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An Ultra-compact antenna test system and its analysis in the context of wireless clock distribution

University of Florida Institutional Repository

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AN ULTRA-COMPACT ANTENNA TEST SYSTEM AND ITS ANALYSIS IN THE CONTEXT OF WIRELESS CLOCK DISTRIBUTION By WAYNE ROGER BOMSTAD II A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2002

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ii ACKNOWLEDGMENTS Iwouldliketobeginbythankingmyadvisor,ProfessorKennethO,forgivingme theopportunitytoworkonthisproject.Hispassionandcommitmentarealwaysapersonal source of inspiration. Iwouldalsoliketothanktherestofmymentoringprofessors(Leffew,Snider, Weller,andZory)fortheirguidance,allowingmetowholeheartedlyclaimafuturecareer path.Additionally,Igivemydeepestrespecttomyrstmentors,andlifelongrolemodels, my parents: Henrietta I. Shuminsky and Wayne R. Bomstad. Alsothisworkwouldnotbepossibleinanytimelymannerwithoutmyteammates. OntheSRCProjectIthankJ.Caserta,X.Guo,R.Li,J.Branch,andT.Dickson.Proper thanksgoouttograduatedPh.D.studentsB.FloydandK.Kimforprovidingmany enlighteningdiscussions.Next,IamgratefultoBruceSmithofPrecisionToolandEngineering for his help in mechanical engineering throughout this project. Idedicatethiswork,andallfutureengineeringwork,tomybeautifulwife, Aleasha. Her love, encouragement, and dedication are behind any achievement of mine.

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iii TABLE OF CONTENTS page ACKNOWLEDGMENTS. . . . . . . . . . . . . . . . . . . . . . . . . .ii ABSTRACT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi CHAPTER 1INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . .1 1.1Emergence of Wireless Interconnects . . . . . . . . . . . . . . .1 1.2Intra-Chip Clock Distribution. . . . . . . . . . . . . . . . . . .1 1.3Overview of Thesis. . . . . . . . . . . . . . . . . . . . . . . .6 2ULTRA-COMPACT ANTENNA TEST SYSTEM. . . . . . . . . . . . . .7 2.1Structural Design . . . . . . . . . . . . . . . . . . . . . . . .7 2.2Electrical Design Considerations . . . . . . . . . . . . . . . . .11 2.3Data Extraction. . . . . . . . . . . . . . . . . . . . . . . . .19 2.4Calibration. . . . . . . . . . . . . . . . . . . . . . . . . . .23 3INTEGRATED RECEIVE ANTENNAS. . . . . . . . . . . . . . . . . .26 3.1Infinitesimal Dipole Antennas . . . . . . . . . . . . . . . . . .26 3.2Radiated vs. Input Power. . . . . . . . . . . . . . . . . . . . .30 3.3Integrated Antennas in the UCATS . . . . . . . . . . . . . . . .34 4PROTOTYPE TRANSMITTER AND WAVEGUIDE ASSEMBLY. . . . . . .37 4.1Waveguide Assembly. . . . . . . . . . . . . . . . . . . . . .37 4.2Prototype Transmitter. . . . . . . . . . . . . . . . . . . . . .42 5PROTOTYPE SYSTEM MEASUREMENTS. . . . . . . . . . . . . . . .51 5.1Testchip Design . . . . . . . . . . . . . . . . . . . . . . . .51 5.2Spatial Wavefront Uniformity Measurements. . . . . . . . . . . .52 5.3Frequency-Dependent Measurements. . . . . . . . . . . . . . . .65 5.4Measurement Summary . . . . . . . . . . . . . . . . . . . . .69

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iv 6SUMMARY AND FUTURE WORK . . . . . . . . . . . . . . . . . .72 6.1Summary . . . . . . . . . . . . . . . . . . . . . . . . . . .72 6.2Future Work. . . . . . . . . . . . . . . . . . . . . . . . . .74 APPENDIX ADRAWINGS FOR THE ULTRA-COMPACT ANTENNA TEST SYSTEM. . . .75 A.1Engineering Drawings for the UCATS . . . . . . . . . . . . . . .75 A.2Photographs of Assembled UCATS. . . . . . . . . . . . . . .84 BFINITE ELEMENT SIMULATIONS. . . . . . . . . . . . . . . . . . .86 B.1Electromagnetic Application of Finite Elements. . . . . . . . . . .86 B.2Simulation of Prototype Transmitter. . . . . . . . . . . . . . . .89 B.3Standing Wave Simulations . . . . . . . . . . . . . . . . . . .92 LIST OF REFERENCES. . . . . . . . . . . . . . . . . . . . . . . . . .98 BIOGRAPHICAL SKETCH. . . . . . . . . . . . . . . . . . . . . . . .99

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v Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulllment of the Requirements for the Degree of Master of Science AN ULTRA-COMPACT ANTENNA TEST SYSTEM AND ITS ANALYSIS IN THE CONTEXT OF WIRELESS CLOCK DISTRIBUTION By Wayne R. Bomstad II December 2002 Chair: Kenneth K. O Major Department: Electrical and Computer Engineering Ithasbeenproposedtogenerateandreceivetheclocksignalusingwirelesscommunicationsystemsasanalternativemeansofmicroprocessorclockdistribution.Asa candidatetoreplacetraditionalwiredinterconnects,wirelessclockdistributionhasseveral potentialadvantagesoveritsconventionalcounterpartincludingsynchronizationovera largerareaandsmallerclockskew.Previouswirelessclockdistributionsystemswere investigatedusingintegratedreceiversandtransmitters.However,operationofthesesystemsishinderedbytheinterferencecausedbycoplanarmetalstructures.Thewayto mitigate this effect is to generate the clock signal off-chip. Theconceptofexternally-transmittedwirelessclockdistribution(ECD),or inter-chipclockdistribution,hasbeenstudiedinthisworkthroughthedevelopmentofan application-specicmeasurementsetup.Thissetupwasdesignedtoserveasatest-bedfor thecharacterizationofECDsystems.Alsointhiswork,aprototypeECDsystem,consist-

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vi ingofonlytransmitandreceiveantennas,wasdesignedandthenmeasuredinthisnew test-bed, called the Ultra-Compact Antenna Test System (UCATS). TheUCATSwasdevelopedtomeasurethegaininthenear-tointermediate-eld regionofatransmittingantennaona3-inchdiameterwafer.Fortheinitialtests,aprototypetransmit-receiveantennasetwascharacterizedbothasabenchmarkforfuture designsandasameansofcharacterizingthetestrange.Specically,a24GHzgaussian opticshornantennawasusedasthetransmitter.Atestchipcontaininganevenly-spaced arrayoffoldeddipoleswasdesignedandusedasthesetofreceiveantennas.Phaseand amplitudedistributionsofthereceivedwavefrontwerecharacterizedbyindividually probing the integrated antennas. Measurementswereperformedfortwodifferentreceiver-transmitterseparation distances,andtheresultswerecomparedintermsoftheoverallgain,magnitude,and phasedistributions.Measurementshaveshownthatawavefrontcanbegeneratedand receivedwithamaximumphasedifferenceof16degreesandameanamplitudedifference of3.77dB.Forthepurposesofclockdeliveryfor3GHzoperation,thiscanbeapproximatedasaplanarwavefrontwithabeamareaof3.8cmx3.1cm,themeasurablesizeof the receiver array. Inconclusion,itwasshownthataplanarwavefrontcanbegeneratedandmeasuredinthenear-tointermediate-eldregionofthetransmittingantennausingthe UCATSandaprototypeECDsystem.Theclockskew,assumingtypicalclockreceiver architecture,wascalculatedtobe3%and1.7%oftheperiodatareceiverdistanceof3 and7.5inches,respectively.Thesemeasurementsweremadeoveranareaof1178mm2,a span of over 3 times the average area of present-day microprocessors.

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1 CHAPTER 1 INTRODUCTION 1.1 Emer gence of W ireless Interconnects Theemergenceofthetechnicaleldofwirelessinterconnectshasoccurredasa meansofaddressingthesomeofthebottlenecksfacingthesemiconductorindustry.As recentlyas2001theSemiconductorIndustryAssociationsInternationalTechnology RoadmapforSemiconductors(ITRS)[SIA01]haspredictedthat,inthenext5years, microprocessorswillhavelocalclockfrequenciesapproaching7GHz,transistorgate lengthwilldecreaseto45nm,andthenumberofmetallayerswillincreaseto9.However, restrictionofthetolerablephasediscrepancyoftheclocksignal,orclockskewrequirement,hasbeenreducedto40psresultingfromtheincreasedfrequency.Asaresultof thesetrends,theglobalclockskewcanlimitthehigh-speedoperationofmicroprocessors, evenwhenusingthestate-of-the-artcopperandlowk interconnecttechnology[Flo01]. Worsethanthis,typicalsystemicclockskewsolutionsinvolveuseofH-treecircuitry,takingupalargeareaandrequiringsymmetry[Rab96].Whatthismeansintermsofclock deliveryisthatasthechipsizeandclockfrequencyareincreasedeachpassingyear,the clockskewbecomeshardertoequalizeacrossthechip,andthetotalareausedinclock deliveryincreases.Thisproblemisoneofthegrandchallengesfacingthesemiconductor industry, that could place serious limitations on the growth of the industry. 1.2 Intra-Chip Clock Distrib ution Feasibility of using wireless interconnects to alleviate some of the interconnect concerns of the semiconductor industry has been proposed [O99] and components for

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2 such a system have been successfully evaluated at a global clock transmission frequency of 15 GHz using integrated receivers and transmitters fabricated on a 0.18 m m silicon CMOS technology [Flo00, Kim00]. A conceptual diagram of the system is shown in Figure 1-1. The transmitter has been placed in the middle of a group of integrated receivers. 1.2.1 Propag ation Inside an Intra-Chip Clock Distrib ution System Figure1-1showsthat,althoughplacementofthetransmitterandreceivercanbe optimizedfromasystemicview,therewillbedifferencesindirect-pathpropagation delaysforskewsevenintheidealsituationbecausethereceiversmustbeplacedatvarying distancesfromthetransmittingantenna.Thedistributionofdelaystothedifferentreceiversbecomesmorecomplexwhenconsideringthatthesignalcanalsotravelunderthesiliconsurface,throughthesiliconsubstrate,andreectoffsurroundingmetallayers [Kim01](Figure1-2).Toalleviatethisproblem,sophisticatedtechniquesarerequired, suchastheinclusionofaproperlyengineeredpropagationlayerunderneaththesilicon surface. RX TX RXRXRX RXRXRXRX RXRXRXRX RXRXRXRX RX=Receiver TX=Transmitter IC edge Figure 1-1Conceptual diagram of an intra-chip clock distribution system.

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3 1.2.2 Clock Recei v er Architecture AblockdiagramoftheclockreceiverisshowninFigure1-3.Toimprovenoise immunity,differentialmodecircuitrywasusedthroughoutthesystem.Tomatewiththe differentialmodecircuitry,balanced-lineantennas(BLAs)suchasdipolesandloopsare neededforsignalreception.Sequentially,thetransmittedsignalattheglobalclockfrequency(GCK)isreceivedbytheBLA,buffered,ampliedbythelow-noiseamplier (LNA),andthenfedtothefrequencydivider.Throughthedivider,thesignalsfrequency isdividedby8tothesystemclockfrequency.Thesignalisthenbufferedagainbefore being sent to the adjacent circuitry. Rx Tx Figure 1-2Possibledisruptionofdirect-pathsignalsintheintra-chipwirelessclock distribution s y stem. LNAAnalog Buffers Output BuffersFrequency Divider GCK BLA +BLASystem Figure 1-3Block diagram of a typical clock receiver. Clock

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4 1.2.3 Inter -Chip Clock Distrib ution System Onewayaroundthisskewforintra-chipclockreceiversistouseaninter-chip clockdistributionsystem.Suchameansofclockdistributionalsousesadistributionof integratedwirelessclockreceiversacrossachip.However,thesignaltransmissionis accomplishedbyaplanewavegeneratorlocatedoff-chip(Figure1-4).Thesignaltravels fromthetransmitter,throughthesilicon,andtothereceivers.Thiskindofsignalpropagationrenderstheinterferenceeffectofsurroundingmetalstructuresnegligible,andbetter ensuresthatthereceiverssynchronouslyreceivetheclocksignalwithoutregardtotheir placement on-chip. 1.3 Ov ervie w of Thesis 1.3.1 Ultra-Compact Antenna T est System (UCA TS) Oneofthegoalssetforthinthisworkwasthedesignofaset-upcapableofcharacterizingthenatureofthetransmitter-to-receiverpropagationinawirelessclockdistributionsystemusingmicrowavescatteringparameters.Intermsofthemechanicaldesign,the clock signal transmitted Transmitting Antenna (Plane Wave Emitter) Integrated Circuits (PC Board/MCM) Receiving Antennas F igure 1-4Conceptual diagram of inter-chip clock distribution system.

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5 UCATSnotonlyhadtobeabletotwithintheexistingmeasurementset-up,forcostpurposes,butalsohadtoallowforsensitiveleveladjustmentandreceiver-transmitterspacing. Electrically,thesystemhadtobeabletoabsorbasmuchreectedradiationaspossible, providingagroundfortheabsorbedradiation.Thus,anisolationchamberwasdesignedto isolatethetransmitterandreceiverfromallsignalsexceptthedirectlinkbetweenthem.A renditionisshowninFigure1-5,wherethefourmainpartsoftheUCATScanbeseen:the isolationchamber,vacuumring,transmitterplatform,andprobeheight-extenders.Finer details on the measurement setup are in Chapter 2. 1.3.2 Prototype T ransmitter -Recei v er P air ToverifytheproperfunctionalityoftheUCATSandtoprovideareferencedesign forfutureinter-chipclockdistributionsystems,aprototypetransmit-receiveantennapair wasalsodesignedaspartofthiswork.Sinceanactualparabolicreectorantenna,asin Figure1-4,wouldnotbecompatibletotheUCATSenvironment,agaussianoptics antenna[Gol82]wasusedinitsstead.Analogousinmanywaystoanelectromagnetic spotlight,thegaussianopticsantenna,canbeusedtoemitaplane-wave-likebeam, whichisonlydiffraction-limitedinthespreadingofitsamplitudeandphaseoverpropagationdistance.AmoredetaileddiscussionofthishorntransmitterispresentedinChapter4. Atestmaskincludingreceiveantennaswasdesignedinordertomeasureandcharacterizethetransmittedwavefrontatthewafersurface.Cellsofvaryingintegratedantennas,werespacedatevenintervalsacrossthewafersurface.Usingthismask,awaferwas fabricatedattheUFMicroelectronicsFabricationFacilityona20 W -cmsiliconsubstrate. This work is also discussed in Chapter 3.

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6 Uponmeasuringthereceivedpowergainusingmicrowavescatteringparameters (s-parameters)ateveryantennaofthesametypeineachcell,thespatialphaseandamplitudedistributionswereobtainedandplotted.Carefulanalysisofthes-parametersandthe antennapropertieshasyieldedaskewof1.7%and3%forreceiver-transmitterseparations of7.5inchesand3inches,respectively.ThesemeasurementsanddataanalysesarepresentedinChapter5.Finally,aspartofChapter6,broaderconclusionsfromthedatawere drawn, and future work was proposed. Wafer Vacuum Ring Tx Transmitter Platform Antenna Chamber Probe Height-extenders RF Probes EM Absorber 14 7 Figure 1-5Cross-sectional layout of the UCATS.

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7 CHAPTER 2 ULTRA-COMPACT ANTENNA TEST SYSTEM 2.1 Structural Design 2.1.1 Ov ervie w ThemechanicaldesignoftheUCATSwasgovernedbythreestipulations.Firstof all,forcostefciencypurposes,thesystemmusttwithintheexistingRFprobestation. Second,inthecontextofexternalclockdistributionnetworks,thedesignmustallowfor accuratemeasurementofphasedifferencesacrosstheentirewafersurface[Wan88]. Finally, the design must permit ne adjustment in receiver-transmitter spacing. 2.1.2 Isolation Chamber Design Theexternaldimensionsoftheisolationchamberandstructuralfoundationofthe UCATSweredeterminedsothatthesystemcouldsnuglytwithintheexistingRFprobe station,couldallowforadequaterangeofmotionoftheprobes,andcouldprovidehousing ofboththereceiveandtransmitantennas.Thechamberwasdesignedtobeave-sided box,consistingoffourdistinctpieces:side-walls(x2),afrontpanelwithanaccessdoor, back-panel,andthetopsurface.TheseindividualpieceswerefabricatedusingAluminum, whichallowforasturdyprobingplatform,agroundforabsorbedradiation,andaninexpensiveandlightweightalternativetostainlesssteel.Theassembledantennachamberis displayedinFigure2-1(a).Details,suchasthescrewholesandspacing,havebeenomitted for simplicity, but the actual drawings have been included in Appendix A.

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8 Theneedtoexploretheeffectsoflayersplacedbetweenthewaferandtransmitter anddifferentvacuumringcongurationshasledtothedesignofamodularvacuumringsystem.Tohelpaccomplishthis,thevacuumringhousingwasdesignedasalarge multi-stepholeinthemiddleofthetopsurface,showninFigure2-2.Inaddition,holesin thevacuumringhousingwereplacedtopermitforleveladjustmentofthevacuumring separately from the transmitter platform via adjustment screws. More detailed drawings Vacuum Ring Access Door (Front Panel) (Top Panel) 7 13.25 (a) (b) 4 7 3 13.25 14 Figure 2-1Diagram of assembled antenna chamber: (a) oblique and (b) top views. Figure 2-2Cross section of antenna chamber top panel. Placement of Vacuum Ring Adjustment Screws

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9 canbefound,onceagain,inAppendixA.Thediscussionoftheprototypevacuumring has been included in the electrical design section. 2.1.3 T ransmitter Platform Thetransmitterplatformresidesinsidetheantennachamber.Thispieceaccomplishesthesensitivetaskofbothallowingforacontinuousrangeofreceiver-transmitter spacing,andleveladjustmentofthetransmittingantenna.Theplatformfastenstothe chamberbyfourlargescrews,6inchesinlengthand0.5inchesindiameter.Thesescrews mateinto4specially-designedL-clamps.Turningallscrewsequallyinonedirection variesthedistancebetweenthereceiverandtransmitter,andcausestheplatformtoslide upordownalongtheinsidewallsoftheantennachamber.Turningonlyacoupleofthese screwsatatimeadjuststheleveloftheantennaplatform.Figure2-3showsacut-away view of the platform, while Appendix A contains more detailed drawings. 2.1.4 Probe Height-Extender Assembly Theantennachamberhasbeendesignedwithagreaterheightthantheexisting probestation.Toallowprobingoftheentiresurfaceofa3-inchdiameterwafersecuredon thevacuumring,aprobeheight-extenderassemblywasdesigned.Aluminumwasagain chosenforitsrigidsupportandlightweight.Thelatterqualitywasvitaltopreventoverloading the calipers, the mechanism for probe deployment. Tx Ant. Tx-Platform Adj. Screws L-ClampsTransmitterPlatformFigure 2-3Cutaway view of transmitter platform inside antenna chamber.

