MEASUREMENTS AND

INSTRUMENTATION

EC2351

Prepared

By

JhansiRani.R AP/ECE

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.

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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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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.

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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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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.

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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.

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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

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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)

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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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AMMETER

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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

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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.

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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.

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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.

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Relative error:

True value

absolute error

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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.

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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.

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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.

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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.

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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.

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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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DYNAMIC CHARACTERISTICS

Speed of response

Fidelity

Lag

Dynamic error

STANDARD VARIATIONS IN I/PT ARE

Sudden, instantaneous and finite change in the input.

i/pt -> Au(t)

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Linear change in i/pt. it changes at a constant rate wrt time.

i/pt -> At u(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.

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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

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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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ERRORS

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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.

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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.

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ERROR ANALYSIS

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STATISTICAL ANALYSIS Arithmetic mean and median:

mean:

Median:

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Deviation from mean:

Average deviation (mean deviation):

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Standard deviation:

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Variance: mean square deviation

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