Meas 201&202 Ch#01 Introduction

8/10/2019 Meas 201&202 Ch#01 Introduction

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Introduction to Measurements


Ebrahim A. Badran Spring 20131

Ebrahim A. BadranPh.D., IEEE Member

[email protected]


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Measurements

Measurement is essentially the act, or the result, of a quantitative comparison

between a given quantity and a quantity of the same kind chosen as a unit.

The physical embodiment of the unit of measurement is called astandard.

The device used for com arin the unknown uantit with the unit of


measurement or a standard quantity is called ameasuring instrument.

As a fundamental principle of science, Lord Kelvin statedWhen you can measure what you are speaking about and express them annumbers, you know something about it and when you cannot measure it or where

you cannot express in numbers, your knowledge is of a meager and unsatisfactorykind. It may be the beginning of knowledge, but you have scarcely in your thought

advanced to the stage of science.


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Elements of Measurement System

The operation of a measurement system can be explained in terms of thefunctional elements of the system.

Every instrument and measurement system is composed of one or more of thesefunctional elements and each functional element is made of a distinct components


or groups o componen s w c per orm requ re an e n e s eps nmeasurement.

Primary Sensing Element

Variable Conversion Element

Variable Manipulation Element

Data Presentation Element

Functional Elements of an lrstrumentation System


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Primary Sensing Element

Measurand,the physical quantity under measurement, makes its first contact withtheprimary sensing elementof a measuring system.Good instruments are designed to minimise the disturbance by the act ofmeasurement.


The transducer is defined as a device, which when actuated by one form ofenergy, is capable of converting it into another form of energy.Certain operations are to be performed on the signal so that the signal may not getdistorted.

The process may be linear such as amplification, attenuation, integration,differentiation, addition and subtraction or non-linear such as modulation,detection, sampling, filtering, chopping and clipping etc.

The process is called thesignal conditioning.So signal conditioner follows the

primary sensing element or transducer.


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Variable Conversion Element

The output signal may or may not suit to the system.

It may be necessary to convert this output to some other suitable form.

If out ut is in analo form and the next sta e of the s stem acce ts the in ut onl


in digital form, then analog-digital converter will be required.

Variable Manipulation Element

The function is to manipulate the signal presented to it while preserving theoriginal nature of the signal.

An electronic amplifier converts a small low voltage input signal into high voltageoutput signal.


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Data Presentation Element

The information regarding measurand is to be conveyed to the system formonitoring, controlling or analysis purpose.

Such devices (read out or display) may be in analog or digital format.


The simplest form of a display device is the common panel meter with some kindof calibrated scale and pointer.

In case, the data is to be recorded, recorders like magnetic tape may be used.For control and analysis purpose computers may be used.


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Methods of Measurements

The methods of measurements may be broadly classified into two categories

direct methodsandindirect methods (directorindirect measurement)

Indirect measurementmethods the unknown quantity is measured directly suchas measurement of current by an ammeter, voltage by voltmeter, resistance by


o mme er, power y wa me er e c.

In indirect measurement methods the unknown quantity is determined bymeasuring other functionally related quantities and calculating the desired quantityrather than measuring it directly such as resistance of a conductor may be

determined by measuring voltage across the conductor, V and current flowingthrough the conductor, I and then calculating it by Ohm's lawi.e.,R=V/I.


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Direct methodsof are of two types namelydeflection methodsandcomparison

methods.

Indeflection methodsthe value of unknown quantity is determined by means ofmeasuring instrument having a scale graduated to the quantity under


measuremen rec y suc as measuremen o curren w an amme er.

In comparison methods the unknown quantity is determined by directcomparison with standard of the given quantity such as measurement of emf bycomparison with the emf a standard cell.


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Comparison methods include the null method, differential method and other

methods.

In null method of measurement the action of the unknown quantity upon theinstrument is reduced to zero, such as measurement of weight by a balance,


, , .

Deflection methods of direct measurement are most widely used in electricalengineering practice, being the most simple and least time consuming, thoughtheir accuracy is not ore than 0.2 to 10%.

Direct measurements have the advantage of introducing a smaller eror than thatachieved in indirect measurements.


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History of Development of Instruments

Mechanical Instruments

Electrical Instruments

Electronic Instruments



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History of Development of Instruments

Electronic Instruments

Electronic instruments make use of semiconductor devices.