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10 Theprobeheight-extenderassemblyconsistsoftwodistinctpieces:theprobe armsandprobeheight-extenders.Theprobeheight-extendersallowtheprobestoberigidlysupportedwellabovethewafersurface,whiletheprobesaremountedontheprobe arms.Additionally,theprobearmswerespeciedtohave2degreesoffreedomandtheir actualdesignwascontractedouttoPrecisionToolandEngineering.Theirassemblywith theantennachambercanbeseeninFigure2-4,whiletheengineeringdrawingscanbe seen in Appendix A. 2.1.5 V acuum Ring Inconsideringitsphysicaltopologyalone,thevacuumringisperhapsthemost complexofthecomponentsoftheUCATS.First,theringmusttwithintheringhousing intheantennachamberandmatetothevacuumringleveladjustmentscrews.Inlooking atFigure2-5,thedesignoftheinnerringradius,ormeasurementaperture,mustnotonly provideaccesstotransmittedsignalsfrombelow,butalsoallowforany3-inchwidewafer (circularorsquare)tocovertheaperturecompletely.Finally,theringmustprovideadeProbe Adjustment Caliper Antenna Chamber Probe Height Extenders Probe Arms Figure 2-4View of probe support assembly (shaded).

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11 quateairevacuationtosecurethewaferinplaceagainstrepeatedprobelandings.Thus, theholesinthevacuumringshouldeachapplyanequaldownwardforceonthewafer. Withthisideaasaguide,thevacuumringcontainsaninternalvacuumchannelconnectingallthevacuumholesandprovidinganoutletforexternalconnectiontoavacuum pump.Onceagain,AppendixAcontainsmoreofthedimensionaldetailsofthevacuum ring. 2.2 Electrical Design Considerations 2.2.1 Antenna Chamber Theantennachamberwasdesignedsothatthesignalwouldtakeonlyonepath, theline-of-sight(LOS)path,topropagatefromtransmittertoreceiver.Appropriate absorbingmaterialhadtobeplacedinsidetheantennachambertoabsorbanyreected Wafer 3 Diameter Circular Wafer Vacuum Holes Vacuum Channel (a) (b) 3 Square Figure 2-5Actual-sizedrawingofvacuumringshowing(a)waferplacementand(b) cross section.

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12 signals.TheabsorberisshowninFigure2-6,a0.5-inchthickatabsorberwasusedfor alloftheinternalsurfacesoftheantennachamber.AsdiscussedinSection2.2.2,itwas determinedbyexperimentalmeansthatthisabsorberwasabetterchoiceforabsorptionat 23.7 GHz, the resonant frequency of the transmitting antenna. 2.2.2 Electromagnetic Absorber Electromagneticradiationabsorptioncanbestbeunderstoodonafundamental levelusingplane-wavetheory.Thisplane-waveradiationcanbedenedbytheformseen inEquation(2.1)intermsoftheelectriceldintensity( E )ormagneticeldintensity( H ) quantities as functions of position ( x,y,z ) and time ( t ). Figure 2-6Antenna chamber with absorber. Transmitting Antenna Thin 0.5 absorber Wafer Vacuum Ring

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13 ,(2.1) Herethewavehasbeenchosentopropagateinthez-directionwhichrepresentstoward thewaferinFigure2-6,wheretheplanewaveisdenedbyitspolarizedamplitude(E0or H0),wavevector( k ),andangularfrequency( w ).Alsotheconventionofusingbold-faced typetoindicateavectorquantityhasbeenutilized.Partialabsorptionthispropagating wave is allowed by the complex k inside the absorbing material. Inotherwords,itwasthoughtthattherecouldbedivergentdirect-pathraysfrom thegaussianopticshorntransmitter.Thus,theconvolutedform(egg-crateabsorber) shouldbeanidealshapewhichallowsforamoreefcientproductionofcurrentsinside thepolyurethaneabsorber.Thiscanbedirectlyobservedfromthemaxwellboundaryconditions for the H eld, given by [Wan88] .(2.2) Thetangentialmagneticeldsinthechamberjustoutsidetheabsorberarerelatedtothe magneticeldsjustinsidetheabsorber( Habsorber)byasurfacecurrentlaunchedjust insidetheabsorber( K ).Theabsorbedenergyisthencarriedbythecurrentthroughthe absorbertogroundviatheconductiveantennachamberwalls.Notetheunitvector( n )is directed out of the absorber. Experimentswereconductedtoverifytheconvolutedabsorberastheinitialchoice tocoattheinsideofthetransmitterplatform.A1.5-inchthickconvolutedabsorberwas speciedbytheCumingsCorporation,thesupplieroftheabsorber,tohavea-40dB reectivityatthefrequencyof30GHzinthefar-eldofanantenna.Thisabsorberwas comparedtolow-prole0.5-inchthickatabsorberofthesamepolyurethan-basedmateE xyzt ,,, () H xyzt ,,, () E0H0 ejkz w t () = H chamber H absorber () n K =

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14 rial.TocheckthesespecicationsfortheUCATS,anear-tointermediate-eldantenna range,measurementswereconductedwiththeset-upseeninFigure2-7.Theresultsofthe correspondingmeasurementsareshownseeninFigures2-8(a)and2-8(b).Asabenchmarkforthisexperiment,theseresultswerecomparedtothelaboratoryfree-spacemeasurementof2-7(c),whichwasperformedinthelaboratorybypointingthetransmitterina direction with no LOS reection path. (a) (b) Absorber-Under-Test Tx Tx Aluminum 3 Figure 2-7Absorberattenuationexperiments:(a)control,(b)experiment,and(c) laboratory free space (no absorber or aluminum). Tx Free space (c) Laboratory

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15 Frequency (GHz) Figure 2-8AbsorberexperimentsinthemeasurementbandwidthoftheUCATS using(a)atabsorberand(b)convolutedabsorberasthe absorber-under-test.(a) 23.023.524.024.525.0 -25.0 -20.0 -15.0 -10.0 -5.0 0.0 Flat Absorber Aluminum 0.0 Laboratory 23.023.524.024.525.0 -25.0 -20.0 -15.0 -10.0 -5.0 0.0 Convoluted Absorber Aluminum Laboratory Free Space (b)Reection Coefcient (dB) Reection Coefcient (dB)Free Space

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16 Acomparisonbetweenthesetwoplotsshowsthattheatabsorberisbetterforthe antennasresonantfrequencyof23.7GHz,attenuatingthesignalatleast15dBbetterthan theconvolutedabsorberandabout5dBbetterthanthefree-spacemeasurement.Infact, theconvolutedabsorberhadevenworseattenuationthantheAluminumcontrolexperiment.Asaresultoftheseexperiments,theatabsorberwaschosenasthedefault absorber in the UCATS. Actualapplicationoftheatabsorbertotheantennachamberonlyincreasesits capabilityofattenuatingreectedwaves,astheexperimentsperformedabovesoughtto examinetheworst-casescenario.Theseexperimentsmeasuredreectivityatnormalincidence,asituationwhichneveroccursintheactualUCATSsincethetransmitterseffectivebeamalignswiththewaferandvacuumringaperture.Thus,theUCATSusesthe absorbertoattenuateraysdivergingfromtheLOSpath,andscatteredrays,whichhave oblique incidence to the absorbers in the UCATS. 2.2.3 Expected Le v el Adjustment Performance Thespecicationforminimumrangeofmotionforleveladjustmenthadabasisin thesystemexpectationsforclockskewinaninter-chipclockdistributionsystem.Even thoughtheindustrystandard[SIA01]hassettheglobalclockskewtoleranceat10%of thesystemclockperiod,optimalsystemperformanceoftenrequiresatighterskewtolerance.Therefore,skewaddedbythemeasurementsetupshouldbenegligible,preferably less than 0.5%. Inordertohaveaglobalskewoflessthan0.5%,ithasbeendeterminedthatthe interchipclockdistributionsystemshouldcontainlessthan10degreesofphaseerrorover a4cm2areaat24GHz.Inlinewiththeseinitialperformancebenchmarks,itmustbe

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17 requiredofthesystemleveladjustmenttobeatleast20xmoresensitive,accountingfora phase difference of 10/20=0.5 degrees at 24 GHz. Theleveladjustmentcriterioncanbedirectlydeterminedusingrst-principle electromagneticwavepropagationtheory.Foraresolutionof20xgreaterthanthespeciedphaseerror,theleveladjustmentmustbeabletocorrectforaphaseerrorof0.5 degreesat24GHz.Usingtheprincipleofopticalpathdifference[Ped93],nominally0.5 degreesforthiscase,thealignmentmustbeabletocorrectforadifferenceinheight( D= R1-R2)asseenbyplanewavespropagatingthroughoppositesidesofthe2cmwidewafer as indicated in Figure 2-9, showingtwodifferentwavespropagatingwithtwodifferentpathlengths(R1andR2).By looking at this picture, Equation (2.3) can then immediately be written down. (2.3) Herethelefthandsidecanbeseentorepresenttheopticalpathdifference,whiletheright handsidehasexpressedthatphasedifferenceintermsofanelectromagneticwavesphase argumentasafunctionofverticalmisalignment( D ),frequency( f ),andspeedoflight( c ). Inthiswaytheequationwassolvedfor D at24GHz,andequatedwithitsexpectation overthe4cm2area.Thus,theminimumtolerablealignmentresolutionwasfoundtobe D ejkRejkR12Figure 2-9Optical path difference and level adjustment of wafer. silicon wafer 0.5 p 180 ----------2 p f c --------R 2 R 1 () 2 p f c --------D ==

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18 0.0035cm-verticalovera2cmwidthhorizontal,aratioof2850to1horizontaltovertical length units. 2.2.4 Probe Isolation Module Theprobeisolationmodule,aseparatepiecewhichispositionedoverthewafer andRFprobes,isresponsibleforisolatingtheprobesandwaferfromerrantsignals.The userplacesthemodule,analuminum-tinalloy,half-pillboxstructurelinedontheinside withthesameatabsorberastheantennachamber.Themoduleisplacedinpositionafter makingconnectionstotheantennassuchthatthecirculartopsurfaceofthemoduleisparallel to the vacuum ring. In position, the module looks like the rendering in Figure 2-10. Theimportanceofthismodulecanbebestseenbymeasurementstakenwith,and withouttheprobeisolationmoduleinplaceinFigure2-11.Themoduleinthesemeasurementshaseffectivelyreducedthevarianceofthemeasurementsby1-3dBdependingon howclosethemeasurementsweretothenoiseoor.Thispicturehasindicatedthatthe laboratoryareaaroundtheUCATSpresentsanon-negligiblemultipathenvironment.The probe shield can be used to provide a degree of isolation from this type of environment. Al-Sb Exterior Shell 0.5 Flat Absorber RF Probes Vacuum Ring Si Wafer Figure 2-10Probe isolation module cross-section.

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19 2.3 Data Extraction 2.3.1 S-P arameters Likemostmicrowavemeasurementtools,theUCATSmeasuresthemicrowave scatteringparameters(s-parameters)ofthedevice-under-test,orDUT.ActingasthecontrolcenteroftheUCATS,theHP8510CVectorNetworkAnalyzer,connectingtoboththe receiveandtransmitantennas,directlyadministersthemeasurementofthetwo-portscatteringparameters[Poz98].The8510CsweepstheRFpowerateachportinfrequencyand measurestheresultingpowerlevelateachport.Associationofthemeasuredsignalin eachporttoitsparentsignalinratioformgivesthes-parameters.Equation(2.4)givesthe explicitformofhowthes-parametersareexpressedintermsofincidentandreected powers for ports of equal characteristic impedance. (2.1) Herethe i or j indexrepresenteitherportoneorporttwo.When i and j arethesame, Siirepresentsareectioncoefcientwith birepresentingthereectedvoltagewave.When theindicesaredifferent, Sijbecomesatransmissioncoefcient,meaningthat biisnowthe transmittedvoltagewave[Poz98].Ineithercase,port j sendstheincidentvoltagewave, aj.Thenetworkanalyzerdoesnotperformmeasurementswithbothportsourcesactiveat thesametime.Therefore,itbecomesnecessarytohavetheinactiveportmatchedandits sourceturnedoff.Thisisrepresentedmathematicallyinequation(2.4)bysetting aiequal to zero. AprioriinformationabouttheDUTgivesadditionalinsightsaboutitsassociated scatteringparameters.InthecaseofpassiveDUTs,thenetworkdoesnotgenerateany S ij b i a j ----a i 0 = =

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20 signal.Therefore,themaximumvalueofanyscatteringparameterisone.IftheDUTisa symmetricandbilateralnetwork,suchasapassivelter,idealmeasurementof S12and S21yieldsthesamevalue.Finally,ifthereisknowledgethattheDUTisalosslessnetwork,thismeansthatapowerbalancemaybeappliedtoeitherport,givingequation(2.5) below for measurements using the port one source. (2.2) ThisjustmeansthatthepowerthatthenetworkanalyzersendstotheDUTiseither reected back to port one, or transmitted without loss to port two. 2.3.2 Equipment Hierarch y TheUCATsusesachainofequipmentinordertoextractthes-parametersoutof theDUT,eachoneservingaparticularfunction.Figure2-11showstheblockdiagramof themeasurementsetup.Thesetuphastwobranchesofequipmentow,oneowgoing throughthetransmissionsideoftheUCATS,theotheristhereceiveside.Thevectornetworkanalyzer(VNA)formstheheadoftheequipmenthierarchy,controllingtheow througheachmeasurementbranch.Chapter3givesmoreinformationonthetransmitside of the set-up, while Chapter 4 contains the details on the receive side. S 11 2 S 21 2 +1 = RF Probes 180deg. Coupler Balun Semi-Rigid Cables Waveguide Assembly 3.5 mm K Mode Launch Isolation HP 8510C Network Analyzer Figure 2-11Block diagram of equipment hierarchy. Vector (VNA)

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21 2.3.3 Balun and Semi-Rigid Cable Assembly The180degreehybridcouplersactasbaluns,convertingthesignalfrombalanced tounbalancedtransmissionlineswithminimalloss.Theneedforthebaluncomesfrom thefactthattheVNAoperatesonacoaxial-basedsystem,atransmissionlinewithunbalancedcenterandouterconductors;andtheintegratedantennastypicallyusedintheintegratedclockreceiverspossessabalancedpairoftransmissionlines[Kim00,Flo00].One cannotsimplyconnectthebalancedlinestotheunbalancedlineswithoutdeleterious effects[Bal97]Theseeffectsintheworstcasecouldamounttoanetcurrentowto ground,reectingallpowersenttotheantenna.Therefore,thebalunassemblybecomes necessary to transition between balanced and unbalanced transmission lines. ThebalunusedintheUCATSwasofthesametypeofdeviceusedinprevious works[Kim00]exceptthatitoperatesoverabroaderfrequencyrange.Thedesignofthe balun,shownasablack-boxinFigure2-12,hasbeenspeciedtosplitpowerbetween ports2and3equallyinmagnitude,allthewhilemaintainingaphasedifferenceof180 degreesbetweenthecenterconductorsofthesesametwoports.Thespecicationsthatthe 50 W 1 2 S D 3 4 -3 dB -3 dB Figure 2-12Balun connection diagram. To Network Analyzer RF Probes SemiRigid Cables 180 Degree Hybrid Coupler (Balun)

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22 couplershouldhavelessthan1dBamplitudemismatchand10degreesphasemismatch between ports 2 and 3 were given to the vendor, Krytar. Toverifythespecications,measurementsweremadeoneachofthe2balunspurchasedfromthevendor,eachwithvaryingresults.Thebestofthetwobalunswasused throughoutthisworkasthedefaultbalun.Themismatchintransmissioncoefcientmagnitudeandphaseforthisbalunwithitssemi-rigidcablesmaybeseeninFigures2-13(a) and2-13(b).Minimumamplitudemismatchismoredesirable,sincethephasedifference between the two different cables was used to compensate for excessive phase mismatch. Thesemi-rigidcablesintheUCATShaveawiderfunctionthanjustconnecting theprobestoabalun.Aspreviouslymentioned,thephasedelaydifferenceinbetweenthe cablesareusedtocompensateforthephasemismatchofthebalun.Thus,eachbalunhas 14.019.024.0 0.00 0.20 0.40 0.60 0.80Mismatch (dB) S21-S31=Mismatch 14.019.024.0 Frequency (GHz) 174.0 176.0 178.0 180.0 182.0Mismatch Phase (Degrees) S21-S31=Mismatch (a) (b) Figure 2-13Difference(mismatch)betweenbalunports2and3intermsof(a) magnitude and (b) phase.

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23 itsownassemblyofsemi-rigidcables.Figures2-13(a)and2-13(b)showboththedenitionofmismatchandthemeasuredmismatchusingthescatteringparametersofthe default balun assembly. 2.4 Calibration 2.4.1 Introduction Whenusingavectornetworkanalyzer,measurementapparatusessuchascoaxial cables,probes,andtransmissionlinetransitionsareoftenneededtoconnecttheDUTto theVNA.Theseextraneousdevicesadderrortothemeasurementsdueinparttointernal mismatches,phasedelays,andsignalattenuation.Calibrationisthenneededtode-embed theDUTss-parametersfromthemeasureddata.Atypicalcalibrationprocedureinvolves measuringstandardizedloadswiththeextraneousequipment,andthencomparingthe loadsmeasureds-parameterswiththeirfactory-measureddenitions(standarddenitions).Inthismannerthes-parametersoftheextraneousdevicesaredeterminedandthen de-coupled from the s-parameters of the DUT. Anexampleoftwo-portcalibrationmethodisthe Short Open Load Through (SOLT).ASOLTcalibrationiswidelyusedformeasurementsinvolving3.5mmcoaxial cables.Itisperformedbyrstmeasuringa Short Open and50 W Load terminationatthe endofeachcable.Next,theportsareconnectedtogetherthroughtheirrespectivecable assemblies in the Through measurement. 2.4.2 Calibration in the UCA TS Foranytwo-portcalibrationprocedure,itisvitaltomakea Through measurement.TheproblemwiththeUCATSisthatitusestwodifferenttypesoftransmissionline antennafeeds:waveguideonthetransmissionsideandRFSignal-Signal(SS)probeson

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24 thereceiveside.Currently,acalibrationkit(standardsandtheirdenitions)existsfor eithertheSSprobesorthewaveguide.However,nokitiscommerciallyavailablefora two-port calibration using both transmission lines. Asaresult,allmeasurementsperformedinthisworkusedthe3.5mmSOLT methodusingtheHP85052Acalibrationkit.Areliable Through calibrationwasobtained usingthismethodattheexpenseofde-embeddingtheeffectsofthebaluns,probes,and waveguides. The resulting DUT is shown in Figure 2-14. Duetotheinclusionofthemismatchassociatedwithusingthebaluns,probes,and waveguideassembly,thegainand S21magnitudemeasurementstakenintheUCATSwere lowerthantheactualcasebyatleast1dB.Someofthereasonsforthisdegradation includeattenuationinthewaveguidesandprobes,andleakageradiationoutoftheprobes andcableinterfaces.Althoughtheabsolutegainmeasurementswillbeinerrorduetothis calibration,theUCATSwillstillbeabletoaccuratelymeasuretherelativegainacrossthe RF Probes 180deg. Coupler Balun Waveguide Assembly Mode Launch Port 1 Port 2 Figure 2-14S-parameter reference planes in the UCATS (effective DUT).

