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7/30/2019 Fundamentals of Electronics - Awais Yasin
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FUNDAMENTALS OF ELECTRONICS
COMPILED BY:
AWAIS YASIN
(COURSE MATERIAL FOR DEPARTMENTAL PROMOTION EXAMINATION (DPE))
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2FUNDAMENTALS OF ELECTRONICS
TABLE OF CONTENTS
CHAPTER 1: REVIEW OF BASIC CONCEPTS ............................................................................. 8BASIC UNDERSTANDING ..................................................................................................... 8
BALANCEOFCHARGE........................................................................................................ 8
CONDUCTORS ....................................................................................................................... 9
INSULATORS.......................................................................................................................... 9
QUANTITYOFCHARGE..................................................................................................... 10
FORCEBETWEENCHARGES:COULOMB'SLAW...................................................... 10
VOLTAGE,CURRENT,ANDPOWERRELATEDCONCEPTS.................................... 12
RESISTORS .......................................................................................................................... 19
Load ........................................................................................................ 20
Labeling ................................................................................................... 21
Color System ............................................................................................ 22
Construction ............................................................................................. 22
Resistively of the Material .......................................................................... 22
Resistor Junctions ..................................................................................... 25
Resistor variations ..................................................................................... 26
Applications .............................................................................................. 27
Specifications ........................................................................................... 28
CAPACITORS ....................................................................................................................... 31
Capacitance .............................................................................................. 32
Capacitor Labeling ..................................................................................... 33
Construction ............................................................................................. 35
Capacitor Materials .................................................................................... 35
Capacitor Junctions ................................................................................... 36
Capacitors in Series ................................................................................... 36
Capacitors in Parallel ................................................................................. 36
RC CIRCUITS ......................................................................................................................... 37
TheTimeConstant .................................................................................................................. 38
GeneralNotesaboutCapacitors ........................................................................................... 40
INDUCTORS ........................................................................................................................... 40
Introduction ............................................................................................. 40
Important Qualities of Inductors ................................................................. 41
Inductance ............................................................................................... 43
Quality factor: Q ....................................................................................... 44Impedance ............................................................................................... 45
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3FUNDAMENTALS OF ELECTRONICS
Inductive Networks ................................................................................... 45
OTHER COMPONENTS ........................................................................................................ 48
Ideal voltage sources ................................................................................. 48
Ideal current sources ................................................................................. 48
Switch ..................................................................................................... 48
Contact Arrangements ............................................................................... 49
DC VOLTAGE AND CURRENT LAWS............................................................................... 51
Ohm's Law ............................................................................................... 51
Kirchhoffs Current Law .............................................................................. 53
Consequences of KVL and KCL .................................................................... 53
NODAL ANALYSIS ............................................................................................................... 57
MESH ANALYSIS .................................................................................................................. 60
THEVENIN / NORTON EQUIVALENTS ............................................................................. 62
Thevenins Equivalents............................................................................... 62
Norton Equivalents .................................................................................... 63
SUPERPOSITION ................................................................................................................... 66
DIAGNOSTIC EQUIPMENT ................................................................................................. 69
DC CIRCUIT ANALYSIS ...................................................................................................... 71
CHAPTER 2: AC CIRCUITS ........................................................................................................... 76
RELATIONSHIP BETWEEN VOLTAGE AND CURRENT ................................................ 76
PHASORS ............................................................................................................................... 77
IMPEDANCE .......................................................................................................................... 78
STEADY STATE .................................................................................................................... 80
CHAPTER 3: TRANSIENT ANALYSIS ......................................................................................... 81
RC CIRCUITS ............................................................................................ 81
RLC CIRCUITS .......................................................................................... 82
CHAPTER 4: ANALOG CIRCUITS ................................................................................................ 87
PASSIVE VERSUS ACTIVE COMPONENTS .................................................................. 88
VACUUM TUBES .................................................................................................................. 88
DIODES ................................................................................................................................... 92
TRANSISTORS ....................................................................................................................... 95
AMPLIFIERS ........................................................................................................................ 104
TRANSISTOR AMPLIFIER CONFIGURATIONS ............................................................. 105
CLASSES ............................................................................................... 108
OPERATIONAL AMPLIFIER ............................................................................................. 109
IDEALOPAMPS...................................................................................................... 113
BASICOP-AMPCONFIGURATIONS................................................................... 114INVERTINGOPAMP.......................................................................... 114
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4FUNDAMENTALS OF ELECTRONICS
NON-INVERTINGOPAMP .................................................................. 117
ADVANCEDOP-AMPCONFIGURATIONS ........................................................ 119
Voltage Follower ................................................................................................................... 119
Difference amplifier ................................................................ ............................................... 120
Summing amplifier ................................................................................................................ 121
Integrator ............................................................. ................................................................. .. 122
Differentiator ................................................................. ......................................................... 123
Real Op Amps ............................................................... ......................................................... 123
DC Behaviour ........................................................................................................................ 124
AC Behaviour ........................................................................................................................ 124
Applications .................................................................. ......................................................... 124
Other Notation ....................................................................................................................... 125
Oscillators .............................................................................................................................. 125
ANALOG MULTIPLIERS ................................................................ .................................... 125
Diode Implementations ............................................................ .............................................. 126
MOS implementation ............................................................... .............................................. 128
CHAPTER 5:DIGITAL CIRCUITS130
OVERVIEW ............................................................................................. 130
BOOLEAN ALGEBRA ................................................................................. 130
Formal Mathematical Operators ............................................................................................... 131
Boolean algebra Laws .............................................................................................................. 132
Associatively ................................................................... ......................................................... 132
Distributives ............................................................................................................................. 132
Commutatively ................................................................ ......................................................... 132
De Morgan's Law ................................................................................................................... .. 132
Notes......................................................................................................................................... 133
Rules .......................................................... ................................................................. .............. 133
Examples .................................................................................................................................. 134
TTL ........................................................................................................ 134
The NOT Gate ............................................................... ......................................................... 134
TTL Inverter (NOT Gate) ...................................................................................................... 135
CMOS .................................................................................................................................... 135
Logic Gates ............................................................................................................................ 136
NOT ....................................................................................................................................... 136
NAND ................................................................ ................................................................ .... 136
AND .................................................................. ................................................................... .. 137
NOR .................................................................. ................................................................... .. 137
OR ........................................................... ................................................................. .............. 137XNOR .................................................................................................................................... 138
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XOR .................................................................. ................................................................... .. 138
INTEGRATED CIRCUIT ..................................................................................................... 138
Overview ............................................................. ................................................................. .. 139
ELEMENTS OF DIGITAL CIRCUITS ............................................................. 139
TRANSISTOR .............................................................. ......................................................... 139
Field Effect Transistor ........................................................................................................... 140
Complementary Metal Oxide Semiconductor .......................................................... .............. 140
Bipolar Junction Transistor .................................................................................................... 141
Construction .................................................................. ......................................................... 141
NPN ....................................................................................................................................... 141
PNP ........................................................................................................................................ 141
Operation................................................................................................................................ 141
BASIC GATES ............................................................. ......................................................... 141
Overview ............................................................. ................................................................. .. 141
Explanation of the gates' operation ........................................................................................ 142
LATCHES AND FLIP FLOPS ............................................................ .................................. 145
RS Flip Flops ......................................................................................................................... 145
D Flip Flops ........................................................................................................................... 146
Toggle Flip Flops .......................................................... ......................................................... 146
JK Flip Flops ................................................................. ......................................................... 147
COUNTERS .......................................................................................................................... 147
Ripple Counters ..................................................................................................................... 147
Synchronous Counters ........................................................................................................... 147
ADDERS................................................................................................................................ 148
Half Adders ................................................................... ......................................................... 148
Full Adders............................................................................................................................. 149
MULTIPLEXERS ......................................................... ......................................................... 150
Overview ............................................................. ................................................................. .. 150
Multiplexer Based Logic .......................................................... .............................................. 150
DECODERS AND ENCODERS ........................................................................................... 151
Decoders ................................................................................................................................ 151
Encoders .............................................................. ................................................................. .. 151
CHAPTER 6: MICROPROCESSORS ........................................................................................... 152
Types of Processors ............................................................................................................... 152
Types of Use .......................................................................................................................... 154
Abstraction Layers ................................................................. ................................................ 154
Moore's Law .......................................................................................................................... 155
Basic Elements of a Computer ............................................................. .................................. 157
Computer Architecture ............................................................. .............................................. 157
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Control ................................................................................................................................... 158
Datapath .............................................................. ................................................................. .. 158
Microprocessor Components ................................................................................................. 159
Instruction Set Architectures ................................................................ .................................. 161
Common Instructions ............................................................... .............................................. 162
Memory ............................................................... ................................................................. .. 162
Microprocessor Components ................................................................................................. 168
Basic Components.................................................................................................................. 168
Registers .............................................................. ................................................................. .. 168
Register File .................................................................. ......................................................... 168
Multiplexers .................................................................. ......................................................... 168
Program Counter ........................................................... ......................................................... 169
Instruction Decoder ................................................................ ................................................ 169
The Instruction Decoder reads the next instruction in from memory, and sends the component
peices of that instruction to the necessary destinations ........................................................ .. 169
RISC Instruction Decoder ...................................................................................................... 169
CISC Instruction Decoder ...................................................................................................... 169
Register File .................................................................. ......................................................... 170
Register File .................................................................. ......................................................... 170
Register Bank ................................................................ ......................................................... 171
Memory Unit ................................................................. ......................................................... 172
Memory Unit ................................................................. ......................................................... 172
Actions of the Memory Unit .................................................................................................. 172
Timing Issues ................................................................ ......................................................... 172
ALU ....................................................................................................................................... 172
Tasks of an ALU .................................................................................................................. .. 173
ALU Slice .............................................................................................................................. 173
Additional Operations .............................................................. .............................................. 175
ALU Configurations .............................................................................................................. 175
Accumulator .................................................................. ......................................................... 176Register-to-Register ................................................................ ............................................... 177
Register Stack ........................................................................................................................ 178
Register-and-Memory .............................................................. .............................................. 179
Complicated Structures ............................................................ .............................................. 179
Example: IA-32 ............................................................. ......................................................... 179
Example: MIPS ............................................................. ......................................................... 180
Floating Point Unit (FPU) ........................................................ .............................................. 180
Floating point numbers .......................................................................................................... 180
IEEE 754 ............................................................. ................................................................. .. 180
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Floating Point Multiplication ................................................................................................. 181
Floating Point Addition ............................................................ .............................................. 181
Floating Point Unit Design .................................................................................................... 181
Control Unit ........................................................................................................................... 182
Simple Control Unit ............................................................................................................... 182
Complex Control Unit .............................................................. .............................................. 182
References: ............................................................................................................................. 182
Suggested Reading Material for further reading .................................................................... 183
Sample Paper (MCQs): .......................................................................................................... 183
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CHAPTER 1: REVIEW OF BASIC CONCEPTS
BASIC UNDERSTANDING
Materialsthatallowelectronstoflowwithminimalresistance.