The response time of such instruments is extremely small as the movementinvolved in electronic devices is only that of electrons and electrons have very


small inertia.

Electronic instruments are gradually becoming more reliable due to improvementsin design and manufacturing processes of semi-conductor devices.

Another advantage of electronic devices is that very weak signals can be detectedby employing pre-amplifiers and amplifiers.

Electronic instruments are light, compact and have a high degree of reliability.

Their power consumption is very small.


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Analog and Digital Modes of Operation

Signals that vary in a continuous fashion and take on an infinite number of values

in any given range are known asanalog signals.

The devices producing such signals are town asanalog devices.


n e o er an , e s gna s w c vary n scre e s eps an us a e up on yfinite different values in a given range are termed asdigital signals.

The devices producing such signals are called thedigital devices.


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Classification of Instruments

Absolute Instruments

Secondary Instrumentso Indicating Instrumentso Recording Instruments


o n egra ng ns rumen

Absolute Instruments

The instruments of this type give the quantity to be measured in terms ofinstrument constant and its deflection.Such instruments do not require any comparison with any other standardinstrument.

Such instruments are seldom used except in standard laboratories.


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Secondary Instruments

The deflection of such instruments gives the magnitude of electrical quantity to bemeasured directly.


absolute instrument.

These instruments are generally used in practice.

Direct measuring instruments convert the energy of the unknown quantity

directly into energy that deflects the moving element of the instrument, the value ofthe unknown quantity being measured by reading the resulting deflection.

Ammeters, voltmeters, wattmeters, fall in this category.


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Comparison instrumentsmeasure the unknown quantity by comparing it with astandard that is often contained in the instrument case such as resistancemeasuring bridges.


Direct measuring instruments are most widely used in engineering practice sincethey are the most simple and inexpensive ones and enable the measurements tobe made in the shortest possible time.

Comparison instruments are used in cases when a higher accuracy of

measurement is needed.


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Electrical measuring instruments may be classified according to:oKind of quantity being measured,oService conditions,


,

oTheir accuracy class,oThe principle of operation of the moving system,oField of application,oProtection against the influence of external fields,oStability against mechanical effects,oMethod of installation and mounting, oroShape and size of the instrument cases and the degree of enclosure they

provide.


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As regards the kind of quantity that is measured,

Quantit Instrument Quantit Instrument


Current Ammeter Frequency Frequency meter

Voltage Voltmeter Resistance Ohm-meter

Power Wattmeter Inductance Inductance-meter

Energy Kilowatt-hour meter Capacitance Capacitance meter


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According to the type of current that can be measured can be classified asinstruments for dc, ac, or dc and ac measurements.


classified aspermanent magnet moving coil(PMMC),moving iron, electrodynamicandinduction types.

Of the moving-coil type measures dc, moving iron and electro-dynamicinstruments may be employed in either dc or ac circuits, and the induction type is

suitable for ac measurements only.


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Indicating Instruments

Indicate the magnitude of an electrical quantity at the time when it is beingmeasured.


Recording Instruments

Keep a continuous record of the variations the magnitude of an electrical quantityto be observed over a definite period of time, the moving system carries an inked

pen which touches lightly a sheet paper wrapped over a drum moving with uniformslow motion.

Such instruments are generally used in power houses where the current, voltageand power etc., are to be maintained within certain specified values.


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Static Characteristics

The static characteristics of an instrument are considered for devices which are

employed to measure an unvarying process condition.

All the static performance characteristics are obtained bycalibration

-


is a device or mechanism used for determining the value or magnitude of aquantity under measurement.

2- Measurementis a process of determining the amount, degree, or capacity by comparison (direct

or indirect) with the accepted standards of the system units being used.


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3- Accuracy

refers to the degree of closeness or conformity to the true value of the quantityunder measurement

#Point Accuracy.the accuracy is stated for only one or more points in its rangei.e.the specification


of such accuracy does not give any information about he general accuracy of theinstrument.This is particularly applicable to temperature-measuring devices, where points areobtained at the melting and vapourizing-temperaturesfpure solids and liquids.

# Percentage of True Value.

When the accuracy of an instrument is expressed in this way, then the error iscomputed as

The percentage error stated is the maximum for any point in the range of theinstrument.