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25 wafersurface.ThesetypesofmeasurementissuesarediscussedinmoredetailinChapters 4 and 5. TheabsoluteS21phasemeasurementswerealsobeaffectedbythiscalibration. Propagationdelaythroughthewaveguides,baluns,semi-rigidcables,andprobesaddedto ameasuredphasedelaymuchhigherthanthetruephasedelayfortheclockdistribution system.However,onlythephasedifferencesacrossthewafersurface,nottheabsoluteS21phase, are needed to determine the clock skew. 2.4.3 Leftv ersus Right-Hand Side Probe Stations Anothercalibrationissueariseswhenmeasuringawaferusingboththeleftand righthandsideprobestationsandthencomparingthedatatakenfromeachprobestation. Forthesetypesofmeasurements,thesameprobeassembly(baluns,semi-rigidcables, andprobes)isusedtocharacterizeantennas.Whentakingmeasurementsonopposite sidesofthewafer,theprobeassemblymustbetakenofftheprobearms,rotated180 degrees,andthenre-mountedontheopposingprobestation(Figure2-15).Becausethe differential-modeSSprobeshavebeenrotatedintheprocess,measurementsperformed withopposite-handedprobestationswillbe180degreesout-of-phasefromoneanother. Therefore,inordertocomparemeasurementsacrossthewaferscenterline,180degrees must be added to the lowest set of S21 phase data of either the left-or right-hand side. Figure 2-15Leftand right-hand side measurements across a wafers center-line. + + wafer center line Left-handed SS Probes Right-handed SS Probes

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26 CHAPTER 3 INTEGRATED RECEIVE ANTENNAS Theapplicationofintegrateddipoleandloopantennastowirelesslinksforclock distributionhasbeensuccessfullydemonstrated[Kim00,Flo00,andO98].Accordingly, theseantennashavebeenexclusivelyusedasthereceiveantennasinthersttestchipfor useinevaluatingtheUCATS.Theuseoftheseintegratedantennashasbeencontinued herebecauseoftheirsmallsize,afundamentalconsiderationinmicroelectronicapplications,andtheirbalancedtransmissionlineconguration.Thus,theseantennas,particularlythedipoleantenna,areexaminedinordertounderstandmeasurementresultsofthe inter-chip clock distribution system presented in this work. 3.1 Innitesimal Dipole Antennas Fromthebeginningsofantennatheory,theinnitesimaldipole,orHertzian dipole,hasbeenusedasabenchmarkforantennadesignandanintroductiontoantenna theoryingeneral[Bal97].Furthermore,analysisofintegrateddipoleantennasfollows directly from the analysis of this fundamental antenna. The Hertzian dipole is physically f q x y z R (R, f,q) J Figure 3-1Cartesianandsphericalcoordinatedescriptionofaninnitesimal dipole antenna. d + -

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27 aninnitelythinrodofperfectlyconductingmaterial,whichmeasuresinelectricallength muchsmallerthanawavelengthofitsexcitingcurrent.Intermsofexcitation,itisfedat thecenteroftherod,suchthatonearmofthedipoleis180degreesoutofphasewiththe other arm as in Figure 3-1. Startingtheanalysis,thevectorpotentialcanbeusedtodenethemagnetic potential.Therstgoalistowritedownthevectorpotentialintermsofthecurrentstraveling along the dipole. This is shown in (3.1). (3.1) Thenextstepintheanalysisprocessistostartwiththedescriptionoftheantennaasa sourceofelectromagneticelds.Applicationofasinusoidally-varyingcurrentofangular frequency( w), theangularglobalclockfrequency tothedipoleantennaallowsanalysis toproceedwithawell-knownequation(3.2)forthevectorpotentialresultingfromthis currentdensity[Jac99].Heretheprimedpositionvectordescribesthedistancefromthe origin to the source, while the un-primed vector locates the point of observation. (3.2) Alsointhisequation,thewavevector( k) replacesthescalarwavenumber( k ).Thedirection of k is the direction of propagation and its magnitude is equal to the wave number. Thispotentialismorecommonlyknownasthetime-retardedpotential[Ula99].In thisequation,thevectorpotentialasafunctionofpositionvectorandtime A( R ,t) ,is determinedbyintegratingthecurrentdensity,writtenintermsofitsconstantspatialdistribution I0ontheantenna,overthevolumeofthesource.Alsointheequation, R representstherelativedistancefromthedipoletotheanalysispoint, k isthewavenumber,and B 0 B A == A R t () m 0 4 p -----JR () e j kRR () () RR ------------------------------------v 'dV=

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28 m0isthepermeabilityoffreespace,themediumforthisanalysis.Thisdipolessmallsize allows the integral to be easily solved for in the form seen in (3.3). .(3.3) Nexttheequationisconvertedtosphericalcoordinates,andthen(3.4)isusedtodetermine the E and B elds. Here, c is the velocity of light in free space. (3.4) Nowtheeldequationsforallspaceandtimecanbewrittendownintermsofspherical coordinates [Ula99], they have been recorded in (3.5), (3.6), and (3.7). (3.5) (3.6) (3.7) Thezero-valuedxandycomponentsof A haveforcedthe f componentof E ,andboththe R and q componentsof B tovanish.Also, h0hasbeenusedtodenotethefree-spacewave impedance of 377 W TheeldexpressionsfortheHertziandipoleoverallspaceandtimeweresolved analyticallyfromtheaboveintegralexpressions.Thistypeofsuccessisrarelyparalleled foractualantennas.Often,theintegralsaretoocomplextoevaluateinclosedformifthe AR t () z m 0 e jkR w t () 4 p R -------------------------------------I 0 d = ER t () c 2 j w -----BR t () = E R Rt () I 0 dk 2 h 0 2 p ---------------------e jkR w t () 1 kR () 2 -------------j kR () 3 -------------- q cos = E q Rt () I 0 dk 2 h 0 4 p ---------------------e jkR w t () j kR -----1 kR () 2 -------------j kR () 3 -------------- + q sin = B f Rt () I 0 k 2 m 0 h 0 4 p ------------------------e jkR w t () j kR () ----------1 kR () 2 -------------+ q sin =

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29 samemethodofndingtheretardedpotentialisused.Inanycase,simplerexpressionsare alwaysfoundwhenthedistancetothereceiver( R )movesveryfaraway,fulllingtheconditionof kR>> 1in(3.5),(3.6),and(3.7).Exactlyhowfardependsontheantenna.Forthe Hertziandipole,thisasymptoticfar-eldformcanbedirectlyobservedasthetermsof order R-2and R-3getvanishinglysmall.Theresultantfar-eldexpressionsfortheelectric and magnetic elds can be seen in (3.8) and (3.9). (3.8) (3.9) Inthenear-andintermediate-eldregions,theradiationcharacteristicsofthe innitesimaldipolecontrastswiththatforthefar-eldlimit.Lookingat(3.5),(3.6),and (3.7),andtakingthelimitas R goestozero,weseethatfortheconditionof kR <<1,the R-1termsvanishinsignicancenexttothe R-3term.Itisconventiontocallthisregionthe near-eldregion.TheregionbetweenthesetwoasymptotesatkR~1,forcingtheinclusion of all terms, is called the intermediate-eld region. Astheradiatedelectromagneticeldsbythedipolearevectorelds,theycontain afundamentaldirection,orpolarization[Wan88].Itisconventiontorefertotheelectric eldpolarizationoftheantennaasthepolarization,sincegivenanoutwardradiation direction[see(3.8)and(3.9)],thepolarizationof B follows.Thus,thepolarizationofthe dipoleantennaisinthezdirection,paralleltothelengthoftheantenna.Theradiationin thefar-eldregionislinearly-polarized,sincethe E and B eldsareinphasewithone another. E q Rt () jdI 0 k h 0 4 p R --------------------e jkR w t () q sin = B f Rt () m 0 E q h 0 ------------B q Rt () ==

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30 Inthefar-eldregion,theelectricandmagneticeldsareperpendiculartothe R direction,whichisthedirectionofpowerowandthewavevector.In(3.10),thePoyntingvector( S )hasunitsofpowerdensity.Itstime-averagedformgivesarealpowerow towards innity or radiation. (3.10) Itshouldbenotedthatlibertiesmayquiteoftenbesuccessfullytakenusingthese limits.Inapproximatingpropagationintheintermediate-eldregion,invocationofeither thenear-orfar-eldlimitissometimesjustiedforroughpredictionsifeitherlimitis almostmet.Suchapproximationsweresuccessfullytakeninthepastinclockdistribution systemanalyses[Kim01].TheseapproximationswillalsobeusedinthisworkwhencalculatingtheradiatedE-eldfromtheprototypetransmitteroftheUCATSatthewafer surface. This discussion is presented in Chapter 5. 3.2 Radiated vs. Input Po wer Astimeaveragingof(3.10)givestherealpowerdensityatadistance R awayfrom theantenna.Integratingovertheareaofthesphereformedby R yieldsthetotalpower radiated.FortheidealcaseofaHertziandipoleformedbyperfectconductors,thispower radiatedisthesameasthepowerinputtotheterminalsoftheantenna.However,imperfectionsintheconductorsandapplicationofthedipoletoasiliconsubstratecomplicate thissituation.Thepowersenttotheterminalsoftheantennais,ingeneral,notequalto the power radiated. Alumped-circuitmodelmaybeusedtosimulatethepowerowintoandoutof theantennafromanimpedancestandpoint.Powersentintofreespaceviaradiationcanbe modeledbyaresistor, Rrad,theradiationresistance.Thepowerdissipatedbythesubstrate SR t () EH =

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31 orconductorsissimilarlyrepresentedbyaresistorwithitsvaluethesameasthetotal powerdissipatedbytheantenna.ThecircuittransformationsshowninFigure3-2canbe used to illustrate how the dipole antennas input impedance models may be derived. Knowledgeoftheradiationresistance,dissipativeresistance,andthespatialdistributionoftheradiatedpowerasafunctionof R translatesdirectlytoinformationonthe radiationefciency,directivity,andantennagain.Thetypicalengineeringdenitionof efciencyissimplythepowerradiateddividedbythepowersuppliedtothetworesistancesinFigure3-2(b).Usingthe I2R denitionofpower,onecanusetheformulain (3.11) to represent the radiation efciency for the simple series circuit in Figure 3-2(b). (3.11) Theantennadirectivityisdeterminedbytheeldsdescriptionoftheradiation. Thedirectivityisameasureoftheantennasabilitytofocusradiatedenergy,asaconsequence,thisvalueisapurenumberoftenexpressedinthe(dB).Themathematicaldeni++++Figure 3-2Variouslevelsofsmalldipolecircuitmodels:(a)idealcaseand(b)nite conductivity dipole. RlossRradRradVsVsVsVs(a) (b) e rad R rad R rad R diss + --------------------------------=

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32 tionsofthedirectivityaregivenin(3.12)and(3.13).Here,theaveragepowerdensity radiated ( Sav) at R normalizes the maximum power density at the same distance ( Smax). (3.12) (3.13) Itisalsotypicaltodeneadirectivitypattern,whichresultsfromusingthespatially-dependentpowerdensity(3.13)insteadofthemaximumpowerdensityin(3.12). Thenormalizationof S ( q,f )versusitsmaximumvalueiscustomarilycalledtheradiation pattern of an antenna. TheantennaparameterwhichmostdirectlyrelatestothemeasurementsperformedintheUCATSistheantennagain,whichisjustthedirectivityofanantenna scaledbytheradiationefciency.Thephysicaldenitionisthepowerradiatedoverthe powerinputtotheantenna.Thesedenitionsaregivenin(3.14)and(3.15).Thetopequationshowshowanantennagainappliestoanantennaoperatinginsignaltransmission modewith etxrepresentingthetransmittersradiationefciency.Theabbreviationof tx and rx insubscriptswillbeusedtodenoteparametersofthetransmitterandreceiver, respectively. (3.14) (3.15) D S max S av ------------= D qf () S qf (,) S av -------------= G tx e tx D tx P rad P in -----------G rx e rx D tx P out P inc -----------

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33 Equation(3.15)depictshowtodescribethegainoftheantennaoperatinginreceivemode. Thepowerradiatedisreplacedbythepowerdetectedbythereceiveratitsterminals,and herethepowerinputtotheantennaistheincidentradiation.Also,thereceiversradiation efciency has been represented by erx. ForthepurposesofdescribinganRF-link,dependentonbothatransmittinganda receivingantenna,adifferentdescriptionofgainmaybeused.Inthiscase,thereceiver antennagain,transmitterantennagainandtheattenuationduetothesphericalspreading of the free-space radiation are combined in (3.16) to form the system antenna gain ( Gsys). (3.16) Thisequationdescribesthegainofanantennasystem,whichisperfectlymatchedatboth thereceiveandtransmitports.Inthisspecialcase,thesystemgainwouldbeequalto |S21|2. G sys G rx G tx l 4 p R ---------2 = Recei v er + RL |S11|2(1 |S11|2) R |S22|2(1 |S22|2) F igure 3-3Schematic for transmitter-receiver link visualization.Pin1 2 -VinIin=*Pout1 2 -I2RL= T ransmitter VinIin

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34 Asapracticalsystemofantennaswithaniteamountofpowerreectionateither port,theUCATSmuststillbeabletoextractthesystemantennagainoutofthemeasured s-parameters.Thesemismatchlossescanbetakenintoconsiderationbyrevising(3.16) intotheversionseenin(3.17).ThisequationisillustratedinFigure3-3andrepresentsthe power traversing the reection boundaries at the input or output ports. (3.17) ThisequationiscalledtheFriistransmissionformula(3.17),andhasbeenwidely utilizedintheeldofelectromagneticmeasurementstondanunknownantennagain usingatransmittingantennawhosegainpatternisknownapriori.FortheUCATS,the systemgainwithouttheextractionoftheindividualantennagainsisextensivelyused.In this work, the system antenna gain will be called the gain. 3.3 Inte grated Antennas in the UCA TS ThesetofintegratedantennasusedintheUCATSrepresentsthesuccessofpast researchresults[Kim00].[Kin91],and[Kat83].Thus,theloopantennawasusedalong withlinear,zig-zag,andfoldeddipoleantennasona20 W -cmsubstratemeasuring0.5 mm in thickness. These antennas have been photographed and shown in Figure 3-4. Foracomparisonbetweentheantennas,thetwo-ports-parametersweremeasured intherangeof23-25GHz,whichisthedefaultmeasurementfrequencybandwidthofthe UCATS.Fromthe S11data,theinputimpedancemaybeextractedusingtheformula given in (3.18), with Z0 being the 50 W characteristic impedance of the s-parameters. (3.18) S 21 2 1 S 11 2 () 1 S 22 2 () G sys = Z in Z 0 1 S 11 + () 1 S 11 ----------------------=

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35 Figure 3-4Waferphotographshowingtheintegratedantennasusedasthe receiver in the UCATS. Zig-zag Dipole Linear Dipoles Loop Folded Dipole 23.023.524.024.525.0 Frequency (GHz) 0 50 100 150Resistance (Ohms) 23.023.524.024.525.0 Frequency (GHz) -100 -50 0 50 100Reactance (Ohms) Folded Dipole Long Dipole Loop Small Dipole Zig-Zag Dipole Figure 3-5Inputresistance(a)andreactance(b)forvarious integrated antennas. (a) (b)

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36 TheinputresistanceandreactancehavebeenplottedversusfrequencyinFigures 3-5(a)and3-5(b),respectively.Periodicresonancesevery0.5GHzcanbeobservedin theseplots.Theseresonancescouldbedueinparttohighcouplingbetweentheantennas onthetestchip,orinaccuraciesassociatedwiththecalibration[Bal89].Theseplotsalso showthat,foreachantenna,theresistancepeaksatthereactancezerocrossings,correspondingtoresonancepoints.Overthisbandwidth,theresistanceofthefoldeddipole appearsclosertothe100 W characteristicimpedanceofthedifferential-modeprobesand clock receivers. Thesame2-ports-parameterdatacanbeusedtocomparethegainsamongthedifferentintegratedantennaswhenusingequation(3.17).Thesedataweretakeninthe UCATSwithaspacingof3inchesbetweenthetransmitterandreceiver.InFigure3-6,it canbeseenthatthefoldedandzig-zagdipolehavethehighestgain,dependingonthefrequencyofobservation.Sinceitsradiationpatternnullisinthedirectionofthetransmitter, theloopantennahadthelowestgainofallthemeasuredintegratedantennas.Itwasthe gaindataofFigure3-6whichhasledtotheselectionofthefoldeddipoleastheprototype receive antenna used in the initial characterization of the UCATS. 23.0 23.5 24.0 24.525.0 Frequency (GHz) -55.0 -50.0 -45.0 -40.0 -35.0Gain (dB) Folded Dipole Linear Dipole (2 mm) Loop Linear Dipole (1 mm) Zig Zag Dipole Figure 3-6Comparisonofthesystemgainusingdifferentintegratedantennas as the receive antennas, taken at R= 3 inches.

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37 CHAPTER 4 PROTOTYPE TRANSMITTER AND WAVEGUIDE ASSEMBLY ThischapterdescribestheprototypetransmittingantennausedintheUCATS.As theantennainquestionisagaussianopticsantenna(GOA),possessingawaveguidefeed structure,thischapteralsoprovidesaquickguidetotheapplicablewaveguidetheory.The discourse then broaches the topic of GOAs and the type of elds they radiate. 4.1 W a v e guide Assembly 4.1.1 Basic W a v e guide Theory Asthefeedtotheprototypetransmitterisawaveguide,itbecomesimmediatelynecessary to understand the characteristics of the electromagnetic elds inside a waveguide. Instead of a general treatment using an arbitrary waveguide, found in such sources as [Bal89],[Jac99],or[Col60],onlythestructureofinteresttothemeasurementsystem,the rectangular waveguide (RWG) is considered. The coordinate system used for the discussion is shown in Figure 4-1 a b z y x ba SFigure 4-1Rectangular waveguide: coordinates, dimensions, and cross-section.