Materialsthatpreventtheflowofelectrons.
Materialswhosebehaviorrangesbetweenthatofaconductorandthatof
an insulatorunder differentconditions.Their conductingbehavior ismainly dependent on
temperature.
Anatomcontainsanucleusandoneormoreelectrons.Theatomexistsinthree
states: neutral,positively charged,and negatively charged.Aneutralatomhas the same
numberofelectronsandprotons,apositivelychargedatomhasmoreprotonsthanelectrons
andanegativelychargedatomhasmoreelectronsthanprotons.
(+)and(-)Ions
Anionisanatomthathasanunequalnumberofelectronsandprotons.Thenatureofatoms
istotrytohaveanequalamountofprotonsandelectrons.Thepositivesideofthebattery
has + ions, meaning there are less electrons than protons, giving it an overall positive
charge,and-side,moreelectronsthanprotons,givingitanoverallnegativecharge.
BALANCEOFCHARGE
Atoms,thesmallestparticlesofmatterthatretainthepropertiesof thematter, aremadeof
protons,electrons,andneutrons. haveapositivecharge; haveanegative
chargethatcancelstheproton'spositivecharge. areparticlesthataresimilartoa
protonbuthaveaneutralcharge.Therearenodifferencesbetweenpositiveandnegative
charges except that particles with the same charge each other and particles with
oppositecharges eachother. Ifasolitarypositiveprotonandnegativeelectronare
placedneareachothertheywillcometogethertoformahydrogenatom.Thisrepulsionand
attraction (forcebetweenstationarychargedparticles) isknownasthe
and extends theoretically to infinity, but is diluted as the distance between particles
increases.
Bothatomsandtheuniversehavea chargeoverallandcomewiththesamenumberofprotonsandelectrons.Whenanatomhasoneormoremissingelectronsitisleftwitha
charge,andwhenanatomhasatleastoneextraelectronithasa charge.
Havingapositiveor anegativechargemakesanatoman .Atomsonlygainand lose
protons andneutrons through fusion, fission, and radioactive decay. Although atomsare
made of many particles and objects aremade of many atoms, they behave similarly to
chargedparticlesintermsofhowtheyrepelandattract.
Inan theprotonsandneutronscombinetoformatightlyboundnucleus.Thisnucleus
issurroundedbyavastcloudofelectronscirclingitatadistancebutheldneartheprotons
byelectromagneticattraction(theelectrostaticforcediscussedearlier).Thecloudexistsasa
seriesofoverlapping inwhichtheinner bandsarefilledwithelectrons
andaretightlyboundtotheatom.Theouter bandscontainnoelectronsexcept
http://en.wikipedia.org/wiki/protonshttp://en.wikipedia.org/wiki/electronshttp://en.wikipedia.org/wiki/neutronshttp://en.wikipedia.org/wiki/Nuclear_fusionhttp://en.wikipedia.org/wiki/Nuclear_fissionhttp://en.wikipedia.org/wiki/Radioactive_decayhttp://en.wikipedia.org/wiki/Radioactive_decayhttp://en.wikipedia.org/wiki/Nuclear_fissionhttp://en.wikipedia.org/wiki/Nuclear_fusionhttp://en.wikipedia.org/wiki/neutronshttp://en.wikipedia.org/wiki/electronshttp://en.wikipedia.org/wiki/protons7/30/2019 Fundamentals of Electronics - Awais Yasin
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9FUNDAMENTALS OF ELECTRONICS
thosethathaveacceleratedtotheconductionbandsbygainingenergy.Withenoughenergy
anelectronwillescapeanatom(comparewiththeescapevelocityofaspacerocket).When
anelectronintheconductionbanddeceleratesandfallstoanotherconductionbandorthe
valencebandaphotonisemitted.Thisisknownasthe .
When electrons travel back and forth between conduction bands emitting
synchronizedphotons.
Whentheconductionandvalencebandsoverlap,theatomisa andallowsforthe
freemovementof electrons.Conductorsaremetalsandcanbethoughtofasabunchof
atomicnucleisurroundedbyachurning"seaofelectrons".
Whenthereisalargeenergylevelgapbetweentheconductionandvalencebands,theatom
isan ;ittrapselectrons.Manyinsulatorsarenon-metalsandaregoodatblocking
theflowofelectrons.
When there isasmallenergy level gap between the conductionand valence bands, the
atomisa .Semiconductorsbehavelikeconductorsandinsulators,andwork
usingtheconductionandvalencebands.Theelectronsintheoutervalencebandareknown
as .Theybehavelikepositivechargesbecauseofhowtheyflow.Insemiconductors
electrons collidewith thematerial and theirprogress ishalted. Thismakes the electronshavean thatislessthantheirnormalmass.Insomesemiconductorsholes
havealargereffectivemassthantheconductionelectrons.
Electronicdevicesarebasedontheideaofexploitingthedifferencesbetweenconductors,
insulators, and semiconductors but also exploit known physical phenomena such as
electromagnetismandphosphorescence.
CONDUCTORS
Inaconductortheelectronsofanobjectarefreetomovefromatomtoatom.Duetotheirmutualrepulsion(calculableviaCoulomb'sLaw),thevalenceelectronsareforcedfromthe
centeroftheobjectandspreadoutevenlyacrossitssurfaceinordertobeasfarapartas
possible.ThiscavityofemptyspaceisknownasaFaradayCageandstopselectromagnetic
radiation,suchascharge,radiowaves,andEMPs (Electro-MagneticPulses)fromentering
andleavingtheobject.IfthereareholesintheFaradayCagethenradiationcanpass.
One of the interesting things todowithconductors isdemonstrate the transfer ofcharge
betweenmetalspheres.Startbytakingtwoidenticalandunchargedmetalsphereswhichare
eachsuspendedbyinsulators(suchasapiece.Thefirststepinvolvesputtingsphere1next
tobutnottouchingsphere2.Thiscausesalltheelectronsinsphere2totravelawayfrom
sphere1tothefarendofsphere2.Sosphere2nowhasanegativeendfilledwithelectrons
andapositiveendlackingelectrons.Nextsphere2isgroundedbycontactwithaconductor
connectedwiththeearthandtheearthtakesitselectronsleavingsphere2withapositive
charge.Thepositivecharge(absenceofelectrons)spreadsevenlyacrossthesurfacedueto
itslackofelectrons.Ifsuspendedbystrings,therelativelynegativelychargedsphere1will
attracttherelativelypositivelychargedsphere2.