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3- Accuracy

refers to the degree of closeness or conformity to the true value of the quantityunder measurement

#Percentage of Full-Scale Deflection.Here the error is calculated on the basis of maximum value of the scale, thus


#Complete Accuracy Statement.the accuracy at a larger lumber of points is specified in tabulated or graphical

form.


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4- Precision

is a measure of the consistency or repeatability of measurementsi.e. successivereadings do not differ.(Precision is the consistency of the instrument output for a given value of input).

It combines the uncertainty due to both random differences in results in a number


o measuremen s an e sma es rea a e ncremen n sca e or c ar g ven as

the deviation of mean value).

It has no guarantee of accuracy.

5- Sensitivity.

The ratio of a change in output magnitude to the change in input which causes itafter the steady-state has been reached.

The sensitivity will be a constant in a linear instrument or elementi.e.where equalchanges of the input signal causes equal changes of output.

Sensitivity is usually required to be high.


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6- Resolution.

The least interval between two adjacent discrete details, which can bedistinguished one from the other.

It may be expressed as an actual value or as a fraction or percentage of the full-scale value.


7- Error.The algebraic difference between the indicated value and the true value of themeasured signal.

Error = Indicated value - True value

8- Expected Value.The design value, i.e. the most probable value that calculations indicate oneshould expect to measure.


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9- Uncertainty

provides the range within which the true value is estimated to lie.

10-Threshold.If the input to instrument is very gradually increased from zero, there will be someminimum value below which no out ut chan e can he observed or detected. This


minimum value is thethresholdof the instrument.

11- Zero Stability.It describes the ability of the instrument to return to zero reading after themeasurand has returned to zero.

The zero setting of good instruments should not be affected by temperaturevariations, vibrations etc.


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12- Zero Error.

It is an error of a device operating under the specified conditions of use when theinput is at the lower range-value.

The termzero-shiftis often used to represent a change or drift in zero error withtime.


13- Span Error.The difference between the actual span and the ideal span is called the span errorand it is usually expressed as a percent of ideal span.

14- Correction.

The algebraic difference between the true value and the indicated value of themeasured signal.

Correction = True value - Indicated value

Correction is a quantity which is added algebraically to the indicated value so as to

have true value.


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15- Hysteresis.

It is that property of an element evidenced by the dependence of the value of theoutput, for a given excursion of the input, on the history of prior excursions and thedirection of the current traversed.

It is usually determined by subtracting the value of the dead band from the


maximum measured separation between up-scale going and down-scale going

indications of the measured variable

after transients have decayed. This measurement is sometimes calledhysteresiserror.

16- Dead Band.It is the range through which an input can be varied without initiating observableresponse and is usually expressed in percentage of span.


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17- Repeatability.

The closeness of agreement among a number of consecutive measurements ofthe output for the same value of the input under the same operating conditions,approaching from the same direction for full range traverses is called therepeatability.


18- Deviation.It is a departure from a desired or expected value or pattern and may also bedescribed as the difference between measured value and true value for aparticular input value.


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19- Linearity.

It is the closeness to which a curve approximates a straight line.It is measured as a non-linearity and expressed as a linearity, e.g.,a maximumdeviation between an average curve and a straight line.

-


each direction.

20- Independent Linearity.It is the maximum deviation of the calibration curve average of up-scale and down-scale readings) from a straight line so positioned as to minimise the maximum

deviation.

21- Drift.It is an undesired change in the output-input relationship over a period of time.


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Dynamic Characteristics

On application of an input to an instrument or measuring system, it cannot attainits final steady-state position instantaneously.

The fact is that the measurement system passes through atransient statebefore itreaches its final steady-state position.


Some measurements re carried out in such conditions that allow sufficient time forthe instrument or measurement system to settle to its final steady state position.

Under such circumstances the study of behaviour of the system under transientstate, known astransient responseis not of much importance; onlysteady-state

responseis to be considered.

On the other hand, in many measurement systems it becomes imperative to studythe system response under both transient-as well as steady-state conditions.


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In many cases the transient response of the system is more important than itssteady-state response.

As we know that the instruments and measurement systems do not respond to theinput immediately due to the presence of energy storage elements (such as


, .

the system.

