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GROUNDINGAND SHIELDING GROUNDINGAND SHIELDING CIRCUITSANDINTERFERENCE SIXTHEDITION RalphMorrison
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ISBN:9781119183747
Typesetin11/13ptTimesLTStdbySPiGlobal,Chennai,India
PrefacetotheSixthEditionxi
AHistoricalPerspectiveintoGroundingandShieldingxv
1.VoltageandCapacitors1
1.1.Introduction1 1.2.ChargesandElectrons4
1.3.TheElectricForceField6
1.4.FieldRepresentations6
1.5.TheDefinitionofVoltage9
1.6.EquipotentialSurfaces10
1.7.TheForceFieldorEFieldBetweenTwoConducting Plates11
1.8.ElectricFieldPatterns12
1.9.TheEnergyStoredinAnElectricField16
1.10.Dielectrics17
1.11.TheDField18
1.12.Capacitance19
1.13.MutualCapacitance21 1.14.DisplacementCurrent22
1.15.EnergyStoredinaCapacitor23
1.16.ForcesintheElectricField24
1.17.Capacitors25
1.18.DielectricAbsorption25
1.19.ResistanceofPlaneConductors26
2.Magnetics27
2.1.MagneticFields27
2.2.Ampere’sLaw29
2.3.TheSolenoid30
2.4.Faraday’sLawandtheInductionField30
2.5.TheDefinitionofInductance32
2.6.TheEnergyStoredinanInductance32 v
2.7.MagneticFieldEnergyinSpace34
2.8.ElectronDrift36
2.9.TheMagneticCircuit36
2.10.AMagneticCircuitwithaGap38
2.11.SmallInductors39
2.12.Self-andMutualInductance40
2.13.TransformerAction40
2.14.HysteresisandPermeability45
2.15.EddyCurrents46
3.DigitalElectronics48
3.1.Introduction49
3.2.TheTransportofElectricalEnergy49
3.3.TransmissionLines–Introduction50
3.4.TransmissionLineOperations52
3.5.TransmissionLineFieldPatterns54
3.6.ATerminatedTransmissionLine54
3.7.TheUnterminatedTransmissionLine56
3.8.AShortCircuitTermination58
3.9.TheRealWorld59
3.10.SineWavesVersusStepVoltages60
3.11.ABitofHistory61
3.12.IdealConditions61
3.13.ReflectionandTransmissionCoefficients62
3.14.TakingEnergyfromanIdealEnergySource63
3.15.ACapacitorasaTransmissionLine63
3.16.DecouplingCapacitorsandNaturalFrequencies65
3.17.PrintedCircuitBoards66
3.18.Two-LayerLogicBoards67
3.19.Vias68
3.20.TheTerminationofTransmissionLines70
3.21.EnergyintheGround/PowerPlaneCapacitance72
3.22.Poynting’sVector73
3.23.SkinEffect74
3.24.MeasurementProblems:GroundBounce75
3.25.BalancedTransmission76
3.26.RibbonCableandConnectors77
3.27.InterfacingAnalogandDigitalCircuits78
4.AnalogCircuits80
4.1.Introduction80
4.2.Instrumentation81
4.3.History83
4.4.TheBasicShieldEnclosure83
4.5.TheEnclosureandUtilityPower86
4.6.TheTwo-GroundProblem88
4.7.InstrumentationandtheTwo-GroundProblem89
4.8.Strain-GaugeInstrumentation92
4.9.TheFloatingStrainGauge93
4.10.TheThermocouple95
4.11.TheBasicLow-GainDifferentialAmplifier (ForwardReferencingAmplifer)96
4.12.ShieldinginPowerTransformers98
4.13.CalibrationandInterference99
4.14.TheGuardShieldAbove100kHz100
4.15.SignalFlowPathsinAnalogCircuits101 4.16.ParallelActiveComponents101
4.17.FeedbackStability–Introduction102
4.18.FeedbackTheory103
4.19.OutputLoadsandCircuitStability105
4.20.FeedbackAroundaPowerStage105
4.21.ConstantCurrentLoops106
4.22.FiltersandAliasingErrors107
4.23.IsolationandDC-To-DCConverters108
4.24.ChargeConverterBasics110
4.25.DCPowerSupplies113
4.26.GuardRings113 4.27.ThermocoupleEffects114
4.28.SomeThoughtsonInstrumentation114
5.UtilityPowerandFacilityGrounding115
5.1.Introduction115
5.2.History116
5.3.Semantics116
5.4.UtilityPower117
5.5.TheEarthasaConductor119
5.6.The Neutral ConnectiontoEarth120
5.7.GroundPotentialDifferences122
5.8.FieldCouplingtoPowerConductors124
5.9. Neutral Conductors125
5.10. k FactorinTransformers126
5.11.PowerFactorCorrection127
5.12.UngroundedPower127
5.13.ARequestforPower128
5.14.EarthPowerCurrents129
5.15.LineFilters129
5.16.IsolatedGrounds130
5.17.FacilityGrounds–SomeMoreHistory132
5.18.GroundPlanesinFacilities134
5.19.OtherGroundPlanes137
5.20.GroundatRemoteSites137
5.21.ExtendingGroundPlanes137
5.22.Lightning138
5.23.LightningandFacilities139
5.24.LightningProtectionforBoatsandShips141
5.25.GroundingofBoatsandShipsatDock143
5.26.AircraftGrounding(Fueling)144
5.27.GroundFaultInterruption(GFI)144
5.28.IsolationTransformers145
5.29.GroundingandthePacificIntertie147 5.30.SolarWind148
6.Radiation149
6.1.HandlingRadiationandSusceptibility149
6.2.Radiation150
6.3.SineWavesandTransmissionLines151
6.4.ApproximationsforPulsesandSquareWaves152
6.5.RadiationfromComponents156
6.6.TheDipoleAntenna157
6.7.WaveImpedance158
6.8.FieldStrengthandAntennaGain159
6.9.RadiationfromLoops160
6.10.E-FieldCouplingtoaLoop162
6.11.RadiationfromPrintedCircuitBoards163
6.12.TheSnifferandtheAntenna164
6.13.MicrowaveOvens165
7.ShieldingfromRadiation166
7.1.CableswithShields166
7.2.Low-NoiseCables168
7.3.TransferImpedance169
7.4.Waveguides172
7.5.ElectromagneticFieldsoveraGroundPlane173
7.6.FieldsandConductors174
7.7.ConductiveEnclosures–Introduction175
7.8.CouplingThroughEnclosureWallsbyanInduction Field176
7.9.ReflectionandAbsorptionofFieldEnergy ataConductingSurface177
7.10.IndependentApertures178
7.11.DependentApertures179
7.12.Honeycombs180
7.13.SummingFieldPenetrations181
7.14.PowerLineFilters182
7.15.BackshellConnectors184
7.16.H-FieldCoupling186
7.17.Gaskets186
7.18.FingerStock187
7.19.GlassApertures188
7.20.GuardingLargeTransistors188
7.21.MountingComponentsonSurfaces188
7.22.Zappers190
7.23.ShieldedandScreenRooms190
AppendixA.TheDecibel192 FurtherReading194 Index195
PREFACETOTHESIXTHEDITION Sixeditionsofabookthatspans50yearsissurelyunique.Iwantto thankJohnWileyforstayingwithmeforallthesedecades.Iwantto thankBrettKurzman,myneweditor,forgettingmeacontract.Iwant tothankmywifeElizabethforhercontinuoussupport.Iwanttothank allthereadersthathavesupportedmeovertheyears.Ifithadnotbeen fortheurgingofDanBeekerofNXPSemiconductor,therewouldnot havebeenafifthedition.Forthisreason,Iowehima“thankyou”for makingasixtheditionpossible.Ihavebeenpuzzlinghowtomakethis editionmoreeffectiveandIfeelmyopeningstatementsarekey.Ineed totellthestorysothatthereaderwillappreciatemyapproach. Therearemanymeaningstothewordsgroundingandshielding. ToanEnglishspeaker,thenonengineeringapplicationoftheword “ground”canincludesuchdiverseusageascoffeegrounds,groundsfor dismissal,playgrounds,groundround,orgroundfloor.Thenonengineeringuseofshieldcanincludesuchtopicsaswindshield,police badge,metalarmor,orprotectiveclothing.Inanelectricalsense, groundcanmeanearth,theminussideofabattery,theconducting planeonacircuitboard,theneutralpowerconductor,orametalcabinet.Peopleinvolvedwithelectricityoftenassociatethesewordswith protectionagainstelectricalinterference.Thebooktitleisintendedto conveythismeaning.Eachreaderofthisbookwillstartwithaunique setofexperiencesassociatedwiththesewords.Iwanttobroadenthat experience.
