磁共振(磁谐振耦合)无线充电技术鼻祖级文章-英文原文.docx
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磁共振(磁谐振耦合)无线充电技术鼻祖级文章-英文原文.docx
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WirelessPowerTransferviaStronglyCoupledMagneticResonances
AndréKurs,1*AristeidisKaralis,2RobertMoffatt,1J.D.Joannopoulos,1PeterFisher,3MarinSoljačić1
1DepartmentofPhysics,MassachusettsInstituteofTechnology,Cambridge,MA02139,USA.2DepartmentofElectricalEngineeringandComputerScience,MassachusettsInstituteofTechnology,Cambridge,MA02139,USA.3DepartmentofPhysicsandLaboratoryforNuclearScience,MassachusettsInstituteofTechnology,Cambridge,MA02139,USA.
*Towhomcorrespondenceshouldbeaddressed.E-mail:
akurs@mit.edu
/www.sciencexpress.org/7June2007/Page4/10.1126/science.1143254
Usingself-resonantcoilsinastronglycoupledregime,weexperimentallydemonstrateefficientnon-radiativepowertransferoverdistancesofuptoeighttimestheradiusofthecoils.Wedemonstratetheabilitytotransfer60Wwithapproximately40%efficiencyoverdistancesinexcessoftwometers.Wepresentaquantitativemodeldescribingthepowertransferwhichmatchestheexperimentalresultstowithin5%.Wediscusspracticalapplicabilityandsuggestdirectionsforfurtherstudies.
Atfirstglance,suchpowertransferisreminiscentoftheusualmagneticinduction(10);however,notethattheusualnon-resonantinductionisveryinefficientformid-rangeapplications.
Overviewoftheformalism.Efficientmid-rangepowertransferoccursinparticularregionsoftheparameterspacedescribingresonantobjectsstronglycoupledtooneanother.Usingcoupled-modetheorytodescribethisphysicalsystem(11),weobtainthefollowingsetoflinearequations
Intheearly20thcentury,beforetheelectrical-wiregrid,NikolaTesla
(1)devotedmuchefforttowardsschemesto
a&m(t)=(iωm-Gm)am(t)+åiκmnan(t)+Fm(t)
n¹m
(1)
transportpowerwirelessly.However,typicalembodiments(e.g.Teslacoils)involvedundesirablylargeelectricfields.Duringthepastdecade,societyhaswitnessedadramaticsurgeofuseofautonomouselectronicdevices(laptops,cell-phones,robots,PDAs,etc.)Asaconsequence,interestinwirelesspowerhasre-emerged(2–4).Radiativetransfer(5),whileperfectlysuitablefortransferringinformation,posesanumberofdifficultiesforpowertransferapplications:
theefficiencyofpowertransferisverylowiftheradiationisomnidirectional,andrequiresanuninterruptedlineofsightandsophisticatedtrackingmechanismsifradiationisunidirectional.Arecenttheoreticalpaper(6)presentedadetailedanalysisofthefeasibilityofusingresonantobjectscoupledthroughthetailsoftheirnon-radiativefieldsformid-rangeenergytransfer(7).Intuitively,tworesonantobjectsofthesameresonantfrequencytendtoexchangeenergyefficiently,whileinteractingweaklywithextraneousoff-resonantobjects.Insystemsofcoupledresonances(e.g.acoustic,electro-magnetic,magnetic,nuclear,etc.),thereisoftenageneral“stronglycoupled”regimeofoperation(8).Ifonecanoperateinthatregimeinagivensystem,theenergytransferisexpectedtobeveryefficient.Mid-rangepowertransferimplementedthiswaycanbenearlyomnidirectionalandefficient,irrespectiveofthegeometryofthesurroundingspace,andwithlowinterferenceandlossesintoenvironmentalobjects(6).
Considerationsaboveapplyirrespectiveofthephysical
natureoftheresonances.Inthecurrentwork,wefocusononeparticularphysicalembodiment:
magneticresonances(9).Magneticresonancesareparticularlysuitableforeverydayapplicationsbecausemostofthecommonmaterialsdonotinteractwithmagneticfields,sointeractionswithenvironmentalobjectsaresuppressedevenfurther.Wewereabletoidentifythestronglycoupledregimeinthesystemoftwocoupledmagneticresonances,byexploringnon-radiative(near-field)magneticresonantinductionatMHzfrequencies.
wheretheindicesdenotethedifferentresonantobjects.Thevariablesam(t)aredefinedsothattheenergycontainedinobjectmis|am(t)|2,wmistheresonantfrequencyofthatisolatedobject,andGmisitsintrinsicdecayrate(e.g.duetoabsorptionandradiatedlosses),sothatinthisframeworkanuncoupledandundrivenoscillatorwithparametersw0andG0wouldevolveintimeasexp(iw0t–G0t).Thekmn=knmarecouplingcoefficientsbetweentheresonantobjectsindicatedbythesubscripts,andFm(t)aredrivingterms.