INSULATORS
Inan insulator theelectronsof anobjectarestuck.Thisallowscharge tobuild uponthe
surface of the object by way of the turboelectric effect. The turboelectric effect (rubbing
electricityeffect) involvesthe exchangeofelectronswhen twodifferent insulatorssuchas
http://en.wikibooks.org/wiki/Modern_Physics:Coulomb%27s_Law_and_the_Electric_Fieldhttp://en.wikibooks.org/wiki/Electronics/Signal_Propagationhttp://en.wikibooks.org/wiki/Electronics/Signal_Propagationhttp://en.wikibooks.org/wiki/Modern_Physics:Coulomb%27s_Law_and_the_Electric_Field7/30/2019 Fundamentals of Electronics - Awais Yasin
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10FUNDAMENTALS OF ELECTRONICS
glass,hardrubber,amber,oreventheseatofone'spants,comeintocontact.Thepolarity
andstrengthof thecharges produceddiffer according to thematerial compositionand its
surfacesmoothness.Forexample,glassrubbedwithsilkwillbuildupacharge,aswillhard
rubberrubbedwithfur.Theeffectisgreatlyenhancedbyrubbingmaterialstogether.
Van de Graff generator: A charge pump (pump for electrons) that generates
electricity.InaVandeGraffgenerator,aconveyorbeltusesrubbingtopickupelectrons,
whicharethendepositedonmetalbrushes.Theendresultisachargedifference.
Becausethematerialbeingrubbedisnowcharged,contactwithanunchargedobjectoran
objectwiththeoppositechargemaycauseadischargeofthebuilt-upstaticelectricitybyway
ofaspark.Apersonsimplywalkingacrossacarpetmaybuildupenoughchargetocausea
sparktotraveloveracentimeter.Thesparkispowerfulenoughtoattractdustparticlesto
cloth,destroyelectricalequipment,ignitegasfumes,andcreatelightning.Inextremecases
thesparkcandestroyfactoriesthatdealwithgunpowderandexplosives.Thebestwayto
remove static electricity isbydischarging it throughgrounding.Humid air will alsoslowly
discharge static electricity. This isone reasonwhy cells and capacitors lose charge over
time.
Note:Theconceptofaninsulatorchangesdependingontheappliedvoltage.Airlooks likean insulator whena low voltage isapplied. But itbreaks downasan insulator,becomes
ionized, at about ten kilovolts per centimeter. A person could put their shoe across the
terminalsofacarbatteryanditwouldlooklikeaninsulator.Butputtingashoeacrossaten
kilovoltpowerlinewillcauseashort.
QUANTITYOFCHARGE
Protons and electrons haveoppositebut equalcharge. Because in almost all cases, the
chargeonprotonsorelectronsisthesmallestamountofchargecommonlydiscussed,the
quantity of charge of one proton is considered one positive elementary charge and thecharge of one electron is one negative elementary charge. Because atoms and such
particles are sosmall, and charge inamountsofmulti-trillionsofelementarychargesare
usuallydiscussed,amuchlargerunitofchargeistypicallyused.Thecoulombisaunitof
charge, which can be expressed as a positive or negative number, which is equal to
approximately 6.24151018 elementary charges. Accordingly, an elementary charge is
equal to approximately 1.60210-19 coulombs. The commonly used abbreviation for the
coulombisacapitalC.TheSIdefinitionofacoulombisthequantityofchargewhichpasses
apointoveraperiodof1second(s)whenacurrentof1ampere(A)flowspastthatpoint,
i.e.,C=AsorA=C/s.Youmayfindithelpfulduringlaterlessonstoretainthispicturein
yourmind (even though youmay not recall the exactnumber). Anampere is oneof thefundamental units in physics from which various other units are defined, such as the
coulomb.
FORCEBETWEENCHARGES:COULOMB'SLAW
Therepulsiveorattractiveelectrostaticforcebetweenchargesdecreasesasthechargesare
located further fromeachotherby thesquareofthedistancebetweenthem.Anequation
calledCoulomb's lawdeterminestheelectrostaticforcebetweentwochargedobjects.The
followingpictureshowsachargeqatacertainpointwithanotherchargeQatadistanceofr
awayfromit.ThepresenceofQcausesanelectrostaticforcetobeexertedonq.
http://en.wikibooks.org/wiki/Electronics/Cellshttp://en.wikibooks.org/wiki/Electronics/Capacitorshttp://en.wikipedia.org/wiki/SIhttp://en.wikibooks.org/wiki/Electronics/Voltage%2C_Current%2C_and_Powerhttp://en.wikipedia.org/wiki/amperehttp://en.wikipedia.org/wiki/amperehttp://en.wikibooks.org/wiki/Electronics/Voltage%2C_Current%2C_and_Powerhttp://en.wikipedia.org/wiki/SIhttp://en.wikibooks.org/wiki/Electronics/Capacitorshttp://en.wikibooks.org/wiki/Electronics/Cells7/30/2019 Fundamentals of Electronics - Awais Yasin
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11FUNDAMENTALS OF ELECTRONICS
ThemagnitudeoftheelectrostaticforceF,onachargeq,duetoanotherchargeQ,equals
Coulomb'sconstantmultipliedbytheproductofthetwocharges(incoulombs)dividedbythe
squareofthedistancer,between thechargesqandQ.HereacapitalQandsmallqare
scalarquantitiesusedforsymbolizingthetwocharges,butothersymbolssuchasq1andq2
havebeenusedinothersources.Thesesymbolsforchargewereusedforconsistencywith
theelectricfieldarticleinWikipediaandareconsistentwiththeReferencebelow.
F = magnitude of electrostatic force on charge q due to another charge Q
r = distance (magnitude quantity in above equation) between q and Q
k=Coulomb'sconstant=8.9875109Nm2/C2infreespace
The value of Coulomb's constant given here is such that the preceding Coulomb's Law
equation will work if both qandQaregiven in units of coulombs, r inmeters, andF in
newtonsandthereisnodielectricmaterialbetweenthecharges.Adielectricmaterialisone
thatreducestheelectrostaticforcewhenplacedbetweencharges.Furthermore,Coulomb's
constantcanbegivenby:
where =permittivity.Whenthereisnodielectricmaterialbetweenthecharges(forexample,
infreespaceoravacuum),
=8.8541910-12C2/(Nm2).
Air isonlyveryweaklydielectricand thevalueabove for willworkwell enoughwithair
betweenthecharges.Ifadielectricmaterialispresent,then
whereisthedielectricconstantwhichdependsonthedielectricmaterial.Inavacuum(free
space),=1andthus=0.Forair,=1.0006.Typically,solidinsulatingmaterialshave
valuesof>1andwillreduceelectricforcebetweencharges.Thedielectricconstantcan
alsobecalledrelativepermittivity,symbolizedasr
Highlychargedparticlesclosetoeachotherexertheavyforcesoneachother;ifthecharges
arelessortheyarefartherapart,theforceisless.Asthechargesmovefarenoughapart,
theireffectoneachotherbecomesnegligible.
Any force on an object is a vector quantity. Vector quantities such as forces arecharacterizedbyanumericalmagnitude(i.e.basicallythesizeoftheforce)andadirection.
http://en.wikibooks.org/wiki/Scalarhttp://en.wikipedia.org/wiki/Electric_fieldhttp://en.wikibooks.org/wiki/Vectorhttp://en.wikibooks.org/wiki/Vectorhttp://en.wikipedia.org/wiki/Electric_fieldhttp://en.wikibooks.org/wiki/Scalar7/30/2019 Fundamentals of Electronics - Awais Yasin
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13FUNDAMENTALS OF ELECTRONICS
Thepotentialdifferencebetweentwotestpoints resultingfrom thedistributionof
chargeinthecircuit,usuallymeasuredinvolts.
Netamountofcharge(numberofelectrons)flowingpastaspecifiedpoint,usually
measured inAmps. In typical components and systems the quantity ofelectrons isquite
largeandtheaggregatechargeflowisreferredtoaselectricity.
Energygiveninacertainamountoftime,usuallymeasuredinwatts.
Oppositechargesattractwhilesimilarchargesrepel.
Whenelectricitypassesthroughawireitcreatesamovingmagneticfieldaround
thewire.ThetypicalunitofmeasureisHenrys.
