Study.of.Microwave.Dielectric.Resonators.and.Filters.pdf

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國立成功大學電機工程學系博士論文微波介電共振器及微波濾波器之研究StudyofMicrowaveDielectricResonatorsandMicrowaveFilters研究生:陳耀忠Student:Yao-ChungCheng指導教授:黃正亮Advisor:Cheng-LiangHuangDepartmentofElectricalEngineeringNationalChengKungUniversityTainan,Taiwan,R.O.C.DissertationforDoctorofPhilosophyJune,2002中華民國九十一年六月 1(2476x3477x16Mjpeg) 2(2469x3472x16Mjpeg) StudyofMicrowaveDielectricResonatorsandFiltersStudent:Yao-ChungChenAdvisor:Cheng-LiangHuangDepartmentofElectricalEngineeringNationalCheng-KungUniversityAbstractDuetothedevelopmentinmobilecommunication,mobiletelephonesystems,aswellasinsatellitebroadcastingsystemswasrapidly,howtodesignthehigh-qualitydevicesappliedinanalogcircuitisthemostimportanthomework.Therearetwoprimarybranchesinthisresearch.Onepartistodevelopthedielectricceramicsystemsthatexhibitgreatdielectricproperties.Theotherpartistodesignandrealizethecoaxial-typedielectricfilters.1.Studyandfabricationsofmicrowavedielectricresonators(a)TheeffectofCuO,ZnOandV2O5additionstoReAlO3(Re=SmandNd)wereinvestigated.ThesinteringtemperaturesofReAlO3ceramicscanbeeffectivelyreducedfrom1650℃to1410~1430℃duetotheliquid-phasesinteringeffect.Atlowconcentrationlevels(0.25-0.5wt％),theReAlO3ceramicsremainedinthesinglephaseandpresentedsecondphaseSm4Al2O9andNd4Al2O9onSmAlO3andNdAlO3,respectivelywithconcentrationsover0.5wt%.TheQ×fvaluesof51000and41000GHzwasobtainedat1430℃for0.25wt%CuOandI ZnO-sinteredSmAlO3ceramics.TheQ×fvalueof63000GHzwasachievedat1410~1430℃for0.25wt%CuO-sinteredNdAlO3.TherelativedielectricconstantofReAlO3remainsintherangefrom19.6to22.5.ThetemperaturecoefficientofReAlO3ceramicsdependsontheadditionsandrangesfrom–30to-65ppm/℃.(b)ThemicrowavedielectricpropertiesandmicrostructureofBa2-xSm4+2x/3Ti8+yO24+2ywereinvestigated.Thetypicaldielectricperformancesofår=68to79andQ×f=11000to12500GHzwereobtainedinwell-sinteredBa2-xSm4+2x/3Ti9O26ceramics.TheôfvaluesofBa2-xSm4+2x/3Ti9O26ceramicswasadjustedfromnegative(－3ppm/℃forx=0)topositive(+6ppm/℃forx=0.3).TheBa2-xSm4+2x/3Ti8+yO24+2yceramicswithx=0.1~0.3andy=0~2formedthecompletesolidsolutionandwereobtainedinthisreach.Thetypicaldielectricperformancesofår=63to85andQ×f=8500to13000GHzwereobtained.TheôfvaluesoftheBSTceramicscanbeadjustedfromanegative–12ppm/℃valuetoapositivevalue17ppm/℃asyincreasesfrom0to2.SecondphasesBa2Ti9O2andTiO2appearedduringsinteringproceduresandwereidentified.Notonlydielectricconstant,butalsoQ×fvaluesaredependentonthedensificationofBSTceramics.2.DesignandconstructionofmicrowaveceramicsdielectricfiltersMicrowavedielectricpropertiesofBa(2-x)Sm(4+2x/3)Ti9O26system(BST)(0.0≦x≦0.3)anddesignproceduresofmicrowavecoaxialdielectricbandpassfilterhavebeeninvestigatedinthiswork.DielectriccoaxialresonatorswithexcellentdielectricpropertiesofårII =75∼80,Q×fvalue=11000andgreattemperaturestabilityattheresonantfrequency.(t=~f0ppm/℃)wereused.Microwavebadnpassfiltersformobilecommunicationsystemwerelconstructedbyusingsuchcoaxialresonators.Bothair-gapcouplinganddirectcoupling4methodswereappliedasthecouplinginstrumentsinthetransformationofelectromagneticenergy.Comb-linetheorywasusedtoadjusttheresponseoffilters.Theresonantfrequencyofeachresonator,couplingcoefficientsbetweenadjacentresonators,andexternalqualityfactorwereadjustedtoachievethetargetspecifications.Themeasuredresponseswereinexcellentagreementwiththeexpectedresults.III 微波介電共振器及微波介電濾波器之研究研究生:陳耀忠指導教授:黃正亮國立成功大學電機工程研究所摘要微波介電共振器，具有高介電常數，低溫度飄移係數及高品質因數等特性，極適合應用於微波類比電路元件。本論文主要在於研發應用於微波類比電路中之共振器及濾波器，並將論文分成兩大研究方向：一、微波介電陶瓷之研發及備製：(a)利用CuO,ZnO和V2O5等不同的參雜物質來達到液相燒結的效果，並達到降低ReAlO3燒結溫度的目的。SmAlO3和NdAlO3兩組材料系統經過添加燒結促進劑後可將燒結溫度從1650℃降到1410℃~1430℃。SmAlO3再添加0.25wt/%CuO且燒結溫度微1430℃時，Q×f可達到51000GHz。在加入0.25wt/%ZnO且燒結溫度微1430℃時Q×f可達到41000GHz。ReAlO3系統在添加促進劑後其介電常數為19.6~22.5。頻率飄移係數為－30~－65ppm/℃。IV (b)利用tungsten-bronze-typestructure此種微架構之結構式，來研究、改良和探討Ba2-xSm4+2x/3Ti8+yO24+2y材料系統之微波特性。當y值固定為1，x值為0.0~0.3時，其Q×f值為9000~11000，介電常數值為75~80，頻率飄移係數為~0ppm/℃。當x值固定為0.1，y=0~2時，BST系統之Q×f值為8500~13000，介電常數值為63~85，頻率飄移係數為－12~17ppm/℃。二、微波介電陶瓷濾波器之設計及製作：(a)本研究以BST材料系統為原始材料，設計、分析並研製了適用於UHF和L頻帶的同軸型介電濾波器，其中包含了前段設計的基本考量，中段製程觀念、和後段的成型及測試。V ContentsAbstractIContentsVAcknowledgeVIIITableCaptionsIXFigureCaptionsXChapter1Introduction1Chapter2TheoryofDielectricResonatorand5MicrowaveFilters2-1TheoryofMicrowaveDielectricProperties52-2AnalysisofDielectricResonator82-3MeasurementofMicrowaveDielectricProperties112-4BasicTheoryofMicrowaveFilters13Chapter3LiquidPhaseSinteringandMicrowaveDielectric17PropertiesofReAlO3(Re=Sm,Nd)Ceramics3-1Introduction173-2ExperimentalProcedures18VI 3-2-1Samplepreparations183-2-2CharacteristicsAnalysisandMeasurementofMicrowave19DielectricProperties3-3ResultsandDiscussions203-3-1MicrostructureofSmAlO3Ceramics203-3-2MicrostructureofNdAlO3Ceramics223-3-3DensificationofSmAlO3Ceramics243-3-4DensificationofNdAlO3Ceramics253-3-5DielectricPropertiesofSmALO3Ceramics263-3-6DielectricPropertiesofNdAlO3Ceramics283-4.Conclusion31Chapter4MicrostructureandMicrowaveDielectric32PropertiesofBa2-xSm4+2/3xTi24+2yO8+yCeramics4-1Introduction324-2StructuralFormulaofTungsten-Bronze-Structure344-3ExperimentalProcedure354-3-1Samplepreparations354-3-2CharacteristicAnalysis364-4ResultsandDiscussion37VII 4-4-1MicrostructureofBa2-xSm4+2/3xTi24+2yO8+yceramics384-4-2DensificationofBa2-xSm4+2/3xTi24+2yO8+yceramics434-4-3MicrowaveDielectricPropertiesofBa2-xSm4+2/3xTi24+2yO8+y43ceramics4-5Conclusions47Chapter5DesignandFabricationofMicrowaveBandpass495-1Filter495-2Introduction505-3FabricationofCoaxialDielectricResonators525-4CouplingAnalyses545-5DesignandConstructionofFilter57FabricationandPerformanceofExperimentFilterChapter6ConclusionsandFutureWork596-1Conclusions596-2FutureWork61Reference63Tables72Figures75VIII TABLECAPTIONSTable1-1Propertiesrequiredformicrowavedielectricresonators72Table1-2-1Recentdevelopmentforthemicrowavedielectricmaterials73Table5-1Specificationsofacompactfilterneededtobeachieved.74IX FIGURECAPTIONSFig.2-1VariouspolarizationmechanismsinmaterialsFig.2-2ThestructureofshieldeddielectricresonatorFig.2-3ThepostmethodwitharadialdielectrometerformicrowavedielectricmeasurementsFig.2-4Threetypesoffilters(a)MaximallyFlat(b)Chebyshev(c)EllipticFunctionFig.2-5Alow-passprototypefilterFig.2-6(a)K-inverter(b)J-inverterFig.3-1FlowchartofexperimentprocedureofdielectricresonatorsFig.3-2X-raydiffractionpatternsofSmAlO3ceramicswith0.25wt%CuOsinteredatdifferenttemperatures.Fig.3-3X-raydiffractionpatternsofSmAlO3ceramicswith0.25wt%and0.5wt%additions(CuOandZnO)sinteredat1410℃.Fig.3-4X-raydiffractionpatternsofSmAlO3ceramicswithvariousamountofCuOadditionssinteredat1430℃.Fig.3-5aEDSanalysisofSmAlO3ceramicsforgeneralregions.Fig.3-5bEDSanalysisofSmAlO3ceramicsforspecificgrainswithSm4Al2O9secondphase.Fig.3-6aSEMmicrographofSmAlO3with0.5wt%CuOsinteredat1430℃.Fig.3-6bSEMmicrographofSmAlO3with1wt%CuOsinteredat1430℃Fig.3-6cSEMmicrographofSmAlO3with0.5wt%ZnOsinteredat1430℃X Fig.3-6dSEMmicrographofSmAlO3with1wt%ZnOsinteredat1430℃.Fig.3-7XRDpatternsofNdAlO3powderscalcinedatdifferenttemperaturesfor2h.Fig.3-8XRDpatternsofNdAlO3ceramicswith0.25wt%CuOsinteredatdifferenttemperatures.Fig.3-9XRDpatternsofNdAlO3ceramicswithvariousCuOconcentrationssinteredat1410℃.Fig.3-10aSEMofNdAlO3ceramicssinteredat1410℃with0.25wt%CuOaddedFig.3-10bSEMofNdAlO3ceramicssinteredat1410℃with0.5wt%CuOadded.Fig.3-10cSEMofNdAlO3ceramicssinteredat1410℃with0.75wt%CuOadded.Fig.3-10dSEMofNdAlO3ceramicssinteredat1410℃with1wt%CuOadded.Fig.3-11aSEMofNdAlO3ceramicswith0.75wt%CuOaddedsinteredat1390℃Fig.3-11bSEMofNdAlO3ceramicswith0.75wt%CuOaddedsinteredat1410℃Fig.3-11cSEMofNdAlO3ceramicswith0.75wt%CuOaddedsinteredat1430℃Fig.3-11dSEMofNdAlO3ceramicswith0.75wt%CuOaddedsinteredat1450℃Fig.3-12GrainsizeofNdAlO3ceramicssinteredat1410℃asfunctionofCuconcentration.Fig.3-13Relativedensitiesofaddition-sinteredSmAlO3ceramicsasafunctionofsinteringtemperatures.Fig.3-14RelativedensitiesofCuO-sinteredNdAlO3ceramicsasafunctionofsinteringtemperature.Fig.3-15DielectricconstantofSmAlO3ceramicswithdifferentadditionsasfunctionofXI sinteringtemperature.Fig.3-16Q×fvaluesofSmAlO3ceramicswithdifferentadditionsasafunctionofsinteringtemperature.Fig.3-17ThecompositiondependenceonôfofSmAlO3ceramicssinteredat1430℃.Fig.3-18DielectricconstantårofNdAlO3ceramicsasafunctionofsinteringtemperature.Fig.3-19Q×fvaluesofNdAlO3ceramicswithvariousCuOconcentrationsasfunctionofsinteringtemperature.Fig.3-20CompositiondependenceonôfofNdAlO3ceramicsasafunctionofsinteringtemperature.Fig.4-1TheSchematicdiagramofBSTceramicswithcomplexphaseoftungstenbronzestructureFig.4-2Projectionofthetungstenbronzestructureinthecplane.Theinsetshowsthepolardirectionsinorthorhombicstructure.Fig.4-3X-raydiffractionpatternsofBa(2-x)Sm(4+2/3x)Ti9O26ceramicssinteredat1360℃for4hourswithx=0.0,x=0.1,x=0.2,x=0.3.Fig.4-4aMicrographofBa(2-x)Sm(4+2/3x)Ti9O26ceramicswithx=0.1sinteredat1340℃Fig.4-4bMicrographofBa(2-x)Sm(4+2/3x)Ti9O26ceramicswithx=0.1sinteredat1360℃Fig.4-4cMicrographofBa(2-x)Sm(4+2/3x)Ti9O26ceramicswithx=0.1sinteredat1380℃XII Fig.4-5aPhotographofthesinteredsurfacewithsecondphaseBa2Ti9O20thatwasidentifiedwiththeenergydispersiveX-rayspectrometer(EDS)analysis.Fig.4-5bEnergydispersiveX-rayspectrometer(EDS)resultofthesinteredsurfaceshowninFig.4-5a.Fig.4-5cPhotographofthesinteredsurfacewithintermediatephaseSm2Ti2O7thatwasidentifiedwiththeenergydispersiveX-rayspectrometer(EDS)analysis.Fig.4-5dEnergydispersiveX-rayspectrometer(EDS)resultofthesinteredsurfaceshowninFig.4-5cFig.4-6Macrodifferentialthermalanalysis(DTA)oftheBa2-xSm4+2x/3Ti8+yO24+2yrawmaterialsFig.4-7X-raydiffractionpatternsofBa2-xSm4+2x/3Ti8+yO24+2y(x=0.1,y=1)ceramicscalcinedatvarioustemperatures.Fig.4-8X-raydiffractionpatternsofBa2-xSm4+2x/3Ti8+yO24+2yceramicssinteredattheirspecificdensifiedtemperatures(+and□markersareidentifiedasthemainphaseBaSm2Ti4O12,BaSm2Ti5O14).Fig.4-9aMicrographofBa2-xSm4+2x/3Ti8+yO24+2yceramicswithy=0sinteredat1400℃Fig.4-9bMicrographofBa2-xSm4+2x/3Ti8+yO24+2yceramicswithy=1sinteredat1370℃Fig.4-9cMicrographofBa2-xSm4+2x/3Ti8+yO24+2yceramicswithy=2sinteredat1330℃Fig.4-10ApparentdensitiesofBa2-xSm4+2/3xTi9O26ceramicsasafunctionofsinteringtemperatureandcompositionXIII Fig.4-11ApparentdensitiesofBa2-xSm4+2x/3Ti8+yO24+2yceramicsasafunctionofsinteringtemperatureandcomposition(x=0.1)Fig.4-12Q×fvaluesofBa2-xSm4+2/3xTi9O26ceramicsasafunctionofsinteringtemperatureandcompositionFig.4-13Q×fvaluesofBa2-xSm4+2x/3Ti8+yO24+2yceramicsceramicsasafunctionofsinteringtemperatureandcomposition(x=0.1).Fig.4-14DielectricconstantofBa2-xSm4+2/3xTi9O26ceramicsasafunctionofsinteringtemperatureandcompositionFig.4-15DielectricconstantofBa2-xSm4+2x/3Ti8+yO24+2yceramicsasafunctionofsinteringtemperatureandcomposition(x=0.1).Fig.4-16TemperaturecoefficientoftheresonantfrequencyôfofBa2-xSm4+2/3xTi9O26ceramicssinteredat1360℃Fig.4-17TemperaturecoefficientôfofBa2-xSm4+2x/3Ti8+yO24+2yceramicssinteredattheirspecificsinteringtemperatureasafunctionofcomposition.Fig.5-1TheconfigurationofasinteredcoaxialresonatorwithcouplingapertureFig.5-2Theconfigurationofathree-stagecapacitivecouplingbandpassfilterFig.5-3TheequivalentcircuitofthefirststageloadedbytheexternalcircuitFig.5-4aTheequivalentcircuitoftwoadjacentresonatorswithcouplingcapacitorFig.5-4bTheequivalentcircuitoftwoadjacentresonatorswithcouplingcapacitorXIV