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38 Thisdrawingreplicatesthecross-sectionofthetypeWR-42waveguideusedinthe UCATS,withthelargelateraldimension(a)measuring0.42inchesandthesmalllateral dimension (b) equal to 0.17 inches. ReferringstilltoFigure4-1,thefoursidewallstogetherformthesurface S ,the transverseboundary.Whiletheeldsareconnedtransversely,thesolutioninthez-directionresemblesthatofplanewavepropagation.Thusthefunctionaldependenceofthevector eld expressions takes the form [Jac99]: .(4.2) Heretheconstantamplitudetermsoftheplane-waveeldexpressionsbecometransversely dependent functions [ E (x,y) and H (x,y) ]. Byassumingsteady-state,sinusoidalsources,Maxwellsboundaryconditions,and thesource-freeformsofMaxwellsequations,theeldexpressionsinEquation(4.2)can besolvedforusingthepartialdifferentialequationeigenmode-eigenfunctiontechnique [Sni99]. The equation to be solved is of the form: .(4.3) Here y couldbetakenasthez-componentofeither E or H ,dependingonthemodeof propagation.Thetransversesolutionsarefoundbysubstitutingtheeigenfunctionsinto Maxwells equations (B.4). Asthissolutionisdescribedinavastnumberofmicrowaveandadvancedelectromagneticssources[Jac99],[Poz98],[Col66],[Bal89],theeigensolutionsarejustquoted here.Thesolutionscanbeclassiedintotwoforms:TE,wheretheE-eldisexpressedas beingcompletelytransversetothedirectionofpropagation,thez-directionandTM, E xyzt ,,, () H xyzt ,,, () E xy () H xy () e jkz w t () = 2 y k 2 y +0 =

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39 wheretheH-eldispurelytransversetothez-direction.Theeigenfunctionscanbe expressedasfunctionsofconstrainedwavevector( kc)andcross-sectionalgeometry( a,b ): (4.4) Inthisaboveequation,theTMeigenfunctionisrepresentedbythetopeigenfunction( Ez), whiletheTEeigenfunction( Hz)isdisplayedinthebottomentry.Theeigenfunctionsare inturnlinkedtotheirrespectiveeigenvaluesbytheindices m and n ,andthecorresponding arbitraryconstants( Amnand Bmn).Thetransversevectorcomponentsolutionsandthedual eldexpression,canthenbedeterminedfromtheeigenfunctionsusingexpressions deriveddirectlyfromMaxwellsEquations[Jac99](AppendixB).Itshouldbeparticularly notedthatonlytheTEeigenfunctioncanbenon-zeroforzero-valuedmodalindices,and even then, only one index can be zero at a time. Theeigenvaluesbecomeevidentwhensubstitutingthepreviously-listedeigenfunctionsintotheoriginalwaveequation,(4.3).Theconstrainedwavevectorthenrelates the free-space wave vector ( k ) and the modal indices as .(4.5) Thisexpressionreduceseasilytothecutoffmodeexpressionwhenevanescent modesareexcluded[Col60].Thismeansthatthesquarerootargumentmustbegreater thanorequaltozeroin(4.5).Nowtheexpressionforthelowestfrequencythatamodecan propagate down the wave guide, the cutoff frequency ( fc mn), can be derived: E z xyz ,, () H z xyz ,, () E mn m p x a ---------sin n p y b --------sin H mn m p x a ---------n p y b --------cos cos e jk c z = k c k 2 m p a ------2 n p b -----2 k 2 p l -----= =

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40 .(4.6) Here m and e arerespectivelytherelativepermeabilityandrelativepermittivity.AsignicantobservationisthattheTEmodecanpropagateatlowerfrequenciesthantheTM mode, since only the TE can have zero-valued m or n Whenthisresultisapplieddirectlytothemeasurementspectrum,0.045-26.5GHz, oftheUCATS,keystatementscanbemade.First,onlytheTE10modecanbedetected propagatinginsidethisfrequencyband.TheTE10cutofffrequencywascalculatedat14.05 GHz,whilethecutoffforthenextmode,TE20wasfoundtobe28.10GHz.Theword, ideally,mustbeinsertedintheabovestatementswiththecutofffrequencyvaluesince alloftheequationswerederivedforasectionofwaveguidewithinnitelyconducting walls.Alsofabricationprocessvariation,andmeasurementresolutioncanalsobelabeled as reasons for deviation from this ideal cutoff frequency calculation. Ifawaveguideisniteinlength,cappedbymetalendsinthezdirection,it becomesaresonantcavity.Thismeansthatthewaveguideeigensolutionsmustinclude anotherindexedterminthez-direction,andtheeigenspectrumbecomesmorecomplicated thanbefore.Howeverthisrepresentsaworst-casescenario,andsinceideallybothendsof thewaveguidearematchedintheUCATS,theeigenspectrummoreresemblesthatofa waveguide than that of a resonant cavity. 4.1.2 Coax-W a v e guide T ransition Thecoax-waveguidetransitionwasusedtotransformthesignalfromthe3.5mm coaxialtestcablestotheWR-42waveguidepropagationenvironmentrequiredbythe horn.ThisisconceptuallyillustratedinFigure4-2.Theparticularcouplingmechanism f c mn 1 2 pme ----------------m p a ------2 n p b -----2 + =

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41 usedintheassemblywasamonopoleprobe.ThisdevicewasselectedforitsefcientcouplingtotheTE10mode[Pozar].Thecompleteanalysisofthisstructurecanbequitecomplex,andiscoveredinsuchworksas[Col60]and[Mar48],andisbeyondthescopeofthis work.TheassumptionthatonlytheTE10modehasbeenexcitedgreatlysimpliesthe analysis [Poz98] and a rst order expression for the input resistance is given by the (4.7). (4.7) Here,theheightoftheprobehasbeenapproximatedtotherstorderof b .Alsowehave continuedtousethefree-spacewavevector k ,thepermeability m0,andpermittivity e0of free-space, and the waveguide transverse dimensions ( a and b ). From(4.7)thescatteringparameterscanthenbedirectlydeterminedusingbasic microwaverelations.S11canbeexpressedasafunctionofcharacteristicandinputimpedance.Furthermore,(2.5)canbeinvokedtondanequationforthetransferredpower, | S21|2, shown in (4.8). However, for the purposes of calculating the path gain in terms of (4.8) Coax 3.5 mm Monopole Probe h Figure 4-2Simplied drawing of coax-waveguide transition. R in b a -k m 0 e 0 -----k 2 k c 2 () 12 / = S 21 2 1 S 11 2 =

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42 theFriisformula,ithassufcedtosimplymeasuretheattenuationonthenetworkanalyzer, the results can be seen in Figure 4-3. Thes-parametersweremeasuredbyconnectingtwocoaxial-WGtransitions togetherincascadewiththeportreferenceplaneslocatedatthecoaxialinputofeachtransition.Theattenuationthroughonecoax-RWGtransitionwasmeasuredat0.37dB,this meansthattheattenuationthroughonetransitionwouldbeabout0.2dB.Returnloss shouldbegreaterthan10dBforone-transition,sincetheantennaisclosetoamatched load. 4.2 Prototype T ransmitter Theprototypetransmitterconsistsofanabruptjunctionmodelauncherandthe GOA.ThemodelauncherconvertsthemodesfromtheTE10modespropagatinginthe rectangularwaveguidetotheTE11andTM11modes.Thelattermodesareneededbythe 14.0 19.024.0 -15.0 -10.0 -5.0 0.0S21 (dB) 14.019.024.0 Frequency (GHz) -30.0 -20.0 -10.0 0.0S11(dB) Figure 4-3Scattering parameters for two cascaded coax-RWG transitions

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43 GOAtolaunchgaussianwaves,whichresembleplanewavesatsufcientlylargedistances. 4.2.1 Abrupt Junction Anabruptrectangular-circularwaveguidetransitionhasbeenbuiltintothehorn, matingdirectlytotherectangularwaveguidedescribedintheprevioussection.Theabrupt junctionrstbroadensitsrectangularcross-sectionbeforeabruptlychangingtoacircular waveguidecross-section.Intermsofmodes,thisjunctionhasbeenshowntoexcitethe HE11mode,acombinationoftheTE11andTM11modes,inthecircularwaveguidesectionofthejunction[Eng73].Thismodehasbeenthoroughlyresearchedinthepastanefcient mode for the production of gaussian beams [Cla69, Cla71]. 4.2.2 Circular W a v e guide Thetransitiontothecircularwaveguidenecessitatestheneedtoknowthetypeof modesallowedbythisstructure.Liketheprevioussection,thedevelopmentoftheeld theoryinvolvesndingtheeigensolutionswhichsatisfyboththewaveequationandthe boundaryconditionsontheedgeofthecircularwaveguidecross-section.Asthedetailed andcompletesolutionmaybefoundinmostgraduateelectromagneticstextbooks,suchas thoselistedintheprevioussection,heresimplythesolutions,showingrsttheeigenfunctions in (4.9) in cylindrical coordinates ( r f ,z) are summarized. .(4.9) The J (...)istheBesselfunctionoftherstkindoforder m ,usingtheradius, a, ofthecircularwaveguideintheargumentforcesthefunctiontomeettheboundaryconditionsat E z rf zt ,,, () H z rf zt ,,, () A mn J m z mn r a -------------B mn J m x mn r a -------------e jm f e jkz w t () =

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44 the n -thzero( zmn)oftheBesselfunction.Similarly,J(...)isthederivativeoftheBessel functionoftherstkindoforderm.The xmntermisthe n -thzeroforthesame m -thorder derivative of the Bessel function. Linkedtotheeigenfunctionsbythemodalindices,theequationsfortheeigenvaluesdictatethemodespropagatingabovecutoffinthetransmittingantenna.Following again the procedure outlined in 4.1.1, the TE eigenvalue equation is .(4.10) Thus,fromtheaboveexpressionsthemodespropagatinginthefeedoftheGOAaredetermined.Thecutofffrequencycanbefoundusingthesameprocedureasintherectangular waveguide case. 4.2.3 Gaussian Optics Horn Antenna The GOA consists of two main parts: the conical horn with tapered corrugation, or scalarhorn,andthesphericallenswhichcoversthescalarhornsaperture.TheGOAand itscomponentsareshowninFigure4-4.Thehornantennais,byitself,alreadyahighly directiveantenna,theadditionofthelensonlyincreasesitsabilitytofocusRFpower.The abilityofthehorntolaunchgaussianwavesevenintheneareldiswhathasledtoits selection as the prototype transmit antenna. TheinternalgeometrywhichcausestheHE11sphericalmodestoexpandtoagaussianmodeisthecorrugationontheinsidesurfaceofthehorn.Itscorrugationteetharelinearlytaperedfromlength(L1)totheshorterlength(L2)locatedneartheapertureofthe horn.Also,thethicknessesoftheteeth(t1)andgaps(w1)increasetot2andw2asthecorrugation approaches the aperture of the horn (Figure 4-5). k c k 2 x mn a ---------2 k 2 p l -----= =

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45 Thesphericalmodespropagatingacrossthecorrugationsurfacearereadily expandableintermsofaGaussian-Hermiteseries.Theradiatedeldsarealsoofthis form,allowingtheeldstobeexpressedintermsofgaussianmodeseveninthenearto intermediate-eld region [Pad87, Gol82]. Fromageometricopticsperspective,thegaussian-spreadingpowerinthefar-eld regioncanberepresentedbyagaussianbeamofrays[Ped93].Theapplicationofthelens Figure 4-4Gaussianlens-hornantennashownwithsourceandsourceimpedance (Zs). Integrated Circuits (PC Board/MCM) ZS Receiving Antennas Corrugated Horn Antenna Dielectric Lens RWG Feed Abrupt Junction w1 t1 Circular WG Feed Horn Aperture t1 w2 L2 L1 Figure 4-5Tapered corrugation on one half of the conical horn antenna.

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46 totheantennalimitsthedivergenceofthebeam,increasingboththedirectivityandgainof theantenna.Theapplicationofgeometricopticstosubmillimeterwaveantennadesignis termed quasi-optical analysis. TheGOAwasdesigned,fabricatedandtestedbyMilltech,LLC.Usingthedrawingssuppliedbythemanufacturer,theantennawassimulatedusingAnsoftHFSS,a nite-elementssimulator.TheresultsaresummarizedinTable4-1.Themaximumantenna gainmeasuredbyMillitechintheirfull-anechoicchamberwas17.7dBi,givenindecibels withrespecttoanisotropicradiators,whiletheniteelementprogramcalculatedagainof 18.5dBi.Fordenitionsofthesefar-eldantennaparameters,[Bal89]or[Ula99]canbe consulted.TheAntennaGainPattern(AGP)inunitsofdecibelswithrespecttoanisotropicradiator(dBi)isdenedby(4.11).AGPisoftenplottedversusspatial f and q .Figure B-2showstheAGPofthehornantennaassimulatedinHFSS.Insuchaplot,Half-Power BeamWidth(HPBW)canbedirectlydeterminedbyndingtheamountofcross-sectional angle in degrees the main lobe covers between the 3 dB points. (4.11) Here G( q,f ) isdenedtobethetransmittersspatially-dependentantennagain,measured atanarbitrary R valueinthefar-eld.Thisgainisnormalizedbythegainofanisotropic point radiator ( Giso) for the same distance. ThisdifferencebetweenthesimulatedandcalculatedvaluesoftheGOAsmaximumgainandHPBWsisconsideredacceptableintermsofarstorderapproximation. Thedifferencestemsmainlyfromtheboundaryconditionsimposedontheniteelement modelofthehornandtheexclusionofthecorrugation.Forreasonsofconvergenceand AGP qf () 10 G qf () G iso -----------------log =

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47 simulationsizeintermsofagoodaspectratio[Sad91],corrugationinsidethehornhas beenleftoutofthemodel.Keepingthecorrugationinthemodelwouldcausesimulation sizetoexceedavailablecomputerresource.Also,forsimplicitythewallsofthehorn antenna have been dened as perfect electric conductors, or E-walls. Theniteelementmodelhasprovenitselftobeanacceptablecomputermodelin approximatingthefar-eldradiationoftheGOA.Theresultsofthefar-eldcomparison canbeseeninTable4-1below.Thisdatatendtosupportthestatementthatthelenscharacteristicstendtodominatethefar-eldcharacteristicsoftheGOA,whichbecomes important later in making gaussian-beam approximations. Theeldsinthefar-eldregionaremucheasiertocalculatethantheeldsinthe near-eldregionfortheGOA.Unfortunately,theUCATSoperationisnotinthefar-eld oftheantenna,asperopticalgaussianbeamtheory[Ped93].Equation(4.12)showsthe calculationofthefar-eldlimit,RFF,Thegaussianbeamwaist(seeFigure4-6),isthe minimum width ( w0) of the gaussian beam, and l is still the wavelength.The beam waist (4.12) Table 4-1 Finite Element Model (FEM) vs. Measured Antenna Parameters for the GOA ParameterFEMMeasuredDifference Azimuthal HPBW (Degrees) 2125.173.88 Elevational HPBW (Degrees) 2427.233.23 Azimuthal Peak Gain (dBi) 18.517.70.8 Elevational Peak Gain (dBi) 18.517.80.7 R FF p w 0 2 l ----------

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48 inturnwasfoundbyusingthefar-eldmeasurementdatasuppliedbythemanufacturer using (4.13). Here Q is the same as the measured HPBW. (4.13) Insummary,fora1.25cmwavelengthand1.81cmbeamwaist,far-eldmeasurementsshouldbetakenatdistancesmuchlargerthan8.23cm,or3.24inches[Gol82]. SincemeasurementsintheUCATSarelimitedinreceiver-transmitterseparationto7.5 inches,measurementstakenusingthissystemareintheintermediate-tonear-eldregion. Forapproximationpurposes,propagationintheintermediate-tonear-eldregions foraconicallens-hornwithtaperedcorrugationcanbeputintogaussianmode form[Gol82].Forsimplicity,couplingtohigherordermodeshasbeenneglected.Using theseapproximations,thecomplexelectriceldsolutioncanbewrittenintheformof equations (4.14), the equation for the fundamental gaussian mode (TEM00). (4.14) Itshouldbeobservedthatboththephaseandamplitudeoftheaboveexpressionhave gaussiandistributions.Therefore,boththephaseandamplitudeapproachauniformdistributionforlargedistancesfromthetransmitter,asdepictedinFigure4-6.Thisapproximationalsoinvolvesplacingthelocationofthebeamwaistatthebeginningofthelens [Gol82]. The location of the beam waist determines the origin of the coordinate system. w 0 2 l pQ ------= E r z () E 0 w 0 wz () -------------e jkz j l z p w 0 2 ---------atan exp jk r 2 2 Rz () -------------exp r 2 w 2 z () -------------- exp = wz () w 0 1 l z p w 0 2 ---------2 + = Rz () z 1 p w 0 2 l z ---------2 + = where:

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49 UsingtheknowledgethattheGOAsradiationcanbedescribedaccordingtogaussianbeamtheory,anexpressionforpowercanbederived.Equation(4.15)istheresultof usingthetime-averagedPoyntingvectorrelationshipof(3.10)andMaxwellsequations (B.5).TheE-eldinthisequationisthesameas(4.14).Thisequationisthepowerina planewave( Ppw),where Z0isthewaveimpedanceoffreespace.Theresultsofthesecalculations were used to compare with the measured data in Chapter 5. (4.15) WiththegaussianmodeequationsoftheGOA,itisthenconvenienttopredictthe measuredpowerfortwodifferenttransmitter-receiverspacings.UsingEquations(4.13) and(4.14),spatialdistributionscanbeplottedforbothpowermagnitudeandE-eldphase with x and y asthedependentparametersforeachconstant-zsurface.Theseequations, however,shouldnotbeusedtocalculatetheabsolutegainbetweenthetransmitterand receiver.Theydonotaccountforthetransmissionthroughthewafer,standingwaves betweenthewaferandlens,diffractionthroughthemeasurementaperture,orreected w0GOA wafer x z y Figure 4-6Gaussian mode radiation from the GOA. Origin ,rPpw1 2 -E2Z0--------=

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50 wavesinsidetheantennachamber.However,thegaussianmodeequationsareusefulto predictthepowerandphasedifferencesacrossthewafersurface.Conveniently,thistype ofdifferenceanalysisiswhatismostimportantforanalysesofclockskewinaclockdistributionsystem.Chapter5containstheresultsofthegaussianmodecalculationsthein the context of UCATS measurements.