Whenelectricfieldsorchargedistributionsarecreatedinaphysicalsystem
that stores recoverable energy, characteristics of the physical components which affect
calculationoftheelectricalquantitiesaredefinedascapacitance.ThebaseunitofmeasureisFarads,howevermicrofarads(F),areusedmuchmoreoften.
Whenpotentialdifferencecreatesmovementofelectronsbetweentwopoints,
someofthepotentialenergyformerlyavailableinthesystemisirreversiblytransferredfrom
theelectricfieldortheelectronsmovingthroughthecomponentviacollisionswithatomsand
moleculeswithinthematerial.Ohm'sLaw,V=IR,definesresistanceasR=V/IwhereVisthe
voltagedifferenceappliedacrossthecomponent,IistheresultingcurrentflowinAmps,and
R isaconstantcreatedbycharacteristics of the componentwhich iscalculated from the
measuredvoltagelossofthemeasuredcurrentpassingthroughthecomponent.
Achargedparticlesuchasaprotonorelectronmay"feel"anelectricalforceonitinacertain
environment.Thisforceistypicallyduetothepresenceofotherchargesnearby.Theforce
willhaveadirectionandmagnitude,andcanberepresentedbyavector.(Avectorissimply
aquantitythatrepresentsthedirectionandmagnitudeofsomething.)Themagnitudeofthe
forcedependsonthechargeoftheparticle,thechargeontheparticlesaroundit,andhow
closeorfarawaytheyare:Highlychargedparticlesclosetoeachotherexertheavyforces
on each other; if the charges are less, or they are farther apart, the force is less. The
directionoftheforcedependsonthelocationofthesurroundingcharges.
Indescribingtheelectricalenvironmentatthatlocation,it issaidthereisanelectricfieldat
thatlocation.Theelectricfieldisdefinedastheforcethatasingleunitofchargewouldfeel
atthatlocation.Insomesystemsofmeasurement,theunitofchargeisthechargeofasingle
proton;inothersitisthecoulomb.Acoulombisthechargeof6.241018protons
Therelationshipbetweenforceandelectricfieldforasinglechargedparticleisgivenbythe
followingequation:
Theboldlettersindicatevectorquantities.Thismeansthatachargeq,inanelectricfieldE,
havingacertaindirectionandmagnitudeE,wouldhaveaforceFonit,inthesamedirection
andwithamagnitudeF.Consideringonly themagnitudes, thefollowingwouldresult fromthedefinition.
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14FUNDAMENTALS OF ELECTRONICS
E=F/qtheseareallmagnitudesornumericalquantities
The net electric fieldE,ata location isdue to the presenceofall otherchargesnearby,
similartothenetelectricforceF,iftherewasachargeqatthatlocation.Thecontributionof
oneoftheseotherchargestothetotal(ornet)electricfieldisavectorEcontribution,which
for apointcharge canbederivedfromCoulomb's Law.Distributionsofcharge density in
variousshapesmayalsoyieldvectorEcontributionstothetotalelectricfield,tobeaddedin
asvectorquantities.Practicallyspeaking,mostelectricians,electricalengineers,andother
electricalcircuitbuildersandhobbyistsseldomdothesesortsofelectricfieldcalculations.
Electricfieldcalculationsofthissortaremoreofatheoreticalphysicsorspecialapplications
problem,sothesecalculationsareomittedhereinfavorofmoreapplicablematerial.Seelink
forsuchinformationonelectricfieldformulas.
Thereisanelectrical forceona chargeonly if thereis achargesubject tothe forceata
locationinanelectric field.However,even ifthere isnosuchchargesubject totheforce,
therecouldstillbeanelectricfieldatapoint.Thismeansthatanelectricfieldisapropertyof
a locationorpoint in spaceand its electrical environment,whichwoulddeterminewhata
chargeqwould"feel"ifitwerethere.
Now,amicro-physicsreview:Workiscausingdisplacement(ormovement)ofanobjector
matteragainstaforce.Energyistheabilitytoperformworklikethis.Energycanbekinetic
energyorpotentialenergy.Kineticenergy istheenergyamasshasbecauseitismoving.
Potential energy in an object, in matter, in a charge or other situation has the ability to
performworkortobeconvertedintokineticenergyoradifferentkindofpotentialenergy.
Areasonwhyaparticleorachargemayhavepotentialenergycouldbebecauseitislocated
atapointinaforcefield,suchasagravitationalfield,electricfield,ormagneticfield.Inthe
presenceof suchafield,gravityor electricormagneticforcescouldcause theparticle or
charge to move faster or move against resistive forces, representing a conversion ofpotential energy to kinetic energy or work. The amount of potential energy it haswould
depend on its location.Moving fromone location toanother couldcause a change in its
potential energy.
For example, an object near the surface of the earth placed high would have a certain
amountofgravitationalpotentialenergybasedon itsmass, location (heightoraltitude) in
and strengthof the earth'sgravitational field. If the object were to drop from this location
(height)toanewlowerlocation,atleastsomeofitsgravitationalpotentialenergywouldbe
converted to kinetic energy, resulting in the object moving down. The difference in
gravitational potential energy could be calculated from one location to another, but
determiningtheabsolutepotentialenergyoftheobjectisarbitrary,sogroundlevelischosen
arbitrarilyas theheightwhere itsgravitational potential energyequalszero. Thepotentialenergyatallotherheightsisdeterminedfromthemassoftheobject,locationrelativetothe
groundlevel,andstrengthofthegravitationalfield.
Allenergyvaluesarenumericalorscalarquantities,notvectors.
Somewhat similarly, a charged particle at a certain point or location in an electrical
environment(i.e.anelectricfield)wouldhaveacertainamountofelectricpotentialenergy
basedonitscharge,location,andtheelectricfieldthere,whichcouldbebasedonquantity
andlocationsofallotherchargesnearby.Ifthechargeweretomovefromthislocationtoa
newlocationorpoint,itcouldcauseachangeinitselectricpotentialenergy.Thisdifferenceinelectricpotentialenergyinthechargeparticlewouldbeproportionaltoitschargeandit
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15FUNDAMENTALS OF ELECTRONICS
couldbeanincreaseoradecrease.Frommeasurementsandcalculations,onemaybeable
todeterminethisdifferenceinelectricpotentialenergy,butcomingupwithanabsolutefigure
for its potential isdifficult and typically not necessary. Therefore, inamanner somewhat
similar to gravitational potential energy, an arbitrary location or point nearby, often
somewhere intheelectric circuit inquestion, ischosen tobethepointwherethe electric
potential energy would be zero, if the charge were there. Often the wiring, circuit, or
appliancewillbeconnectedtotheground,sothisgroundpointisoftenchosentobethezero
point.Theelectricpotentialenergyatallother points isdetermined relativeto theground
level.TheSIunitofelectricpotentialenergyis,ofcourse,thejoule.
Becausetheelectricpotentialenergyofachargedparticle(orobject)isproportionaltoits
chargeandotherwisesimplydependentonitslocation(pointwhereit'sat),ausefulvalueto
use iselectricpotential. Electric potential (symbolizedbyV) at a point is defined as the
electricpotentialenergy(PE)perunitpositivecharge(q)thatachargewouldhaveatthat
givenpoint(location).Atapointa,theelectricpotentialataisgivenby:
Va=(PEofchargeata)/qSomewhatanalogouslytoanelectricfield,electricalpotentialisapropertyofalocationand
theelectricalconditionsthere,whetherornotthereisachargepresenttheresubjecttothese
conditions.Ontheotherhand,electricpotentialenergyismoreanalogoustoelectricforcein
thatforittobepresent,thereshouldbeasubjectchargedparticleorobjectwhichhasthat
energy.Electricpotentialisoftensimplycalledpotentialbyphysicists.BecausetheSIunitof
electricpotentialenergyisthejouleandbecausetheSIunitofchargeisthecoulomb,theSI
unitforelectricpotential,thevolt(symbolizedbyV),isdefinedasajoulepercoulomb(J/C).
Becauseelectricpotentialenergyisbasedonanarbitrarypointwhereitsvalueissetatas
zero,thevalueofelectricpotentialatagivenpointisalsobasedonthissamearbitraryzero
point(referencepointwherethepotentialissetatzero).Thepotentialatagivenpointaisthenthedifferencebetweenpotentialsfrompointatothezeropoint,oftencalledaground
node(orjustground).
Calculationsofelectricpotential energyorelectricpotentialbasedonCoulomb's Laware
sometimestheoreticallypossible,suchasmightbeforelectricfieldcalculations,butagain
these are of mostly theoretical interest and not often done in practical applications.
Therefore,suchcalculationsarealsoomittedhereinfavorofmoreapplicablematerial.
