the instrument should not exceed the value to be measured.
R.JhansiRani AP/ECE
Resolution means smallest measurable input change.
Threshold:
If the i/pt is slowly varied from zero, the o/pt does not change until some minimum value of the i/pt is exceeded. This minimum value of the i/pt is called threshold.
Threshold is the smallest measurable i/pt.
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LINEARITY THE CLOSENESS TO WHICH A CURVE APPROXIMATES A
STRAIGHT LINE.
DEFINITION: IT IS DEFINED AS THE MAXIMUM DEVIATION OF THE ACTUAL
CALIBRATION CURVE (O/PT) FROM THE IDEALIZED ST.LINE, EXPRESSED AS
A % OF FULL SCALE READING OR A % OF THE ACTUAL READING.
R.JhansiRani AP/ECE
Zero drift:
The deviation in the instrument output with time from its zero value, when the variable to be measured is a constant.
Reproducibility:
It is the degree of closeness with which a given value may be repeatedly measured.
Reproducibility and repeatability are a measure of the closeness with which a given i/pt may be measured again and again.
R.JhansiRani AP/ECE
Stability:
Ability of an instrument to retain its
performance throughout its specified
operating life and the storage life.
Tolerance:
The maximum allowable error in the
measurement is specified interms of some
value which is called tolerance.
Bias:
The constant error which exists over the full
range of measurement of an instrument is
called bias.
R.JhansiRani AP/ECE
Hysteresis If the i/pt to the instrument is increased from a negative value, the o/pt also increases : curve 1 If the curve is decreased steadily, the o/pt does not follow the same curve but lags by certain value: curve 2 Difference b/w two curves is called HYSTERESIS. The noncoincidence of loading and unloading curves
Dead space: Range of i/pt values were there is no change in o/pt is called dead space.
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STANDARD VARIATIONS IN I/PT ARE
Sudden, instantaneous and finite change in the input.
i/pt -> Au(t)
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i/pt is proportional to the square of the time & hence
represents constant acceleration
i/pt -> At2 u(t)
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It exist only at t=0 & zero otherwise
Area under it is its magnitude and if its unity it is called
delta function δ(t)
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i/pt which changes in acco9rdance with a sinusoidal
function of constant amplitude. Frequency is the
independent variable in this case.
R.JhansiRani AP/ECE
Speed of response:
It gives information about how fast the system reacts to the changes in the input.
Fidelity:
it is defined as the degree to which an instrument indicates the changes in the measured variable without dynamic error.
Lag:
Delay in the response of a system.
retardation lag: response of the system begins immediately after a change in the variable has occurred.
time delay: response begins after some time called dead time, after the application of input.
Dynamic error
• Difference between the true value of the variable to be measured changing with time and the value indicated by the measurement system assuming zero static error
R.JhansiRani AP/ECE
UNITS
It is necessary to specify type & magnitude for the
reading. Where unit represents the type of the
physical quantity and reading on the instrument
represents its magnitude
Different system of units are
M.K.S
C.G.S
S.I (system international units)
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UNITS
The S.I system of units is divided into 3 categories
Fundamental units
Supplementary units
Derived units
Fundamental units:
units which are independently chosen and not
dependent on any other units are called fundamental
units or base units
Ex: meter (m), kilogram (Kg), second (s), Ampere (A)
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Supplementary units:
Radian for the plane angle: (θ,Φ)
Plane angle subtended by an arc of a circle equal in
length to the radius of the circle.
Steradian for the solid angle: (θs,Φs)
Angle subtended at the center of the sphere by the
surface whose area is equal to the square of the radius of
the sphere.
Derived units:
These units are derived from fundamental and
supplementary units
Ex: velocity- m/s, acceleration- m/s2, force- Newton(N)
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MEASUREMENT STANDARDS
A standard of measurement is a physical representation of
a unit of measurement.
A standard means known accurate measure of physical
quantity.
ex: unit of mass: Kg
Kilogram is defined as the mass of cubic decimeter of
water as its temperature of maximum density of 4 degree
Celsius
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TYPES OF STANDARDS
1. International standards
2. Primary standards
3. Secondary standards
4. Working standards
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INTERNATIONAL STANDARDS
These standards are maintained at the international bureau of weights and measures and are periodically evaluated and checked by absolute measurements.
These standards are not available for ordinary users for calibration.
For accuracy they are replaced by absolute units which are more accurate than international standards.
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PRIMARY STANDARDS
They are maintained at national standard laboratories in different countries.
These standards represents fundamental units as well as electrical and mechanical derived units calibrated by absolute measurements at each national laboratories.
used for calibration and verification of secondary standards.
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SECONDARY STANDARDS
Since primary standards are not available for outside
users, various industries need some reference.
They are used by measurement and calibration
laboratories and are maintained by the particular industry
to which they belong.
Each industry has its own standards.
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WORKING STANDARDS
These are the basic tools of a measurement laboratory
use to check and calibrate for accuracy.
ex: resistor industry maintains a standard resistor for
checking the values of manufactured resistors.
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SOURCES OF ERRORS 1. Faulty design of instrument
2. Insufficient knowledge of quantity and
design conditions
3. Improper maintenance of the instrument.
4. Sudden change in the parameter to be
measured.
5. Unskilled operator
6. Effects of environmental conditions.
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TYPES OF ERRORS
static errors are classified as,
1. Gross error
2. Systematic error
3. Random error
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GROSS ERROR: (PERSONAL ERRORS)
Occurs due to carelessness of human while
reading, recording and calculating results.
Due to incorrect adjustments of instruments.
To eliminate error:
Take care while reading, recording and
calculating results.
Take 3 or more readings with 3 or more persons.
R.JhansiRani AP/ECE
SYSTEMATIC ERROR
A constant uniform deviation of operation in instruments
known as systematic error.
Due to short comings and characteristics of the material
used in instrument like worn parts, ageing effects etc;
Types:
a) Instrumental error
b) Environmental error
c) Observational error
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INSTRUMENTAL ERROR
shortcomings of instrument:
Due to mechanical structure of the instruments.
Ex: Friction in bearings,
Irregular spring tension,
variation in air gap.
To eliminate error:
1. select proper instrument and select proper procedure.
2. Identify effect of errors and correct it.
3. Calibrate the instrument.
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Misuse of instruments: Ex: poor initial adjustments
improper zero setting
using leads of high resistance
Loading effects: Ex: connecting a well calibrated voltmeter
across the 2 points of high resistance circuit.
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ENVIRONMENTAL ERROR
They are due to
temperature changes
pressure changes
thermal e.m.f
stray capacitance
cross capacitance
To eliminate error:
1. proper correction factors given by the manufacturer.
2. make arrangements to keep surrounding constant
like using A.C.
3. sealing the components to avoid dust, humidity.
4. providing magnetic or electrostatic shields.
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OBSERVATIONAL ERROR
errors made by observers
Ex: parallax error while reading a
meter, wrong scale selection
To eliminate error:
1. use instruments with mirrors.
2. knife edged pointers.
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RANDOM ERROR
Causes of errors which are unknown are
random errors.
Due to accumulation of large number of
small effects
They cannot be corrected by any method.
use statistical methods to obtain best
approximation of reading.
R.JhansiRani AP/ECE
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