The system exhibits a characteristic sluggishness due to the presence of theseelements.

In measurement systems having inputs dynamic in nature, the input varies frominstant to instant, so does the output.

The behaviour of the system under such conditions is dealt by the dynamicresponseof the system, and its characteristics are given below in brief.


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1- Dynamic Error.It is the difference of true value of the quantity changing with time and the valueindicated by the instrument provided static error is zero.

2- Fidelity.


.

In the definition of fidelity any time lag or phase difference is not included.

Ideally a system should have 100% fidelity and the output should appear in thesame form as the input and there is no distortion produced by the system.

3- Speed Response.it is the speed with which an instrument responds to variations in the quantityunder measurement.


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4- Response Time.It is the time required by the instrument or measurement system to settle down toits final steady-state position after the application of the input.

For portable instruments, it is the time taken by the pointer to come to rest within0.3% of its final scale length while for panel type instruments, it is the time taken


y e po n er o come o res w n o s na sca e eng .

5- Measuring LAG.It is defined as the delay in the response of an instrument to a change in themeasurand. This lag is usually quite small but it becomes quite significant wherehigh speed measurements are required.

Measurement lag is of two types. In retardation type, the response of theinstrument begins immediately after a change in the measurand has occurred.

Intime delay type,the response of the system begins after adelay timeafter theapplication of the input.


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Loading Effect

The ideal situation in a measurement system is that when on introducing an

element, used for any purpose into the system, the original signal remainsundisturbed.

However, in practical conditions it has been found that when an element is


n ro uce n a measuremen sys em, ex rac s some energy rom e sys em

and, therefore, original signal is distorted.

Such distortion may take the form of attenuation (reduction in magnitude),waveform distortion, phase shift and many a time all these undesirable featuresput together.

Thus ideal measurement is not practicable. This is known as theloading effect.

I t d ti t M t


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Loading Effect

A measurement system consists of three distinct stages:

(i) detector-transducer stage,(ii) signal conditioning stage including original transmission stage,(iii) signal presentation stage.


e oa ng e ec no on y occurs n e rs s age.

While the first stage detector-transducer loads the input signal, the second stageloads the first stage and finally the third stage loads the second one.

In fact, the loading problem may be carried right-down to the basic elementsthemselves.

The loading effects are due to impedances of various elements connected in asystem.

I t d ti t M t


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Loading Effect

Loading Effects Due To Shunt-Connected Instruments.

In voltage measuring, voltmeters are connected across the circuiti.e.,in parallel(or shunt) with the circuit.


Thevenin's voltage source E0 in series with anoutput impedance Z0,Let the load in the present case be a voltmeter ofinput impedance ZL.

When the load (measuring device or voltmeter) is not connected to its terminals,the voltage across terminals AB will be equal to E0.

Ideally when the load is connected across the terminals A and B, the outputvoltage should remain the same.



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Loading Effect


However, the load impedance is not infinite and therefore when a voltmeter withan input impedance ZL is connected across terminals A and B, it draws somecurrent, say IL amperes.


This causes a voltage drop of ILZ0across the output impedance of the source.

Thus output voltage under loaded condition(i.e.voltage across terminals AB whenload is connected across them),



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Loading Effect


Ratio of actual voltage appearing across the load to the voltage under open-circuited conditions (ideal in this case) is given as


actual voltage measured

Thus the voltage, which is measured, is modified both in phase and magnitude.

This means that the original voltage signal is distorted due to connection ofmeasuring device across it.



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Loading Effect


It is obvious that in order to keep original signal E0undistorted:

the value of the instrument input impedance ZLshould be infinite, or


the value of output impedance of the source, Z0

should be equal to zero which

cannot be attained in practice.

So to have distortion, as small as possible, the input impedance of-the instrument(ZL) should be very large in comparison with source output impedance (Z0).

Since Z0 and ZL depend upon the frequency, the indicated voltage value willdepend upon the frequency of operation.



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Loading Effect


Due to input capacitance effects of the instrument, the value of input impedance ZLbecomes low at high frequencies with the result that the input signal issubstantially distorted at high frequencies.


Thus not only the magnitude of input signal is affected but also its phase at highfrequencies.



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Loading Effect

Loading Effects Due To Series-Connected Instruments.