Often it isof interest tocomparethepotentialsat twodifferentpoints,whichwemay call
pointaandpointb.Thentheelectricpotentialdifferencebetweenpointsaandb(Vab)would
bedefinedastheelectricpotentialatbminustheelectricpotentialata.
Vab=Vb-Va
Theunitforelectricpotentialdifferenceisthevolt,thesameasforelectricpotential.Electric
potential difference is often simply called potential difference by physicists. Under direct
current (DC) conditions and at any one instant in time under alternating current (AC),
potential andpotentialdifference arenumerical orscalarquantities,notvectors,andthey
canhavepositiveornegativevalues.
iselectricpotentialexpressedinvolts.Similarly, potential differenceexpressed in
voltsisoftencalled oroftenreferredtoasvoltageacrosstwopointsor
across an electrical component. The terms electric potential, potential, and potentialdifferencearetermsmoreoftenusedbyphysicists.Sincethesequantitiesarealmostalways
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16FUNDAMENTALS OF ELECTRONICS
expressed in volts (or some related unit such as milli volts), engineers, electricians,
hobbyists, and common people usually use the term voltage instead of potential.
Furthermore, inpracticalapplications,electrical force,electricfield,andelectricalpotential
energyofchargedparticlesarenotdiscussednearlyasoftenasvoltage,power,andenergy
inamacroscopicsense.
Additionalnote:Thefollowingexplainswhyvoltageis"analogous"tothepressureofafluid
inapipe(although,ofcourse,itisonlyananalog,notexactlythesamething),anditalso
explains the strange-sounding "dimensions" of voltage. Consider the potential energy of
compressedairbeingpumpedintoatank.Theenergyincreaseswitheachnewincrementof
air.Pressureisthatenergydividedbythevolume,whichwecanunderstandintuitively.Now
considertheenergyofelectriccharge(measuredincoulombs)beingforcedintoacapacitor.
Voltage is that energy per charge, so voltage is analogous to a pressure-like sort of
forcefulness.Also,dimensionalanalysistellsusthatvoltage("energypercharge")ischarge
perdistance,thedistancebeingbetweentheplatesofthecapacitor
Whenanelectriccircuitisoperatingin DirectCurrent (DC)mode,allvoltagesandvoltagedifferences in the circuit are typically constant (do not vary)with time.When a circuit is
operating under Alternating Current (AC) conditions, the voltages in the circuit vary
periodicallywithtime;thevoltagesareasinusoidalfunctionoftime,suchasV(t)=asin(bt)
withconstantaandb,orsomesimilarfunction.Thenumberoftimestheperiodrepeats(or
"cycles") per unit time iscalled the frequencyofV(t).UnderDC conditionsoratanyone
instantintimeunderAC,potential(orvoltage)andpotentialdifference(orvoltagedifference)
are numerical or scalar quantities, not vectors, and they can have positive or negative
values. However, in AC mode, the overall function of voltage with time V(t), can be
expressedasacomplexnumberoraphasorforagivenfrequency.Thefrequencycanbe
expressed in cycles per second or simply sec-1, which is called (Hz) in SI units.TypicalcommercialelectricpowerprovidedintheUnitedStatesisACatafrequencyof60
Hz.
Ground isshownonelectronicsdiagrams, but it isn't really acomponent. It issimply the
nodewhichhasbeenassigneda voltageofzero. It is representedbyoneof thesymbols
below. Technically, any single node can beassigned asground, and other voltagesare
measured relative to it.However, the convention is toonly assign it inone of two ways,
relatedtothetypeofpowersupply.Inasinglesupplysituation,suchasacircuitpoweredby
a single battery, the ground point is usually defined as themore negative of the power
source's terminals. Thismakesall voltages in the circuit positivewith respect to ground
(usually),andisacommonconvention.Forasplit-supplydevice,suchasacircuitdrivenby
acenter-tappedtransformer,usuallythecentervoltageisdefinedasground,andthereare
equalandroughlysymmetricalpositiveandnegativevoltagesinthecircuit.
Signal
Ground
Chassis
Ground
Earth
Ground
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Groundforasignal.Sincewireshaveacertainamountofresistancetothem,groundpoints
inacircuitaren'tallatexactlythesamevoltage.Itisimportantinpracticalcircuitdesignto
separatethepowersupplygroundfromthesignalgroundfromtheshieldingground,etc.In
circuitswhereminimumnoiseisespeciallyimportant,powerregulatorcircuitryshouldhave
thickwiresortracesconnectingthegrounds,inasequence fromthepower supply tothe
"cleanest"groundattheoutputofthefiltersofthepowersupply,whichwillthenbea"star
point"forthegroundsofthesignalcircuitry.
Adirectconnectiontothechassisofthedevice.This isused forEMIshieldingandalsofor
safetygroundinlineACpowereddevices.
Usedinradioorpowerdistributionsystems,aconnectiontotheEarthitself.Alsotheother
endoftheconnectionfor the safetyground,sincethepower linevoltagewillseekapath
throughtheEarthbacktothepowerlinesupplystation.Thiswastheoriginalusageofthe
word"ground",andthemoremodernmeaningofthewordwouldhavebeencalleda"floatingground".
Theearthgroundsymbolandsignalgroundsymbolareofteninterchangedwithoutregardto
their original meanings. As far as signal-level electronics (and this book) is concerned,
groundalmostalwaysmeansasignalgroundorfloatingground,notconnectedtotheearth
itself.
oftencalledjustcurrent,isthemovementofchargeinaconductor(suchas
awire)orinto,outof,orthroughanelectricalcomponent.Currentisquantifiedasarateof
positivechargemovementpastacertainpointorthroughacross-sectionalarea.Simplyput,
current isquantified aspositive charge per unit time.However, sincecurrent isa vector
quantity, the direction inwhich the current flows is still important.Current flow inagiven
directioncanbepositiveornegative;thenegativesignmeansthatpositivechargesmove
opposite of the given direction. The quantity of current at a certain point is typically
symbolizedbyacapitalorsmall letter Iwithadesignationwhichdirectionthecurrent I is
moving.TheSI unitofcurrentistheampere(A),oneofthefundamentalunitsofphysics.
See ampere for thedefinitionofampere.Sometimes, ampere is informallyabbreviated to
amp. The definition of a coulomb (C), the SI unit of charge, is based on an ampere. A
coulomb is the amount of positive charge passinga pointwhen a constant one ampere
currentflowsbythepointforonesecond.ThesecondistheSIunitoftime.Inotherwords,acoulombequalsanampere-second(As).Anampereisacoulombpersecond(C/s).
Typically,currentisinametalandconstitutesmovementofelectronswhichhavenegative
charge;however,peopleinitiallythoughtthatcurrenthadapositivecharge.Theresultisthat
even though current is the flowofnegativeelectronsand flows from the negative to the
positiveterminalofabattery,whenpeopledocircuitanalysistheypretendthatcurrentisa
flowofpositiveparticlesandflowsfromthepositivetothenegativeterminalofabattery(or
otherpowersource).Actually,itismorecomplicatedthanthis,sincecurrentcanbemadeup
ofelectrons,holes,ions,protons,oranychargedparticle.Sincetheactualchargecarriers
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areusuallyignoredwhenanalyzingacircuit,current issimplifiedandthoughtofasflowing
frompositivetonegative,andisknownasconventionalcurrent.
Analogytopebbletossing:IhavepebblesandIamthrowingthemintoabasket.Indoingthis
thebasketgainspebblesandIlosepebbles.Sothereisanegativecurrentofpebblestothe
basket because it is gaining pebbles, and there is a positive current of pebbles to me
because I am losing pebbles. In pebble tossing the currents have equal strength but in
oppositedirections.
CurrentIisrepresentedinamperes(A)andequalsxnumberofy
Powerisenergyperunitoftime.TheSIunitforpoweristhe (W)whichequalsa
(J/s),withjoulebeingtheSIunitfor andsecondbeingtheSIunitfor .
When somebody plugs an appliance into a receptacle to use electricity to make that
appliancefunction,thatpersonprovideselectricalenergyfortheappliance.Theappliance
usually functions by turning that electrical energy into heat, light, or work or perhapsconvertsitintoelectricalenergyagaininadifferentform.Ifthissituationisongoing,itissaid
thatthereceptacleorelectricpowercompanydeliverspowertotheappliance.Thecurrent
fromthereceptaclegoinginandoutoftheapplianceeffectivelycarriesthepowerandthe
applianceabsorbsthepower.
Multiplyingaunitofpowerbyaunitoftimewouldresultinaunitthatrepresentsaquantityof
energy.Therefore,multiplyingakilowattbyanhourgivesakilowatt-hour(kWh),aunitoften
usedbyelectricalpowercompaniestorepresentanamountofelectricalenergygeneratedor
providedtoconsumers.