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51 CHAPTER 5 PROTOTYPE SYSTEM MEASUREMENTS Utilizingtheultra-compactantennatestsystem,measurementswereperformed usingatestchipdesignedtocharacterizetheplanarqualityofthewaveformincidentupon thechipinthecontextofwirelessclockdistribution.Inaddition,thedataweretakenin order to verify the measurement consistency of the UCATS. 5.1 T estchip Design Thetestchipusedinthischapterwasdesignedsothatthespatialdistributionof poweracrossthewafersurfacecouldbedetermined.Thechipcontaineda13x13arrayof antennacells.Eachcellcontainedacollectionof6differentintegratedantennas.Thepresenceofthevacuumringlimitedthetotalnumberofmeasurableantennas.Sinceportions ofthewaferwerecoveredbythevacuumring(Figure2-5),therewereantennaswhich eitherfullyorpartiallyblockedbythevacuumring.Theseantennashadimpedanceand Figure 5-1Testchip layout showing measurement aperture. Measurement Aperture Footprint

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52 radiationcharacteristicsmuchdifferentthanthoseantennasinthemorecentralcellsand wereomittedinthestatisticalanalyses.Thetotalarrayalongwiththefootprintofthemeasurementaperture,asshowninFigure5-1.Notethateachcellhasbeenlabeledbyrowand column in the array using a matrix-style notation. 5.2 Spatial W a v efront Uniformity Measurements 5.2.1 W a v efront Uniformity Mapping at 3-Inch Separation Inordertoverifytheuniformityofthetransmittedwaveform,acriticalparameter forclockapplications,measurementsweremadeonthefoldeddipoleelementineachcell. Thecollectionofcellswaschosentobea7x9setofcellsawayfromtheedgeofthevacuumring.Forcomparisonpurposes,fourantennaslyingontheedgeofthemeasurement aperturewereincludedinsomeoftheplots.Also,twosetsofdataweregathered:onewith areceiver-transmitterspacingof3inches,andtheotherattheUCATSmaximumspacing of 7.5 inches. Thedatawereassembledintoaseriesofspatialdistributionplotsofrelativegain andphaseinordertobettervisualizetheuniformity.Thespatialgainplotswereextracted usingequation(3.12)andtherelativephasedistributionswereplotteddirectlyasthephase of S21.Allthedatausedintheseplotshavebeennormalizedtothecentercell,#66,and analyzed at 23.7 GHz, where the S11 of the transmitter is a minimum. Correspondingly,thephasealsohadtobenormalized.Phasedataontheright-side ofthewaferwasconsistently180degreesout-of-phasewithdataontheleft-sideofthe waferduetotheprobingissuesdiscussedinSection2.4.3.Therelativegainandphase dataforareceiver-transmitterspacingof3incheswerecollectedandplottedinFigures 5-2and5-3.Thegainfromthiscentercell,wasobservedtobeconsiderablyhigherin value than that of adjacent cells, by about 6.8 dB. The antennas lying over the edge of

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53 Relative Gain from Center Point (dB) Relative Gain from Center Point (dB) Y Position (cm)X Position (cm)Figure 5-2Spatialdistributionofrelativegainfromcenterfor3-inchseparation (mean= -7.52 dB, standard deviation= 2.85 dB).

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54 Figure 5-3Spatial distribution of relative phase for 3-inch separation (mean = -30 degrees, standard deviation= 18.5 degrees).Y Position (cm)X Position (cm)Relative Phase from Center Point (degrees)

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55 thevacuumring,seenasthefourcornerpointsinFigures5-2and5-3,weremeasuredto havegainlowerthanthecenterbyapproximately25dB.Overalltheaveragegainrelative tothepeakvalueatthecenterwas-7.52dBwithastandarddeviationof2.85dBexcluding the four corner points. Thephasedistributionforthe3-inchseparationmeasurementsvariedinboththe positiveandnegativedirectionsfromthecentraldatum.However,thepointswhichvaried inthepositivedirectionfromthecenterwerecelllocations64,65,and67.Again,thecornerpointsdeviatedsignicantlyatanaverageof-77degreesfromthecentervalue.Altogetherthemeasurementstatisticsforthephasedataamountedtoanaveragerelativephase shift of -30 degrees from cell #66 with a standard deviation of 18.5 degrees. 5.2.2 W a v efront Uniformity Mapping at 7.5-Inch Separation Eventhoughpracticalapplicationofthewirelessclockdistributionrequiresthe receiverandtransmittertobeplacedataminimumdistancefromoneanother,forcomparisonitwasusefultoperformthesamemeasurementsatadistanceclosertothefar-eldof thetransmitter.Thedistanceof7.5incheswaschosenbecauseitcoincideswiththemaximumrangepossibleintheUCATS.However,thelowS21measuredatthisspacing,from therangeof(between-45and-58dB),meantmorevarianceinthemeasurementsdueto thecloserproximitytothe-75dBnoiseoorofthemeasurementsystem.Thespatialdistributionpatternofthegain(Figure5-4),likeits3-inchseparationcounterpart,was peakedatthecentercellofthemeasurementarray.However,therestofthedistribution didnotfalloffinthesamemonotonicmannerasthedatasetinFigure5-2.Instead,there wasasetofpeaksandnullslocatedjustoutsidethecenter,varyingabout3dBfromcrest totrough.Nevertheless,excludingtheedgepointslocatedontheedgeofthemeasurement

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56 Relative Gain from Center Point (dB) Y Position (cm)X Position (cm)Figure 5-4Spatial distribution of relative gain for 7.5-inch separation (mean= -3.77 dB, standard deviation= 2.90 dB).

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57 Figure 5-5Spatial distribution of relative phase for 7.5-inch separation (mean= -15.6 degrees, standard deviation= 10.5 degrees).Relative Phase from Center Point (degrees) Y Position (cm)X Position (cm)

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58 aperture,thedatadidhavelessvariancethanthe3-inchdatawithameanrelativegainof -3.77dBandastandarddeviationof2.90dB.Interestinglyenough,thecornerpointsvariedlessfromthecenterthantherstsetofdata,rangingfrom-10to-20dBdownfromthe center. Correspondingly,thephasedataalsosawasetofminimaandmaxima,distributed aroundthecenterpoint.Alsofollowinginthesametrendasthe3-inchseparationdata,the positivedeviationwasclusteredaroundthecenter,withcell#67havingavalueof12 degreesabovethecenterpoint.Themeanforthissetofdatawas-15.6degreesphase delay relative to the center, while the standard deviation was 10.5 degrees. 5.2.3 Estimated Clock Sk e w from the Uniformity Data Oneofthedeningmetricsintheanalysisofclockdistributionsystemsisthe clockskew.Therefore,itisdesirabletobeabletodeterminethetotalclockskewofthe transmitter-receiversystemundertestinsidetheUCATS.Findingaconservativeestimate forclockskewoftheprototypeGOA/foldeddipolecombinationinvolvessimplydeterminingtherangeofdeviation,dividingby8,andthendividingby360degreestondthe clockskewasapercentoftheperiod.Thefactorof8inthedenominatorisduetothefact thatthecurrentwirelessclockdistributionreceiversfeatureadivide-by-8countingarchitecture. Usingthedatafromtheuniformitymeasurementsintheprevioussectionsandthe formula for clock skew, explicitly written in equation (5.1). (5.1) Skew MaxMin 8 -----------------------------1 360 ----------=

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59 Clockskewfortheprototypesystemmaynowbedetermined.Equation(5.1)onlycalculatesskewbasedonphasedata,thefactthatskewmayalsobedependentonthesignal amplitudedeviationacrossthewaferisalsoconcern.This,however,isleftforfuturework, as it is currently believed that the skew is much more sensitive to phase mismatches. Theresultoftheskewcalculationat3GHzhasbeentabulatedinTable5-1.A clockskewof1.7%oftheperiodfoundforthe7.5-inchseparationdataand3%clock skewwascalculatedforthe3-inchcase.Botharewellwithinthecurrentskewtolerance limitsformicroprocessors.Inaddition,theseskewvaluesrepresentedsynchronization overa3.8cmx3.1cmareaat3GHz,whichisamuchlargerareathanpreviouslythought possible. 5.2.4 Comparison with Gaussian Beam Theory and FEM Simulations Thegaussianmodeequationsofthelens-hornantenna(4.14)canbeusedwith varyingsuccesstopredictthemeasuredwavefrontsdetectedwhenthefoldeddipolesare probed.Thevariedsuccessmaybeparticularlyseenwhenthedatacollectedduringthe previouslydescribeduniformitymeasurementsetsat23.7GHzareorganizedbyrowsand comparedwiththeplotsaccordingtoequation(4.15)usingthecoordinatesystemdened inFigure4-5.Theresultsofthiscomparisonbetweenthegaussianoptics(GO)andFEM calculationsandthemeasureddataforrow6,gainandphase,havebeenplottedinFigures 5-6(a)and5-6(b),respectively.Thereweretwosetsofmeasureddata,correspondingto Table 5-1Clock skew for prototype external clock distribution system Measurement Set Mean (Degrees) Range (Degrees) Skew (% Period) 3 inch-15.6753.0 7.5 inch-10.6501.7

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60 thedatatakenfromprobestationsonoppositesidesofthewafer.Forthesetwoplotsthe measureddatacorrelatedmorewiththecalculatedtowardstheedgeofthewafer,andthe correlationwastheworstwhenthedistancefromthewafercenter( r )rangedbetween0.5 to 1 cm. Inaddition,theseplotsshowthattheFEMsimulationsagreedmuchbetterwiththe measuredphasedatathanthegaussianopticscalculationswiththeexceptionofthe r =1.9 cmpoints.TheFEMphasesimulationsontheedgeofthewaferwerepossiblyaffectedby edgecurrents,whichwerecausedbyedgediffractionintheFEMmodel(FigureB-4). Conversely,theGOcalculationswerelargelyinerrorforthemiddlethreedatapoints,but morecloselymatchedthemeasureddataattheedgepoints.(Thisdisagreementbetween theGOcalculationsandthemeasureddatawasexpectedsincethegaussian-beamcalculationsdidnotaccountforanyreectedsignalsorstandingwavesbetweenthewaferand lens.)Distance from Center (cm)Figure 5-6CenterrowcomparisonbetweenGOcalculated,FEMsimulated,and measured (a) gain and (b) phase at 3-inch transmitter-receiver spacing. (a) (b) -2.0-1.00.01.02.0 15.0 10.0 -5.0 0.0 -2.0-1.00.01.02.0 -55.0 -50.0 -45.0 -40.0 -35.0 -30.0 -25.0 -20.0 -15.0 -10.0 -5.0 0.0 5.0 10.0 GO Right-Side Probe Left-Side Probe FEM GO Right-Side Probe Left-Side Probe FEM

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61 TherestoftherowsareplottedagainsttheirrespectiveGOandFEMcalculations inFigures5-7(a)and5-7(b).ThedifferencebetweenthemeasuredcurvesandtheGOcalculationsissmallerascellrowsfartherfromthecenterareplotted.TheGOcalculations showninthesegureswereslightlybetteratpredictingthemeasurementssincethestandingwavemagnitudehasdecreasedinthisregion.Howeverineachsetofplots,thedifferencebetweentheGOcalculatedandmeasuredphasewasalwaysmuchhigherthanthe gaindifferences.Overall,theFEMcalculationswerebetterthantheGOcalculationsat predicting the measured gain and phase variations across the wafer. Distance from Center (cm) Figure 5-7MeasuredversusGO-predictedgainandS21phasevaluesat(a)row7 and (b) row 8 at R=3 inches. -2.0-1.00.01.02.0 Distance from Center (cm) -10 -8 -6 -4 -2 0 2Gain (dB) GO Calculated Right Side Probe Left Side Probe FEM -2.0-1.00.01.02.0 -45 -35 -25 -15 -5 5 -2.0 -1.00.01.0 2.0 -40 -30 -20 -10 0 10 -2.0-1.0 0.01.0 2.0 -10 -5 0 Phase (Degrees) Phase (Degrees) Gain (dB) (a) (b)

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62 ThedatafortheR=7.5-inchseparationmeasurementsappearedtobelessconformingtocalculations,possiblysuggestingotherinterferingphenomena,suchas reectedwavesintheisolationchamber,ordiffractionthroughthemeasurementaperture (Figure5-8).Inaddition,duetocomputerresourcelimitationsandconvergencedifculties, the 7.5-inch separation case could not be simulated by FEM. -2.0-1.00.01.02.0 -10 -8 -6 -4 -2 0Gain (dB) -2.0-1.00.01.02.0 -30 -20 -10 0 10 20Phase (Degrees) -2.0-1.00.01.02.0 -4 -2 0 2 4Gain (dB) -2.0-1.00.01.02.0 -40 -20 0 20 40 Distance from Center (cm) -10 -5 0 5 Distance from Center (cm) -25 -15 -5 5 15 25 35 Calculated Right Side Probe Left Side Probe (a) (b)Phase (Degrees)-2.0-1.00.01.02.0-2.0-1.00.01.02.0Gain (dB) Phase (Degrees) Figure 5-8Gaussiancalculationcomparisons forR=7.5inches:(a)row6,(b) row 7, (c) row 8.

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63 Thediffractioncouldcomefromthecurrentsexcitedaroundedgeofthemeasurementaperturebythetransmittedwavefront.AttheR=3-inchseparation,thiswasnota problem,sincethetransmittedbeamdidnotsufcientlyspreadfromitsbeamwaistdiametertoexcitetheseedgecurrents.AtR=7.5-inchesawider,moreplanewavebeamis transmittedbytheGOA,inducingedgecurrentsintheabsorberaroundthemeasurement aperture.Fromelectromagnetictheory[Jac99],signicantcurrentscirculatingaroundthe edgeofanapertureonanopaquescreen(transmitterplatform)aresourcesfordiffraction. However,moreworkisneededtofullyunderstandthedifferencesbetweenthemeasured and simulated data. 5.2.5 Standing W a v es WhenR=3inches(Figures5-6and5-7),thedisagreementbetweentheGOcalculationsandmeasureddatacanbereconciledwhenoneassumestheexistenceofaspatially-connedstandingwave.Thisstandingwave,thoroughlyresearchedinlaser resonators[Ver89],iscreatedbetweenthewaferandthelensinsidetheUCATS(Figure B-4).Duetothecurvatureofthelensandtheplanarboundaryformedbythewafer, E-eldwavesincidentuponthecenterofthelensaregraduallyguidedwitheach lens-reectionawayfrom r =0,towardstheabsorbingwallsintheantennachamber.Interferencewithotherwaves,includingthedirectpath,islimitedtoonlyafewpasses.Thus, thestandingwaveisconnedinspace,andisresponsibleforaseriesofminimaandmaxima across the wafer surface. SincetheGOcalculationsassumeonlyone-waypropagationalongtheLOSpath, onlytheFEMsimulationswereofuseindescribingthiseffect.Thesimulationsforthe 3-inchseparationcaseshowedthatthereisavariationinpowerandphaseoverthesurface

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64 ofthewaferinagreementwiththemeasureddata(Figure5-5).However,forthe R=7.5-inchcase,duetocomputerresourcelimitations,thestandingwavecouldnotbe simulated using nite elements. 5.2.6 Rightv ersus Left-Hand-Side Measurements InorderfortheUCATStobeausefulmeasurementplatform,themeasurement offsetsusingtheright-versusleft-handside(RHSversusLHS)probestations,which allowsmappingofa3.8cmx3.1cmarea,mustbeanalyzed.Thisanalysiscanbeperformedbycheckingthecenterrow.Sinceaprobemountedononeofthetwoopposing probestationscanreachexactlyhalfofthewaferplusthecenterrow,measurementoffset maybestudiedbyperformingcenterrowmeasurementsfromprobesmountedoneach side.Asthemeasurementsfromeachsideareperformedatdifferenttimes,underdifferent calibrations,andwithdifferentprobelandings,thiscanalsobeseenasawaytogauge measurementrobustnessintheUCATS.Thedataforthemaximumandaveragegainand phasedifferencesacrosstherowsforbothseparationdistanceshavebeenincludedin Table 5-2. Table 5-2 Center-row reliability check data Separation/ Parameter Max Difference Max. Location (cell #) Mean Difference (Offset) 3/ Gain (dB) 2.55#621.35 3/ Phase (deg.) 13#635.5 7.5/ Gain (dB) 3.05#671.2 7.5/ Phase (deg.) 31#6813

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65 5.3 Frequenc y-Dependent Measurements 5.3.1 Measurement Dependence on Probes Foranacceptablemeasurementsetacrossthewafersurface,theimpedanceofthe transmittershouldnotbechangeduponvaryingthelocationoftheprobesonthewafer surface[Rep88]and[Pet93].The S11hasbeenmeasuredforvariousprobelocations acrossthewaferatthetwoseparationsusedintheuniformitymeasurements.Thiscanbe usedtoinvestigatetheprobe-transmittercouplingeffect(Figure5-9).Thetransmitters 23.023.524.024.525.0 -20.0 -15.0 -10.0 -5.0 0.0S11(dB) 23.023.524.024.525.0 -30.0 -20.0 -10.0 0.0S11(dB) 23.023.524.024.5 25.0 Frequency(GHz) -20.0 -15.0 -10.0 -5.0 0.0S11(dB) R= 3 inch R= 7.5 inch Figure 5-9 S11stabilityforvarioussame-rowcelllocations:(a)R=3inches,(b)R= 7.5 inches, (c) no wafer.