Fig.5-5Theequivalentcircuitofthethree-stagebandpassfilterwiththeexternalcircuit.Fig.5-6aTheschematicdiagramoftotalcapacitancebetweentwoadjacentresonatorsandthegroundwhenthetransmissionlinesaredriveninoddmode.Fig.6bTheschematicdiagramoftotalcapacitancebetweentwoadjacentresonatorsandthegroundwhenthetransmissionlinesaredriveninevenmode.Fig.5-7aThefrequencyresponseoftheexperimentalbandpassfiltersbyair-gapcouplingFig.5-7bThefrequencyresponseoftheexperimentalbandpassfiltersbydirectcouplingXV Chapter1GeneralIntroductionDuetothedevelopmentincommercialwirelesstechnologiessuchascellularphones,globalpositionsystem,aswellasinsatellitebroadcastingsystemswasrapidly,howtodesignthehigh-qualitydevicestoimprovetheperformanceofthemobilecommunicationisveryimportant.Inordertoachievethepurposeofminiaturizationofthedimensionsofthedevicesandservethesystemworkwithhighefficiencyandstability,thematerialsformicrowaveresonatorsarerequiredtobeexcellentinthreedielectriccharacteristicsandtherequirementsareshowninTable1-1[1,2].Thefirstcharacteristicishighdielectricconstant(år),becausethemicrowavewavelengthisinverselyproportionaltoeofthedielectricmaterial(ë=ëo/e),whereëoistherrwavelengthinair.ThesecondoneishighQvalue,whichistheinverseofthedielectriclosstanä,isrequiredtoachievehighfrequencyselectivityandstabilityinmicrowavetransmitterandreceivercomponents.Thethird,temperaturecoefficientoftheresonantfrequency(ôf),isrequiredtobeascloseto0ppm/℃aspossible.Inthe1960s,TiO2andTi-basedceramicswerewidelyusedfordielectricresonator.However,thetemperaturecoefficientofitistoolargeforpracticalapplications.RelativeresearchanddevelopmentonthetemperaturestabilityoftheDRsweremade.Inthepastyears,severalsystemsofdielectricceramicsweredevelopedtoachievetherequirementsoftheceramics1 appliedatmicrowavefrequency.Thebriefdescriptionoftherecentdevelopmentforceramicsystemswiththeirdielectricconstantsrangingfrom10to90areasfollows:(1)Ba(Mg1/3Ta2/3)O3andBa(Zn1/3Ta2/3)O3aretheceramicsthathavethehighestQ×fvalues.TheirQ×fvaluesare100000~120000and200000~250000,respectively[3,4,13,14].(2)(Mg,Ca)TiO3ceramicsystemisuniversallyappliedfortemperaturecompensatingcapacitors.Theceramicmadeof0.95MgTiO3-0.05CaTiO3exhibitsexcellentdielectricproperties[5,25].(3)(Zr0.8Sn0.2)TiO4materialhasthehighQ×fvalueof50000andgreattemperaturestability.ThesinteringconditionsofZSTceramicswereimprovedbymodificationtocompositionadditions,andprocessing[16,17,23,24,27].(4)Ba-Re2O3-TiO2(Re=Sm,La,Nd)systemsbelongtotheperovskitestructureceramicsandhavebeenwidelystudiedforpracticalapplicationsatbroadbandfrequency[21,22,30,32-36,44-47].(5)Re2O3-Al2O3(La,Nd,Sm,etc.)systemsexhibithighQvalue(Q×f=~60000GHz).ThesystemsweremodifiedbyCuO,ZnOandV2O5toadjustthesinteringconditions[10,11,18].OtherrecentdevelopmentforthemicrowavedielectricceramicsareshowninTable1-2[6,12,15,20].HighQdielectricceramicresonatorswithhighdielectricconstantcanefficientlyreducethesizeoffilters.Furthermorethesmalltemperaturecoefficientcontributesthesystemhighstability.Withthecharacteristics,dielectricresonatorswereinvestigatedandwidelyusedin2 thefabricationsofmicrowavefiltersandoscillators[48-50,59-63].Abriefdescriptionofthethesis’contentsexpressedasfollowing.IntroductionofthischapterreviewsthecharacteristicsrequiredofmicrowaveDRsandgivesanoverviewofthedissertation.Dielectrictheorem,microwavedielectricmeasurementofDRsandrelativetheoryofmicrowavefilterarereviewedinChapter2.Inordertolowerthesinteringthesinteringtemperatureandimprovethemicrowavedielectricproperties,liquidphasesuchasCuO,ZnOandV2O5wereaddedintheRe2O3-Al2O3(Re=Sm,Nd)ceramics.ThemicrowavedielectricpropertiesofRe2O3-Al2O3ceramicsweredependentontherawmaterials,theadditives,andthemicrostructure.TheeffectofCuO,ZnOandV2O5additiononthemicrostructuresandthemicrowavedielectricpropertiesofReAlO3ceramicswereinvestigatedinChapter3[10-31].Thetungsten-bronze-typeBaO-Sm2O3-kTiO2(k=4~5)solidsolutionsarewellknownasmicrowavedielectricceramicresonatorswithhighdielectricconstant[32-47].TheoptimumsubstitutionofBaforSmwasobtainedbasedonthestructuralformula.ThedecreaseofsinteringtemperatureandadjustmentoftemperaturecoefficientattheresonantfrequencytozerowereachievedbyincreaseofTiamount.Therelationshipsbetweenmicrostructureandmicrowavedielectricpropertiesbasedonthetungsten-bronze-typestructuralformulawerestudiedandinvestigatedinChapter4.InChapter5,dielectricresonatorsappliedinUHF~LBandwerefabricated.TheDRsof3 BaO-Sm2O3-TiO2withhighdielectricconstant,hightemperaturestabilityandhighQ×fvalueswereappliedintheconstructionofabandpassfilter.Microwavebandpassfiltersformobilelcommunicationsystemwereconstructedbyusingsuchcoaxialresonators.Bothair-gap4couplinganddirectcouplingmethodswereappliedasthecouplinginstrumentsinthetransformationofelectromagneticenergy.Amethodofdesigningcapacitivecoupledbandpassfilterswitharbitrarilystructuredresonatorswasinvestigatedandestablished[48-63].AtlasttheconclusionsandthefutureworkaresummarizedinChapter6.4 Chapter2TheoryofDielectricResonatorandMicrowaveFilters2-1TheoryofMicrowaveDielectricPropertiesThedielectricpropertiesofmaterialsareresultedfromthepolarizationphenomenonduetothechargesinthematerialsunderexternalelectricfield.Therearefourtypesofpolarizablemechanisms.Theyareelectronpolarization,ionicpolarization,orientationpolarizationandspacechargepolarization,asshowninFig.2-1.Thepolarizationofmaterials（t）canbeindicatedas:αt=αe+αi+αo+αs（2-1）whereαtisthetotalpolaribilityαeistheelectronpolaribilityαiistheionicpolaribilityαoistheorientationpolaribilityαsisthespacechargepolaribilityThedominantpolarizablemechanismofmaterialisuncertain.Itisveryrelativetotheoperatingfrequency.Inmicrowavefrequency,thepolarizablemechanismscontributetodielectricconstantismostlyionicpolarizationforanisotropicdielectricmaterial.Itoriginatesinthedisplacementofionsonanelectricfieldfromequilibriumposition.The5 phenomenahadbeenexplainedaccordingtoclassicaldispersiontheory[1,2],whichdescribedthemechanismsofionicpolarizationinsolidbyconsideringasimplemodelofLorenzoscillator.TheactionofLorenzoscillatorcanberepresentedasfollowing:2dxdx2m+mr+mwx=q×E×exp(jwt)(2-2)2oodtdtwheremisthemassofionic.xisthedistancebetweenionicsγisdampingcoefficient.ωoisnaturalresonantfrequency.qisthechargeontheionic.│Eo│isthemagnitudeofexternalelectricfield.ωisthefrequencyofexternalelectricfield.Thecomplexdielectricconstantε（ω）canbeobtainedasfollowing:2qe(w)=4pN+1（2-3）22m[(w-w)+jwr]oLet2224pNq(wo-w)e(w)=()×+1（2-4）122222m(w-w)+wg06 24pNqwge(w)=()×（2-5）22222m(w-w)+wg0Soe(w)=e-je（2-6）12whereNistheionicvolumedensity.e(w)isthepolarizationpartinmaterial.1e(w)isthedielectriclossfactorinmaterial.2Inmicrowavefrequencyrage,Eq.（2-4）and（2-5）canbeapproximatedby：24pNqe»（2-7）12mw0e2wgtand=»（2-8）2ew10Consequently,Eq.（2-7）showsthatthedielectricconstantεrisindependentoffrequency.Equation（2-8）exposesthatthetanδinmaterialsincreasedwithincreasingfrequency.Thelossisresultedfromaharmonicinteractionorlatticevibration.Actually,itisalsoproducedbyporosity,secondphase,etc.7 2-2AnalysisofDielectricResonatorConsiderthesystemofFig.2-2,acylindricaldielectricresonatorwithheightL,radiusa,dielectricconstantεr,issituatedonadielectricsubstratewithdielectricconstantεsofthicknessL2,thetopmetalcoverisseparatedatdistanceL1abovetheresonator.Mostoftheelectromagneticenergyisstoredinregion1andthefielddecaysexponentiallyinregion2,3,and4.Withasmallamountofenergybeingconfinedinregionsof2~4andevenlessamountofenergyinregions5and6,onlylittleerror,therefore,isintroducedinthecalculationofresonantcharacteristicsifoneignoresthefieldsin5and6.Fromtheelectromagneticwavetheory,boththeelectricandmagneticfieldofinsideandoutsideofthedielectricmaterialmustsatisfytheMaxwellequationandboundaryconditions.Hence,itisnecessarytomatchthefieldonlyontheboundariesofregion1.Thefollowingcharacteristicequationswereobtained:222region1kp1+β=k0εr（2-9）region2222（2-10）kp1-kz2=k0εsregion3222（2-11）kp1-kz3=k0region4222（2-12）β-kz4=k08 wherek=wue0000Thetranscendentaleigenvalueequationcanbeexpressedas:2F(x)×F(x)-F(x)=0（2-13）123HereJ'(x)K'(x)mmF(x)=+1x×J(x)e×y×K(y)mrmJ'(x)K'(x)mmF(x)=+2x×J(x)y×K(y)mmmb11F(x)=(+)322kexyorwherex=kñ1áandy=kñ4áaretheeigenvaluesofJmandKm,respectively.JmistheBesselfunctionofthefirstkindwithm-thorder.KmisthemodifiedBesselfunctionofthesecondkindwithm-thorder.kñ1istheradialpropagationconstantinsidetheDR（ña）.βistheaxialpropagationconstantinsideheight（L）oftheDR.kz2istheaxialattenuationconstantinregion2.kz3istheaxialattenuationconstantinregion3.TheresonantmodesofTEmnp,TMmnp,andHEMmnpindielectricresonatorcanbeanalyzedfromeq.（2-13）:9 （1）TMo,n,,p+ämodes:F1（χ）=0keke-1z3r-1z2rbL=tan[×tanh(k×L)]+tan[×tanh(kL)]+pp（2-14）z31z22bbes（2）TEo,n,,p+ämodes:F2（χ）=0kek-1z3r-1z2bL=tan[×coth(k×L)]+tan[×coth(kL)]+pp（2-15）z31z22bb（3）HEMo,n,,p+ämodes:2F1（χ）‧F2（χ）-F3（χ）=0（i）ForHEMo,2n,,p+ämodes,whichcontainstheirmostenergyintheTEpart,arealsocalledquasi-TEmodes:（ii）kek-1z3r-1z2bL=tan[×coth(k×L)]+tan[×coth(kL)]+pp（2-16）z31z22bb（ii）ForHEMo,2n+1,,p+ämodes,whichcontainstheirmostenergyintheTMpart,arealsocalledquasi-TMmodes:keke-1z3r-1z2rbL=tan[×tanh(kL)]+tan[×tanh(kL)]+pp（2-17）z31z22bbesIngeneralmeasurement,L1=L2=0,fromeq.（2-14）and（2-15）:lgp×()=L（2-18）210 Inashieldingcondition（L1orL2¹0）,theresonantmodesofTMonä,TEonäandHEMonä（m¹0）canbeexited,whereäislessthanunity.ä=（âL）/ð（2-19）2-3MeasurementofMicrowaveDielectricPropertiesThemicrowavemeasurementtechniquescanbedividedintotwogroups:1ResonanceTechniques,and2TransmissionTechniques.Usually,thedielectricpropertymeasurementbytheresonancetechniqueshashigheraccuracythanthatbythetransmissiontechniquesespeciallyfordielectricloss.Threedifferentdielectricresonancemethodsarenowusedi）PostResonanceTechnique,ii）CylinderCavityResonanceTechnique,andiii）WaveguideReflectionResonanceTechnique.Thedifferencesbetweenthosetechniquesarebasedonthedifferentgeometricalarrangementsofmetalshields.PostResonanceTechniquewasoriginallysuggestedbyHakkiandColemanin1960[7].Thismethodhasbeenwidelyusedandhasbecomethemostpopulardielectricresonancemethodformeasuringthecomplexpermittivityofhighdielectricconstantandlowlossmaterialsinmicrowaveregions.AcylindricaldielectricrodisplacedbetweentwoparallelmetalplatesasshowninFigure2-3.Twocouplingantennaswereusedtocouplethepowerinandout.Therearevariousdielectricresonancetechniquesformeasuringthedielectric11 propertiesofdielectricsamples.ThelowestTEmodeofacylindricaldielectricsampleisalwaysusedformeasurementsbecauseitiseasytoidentifytheresonantpeak,andthecalculationequationsforthedielectricpropertiesaremoreeasilyderivedthanthoseofothermodes.Theresonantfrequencyf0,thehalfpowerbandwidth,theinsertionlossS12,andthedimensionsofthespecimenwererecordedforthecalculationofthecomplexpermittivity.Thetotallossofthesystemisthesummationofthedielectriclossofthesample,theconductorlossofthemetalshields,thelossofthesurroundingair,andtheradiationloss.Theaccuratecalculationofconductorlossisacriticalpointforcorrectcomputationofdielectricloss.Therefore,Kobayashietal,suggestedamethodusingtwocylindricalsamplescutfromasamerod[8],onesamplewiththicknessNtimes（NisforTE01Nmode）theothersample.TheresonantfrequencyoftheTE011modeoftheshortsampleisthesameasthatoftheTE01Nmodeofthelongsample.Theyderivedtheequationforcalculatingthesurfaceresistancebasedontheassumptionthatthetwosampleshavethesamelosstangentvalueatthesamefrequency.Thelossofthesurroundingairdependsontheambienthumidityandthedensityofthesample.Theradiationlosscanbealwaysneglected.Acomputerprogramwasusedforthecalculationsofthedielectricconstantandthedielectricloss.Themainadvantageforthispostresonancemethodisthatequationsshownaboveforthecalculationsofdielectricpropertieswerewelldeveloped,muchsimplerthanotherdielectricresonancemethods.Inaddition,theaccuracyofthoseequationsishigh.Therefore,the12 