Fordirectcurrent(DC),powerPcanbecalculatedbymultiplyingthevoltageandcurrent,
whentheyareknown.
P=VI
Notethatenergy/chargeismultipliedbycharge/timetogiveenergy/time.Atanyonepointin
timetinalternatingcurrent(AC)circuitry,powerP(t)equalsvoltageV(t)timescurrentI(t).
P(t)=V(t)I(t)atanyonetimet
CalculationsofACpoweraveragedovertimewillbediscussedunderACpower.
An electronic is a system in which conventional current flows from the positive
terminalofasource,throughaload,tothenegativeterminalofthesource.
Ashortcircuitisanothernameforanode,althoughitusuallymeansanunintentionalnode.
Hascurrentthroughitbutnovoltageacrossit.
Haspotentialacrossitbutnocurrentthroughit.
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Theoretical circuit connection (wire) has no resistance or inductance. Real wires always
have voltage over them if there is current flowing through them (resistance). On high
frequencies there are markable voltage potentials over wire links if there is flowing
alternatingcurrentthroughwires(inductancelikeininductors).
Twomaterials with a voltage difference between them.This causes current to flow
whichdoeswork.Electronstravelfromthecathode,dosomework,andareabsorbedbythe
anode.
Destinationofelectrons.
Sourceofelectrons.
Anatomwithanimbalanceofelectrons.thecellrunsandelectronsaredepletedatthecathodeandaccumulateatthe
anode.Thiscreatesareversevoltagewhichstopstheflowofelectrons.
oncethecellrunsoutofjuiceitisdead.
abletorunthecellbackwards.
thecellcanberunbackwardsbytheapplicationofelectricity.
humidairwilldischargecells.
cellsareusuallymadeoftoxicorcorrosivesubstances,forexampleleadandsulphuricacid.
Theyhavebeenknowntoblowup.
Whatistherelationshipbetweenvoltageandelectronegativity?
isaconceptinchemistryusedtomeasureandpredicttherelativelikilihood
ofachemical reactioncausingelectronsto shift fromonechemicalto anotherresulting in
ionsandmolecularbonds.Abatterycell operatesbyallowing twochemicals to reactand
supply ions to theanodeand cathode.When the supply of a reactant is consumed, the
batteryisdead.Itnolongerproducesdifferentelectricalpotentialattheanodeandcathode
drivenbythechemicalreaction.
Voltageistheelectricalpotentialofapointduetosurroundingmeasurableelectriccharge
distributions and points as calculated by application Coulomb's Law. Voltage difference
betweentwopointsconnectedbyaconductorresultsinelectronflow.
RESISTORS
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Aresistorisablockofmaterialthatlimitstheflowofcurrent.Thegreatertheresistance,the
lowerthecurrentwillbe.Sinceconductorshavean"electronsoup"aroundtheatoms,they
behave like a wide pipe filled with water, and have low resistance to a flow of water.
Insulators,ontheotherhand,behavemorelikeatinypipe,orasponge-filledpipe.While
theyareporousandallowcurrenttoflow,aspongethatismoredenseandhaslessholes
willhaveahigher resistanceanda smallerflowof current,if thepressurepushingon the
wateristhesame.
Resistancecanvaryfromverysmalltoverylarge.Asuperconductorhaszeroresistance,
whilesomethingliketheinputtoanop-ampcanhavearesistancenear1012,andeven
higher resistances arepossible. Formostmaterials, as temperature increases resistance
tendstoincreaseaswell.Resistanceconvertselectricalenergyintoheat.Resistorswhich
dissipate largeamountsofpowerarecooledso thattheyarenot destroyed, typicallywith
finnedheatsinks.
Resistorshavetwo leads (pointsofcontact) towhich the resistorcanbe connected toan
electricalcircuit.Asymbolforaresistorusedinelectricalcircuitdiagramsisshownbelow.Thetwoblackdotsindicatethepointsofcontactfortheresistor.Theratioofthevoltageto
currentwillalwaysbepositive,sinceahighervoltageononesideofaresistorisapositive
voltage,and a currentwill flow from the positiveside to the negative side, resulting in a
positivecurrent.Ifthevoltageisreversed,thecurrentisreversed,leadingagaintoapositive
resistance.
TheratioofvoltagetocurrentisreferredtoasOhm'sLaw,andisoneofthemostbasiclaws
thatgovernelectronics.
(Ohm'slawisnotnecessarilyexpressedinthisway,butdoesexpressthatanoppositionis
equivalenttotheratioofacausetotheeffect)
Unlikesomeelectricalcomponents,itdoesnotmatterwhichwayyoupluginresistors;they
have no polarity. Also, asmost electronics components have internal resistance, this is
sometimesshownbyputtingaresistorinserieswiththecomponenttotaketheresistance
intoaccount.
Resistanceisgiveninohms()where:
Anohmis theamountof resistancewhichpassesoneampereofcurrentwhenaonevolt
potentialisplacedacrossit.(Theohmisactuallydefinedastheresistancewhichdissipates
onewattofpowerwhenoneampereofcurrentispassedthroughit.)
Lowervaluedresistorsaresometimesreferredtoasa load.Aresistordissipatesenergyas
electronsstriketheatomsandtransfertheenergytotheresistormaterial.Aloadisdefined
as the power dissipated between two terminals. Usually, this is an output, and the
compositionoftheloadisunknown.Thismeasureisnotrelatedtotheconductance,whichistheinverseofresistance.ConductanceismeasuredinSiemens(S)orsometimesreferredto
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asMhos (-1).Used as an adjective, a load hasa load with ameasurable power draw
(expressedinWatts).Thepowerdrawn(load)istheamountofvoltageacrosstheterminals
multipliedbythecurrentthroughtheterminals.
Power:
AfterOhm'slawissubstitutedintotheequation
:
ForanACsignaloranykindofchangingsignal,theaveragepowerdissipatedisrelatedto
theRMSvalueofthevoltage,notthepeak-to-peakvoltage:
Forapuresinewave,therelationshipbetweenpeak-to-peakvoltageandRMSvoltageis
Soaresistorwith1VDCacrossitandanequal-valueresistorwith1VRMS=1.414VPPAC
sinusoidwillbothdissipatethesameamountofpower(heat).
Consider thedefinitionofPowerRating,below.When associating resistors toproducean
equivalentLoad,wecanhaveanequivalentresistancewhichislargerorsmallerthaneach
individualelement, dependingon the typeofassociation beingseries orparallel, but the
equivalent power ratingwill always be larger thaneach individual powerratings. Inother
words:Twoequalvalueresistorsinparallelwillhavehalftheresistancebuttwicethepowerrating.
Twoequalvalueresistorsinserieswillhavetwicetheresistanceandtwicethepowerrating.
Amanufacturedresistorisusuallylabeledwiththenominalvalue(valuetobemanufactured
to) and sometimes a tolerance. Rectangular resistors will usually contain numbers that
indicatearesistanceandamagnitude.Iftherearethreeorfournumbersontheresistor,the
firstnumbersarearesistancevalue,andthelastnumberreferstothemagnitude.Ifthereis
anRinthevalue,theRtakestheplaceofthedecimalpoint.
2003means200103=200k
600means60100=60
2R5means2.5
R01means0.01
Cylindrical resistors (axial) usually have colored bands that indicate a number and a
magnitude.Resistancebandsarenexttoeachother,withatolerancebandslightlyfarther
awayfromtheresistancebands.Startingfromtheresistancebandsideoftheresistor,each
colorrepresentsanumberinthesamefashionasthenumbersystemshownabove.
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COLORSYSTEM
Black Brown Red Orange Yellow Green Blue Violet Grey White
0 1 2 3 4 5 6 7 8 9
B.B.ROYofGreatBritainwasaVeryGoodWorker.
A gold band in the magnitude position means -1, but means a 5%
tolerance.Asilverbandinthemagnitudepositionmeans-2,butmeansa10%tolerance.
The resistanceR ofacomponent isdependentonitsphysicalcharacteristicsandcanbe
calculatedusing:
whereistheelectricalresistively(resistancetoelectricity)ofthematerial,Listhelengthof
thematerial,andAisthecross-sectionalareaofthematerial.
IfyouincreaseorLyouincreasetheresistanceofthematerial,butifyouincreaseAyou
decreasetheresistanceofthematerial.
RESISTIVELY OF THEMATERIAL
Everymaterialhasitsownresistively,dependingonitsphysicalmakeup.Mostmetalsareconductorsandhaveverylowresistively;whereas,insulatorssuchasrubber,wood,andair
allhaveveryhighresistively.Theinverseofresistivelyisconductivity,whichismeasuredin
unitsofSiemens/meter(S/m)or,equivalently.Mhos/meter.