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66 returnlossdataareaffectedbylessthan0.5dBfordifferentprobelocations.Alsoshown inthisgureistheshiftingofthe24.5GHznullasthedistanceisincreasedfromR=3 inchestoR=7.5inches.Figure5-9(c)showshowtheS11oftheGOAdecreasesbyabout 4dBwhenthereisnowaferonthevacuumring.Thisisaclearindicationofthepresence ofastandingwave,sincewithawaferoverthetransmitter,therewouldbeasignicantly larger amount of the power reected back into the GOA. 5.3.2 Frequenc y Dependent Gain Data Asindicatedinthewaferuniformitydata,thefrequencydependentgainofthe foldeddipolevariedsignicantlyfromonecelllocationtoanother.Goingdownarowon thetestchip,thegaintowardsthecenterofthewafertendedtobepeakedat23.7GHz,the frequency of uniformity analysis and the resonant frequency of the transmit antennaGain (dB)Figure 5-10Frequency-dependent gain plots for: (a) R = 3 inches, (b) R= 7.5 inches. 23.0 23.524.024.525.0 -60.0 -50.0 -40.0 -30.0Gain (dB) 23.023.524.024.525.0 -60.0 -55.0 -50.0 -45.0 -40.0 Cell 61 Cell 62 Cell 63 Cell 64 Cell 65 Cell 66 (a) (b)

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67 (Figure5-10).Alsoineachplot,oneverycelllocation,therearefrequency-dependent nulls.Furthermore,thelocationofthenullschangedfordifferentcelllocations.Finally,as intheuniformitydata,therewasmoregainvariationacrossthefrequencyrangewhenthe separation distance is increased to 7.5 inches. Thedataforcelllocation61,previouslyleftoutoftheuniformitydata,havebeen includedinFigure5-10forcomparativepurposes.Comparedtocelllocationsnotborderingontheapertureedge,ithadthepoorestgainoverthefrequencyband,thesteepestdip ofallthecelllocations,andamuchhigherphasedelay(Figure5-11).Thehighphase delay was observed due to its proximity to the vacuum ring. In order for the signal to be Frequency (GHz) Figure 5-11Frequency-dependentS21phaseplotsfor:(a)R=3inches,(b)R=7.5 inches. 23.023.5 24.0 -800 -600 -400 -200 0 Cell 61 Cell 62 Cell 63 Cell 64 Cell 65 23.0 23.5 24.0 -600 -400 -200 0 200S21 Phase (Degrees) S21 Phase (Degrees)(a) (b)

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68 detectedbythisantenna,partofthesignalhadtopropagatethroughthedielectricvacuum ring with a higher permittivity. Thereasonsforthesignicantvariationinthegain-frequencyplotscouldbea combinationofcouplingbetweentheantennaelements,measurementreliability,standing waveeffects,orresonanceintheisolationchamber.Figure5-12showsanothercollection ofgaindata,whichfurtherillustratesthegainvariations.Theseplotscontainthesame trendasbothofthegain-versus-frequencyplotsinFigure5-10:thegaindecreasesinoverall magnitude for cell sites farther from the center. In Figure 5-12(b), both the gain and Frequency (GHz) Figure 5-12Column-wisecomparisonsoffrequency-dependentgaindatafor:(a)R= 3inches, (b) R= 7.5 inches. (a) (b) 23.023.524.024.525.0 -60.0 -50.0 -40.0 -30.0 Cell 62 Cell 82 Cell 63 Cell 83 Cell 66 Cell 86 23.023.524.024.525.0 -60.0 -55.0 -50.0 -45.0 -40.0 Gain (dB) Gain (dB)

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69 nullmagnitudesincreasealongallthreecolumnsastherownumberchangesfrom6to8. The relation between the data of Figures 5-12 and 5-10 further emphasizes the need to identifythesourcesofthenullsatthe7.5-inchseparation,sincethenullseverityandgain degradation increase with distance in any direction from the center cell. 5.4 Measurement Summary 5.4.1 Uniformity Measurements Asdiscussedearlier,spatialplotsofrelativegainandS21phaseattwodifferent receiver-transmitterseparationswereassembledwiththepurposeofdeterminingtheuniformityofthetransmittedwavefront.Thedatawerecollectedbyindividuallyprobingthe foldeddipoleantennasineachcellovera3.8cmx3.1cmareaonthetestchip.ThestatisticsaresummarizedinTable5-3belowalongwiththeoffsetforRHSversusLHSprobe measurements.Alldataarereferencedtothecentercellmeasurement.Thedataindicate that,whenttoaunimodalnormaldistribution,theshapeofthegaindistributionis roughlythesameforeachseparationvalue.However,measuredgainforthe3-inchseparationvariedmoreonaveragethanthedataforthe7.5-inchseparation.Forthephasedata, theuniformityimprovedinbothshapeandaveragedeviationwhenthereceiverismoved from 3 inches to 7.5 inches away from the transmitter. Table 5-1 Uniformity statistics for relative gain and phase Separation/ Parameter Mean Deviation s 3 s LHS/RHS Offset MaxMin 3 Gain -7.522.858.55+/1.514.7 3 Phase -3018.555.5+/5.597 7.5 Gain -3.772.908.7+/1.213.6 7.5 Phase -1610.531.5+/1351

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70 Fromthephasedata,theclockskewwascalculatedassumingadivide-by-8 receiverarchitecture.MeasurementstakenatR=3inchesyieldedaskewof3.0%,while. measurements for full separation (R=7.5 inches) corresponded to a skew at 1.7% 5.4.2 Uniformity Measurements v ersus Predictions Therewasonlypartialagreementoftheabovemeasureddatawiththetheoretical gaussianoptics(GO)calculationsatthe3-inchseparationduetotheproposedpresenceof astandingwaveconnedtothecenterofthewafer.ThedataagreedbetterwiththeGO calculationswhenthedatawereanalyzedalongrow8,therowfarthestfromthecenter row.TherewaslittleagreementbetweentheGOcalculationsandthedatatakenatrow6, thecenterrowofthewafer,exceptattheedgesofthewafer.However,thesimulationsperformedusingtheniteelementmethod(FEM)agreedbetterwiththephasedatainthe centralregionofthisrow.Infact,overalltheFEMcalculationsagreedwiththemeasured datamuchbetterthantheGOcalculations.Thiscanbeseenwhenthemeasuredgainand phase are plotted with the two calculation methods along row 7 and row 8 (Figure 5-7). Thegaussiancalculationsdidnothaveanycorrelationwiththedatawhentheseparationwasincreasedto7.5inches.Also,becauseoftheprohibitivesize,noFEMsolution couldbegeneratedatthisseparation.ThelackofagreementbetweentheGOcalculations andthedatacouldpossiblystemfromdiffractionthroughthevacuumringaperture,or reected waves and resonances inside the antenna chamber. 5.4.3 Frequenc y Dependence Whenthegainwasanalyzedversusfrequency,themeasureddatabetweenthetwo differentseparationsbecameevenmoredisparate.Inbothrowandcolumnanalysis,the gainplotsforR=7.5inchesshowedthattherewerefrequency-dependentnulls,which

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71 becameworseforincreasingdistanceawayfromthecentercell.Forbothseparationplots thegainmagnitudeovertheentirebandwidthdecreasedasthedistancefromthecenterof the wafer increased, in agreement with the uniformity data. ThemeasuredS11dataforbothseparationsshowedhowprobingdifferentlocationsminimallyinuencedthesemeasurements.However,theS11wasstronglyinuenced by the separation distance.

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72 CHAPTER 6 SUMMARY AND FUTURE WORK 6.1 Summary Anultra-compactantennatestsystem(UCATS)hasbeendevelopedforspecic applicationtoexternally-transmittedclockdistributionsystems(ECDS)operatingatthe globalclockfrequencyrangeof14-26GHz.Someoftheuser-friendlyfeaturesincluded continuously-variablereceiver-transmitter(RX-TX)spacing,modularvacuumring design,andcompatibilitywithstandardvectornetworkanalyzersandRFprobestations. TheUCATSisalsotherstknownnear-tointermediate-eldelectromagneticmeasurementenvironmentintermsofitssmallphysicalsizerelativetofrequencybandwidth,the useofadensely-packed(spacing<< l /2)silicon-integratedprobearrayforsignaldetection [Wan88, Pet94, and Rep88]. Inordertocharacterizethemeasurementsystemandtoprovideabenchmarkfor futuredesigns,aprototypeECDSwasalsodesignedaspartofthiswork.Agaussian opticshornantenna(GOA)wasusedasthetransmitterduetoitscapabilityofemitting gaussianwaves,whichcloselyapproximateplanewaves.Anarrayofintegratedantennas typicallyusedinwirelessclockreceiverswereusedasthereceiveantennas.Frominitial measurementresults,thefoldeddipolewaschosenasthedefaultantennaforcharacterization of the UCATS. MeasurementresultsusingtheUCATSshowedpromisingresultsforthemeasurementsetcollectedataspacingof3inches.Tofacilitateusefulnesstoclockdistribution

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73 development,datawereexpressedasrelativegainandphasetothoseofthewafercenter. Themeasurementsalongarrayrowsshowedagreementwiththegaussianbeamtheory. However,theagreementwasbetterfordatafromthecellrowsawayfromthemiddleof thewafer,particularlyalongrow8.Datafromthecenterrowwaslargelydifferentthanthe GO-calculateddata,suggestingastandingwavebetweenthewaferandlens.Finiteelementsimulationsconrmedtheseassumptions,andoverallagreedbetterwiththemeasurementsatthecenterrowthantheGOcalculations.Measurementsatthisrangeshowed aclockskewof3%at3GHzovera3.4x3.1cm.Thiswaswellwithinthesuggested10% globalskewtoleranceoveranareawellbeyondthecurrentorprojectedsizeofmicroprocessors [SIA01]. ThemeasurementsperformedatanRX-TXspacingof7.5inches,themaximum separationallowedintheUCATS,werebothpromisingandsurprising.Unliketheresults forthe3-inchcase,themeasurementsstronglydisagreedwithgaussianbeampredictions. However,evenwiththisvariation,theresultsyieldedameasuredclockskewof1.7%over a 3.4 x 3.1 cm area. Inconclusion,theUCATSprovedtobeareliableplatformforECDScharacterization.Thefactthattheantennameasurementsagreedbetterwiththeunderlyingtheoryfor decreasingreceiver-transmitterspacing,shouldnotmitigateitsusefulnesstothemicroprocessorindustry.Infact,inapracticalECDS,thetransmittershouldbeplacedataminimumdistancefromthereceiverforcompactness,makingdecreasedspacingdesirable. Measurementstakenwithaprototypeinter-chipclockdistributionsystemsuggestthatit maybepossibletoincreasethesizeofmulti-GHzsynchronoussystemswellbeyondwhat is currently believed possible

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74 6.2 Future W ork ThereismuchworkwhichcouldimprovetheperformanceofwirelessclockdistributionusingtheUCATS.Sucheffortscouldincludeanimprovedvacuumringdesignto eliminatemultipath,numericalalgorithmssuchaswaveletstoincreasestanding-wave analysiscapabilities,andinvestigationusingfurtherwavefrontuniformitymappingsata widerrangeofRX-TXdistances.Finally,theinclusionofamatchinglayerbelowthe wafer could effectively take out the dependence on the spatially-conned standing wave. Inaddition,thetaskofdevelopingthetransmitterandreceiverfortheinterchip clockdistributionsystemsisalsoacriticalareaforfuturedevelopmentwork.Fittinga longerelectrical-lengthantennaintoasmallerareaisstillanopentask.Possibleantenna structures include log-periodic and fractal antennas. Likewise,furtherworkstudyingthefeasibilityoftheECDScouldprovetobe technicallychallenging.Suchworkwouldeventuallyinvolvetheinsertionoftheheatsink andpackagingbetweenthereceiverandtransmitterlink.Thecontinueddevelopmentof externalclocktransmittersshouldproceedinlinewiththefeasibilitystudies.Practical transmittersshouldbemoreplanarinstructurethanthelens-horncombinationprototype usedinthiswork,makingtheirsizeeasiertotinsideacomputersystem.Suchstructures couldincludemicrostriparrays,whichcouldgivethefreedomofaligninggainmaxima with receivers.

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75 APPENDIX A DRAWINGS FOR THE ULTRA-COMPACT ANTENNA TEST SYSTEM A.1 Engineering Dra wings for the UCA TS Theassemblydrawingsareshownhereastheyweresentouttothemachineshop. AllpartswerefabricatedinAluminum,exceptforvacuumring,whichwasfabricatedin polyethylene.Graphicsmayappeardistorted,sincetheyhavebeenreshapedtottheformatofthisdocument.Inaddition,photographsoftheassembledUCATSareshowninthe nal section, A.6. 3 1.5 13.25 14 7 1.5 3.5 3.5 13.25 6.125 0.5 1/4 1/4 4 2 3 2 6.125 Figure A-1Isolation chamber sidewalls.

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76 14 6 0.5 3.5 3.5 3.5 14 6 3 1/4 4 2 2 3 3 Figure A-2Back-panel of isolation chamber. 6 3 0.5 T op V ie w Figure A-3Top view of back-panel.

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77 1 14 6 1 1.5 Cut this section out of panel Edges are rounded 0.5 5 1/16 (or space which best gives optimum door clearance) placement of hinge machine shop choice 4 2 Cut door(dotted line) out of left over piece 0.5 0.5 2 4 1.5 2 0.5 3.5 3.5 7 14 0.5Figure A-4Front-panel of isolation chamber with access door.

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78 6 12.25 1.5 diameter hole for antenna threaded holes to t antenna clamp in size and location 0.75 spacing from edge typical 6.125 3 ~ 9/16 smoothbored hole 2.5 2.75 2.75 1.25 (typical spacing) Figure A-5Transmitter platform.

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79 2 1/8 2 3 holes drilled completely through part XCA XCB 1/8 diameter circular groove 5/16 Figure A-6Vacuum ring.

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80 5/16 0.5 1 1/8 diam. hemispherical groove (h. g. ) 1/16 diam. h. g. 1/8 diam. screw drilled ~ 1/4 deep screw 1/16 diam. h. g. 7/16(countersunk)( for O-ring) 7/32 5/32 XCB 5/16 1/8 h. g. ( note all measurements on grooves are the same as XCA Figure A-7Vacuum ring cross section.

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81 1.5 Top View 0.5 4 4 2 3/4 2.5 1.5 3/4 3/4 3/4 1.25 to accomodate 6 1/2 diameter SHC screws Figure A-8Threaded L steps.

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82 7 6.125 3 1/4 1/4 1/4 1/4 2.25 diam. 1 wide channel cut 0.5 deep 60 degrees 4 adjustment screws 4 x 10-32 1/4 diam. 1/4 4.125 Figure A-9Vacuum ring platform.

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83 0.5 2.25 diameter hole 7 3.5 1/4 1/4 4.125 diameter cut3/4 Figure A-10Cut-away view of vacuum ring platform.

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84 A.2 Photographs of Assembled UCA TS TheUCATSwasphotographed,andtheresultsareshownbelowinFigureA-1. ThetoppaneloftheantennachamberhasbeentakenofftorevealtheGOAtransmitteron Figure A-11PhotographsoftheassembledUCATS:(a)insidetheantennachamber and (b) top-down view showing through the vacuum ring.(a) (b)

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85 thetransmitterplatform,surroundedbyabsorber[FigureA-11(a)].FigureA-11(b)shows atop-downviewoftheUCATS.Here,thetransmittercanbeseenthroughthemeasurement aperture in the white-colored polyethylene vacuum ring.

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86 APPENDIX B FINITE ELEMENT SIMULATIONS B.1 Electromagnetic Application of Finite Elements B.1.1 Introduction to the Theory of Finite Elements Thetheoryofniteelementswasoriginallyappliedbycivilengineerstotheanalysisofstructures.However,thisnumericaltechniqueforsolvingpartialdifferentialequationshasbeengeneralizedtoallengineeringelds.Inelectricalengineering,this techniqueisusedtoprovidenumericalsolutionstoMaxwellsEquations,(Eq.B.1),in 3-dimensionalphysicalspace.Thesources,orparticularsolutionstothepartialdifferentialequation,arerepresentedby r ,thechargedensityinthemedium,andthecurrentdensity source, J (B.1) Nowtheconstitutiveequations(B.2)areusedtoexpressintermsofthe H and E elds. Here s has been taken as the conductivity of the domain being analyzed. (B.2) Usingthisrelationbetween J and E ,assumptionofatime-harmoniccurrentdensity source, the complex permittivity, e in (B.4), and the time-harmonic eld B 0 = D r = E t B = H J t D + = J s E = D e E = B m H =

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87 (B.3) expressions,Maxwellsequationsmaybeexpressedas(B.4).Notethat r hasdisappeared. Itisassumedthatoursystemispurelyelectrodynamic,ornoinitialchargeexistspriorto source application. (B.4) Withthissuggestiveform,Maxwellsequationscondenseintothevectorwave equation,(B.5).Inthisequation,kisthesameas w2me. Thisisthepartialdifferential equationtowhichthesoftwarepackage,AnsoftsHFSS,nowappliestheniteelement method. (B.5) Theniteelementmethodstartsbyprojectingtheaboveequationoverthedomain ofanalysis( W )usingacollectionofweights( Wn),forexample,thelens-hornantenna,as in(B.6).Thedomaindiscretizesinto N smalltetrahedron-shapedsubdomains( Wi),or nite elements. (B.6) Thespacespannedbytheprojectingbasisfunctionsistypicallyapiecewisepolynomialspace[Bre94],andmustadequatelyrepresentthevariationoftheeldsovereach smalltetrahedron.Foragiven,non-trivial,elddistribution,thechoiceofasimplebasis functionimpliesdecompositionintoalargernumberofelementsthanamorecomplex e e j s w --+ = m H 0 = e E 0 = E j wm H = H j we E = E () k 2 E = E () k 2 E [] W n W ii 1 = N0 =

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88 basisfunction.Inotherwords,thesolvermustbeabletowritetheE-eldlocallyoneach subdomain in the form of (B.7). (B.7) Inordertoincorporatesurfaceboundaryconditions( BC )intothesolution,(B.8) canbewritten,withthehelpofGreenstheorem,intheformof(B.8).Theboundaryintegral is evaluated over the surface of the domain ( dW). (B.8) ThesoftwarethensolvesfortheeldsbyusingtheexpansionofE,with(B.7)in(B.8). Equation (B.9) represents this development. (B.9) Thisequation,summedover m and n ,enablesmatrixformulationoftheform:Ax=bwith xandbascolumnvectors.SolutionofthisequationistheE-elddistributionoverthe entire domain. B.1.2 Con v er gence by Error Analysis Becausetheinitialmesh,ordecompositionofthedomainintosubdomains,might notleadtoanacceptablyaccuratesolution,ameshmustberenedtoobtainamoreaccuratesolution.Theanalysisoftheerrorandre-meshingofthedomainintosmallersubdomainsallowthiseventualconvergenceuponthedesiredsolution.Thesoftwarecomputes thepercentdifferenceinpoweroftheelds, D S,aftereachmesh.Ifthepercentdifference E x n W n n 1 = N= W n () E () k 2 EW n () d W WBC WdW = x m W n () W m () k 2 W m W n () d W W mBC WdW =

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89 intheeldsisequaltoorlessthantheuser-denedstoppingcriterion,there-meshing stops and the eld solution after the last mesh is the nal solution to the problem. B.2 Simulation of Prototype T ransmitter B.2.1 Model Thegaussianlens-hornantenna,inordertoverifymanufacturerspecications, wasdrawninsideAnsoftHFSSusingitsCAD-styleinterface.Duetothesymmetryofthe structure,andtheresultingsymmetryoftheeldsinside,itwasnecessarytodrawonly halfofthestructure,andinfactitcouldalsobedonewithaquarterofthesystem.Figure B-1 shows the simulated system. Figure B-1The prototype transmitter, as drawn inside Ansoft HFSS. Lens (Rexolite) Horn (Perfect E) Port (and origin) Symmetry Plane z y PMLyz PMLxyz PMLz PMLy PMLx er=1.25 x

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90 B.2.2 Sources and Boundaries Themodel,drawnaboveingureB-1,wasthenassignedasetofboundaryconditions.Thecross-sectionalplaneofthemodelwasgiventhe H-symmetry boundary.When thisboundaryconditionisappliedtoasurface,HFSSassumessymmetrywithrespectto theselectedsurface,keepingtheH-eldstangentiallycontinuousacrosseitherside.Next, theinsideofthehornwasdesignateda PerfectE boundary,effectivelymakingthissurface aperfectconductorandforcingtheE-eldstobenormalatthisboundary.Also,thewall framing the lens and horn aperture was also assigned a Perfect E boundary. Aroundthelens,aboundingboxof PerfectlyMatchedLayers(PMLs) wereplaced. Theseboundaries,drawnanddenedautomaticallyusingamacroinsideHFSS,havebeen developedbyAnsofttoefcientlysolveforradiatedeldsfromanantenna.Thenotation, xy,xyz,x,etc.,hasbeenusedtodesignatetheaxisofanisotropy,asthePMLsarebasically a virtual anisotropic material. Finally,thesemi-circularcapattheendofthehornwasassigneda port designation.Thissourcehasbeendenedasanidealwaveguidesource,excitingthewaveguide feedofthehorn,asifthewavesweresentfromaninnitedistanceaway.Ineachsimulation, excitation control of the entire model is given to the port source. B.2.3 Single Frequenc y Simulation at 23.7 GHz Asinglefrequencysimulationat23.7GHzwasperformedinordertondanaccurateeldsolutionattheUCATSfrequencyofanalysis.Aconvergencevalueof0.001W/ m2using40,000tetrahedrawasachievedusingthismodel.Theresultsaresummarizedin Table4-1,butthephiandthetaplotsfortheantennagainpatternareshowninFiguresin Figure B-1.