When the signal is of the form of current then series input devices are used. It ishelpful to use the concept of input admittance in such cases.


Norton's constant current-source I0 in parallel withadmittance Y0.

Let the load in the present case be an ammeter ofinput admittance Yin.

The value of current flowing between terminals A and B under ideal conditions isI0, which is the current that flows when terminals A and B are short-circuited.

When the signal is of the form of current then series input devices are used. It ishelpful to use the concept of input admittance in such cases.



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Loading Effect

Loading Effects Due To Series-Connected Instruments.

When we actually measure the current, an ammeter, is to be connected betweenterminals A and B.


actual current measured

The above equation shows that the input admittance of the series element shouldbe very large as compared with the output admittance of the current-source so asto reduce the loading effect



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t oduct o to easu e e ts

Loading Effect

Ex. 1

A multimeter having an input resistance of 25 kis used to measure the voltageacross a circuit having an output resistance of 1.0 kand an open-circuit voltageof 12 V. Find the error in measurement.



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Nature Of Units

In engineering, quantities of different kinds are involved, including physical,

chemical, mechanical, thermal, electrical and physiological ones.In order to record or to compare magnitude of quantities, some one magnitude ofeach kind must be taken as basis or unit.


Each unit, either must be represented by a physical standard of some kind, natural

or artificial or must be derived from a combination of other units represented bysuch standards.

So the number of times the unit occurs in any given amount of same quantity isthe number of measure.

For example when it is said that length A is 5 metres, it indicates that the metre isthe unit of length and that the number of units of length is five.

So the physical quantity, length is defined by the unit metre. Without unit, thenumber of measure has no physical meaning



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Fundamental And Derived Quantities

Experience shows that three basic ideas or units are sufficient to describe

quantitatively all the phenomena encountered in mechanical science.

These are length, mass and time and are calledfundamental units.


nce eng , mass, an me are un amen a o mos o er p ys ca quan es

besides those in mechanics, they are calledprimary fundamental units.

Measure of certain physical quantities in the thermal, electrical, and illuminationscience are also represented by fundamental units and these are used only whenthese particular physical quantities are involved and so these units are called

auxiliary fundamental units.


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Systems Of Electrical Units

Whereas, three basic concepts and three fundamental units are sufficient for

description and measurement in mechanical science, experience shows that, inelectrical science, four concepts or dimensions and four arbitrarily definedfundamental units are necessary to obtain a complete system of dimensions andunits.


At least one of these four units must be electrical in character.

the various electrical unit systems used are:1. The CGS Electrostatic System of Units (CGS ESU).2. The CGS Electromagnetic System of Units (CGS EMU).

3. The Practical System of Units.4. The MKS System of Units5. Rationalized MRS System of Units6. The Rationalized MKSA System of Units



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1- The CGS Electrostatic System of Units (CGS ESU).

It is an absolute system based on the centimetre, gram and second as the

fundamental mechanical units and permittivity () of the media as fourthfundamental unit.


The unit of permittivity () is of such a size that the measure number of permittivityfor free space is unity,i.e.0= 1.

These units are commonly designated by using the prefixstatwith the name ofcorresponding practical unitse.g. statvolt.



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2- The CGS Electromagnetic System of Units (CGS EMU).

It is another absolute system based on the centimetre, gram and second as thefundamental mechanical units and permeability () of the media as fourthfundamental unit.


The unit of permeability is of such a size that the measure number of permeability

for free space is unityi.e.0=1.

These units are commonly designated by using ab with the name of thecorresponding practical unitse.g. abvolts.

The electro magnetic system is more convenient from the point of view of mostelectrical measurements, and is, therefore, much more generally used than theelectrostatic system .



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3- The Practical System of Units.

Since neither CGS electrostatic units nor CGS electromagnetic units were ofconvenient size for the purpose of practical work, a practical system of units inwhich unit current (ampere) = 1/10 cgs emu of current and unit of potential

= 8


.

Though the practical system is sufficiently extensive to deal with the vastproportion of every day calculations of electrical engineering, but it has gotfollowing defficiencies:(i) The absence of recognised units for magnetic and electrostatic relations,

therefore, some or all the magnetic units used to be expressed in cgs emusystem.

(ii) The practical units are related by conversion factors to those systems of units(cgs esu and cgs emu) in which theoretical relations of the science have beencommonly developed in the past.