techniqueisstillusedbyalotofpeople.2-4BasicTheoriesofMicrowaveFiltersFiltersareusedinallfrequencyrangestoprovideasnearlyperfecttransmissionaspossibleforsignalsfallingwithindesiredpassbandfrequencyranges,togetherwithrejectionofthosesignalsandnoiseoutsidethedesiredfrequencybands.Filtersfallintothreemaincategories:（1）low-passfilters（2）high-passfiltersand（3）bandpassfilters.Accordingtothetypesofrippleinthepassbandandslopeinthestopband,thefiltersdivideintothreetypes：（a）MaximallyFlatFilter,（b）EqualrippleFilter（Chebyshev）and（c）EllpticFunctionFilter,asshowninFig.2-4Insertionlossistheinternallossthroughthefilterinthebandtobepassed.Nodevicewillhavezerolossthroughitsimplybecausethereisenergypassingthroughatransmissionline.Thereis,therefore,asmalllosseveninthebandtobepassed.Thepassbandisthebandoffrequenciesthatareaffectedonlybytheinsertionlossofthefilter.Therejectiondescribesthattheundesiredfrequenciesareattenuated.Todesignabandpassfilter,thetargetcharacteristicsofbandpassfilter,suchasthepassbandcenterfrequency,bandwidth,insertionloss,andrejectionslopemustbedefinedfirst.Basedonthetargetcharacteristics,thenumberofpoles,couplingcoefficients,andfiltersize13 aredefined.Theequivalentcircuitofbandpassfilteriscomputed,andthestructureofbandpassfilterisdesignedaccordingtotheequivalentcircuit.Thenumberofpolesi.e.theelementnumberoffilter,isdeterminedasfollowed:-1(La)(Lar/10)cosh[1010-1/(10-1]n³（2-20）-1cosh(w'/w')a1wherew'istheoperatingfrequencyaw'istheripplecutofffrequency1Lar=passbandripple(dB)La=attention(dB)atoperationfrequencyAlow-passprototypefilterisshowninFig.2-5.Thegeneratorimpedanceischosenequalto1ohm.Oneofthefiltersisdualtotheother.Bothfilterscanbedesignedtogivesamepowerlossratio.ForChebyshevresponseinpassband,theladdernetworkissymmetricforanoddnumberofelements.Theelementvaluesg0,g1,…gn,gn+1ofthelow-passprototypefiltersaredefinesfollowed:Larb=ln(coth)（2-21）17.37bg=sinh()（2-22）2n(2k-1)pa=sin[]k＝1,2,3…n（2-23）k2n22kpb=g+sin()k=1,2,3…n(2-24)kn2a1g=（2-25）1g14 4aak-1kg=k＝2,3,4…n(2-26）kbgk-1k-1gn+1=1fornodd2bg=coth()forneven（2-27）n+14wheren:elementnumbersofreactanceLar:bandpasripple（dB）Toobtainthecouplingcoefficients,theJ,KinvertersareusedasshowninFig.2-6.ForKinverterwdX(w)ojx=w=wohms(2-28)jo2dwRxwA1K=（2-29）01gg01xxjj+1K=wj=1,2,……..,n-1(2-30)j,J+1ggjj+1RXwBnK=（1-14）(2-31)n,n+1ggnn+1whereRa、Rb=sourceloadω=fractionalbandwidthForJinverter:wdB(w)ojb=w=wohms（2-32）jo2dwGbwA1J=（2-33）01gg01bbjj+1J=w（2-34）j,J+1ggjj+115 GbwBnJ=(2-35)n,n+1ggnn+1whereGa,Gb=sourceconductanceTheinsertionlossofmulti-resonatorsisdeterminedas:fngoiL=4.343å(2-36)BWi=1QuiwhereF0=centerfrequencyBW=3dBbandwidththQi=iresonator’sunloadedQthgi=iprototypevaluefromthedesigntables16 Chapter3LiquidPhaseSinteringandMicrowaveDielectricPropertiesofReAlO3(Re=Sm,Nd)Ceramics3-1IntroductionCommercialwirelesstechnologies,suchascellularphones,directbroadcastingsatellitesandglobalpositionsystems,havebeenmakingrapidprogressduetotheimprovedperformanceofdielectricresonatorsatmicrowavefrequencies.Requirementsforthesedielectricresonatorshavetobecombinedwithahighdielectricconstantårforpossiblesizeminiaturizationandalowdielectriclossforfrequencyselectivityandlowsignalattenuation.Thethirdcharacteristicoftheresonatorisasmalltemperaturecoefficientattheresonantfrequencyfortemperaturestablecircuit.Aresearchonthemicrowavedielectricpropertiesoftherare-earthaluminateswasinvestigatedbyS.Y.Choetal.fortheirgreatcharacteristicsatX-bandapplications[10,11].SmAlO3andNdAlO3ceramicsexhibitedgoodmicrowavedielectricpropertiesofhighdielectricconstant(20~22.5)andgoodqualityfactor(Q×f60000~65000GHz).TheReAlO3ceramicshasbeenusedassubstrateformicrowavecomponentssinceitprovidesahighqualityfactor,excellentlatticematchingandagoodmatchingforthermalexpansion.However,ReAlO3ceramicsrequiredaveryhighsinteringtemperature(1650℃)andweredifficulttobewelldensifiedwithoutanyadditions.For17 practicalapplications,itisnecessarytoreducethesinteringtemperatureofReAlO3ceramics.Recently,low-meltingaddition,chemicalprocessing,andusingstartingmaterialswithsmallerparticlesizesarecommonlyusedinreducingthesinteringtemperatureofdielectricceramics[12-31].Theliquid-phasesinteringbyglassadditionwasfoundtoeffectivelylowerthefiringtemperature,whileitalsodecreasedthemicrowavedielectricpropertiesoftheceramicsduetothelowdensitieswithglassaids[15-17].Anothermethodappliedforlowingthesinteringtemperaturewaschemicalprocessing[12-14],whichoftenrequiredaflexibleprocedurethatwouldincreasethecostandtimeinfabrication.Inthepast,liquidphasefluxsuchasB2O3,CuO,V2O5andBi2O3wereintroducedassinteringaidsinloweringthesinteringtemperatureofceramicsandobtaininggooddielectricproperties.Inthisstudy,CuO,V2O5andZnOwereaddedinReAlO3ceramicstolowerthesinteringtemperature.TheinfluenceofCuO,V2O5andZnOadditionsonthesinteringtemperaturesandthemicrowavedielectricpropertiesofReAlO3ceramicswerealsobeeninvestigatedinthisstudy[18-31].3-2Experimentalprocedures3-2-1SamplepreparationsSamplesofReAlO3werepreparedbyconventionalsolid-statemethodsfromindividualreagent-gradeoxidepowders:Sm2O3,Nd2O3andAl2O3.Theserawpowderswereweighedaccordingtothedesiredstoichiometrywithvariousamountsofadditions,CuO,V2O5andZnOindividually.Thestartingmaterialsweremilledinaplasticjarwithzirconium18 ballsunderpurewaterfor6hours.Themixturesweredriedandforcedthrougha320-meshsieveandthencalcinedat1150℃for2hours,dried,ball-milledandgranulatedbysievingthrough175mesh.Thecalcinedpowderswereremilledfor12hourswithsuitableamountof3%solutionofpolyvinylalcohol(PVA)asthebinderandcompactedintodisks11mmindiameterby5mminheight.Afterdebinding,thedisksweresinteredatthetemperaturefrom1390℃to1470℃inairatmospherefor2hourswiththeheatingrate10℃/min.TheflowchartofDRs’experimentalproceduresisshowninFig.3-1.3-2-2CharacteristicsAnalysisandMeasurementofMicrowaveDielectricPropertiesThecrystallinephasesofthesinteredceramicswereidentifiedbyX-raydiffractionpatternanalysis.Microstructureobservationsofthesinteredsurfaceswereperformedbyscanningelectronmicroscopy(SEM).Energydispersivespectroscopy(EDS)wasalsoperformedtoidentifytheexistencesofsecondphases.ThebulkdensitiesofsinteredsamplesweremeasuredbytheArchimedesmethod.Microwavedielectricpropertieswerecalculatedwithsizesofthesampleandthe’resonantfrequencybyusingtheHakkiandColemansdielectricresonatormethodunderTE011andTE01ämodes[7-9].Acylindricaldielectricresonatorwaspositionedbetweentwobrassplatesconnectedtothemeasuringsystem.AHP8757DnetworkanalyzerandaHP8350Bsweeposcillatorwereemployedinthemeasurement.Thedielectricconstantårwas19 approximatedusingthevaluesofresonantfrequencyandthesizeofthefireddisk.Sincetheshrinkageofallthespecimenswasnotuniform,theQvaluesweremeasuredatdifferentfrequencies(9.5~10.5GHz).Thetemperaturecoefficientofresonantfrequency(ôf)representsthetemperaturedependenceoftheresonantfrequencyandistypicallydefinedas:tt=-(a+e)(3-1)f2t=t+a(3-2)cewhereáisthethermalexpansioncoefficient,tisthetemperaturecoefficientoftheedielectricconstantandtisthetemperaturecoefficientofthecapacitance.cTemperaturecoefficientofresonantfrequency(tf)wasmeasuredbychangingtemperaturemainlyfrom20℃~80℃andcalculatedfromtheequation:f80-f206tf=´10(ppm/℃)(3-3)f´6020wherefistheresonantfrequencyofthedielectricresonatorattemperatureT℃.T3-3Resultsanddiscussions3-3-1MicrostructureofSmAlO3ceramicsFig.3-2showstheXRDpatternofSmAlO3ceramicswith0.25wt.％CuOadditionssinteredatdifferenttemperaturesfor2hours.Theexistingphasesateachtemperaturewere20 observedasillustratedinthefigure.HomogeneousSmAlO3phasewithtetragonalstructurewasobtainedbelow1450℃.Withtheincreaseofsinteringtemperature,themixedpowdersreactedmoreandtheintensityofSmAlO3phaseenhanced.ThecrystallinephaseofSmAlO3ceramicswithdifferentamountofCuOandZnOadditionssinteredat1410℃for2hourswereidentified.TheXRDdiffractionpatternsshowninFig.3-3.TheSmAlO3phasesexistedasthemaincrystallinephasesandnoothercrystallinephasewasformedforCuO-sinteredandZnO-sinteredceramicsascomparingtotheXRDspectraofpureSmAlO3phases.ItimpliedthatsinglephaseSmAlO3couldbeobtainedwithadditionsunder1410℃atthelevelof0.25-0.5wt%additions.Fig.3-4showstheX-raydiffractionpatternsofSmAlO3ceramicswithvariousamountsofCuOadditionssinteredat1430℃.XRDshowedthatSmAlO3ceramicswithCuOadditionexhibitedalmostsinglephasesincethatthedetectionofaminorphasebyX-rayisextremelydifficult.AlthoughsomeofthemwereoverlappingtothemainphasesanddifficulttoidentifyfromXRDdiffractionpatterns,however,secondphaseSm4Al2O9wasdetectedbyquantitativeanalysis.Toprovetheexistenceofsecondphase,EDSanalysisofSmAlO3ceramicswith0.75wt%additionwasperformedanddemonstratedinFig.3-5a,b.Sincethegrainmorphologywasalmostsimilar,thegrainsofdifferentphasesweredistinguishedbybackelectronimage(BEI).Afterenoughtrials,theconstituentratioofSmandAlwereobtainedandlocatedat45.62:46.67(%)forthegeneralregionsasshowedinFig.4a.ThesecondphasedetectedbyEDSspectrawasSmrichascomparedwiththematrix21 grains.Atcertainspecificgrains,therelativeratioofSmandAlwas32.71:62:39(%)typically,i.e.theratioofSm:Alwas2:1.ItsuggestedtheexistenceofsecondphaseSm4Al2O9.TheadditionsCuOandZnOdidnotdiffuseintograinsbutconcentratedontheboundaries.TheSEMphotographsofSmAlO3ceramicswithdifferentadditivessinteredat1430℃for2hourswereillustratedinFig.3-6abcd.Allsamplesshowedhomogeneousgrainsize.Thegrainsizeslightlyincreasedwiththesinteringtemperatureaswellastheadditivesduetotheliquidphaseeffect.Theliquidphasewassuggestedcausedbyeutecticreaction.Theadditives,CuOandZnOintheSmAlO3ceramicsappearedonthesinteredsurfaceratherthanatthegrainboundary.ThatwasexaminefromSEManddetectedbytheEDSquantityanalysis.3-3-2MicrostructureofNdAlO3ceramicsInordertoexaminethechemistryofcalcinedNdAlO3powdersandselectasuitablecalciningtemperature,thestartingmaterialswerepreparedat1050℃,1150℃and1250℃.Fig.3-7showstheXRDpatternofNdAlO3powderscalcinedatdifferenttemperaturesfor2h.Theexistingphasesateachcalciningtemperaturewereobservedasillustratedinthefigure.Withincreasingcalciningtemperature,themixedpowdersreactedmoreandtheintensityofmajorNdAlO3phaseswasenhanced.HomogeneousNdAlO3phasewitharhombohedralstructurecouldbeobtainedat1150℃.However,thesecondphases22 coexistwiththemajorphaseandperhapsseriouslyaffectthemicrowavedielectricpropertiesofNdAlO3ceramics.Thiswasthereasonforchoosing1250℃asthecalciningtemperature.Fig.3-8showstheXRDpatternofNdAlO3ceramicswith0.25wt％CuOadditionsinteredatdifferenttemperaturesfor2h.Withtheincreaseofsinteringtemperature,theintensityoftheNdAlO3phasewasenhanced.Asecondphasewasnotobservedinallcases.ThecrystallinephaseofNdAlO3ceramicswithdifferentamountsofCuOconcentrationsinteredat1410℃for2hwereidentifiedandtheXRDdiffractionpatternsareshowninFig.3-9.TheNdAlO3phasesexistedasthemaincrystallinephasesandnoothercrystallinephasewasformedforCuO-sinteredceramicsascomparedtotheXRDspectraofpureNdAlO3phases,implyingthatsingle-phaseNdAlO3couldbeobtainedwithCuOadditions(0.25-0.5wt%)at1410℃.ThedataalsoshowthatNdAlO3ceramicswithCuOadditionexhibitedalmostasinglephasesincethedetectionofaminorphasebyXRDisextremelydifficult.AlthoughsomeofthemoverlappedthemainphasesandweredifficulttoidentifyfromXRDdiffractionpatterns,secondphasesNdAl11O18andNd4Al2O9weredetectedbyquantityanalysis.Toconfirmtheexistenceofsecondphases,EDSanalysisofNdAlO3ceramicswith0.75wt%and1wt%additionswereperformed.Sincethegrainmorphologywassimilar,thegrainsofdifferentphasesweredistinguishedbybackscatteredelectronimage(BEI).Aftersufficienttrials,theconstituentratioofNdandAlwasobtainedandwas45.62:46.67(%)forthegeneralregions.ThesecondphasewasdetectedbyEDSspectraforcertainspecificgrains,andtherelative23 