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91 Figure B-2AntennaGainPattern(AGP)plotsfor(a) f =90degrees,(b) q =90degrees in spherical coordinates. 0.050.0100.0150.0200.0 Theta (degrees) -25.0 -20.0 -15.0 -10.0 -5.0 0.0 5.0 10.0 15.0 20.0AGP (dBi) 0.050.0100.0150.0200.0 Phi (degrees) -30.0 -25.0 -20.0 -15.0 -10.0 -5.0 0.0 5.0 10.0 15.0 20.0AGP (dBi) HPBW

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92 B.3 Standing W a v e Simulations Insteadofanalysisusingcomplicatedspecialfunctiontheory,thestandingwave insidetheUCATSwasinvestigatedusingAnsoftHFSS.Thiswasaccomplishedbythe inclusionofthewaferintothemodelusedinSectionB.3,andreductiontohalfofthe modelsizeusingsymmetry.ThenewmodelhasbeendenedasinFigure5-2.However, duetoitslargersizecomparedtothepreviousmodelofonlythelens-hornantenna,the convergencecriterionwasrelaxedtounder0.008(W/m2)inordertopreventoverowof virtual boxes (used to optimize meshing) 1/4 of wafer Surrounding PMLs (Ideal Absorber) lens-horn combination Figure B-3FiniteelementmodelusedtosimulateR=3-inchseparationcaseinside the UCATS. symmetry planes y source x Impedance BC at wafer surface

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93 computerresource.InFigureB-4,thephaseandpowerofEf,isplottedversusthedistancefromthewafer.Theincreaseinthegainaround2cmiswhatwasreferredtoasthe gain due to the diffraction-induced currents in Section 5.2.5 Figure B-4Plot of E f s power and phase over lateral dimension of wafer. 0.00.51.01.52.0 -4.0 -3.0 -2.0 -1.0 0.0Relative Power (dB) 0.00.51.01.52.0 Distance from Wafer Center (cm) 90.0 100.0 110.0 120.0 130.0E-field Phase (degrees)

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94 Next,thespatialdistributionofE-eldstrengthacrossthesimulatedwaferis showninFigureB-5.Note,again,thatthemaximumshownattheedgeofthewaferdid notcorroboratewiththemeasureddata,andcouldbeasimulationartifactresultingfrom thefactthatourwaferissuspendedinfreespaceinthemodel.Therefore,thisareaof higheldstrengthinthesimulatorcouldbeduetotheedgediffractionoftheincident radiation around the edge of the wafer. FigureB-6showsaspatialdistributiononthex-zplaneofthetypicalminimaand maximaassociatedwithstandingwavesalongthey-dimensionbetweenthewaferand GOA.Thepowerandphaseofthestandingwaveareplottedsingle-dimensionallyversusy in Figure B-7. Figure B-5DistributionofFEM-simulatedE-eldstrengthacrosstheareaofthe wafer.

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95 Scale White= 1800 V/m Black= 0 V/m GOA PMLs wafer source maxima minima Figure B-6E-eld distribution of the GOA-wafer standing wave at 3-inch separation.

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96 Itcanbeobservedinthisplotthatthemaximaarespacedapproximately0.4cm apart.Thewavelengthofa23.7GHzwaveisabout0.63cmandaplanewavestanding waveinarectangulargeometryshouldhaveamaximaspacingof l /2.However,thecon5.07.09.011.013.0 -17.5 -12.5 -7.5 -2.5Relative Power from Peak (dB) Distance from Port to Wafer (cm) -180.0 -150.0 -120.0 -90.0 -60.0 -30.0 0.0 30.0 60.0 90.0 120.0 150.0 180.0E-field Phase (degrees) 5.07.09.011.0 1 13.0 Figure B-7Standing wave power and phase versus y dimension.

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97 ninggeometryinsidetheUCATSismorecomplicatedasstandingwavesareformedby gaussian waves reecting off a planar wafer at one end, and a spherical lens at the other.

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98 LIST OF REFERENCES [Bal89]C.A.Balanis, AdvancedEngineeringElectromagnetics ,2ndedition,New York: Wiley, 1989. [Bal97]C.A.Balanis, AntennaTheory:AnalysisandDesign ,2ndedition,New York: Wiley, 1997. [Bom02]W.R.BomstadandK.K.O,Phaseandamplitudedistributionmeasurementsusingacompactantennatestrangeapplicabletowirelessclockdistribution, 2002IEEEAntennasandPropagationSocietyInternational Symposium pp. 726-730, June 2002, San Antonio, TX. [Bre94]S.C.BrennerandL.R.Scott, TheMathematicalTheoryofFiniteElement Methods New York: Springer-Verlag, 1994, pp.67-85. [Bur01]R.L.BurdenandJ.D.Faires, NumericalAnalysis ,7thedition,Pacic Grove, CA: Brooks/Cole, 2001. [Cla69]P.J.B.ClarricoatsandP.K.Saha,Analysisofsphericalhybridmodesin a corrugated conical horn, Electron Lett ., vol. 5, pp. 189-190, May 1969. [Cla71]P.J.B.ClarricoatsandP.K.Saha,Propagationandradiationbehaviourof corrugatedfeeds, Proc.Inst.Elec.Eng .,vol.118,pp.1167-1176,Sept. 1971. [Col60]R.E.Collin, FieldTheoryofGuidedWaves ,NewYork:McGrawHill. 1960. [Col66]R.E.Collin, FoundationsforMicrowaveEngineering ,NewYork: McGraw Hill. 1966. [Dav95]H.F.DavisandA.D.Snider, IntroductiontoVectorAnalysis, 2ndedition, Dubuque, IA: WCB Communication, 1995. [Eng73]W.J.English,Thecircularwaveguidestep-discontinuitymodetransducer, IEEETrans.MicrowaveTheoryTech. ,vol.MTT-21,pp.633-636, Oct. 1973.

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99 [Flo99]B.A.FloydandK.K.O,Theprojectedpowerconsumptionofawireless clockdistributionsystemandcomparisontoconventionaldistributionsystems, Proc.InternationalInterconnectTechnologyConference ,pp.248250, May 199 [Flo00]B.A.Floyd,K.Kim,andK.K.O,WirelessInterconnectioninaCMOS ICwithIntegratedAntennas, ISSCCDigestTechnicalPapers ,pp.328329 Feb. 2000. [Flo01]B.A.Floyd,ACMOSWirelessInterconnectSystemforMultigigahertz clockdistribution,Ph.D.Dissertation,UniversityofFlorida,Gainesville, FL, 2001. [Gol82]P.F.Goldsmith,Quasi-opticalTechniquesatMillimeterandSubmillimeterWavelengths,in InfraredandMillimeterWaves ,vol.6,NewYork: Academic, 1982, pp. 277-343. [Guo01]X.Guo,J.Caserta,R.Li,B.Floyd,K.K.O,PropagationLayersforIntrachipWirelessInterconnectionCompatiblewithPackagingandHeat Removal, 2002SymposiumonVLSITechnology ,pp.36-37,Honolulu,HA, 2002. [Ham97]M.HamidandR.Hamid,EquivalentCircuitofDipoleAntennaofArbitraryLength, IEEETrans.onAntennasandPropagation ,vol.45,no.11, Nov. 1997, p. 1695. [Jac99]J.D.Jackson, ClassicalElectrodynamics ,3rdedition,NewYork:Wiley. 1999. [Kat83]P.B.KatehiandN.G.Alexopoulos,OntheEffectofSubstrateThickness andPermittivityonPrintedCircuitDipoleProperties, IEEETrans.on Antennas and Propagation vol. 31, no. 1, Jan. 1983, pp. 34-39. [Kim00]K.Kim,DesignandCharacterizationofRFComponentsforInter-and Intra-chipWirelessCommunications,Ph.D.Dissertation,Universityof Florida, Gainesville, FL, 2000. [Kim01]K.KimandW.R.Bomstad,APlaneWaveApproachtoUnderstanding PropagationinanIntra-chipCommunicationSystem, IEEEAntennasand PropagationSocieyInternationalSymposium ,pp.166-170,Boston,MA, 2001. [Kin91]R.W.P.King,TheElectromagneticFieldofaHorizontalElectricDipole intheprescenseofaThree-LayeredRegion, JournalofAppliedPhysics vol. 69, no. 12, June 1991.

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100 [Mar48]N.Marcuvitz, WaveguideHandbook ,vol.10ofMITRad.LabSeries,New York: McGraw Hill. 1948. [O97]K.K.O,K.Kim,B.Floyd,andJ.Mehta,InterandIntra-chipClockSignalDistributionUsingMicrowaves, 1997IEEESolidStateCircuitsand TechnologyCommitteeWorkshoponClockDistribution ,Oct.1997, Atlanta, GA. [O99]K.K.O,K.Kim,B.A.Floyd,J.Mehta,andH.Yoon,Interandintra-chip wirelessclocksignaldistributionusingmicrowaves:astatusofafeasibility study, 1999Govt.MicrocircuitApplicationsConf.Dig.Papers ,pp.306309, Mar. 1999. [Pad87]R.Padman,J.A.Murphy,andR.E.Hills,GaussianModeAnalysisof CassegrainAntennaEfciency, IEEETrans.onAntennasandPropagation vol. AP-35, no. 10, Oct. 1987. [Ped93]F.L.Pedrotti,S.J.,andL.S.Pedrotti, IntroductiontoOptics ,2ndedition, New Jersey: Prentice Hall, 1993, pp. 464-480. [Pet94]P.PetreandT.K.Sarkar,PlanarNear-eldtoFar-eldTransformation UsinganArrayofDipoleProbes, IEEETransactionsonAntennasand Propagation vol. 42, no. 4, pp. 534-537, April 1994. [Poz98]D.M.Pozar, MicrowaveEngineering ,2ndedition,NewYork:Wiley,1998. [Rab96]J.M.Rabaey, DigitalIntegratedCircuits:aDesignPerspective ,New Jersy: Prentice Hall, 1996. [Rep88]A.G.Repjar,A.C.Newell,andM.H.Francis,AccurateDeterminationof PlanarNear-eldCorrectionParametersforLinearlyPolarizedProbes, IEEE Trans. on Antennas and Propagation vol. 36, no. 6, June 1988. [SIA01]SemiconductorIndustryAssociation, TheInternationalTechnologyRoadmap for Semiconductors: 2001 Edition San Jose, CA: SIA, 2001. [Sni99]A.D.Snider, PartialDifferentialEquations:SourcesandSolutions ,New Jersey: Prentice Hall, 1999. [Ula99]F.T.Ulaby, FundamentalsofAppliedElectromagnetics, 1999edition,New Jersey: Prentice Hall. [Ver89]J.Y.Verdeyen, LaserElectronics ,2ndedition,NewJersey:PrenticeHall. 1989.

PAGE 107

101 [Wan86]R.K.Wangsness, ElectromagneticFields ,2ndedition,NewYork:John Wiley & Sons, 1986. [Wan88]J.J.H.Wang,AnExaminationoftheTheoryandPracticesofPlanar Near-FieldMeasurement, IEEETrans.onAntennasandPropagation ,vol. 36, no. 6, pp. 746-753, June 1988.

PAGE 108

102 BIOGRAPHICAL SKETCH WayneR.BomstadIIwasborninWinterPark,FloridaonDecember4,1975.He graduatedcumlaudewithaB.SinElectricalEngineeringintheHonorsProgramatthe UniversityofSouthFloridainTampa,Floridain1999.HisachievementattheUniversity ofSouthFloridaalsoearnedhimthe OutstandingStudentPerformanceinElectricalEngineeringAward ,giventothetopelectricalengineeringstudent.Duringthesummersof 1998and1999,heworkedattherespectivecompaniesofLockheedMartin,andIntersil Corp.inantennatest,antennadesign,andintegratedcircuitdesigncapacities.Inaddition, hehasalsoworkedasaresearchscientistintheeldofmedicalimagingatMRIDevices Corp.intheSummerof2001.In2000,hejoinedtheSiliconMicrowaveIntegratedCircuitsandSystemsGroupwherehehasworkedonthedevelopmentofinter-andintra-chip clocksystemsunderthesupportoftheSemiconductorResearchCorporation.Inaddition toantennas,hisresearchinterestsincludemedicalimaging,numericalpartialdifferential equations,niteandLiegroups,andSU(n)algebraicstructures.Wayneplanstocontinue graduatestudiesinthePhysicsDepartmentattheUniversityofFloridainpursuitofthe Ph.D. degree in Physics.


Permanent Link: http://ufdc.ufl.edu/UFE0000507/00001

Material Information

Title: An Ultra-compact antenna test system and its analysis in the context of wireless clock distribution
Physical Description: Mixed Material
Language: English
Creator: Bomstad, Wayne Roger ( Dissertant )
O, Kenneth K. ( Thesis advisor )
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2002
Copyright Date: 2002

Subjects

Subjects / Keywords: Electrical and Computer Engineering thesis, M.S
Dissertations, Academic -- UF -- Electrical and Computer Engineering
Very high speed integrated circuits -- Design and construction   ( lcsh )
Wireless communication systems -- Design and construction   ( lcsh )

Notes

Abstract: It has been proposed to generate and receive the clock signal using wireless communication systems as an alternative means of microprocessor clock distribution. As a candidate to replace traditional wired interconnects, wireless clock distribution has several potential advantages over its conventional counterpart including synchronization over a larger area and smaller clock skew. Previous wireless clock distribution systems were investigated using integrated receivers and transmitters. However, operation of these systems is hindered by the interference caused by coplanar metal structures. The way to mitigate this effect is to generate the clock signal off-chip. The concept of externally-transmitted wireless clock distribution (ECD), or inter-chip clock distribution, has been studied in this work through the development of an application-specific measurement setup. This setup was designed to serve as a test-bed for the characterization of ECD systems. Also in this work, a prototype ECD system, consisting of only transmit and receive antennas, was designed and then measured in this new test-bed, called the Ultra-Compact Antenna Test System (UCATS). The UCATS was developed to measure the gain in the near- to intermediate-field region of a transmitting antenna on a 3-inch diameter wafer. For the initial tests, a prototype transmit-receive antenna set was characterized both as a benchmark for future designs and as a means of characterizing the test range. Specifically, a 24 GHz gaussian optics horn antenna was used as the transmitter. A test chip containing an evenly-spaced array of folded dipoles was designed and used as the set of receive antennas. Phase and amplitude distributions of the received wave front were characterized by individually probing the integrated antennas. Measurements were performed for two different receiver-transmitter separation distances, and the results were compared in terms of the overall gain, magnitude, and phase distributions. Measurements have shown that a wave front can be generated and received with a maximum phase difference of 16 degrees and a mean amplitude difference of 3.77 dB. For the purposes of clock delivery for 3 GHz operation, this can be approximated as a planar wave front with a beam area of 3.8 cm x 3.1 cm, the measurable size of the receiver array. In conclusion, it was shown that a planar wave front can be generated and measured in the near- to intermediate-field region of the transmitting antenna using the UCATS and a prototype ECD system. The clock skew, assuming typical clock receiver architecture, was calculated to be 3% and 1.7% of the period at a receiver distance of 3 and 7.5 inches, respectively. These measurements were made over an area of 1178 mm2, a span of over 3 times the average area of present-day microprocessors.
General Note: Title from title page of source document.
General Note: Includes vita.
Thesis: Thesis (M.S.)--University of Florida, 2002.
Bibliography: Includes bibliographical references.
General Note: Text (Electronic thesis) in PDF format.

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: aleph - 002898309
System ID: UFE0000507:00001

Permanent Link: http://ufdc.ufl.edu/UFE0000507/00001

Material Information

Title: An Ultra-compact antenna test system and its analysis in the context of wireless clock distribution
Physical Description: Mixed Material
Language: English
Creator: Bomstad, Wayne Roger ( Dissertant )
O, Kenneth K. ( Thesis advisor )
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2002
Copyright Date: 2002

Subjects

Subjects / Keywords: Electrical and Computer Engineering thesis, M.S
Dissertations, Academic -- UF -- Electrical and Computer Engineering
Very high speed integrated circuits -- Design and construction   ( lcsh )
Wireless communication systems -- Design and construction   ( lcsh )

Notes

Abstract: It has been proposed to generate and receive the clock signal using wireless communication systems as an alternative means of microprocessor clock distribution. As a candidate to replace traditional wired interconnects, wireless clock distribution has several potential advantages over its conventional counterpart including synchronization over a larger area and smaller clock skew. Previous wireless clock distribution systems were investigated using integrated receivers and transmitters. However, operation of these systems is hindered by the interference caused by coplanar metal structures. The way to mitigate this effect is to generate the clock signal off-chip. The concept of externally-transmitted wireless clock distribution (ECD), or inter-chip clock distribution, has been studied in this work through the development of an application-specific measurement setup. This setup was designed to serve as a test-bed for the characterization of ECD systems. Also in this work, a prototype ECD system, consisting of only transmit and receive antennas, was designed and then measured in this new test-bed, called the Ultra-Compact Antenna Test System (UCATS). The UCATS was developed to measure the gain in the near- to intermediate-field region of a transmitting antenna on a 3-inch diameter wafer. For the initial tests, a prototype transmit-receive antenna set was characterized both as a benchmark for future designs and as a means of characterizing the test range. Specifically, a 24 GHz gaussian optics horn antenna was used as the transmitter. A test chip containing an evenly-spaced array of folded dipoles was designed and used as the set of receive antennas. Phase and amplitude distributions of the received wave front were characterized by individually probing the integrated antennas. Measurements were performed for two different receiver-transmitter separation distances, and the results were compared in terms of the overall gain, magnitude, and phase distributions. Measurements have shown that a wave front can be generated and received with a maximum phase difference of 16 degrees and a mean amplitude difference of 3.77 dB. For the purposes of clock delivery for 3 GHz operation, this can be approximated as a planar wave front with a beam area of 3.8 cm x 3.1 cm, the measurable size of the receiver array. In conclusion, it was shown that a planar wave front can be generated and measured in the near- to intermediate-field region of the transmitting antenna using the UCATS and a prototype ECD system. The clock skew, assuming typical clock receiver architecture, was calculated to be 3% and 1.7% of the period at a receiver distance of 3 and 7.5 inches, respectively. These measurements were made over an area of 1178 mm2, a span of over 3 times the average area of present-day microprocessors.
General Note: Title from title page of source document.
General Note: Includes vita.
Thesis: Thesis (M.S.)--University of Florida, 2002.
Bibliography: Includes bibliographical references.
General Note: Text (Electronic thesis) in PDF format.