Welimitthetreatmenttothecaseoftwoobjects,denotedbysourceanddevice,suchthatthesource(identifiedbythesubscriptS)isdrivenexternallyataconstantfrequency,andthetwoobjectshaveacouplingcoefficientk.Workisextractedfromthedevice(subscriptD)bymeansofaload(subscriptW)whichactsasacircuitresistanceconnectedtothedevice,andhastheeffectofcontributinganadditionaltermGWtotheunloadeddeviceobject'sdecayrateGD.TheoveralldecayrateatthedeviceisthereforeG¢D=GD+GW.Theworkextractedisdeterminedbythepowerdissipatedintheload,i.e.2GW|aD(t)|2.MaximizingtheefficiencyhofthetransferwithrespecttotheloadingGW,givenEq.1,isequivalenttosolvinganimpedancematchingproblem.Onefindsthattheschemeworksbestwhenthesourceandthedeviceareresonant,inwhichcasetheefficiencyis
TheefficiencyismaximizedwhenGW/GD=(1+k2/GSGD)1/2.Itiseasytoshowthatthekeytoefficientenergytransferistohavek2/GSGD>1.Thisiscommonlyreferredtoasthestrongcouplingregime.Resonanceplaysanessentialroleinthis
powertransfermechanism,astheefficiencyisimprovedbyapproximatelyw2/GD2(~106fortypicalparameters)comparedtothecaseofinductivelycouplednon-resonantobjects.
Theoreticalmodelforself-resonantcoils.Ourexperimentalrealizationoftheschemeconsistsoftwoself-resonantcoils,oneofwhich(thesourcecoil)iscoupledinductivelytoanoscillatingcircuit,whiletheother(thedevicecoil)iscoupledinductivelytoaresistiveload(12)(Fig.1).Self-resonantcoilsrelyontheinterplaybetweendistributedinductanceanddistributedcapacitancetoachieveresonance.Thecoilsaremadeofanelectricallyconductingwireoftotallengthlandcross-sectionalradiusawoundinto
Giventhisrelationandtheequationofcontinuity,onefindsthattheresonantfrequencyisf0=1/2p[(LC)1/2].Wecannowtreatthiscoilasastandardoscillatorincoupled-modetheorybydefininga(t)=[(L/2)1/2]I0(t).
Wecanestimatethepowerdissipatedbynotingthatthesinusoidalprofileofthecurrentdistributionimpliesthatthespatialaverageofthepeakcurrent-squaredis|I0|2/2.Foracoilwithnturnsandmadeofamaterialwithconductivitys,wemodifythestandardformulasforohmic(Ro)andradiation(Rr)resistanceaccordingly:
µ0ω l
ahelixofnturns,radiusr,andheighth.Tothebestofourknowledge,thereisnoexactsolutionforafinitehelixintheliterature,andeveninthecaseofinfinitelylongcoils,thesolutionsrelyonassumptionsthatareinadequateforour
Ro=
2σ4πa
µ⎛π
⎛ωr⎞4
2⎛ωh⎞2⎞
(6)
system(13).Wehavefound,however,thatthesimplequasi-
R= 0⎜
n2 + ⎟
(7)
staticmodeldescribedbelowisingoodagreement
r ε⎜12
⎜c⎟
3π3⎜
c⎟⎟
(approximately5%)withexperiment.
Westartbyobservingthatthecurrenthastobezeroattheendsofthecoil,andmaketheeducatedguessthattheresonantmodesofthecoilarewellapproximatedbysinusoidalcurrentprofilesalongthelengthoftheconductingwire.Weareinterestedinthelowestmode,soifwedenotebystheparameterizationcoordinatealongthelengthoftheconductor,suchthatitrunsfrom-l/2to+l/2,thenthetime-dependentcurrentprofilehastheformI0cos(ps/l)exp(iwt).Itfollowsfromthecontinuityequationforchargethatthelinearchargedensityprofileisoftheforml0sin(ps/l)exp(iwt),sothetwohalvesofthecoil(whenslicedperpendicularlytoitsaxis)containchargesequalinmagnitudeq0=l0l/pbutoppositeinsign.
Asthecoilisresonant,thecurrentandchargedensityprofilesarep/2outofphasefromeachother,meaningthattherealpartofoneismaximumwhentherealpartoftheotheriszero.Equivalently,theenergycontainedinthecoilis
0⎝ ⎝ ⎠ ⎝ ⎠⎠
ThefirstterminEq.7isamagneticdipoleradiationterm(assumingr<<2pc/w);thesecondtermisduetotheelectricdipoleofthecoil,andissmallerthanthefirsttermforourexperimentalparameters.Thecoupled-modetheorydecayconstantforthecoilisthereforeG=(Ro+Rr)/2L,anditsqualityfactorisQ=w/2G.
WefindthecouplingcoefficientkDSbylookingatthepowertransferredfromthesourcetothedevicecoil,assumingasteady-statesolutioninwhichcurrentsandchargedensitiesvaryintimeasexp(iwt).
DS S D
P =òdrE(r)×J(r)
=-òdr(A&S(r)+ÑfS(r))×JD(r)
atcertainpointsintimecompletelyduetothecurrent,andatotherpoints,completelyduetothecharge.Usingelectromagnetictheory,wecandefineaneffectiveinductanceLandaneffectivecapacitanceCforeachcoilasfollows:
=-1òòdrdr¢⎛µJ&S(r¢)+ρS(r¢)4π ⎝ |r-r| ε0
⎜0¢
º-iωMISID
r¢-r⎞
⎠
¢
|r¢-r|3⎟×JD(r)
(8)
2
L= µ0
4π|I0|
òòdrdr¢J(r)×J(r¢)
|r-r¢|
wherethesubscriptSindicatesthattheelectricfieldisduetothesource.Wethenconcludefromstandardcoupled-modetheoryargumentsthatkDS=kSD=k=wM/2[(LSLD)1/2].When
1 1 ρ(r)ρ(r¢)
thedistanceDbetweenthecentersofthecoilsismuchlarger
2
=
C 4πε
0|q0|
òòdrdr¢
|r-r¢|
(4)
thantheircharacteristicsize,kscaleswiththeD-3dependencecharacteristicofdipole-dipolecoupling.BothkandGarefunctionsofthefrequency,andk/Gandthe
wherethespatialcur
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