ratioofNdandAlsuggestedtheexistenceofsecondphasesNd4Al2O9andNdAl11O18.SEMmicrographsofNdAlO3ceramicssinteredat1410℃for2hwithdifferentCuOconcentrationarepresentedinFig.3-10Allsamplesshowedhomogeneousgrainsize.ThegrainsizeincreasedlinearlywiththeamountofCuOaddedduetotheliquid-phaseeffect[18-20].Theliquidphasewasconsideredtobecausedbyeutecticreaction.SEMphotographsofNdAlO3ceramicssinteredatdifferenttemperaturesfor2hwith0.75wt%CuOadditionsareshowninFig.3-11.Thegrainsizeincreasedslightlywiththeincreasingsinteringtemperature.Itwaseasilydeterminedthatthehighersinteringtemperaturesresultedinsuperiordensification.TheaddedCuOintotheNdAlO3ceramicssegregatedonthesinteredsurfacemorethaninsidetheceramicbody,asdeterminedbySEMandalsodetectedbytheEDSquantityanalysis.ThegrainsizesofNdAlO3ceramicswithdifferentCuOconcentrationasafunctionofsinteringtemperatureareillustratedinFig.3-12.ThegrainsizesincreasedwithincreasingCuOconcentrationasshowninFig.3-10.Therelationshipbetweengrainsizeandsinteringtemperaturerevealedthesametrendasthatbetweenrelativedensityandsinteringtemperature.Grainsizesof1.8~4.8mmwereobtainedinthisexperiment.ItisbelievedthatthegrainwettabilityisdirectlydependentontheamountofCuOadditions.3-3-3DensificationofSmAlO3ceramicsTherelativedensitiesofadditions-sinteredSmAlO3ceramicsasafunctionofsintering24 temperatureswereindicatedinFig.3-13.ThedensitiesofSmAlO3ceramicsincreasedwithincreasingCuOandZnOadditionsupto1wt%.TheTDsofSmAlO3ceramicswithCuOsinteredat1410℃increasedfrom95.2%to98.36%astheadditionsincreasedfrom0.25wt%to1wt%whiletheTDsofZnO-sinteredSmAlO3ceramicsincreasedfrom95.15%to97.68%,respectively.Thedensityincreaseswiththeincreaseofadditionswasduetoenlargedgrainsize.TherelativedensitiesofSmAlO3ceramicswith0.25wt%and0.75wt%CuOincreasedfrom93.5%to96%and95.36%to98.16%,respectively,asthesinteringtemperatureincreasedfrom1390℃to1450℃.TheZnO-sinteredSmAlO3ceramicsshowedthesimilartrend.Afterreachingamaximumvalueatvicinityof1430~1450℃,theTDsofSmAlO3decreased.ItwaseasytofindthatTDsatthelevelof95~98%couldbeobtainedwithdifferentkindsandvariousamountofadditionsatsinteringtemperaturesfrom1410℃to1430℃.ThegreatdensificationatlowersinteringtemperaturewasachievedbytheliquidphaseeffectofadditionssincethemeltingtemperatureofCuOandZnOaremuchlowerthanthesinteringtemperatureofthepureSmAlO3[18-20,14-15].Thesinteringtemperature1410℃~1450℃wereselectedsincethatallthesampleshavedensitieshigherthan95％theorydensities.3-3-4DensificationofNdAlO3ceramicsTherelativedensitiesofCuO-sinteredNdAlO3ceramicsasafunctionofsintering25 temperatureareindicatedinFig.3-14.ThedensitiesofNdAlO3ceramicsincreasedwithincreasingCuOconcentrationupto1wt%.Therelativedensities(RDs)ofNdAlO3ceramicssinteredat1430℃increasedfrom95.2%to98.26%astheCuOadditionincreasedfrom0.25wt%to1wt%.TherelativedensitiesofNdAlO3ceramicswith0.25wt%and1wt%CuOincreasedfrom93.5%to95.36%and96%to98.26%,respectively,asthesinteringtemperatureincreasedfrom1390℃to1450℃.Afterreachingamaximumvalueinthevicinityof1410~1430℃,theRDsofNdAlO3decreasedwithincreasingtemperature.ItwaseasilydeterminedthatRDsatthelevelof94~98%couldbeobtainedwithvariousamountofadditionsatsinteringtemperaturesof1410~1430℃.Themarkeddensificationatlowersinteringtemperatureswasachievedbytheliquid-phaseeffectofCuOaddition.Thesinteringtemperaturesof1410~1430℃wereselectedsinceallofthesamplespossessedtheoreticaldensitieshigherthan95%.3-3-5DielectricpropertiesofSmAlO3ceramicsFig.3-15showedthedielectricconstantofSmAlO3ceramicswithdifferentadditivesasafunctionofsinteringtemperature.Therelationshipsbetweenårvaluesandsinteringtemperaturesrevealthesametrendwiththatbetweendensitiesandsinteringtemperatures.Theincreaseofårcouldbeexplainedowingtohigherdensitiessincehigherdensitiesmeanslowerpore.TheårvaluesofdensifiedSmAlO3ceramicsrangedfrom19.4to20.6.26 Manyfactorswerebelievedtoaffectthemicrowavedielectriclossandcouldbedividedintotwofields,theintrinsiclossandextrinsicloss.Theintrinsiclossesweremainlycausedbylatticevariationmodeswhiletheextrinsiclossesweredominatedbysecondphases,oxygenvacancies,grainsizesanddensificationorporosity.Interfacialpolarizationwasthoughttoplayanimportantroleinporousmaterials.Fig.3-16illustratestheQ×fvaluesofSmAlO3ceramicswithdifferentadditivesasafunctionofsinteringtemperature.TheQ×fvaluesofSmAlO3ceramicsincreasewiththeincreaseofsinteringtemperature.ForCuO-sinteredSmAlO3,theQ×fvaluesmaintainedgoodpropertiesatlowsinteringtemperatures.TheQ×fvaluesreachedamaximumvalveof51000(GHz)at1430℃.TheZnO-sinteredSmAlO3hasamaximumQ×fvalueof41000with0.25wt%additionsinteredat1450℃.TheQ×fvalueofSmAlO3ceramicsdecreasedwithfurtherincreaseintheadditiveamountandchangefrom51000(0.25wt％)to12000(1wt％)and41000(0.25wt％)to9000(1wt％)inCuO-andZnO-dopedcases,respectively.Infact,theeffectsofCuOandZnOadditionsonmicrowavedielectriccharacteristicofSmAlO3mightdependonthechemistryoftheadditions,therelatedchemistryreactions,thephasechangesduringsinteringandthefinaldensity.Ingeneral,theQ×fvalueswereindependentofthedensityortheporosityforTDs>95％.ItcouldbeconcludedthattheQ×fvalueofSmAlO3ceramicswereindependentofthedensificationsincethedensitiesofthesamplesinvestigatedinthisstudieswerehigherthan95％TDs.GrainsizesmightbesuggestedtoaffecttheQ×fvalueofSmAlO3ceramicsdueto27 largergrainsresultedinlessgrainboundary,whichmeantlesslatticemismatchandlowerdielectricloss.AfteralltheexistenceofsecondphaseSm4Al2O9,whichhasaQ×fvaluelessthan10000(GHz),playedanimportantroleindeterminingthecharacteristicofqualityfactor.AstheobservationsfromXRDdiffractionsanddetectionsofEDSanalysis,thesecondphaseappearedattheadditionlevelover0.5wt%andseriouslyaffectedtheQ×fvalueofSmAlO3ceramics.Fig.3-17showsthecompositiondependenceofôfintheSmAlO3ceramicssinteredat1430℃.Thetemperaturecoefficientofresonantfrequencywaswellknownrelatedtothecomposition.TheôfvalueofZnO-sinteredSmAlO3ceramicsexhibitednosignificantchangewithdifferentdopinglevelat1430℃.However,itvariedfrom-45to-65ppm/℃astheamountofCuOadditionsincreasedfrom0.25to1wt%.3-3-6DielectricpropertiesofNdAlO3ceramicsFig.3-18showsthedielectricconstantofNdAlO3ceramicswithdifferentCuOconcentrationsasafunctionofsinteringtemperature.Therelationshipsbetweenårvaluesandsinteringtemperaturesrevealthesametrendasthatbetweendensityandsinteringtemperature.Theincreaseofårcouldbeexplainedasbeingduetohigherdensitiessincehigherdensitiesmeanfewerpores.TheårvaluesofwelldensifiedNdAlO3ceramicsexhibitednosignificantdifferenceswithvariousCuOconcentrationsatdifferentsinteringtemperaturesandranged28 from21.5to22.6.Manyfactorsarebelievedtoaffectthemicrowavedielectriclossandcanbedividedintotwocategories,theintrinsiclossandtheextrinsicloss.Theintrinsiclossesaremainlycausedbylatticevibrationmodeswhiletheextrinsiclossesaredominatedbysecondphases,oxygenvacancies,grainsizesanddensificationorporosity.Interfacialpolarizationwasthoughttoplayanimportantroleintheporosityofmaterials.Fig.3-19illustratestheQ×fvaluesofNdAlO3ceramicswithdifferentCuOconcentrationasafunctionofsinteringtemperature.TheQ×fvaluesofNdalO3ceramicsincreasewiththeincreasingsinteringtemperature.TheQ×fvaluesofCuO-sinteredNdAlO3stablyshowedgoodpropertiesatlowsinteringtemperatures.TheQ×fvaluesreachedamaximumvalueof63000GHzat1410~1430℃.TheQ×fvalueofCuO-sinteredNdAlO3ceramicsdecreasedwithfurtherincreaseintheCuOconcentrationandchangedfrom63000GHz(0.25wt％)to18000GHz(1wt％).TheeffectsofCuOadditiononthemicrowavedielectriccharacteristicofNdAlO3mightdependonthechemicalpropertiesofCuO,therelatedchemicalreactions,phasechangesduringthecalciningprocedure,sinteringprocedureandthefinaldensity.Ingeneralcases,theQ×fvalueswereindependentofthedensityortheporosityforRDs＞90％.ItcanbeconcludedthattheQ×fvalueofNdAlO3ceramicswereindependentofthedensificationsincethedensitiesofthesamplesinvestigatedinthisstudyishigherthan95％RD.GrainsizesaresuggestedtoaffecttheQ×fvalueofNdAlO3ceramicsduetolargergrainsresulting29 infewergrainboundaries,whichmeanslesslatticemismatchandlowerdielectricloss.However,theQ×fvaluesofNdAlO3decreaseasthegrainsizesincreasewithincreasingCuOconcentration.Afterall,thesecondphasesproducedduringthepreparationproceduresgovernthelosscharacteristic.Sincethecalciningtemperaturewassetat1250℃,notonlywasthemajorNdAlO3phaseobtainedbutalsothegenerationofsecondphasesNdAl11O18andNd4Al2O9couldbeavoided.TheQ×fvaluesofNdAl11O18andNd4Al2O9sinteredat1410℃arelessthan13000and10000,respectively,andseriouslyaffectthecharacteristicofqualityfactor.FromtheobservationsbyXRDanalysisandEDSanalysis,thesecondphaseappearedattheCuOconcentrationlevelover0.75wt%andmarkedlyaffectedtheQ×fvalueofNdAlO3ceramics.ThequalitycharacteristicofCuO-sinteredNdAlO3ceramicssinteredatlowertemperatureshasalargeQ×fvalueof63000GHz,whichisanimprovementonthepropertiesobtainedinpreviousstudies.Thiswasduetothesuitableselectionofcalciningtemperatureandwell-controlledextrinsicloss.Fig.3-20showsthecompositiondependenceofôfintheNdAlO3ceramicssinteredat1410℃.Thetemperaturecoefficientofresonantfrequencywaswellknowntoberelatedtothecomposition.TheôfofNdAlO3ceramicsexhibitedalargernegativevaluewithincreasingofCuOconcentration.Thetemperaturecoefficientrangesfrom－30ppm/℃to－45ppm/℃.Forpracticalapplications,amodificationofthetemperaturestabilitymustbeachievedinNdAlO3ceramics.30 3-4ConclusionsThesinteringtemperaturesofSmAlO3andNdAlO3ceramicswithsinteringaidswereeffectivelyreducedfrom1650℃to1430℃.SmAlO3ceramicswithproperCuOorZnOadditionscanbewellsinteredtoapproach96%TDunder1430℃duetoliquidphasesinteringeffect.TheQ×fvaluesofSmAlO3ceramicsof51000and41000GHzcouldbeobtainedat1430℃with0.25wt%CuOandZnOadditions,respectively.Q×fvalueofNdAlO3ceramicsof63000GHzwasachievedat1410~1430℃with0.25wt%CuO.Atlowadditionlevel(0.25-0.5wt％),theSmAlO3andNdAlO3ceramicsremainedsinglephaseandpresentedsecondphasesSm4Al2O9andNd4Al2O9withadditionsover0.5wt%asexaminedintheXRDpatternsandEDSquantityanalysis.TheexistenceofthesecondphasewouldseriouslydecreasetheQ×fvaluesofSmAlO3andNdAlO3ceramics.NosignificantchangewasobservedinthedielectricconstantsfordensifiedSmAlO3andNdAlO3ceramics.Thetemperaturecoefficientoftheresonantfrequencyôfdependedontheadditionsandrangedfrom–40to-65ppm/℃and–30ppm/℃to–45ppm/℃forSmAlO3andNdAlO3ceramics,respectively.31 Chapter4MicrostructureandMicrowaveDielectricPropertiesofBa2-xSm4+2/3xTiyO8+2yCeramics4-1IntroductionDuetotherapiddevelopmentinmobilecommunication,mobiletelephonesystems,aswellasinsatellitebroadcastingsystems,howtodesignthehigh-qualitydevicesisthemostimportanthomework.Inordertoachievethepurposeofminiaturizationofthedimensionsofthedevicesandservethesystemworkwithhighefficiencyandstability,thematerialsformicrowaveresonatorsarerequiredtobeexcellentinthreedielectriccharacteristics.Thefirstcharacteristicishighdielectricconstant(år),becausethemicrowavewavelengthisinverselyproportionaltoeofthedielectricmaterial(ë=ëo/e),whereëoisthewavelengthinair.ThesecondonerrishighQvalue,whichistheinverseofthedielectriclosstanä,isrequiredtoachievehighfrequencyselectivityandstabilityinmicrowavetransmitterandreceivercomponents.Thethird,temperaturecoefficientoftheresonantfrequency(ôf),isrequiredtobeascloseto0ppm/℃aspossible.BaO-R2O3-kTiO2ceramicswerereportedasaternarysystemandwereextensivelyusedasthebestsystemofmicrowaveceramics,whereR=Sm,Nd,Pr,Laarerareearthelementswithk=3~5[30-36,40-45].Ask=4,theconventionalformulaBa6-3xR8+2xTi18O54waspopularlyusedfortheBaO-R2O3-4TiO2ceramicstoinvestigatetherelationshipsbetween32 