Ihavebeeninvolvedinelectricalgroundingandshieldingforover 50years.Myunderstandingcomesfrommyexperiences,myinterests, andfrommyeducation.Ihaverewrittenthisbookevery10yearssince 1967becausetheelectricalworldkeepschanging.Also,Ikeeplearning andthebooksdosell.GroundingandShieldingisanimportanttopic asitrelatestobothcostandperformanceinabouteveryaspectofour moderntechnology.Thesubjectisdifficulttopresentformanyreasons.
First,itisrelatedmorecloselytoconductorgeometrythanitisto circuitcontent.Next,alotoftheinformationthatispassedonthrough usageissimplyloreandsomeofitiswrongormisleading.Thismeans thatoftenengineershavepreconceivedideasandneedtodosome unlearningtogetthingsstraight.Insomecases,thegroundingrules ausermustfollowareapartofacodeoraregulationthatleavesno choices.Whentherulesareprintedonfancypaper,itiseasytoassume theyarevalid.Iftherulesareinerror,arguingagainsttheestablishment canbeveryfrustrating.Unfortunately,notallrulesareeffectiveor practical.Andfinally,thesubjectisnottaughtinschoolsandengineers areoftenontheirowntofindanswers.Ihavealsofoundthatquality controlpeoplewillfollowwrittenrulesratherthantheopinionofone outsideengineerorauthor.Theyrespectauthority,whichiswhatthey areexpectedtodo.Ihavehadsomepoliteargumentsthathavelasted years,wheremyviewpointkeepsbeingquestioned.Fromthisfact alone,Iknowjusthowingrainedsomeviewpointscanbecome. Thesubjectofgroundingandshieldingcomesupinmostdesigns. Becauseitisnotanexactscience,therecanbemanyopinionsasto wheretoconnectshieldsandreferencesignals.Someapproachesare loreandarepassedonbycopyingpastdesignsorbywordofmouth. Inmostcases,thereisnosimpletestthattellsifaviewpointisvalid. Wemayknowhowtotestapieceofhardwarebuttestingabuilding isanothermatter.Thereisanimportantquestionthatmustbeasked. Whatmeasurementswouldyouliketomake?WheredoIputmyvoltageprobes?Eveniftestscouldbemade,makingchangestoalarge systemcanbeveryexpensive.Inmanycases,theideasusedinadesign arevalidbutoversomelimitedrange.Apersonwithamisconception mayfinditdifficulttoacceptadifferentexplanation.Thisisespecially truewhenmanydifferentopinionshavebeenexpressed.Ifindthatfor goodreason,engineersareveryskepticalaboutanexplanationthatsuggestsanewviewpoint.Theydonotknowwhatorwhomtobelieve. Anotherproblemisthattheengineeringidiomisconstantlychanging andsometimesvalidexplanationsfailtocommunicate.Thesubjectlies somewherebetweentradepracticesandphysicsandthisisawideseparation.Itisasubjectareathatdoesnotfitintoacademia.Tosome managers,groundingseemslikeajobforatechnician.Inreality,itis oftenaverysophisticatedandcomplexissue.Fortheseandmanyother reasons,itistimetowriteasixthedition.Iwanttotrytogetthemessageacrossfortoday’sdesigners.Asmuchaspossible,Iwanttokeep opinionstoaminimumandIwanttofocusonconnectingthissubjectto basicprinciples.Iwanttousephysicsasthebasisforexplanationsbut withoutgettingtoomathematical.
IhavetakenwhatIfeelisauniquepositionindiscussinggrounding andshielding.Circuittheoryleavesthedistinctimpressionthatconductorscarrysignals.Thefactisthatconductorsguidetheflowoffield energyandthisfieldenergycancarrysignals,interference,andoperate components.Naturedoesnotdistinguishbetweenthesethreefunctions. Wedefinitelyneedcircuitstodescribeourintentions.Weneedcircuit theorytoanalyzethesecircuits.Weneedtoapplybasicphysicswhen circuittheoryisnotsufficient.Wehavetokeeppower,signals,andinterferenceseparatedbecausenatureisnotgoingtoofferanyhelp.We needtoappreciatethatnearlyallelectricalactivitytakesplaceinthe spacesbetweenconductors.Itistheintentofthisbooktoclearlypoint outhowthisverykeyideacansolveproblems.Thisfieldtransportidea iscoveredinphysicscourses.Theconnectionbetweentheseideasand practicaldesigningisusuallymissingintextbooksandintheclassroom. Thearrangementofthespacesbetweenconductorscankeepvarious fieldsseparated.Thiscontrolofconductorgeometryisthejobofthe designer.Thisisthecentralthemeofthisbook.
Thisbookisnotanintroductiontocircuittheory.Iassumethereader isfamiliarwithhowacircuitworks.Itisalsonotanintroductionto appliedphysics.Itisaboutallthethingsthathappenwhenaneducationmeetstherealworld.Theproblemsthataresolvedinatextbook arenothingliketheproblemsthatarefacedbythenewdesigner.After graduation,therearenoteachersaroundtoexplainhowtoproceed.
Isolvedmanyproblemsusingmyintuitionandmypastexperiences. Littlebylittlemyunderstandinggrew.Overtime,itbecameclearthatI shouldhaveusedmoreofmyeducationandlessofmyintuition.Thisis easytosayandnotveryeasytodo.Intherealworld,problemsmustbe resolvednotstudied.Mostproblemsaremultidimensionalanddonotfit justonesubject.Findingawaythroughamazemaynotbeveryefficient butexperimentingwiththemazetolearnmoreisnotoftendone.That takestimeandthatmeansspendingresources.
Iwastoldaboutdisplacementcurrentincollege.IneverappreciatedthevalueofthisconceptuntilIbeganwritingaboutdigitalcircuits. ThenIdiscoveredthisidealetmeexplainhowcurrentflowsintothe distributedcapacitanceofatransmissionline.Inreadingtheliterature, Ihadneverseenthisexplanation.IpresentthisideainthisbookandI hopeithelpstoexplaintherealworldtoothers.
Inlookingbackatthefifthedition,InoticedhowaustereChapter 1appeared.Readingthismaterialseemedalittleliketakingmedicine togetwell.Itisnotfun.EventhoughIwroteitwithgoodintentions andIwasexcitedtotellthisstory,thematerialdidnotappearinviting. Tocorrectthiscondition,Idecidedtoopenthissixtheditionwithsome
ofmybackgroundanddescribeafewofmyexperiencestoillustrate whythisbasicphysicsiscriticaltoanunderstandingofgroundingand shielding.SostaywithmeasIgobackintime.Ithinkthehistoryisboth interestingandinsightful.