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4- The MKS System of Units

It is an absolute system based on the metre, kg and second as fundamentalmechanical units and permeability of the media as fourth unit.

The unit of ermeabilit is of such a size that measure number of ermeabilit for


free space is 10-7.

Its great advantage is that its units are identical with those of practical system andare the same whether built up from the electromagnetic or electrostatic theory.

The value of permittivity for free space, 0in mks system can be determined from

the relation



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5- Rationalized MKS System of Units

The above unrationalized system has been further rationalized by assigningdifferent values to r0and e0. Rationalization means the removal of quantity it from

the places, where its appearance is unnatural, irrational and geometrically


.

By doing so, most of the equations and formulas in electrical engineering havebecome simple and logical.

In RMKS system, the permeability of free space, 0 = 4x10-7 H/metre and

permittivity of free space 0= 8.854 x 10-12 F/metre. The change in the values of

0and 0does not change the values of electrical units but does change the unitsof mmf, magnetizing force etc.

It was Prof. G. Giorgi, who first of all, suggested this system in 1901. After thename of Prof. Giorgi, it is also known asGiorgi system of units.



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The important characteristics of the system are given below:1- A single set of units covers all electrical and magnetic quantities and is

applicable to both electromagnetic and electrostatic effects.


- e va ues o un s use n c rcu eory are en ca w e un s o prac ca

system described above.3- A unit magnetic pole emits a unit magnetic flux and not 4units flux.

4- In cgs systems, the numerical values of magnetizing force H and flux density Bare equal in vacuum, but in rmks system the values of B and H in vacuum are

not equal but are linked through a constant0. B=0Hwhere 0 is named as permeability of free space and its value has beenapparently chosen as 4x 10-7

In magnetic materials B = 0rH, where ris the relative permeability of thematerial and is equal to permeability value in cgs system.



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The important characteristics of the system are given below:5- Similarly in a dielectric flux density, D = o rE (field strength) where oand r

are the permittivity of free space and relative permittivity of the medium.


6- The relation ( ) = velocity of light holds good numerically as well as

dimensionally.

Since these properties (permeability and permittivity of free space) althougheminently suitable as physical reference standards, are less easilycomprehended than such concept as ampere, charge, potential difference or

resistance, therefore, it has been agreed to make, ampere defined from itsmagnetic effect as fourth fundamental quantity and the system developed soi.e. employing metre, kilogram, second and ampere as fundamental units iscalled as RMKSA system

oo


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Introduction To SI System Of Units

Quantity Unit Symbol

Length metre m

Muss kilogram kg


Time second s

Intensity of electric current ampere A

Thermodynamic temperature Kelvin K

Luminous intensity candela cd

Amount of substance mole mol


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The seven basic units as recognised by the General Conference of Weights andMeas-ures are defined as below

(v) Kelvin. The Kelvin is the fraction of the thermo dynamic temperature of 273.16the triple point of water.


(vi) Candela. The candela is the luminous intensity in the perpendicular direction,

of a surface of 1/600 000 square metre of a black body at the temperature offreezing platinum under standard atmosphere pressure.

(vii) Mole. The mole is the amount of substance of a system which contains asmany elementary entities as there are atoms in 0.012 kg carbon 12.

When the mole is used, the elementary entities must be specified and may beatoms, molecules, ions, electrons, other particles, or specified groups of suchparticles



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The SI system, besides seven base units, has following

supplementary units.

Quantity Unit Symbol


ane ang e ra an ra

Solid angle steradian sr



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Introduction To SI System Of UnitsSome of the derived units in SI system are tabulated below:

Quantity Quantity Symbol Unit Unit Symbol

Area A square metre m2

Volume V cubic metre m3

Frequency f hertz Hz

3


Velocity v metre per second m/s

Angular velocity cd radian per second rad/s

Acceleration a metre per second squared m/s2

Angular acceleration a radian per second squared rad/s2

Force F newton N

Torque T newton-metre N-m

Pressure P newton per square metre N/m2

Dynamic viscosity newton-second per square metre Ns/m2

Kinemetic viscosity square metre per second m2/s

Work, energy, quantity of heat E joule J (N-m)


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Meas 201&202 Ch#01 Introduction

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