microstructuresandmicrowavedielectricpropertiesforeachrare-earthelementwithvariousxvalues.Dielectricproperties,structureformula,microstructuresandreactionsequencesoftheBaO-R2O3-4TiO2solidsolutionwerewidelystudied[41-43].Ask=5,Ba1-3xR2+2xTi5O14wasusedforinvestigatingtheBaO-R2O3-5TiO2ceramics[46,47].TherewasacommonresultthatthecrystalstructureoftheBaO-R2O3-kTiO2ceramicsisauniformmatrixphasebelongingtotungsten-bronze-typestructurewithslightlysecondphases.However,themainphaseoftheBaO-R2O3-kTiO2ceramicswasreportedasBaO-R2O3-4TiO2orBaO-R2O3-5TiO2indifferentstudies.Thepossibleexistencesofsolidsolutionsonthetie-lineofBaO-Sm2O3-3TiO2andBaO-Sm2O3-5TiO2werealsosuggested[45,46].S.Nishigakietal.hadalsostudiedthemicrowavedielectricpropertiesofBaO-Sm2O3-kTiO2inTi-richregion,0.15BaO-0.15Sm2O3-0.7TiO2and0.17BaO-0.13Sm2O3-0.7TiO2.Thesetwoceramicsystemswereequivalenttok=4.7and4.8,respectively[46].However,fewworkhasbeendoneininvestigatingthesolidsolubilityoftheBaO-Sm2O3-kTiO2withk≠4.Inthisstudy,thecompositionofBaO-Sm2O3-kTiO2ceramicswithk=4.5wasselectedandexpressedintheformulaBa2-xSm4+2x/3Ti9O26.TheconventionalformulaBa6-3xR8+2xTi18O54forBaO-Sm2O3-4TiO2isbasedonthesuggestionthatthemicrostructureofsystemisjustthe2+3+perovskitestructurewithsomedivalentBasubstitutionfrotrivalentSm.TheaspecttouseBa2-xSm4+2x/3Ti9O26forBaO-Sm2O3-4.5TiO2isbasedontworeasons.OneistoinvestigatethesolidsolubilityofBaO-Sm2O3-4.5TiO2ceramicsandsuggeststhemicrostructureofit33 containstungsten-bronze-typestructure[36-40].Anotheristousethestructureformulaoftungsten-bronze-typestructuretofindoptimumextentofSmwhichdeterminesexcellentdieletricproperties.AnothertargetinthisstudyistoinvestigatethemicrowavedielectricpropertiesofBSTceramicswiththecompositionrangeofx=0.1andy=0~2astheschematicdiagramshowninFig.4-1.SincetheextentandeffectofsamariumoftheBSTceramicshadbeenstudied,theBSTceramicswithxvalueatthevicinityof0.1exhibitedthebestpropertiesandwasselectedasthetypicalcharacteristicstoinvestigatetherelationshipsbetweenmicrowavedielectricpropertiesandyvaluesinthiswork.Therelationshipsbetweenthemicrowavedielectricpropertiesandthecrystalstructureswerealsodiscussedtoestablishsomeguidelinesforobtainingbetterbariumsamariumtitaniumoxidesystems.4-2StructuralFormulaofTungsten-Bronze-Structure-2Thetungsten-bronze-structureismadeupofcornerssharingTiO6octahedral,whichextendintheshortaxisdirectionandformanetworkofrhombicandpentagonalchannels[]35,37-39].Suchastructureistypifiedbyoxygenoctahedrallinkedtogetherattheircornersinacomplexwaytoyieldthreetypeofopeningswithdifferentshapesandsizes.ThespacesbetweentheMO6octahedraformthreedifferentkindsoftunnels,whicharetetragonalopenings(A1sites),pentagonalopenings(A2sites),andtriangleopenings(A3sites),respectively.(M=W,Ta,Nb,Tietc.).Lower-valencycations(Ba,Sm)arelocatedinsitesinthesetunnelsaboveandbelowthe34 planeshowninFig.4-2.TherearesevenAsitesandtenoctahedralinasimplestunitcell.Thisfollowsthatthegeneralformulaforatungstenbronzecouldbepresentedas[(A1)2(A2)4A3][(B1)2(B2)8]O30++2whereA3arenormallyvacantunlesssmallcations(r6=50-70pm)suchasLiorMgarepresent.Sothestructuralformulacouldbeexpressedinasimplerform(A2)2(A1)4B10O30.Basedonthissuggestion,Ba2-xSm4+2/3xTi9O26wasselectedforBaO-Sm2O3-4.5TiO2ceramics.ThemainpurposeofthisstudyistoshowthatBa2-xSm4+2/3xTi9O26ceramicspossesscompletesolidsolubilitywithgreatmicrowavedielectriccharacteristicsandestablishingsomeguidelinesforthedesignofBaO-R2O3-kTiO2dielectricmaterialsbaseonthestructuralformulaoftungstenbronzestructure.4-3ExperimentalProcedure4-3-1SamplepreparationsSamplesofBa2-xSm4+2/3xTiyO8+2ywerepreparedbyconventionalsolid-statemethodsfromindividualreagent-gradeoxidepowders:BaCO3,Sm2O3andTiO2.FirsttheserawpowderswereweighedaccordingtothecompositionratioofBa2-xSm4+2/3xTi9O26withvariousxvalues(0.0~0.3).Thestartingmaterialsweremilledinaplasticjarwithzirconiumballsunderpurewaterfor6hours.Themixturesweredriedandforcedthrougha325-meshsieveandthencalcinedat1050℃35 and1100℃for4hours,dried,ball-milledandgranulatedbysievingthrough175mesh.Thecalcinedpowderswereremilledfor12hourswithsuitableamountof5%solutionofpolyvinylalcohol(PVA)asthebinderandcompactedintodisks11mmindiameterby5mminheight.Afterdebinding,thedisksweresinteredattheatemperaturefrom1310℃to1400℃inairatmospherefor4hourswiththeheatingrate5℃/min.SamplesofBa2-xSm4+2x/3Ti8+yO24+2ywithx=0.1andvariousyvaluesweresynthesizedbythesameconventionalsolid-statemethods.4-3-2CharacteristicAnalysisThecrystallinephasesofthesinteredceramicswereidentifiedbyX-raydiffractionpatternanalysis.Microstructureobservationofthesinteredsurfaceswasperformedbyscanningelectronmicroscopy(SEM).EDSwasalsoperformedtoidentifytheexistencesofsecondphases.ThebulkdensitiesofsinteredsamplesweremeasuredbytheArchimedesmethod.Microwave,dielectricpropertiesweremeasuredbyusingtheHakkiandColemansdielectricresonantmethodunderTE011andTE01ämodeswithaHP8757DnetworkanalyzerandaHP8350Bsweeposcillator.Thedielectricconstantårwasapproximatedusingthevaluesofresonantfrequencyandthesizeofthefireddisk.TheunloadQvalueoftheceramicsatmicrowavefrequencywasmeasuredbyplacingthediskspecimenbetweentwobrassplatesundertheTE01ämode.Temperaturecoefficientofresonantfrequency(tf)wasalsomeasuredbythesamemethodwithchangingtemperaturemainlyfrom20℃~80℃andcalculatedfromtheequation:36 f80-f206tf=´10(ppm/℃)f´6020WherefistheresonantfrequencyofthedielectricresonatorattemperatureT℃.T4-4ResultsandDiscussionThereactionsequencesfortheBa2-xSm4+2/3xTiyO8+2yceramicscouldbeexpressedasfollowing:BaCO3+4TiO2→BaTi4O9+CO2(4-1)Sm2O3+2TiO2→Sm2Ti2O7(4-2)8BaTi4O9+3Sm2O3→2Ba4Ti13O30+3Sm2Ti2O7(4-3)Sm2Ti2O7+BaTi4O9→BaSm2Ti4O12+2TiO2(4-4)4Sm2Ti2O7+Ba4Ti13O30→4BaSm2Ti5O14+TiO2(4-5)2BaTi4O9+TiO2→Ba2Ti9O20(4-6)Equation(4-4)and(4-5)suggestthattheformationofmajorphasesBaO-Sm2O3-4TiO2orBaO-Sm2O3-5TiO2wereattheconsumptionoftheintermediatephases,Sm2Ti2O7,BaTi4O9andBa4Ti13O30.Thissuggestionisconsistentwithseveralpreviousreportsonthesimilarseriescompounds[46].ItshouldbenotedthattheremightbecertainamountofTiO2andBa2Ti9O20leftduringthereactionsequencesafterformationofthemainphaseBaSm2Ti4O12andBaSm2Ti5O14.TheintermediatephaseTiO2(rutile)notonlyaffectsthemicrowavedielectricpropertiesduetoitshighdielectricconstant(år=104)andhightemperaturecoefficient(+427ppm/℃),butalso37 influencethesinteringtemperatureforoptimumdensification.4-4-1MicrostructureofBa2-xSm4+2/3xTiyO8+2yceramicsThecrystallinephasesoftheBa2-xSm4+2x/3Ti9O26systemsinteredatdifferenttemperatureswereidentifiedwithX-raydiffraction.Fig.4-3showstheX-raydiffractionpatternsofBa2-xSm4+2x/3Ti9O26systemsinteredat1360℃withvariousxvalues.ThecrystalstructuresofBa2-xSm4+2x/3Ti9O26wereknownasthetungstenbronzetypewithorthorhombicstructure.WhenSmwasusedassubstitutefortheBasites,thesinteredBa2-xSm4+2x/3Ti9O26ceramicsexhibitnophasedifferencesfordifferentxvalues.ItwasfoundthatthecrystallinephasesareamatrixofmainphaseBaSm2Ti4O12orthorhombicstructureaccompanieswithsecondphases.ThesecondphasesTiO2andBa2Ti9O20mightexistinthesinteredceramicsbutarenoteasilydifferentiatedformthemajorphaseintheX-raydiffractionpatternsbecauseofoverlappingwithprimarycrystallinephase.However,theexistencesofsecondphasesTiO2andBa2Ti9O20oranotherintermediatephasecouldbeidentifiedbyquantityanalysis,energydispersiveX-rayspectrometer(EDS)results.WhenSmisusedassubstituteforBasitesofBa2-xSm4+2x/3Ti9O26ceramics,thesinteredceramicsexhibitsmallerlatticeparametersduetothedifferencesbetweenSmandBainionradius,whichdropsahintthat2èwilltakelargervalues.The2èpeaksoftheXRDdiffractionpatternsshifttothelargervaluesasxvalueincrease,asshowninFig.4-3.Thisisinagreement38 withthehintandsuggeststhattheBa2-xSm4+2x/3Ti9O26systemwillhavesmallerdielectricconstantwithlargerxvalue.TheresultsalsosuggestthattheBa2-xSm4+2x/3Ti9O26ceramicsformasolidsolutionwithxvaluerangesfrom0.0to0.3.Toinvestigatethemorphologiesofthesamples,thesurfacesofsinteredspecimenswereexamined.Fig.4-4illustratesthesinteredsurfacesofBa2-xSm4+2x/3Ti9O26ceramicswithx=0.1atdifferentsinteringtemperaturesfor4hoursforthepowdercalcinedat1050℃.Itshowsthatthemaincrystalswereaciculargrainswithslightamountofblock-shapedcrystals.Thelengthoftheaciculargrainstendedtoincreasewithsinteringtemperaturesespeciallyabove1370℃.Atthesinteringtemperaturesarebelow1370℃,thegrowthofgrainsresultsinthedecreaseoftheporosityinthemicrostructureandtheapparentdensityincreaseswithincreasingsinteringtemperatures.Atthesinteringtemperaturesabove1370℃,thelongaciculargrainsgrowattheexpenseofshortones,whichresultedintheformationofnewvoidswheretheshortergrainswereoriginallylocated.Thegrowthdirectionofthebarwasinthelongitudinaldirectionofthecrystal.Asthelongaciculargrainscomeintocontact,continualgrowthmaysqueezethemawayfromoneanother,whichmayresultintheformationofnewandlargervacantpositions.Thiscausedexpansionofthespacebetweenbar-shapedgrainsandresultsintheincreaseofporosityandthedecreaseinbulkdensities[46].Thesizeanddistributionofaciculargrainsweremainlydeterminedbysinteringtemperature.Fromthephotomicrographsofthesinteredsurfaces,itwasfoundthatthecrystalsarealmostsimilarandconsistofseveraldifferenttypesofsecondphases.Fig.4-5aillustratesthephotograph39 ofthesinteredsurfacewithsecondphaseBa2Ti9O20,whichwasidentifiedwiththeenergydispersiveX-rayspectrometer(EDS),asshowninFig.4-5b.Fig.4-5cillustratesthemicrograph,whichistheblock-shapedgrainonthesinteredsurfaceandhasbeenidentifiedastheintermediatephaseSm2Ti2O7byEDSresultshowninFig.4d.Table1illustratesthebulkdensityandthemicrowavedielectricpropertiesofBa2-xSm4+2x/3Ti9O26systemwithdifferentsinteringtemperaturesandvariousxvalues.Differentialthermalanalysis(DTA,SETARAM,TAG24,France)wasperformedtodeterminethesinteringconditionsofBa2-xSm4+2x/3Ti8+yO24+2yceramicswithx=0.1andyvariousvalues.TwoendothermicpeaksappearedontheDTAcurvesforthestartingmaterialsshowninFig.4-6.Thefrontpeakislocatedataround1350℃thatistheeutectictemperatureandtheotheroneislocatedataround1500℃,whichistheliquidustemperatureofthecompound.Thefrontpeakswillgiveimportantinformationforchoosingthesuitablesinteringtemperatures,becausesinteringwilloccurataroundthetemperaturethattheliquidphaseappearsandtheliquidphasepromotesthesintering.Betweentwotemperaturestheobjectcompoundcouldbewellsintered.Itiseasilyfoundthatthetemperaturerangebetweentwoendothermicpeaksdecreasesandthesecondendothermicpeakmovesforwardlowertemperatureastheyvalueincrease.ThissuggeststhattheBSTceramicscouldbedensifiedinasmallertemperaturerange.ItalsoshowedthattheBSTceramicshavealowersinteringtemperatureastheincreaseofTiamount.Inanotherwords,theBSTceramicswithvariousy40 