July1,2015
SanBruno,CA
RALPH MORRISON
AHISTORICALPERSPECTIVEINTOGROUNDING ANDSHIELDING Asateenager,in1940,Ibuiltmyowncrystalset.Irememberconnectingthecircuitcommon(ground)toawaterpipesome20ftawayfrom myset.Theconductorwentoutthroughaholeinawiremeshwindow screen.Ifoundoutthatroutingtheantennamadeadifference,soIkept tryingdifferentapproachestoreceivemoreradiostations.LittledidI knowofthecomplexnatureofcouplingtoatransmittedradiosignal. Thiswasmyfirstassociationwithgrounding(makinganearthconnection).
Myinterestinelectronicsextendedtohowaradioworksandbefore longIwasspendingtimeintheneighborhoodradiorepairshop,where Ilearnedhowtotestvacuumtubes.Iwasgivenadiscardedradio asapresentbecausetheplasticcasehadbeensmashed.Ifreedthe speakerconeandIhadmyownworkingradio.Theradiohadaground clipthatsuggestedthatagroundingwiremightimprovereception. Asateenager,Ispenttimewithseveralclassmatesthathadacquired theskillsneededtobeamateurradiooperators.Theywerealways discussingtheirantennasandthegroundingoftheirtransmitters. IborrowedacopyoftheARRLhandbooktogetsomeideaoftheir hobbyandwhatitmeanttobeahamradiooperator.Iwasanobserver asIdidnothavetheresourcestoenterthishobby.
IwasdraftedintothearmyinWW2atage18.Eventually,Ibecamea radiorepairmanintheinfantryandfixedradiosinPatton’sthirdarmyas itcrossedGermany.TheradiosIservicedhadnoconnectionstoearth astheyhadtobeverymobile.Inevergavegroundingasecondthought. AfterIreturnedhome,theGIbillgavemetheopportunitytogoto CaltechandgetaBSdegreeinphysics.Iremembertakingcoursesin electricityandmagnetism,notrealizingtheimpactthissubjectwould haveonmyfuture.Iremembersolvingdifferentialequationsandfumblingthroughsystemsofunits.IwasintroducedtoMaxwell’sequations. Atthetime,Ihadnowayofassigningsignificancetothisinformation. ItwasasifIwasreadingthefirstparagraphofmanydifferentchapters inmanydifferentbooks.
Aftergraduationin1949,IstartedworkingasanelectronicsengineeratacompanycalledAppliedPhysicsCorporationlocatedin Pasadena,CA.MyfirstbosswasGeorgeW.Downs,awell-respected entrepreneur.Duringthewar,hehadworkedasahigh-levelconsultant andwasassociatedwiththeAtomicEnergyCommission.Ihadalot tolearn.Thecompanyproductsincludedoscillographs,electrometers, andspectrophotometers.Iwasimpressedwiththebeautifulpackaging andthefacttheyweresowellrespectedbytheircustomers.Alloftheir productsusedvacuumtubesandIsaw“grounding”forthefirsttime. Theyexplainedtomehowtheyusedagroundingstudthatcollectedall thecommonleadsusedintheinstrument.Thisincludedthemetalcase, theequipmentground,thecentertaponthesecondaryofthepower transformer,thetransformershield,andthevariouscircuitcommons. Therewasnoexplanationgiventomeastowhythiswasthebest solution.Iwastoldthattheorderusedinplacingtheseconductorson thestudwasimportant,andtheyhadfoundasolutionthatmadethe instrumentfreeofnoise.Inlateryears,thisstar-groundingconfigurationwouldappearinveryunusualplaces.Atthetime,Ihadnobasis tobecriticalofstar-groundingmethods.Theproductsworkedwell andengineerswithyearsofexperiencehadspoken.Donotmistake me.Agroundingstudwasavalidapproachtobuildingthisproduct. Itisnothoweverasolutiontogroundingingeneral.Askingquestions didnotyieldusefulanswersandIdidwhateveryoneelsedid–Iused commonsense,Icopiedtheproceduresusedinotherproducts,andI experimentedwhenIcould.Iwasapartoftheworkforce.
Myfirstassignmentasanengineerwastodesignadcinstrumentation amplifier.Thistypeofinstrumentwasneededinconditioningsignals fromstraingages,positionsensors,andthermocouples.Iwasshowna circuitapproachthathadbeendevelopedbyRCAthatusedamechanicalchoppertocorrectfordcdrift.Iwassoonimmersedinregulateddc powersupplies,transformers,filaments,tubetypeselections,andfeedback.Imanagedadesignonechannelofdcamplifierincludingapower supplythatweighedover70lb.Donotforgetthatvacuumtubestake severalhundredvoltstooperateandthesevoltageshadtobeverycarefullyregulated.WhenIlookbackatthoseearlydays,Icanseehow farelectronicinstrumentationhascomeandinparticularhowmuchI hadtolearn.Atthebeginning,therewerenoshieldedtransformers, feedbacktechniqueswereprimitive,noiseandhumwereproblems,and therewasalimitedunderstandingofsignalisolation.Therewereseleniumrectifiersthatdidnotworkverywell.Dcamplifiersandvacuum tubesareadefinitemismatch.Inthosedays,thatwasalltherewas.
Thetechniquesofdifferentialamplificationandcommon-moderejectionhadnotyetenteredmyunderstanding.Mybosswaslearningfrom me.Wehadtostartsomewhere.
TheperiodafterWW2sawthegrowthoftheaerospaceindustry.Iwas projectengineeronseveralanalogcomputersthatweresoldtoDouglas,Northrup,andLockheed.Thesecomputershelpedinthedesign ofthefirstcommercialjetaircraft.Thecomputerdesignwasbasedon workdoneatCaltechandincludedsomedcamplifiersIhaddeveloped. Afterthisprojectwascompleted,ourinstrumentationgroupwassoldto acompanyinthetransformerbusiness.Ourfirstprojectwastodevelop ahigh-speedrecordingoscillograph.Thephotographicpaperspeedin thismachinewasover200ft/s.Needlesstosay,Kodakappreciatedour business.Gettingthepaperuptospeedinmillisecondswasnosmall task.1 Idesignedtheamplifiersthatdrovethegalvanometers.Ifound outaboutthelimitationsimposedbyusingacommonpowersupplyto poweragroupofsingle-endedinstruments.Itwasobviousthatthere wasalottobegainedbyusingaseparatepowersupplyforeachsignal channel.Tomeetthischallenge,Ibeganworkingonnewtechniquesto reducecostandsizeandavoidtheuseofcommonsupplies.Iinventeda methodofusingACcouplingandaparallelfeedbacknetworktomake adcinstrument.Thecompanyrejectedmyproposalsforanewproductline.Irecognizedtherelevanceofmynewideas,andItalkedwith twootherengineerstoleaveandformanewcompany.Georgeactually helpedusmakethetransition.
