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1、CHAPTERIINTRODUCTIONTOINDUCTANCETheimpactofinductancehasbeenacriticalissueintheprintedcircuitboard(PCB)designforquitesometime.SinceaPCBhasbothnearlyperfectdielectricandgroundplane,resistivelossesinconductorsaswellasdielectricsarereasonablyignored.Theinductanceandcapacitancearethemajorconcernsinterms
2、oftheon-boardsignaltransmission.Inaddition,thedimensionofaPCBisrelativelylargecomparedwiththesignalwavelength,especiallyintheradio-frequency(RF)andmicrowaveregime.Forexample,a1GHzsignalhasawavelengthof30cminfreespacewhileatypicalPCBcaneasilyhaveoneofitsdimensionslargerthanseveralinches.Thismeanstheb
3、oardhastobetreatedasadistributedsystemwherethetransmissionlinetheoryinsteadofKCLandKVLapplies.Thesignificanceofinductanceincludesincreasedtransmissiondelay,signalreflectionandringing,inductivecoupling,anddigitalswitchingnoiseduetoACvoltagedrop.However,inductancehasbeenlargelyignoredinanon-chipenviro
4、nment,whereresistivetogetherwithcapacitiveeffectsarebiggerconcerns.Inaddition,thechipsizeisnolargerthanseveralmillimeters,whichistinyenoughcomparedwithsignalwavelengths.141Withtheoperatingfrequenciesloomingintothegigahertzrange,inductanceisquicklycomingintoplay.Ononehand,theparasiticinductanceofon-c
5、hipinterconnectsgivesrisetosignaldelayandcrosstalkbetweendifferentsignalpaths.Ontheotherhand,spiralinductorshavebeenspecificallydesignedandintegratedontoachiptoachieveenhancedsystemintegrity.ThereforethereisadramaticallyincreaseddemandofICdesignersforanaccurateinductancemodel,bothanalyticalandcomput
6、ational.MAXWELLEQUATIONSMaxwell’sEquationsarethecompletesetoflawsfortime-varyingelectromagneticphenomena.Thefourphysicaltermsthatdescribeelectromagneticfieldsaretheelectricfield,electricdisplacement,magneticfield,andmagneticintensity.andareanalogousinnatureinthattheybothgivetheforceonamovingchargegi
7、venby,(1)whereisthevelocityofthecharge.andareanalogousbecausetheyareindependentofmaterialpropertiesandcorrespondtothespacefreechargeandcurrent141respectively.andarerelatedtoandthroughtheelectricandmag