valueswillhaveitscertaindensifiedtemperature.Thiswaswellprovedandingoodagreementwiththetemperaturedependenceofbuckdensity.TheX-raypowderdiffractionoftheBST(x=0.1,y=1)powderscalcinedatdifferenttemperatureswasshowninFig.4-7.BaTi4O9andSm2Ti2O7revealontheX-raypatternsoftheBSTceramicscalcinedat950℃,1000℃,1050℃and1100℃.TheresultssuggestthattheintermediatephasesofBaTi4O9andSm2Ti2O7producedbeforetheBaSm2Ti4O12orBaSm2Ti5O14(BST)phasesformed[46-47].ThemainphaseBaSm2Ti4O12orBaSm2Ti5O14formsandcoexistswiththeintermediatephases,BaTi4O9andSm2Ti2O7asthecalciningtemperatureisover1050℃.AstheBSTceramicscalcinedat1300℃,slightminorphasesmightexistinthecalcinedpowder,however,itisdifficulttodistinguishfromthemainphasebecauseofoverlappingwiththemaincrystallines.Fig.4-8showstheX-raydiffractionpatternsofthesinteredBa2-xSm4+2x/3Ti8+yO24+2yceramicswithx=0.1andvariousyvalues.AsshowninFig.4-8,BaSm2Ti4O12andBaSm2Ti5O14presentasthemaincrystallinephaseandmightbeinassociationwithSm2Ti2O7,Ba2Ti9O20andTiO2astheminorphases[36,46-47].Whenyincreasesfrom0to2,thecrystallinephasesofallcompositionsrevealthesimilarresults.ConsideringtheresultsshowninFig.4-8,asTiincrease,theBSTceramicsexhibitalmostnophasedifferencesfordifferentyvalues.XRDoftheBSTceramicsshowalmostthemainphasesofBaSm2Ti4O12orBaSm2Ti5O14thatwereidentifiedasthetungsten-bronze-typeorthorhombicphase[35-38,46].Themaincrystallinephasesmightconsistofslightsecond41 phases.ThesecondphasesarenoteasilydifferentiatedformthemajorphaseintheX-raydiffractionpatternsbecauseofoverlappingwiththemainlycrystallinephase.However,theexistenceofsecondphasesTiO2andBa2Ti9O20,Sm2Ti2O7couldbeidentifiedbysomequantitativeanalysis,andwereprovedbyenergydispersiveX-rayspectrometer(EDS).ThesecondphasewasdetectedbyEDSspectraatcertainspecificgrains,andtherelativeratioofBa,SmandTisuggestedtheexistenceofsecondphases,Sm2Ti2O7,Ba2Ti9O20andTiO2.WhenSmwasusedassubstituteforBasitesoftheBSTceramics,thesinteredceramicsexhibitsmallerlatticeparametersduetothedifferencesbetweenSmandBainionradius,whichdropsahintthat2èwilltakethelargervalues.The2èpeaksoftheX-raydiffractionpatternsshifttolargervaluesastheyvalueincreases.TheresultsalsosuggestthattheBa2-xSm4+2x/3Ti8+yO24+2yceramicformacompletesolidsolution(x=0.1,y=0~2).Toinvestigatethemorphologiesofthesamples,thesurfacesofthesinteredspecimenswereexamined.Fig.4-9illustratesthesinteredsurfacesofBa2-xSm4+2x/3Ti8+yO24+2yceramicswithx=0.1forvariousyvalues.Itshowsthatthemaincrystalswerebar-shapedgrainswithslightamountofblock-shapedcrystals.Thelengthofthebar-shapedcrystaltendedtoincreasewithsinteringtemperaturesespeciallyabovedensifiedtemperatures.Asthesinteringtemperaturesarebelowdensifiedtemperatures,thegrowthofgrainsresultinthedecreaseoftheporosityinthemicrostructureandtheapparentdensityincreaseswithincreasingofsinteringtemperatures.42 4-4-2DensificationofBa2-xSm4+2/3xTiyO8+2yceramicsTheapparentdensitiesofBa2-xSm4+2x/3Ti9O26ceramicswithvariousxvaluesasafunctionoftheirsinteringtemperaturesareindicatedinFig.4-10.Itwasfoundthatthebulkdensityhasthemaximumvalueattemperaturesaround1370℃.Eitherhigherorlowersinteringtemperaturesmaycausethebulkdensitytodecrease,especiallyifthesinteringtemperatureisbelow1320℃orabove1370℃.Thedensifiedtemperaturesdefinedherearethetemperatures,whichcouldachievethehighestrelativedensityforeachcomposition.TheapparentdensitiesoftheBa2-xSm4+2x/3Ti8+yO24+2yceramics(x=0.1)asafunctionofthesinteringtemperaturesareillustratedinFig.4-11.Itshowsthattheapparentdensitiesaredependentonsinteringtemperaturesastheyvalueswerefixed.Eachcompositionhasitsownspecificdensificationtemperaturerange.ThesaturatedbulkdensitiesoftheBSTceramicsslightlydecreasewiththeincreaseinyvalueandthedensificationtemperaturesdecreasefrom1390℃to1330℃asyvalueincreasesfrom0to2,respectively.4-4-3MicrowavedielectricpropertiesofBa2-xSm4+2/3xTiyO8+2yceramicsFig.4-12showstheQ×fvaluesofBa2-xSm4+2x/3Ti9O26(x=0.1~0.3)ceramicsasa43 functionofthesinteringtemperaturesforvariousvalues.ThemeasuredQfactorswereobtainedatdifferentresonantfrequenciesdependingonthephysicaldimensionsandrelativedielectricconstants.Accordingtothegenerallyobservedrelationship,f×Q=constant,wherefistheresonantfrequencyandQisthevaluecalculatedfromthewaveguidemethodonTE01ó.Manyfactorswerebelievedtoaffectthemicrowavedielectriclossandcouldbedividedintotwofields,theintrinsiclossandextrinsicloss.Theintrinsiclossesweremainlycausedbylatticevariationmodeswhiletheextrinsiclossesweredominatedbysecondphases,oxygenvacancies,grainsizesanddensificationorporosity.Densificationandphaseassemblagearethemainfactorsthatdeterminethedielectriclossandhadbeenseeninseveralmicrowavedielectricmaterialsystem.Forallcompositions,theQ×fvaluesincreasewithincreasingofsinteringtemperatures.AfterreachingthemaximumQ×fvalueataround1370℃,theQ×fvaluedecreases.ItwasfoundthattheQ×fvaluesrevealthesimilartrendasobservedintheapparentdensities.ItsuggeststhatthedenserceramicshavethehigherQ×fvalue.ThemicrowavedielectriccharacteristicsandthemicrostructuresofBa2-xSm4+2x/3Ti9O26ceramicsweredeterminedbythechemicalcompositionsandsinteringconditions.Fig.4-13showstheQ×fvaluesoftheBSTceramicsasafunctionofthesinteringtemperatureswithx=0.1.TheQ×fvaluesoftheBSTceramicsvaryfrom9500GHzto13000GHzwasobtained.Fig.4-14showstheplotsofthedielectricconstantasafunctionofsinteringtemperaturesforvariousxvaluesofBa2-xSm4+2x/3Ti9O26ceramics.Therelativedielectric44 constantsårdecreaseastheamountofsubstitutionofSmforBaincrease.Thisisingreat3+2+agreementwiththeX-raypatternsdiscussedabove.AstheSmionssubstitutefortheBaions,notonlythevacancieswerecreatedtomaintainchargeneutralitybutalsothelattice3+2+parameterswerechangedduetothedifferenceinionicradiusbetweenSmandBa.Thedifferenceofionradiusdirectlyaffectsthelengthofc-axis,whichistheimportantcharacteristicofthetungstenbronzetypestructure.Thedecreaseofthelatticeparametersalsopromotestheshrinkageoftheoctahedraanddecreasesthedielectricconstantindirectly.Therelativedielectricconstantsweregenerallyproportionaltosinteredbulkdensities.Thespecimenshavemaximumdielectricconstantat1360℃~1370℃whichagreeswellwiththatgivingthehighestdensities.Fig.4-15illustratedtherelativedielectricconstantasafunctionofsinteringtemperatureforvariousyvaluesoftheBSTceramics.ItisworthnotingthattheårvaluesoftheBa2-xSm4+2x/3Ti8+yO24+2yceramicdecreaseslightlywiththeincreasingofyvalue.SincethedielectricpropertiesdependonthelatticeparametersandtheincreaseofTiamountmightcausetheshrinkageoftheperovskiteoctahedral,thisresultstheBSTceramicswithsmallerdielectricconstantastheyvaluesincrease.Thewell-sinteredBSTceramicssaturateat62-85asy=0~2.Therelationshipsbetweendielectricconstantandsinteringtemperaturesrevealthesameasthatbetweendensitiesandsinteringtemperatures.Theårvalueincreaseswiththeincreaseofsinteringtemperaturesowingtotheincreaseindensities.45 Fig.4-16showsthecompositiondependenceofôfintheBa2-xSm4+2x/3Ti9O26systemsinteredat1360℃.Theintrinsicfactorofmicrostructurevariationandextrinsicofphaseassemblagewerebelievedtodeterminetheôfcharacteristic.Itwasobservedthattheôfvalueincreaseswithincreasingofxvalue.Thiscouldbeexplainedfromthestructuralformulaoftungstenbronzetypestructureandthereactionsequencesinequation4andequation5.ThemainphasesweremoreeasilyformedwithlargerxvaluesandmoreamountofsecondphaseTiO2appeared,whichhaslargepositiveôf(+427ppm/℃)andindirectlyaffecttheôfcharacteristic.Theôfvaluevariesfrom–3.4to+6ppm/℃asxvalueincreasesfrom0to0.3at1360℃.Itwasobservedthattheplotlinecrossedôf=0,whichimpliesthatôf=0couldbeobtainedbyadjustingxvalue.Theabsolutevalueofôfvalueincreaseswiththevariationinthethermalexpansioncoefficient,becausethedecreaseofthelatticeparameterspromotesshrinkageoftheoctahedron.Fig.4-17showsthecompositiondependenceofôfintheBa2-xSm4+2x/3Ti8+yO24+2ysystemsinteredattheirdensifiedtemperatures.Theôfvaluevariesfrom–12ppm/℃forBa2-xSm4+2x/3Ti8O24(x=0.1,y=0)to17ppm/℃forB2-xSm4+2x/3Ti10O28(x=0.1,y=2).TheextrapointswereexaminedtofurtherconformthemanneroftheôfvaluetovariousamountsoftheTiadditive.Thelineswithvariousyvaluescrossedôf=0atspecificxvalue.ThiscouldbeexplainedthattheexistenceofsecondphaseTiO2affectsthetemperaturecharacteristicoftheBSTceramics[35,45-46].Therelationshipsandtrendsbetweenôfandx,yvaluesaresimilar46 withtheresultswhenSrwasusedasthesubstitutionforBaindifferentBSTceramicsasreported[46-47].Thisimpliesthatôf=0canbeobtainedbyadjustingtheamountsofSmsubstitutionforBaandtheTiadditions.4-5ConclusionsTheoptimizedconstituentratioofBaO-Sm2O3-4.5TiO2ceramicswasselectedbaseonthesitesoccupanciesinperovskiteblocksandthepentagonalcolumnsfromstructuralformulaoftungstenbronzetypephases.BothcharacteristicsofthetungstenstructureandsiteoccupiesofcationswereconcernedtosynthesizetheBSTceramics.ThecrystallinephasesofsinteredceramicswereidentifiedasthetungstenbronzestructuresbyX-raydiffractionpattern.ThedetailsandtheextentoftheBa2-xSm4+2x/3Ti9O26solidsolutionsystemaredependonxandyvalues.Thetypicaldielectricperformancesofår=68to79andQ×f=11000to12500GHzwereobtained.TheôfvaluesofBa2-xSm4+2x/3Ti9O26ceramicswasadjustedfromnegative(－3ppm/℃forx=0)topositive(+6ppm/℃forx=0.3).SecondphasesBa2Ti9O2andTiO2appearedduringsinteringproceduresandwereidentified.TheBa2-xSm4+2x/3Ti8+yO24+2yceramicswithx=0.1~0.3andy=0~2formedthecompletesolidsolutionandwereobtainedinthisreach.Thetypicaldielectricperformancesofår=63to85andQ×f=8500to13000GHzwereobtained.TheôfvaluesoftheBST47 ceramicscanbeadjustedfromanegative–12ppm/℃valuetoapositivevalue17ppm/℃asyincreasesfrom0to2.SecondphasesBa2Ti9O2andTiO2appearedduringsinteringproceduresandwereidentified.ForvariousTicontents,theBSTceramicscanbesinteredwellateachspecificsinteringtemperature.Notonlydielectricconstant,butalsoQ×fvaluesaredependentonthedensificationofBSTceramics.Comparedwithothermicrowavematerials,Ba2-xSm4+2x/3Ti8+yO24+2yceramicswithhighdielectricconstant,highQ×fvaluesandadjustableôfvaluesarethegreatestdielectricmaterialsfortheapplicationinmicrowavecommunicationsystems.TheresultsofthisworksuggestthatBaO-Sm2O3-kTiO2(k=4~5)ceramicscontainstheperovskite-like,thetungsten-bronze-typestructureandBa2-xSm4+2x/3Ti9O26ceramicsformacompletesolidsolution.ThiscontributesanimportantaspecttoinvestigatethemicrostructureofBaO-Sm2O3-TiO2ceramicsinTirichregion.TherelationshipsbetweenmicrostructureanddielectricpropertiesofBaO-Sm2O3-kTiO2(k≠4)couldbeconstructedwiththesimilaraspectfromthestructureformulaoftungsten-bronze-typestructure.48 Chapter5DesignandFabricationofMicrowaveBandpassFilter5-1IntroductionToobtainthecompactanalogpartoftheradiocommunicationsystemisthesignificantfactortoreducethedimensionofthemobilecommunicationequipments.Microwavefiltersoccupyalargevolumeintheanalogpart,sofabricationacompactfilteristhemostimportantmethodtoreducethesizeofthecommunicationsystem.Conventionalwaveguidecomponentshavelowinsertionlossandexcellentresponsesatresonantfrequency,buttheyaretoolargeforUHFapplications[55-56].SurfaceAcousticWaveFilters(SAWF)wereusedtoreducethedimensionefficiently,althoughtheirinsertionlossandpowerhandlinglimittheirpracticalapplication.HighQdielectricceramicresonatorswithhighdielectricconstantcanefficientlyreducethesizeoffiltersfurthermorethesmalltemperaturecoefficientcontributesthesystemhighstability.Withthegreatcharacteristics,dielectricresonatorswerewidelyusedinthefabricationsofmicrowavefilters[48-50,58-63].Manyassemblymethodsofcoaxialdielectricresonatorsincludingwereinvestigatedandappliedtosolvetherestrictionsoffabricationcostandsizereducing[50,61,62].Stepimpedanceresonators(SIR)filterandmonoblockdielectricfiltershavetheadvantageofsmallsizeandwerealsostudiedanddesignedintensively[49-51,59].Manyanalysistheorems,simulation49 