ThenewcompanywascalledDynamicsInstrumentation.Wemanufacturedinstrumentationamplifiersforaerospace.Theproductlinewas basedonthedesignideasIhadproposed.Icouldnowcontactusers directlyandIbegantounderstandtheirdilemma.Inrocketteststands, vacuumtubeelectronicshadtobemountedinablockhousehundreds offeetawayfromtherocketenginesandanysensors.Thismeantlong inputcableshadtocarrymillivoltsignalsbetweenstructures.Thisraised issuesofwheretoconnecttheinputandoutputsignalcableshields.I hadsomeideasonhowtohandletheseissuesandwrotesomearticleson thesubject.Ipassedthesearticlesouttopotentialcustomers.Iwassurprisedatthereceptionthesearticlesreceived.Itwasobvioustherewas verylittleinformationavailableonwheretoconnectshieldsonlarge systems.Yearslater,engineerswouldpullthesearticlesoutoftheirfiles toshowthemtome.Now,whenIlookbackatthatperiod,Itoohada
1 ThemechanicalengineerwasWilliamMcLellanalsoaCaltechgraduate.Hewasthe engineerthattookthechallengefromDr.RichardFeynmantobuildaworkingmotor 1/64ofaninchonaside.ThismotorisonexhibitatCaltech.
lottolearn.Icouldtellthatthiswasadifficultproblemandthesizeofa companyhadnothingtodowithunderstandingtheissues.Rocketdyne wasinterestedindesigningrocketenginesnotwheretoconnectshields. Ifoundoutthatinterferenceresultedfromtheflowofpower currentininputconductors.Remembertherewerehundredsofvolts onthesecondarycoilsofthepowertransformers.Simplyput,Iwas theculprit.Thiscurrentcouldbelimitedbytheuseoftransformer shields.Ibuiltmyownpowertransformersandplayedwiththe shieldinguntilIunderstoodwhatwashappening.Mycompetition builtacarrier-typedifferentialdcamplifierthatusedamechanical modulator/demodulatorandamultishieldedinputtransformer.Being differentialallowedinputandoutputcommonstobegroundedseparatelywithoutcreatingagroundloop.Itriedtoduplicatethisapproach, butIhadproblemsbuildingtheinputtransformers.Instead,Ibuilta postmodulator/demodulatoraroundapostcarriertransformerusing newlyavailabletransistorsandmanagedineffecttobuildawide-band differentialamplifier.Themechanicalmodulatorapproachhad100Hz bandwidthandthepost-transistormodulatorinstrumentIbuilthad 10kHzbandwidth.IhadanewproductandIhadanewdefinitionof theworddifferentialasappliedtoinstrumentamplifier.
IneededthreeshieldsinthepowertransformersIusedinthisdesign. IgotacompanyinSanDiegotobuildthemforme.Inoticedonedayin anelectronicsmagazinethatthiscompanywasofferingwhatitcalled “isolation”transformerswithfourshields.Onmynextvisit,Iasked thecompanyownerwhathisrecommendationwasforusingafourth shield.Hedidnotknow.Ithenaskedwhyheofferedit.Theanswer wassimple:“Theysellbetter.”Ihadaidedintheformationofanew businessbasedonaddingmultipleshieldstodistributiontransformers. Ihadusedshieldstomakeoneinstrumentworkandtheindustryhad decidedtousethesesamemethodsto“cleanup”systems.Tome,they hadasolutionlookingforaproblem.Tome,themultishieldsolution onlyworkedforoneinstrument.Later,Iwouldtakeabroaderviewof thisshielding.Ialsosawmarketingatwork.
IbegantofeelIhadsomethingimportanttoofferotherengineers. Isawapatterninhowshieldsworkedandhowtheycontrolledtheflow ofinterferingcurrent.ItwasalltiedtotheelectrostaticsIhadstudiedin school.SointhedaysofribbontypewritersandcarbonpaperIstarted thetaskofwritingabook.IshowedthemanuscripttoDrErnstGuillemanofMITandhewasenthusiastic.Ithensubmittedamanuscriptto GeorgeNovotnytheeditoratJohnWiley,where,muchtomysurprise,it wasacceptedforpublication.ThefirsteditionofGroundingandShieldingwaspublishedin1967.
Myfirstanalogdesignsusedshieldedconductorstocarrysignals onthecircuitboard.IwasemulatingtheapproachusedatApplied Physics.WhenIdesignedmylastinstrumentamplifier,therewas notoneshieldedconductorinsidethepackage.Thecircuitboarddid nothaveagroundplane.Ihadlearnedhowtocontrolthelayoutso thatshieldingsignalleadswasunnecessary.Myapproachwassimple. Iunderstoodhowtolimittheareabetweenconductorsthatcarriedthe fieldsofthesignals.Icouldrunsignalsnearpowertransformersand avoideven1 μVofcoupling.ThenoiselevelsIattainedwereatthe theoreticallimitsofthecomponentsandmyinstrumentbandwidths wereover100kHz.Theuserswerestillrequiredtoshieldinputsignal cablesbetweenthetransducersandtheinstruments.
Havingapublishedbookprovidedmewiththeopportunitytodo consulting.Iwasnowacceptedbysomeasanexpert.Sellinginstrumentationallowedmeaccesstomanymilitaryandaerospacefacilities. Thisinturnallowedmetoseehowfairlylargeinstallationsusedtheir instrumentation.ItwasthenthatIbegantoseetheconflictsimposed byregulationsandcontrols.Ifoundoutthatmostofmyrecommendationswerenotfollowed.Theengineerswerehappybecausetheperformancewasbetterthantheyhadexpected,andIwasdisappointed becausethingswerejustnotverygood.Theengineerswereconstrained byrulesthatsimplymadenosensetome.Asanexample,Ifoundthat theyhadcollectedinputandoutputshieldsinbundlesandbroughtthem toasinglegroundpoint.ThiswasthestarconnectionIhadseenusedat AppliedPhysicsbutappliedinanentirebuildingfullofelectronics.This isagoodexampleofhowlorecandodamagewhenitisnotcontrolled. Inmyearlyexperiences,IexpectedlogictoprevailandthatIwouldbe heard.Isoonfoundouthowmuchinertiatherewasandthatthestatus quowouldprevail.Thiswasallabigdisappointment.Iwasnotheard. Iwaspolitelyignored.WhenIthinkaboutit,theseengineershadlittlechoice.Thesystemwasnotdesignedtoacceptanystepchangesto approach.Thebosseswerefromadifferenteraandtheywrotetherules. SomehowtheygotbyandsodidI.
IleftDynamicsduringaneconomicdownturnandspentafewyears inacompanythatbuiltperipheraltestingequipmentforthetelephone industry.Thenewbuildingwewereusinghadaso-calledcleangroundingconductorthatwasbroughtintotheengineeringarea.Theheadof engineeringhadspecifiedanapproachthatwasastandardpracticein telephoneofficedesign.Somehowthefeelingthatprevailedwasthat thiswasa“quiet”groundthatwouldbeusedtoreducenoiseintesting hardware.Ihadahardtimeacceptingthisstrangelogic,butIsaid nothing.ThisgroundingrodwasliketheonesIhadseeninaerospace.
Italmostseemedthatengineershadinventedanewphysics,where noiserunsdownhillintoasumpandneverreturns.Thisviolatedmy understandingthatcurrentflowsinloopsbuthereagainthesewere experiencedengineersdoingthefacilitydesign.Iwonderedifthefirst userwouldcontaminatethegroundingrodforanysubsequentusers. Duringmyyearsatthiscompany,Ineveronceusedthis“quiet”ground connection.
Beforetheeraoffiberopticsandmicrowavetransmission,telephone linksreliedoncopperconnections.Thefactthattheentirecountrywas crisscrossedwithhardwirewasimpressive.Toreducecosts,thering (bell)circuitsoftenusedtheearthasoneoftheconductors.Thismade itanecessarytoprovideagoodearthconnectionateachcentraloffice. Theheadofengineeringwassimplyfollowingthegoodpracticerules hehadlearnedinthetelephoneindustry.