In the following chart, it is not immediately obvioushow the unit ohm-meter is selected.
Consideringasolidblockofthematerialtobetested,onecanreadilyseethattheresistance
oftheblockwilldecreaseasitscross-sectionalareaincreases(thuswideningtheconceptual
"pipe"),andwillincreaseasthelengthoftheblockincreases(lengtheningthe"pipe").Given
a fixed length, the resistance will increase as the cross-sectional area decreases; the
resistance, multiplied by the area, will be a constant. If the cross-sectional area is held
constant,asthelengthisincreased,theresistanceincreasesinproportion,sotheresistance
dividedbythelengthissimilarlyaconstant.Thusthebulkresistanceofamaterialistypically
measuredinohmmeterssquaredpermeter,whichsimplifiestoohm-meter(-m).
Silver 1.5910-8
Copper 1.610-
Gold 1.710-8
Aluminum 2.8210-
Tungsten 5.610-
Iron 1010-
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Platinum 1110-
Lead 2210-
Nichrome1.5010- (Anickel-chromiumalloycommonlyusedinheating
elements)
Graphite ~10-
Carbon 3.510-
PureGermanium 0.6
PureSilicon 640
Common purified
water~103
Ultra-purewater ~105
Pure Gallium
Arsenide~106
Diamond ~1010
Glass 10 to10
Mica 91013
Rubber 10 to10
Organicpolymers ~1014
Sulfur ~10
Quartz(fused) 5to751016
Air veryhigh
Silver, copper,gold,andaluminumarepopularmaterials forwires,dueto low resistively.
Siliconandgermaniumareusedassemiconductors.Glass,rubber,quartzcrystal,andair
arepopulardielectrics,duetohighresistively.
Manymaterials,suchasair,haveanon-linearresistancecurve.Normalundisturbedairhas
a high resistance, but air with a high enough voltage applied will become ionized and
conductveryeasily.
Theresistivelyofamaterialalsodependsonitstemperature.Normally,thehotteranobjectis, themore resistance it has.Athigh temperatures, the resistance isproportional to the
absolute temperature. At low temperatures, the formula is more complicated, and what
countsasa highor low temperaturedependsonwhat theresistor ismade from.Insome
materials the resistively drops to zero below a certain temperature. This is known as
superconductivity,andhasmanyusefulapplications.
(Somematerials,suchassilicon,havelessresistanceathighertemperatures.)
For all resistors, the change in resistance for a small increase in temperature is directly
proportionaltothechangeintemperature.
Currentpassing througha resistorwillwarm it up. Many componentshaveheat sinks to
dissipatethatheat.Theheatsinkkeepsthecomponentfrommeltingorsettingsomethingonfire.
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unitsm2cancel:
Which,afterevaluating,givesyouafinalvalueof8.010-6,or8microohms,averysmall
resistance? The method shown above included the units to demonstrate how the unitscancelout,butthecalculationwillworkaslongasyouuseconsistentunits.
InternetHint:Googlecalculatorcandocalculationslikethisforyou,automaticallyconverting
units.Thisexamplecanbecalculatedwiththislink:[1]
Usedfor power resistors, sincethepower per volume ratiois highest.These
usuallyhavethelowestnoise.
These areeasy to produce, but usually have lots of noise because of the
propertiesofthematerial.
These resistors have thermal and voltage noise attributes that are between
carbonandwirewound.
Usefulforhighfrequencyapplications.
RESISTORJUNCTIONS
Resistors in series are equivalent to having one long resistor. If the properties of tworesistors are equivalent, except the length, the finalresistancewillbethe sumof the two
constructionmethods:
Thismeansthattheresistorsaddwheninseries.
Christmastreelightsareusuallyconnectedinseries,sothatifonelightblows,theotherswillallgoout.However,moststringshavebuiltinshuntresistorsinparalleltothebulb,sothatcurrentwillflowpasttheblownlightbulb.
Inaparallelcircuit,currentisdividedamongmultiplepaths.Thismeansthattworesistorsinparallelhavea lowerequivalent resistance thaneitherof theparallel resistors,sinceboth
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resistorsallowcurrenttopass.Tworesistorsinparallelwillbeequivalenttoaresistorthatis
twiceaswide:
Sinceconductance(theinverseofresistance)addinparallel,yougetthefollowingequation:
Forexample,two4resistorsinparallelhaveanequivalentresistanceofonly2.
To simplify mathematical equations, resistances in parallel can be represented with two
verticallines"||"(asingeometry).Fortworesistorstheparallelformulasimplifiesto:
Resistorsinparallel areevaluatedas if inamathematicalsetof "parentheses."Themost
basicgroupofresistorsinparallelisevaluatedfirst,thenthegroupinserieswiththenew
equivalentresistor,thenthenextgroupof resistorsinparallel,andsoon.Forexample,the
aboveportionwouldbeevaluatedasfollows:
RESISTOR VARIATIONS
Variableresistorsaretunable,meaningyoucanturna
dialorslideacontact andchange the resistance.Theyare usedasknobs tocontrol the
volumeofastereo,orasadimmerforalamp.Oftenabbreviatedas'pot'.Itisconstructed
likearesistor,buthasaslidingtapcontact.Potentiometersareusedas VoltageDividers.It
is rare to finda variable resistorwith only two leads.Most are potentiometerswith three
leads,evenifoneisnotconnectedtoanything.
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29FUNDAMENTALS OF ELECTRONICS
entirerangeofspecificationsshouldbeconsidered.Usually,exactvaluesdonotneedtobe
known,butrangesshouldbedetermined.
The nominal resistance is the resistance that can beexpected whenordering a resistor.
Finding a range for the resistance is necessary, especially when operating on signals.
Resistorsdonotcomeinallofthevaluesthatwillbenecessary.Sometimesresistorvalues
can be manipulated by shaving off parts of a resistor (in industrial environments this is
sometimesdonewithaLASERtoadjustacircuit),orbycombiningseveralresistorsinseries
andparallel.
Available resistor values typically comewith a resistance value from a so called resistor
series.Resistorseriesaresetsof standard, predefinedresistancevalues.Thevaluesare
actuallymadeupfromageometricsequencewithineachdecade.Ineverydecadethereare
supposedtobenresistancevalues,withaconstantstepfactor.Thestandardresistorvalues
withinadecadearederivedbyusingthestepfactori
roundedtoatwodigitprecision.ResistorseriesarenamedEn,accordingtotheusedvalue
ofnintheaboveformula.
nValues/DecadeStepfactoriSeries
----------------------------------------
61.47E6
121.21E12
241.10E24
481.05E48
For example, in the E12 series for n = 12, the resistance steps in a decade are, after
roundingthefollowing12values:
1.00,1.20,1.50,1.80,2.20,2.70,
3.30,3.90,4.70,5.60,6.80,and8.20
andactuallyavailableresistorsfromtheE12seriesareforexampleresistorswithanominal
valueof120or4.7k.
Amanufacturedresistorhasacertaintolerancetowhichthe resistancemaydifferfromthe
nominalvalue.Forexample,a2kresistormayhaveatoleranceof5%,leavingaresistor
withavaluebetween1.9kand2.1k(i.e.2k100).Thetolerancemustbeaccounted
forwhendesigningcircuits.Acircuitwithanabsolutevoltageof5V0.0Vinavoltagedividernetworkwithtworesistorsof2k5%willhavearesultantvoltageof5V10%(i.e.5V0.1V).
The finalresistor tolerancesare foundby taking the derivativeof the resistorvalues,and
pluggingtheabsolutedeviationsintotheresultingequation.
TheabovementionedE-serieswhichareusedtoprovidestandardizednominalresistance
values, are also coupled to standardized nominal tolerances. The fewer steps within a
decadethereare,thelargertheallowedtoleranceofaresistorfromsuchaseriesis.More
preciseresistors,outsideofthementionedE-seriesarealsoavailable,e.g.forhigh-precision
measurementequipment.Commontolerances,colorsandkeycharacters used to identify
themareforexample:
SeriesValues/DecadeToleranceColorCodeCharacterCode
--------------------------------------------------------------
E6620%[none][none]
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resistoristobeusedasathermostatinthoseranges.Thesimplifiedlinearizedformulafor
theaffectontemperaturetoaresistorisexpressedinanequation:
R=R0[1+(TT0)]
Real world resistors not only show the physical property of resistance, but also have a
certaincapacityandinductance.Thesepropertiesstarttobecomeimportant,ifa resistoris
used in some high frequency circuitry. Wire wound resistors, for example, show an
inductancewhichtypicallymakesthemunusableabove1kHz.