packagesandcomputeradddesignmethodsareappliedtoestablishafabricationprocedureofmicrowavefilters.Althoughthestructuresimulationsandtheanalysisofcouplingwereperformedinthedesignprocedures,unfortunatelytherelationshipsbetweenthecouplingsaturationandthephysicalstructurewerenoteasilydefinedandrestrictedtheirdevelopments.Microwavedielectricmaterialsarerequiredtobeexcellentinthreedielectriccharacteristics.Ahighdielectricconstant(år),ahighqualityfactor(Q),andaverystabletemperaturecoefficient(t＝~0ppm/℃)attheresonantfrequency.TheBaO-R2O3-TiO2(R=Sm,Nd)fceramicsystemhasthegreatmicrowavedielectriccharacteristicsandwaswidelyusedinthefabricationofsubstratesandresonatorsthatwereappliedintheconstructionsofmicrowavefilters.Thebandpassfiltersdescribedinthispaperoperatingatmobilecommunicationlfrequencywereconstructedwithcoaxialdielectricresonators.Theresonatorsweremade4ofhighQdielectricceramicswithhighdielectricconstant(e=75∼80,Q´f=11000rGHz).Thecouplingbetweenadjacentresonatorswasobtainedviatheaperturesformedontheoutersidesurfacesoftheresonatorswithair-gapcouplinganddirectcouplingindividually,furthermorethecomb-linetheorywasappliedtogetthetargetresponsewithoutmodifyingthestructureofthefiltersafterassembly.5-2FabricationofcoaxialdielectricresonatorsThecoaxialdielectricresonatorsdiscussedinthispaperweremadeofBSTsystem.The50 startingmaterialoftheBSTsystemconsistsofBaCO3,Sm2O3,andTiO2.Therawmaterialsowerepreparedandmixedinaplasticjarfor12hoursandwerecalcinedat1050C.Thenthe2materialwaspressuredintocoaxialspecimensunderthepressureof1500kg/cm.Atlasttheosamplesweresinteredat1350Cunderaircondition.Fig.5-1showstheconfigurationofasinteredresonator.Theresonatorisrectangularshapedblockwithametallizedcylindricalholethatactsasinnerconductorsattheircenter.Thesurfacesofthecoaxialresonators,exceptthetopendsurfaceandthesurfacesbetweentwoadjacentresonators,werefullymetallized.Theapertureswereformedontheadjacentsurfacesofeachresonatorasacouplinginstrument.Thetopendwasarrangedtobeanopen-circuitsurface,whiletheoppositeendsurfacewasashort-endsurface.TheresonantfrequencyoftheresonatorsdependsonthelengthLoftheresonators.Thecenterfrequencyfoofthefiltercouldbeexpressedas:ccf==(5-1)ol×e4Legrrwherecisthepropagatingvelocityoftheelectromagneticwave,ëgisthewavelength,Listhelengthofresonator,åristheeffectivedielectricconstant.Thelengthoftheresonatorisaboutl/4atresonantfrequency,wherelisawavelengthofelectromagneticplanewaveintheggdielectricmedium.Thediameterofthecenterhole,Dandthewidthoftherectangular,waretheboundaryconditions,whichdeterminetheunloadedQofeachresonatorandcoupling51 coefficientsbetweentwoadjacentresonators.Therelationshipsbetweenthephysicalstructureandtheelementvalueofeachresonatorcouldbeinvestigatedandestablishedbythenumericalanalysis.Comb-linetheorywasappliedtoadjusttheelectricallengthinordertoachievethetargetcharacteristicsofthefrequencyresponse.5-3DesignandconstructionoffilterAconventionaldesignmethodformicrowavedielectriccoaxialresonatorfiltersissuggestedinthiswork.Thismethodisbasedonarigorousanalysisandrelatedtheoriesofmicrowavefilters.Thereareseveralbasicelectricalspecificationsofaconventionalmicrowavefilter,suchasthepassbandcenterfrequency,insertionlossatresonantfrequency,bandwidthofpassband,rippleofpassbandorstopband,andrejectionslopeneedtobeachieved.Basedonthetargetcharacteristicsofafilter,thelengthoftheresonator,thefrequencyresponsetype,thenumberofstages,andthenumberofadditionalpolecouldfirstbecalculated.Bymodelingtheequipmentcircuitofthefilters,thecouplingcoefficientsandthephysicaldimensionsofeachresonatorcouldbedefined.Theconfigurationofathree-stagecapacitivecouplingbandpassfilterwasshowninFig.5-2.Theresonatorswerearrangedsidebysidetoformathree-stagefilterbeforeassemblyandweretunedtoworkattheuniformdesiredresonantfrequencybycontrollingthelengthoftheresonator.Thelengthofthe52 resonatoristhemostimportantparametertocontroltheresonantfrequency.Duetothedifferenceofmetallizedareaoftheinputandoutputstageislargerthantheareaofthemediumstage.Thecomb-linetheorywasappliedandpartialareaoftheopen-circuitendsurfacewasmetalizedtochangetheequivalentelectricallengthoftheresonators.Theseparationdistancebetweentwoadjacentresonatorsdeterminesthecouplingamountinair-gapcouplingmethod.Thedistancealsoaffectstheresponseofbandwidthandrippleofthefilteratpassbandfrequency.Bycontrollingtheseparationdistanceandboundaryconditionsbetweentwoadjacentresonators,thedemandsoffilterspecificationcouldbeachieved.Inordertohavecompactfilters,directcouplingcanbeusedtoachievetherequirement.Asdirectcouplingmethodwaschosentocoupleelectromagneticenergy,arectangularapertureneedstobeformedontheadjacentsurfacesbetweentworesonators.Theresonatorswerearrangedsidebysidewiththesameendshortedwithoutseparationdistance.Thearrangementformedadirect-couplingbandpassfilter.Couplingofelectromagneticenergybetweenwasobtainedviaaperturesanddependsonthedimensionandpositionoftheapertures.Thestrongestelectricandmagneticfieldsarelocatedattheopen-circuitendandshort-circuitend,respectively.Thesize,shape,andlocatingpositionoftheaperturesdeterminethecouplingconditionbetweentwoadjacentresonatorsandindirectlyinfluencedthefrequencyresponseofthefilter.Therelationshipsbetweenthephysicalstructuredimensionsandthefrequencyresponsecouldbeestablishedwiththenumericalanalysisandthesimulationoftheequipment53 circuitofthefilter.5-4CouplinganalysesTheequivalentcircuitofthefirststageloadedbytheexternalcircuitisshowninFig.5-3.AparallelconnectionofCr,Lrrepresentstheunloadedresonatorwitharesonantfrequencyfo.Zirepresentstheimpedanceoftheexternalcircuit.ReandCearetheequivalentresistiveandcapacitiveelementsoftheexternalcircuitappearingacrosstheidenticalresonatorcircuit.C01isthecouplingcapacitancebetweentheexternalcircuitandtheresonator.Thetransformationofelectromagneticenergyiscoupledbythecapacitancebetweentheexternalterminalandtheinnerconductingcylinderhole.TheequivalentcircuitoftworesonatorswithcouplingcapacitorcouldbeassumedandisshowninFig.5-4a.LriandCriareequivalentinductiveandcapacitiveelementsofeachë/4resonator,respectively.C12representstheequipmentmutualcouplingcapacitor,whichcouplestheelectromagneticenergybetweenthefirsttwoadjacentresonators.TheequivalentcircuitcouldbetransferredintoFig.5-4bwithanadmittance’inverter,J12.C12istheequivalentcapacitor,whichaccountsforthemutualcouplingmechanism.Bycontrollingtheair-gapsandaperturesbetweentwoadjacentresonators,theboundaryconditionsofthetransmissionlines,C12couldbedeterminedanddirectlyinfluencedthecouplingamount.Thisalsoaffectsthefrequencyresponseofbandwidthand54 insertionlossatcenterfrequency.Theresonantfrequencyfocouldbedeterminedfromtheidenticalequivalentcircuitandtherelationswereexpressedasfollowingequations:1f=(5-2)o'2pLr(C+C+C12)er11f=(5-3)o,'2pLr(C12+Cr2+C23)1f=(5-4)o'2pLr(C23+Cr3+Co)1f=(5-5)r2pLCrrTheoriginalresonantfrequencyofeachresonator,fr,shirtsandisdifferentfromthecenterfrequencyofthefilter,fobecausethecouplingcapacitancebetweenexternalcircuitandtheresonatorsandthecapacitancebetweentwoadjacentresonatorsthemselveschangethe''equivalentelectricallengthofeachresonator.C12,C23aretheequivalentcapacitorswhichaccountfortheeffectofcouplingmechanismthatcontributesthefrequencyshift.Come-linetheorycouldbeusedheretoformsomesuitablecompensativecapacitanceontheopenendsoftheresonators.Thismadethedevicetune-freeafterassembly.Fig.5-5showstheequivalentcircuitofthethree-stagebandpassfilterwiththeexternalcircuit.TheareaboundedbybrokenblockrepresentsthecouplingmechanismoftwoadjacentresonatorswiththecouplinginvertersJ12andJ23.Insuchacoaxialresonatorstructureliketheconfiguration55 showninFig.5-2,electromagneticenergytransfersinTEMmodeandtwodifferentkindsoffileddistributions,evenmodeandoddmode,existintheTEMmodetransmissionline.ThecharacteristicimpedanceZoofthetransmissionlinecouldbeexpressedas2ZZoeooZ=(5-6)oZ-ZoeooZAndZarethecharacteristicimpedancesofevenandoddmodes,respectively.TheoeoocharacteristicimpedanceZandZofaTEMmodetransmissionlineisrelatedtoitsshuntoeoocapacitanceandisexpressedas1Z=(5-7)oevCe1Z=(5-8)oovCoCeandCoarethecapacitancesofevenandoddmodes,respectively.Thesecharacteristicimpedancesaredependentonthetotalstaticcapacitancesappearingacrossthecylinderholesandground.ThetotalstaticcapacitancesincludethemutualcapacitancebetweentheneighborholesoftheadjacentresonatorsC12andtheself-capacitanceCroftheresonatoritself.Fig.5-6ashowsthetotalcapacitancebetweentwoadjacentresonatorsandthegroundwhenthetransmissionlinesaredriveninoddmode.Incontrasttothis,Fig.5-6bshowsthetotal56 capacitancewhenthetransmissionlineisdriveninevenmode.Numericalfieldsanalysis,liketwo-dimensionalfiniteelementmethod(2DFEM)or3DFEMcouldbeappliedtosolvethefielddistributionsoftheresonatorsandcharacterizethestructureoftheresonators.Afterthefileddistributionsbetweentheadjacenttransmissionlinesareobtained,theelectricfield,capacitance,equivalentdielectricconstantandcouplingcoefficientscanbecalculatedindirectly.5-5FabricationandperformanceoftheexperimentfilterBa(2-x)Sm(4+2x/3)Ti9O26(BST)system(x=0.05)withår=75,Q´f=11000,andôf=~0ppm/℃wasusedforthefabricationofmicrowavedielectricfilter.ThespecificationsofabandpassfilterneedtobeachievedarelistedinTable5-1.ThecouplingcoefficientsandexternalQcouldbecalculatedbythefollowingequations:BW1k=´(9)i,i+1fg×goii+1foQ=´g×g(10)eii+1BWwhereBWandfoarethe3-dBbandwidthandthecenterfrequencyofthebandpassfilter,57 respectively,andgiaretheprototypeelementvalues(i=0,1,2,3,．．．).InsertionlossofabandpassfilteratcenterfrequencyisdependentontheunloadedQofeachresonator,thedesiredbandwidthofthefilter,andthenumberofresonatorstagesandcanbeexpressedas:nfgoiL=4.343å(11)BWi=1QuiListheinsertionlossatcenterfrequency(dB),giareprototypeelementvalues,QuiareunloadedQofi-thresonator.Theadjustmentoftheresonantfrequencywasperformedbyformingthecompensatecapacitancetochangetheelectricallengthofeachresonator.Thedistanceoftheair-gapbetweentwoadjacentresonatorsandtheaperturesofeachresonatorthatdeterminethecouplingcoefficientswereformedasdescribedbefore.Thefrequencyresponseoftheexperimentalbandpassfiltersbyair-gapcouplinganddirectcouplingweremeasuredandshowninFig.5-7aandFig.5-7b,respectively.Thecenterfrequencycouldbetunedinthevicinityof900MHzforpersonalcommunicationsystem.Thetargetcharacteristicsofbandwidthandinsertionlossunder30MHzand3dBwereachievedandingoodagreementwiththespecifications.58 Chapter6ConclusionsandFutureWork6-1Conclusion(1)TheeffectofCuO,ZnOandV2O5additionstoReAlO3(Re=SmandNd)wereinvestigated.ThesinteringtemperaturesofReAlO3ceramicscanbeeffectivelyreducedfrom1650℃to1410~1430℃andcanwellsinteredtoapproach97%duetotheliquid-phasesinteringeffect.ThedielectricconstantandqualityfactoroftheReAlO3ceramicsremainsgoodcharacteristicsatlowsinteringtemperature.Theeffectofadditionsonthedevelopmentofthemicrostructureandthemicrowavedielectricpropertiesdependsontheconcentrations.Atlowconcentrationlevels(0.25-0.5wt％),theReAlO3ceramicsremainedinthesinglephaseandpresentedsecondphaseSm4Al2O9andNd4Al2O9onSmAlO3andNdAlO3,respectivelywithconcentrationsover0.5wt%asdeterminedbyXRDandEDS.TheQ×fvaluesof51000and41000GHzcouldbeobtainedat1430℃for0.25wt%CuOandZnO-sinteredSmAlO3ceramics.TheQ×fvalueof63000GHzwasachievedat1410~1430℃for0.25wt%CuO-sinteredNdAlO3.TherelativedielectricconstantofReAlO3remainsintherangefrom19.6to22.5.ThetemperaturecoefficientofSmAlO3ceramicsdependsontheadditionsandrangesfrom–40to-65ppm/℃.ThetemperaturecoefficientofCuO-sinteredNdAlO3remainsintherangeof–30ppm/℃to–45ppm/℃.59 (2)TheconstituentratioofBaO-Sm2O3-TiO2ceramicswasselectedbaseonthesitesoccupanciesinperovskiteblocksandthepentagonalcolumnsfromstructuralformulaoftungstenbronzetypephases.BothcharacteristicsofthetungstenstructureandsiteoccupiesofcationswereconcernedtosynthesizetheBSTceramics.ThecrystallinephasesofsinteredceramicswereidentifiedasthetungstenbronzestructuresbyX-raydiffractionpattern.ThedetailsandtheextentoftheBa2-xSm4+2x/3Ti8+yO24+2ysolidsolutionsystemaredependonxandyvalues.Thetypicaldielectricperformancesofår=68to79andQ×f=11000to12500GHzwereobtainedinwell-sinteredBa2-xSm4+2x/3Ti9O26ceramics.TheôfvaluesofBa2-xSm4+2x/3Ti9O26ceramicswasadjustedfromnegative(－3ppm/℃forx=0)topositive(+6ppm/℃forx=0.3).TheBa2-xSm4+2x/3Ti8+yO24+2yceramicswithx=0.1~0.3andy=0~2formedthecompletesolidsolutionandwereobtainedinthisreach.Thetypicaldielectricperformancesofår=63to85andQ×f=8500to13000GHzwereobtained.TheôfvaluesoftheBSTceramicscanbeadjustedfromanegative–12ppm/℃valuetoapositivevalue17ppm/℃asyincreasesfrom0to2.SecondphasesBa2Ti9O2andTiO2appearedduringsinteringproceduresandwereidentified.Notonlydielectricconstant,butalsoQ×fvaluesaredependentonthedensificationofBSTceramics.Comparedwithothermicrowavematerials,Ba2-xSm4+2x/3Ti8+yO24+2yceramicswithhighdielectricconstant,highQ×fvaluesandadjustableôfvaluesarethegreatestdielectricmaterialsfortheapplicationinmicrowavecommunicationsystems.60 (3)Coaxial-typedirectandaircouplingmicrowaveceramicsbandpassfilterswerefabricatedousingBSTdielectricmaterial(e=80,Q×f=13000at4.3GHzandt~0ppm/C).rfThefilterswerecomposedofthreequarter-wavelengthcoaxial-typeresonators.Sincecouplingbetweenadjacentresonatorsisviaanopenedwindow,additionalcouplingelementsarenotneeded.Electriccouplingormagneticcouplingcanbechosenbymovingthelocationandvaryingthedimensionoftheaperture.Filterswithinsertionlosslessthan3dBwereobtainedeitherthroughelectriccouplingorthroughmagneticcoupling.ThisstructurecaneffectivelyreducethesizeandthecostoffiltersintheUHFfrequencyrange.Furthermore,itcanbeappliedtofabricatecrosscouplingfilterwithellipticalresponse.6-2FutureWorkForfuturetrend,somesubjectswiththepotentialsrelatedtothisthesisareindicatedasfollow:(1)Todevelopanewlowtemperaturesinteringmicrowavedielectricmaterialwithpracticalcharacteristics.(2)Todevelopnewceramicsystemwithhighdielectricconstant(år>100),highQvalueandlowfrequencytemperaturecoefficient(3)TodevelopfilterswithattenuationpolesinthestopbandfortheapplicationsinLandSBand.61 (4)Todeveloptheprocesstopreparethemicrowavedielectricfilms.(5)Todevelopplanarmicrowavedeviceswithrelativeco-firetechnology.(6)Todevelopamethodformodelinganddesigningofthecoaxial-typemicrowavedielectricfilters.62 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E=0Eelectronicpolarization++atomicpolarization+-+-orientationpolarizationspacechargepolarization+-+-++++---+-+-+--+-+-+-++++---+-+-++---Fig.2-1Variouspolarizationmechanismsinmaterials75 Fig.2-2Thestructureofshieldeddielectricresonator76 Fig.2-3thepostmethodwitharadialdielectrometerformicrowavedielectricmeasurements77 LALALArLArLAr010101wwwChebyshevresponseEllipticresponseMaximallyflatresponseFig.2-4Threetypesoffilters(a)MaximallyFlat(b)Chebyshev(c)EllipticFunction78 Fig.2-5Alow-passprototypefilter79 GJB(w)JB(w)JB(w)JG001112223nn,n+1n+1X(w)X(w)X(w)12nRKKKKR0011223n,n+1n+1Fig.2-6(a)K-inverter(b)J-inverter80 RawmaterialsPVAbinderBallmillingGranulatingDryingColdPressingCalcinationDebinderBallmillingSinteringDryingDenseBulkFig.3-1Flowchartofexperimentprocedureofdielectricresonators81 Fig.3-2X-raydiffractionpatternsofSmAlO3ceramicswith0.25wt%CuOsinteredatdifferenttemperatures.82 Fig.3-3X-raydiffractionpatternsofSmAlO3ceramicswith0.25wt%and0.5wt%additions(CuOandZnO)sinteredat1410℃.83 Fig.3-4X-raydiffractionpatternsofSmAlO3ceramicswithvariousamountofCuOadditionssinteredat1430℃.84 Fig.3-5(a)EDSanalysisofSmAlO3ceramicsforgeneralregions.Fig.3-5(b)EDSanalysisofSmAlO3ceramicsforspecificgrainswithSm4Al2O9secondphase.85 Fig.3-6(a)SEMmicrographofSmAlO3with0.5wt%CuOsinteredat1430℃.Fig.3-6(b)SEMmicrographofSmAlO3with1wt%CuOsinteredat1430℃Fig.3-6(c)SEMmicrographofSmAlO3with0.5wt%ZnOsinteredat1430℃Fig.3-6(d)SEMmicrographofSmAlO3with1wt%ZnOsinteredat1430℃.86 Fig.3-7XRDpatternsofNdAlO3powderscalcinedatdifferenttemperaturesfor2h.87 Fig.3-8XRDpatternsofNdAlO3ceramicswith0.25wt%CuOsinteredatdifferenttemperatures.88 Fig.3-9XRDpatternsofNdAlO3ceramicswithvariousCuOconcentrationssinteredat1410℃.89 Fig.3-10(a)SEMofNdAlO3ceramicssinteredat1410℃with0.25wt%CuOadded.Fig.3-10(b)SEMofNdAlO3ceramicssinteredat1410℃with0.5wt%CuOadded.Fig.3-10(c)SEMofNdAlO3ceramicssinteredat1410℃with0.75wt%CuOadded.Fig.3-10(d)SEMofNdAlO3ceramicssinteredat1410℃with1wt%CuOadded.90 Fig.3-11(a)SEMofNdAlO3ceramicswith0.75wt%CuOaddedsinteredat1390℃Fig.3-11(b)SEMofNdAlO3ceramicswith0.75wt%CuOaddedsinteredat1410℃Fig.3-11(c)SEMofNdAlO3ceramicswith0.75wt%CuOaddedsinteredat1430℃Fig.3-11(d)SEMofNdAlO3ceramicswith0.75wt%CuOaddedsinteredat1450℃91 6543Grainsizes(um)20.25wt%CuO0.5wt%CuO10.75wt%CuO1wt%CuO0138013901400141014201430144014501460oSinteringTemperature(C)Fig.3-12GrainsizeofNdAlO3ceramicssinteredat1410℃asafunctionofCuOconcentration.1000.25wt%CuO990.5wt%CuO1wt%CuO0.5wt%ZnO981wt%ZnO979695RelativeDensity(%)94939213801390140014101420143014401450146014701480oSinteringTemperature(C)Fig.3-13Therelativedensitiesofaddition-sinteredSmAlO3ceramicsasafunctionofsinteringtemperatures.92 9998979695940.25wt%CuO93RelativeDensity(%)0.5wt%CuO920.75wt%CuO911wt%CuO901350137013901410143014501470SinteringTemperature(oC)Fig.3-14RelativedensitiesofCuO-sinteredNdAlO3ceramicsasafunctionofsinteringtemperature.2120.5)r2019.50.25wt%CuO190.5wt%CuODielectricConstant(å1wt%CuO0.5wt%ZnO18.51wt%ZnO1813801390140014101420143014401450146014701480SinteringTemperature(oC)Fig.3-15DielectricconstantofSmAlO3ceramicswithdifferentadditionsasfunctionofsinteringtemperature.93 700000.25wt%CuO0.5wt%CuO600001wt%CuO0.25wt%ZnO500000.5wt%ZnO4000030000Q×f(GHz)2000010000013801390140014101420143014401450146014701480SinteringTemperature(oC)Fig.3-16Q×fvaluesofSmAlO3ceramicswithdifferentadditionsasafunctionofsinteringtemperature.-30-35)f-40-45-50-55-60CuOTemperatureCoefficient(ôZnO-65-7000.250.50.7511.25AmountofAdditions(wt%)Fig.3-17ThecompositiondependenceonôfofSmAlO3ceramicssinteredat1430℃94 2322.52221.5210.25wt%CuODielectricconstant(år)0.5wt%CuO0.75wt%CuO20.51wt%CuO20136013801400142014401460Sinteringtemperature(0C)Fig.3-18DielectricconstantårofNdAlO3ceramicsasafunctionofsinteringtemperature.800000.25wt%CuO0.5wt%CuO700000.75wt%CuO1wt%CuO600005000040000f×Q(Hz)3000020000100000138013901400141014201430144014501460SinteringTemperature(oC)Fig.3-19Q×fvaluesofNdAlO3ceramicswithvariousCuOconcentrationsasfunctionsofsinteringtemperature.95 -10-150.25wt%CuOf)τ0.5wt%CuO-200.75wt%CuO-251wt%CuO-30-35-40TemperatureCoefficient(-45-50138013901400141014201430144014501460SinteringTemperature(℃)Fig.3-20CompositiondependenceonôfofNdAlO3ceramicsasafunctionofsinteringtemperature.96 Fig.4-1TheSchematicdiagramofBSTceramicswithcomplexphaseoftungstenbronzestructure97 Fig.4-2Projectionofthetungstenbronzestructureinthecplane.Theinsetshowsthepolardirectionsinorthorhombicstructure.98 Fig.4-3X-raydiffractionpatternsofBa(2-x)Sm(4+2/3x)Ti9O26ceramicssinteredat1360℃for4hourswithx=0.0,x=0.1,x=0.2,x=0.3.99 Fig.4-4aMicrographofBa(2-x)Sm(4+2/3x)Ti9O26ceramicswithx=0.1sinteredat1340℃Fig.4-4bMicrographofBa(2-x)Sm(4+2/3x)Ti9O26ceramicswithx=0.1sinteredat1360℃Fig.4-4cMicrographofBa(2-x)Sm(4+2/3x)Ti9O26ceramicswithx=0.1sinteredat1380℃100 Fig.4-5aPhotographofthesinteredsurfacewithsecondphaseBa2Ti9O20thatwasidentifiedwiththeenergydispersiveX-rayspectrometer(EDS)analysis.Fig.4-5bEnergydispersiveX-rayspectrometer(EDS)resultofthesinteredsurfaceshowninFig.4-5a.101 Fig.4-5cPhotographofthesinteredsurfacewithintermediatephaseSm2Ti2O7thatwasidentifiedwiththeenergydispersiveX-rayspectrometer(EDS)analysis.Fig.4-5dEnergydispersiveX-rayspectrometer(EDS)resultofthesinteredsurfaceshowninFig.4-5c102 Fig.4-6Macrodifferentialthermalanalysis(DTA)oftheBa2-xSm4+2x/3Ti8+yO24+2yrawmaterials103 Fig.4-7X-raydiffractionpatternsofBa2-xSm4+2x/3Ti8+yO24+2y(x=0.1,y=1)ceramicscalcinedatvarioustemperatures.104 Fig.4-8X-raydiffractionpatternsofBa2-xSm4+2x/3Ti8+yO24+2yceramicssinteredattheirspecificdensifiedtemperatures(+and□markersareidentifiedasthemainphaseBaSm2Ti4O12,BaSm2Ti5O14).105 Fig.4-9aMicrographofBa2-xSm4+2x/3Ti8+yO24+2yceramicswithy=0sinteredat1400℃Fig.4-9bMicrographofBa2-xSm4+2x/3Ti8+yO24+2yceramicswithy=1sinteredat1370℃Fig.4-9cMicrographofBa2-xSm4+2x/3Ti8+yO24+2yceramicswithy=2sinteredat1330℃106 5.9)35.75.5x=0.05.3apperantdensity(g/cmx=0.1x=0.2x=0.35.113201340136013801400sinteringtemperature(℃)Fig.4-10ApparentdensitiesofBa2-xSm4+2/3xTi9O26ceramicsasafunctionofsinteringtemperatureandcomposition65.8)35.65.4y=0Density(g/cmy=0.55.2y=1y=1.5y=251300132013401360138014001420Temperature(℃)Fig.Fig.4-11ApparentdensitiesofBa2-xSm4+2x/3Ti8+yO24+2yceramicsasafunctionofsinteringtemperatureandcomposition(x=0.1)107 15000x=0.0x=0.112000x=0.2x=0.39000(GHz)6000Q×f30000130013201340136013801400sinteringtemperature(℃)Fig.4-12Q×fvaluesofBa2-xSm4+2/3xTi9O26ceramicsasafunctionSinteringtemperatureandcomposition1400012000100008000f.Qvalue(GHz)6000y=0y=0.5y=14000y=1.5y=2200013101320133013401350136013701380139014001410Temperature(℃)Fig.4-13Q×fvaluesofBa2-xSm4+2x/3Ti8+yO24+2yceramicsceramicsasafunctionofsinteringtemperatureandcomposition(x=0.1).108 81)78r75726966x=0.0x=0.1dielectricconstant(å63x=0.2x=0.360130013201340136013801400sinteringtemperature(℃)Fig.4-14DielectricconstantofBa2-xSm4+2/3xTi9O26ceramicsasafunctionofsinteringtemperatureandcomposition8580r757065y=0y=0.5Dielectricconstantå60y=1y=1.555y=2501300132013401360138014001420Temperature(℃)Fig.4-15DielectricconstantofBa2-xSm4+2x/3Ti8+yO24+2yceramicsasafunctionofsinteringtemperatureandcomposition(x=0.1).109 )9℃630-3temperaturecoefficient(ppm/-600.050.10.150.20.250.30.35xvalueFig.4-16TemperaturecoefficientoftheresonantfrequencyôfofBa2-xSm4+2/3x)Ti9O26ceramicssinteredat1360℃20151050-5y=0Temperaturecoefficienty=0.5-10y=1y=1.5-15y=2-2000.050.10.150.20.250.3xvalueFig.4-17TemperaturecoefficientôfofBa2-xSm4+2x/3Ti8+yO24+2yceramicssinteredattheirspecificsinteringtemperatureasafunctionofcomposition.110 Fig.5-1TheconfigurationofasinteredcoaxialresonatorwithcouplingapertureFig.5-2Theconfigurationofathree-stagecapacitivecouplingbandpassfilter111 Fig.5-3TheequivalentcircuitofthefirststageloadedbytheexternalcircuitFig.5-4aTheequivalentcircuitoftwoadjacentresonatorswithcouplingcapacitor112 Fig.5-4bTheequivalentcircuitoftwoadjacentresonatorswithcouplingcapacitorFig.5-5Theequivalentcircuitofthethree-stagebandpassfilterwiththeexternalcircuit.113 Fig.5-6aTheschematicdiagramoftotalcapacitancebetweentwoadjacentresonatorsandthegroundwhenthetransmissionlinesaredriveninoddmode.Fig.6bTheschematicdiagramoftotalcapacitancebetweentwoadjacentresonatorsandthegroundwhenthetransmissionlinesaredriveninevenmode.114 Fig.5-7aThefrequencyresponseoftheexperimentalbandpassfiltersbyair-gapcouplingFig.5-7bThefrequencyresponseoftheexperimentalbandpassfiltersbydirectcoupling115