Atonepointinmycareer,Ineededsomeadditionalincome.Inoticed acompanythatofferedaseminarcalledGroundingandShielding. IcontactedDonWhiteAssociatessuggestingwemightbeableto worktogetherasIhadabookpublishedwiththissametitle.Don WhiteagreedandIattendedseveralofhisgroundingseminars.Inthis course,hefocusedhisattentiononthetreatmentofhigh-frequency interference.HediscussedtopicssuchasESD,lightning,radar,rffilters, radiationstandards,coaxialcables,andgroundplanesincomputer installations.EventhoughIhadbeenaphysicsmajor,Ihadalotto learn.Eventually,Imanagedtocatchupwiththejargonandwasable toteachcoursesinthesenewtopics.Ibegantoseethattherewasreally noseparationbetweenanalogandrf.Itwasonecontinuoussubject.His coursegavemeanunderstandingofthespecificproblemsengineers encounteredingroundingandshieldingathighfrequencies.Myanalog designexperiencesdidnotincluderadiation.Don’sexperiencedid notinvolveinstrumentation.Dongavememanyopportunitiestodo consulting.Obviously,Ihadnewmaterialforanothereditiontomy book.Ialsofoundoutthattheproblemsofradiationwerefarmore commoninindustrythantheproblemsIencounteredinamplifying signalsrepresentingstress,strain,andtemperature.Radiatedinterferencethataffectedradioandtelevisionreceptionwasregulatedby theFCC.Interferencethataffectedstraingagemeasurementwasa minordistractionbycomparison.Therewerenoagenciesregulating performanceininstrumentation.IneededDon’shelp,buthedidnot needmine.
LivinginSouthernCaliforniagavemeaccesstotheaerospaceindustry,whichincludedtheJetPropulsionLaboratories,aircraftcompanies, EdwardAirforceBaseaswellasGoldstone.Ihadtwoclosefriends,
WarrenLewisandFredKalbachthatwerefull-timeconsultants.They ofteninvitedmetojointhemontheirconsultingfieldtrips.Warrenwas investedinabusinessthatsoldpowerisolationtransformers.Oneof thesetripswastoGoldstone,wherelightninghadknockedoutadistributiontransformer.ThiswaspotentialbusinessforWarren.Goldstone iswhereNASAlocatedtheantennasthatcommunicatedwithdeep space.ItislocatedintheMohaveDesertfarfromhabitation.Thisisolatedlocationisnecessarytoavoidautoignitionnoiseaswellasradio andtelevisionsignals.Thedeepspaceantennasandtheassociatedelectronicsarelocatedinstructuresspreadoutovermanyacresofland.Just areminder,thesespaceantennasarenearlythesizeoffootballfields.
Asingle-pointgroundwasprovidedforallsignalsandshields.This centralgroundingstructurewasaconductingrodplacedinadeepwell locatedatapointequidistantfromeachbuilding.Thepowerdistributiontransformersforeachbuildingweregroundedlocallypercode.In thisconfiguration,iflightninghitanywherenearthecentralgrounding rod,thepotentialdifferenceappearingacrossthewindingsinthedistributiontransformerscouldexceedtheirratedbreakdownvoltage.This indeedhappenedandtheywereblowinguptransformersduringsummerthunderstorms.Hereisagoodexampleofwheresingle-pointsignal groundingisnotacceptable.Thepotentialdistributionsintheearththat canoccurduringlightningactivityarediscussedlaterinthebook.
TheNationalElectricCodeprovidestherulesusedindistributing powertoresidencesandfacilities.Thecodewasdevelopedinthe earlyhistoryofpowerdistributionunderpressurefrombanksand insurancecompanies.Withoutcontrols,thereweretoomanyfiresand lightning-relatedincidents.Thiscodeisconstantlybeingrevisedto reflectbestpractice.Inthemid-1980s,IwroteabookwithWarren LewistitledGroundingandShieldinginFacilities.Iusedthebookas anopportunitytoprovidearationalebehindthecoderules.Inmy consultingexperience,Ifoundengineerswereoftentryingtoavoid thecodetosolvesomeinterferenceproblem.Ifinterferencecurrents flowinginaneutralconductorwereaproblem,theypressuredto ungroundtheneutral.Myjobwastofindanothersolutiontothe problem.Anungroundedneutralinafacilitycanbeverydangerous. Thecodedoespermitthispracticebutonlyundercarefullycontrolled conditions.
Therewasaneconomicdownturnin1991,andIdecidedtosellmy secondbusiness.Ihadbeeninvolvedinasmallnichemarket.Ihadsurvivedandearnedaliving,butIwasneverwasabletogrowasacompany. Afterthesale,Ispentmytimewritingandgivingseminars.Ireceived acallfromDanBeekeratFreescale2 askingmeifIcouldgiveatalk 2 “FreescaleisnowNXPSemiconductor.”
ataFreescaleforum.Hehadfoundmynameononeofmybooksin hislibrary.Thatcontactwasthebeginningofalongrelationshipthat haslasteduntilthepresent.Freescaleisinthesemiconductorbusiness andtheircustomersdesigndigitalcircuitboards.Whentheboardsdon’t work,usersblamethecomponents.Freescalehadtogoontheoffensive andhelpsolvetheirproblemortheywouldloseacustomer.Thereasonissimple.Itiseasiertoblamethesemiconductorsthantoredesign theboard.IworkedwithDanandgaveseminarstotheircustomerbase emphasizingtransmissionlines,themovementofenergy,andthenature ofinterference.Ittookawhile,butDanfinallygraspedtheideathatthe spacesontheboardweremoreimportantthanthetraces.Hebecame veryeffectiveinshowingengineershowtoavoidproblemsinboardlayout.Asaresultofthiseffort,Iincreasedmyunderstandingofkeyissues inmultilayerprintedcircuitboarddesign.Iwroteabooktitled Digital CircuitBoards-Mach1GHz thatwaspublishedin2012.Danrarelyhas todesignaboardthesecondtime.Layoutsbasedonanunderstanding offieldsdowork.Ihavealottosayinthisbookaboutenergyflowon transmissionlines.Aslogicgetsfasterandfaster,afieldunderstanding becomesanecessity.
Naturemovesenergy.Shewilltakeeveryopportunitytomovetoa lowerpotentialenergystate.Ifweareclever,wecanusenaturetodoour bidding.Wethinkintermsofvoltageaswedonothaveenergyprobes. Tobeeffective,wemustunderstandhownatureworks.Wemustplay bynature’srules.Thatisthesubjectofthisbook.
InthissixtheditionIhaverearrangedtheorderofpresentationto reflectcurrenttrends.Ihaveaddednewmaterialwhereappropriate, andIhavedroppedmaterialthatisnolongerofinterest.Ihopethis bookwillmakeiteasierforengineerstodotheirjob.
CHAPTER1 VoltageandCapacitors OVERVIEW Thisfirstchapterdescribestheelectricfieldthatisbasictoallelectricalactivity.TheelectricorEfieldrepresentsforcesbetweencharges. Thebasicchargeistheelectron.Whenchargesareplacedonconductivesurfaces,theseforcesmovethechargestopositionsthatstorethe leastpotentialenergy.Thisenergyisstoredinanelectricfield.Thework requiredtomoveaunitofchargebetweentwopointsinthisfieldisthe voltagebetweenthosetwopoints.
Capacitorsareconductorgeometriesusedtostoreelectricfield energy.Theabilitytostoreenergyisenhancedbyusingdielectrics.It isconvenienttousetwomeasuresoftheelectricfield.Thefieldthatis createdbychargesiscalledtheDfieldandthefieldthatresultsinforces istheEfield.AchangingDfieldrepresentsadisplacementcurrent inspace.Thischangingcurrenthasanassociatedmagneticfield.This displacementcurrentflowswhenchargesareaddedorremovedfrom theplatesofacapacitor.