Resistorscanbepackagedinanywaypossible,butaredividedintosurfacemount,through
hole,solderingtagandafewmoreforms.Surfacemountisconnectedtothesamesidethat
the resistor ison. Throughhole resistors have leads (wires) that typically go through the
circuit boardand are soldered to the boardon the side opposite the resistor, hence the
name.Resistors with leads are also used in point-to-point circuitswithout circuit boards.Solderingtagresistorshavelugstosolderwiresorhighcurrentconnectorsonto.
Usualpackagesforsurfacemountresistorsarerectangular,referencedbyalengthanda
widthinmils(thousandsofaninch).Forinstance,an0805resistorisarectanglewithlength
.08"x.05",withcontacts(metalthatconnectstotheresistor)oneitherside.Typicalthrough
holeresistorsarecylindrical,referencedeitherbythelength(suchas0.300")orbyatypical
powerratingthatiscommontothelength(a1/4Wresistoristypically0.300").Thislength
doesnotincludethelengthoftheleads.
CAPACITORS
Acapacitor(historicallyknownasa"condenser")isadevicethatstoresenergyinanelectric
field,byaccumulatinganinternalimbalanceofelectriccharge.Itismadeoftwoconductors
separatedbyadielectric(insulator).Usingthesameanalogyofwaterflowingthroughapipe,
acapacitorcanbethoughtofasatank,inwhichthechargecanbethoughtofasavolumeof
waterinthetank.Thetankcan"charge"and"discharge"inthesamemannerasacapacitor
doestoanelectriccharge.Amechanicalanalogyisthatofaspring.Thespringholdsa
chargewhenitispulledback.
Whenvoltageexistsoneendofthecapacitorisgettingdrainedandtheotherendisgetting
filledwithcharge.Thisisknownascharging.Chargingcreatesachargeimbalancebetweenthe twoplatesandcreatesareversevoltage thatstopsthecapacitor fromcharging.Asa
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32FUNDAMENTALS OF ELECTRONICS
result, when capacitors are first connected to voltage, charge flows only to stop as the
capacitor becomes charged. When a capacitor is charged current stops flowing and it
becomesanopencircuit.Itisasifthecapacitorgainedinfiniteresistance.
Youcanalsothinkofacapacitorasafictionalbatteryinserieswithafictionalresistance.
Starting the charging procedure with the capacitor completely discharged, the applied
voltageisnotcounteractedbythefictionalbattery,becausethefictionalbatterystillhaszero
voltage,andthereforethechargingcurrentisatitsmaximum.Asthechargingcontinues,the
voltageof the fictional battery increases, and counteracts the appliedvoltage,sothat the
chargingcurrentdecreasesasthefictionalbattery'svoltageincreases.Finallythefictional
battery'svoltageequalstheappliedvoltage,sothatnocurrentcanflowinto,noroutof,the
capacitor.
Justasthecapacitorchargesitcanbedischarged.Thinkofthecapacitorbeingafictional
battery that supplies at first a maximum current to the "load", but as the discharging
continuesthevoltageof thefictionalbatterykeepsdecreasing,andthereforethedischarge
currentalsodecreases.Finallythevoltageofthefictionalbatteryiszero,andthereforethe
dischargecurrentalsoisthenzero.
This is not the same asdielectric breakdown where the insulator between the capacitorplatesbreaksdownanddischargesthecapacitor.Thatonlyhappensat largevoltagesand
the capacitor is usually destroyed in the process. A spectacular example of dielectric
breakdownoccurswhenthetwoplatesofthecapacitorarebroughtintocontact.Thiscauses
allthechargethathasaccumulatedonbothplatestobedischargedatonce.Suchasystem
ispopularforpoweringlaserswhichneedlotsofenergyinaverybriefperiodoftime.
CAPACITANCE
Thecapacitanceofacapacitorisaratiooftheamountofchargethatwillbepresentinthe
capacitorwhenagivenpotential(voltage)existsbetweenitsleads.Theunitofcapacitance
isthefaradwhichisequaltoonecoulombpervolt.Thisisaverylargecapacitanceformost
practical purposes; typicalcapacitors have valueson theorder ofmicrofaradsor smaller.
Thebasicequationforcapacitanceis.
Where C is the capacitance in farads, V is the potential in volts, and Q is the charge
measuredincoulombs.Solvingthisequationforthepotentialgives:
Theimpedanceofacapacitoratanygivenangularfrequencyisgivenby:
wherejis ,istheangularfrequencyandCisthecapacitance.
Thechargeinthecapacitoratanygiventimeistheaccumulationofallofthecurrentwhich
hasflowedthroughthecapacitor.Therefore,thepotentialasafunctionoftimecanbewritten
as:
Wherei(t)isthecurrentflowingthroughthecapacitorasafunctionoftime.
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TantalumcapacitorshavehighcapacitanceandlowESR,butlowoperatingvoltages.When
tantalumcapacitorsfail,ittendstobe"spectacular,"theyessentiallyblowup.
Thecapacitanceofaparallel-platecapacitorconstructedoftwoidenticalplaneelectrodesof
areaAatconstantspacingDisapproximatelyequaltothefollowing:
where C is the capacitance in farads, 0 is thePermittivity of Space, r is theDielectric
Constant,Aistheareaofthecapacitorplates,andDisthedistancebetweenthem.
Adielectricis thematerialbetweenthetwochargedobjects.Dielectricsareinsulators.They
impede the flowofcharge innormaloperation.Sometimes,whena too large voltagehas
been reached,chargestarts flowing.This iscalleddielectric breakdownand
Beginnerssometimes misunderstand this. Timing circuits do measure the
rate at which a capacitor charges, but they measure a threshold voltage instead
of allowing the voltage to build up until dielectric breakdown. (A device which
does function this way is a spark gap.)
No charge should ever flow from one plate to the other. Although a current does
flow through the capacitor, charges are not actually moving from one plate to
the other. As charges are added to one plate, their electric field displaces like
charges off of the other plate. This is called a displacement current.
CAPACITORMATERIALS
Capacitors can be made either polarized or non-polarized. A polarized capacitor
requires that the capacitor be hooked up such that the voltage is always biased
in one direction. Hooking a polarized capacitor backwards will result in the
capacitor exploding, sometimes releasing harmful fumes. Non-polarized
capacitors can be biased in either direction without harm to the capacitor.
Polarized and non-polarized capacitors have an upper limit of voltage, where the
material will break down and the capacitor will no longer function. This can also
cause fumes to be released depending on the type of material.
Different materials and their properties.These are normally low capacitance (between ~1pF to ~1F). Ceramic
capacitors have a very low inductance due to the shape. This means that the
capacitance value continues into extremely high frequencies, making them
perfect for RF applications. However, ceramic capacitors tend to vary their
capacitance with temperature.
C0G or NP0 - Typical 4.7 pF to 0.047 F, 5%. High tolerance and temperature
performance. Larger and more expensive.
X7R - Typical 3300 pF to 0.33 F, 10%. Good for non-critical coupling, timing
applications.
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Z5U - Typical 0.01 F to 2.2 F, 20%. Good for bypass, coupling applications.
Low price and small size.
Slightly larger than ceramic, but still has small values (usually in
the picofarad range).
Polyester: from about 1 nF to 1 F
Polypropylene: low-loss, high voltage, resistant to breakdownThese are polarized capacitors that are still small enough to be
surface mount. Normally the dielectric breakdown voltage is rather low, so the
capacitors are not suitable for high voltage applicatons, typcially greater than 20
volts. Tantalum capacitors have a stable capacitance across varying
temperatures, and low ESR.
These are also polarized, are much larger than tantalums. The
dielectric strength is much higher in these, and so is the capacitance.
Capacitance values can range between 1F and 1mF (sometimes up into the
farad range). These are compact capacitors that are also very loss. They are
useful for smoothing power supplies because of the high capacitance.Air-gap
These capacitors are more compact than normal electrolytic capacitors,
giving capacitance values in the farad range, but normally have an extremely
low breakdown voltage.
Super capacitors 2500 F to 5000 F
CAPACITORJUNCTIONS
Capacitors in SeriesCapacitors in series are the same as increasing the distance between two
capacitor plates. As well, it should be noted that placing two 100 V capacitors in
series results in the same as having one capacitor with the total maximum
voltage of 200 V. This, however, is not recommended to be done in practice.
Especially with capacitors of different values. In a capacitor network in series,
.
In a series configuration, the capacitance of all the capacitors combined is the
sum of the reciprocals of the capacitance of all the capacito
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