1.1INTRODUCTION Everypersonthathasdesignedacircuithasconsideredissuesof groundingandshielding.Everypersonthathasusedelectronicsto makemeasurementshasencounteredinterferenceofsomesort.The problemsvaryasthetechnologyevolves.Searchingforwaystodeal withtheseissuesconsumesalotofengineeringtime.Itistheintent ofthisbooktoprovidethereaderwithsomeinsightastowhatis happening.Thesensingofsignaltakesplaceintheanalogworld.The computationsinvolvingdatatakeplaceinthedigitalworld.Theenergy tooperateelectronicscomesfromthepowerutilityworld.Itmakes
GroundingandShielding:CircuitsandInterference,SixthEdition.RalphMorrison. ©2016JohnWiley&Sons,Inc.Published2016byJohnWiley&Sons,Inc.
sensethattheengineermustbefamiliarwithallthreeareasifhewants tounderstandwhatishappening.
Theparallelwithautomobiletravelisinteresting.Afineautomobilemakessenseonlyifthereisaninfrastructure.Weneedhighways, bridges,repaircenters,andgasstationsorthesystemcannotwork.The piecesofthesystemmustworktogetherforcarstobeeffective.Fuels mustmatchengineneeds,curvesmustmatchdrivingspeeds,andthe numberoflanesmustmatchtrafficrequirements.
Thisbookmakesanattempttobringseveraldisciplinestogetherso thatworkinginelectronicsisaloteasier.Thesedisciplinesinvolvethe physicsofelectricity,thenatureofthedigitalworld,theshieldingof theanalogworld,andfinallythedistributionofpowerintheutility world.Tofullyunderstandgrounding,shielding,andinterference,we mustspendtimeinalloftheseareas.Adiscussionofutilitypoweris importantbutunlesstransmissionlinesandradiationareunderstood, thesubjectofinterferencewillmakenosense.Shieldingmakesnosense unlesstheanalogworldisexplained.Thereisatendencytospecialize inelectronics.Thisbookisanattempttobroadentheviewandaddto thegeneralunderstandingofhownaturefunctions.
Howdoesacircuitwork?Oneansweristodoasinusoidalanalysis usingKirchhoff’slaws.Anotheransweristowriteasetoflogicstatements.Theseresponsesprovideasmallpartoftheanswer.Thefull answerisburiedinamountainofdetails.Inthisbook,wearegoing tolookatsomeofthisdetailbutinanon-circuitway.Wewilltake thisapproachbecausecircuitdiagramsandcircuittheorybytheirvery naturemustleaveoutalotofpertinentdetail.Thisdetailisimportant forqualityperformancewhetheritbeforwidebandwidthoramplifying verylow-levelsignals.Itisalsoimportantwhenradiation,interference, orsusceptibilityisinvolved.Wiresize,connectionsequences,componentorientation,andleaddressareoftencriticaldetails.Iliketocall thesedetails“circuitgeometry.”Thesedetailsingeometryareimportantinanalogcircuits,powercircuits,andespeciallyindigitalcircuits, whereclockratesriseyearbyyear.
Whenacircuitisputtopractice,therearemanydetailsthatwetake forgranted.Thecomponentswillmostlikelybeconnectedtogetherby stripsorcylindersofcopper.Theywillbesolderedintoeyeletsoronto copper-orgold-platedpads.Traceswillgobetweenlayersonaprinted circuitboardusingvias.Theseareafewofthedetailsinadesignthat arenotquestioned.Therearedetailsofamoresubtlenaturesuchas thethicknessofatraceorgroundplaneorthedielectricconstantofan epoxyboard.Inmostcases,wedonotquestionhowthingsaredone
becausewetendtorelyon“acceptedpractice.”Circuitsbuiltthisway inthepasthaveworked,sowhymakechanges?
Takingthingsforgrantedisnotalwaysgoodengineering.Notethat digitalclockrateshavechangedfrom1MHzto1GHzin20years.That isthreeordersofmagnitude!Imaginewhatwouldhappenifautomobile speedswentuponeorderofmagnitude.Thatis600mphorjetaircraftspeed.Evenamodestincreaseinautomobilespeedwouldrequire extensivechangestothedesignofourroadsandcitiesnottomention extensivedrivertraining.
Inelectronics,anincreaseinspeeddoesnotposeasafetyhazard. Therearehoweverdifferencesandlimitationsinperformancethat shouldbeunderstood.Oftenaneffectisnotsenseduntilthenext generationindesignisintroduced.Understandingandcorrectingthese effectsrequiresanunderstandingofbasicprinciples.Thedetailswe willlookintodonotappearonacircuitdiagram.Wewilladdressthese detailsbecausethroughunderstandingwecanimproveperformance, reducecosts,andhopefullystayoutoftrouble.
Electronicsoftenmakesuseofpowerfromthelocalutility.Forreasonsofsafety,theutilityconnectsoneofitspowerconductorstoearth. Electronichardwaremustofteninterfacewiththispowerandsharethis sameearthconnection.Theresultcanbeinterference.Iwilldiscussthe relationbetweenpowerdistributionandcircuitperformancethroughoutthebook.
Acircuitdiagramisonlyaplanoranorganizationofideas.Circuit theoryappliedtoacircuitdiagramprovidesabasicoverviewofcircuit performance.Circuitsymbolsareapartoftheproblem.Theyarenecessarilyverysimplerepresentationsofcomplexobjects.Everycapacitorhasaseriesresistanceandaninductance.Itcanalsobeconsidered atransmissionlinestub.Atsomelevelithasitsnonlinearities.Every inductorhasseriesresistanceandshuntcapacitance.Theseconsiderationsonlybegintotelltheentirestory.Forexample,athighfrequencies, dielectricsarenonlinear.Formagneticmaterials,permeabilityfallsoff withfrequency.Thus,circuitsymbolscanonlyconveylimitedinformation.Further,wedonothavesymbolsforskineffect,transittime,radiation,orcurrentflowpatterns.Astraightlineonadiagrammayactually beaverycomplexpathintheactualcircuit.Inshort,aschematicdiagramprovideslittleinformationonphysicalstructureandthiscanlimit ourappreciationofwhatisactuallyhappening.Ifwehadallthisdetail, wewouldbeoverwhelmed.Itisimportanttobeabletobackoffand takethebroadviewandstillbeawarethatmanydetailshavebeenintentionallydisregarded.Agooddesignerwalksafineline,alwaysaware thattherearedetailsinhisfieldthatheisnotyetfamiliarwith.
Theperformanceofmanycircuitsorsystemsiscloselyrelatedtohow theyarebuilt.Itisnotaquestionofwhetherthereisanelectricalconnectionbutwheretheconnectionistobemade.Inananalogcircuit, itisoftenimportanttoknowwhichendofashieldisgroundednot whetheritisgrounded.Hereisagoodquestion.Howshouldadigitalcircuitboardgroundplanebeconnectedtothesurroundingchassis? Theanswertothisquestionisnotavailablefromaschematicdiagram. Hereistheanswer:Ifpossible,theconnectionshouldbearrangedso thatgroundcurrentdoesnotflowinthegroundplaneoftheboard.
Arepeatedthemediscussedinthisbookrelatestohowsignalsand poweraretransportedincircuits.Thisapproachwillleadtoanunderstandingofmanyissuesthatareoftenpoorlyunderstood.Inorderto discussthetransportofelectricalpowerandsignals,theelectricand magneticfieldsrelatedtovoltagesandcurrentsmustbediscussed.To beginthisdiscussion,weintroducetheelectron.Don’tdespair.Thetime spentreviewingbasicphysicswillmakeitmucheasiertounderstandthe ideaspresentedinthisbook.Evenifyoudonotfollowthemathematics, theideaswillbeclearlystated.
1.2CHARGESANDELECTRONS Circuittheoryallowsustorelatecircuitvoltagesandtheflowof currentinagroupofinterconnectedcomponents.ForRLCnetworks (resistor–inductor–capacitor),thisanalysisisstraightforwardusing Kirchhoff’slaws.TheprocessesIwanttodiscussdonotinvolvethis approach.Tounderstandthefundamentalsofcircuitperformance,we willusebasicphysicstoexplainmanydetailsthatareoftenignored. Ourstartingpointmayseemabitremotebutpleasereadon.
Atomsarecomposedofanucleusofprotonsandneutrons surroundedbyelectrons.Forourpurposes,theelectronscanbe considerednegativelychargedparticleslocatedinshellsaroundthe atom.Thequantummechanicalviewofelectronsinatomsisthat theyareoverlappingwavesdescribedbyquantumnumbersanda probabilityfunction.Wewillusetheshellviewpointoftheatomas wearenotinvolvedinnuclearphysicsorquantummechanics.We cantreatelectronsasparticlesandnotgetintotrouble.Theelectrons haveanegativechargeandthematchingprotonsinthenucleushave apositivecharge.Inaneutralatom,thepositiveandnegativecharges areexactlyequal.Eachelectronicshellislimitedtoafixednumberof electrons.Thenumberofelectronsintheoutershellsaysalotabout thecharacteroftheatom.Asanexample,copperhasjustoneelectron
initsoutershell.Thisouterelectronhasagreatdealofmobilityandis involvedinelectricalconductivity.Becauseprotonsarecomparatively heavyandtheshellsofelectronsshieldthem,theyarenotdirectly involvedintheelectronicswearegoingtoconsider.
Moleculesareformedfromatomsthatbondtogether.Bonding reallymeansthatelectronsfromoneatomsharespacesintheshellsof otheratoms.Foraninsulator,thisbondinggreatlyrestrictstheactivity ofoutershellelectrons.Typicalinsulatorsmightbenylon,air,epoxy, orglass.Thisbonddoesvarybetweeninsulators.Iftwoinsulatorsare rubbedtogether,suchasasilkclothagainstarubberwand,someofthe sharedelectronsonthewandwilltransfertothecloth.Inthiscase,the silkclothwithextraelectronsiscalledanegativelychargedbody.We willcalltheabsenceofnegativechargeapositivecharge.Therodissaid tobepositivelycharged.Inreality,thepositivechargestemsfromthe immobileprotonsinthenucleusofatomsthatdonothavematching outershellelectrons.Theabsenceofnegativechargesbehavesthe sameasiftherewerefictitiouspositivechargesonthesurfaceofthe insulator.Ananalogycanhelp.Consideranauditoriumfullofpeople. Thereisoneemptyseat.Whenapersonmovesleftintothisseat,the vacantseathasmovedtotheright.Ifpeoplekeepchangingseatsthis way,wecanseetheflowasmovingemptyseats.Nowconsiderthe emptyseatasapositivecharge.
Experimentswithchargedbodiescandemonstratethenatureof theforcesthatexistbetweencharges(electrons).Thesesameforces existfortheabsenceofchargethatwewillcallapositivecharge.Ifone chargedbodyrepelsanother,itisactuallythefieldsofelectronsthat areinvolved.Ifyourememberyourphysicsclass,theseforcescanbe demonstratedusingpithballsthathangbyastring.Herethecharges areattachedtosmallmassesandwecanseethepithballsattractor repeleachother.Fortheretobeanattraction,onepithballneedsto haveextraelectronsandtheotheranabsenceofelectrons.
Thepercentageofelectronsinvolvedinanyoftheseexperiments isextremelysmall.Toillustratethispoint,Iwanttoparaphrasethe writingofDr.RichardFeynman.1 Iftwopeoplearestandingafew feetapart,whatwouldbetheforceofrepulsionif1%oftheelectrons ineachbodyweretorepeleachother?Woulditbeafewpounds? More!Woulditbegreaterthantheirweight?More!Woulditlifta building?More!Woulditliftamountain?Theanswerisastounding. Theforcewouldbegreatenoughtolifttheearthoutoforbit.Thisis
1 TheFeynmanLecturesonPhysicsVolume2page1-1.AddisonWesleyPublishing CompanyInc.Copyright1964,CaliforniaInstituteofTechnology.
whygravityiscalledaweakforceandtheforcebetweenelectronsis calledastrongforce.Thisalsotellsussomethingaboutnature.The percentageofelectronsinvolvedinelectricalactivityisextremelysmall. Weknowthattheforcesinacircuitdonotmovethecomponentsorthe traces.Obviously,sinceelectricalforcesaresolarge,electricalactivity inacircuitinvolvesanextremelysmallpercentageoftheavailable electrons.Yettherearesomanyelectronsonthemove,wecanthink ofanytypicalcurrentflowasbeingcontinuousandseamless.
1.3THEELECTRICFORCEFIELD Whenweencounterforcesatadistance,weusetheexpressionforce field.Weexperienceaforcefieldatalltimesasweliveinthegravitationalforcefieldoftheearth.Everymasshasaforcefieldincludingthe earth.Theearthhasthedominantfieldbecausetheearthissomassive. Theresultisthateachmassonearthisattractedtowardthecenterof theearth.Theforcesofattractionbetweenindividualobjectsonthe eartharesosmallthattheyareverydifficulttomeasure.Ontheearth’s surface,theforcefieldisnearlyconstant.Wewouldhavetogoout thousandsofmilesintospacetoseeasignificantreductionintheforce ofgravity.
Theelectricalandgravitationalforcefieldsaresimilarinmanyways. Everyelectroncarrieswithitanassociatedforcefield.Thisforcefield repelseveryotherelectroninthearea.Ifagroupofextraelectrons arelocatedonanisolatedmass,wecallthismassachargedbody.We refertotheextraelectronsasacharge.Ifthismassisaconductor,the extraelectronswillmoveapartuntilthereisabalanceofforces.On aconductingisolatedsphere,theextraelectronswillmoveuntilthey areevenlyspacedovertheentireoutersurface.Noneoftheseexcess electronswillremainontheinsideoftheconductor.Foraperfect insulator,extraelectronsarenotfreetomoveabout.Extraelectrons ontheinsideofthismaterialarecalledtrappedelectrons.Itisalso possibletohavetrappedabsencesofelectrons.
1.4FIELDREPRESENTATIONS Theelectricforcefieldinavolumeofspacecanbemeasuredbynoting theforcesonasmalltestchargeinthatspace.Atestchargecanbe formedusingasmallmasswithasmallexcessofelectronsonitssurface. Theforceonthistestchargehasamagnitudeanddirectionateach
Figure1.1 Theforcefieldlinesaroundapositivelychargedconductingsphere pointinspace.Havingdirection,theforcefieldiscalledavectorfield. Tobeeffective,thistestchargemustbesmallenoughsothatitdoes notinfluencethechargedistributionontheobjectsbeingmeasured. Performingthisexperimentisdifficultbutfortunatelywecandeduce thefieldpatternwithoutperforminganactualtest.
Itisconvenienttorepresentaforcefieldbylinesthatfollowthedirectionoftheforce.Foranisolatedconductingchargedsphere,thelinesof forceareshowninFigure1.1.
Notethatthefieldexistseverywherebetweenthelines.Thelinesare simplyawayofshowingthefloworshapeofthefield.Aspointedout, thenumberofextraelectronsthatformthecharge Q onthesurfaceof aconductorissmallcomparedtothenumberofelectronsintheconductor.Inspiteofthisfact,thenumberofelectronsisstillsolargethat wecanconsiderthechargeasbeingcontinuouslydistributedoverthe surfaceofinterest.Thisisthereasonwewillnotconsidertheforcefield asresultingfromindividualelectrons.Fromhereon,wewillconsiderall chargedistributionsasbeingcontinuous.Thetotalchargeonthesurface ofthesphereinFigure1.1is Q.Thechargedensityonthesurfaceofthe sphereis
Wewillusetheconventionthatalinestartsonaunitofpositivecharge andterminatesonaunitofnegativecharge.Thisunitcanbeselectedso
thatthegraphicalrepresentationofthefieldisuseful.Ifthetotalcharge isdoubled,thenthenumberoflinesisdoubled.Forrepresentationsin thisbook,noattemptwillbemadetorelatethenumberoflinestoany specificamountofcharge.Ingeneral,weareinterestedintheshapeof thefield,areasoffieldconcentration,andwherethefieldlinesterminate.Fortheidealsinglesphere,thefieldlinesarestraightandextend fromthesurfacetoinfinity.
InFigure1.1,theforce f onasmalltestcharge q inthefieldofacharge Q locatedonasphereisproportionaltotheproductofthetwocharges andinversetothesquareofradius r or
Theconstant ��0 iscalledthepermittivityoffreespace.Equation1.2is knownasCoulomb’slaw.Theforceperunitchargeor f ∕q isameasureoftheelectricfieldintensity.TheletterEisusedforthismeasure. TheforcefieldaroundagroupofchargesisreferredtoasanEfield. Mathematically,theEfieldaroundacharge Q is
TheEfieldfallsoffasthesquareofthedistance r.InFigure1.1,the forcefieldintensityEdecreasesasthefieldlinesdiverge.Theforcesare greatestatthesurfaceofthesphere.Notethatthefieldlinesdonot enterthesphere.Thisisbecausetherearenoexcesschargesinsidethe conductor.Thefieldlinesmustterminateonthesphereperpendicular toitssurface.Iftherewereatangentialcomponentofforceonthesurface,thechargesonthesurfacewouldbeaccelerated.Iftherewerean absenceofelectronsonthesurface,thisabsenceofchargewouldalso beaccelerated.Remembertheabsenceofnegativechargecanbeconsideredthepresenceofapositivecharge.Forconductors,themobility ofagroupofelectronsisnodifferentthanthemobilityofanabsence ofelectrons.Exceptforthedirectionassignedtotheforcefield,we willassumethatpositiveandnegativechargesbehavethesameway. Figure1.1showsaspherewithapositivecharge Q.Ifthechargewere negative(thepresenceofelectrons),thefieldlineswouldbeshownwith thearrowspointinginward.
ThefieldlinesinFigure1.1startatthesurfaceofthesphere.Ifthe charge Q werelocatedatthecenterofthesphereandthespherewere removed,thefieldpatternateveryinitialvalueof r wouldbeunchanged. Apointcharge Q impliesaninfinitechargedensity,whichisimpossible. Oftenitismathematicallyconvenienttoconsiderthefieldsfrompoint chargeseventhoughthiscannotexist.
N.B.
TheelectricforcefieldEiscalledavectorfieldasithasamagnitude anddirectionateverypointinspace.
N.B.
Thefieldintensityisgreatestwherethelinesareclosesttogether.
1.5THEDEFINITIONOFVOLTAGE Atestcharge q inthefieldofacharge Q experiencesaforce f given byEquation1.2.Theworkrequiredtomovethetestchargeasmalldistance Δd is f ⋅ (Δd).Theworktomoveitfrominfinitytoapoint r1 isthe integralofforcetimesdistancefrominfinityto r1 .Ifwefollowoneof thefieldlines,theforceisalwaystangenttothisline.Theworkis
Ifwedividebothsidesofthisequationby q,weobtaintheworkper unitcharge.Thistermhasthefamiliarnamevolts.Inequationform, thevoltageVisgivenby
DEFINITION Avoltagedifferenceistheworkrequiredtomoveaunitcharge betweentwopointsinspaceinanelectricfield.
InEquation1.4,wecanmaketheassumptionthatthevoltageatinfinity iszero.Thisallowsustoassignavoltagetointermediatepointsinspace. Inacircuit,theworkrequiredtomoveaunitchargebetweentwoconductingsurfacesiscalledapotentialdifferenceoravoltagedifference.It isimportanttorealizethatpotentialdifferencesdoexistbetweenpoints inspace.Ofcourse,itisdifficulttoplaceavoltmeterinspacetogeta measureofthisvoltage.
Thevoltagedifferencebetweentwopointsinspaceis
N.B.
Avoltagedifferencecannotexistwithoutthepresenceofanelectric field.
Inthepresenceofconductors,anelectricfieldcannotexistwithout chargesonthesurfaceoftheseconductors.Thesechargesarenot apparentfromaschematicdiagram.
Whenacircuitisinoperation,therearesurfacechargeseverywhere andtherearevoltagedifferences.Thesesurfacechargesarethefirst chargesthatmovewhenarequestismadetomoveenergy.Inadccircuit,electronsmoveintheentireconductor.Acurrentisconsidereddc onlyafteraperiodoftimehaselapsedandnofurtherchangeintheflow patterncanbedetected.
N.B.
Fieldsandchargesarenotshownonschematicdiagrams.
1.6EQUIPOTENTIALSURFACES Asthewordimplies,anequipotentialsurfaceisasurfaceofequalvoltage.Noworkisrequiredtomoveatestchargeonthissurface.This surfacecanbeinspaceoronaconductor.Figure1.2showsequipotentialsurfacesaroundthechargedsphereinFigure1.1.Notethatthese surfacesarealsospheresandtheEfieldlinesarealwaysperpendicular totheseequipotentialsurfaces.
N.B.
Conductingsurfacesareequipotentialsurfacesregardlessoftheir shape.Thisassumesthatthesurfacechargesarenotinmotion.
Inpractice,aconductingsurfaceisanequipotentialsurfaceevenwhen thechargedistributionisnotuniform.Thisistrueevenwhenthereare
Equipotential surface
Figure1.2 Equipotentialsurfacesaroundachargedsphere areasofpositiveandnegativechargesonthesameconductor.Wewill assumeittakesnoworktomovechargesonthesurfaceofaconductor. Ifworkwererequired,therewouldbeatangentialelectricfieldandthis meansthatfreechargeswouldhavetobeinmotion.
1.7THEFORCEFIELDOREFIELDBETWEENTWOCONDUCTING PLATES Considertwoconductingplatesseparatedbyadistance h.Onthetop platethereisacharge +Q andonthebottomplatethereisacharge Q. ThisconfigurationisshowninFigure1.3.
Ifweignoreedgeeffects,theforcefieldcanberepresentedbyequally spacedstraightlinesthatrunfromthetopplatetothebottomplate.2 In thisconfiguration,thenetchargeinthesystemiszero.Thereisnoloss ingeneralityifweassumethatallofthefieldlinesstayinthevolume betweenthetwoplates.Sincethelinesdonotdiverge,theforceonatest charge q isconstanteverywhereinthespacebetweentheplates.Inother
2 Edgeeffectscanbeignoredwhenthespacingbetweenconductorsisverysmall.