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: aleph - 002898309
System ID: UFE0000507:00001


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AN ULTRA-COMPACT ANTENNA TEST SYSTEM AND ITS ANALYSIS IN THE
CONTEXT OF WIRELESS CLOCK DISTRIBUTION













By


WAYNE ROGER BOMSTAD II


A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE


UNIVERSITY OF FLORIDA


2002















ACKNOWLEDGMENTS

I would like to begin by thanking my advisor, Professor Kenneth O, for giving me

the opportunity to work on this project. His passion and commitment are always a per-

sonal source of inspiration.

I would also like to thank the rest of my mentoring professors (Leffew, Snider,

Weller, and Zory) for their guidance, allowing me to wholeheartedly claim a future career

path. Additionally, I give my deepest respect to my first mentors, and lifelong role mod-

els, my parents: Henrietta I. Shuminsky and Wayne R. Bomstad.

Also this work would not be possible in any timely manner without my teammates.

On the SRC Project I thank J. Caserta, X. Guo, R. Li, J. Branch, and T. Dickson. Proper

thanks go out to graduated Ph.D. students B. Floyd and K. Kim for providing many

enlightening discussions. Next, I am grateful to Bruce Smith of Precision Tool and Engi-

neering for his help in mechanical engineering throughout this project.

I dedicate this work, and all future engineering work, to my beautiful wife,

Aleasha. Her love, encouragement, and dedication are behind any achievement of mine.















TABLE OF CONTENTS

page

ACKNOWLEDGMENTS ................. ............................. ii

ABSTRACT ......... ........................................ ......... vi

CHAPTER

1 INTRODUCTION .................................................1

1.1 Emergence of W wireless Interconnects ............................ 1
1.2 Intra-Chip Clock Distribution ............... ..................1
1.3 Overview of Thesis. ........................................... 6

2 ULTRA-COMPACT ANTENNA TEST SYSTEM .......................... 7

2 .1 Stru ctural D esign ................... ................... ...... 7
2.2 Electrical Design Considerations ............... .............. 11
2.3 Data Extraction ..................................... .......... 19
2.4 Calibration ..................................................23

3 INTEGRATED RECEIVE ANTENNAS ...............................26

3.1 Infinitesimal Dipole Antennas ................. ......... ..... 26
3.2 Radiated vs. Input Power. ................ ................... 30
3.3 Integrated Antennas in the UCATS .............. ............. 34

4 PROTOTYPE TRANSMITTER AND WAVEGUIDE ASSEMBLY ........... 37

4.1 W aveguide A ssem bly .......................................... 37
4.2 Prototype Transmitter. ........................................42

5 PROTOTYPE SYSTEM MEASUREMENTS ............................. 51
5.1 Testchip Design ..................................... ........ 51
5.2 Spatial Wavefront Uniformity Measurements ...................... .52
5.3 Frequency-Dependent Measurements ............................ 65
5.4 Measurement Summary ..................................... .69










6 SUMMARY AND FUTURE WORK ..................................72

6.1 Summary ...................................................72
6.2 Future Work .................................................74

APPENDIX

A DRAWINGS FOR THE ULTRA-COMPACT ANTENNA TEST SYSTEM. ..... 75

A.1 Engineering Drawings for the UCATS ............................ 75
A.2 Photographs of Assembled UCATS. ........................... 84

B FINITE ELEMENT SIMULATIONS .............................. 86
B.1 Electromagnetic Application of Finite Elements .......... ....... 86
B.2 Simulation of Prototype Transmitter ................. ........... 89
B.3 Standing Wave Simulations ............... ................... 92

LIST OF REFERENCES ................. ............................... 98

BIOGRAPHICAL SKETCH ....... ................................. 99















Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science

AN ULTRA-COMPACT ANTENNA TEST SYSTEM AND ITS ANALYSIS IN THE
CONTEXT OF WIRELESS CLOCK DISTRIBUTION

By

Wayne R. Bomstad II

December 2002

Chair: Kenneth K. O
Major Department: Electrical and Computer Engineering

It has been proposed to generate and receive the clock signal using wireless com-

munication systems as an alternative means of microprocessor clock distribution. As a

candidate to replace traditional wired interconnects, wireless clock distribution has several

potential advantages over its conventional counterpart including synchronization over a

larger area and smaller clock skew. Previous wireless clock distribution systems were

investigated using integrated receivers and transmitters. However, operation of these sys-

tems is hindered by the interference caused by coplanar metal structures. The way to

mitigate this effect is to generate the clock signal off-chip.

The concept of externally-transmitted wireless clock distribution (ECD), or

inter-chip clock distribution, has been studied in this work through the development of an

application-specific measurement setup. This setup was designed to serve as a test-bed for

the characterization of ECD systems. Also in this work, a prototype ECD system, consist-






vi

ing of only transmit and receive antennas, was designed and then measured in this new

test-bed, called the Ultra-Compact Antenna Test System (UCATS).

The UCATS was developed to measure the gain in the near- to intermediate-field

region of a transmitting antenna on a 3-inch diameter wafer. For the initial tests, a proto-

type transmit-receive antenna set was characterized both as a benchmark for future

designs and as a means of characterizing the test range. Specifically, a 24 GHz gaussian

optics horn antenna was used as the transmitter. A test chip containing an evenly-spaced

array of folded dipoles was designed and used as the set of receive antennas. Phase and

amplitude distributions of the received wave front were characterized by individually

probing the integrated antennas.

Measurements were performed for two different receiver-transmitter separation

distances, and the results were compared in terms of the overall gain, magnitude, and

phase distributions. Measurements have shown that a wave front can be generated and

received with a maximum phase difference of 16 degrees and a mean amplitude difference

of 3.77 dB. For the purposes of clock delivery for 3 GHz operation, this can be approxi-

mated as a planar wave front with a beam area of 3.8 cm x 3.1 cm, the measurable size of

the receiver array.

In conclusion, it was shown that a planar wave front can be generated and mea-

sured in the near- to intermediate-field region of the transmitting antenna using the

UCATS and a prototype ECD system. The clock skew, assuming typical clock receiver

architecture, was calculated to be 3% and 1.7% of the period at a receiver distance of 3

and 7.5 inches, respectively. These measurements were made over an area of 1178 mm2, a

span of over 3 times the average area of present-day microprocessors.















CHAPTER 1
INTRODUCTION

1.1 Emergence of Wireless Interconnects

The emergence of the technical field of wireless interconnects has occurred as a

means of addressing the some of the bottlenecks facing the semiconductor industry. As

recently as 2001 the Semiconductor Industry Association's International Technology

Roadmap for Semiconductors (ITRS) [SIA01] has predicted that, in the next 5 years,

microprocessors will have local clock frequencies approaching 7 GHz, transistor gate

length will decrease to 45 nm, and the number of metal layers will increase to 9. However,

restriction of the tolerable phase discrepancy of the clock signal, or clock skew require-

ment, has been reduced to 40 ps resulting from the increased frequency. As a result of

these trends, the global clock skew can limit the high-speed operation of microprocessors,

even when using the state-of-the-art copper and low-K interconnect technology [Flo01].

Worse than this, typical systemic clock skew solutions involve use of H-tree circuitry, tak-

ing up a large area and requiring symmetry [Rab96]. What this means in terms of clock

delivery is that as the chip size and clock frequency are increased each passing year, the

clock skew becomes harder to equalize across the chip, and the total area used in clock

delivery increases. This problem is one of the grand challenges facing the semiconductor

industry, that could place serious limitations on the growth of the industry.

1.2 Intra-Chip Clock Distribution

Feasibility of using wireless interconnects to alleviate some of the interconnect

concerns of the semiconductor industry has been proposed [099] and components for

1








such a system have been successfully evaluated at a global clock transmission frequency

of 15 GHz using integrated receivers and transmitters fabricated on a 0.18 jPm silicon

CMOS technology [Flo00, KimOO]. A conceptual diagram of the system is shown in Fig-

ure 1-1. The transmitter has been placed in the middle of a group of integrated receivers.
IC edge

RX RXh RXh RXh


RX RX4 RXs RXI
TX
RXI RXI RXIs RXf

RXh RXh RXh RXh

RX= Receiver
TX=Transmitter
Figure 1-1 Conceptual diagram of an intra-chip clock distribution system.


1.2.1 Propagation Inside an Intra-Chip Clock Distribution System

Figure 1-1 shows that, although placement of the transmitter and receiver can be

optimized from a systemic view, there will be differences in direct-path propagation

delays for skews even in the ideal situation because the receivers must be placed at varying

distances from the transmitting antenna. The distribution of delays to the different receiv-

ers becomes more complex when considering that the signal can also travel under the sili-

con surface, through the silicon substrate, and reflect off surrounding metal layers

[Kim01](Figure 1-2). To alleviate this problem, sophisticated techniques are required,

such as the inclusion of a properly engineered propagation layer underneath the silicon

surface.
























Figure 1-2 Possible disruption of direct-path signals in the intra-chip wireless clock
distribution system.

1.2.2 Clock Receiver Architecture

A block diagram of the clock receiver is shown in Figure 1-3. To improve noise

immunity, differential mode circuitry was used throughout the system. To mate with the

differential mode circuitry, balanced-line antennas (BLAs) such as dipoles and loops are

needed for signal reception. Sequentially, the transmitted signal at the global clock fre-

quency (GCK) is received by the BLA, buffered, amplified by the low-noise amplifier

(LNA), and then fed to the frequency divider. Through the divider, the signal's frequency

is divided by 8 to the system clock frequency. The signal is then buffered again before

being sent to the adjacent circuitry.


BLA
+
GCK / System
SClock
LNo Frequency
("L ADivider


Block diagram of a typical clock receiver.


Figure 1-3









1.2.3 Inter-Chip Clock Distribution System

One way around this skew for intra-chip clock receivers is to use an inter-chip

clock distribution system. Such a means of clock distribution also uses a distribution of

integrated wireless clock receivers across a chip. However, the signal transmission is

accomplished by a plane wave generator located off-chip (Figure 1-4). The signal travels

from the transmitter, through the silicon, and to the receivers. This kind of signal propaga-

tion renders the interference effect of surrounding metal structures negligible, and better

ensures that the receivers synchronously receive the clock signal without regard to their

placement on-chip.
Receiving Antennas
I xxxx x xxxxx (PC Board/MCM)
Integrated
Circuits


transmitted
clock signal




Transmitting
Antenna (Plane Wave
Emitter)

Figure 1-4 Conceptual diagram of inter-chip clock distribution system.

1.3 Overview of Thesis

1.3.1 Ultra-Compact Antenna Test System (UCATS)

One of the goals set forth in this work was the design of a set-up capable of charac-

terizing the nature of the transmitter-to-receiver propagation in a wireless clock distribu-

tion system using microwave scattering parameters. In terms of the mechanical design, the









UCATS not only had to be able to fit within the existing measurement set-up, for cost pur-

poses, but also had to allow for sensitive level adjustment and receiver-transmitter spacing.

Electrically, the system had to be able to absorb as much reflected radiation as possible,

providing a ground for the absorbed radiation. Thus, an isolation chamber was designed to

isolate the transmitter and receiver from all signals except the direct link between them. A

rendition is shown in Figure 1-5, where the four main parts of the UCATS can be seen: the

isolation chamber, vacuum ring, transmitter platform, and probe height-extenders. Finer

details on the measurement setup are in Chapter 2.

1.3.2 Prototype Transmitter-Receiver Pair

To verify the proper functionality of the UCATS and to provide a reference design

for future inter-chip clock distribution systems, a prototype transmit-receive antenna pair

was also designed as part of this work. Since an actual parabolic reflector antenna, as in

Figure 1-4, would not be compatible to the UCATS environment, a gaussian optics

antenna [Gol82] was used in its stead. Analogous in many ways to an electromagnetic

"spotlight", the gaussian optics antenna, can be used to emit a plane-wave-like beam,

which is only diffraction-limited in the spreading of its amplitude and phase over propaga-

tion distance. A more detailed discussion of this horn transmitter is presented in Chapter 4.

A test mask including receive antennas was designed in order to measure and char-

acterize the transmitted wave front at the wafer surface. Cells of varying integrated anten-

nas, were spaced at even intervals across the wafer surface. Using this mask, a wafer was

fabricated at the UF Microelectronics Fabrication Facility on a 20 Q-cm silicon substrate.

This work is also discussed in Chapter 3.








Upon measuring the received power gain using microwave scattering parameters

(s-parameters) at every antenna of the same type in each cell, the spatial phase and ampli-

tude distributions were obtained and plotted. Careful analysis of the s-parameters and the

antenna properties has yielded a skew of 1.7% and 3% for receiver-transmitter separations

of 7.5 inches and 3 inches, respectively. These measurements and data analyses are pre-

sented in Chapter 5. Finally, as part of Chapter 6, broader conclusions from the data were

drawn, and future work was proposed.

RF Probes

Vacuum Ring,& Wafer




Antenna Chamber EM Absorbe

14" 7.


Probe Height-extenders

S1-5 C -s l o 7"UCA
Figure 1-5 Cross-sectional layout of the UCATS.















CHAPTER 2
ULTRA-COMPACT ANTENNA TEST SYSTEM

2.1 Structural Design

2.1.1 Overview

The mechanical design of the UCATS was governed by three stipulations. First of

all, for cost efficiency purposes, the system must fit within the existing RF probe station.

Second, in the context of external clock distribution networks, the design must allow for

accurate measurement of phase differences across the entire wafer surface [Wan88].

Finally, the design must permit fine adjustment in receiver-transmitter spacing.

2.1.2 Isolation Chamber Design

The external dimensions of the isolation chamber and structural foundation of the

UCATS were determined so that the system could snugly fit within the existing RF probe

station, could allow for adequate range of motion of the probes, and could provide housing

of both the receive and transmit antennas. The chamber was designed to be a five-sided

box, consisting of four distinct pieces: side-walls (x2), a front panel with an access door,

back-panel, and the top surface. These individual pieces were fabricated using Aluminum,

which allow for a sturdy probing platform, a ground for absorbed radiation, and an inex-

pensive and lightweight alternative to stainless steel. The assembled antenna chamber is

displayed in Figure 2-1(a). Details, such as the screw holes and spacing, have been omitted

for simplicity, but the actual drawings have been included in Appendix A.










Vacuum Ring
(Top Panel)





3" ----

14"
(. )13.25"
Access Door
(Fron Panel) -4"--




13.25"

-- 7"-
-- -7" --
(a) (b)
Figure 2-1 Diagram of assembled antenna chamber: (a) oblique and (b) top views.

The need to explore the effects of layers placed between the wafer and transmitter

and different vacuum ring configurations has led to the design of a modular vacuum ring-

system. To help accomplish this, the vacuum ring housing was designed as a large

multi-step hole in the middle of the top surface, shown in Figure 2-2. In addition, holes in

the vacuum ring housing were placed to permit for level adjustment of the vacuum ring

separately from the transmitter platform via adjustment screws. More detailed drawings

Adjustment Screws


Cross section of antenna chamber top panel.


Figure 2-2






9

can be found, once again, in Appendix A. The discussion of the prototype vacuum ring

has been included in the electrical design section.

2.1.3 Transmitter Platform

The transmitter platform resides inside the antenna chamber. This piece accom-

plishes the sensitive task of both allowing for a continuous range of receiver-transmitter

spacing, and level adjustment of the transmitting antenna. The platform fastens to the

chamber by four large screws, 6 inches in length and 0.5 inches in diameter. These screws

mate into 4 specially-designed "L-clamps". Turning all screws equally in one direction

varies the distance between the receiver and transmitter, and causes the platform to slide

up or down along the inside walls of the antenna chamber. Turning only a couple of these

screws at a time adjusts the level of the antenna platform. Figure 2-3 shows a cut-away

view of the platform, while Appendix A contains more detailed drawings.

\ Tx-Platfor ^
'"- _-'Adj. Screws '""

Transmitter Tx Platform
Ant.


-,, "L"-Clamps ,
Figure 2-3 Cutaway view of transmitter platform inside antenna chamber.


2.1.4 Probe Height-Extender Assembly

The antenna chamber has been designed with a greater height than the existing

probe station. To allow probing of the entire surface of a 3-inch diameter wafer secured on

the vacuum ring, a probe height-extender assembly was designed. Aluminum was again

chosen for its rigid support and light weight. The latter quality was vital to prevent over-

loading the calipers, the mechanism for probe deployment.






10

The probe height-extender assembly consists of two distinct pieces: the probe

arms and probe height-extenders. The probe height-extenders allow the probes to be rig-

idly supported well above the wafer surface, while the probes are mounted on the probe

arms. Additionally, the probe arms were specified to have 2 degrees of freedom and their

actual design was contracted out to Precision Tool and Engineering. Their assembly with

the antenna chamber can be seen in Figure 2-4, while the engineering drawings can be

seen in Appendix A.

Probe Arms

Antenna Chamber

Probe Height
Extender

Probe Adjustment
Caliper







Figure 2-4 View of probe support assembly (shaded).



2.1.5 Vacuum Ring

In considering its physical topology alone, the vacuum ring is perhaps the most

complex of the components of the UCATS. First, the ring must fit within the ring housing

in the antenna chamber and mate to the vacuum ring level adjustment screws. In looking

at Figure 2-5, the design of the inner ring radius, or measurement aperture, must not only

provide access to transmitted signals from below, but also allow for any 3-inch wide wafer

(circular or square) to cover the aperture completely. Finally, the ring must provide ade-






11

quate air evacuation to secure the wafer in place against repeated probe landings. Thus,

the holes in the vacuum ring should each apply an equal downward force on the wafer.

With this idea as a guide, the vacuum ring contains an internal vacuum channel connect-

ing all the vacuum holes and providing an outlet for external connection to a vacuum

pump. Once again, Appendix A contains more of the dimensional details of the vacuum

ring.


3" Diameter 3" Square
Circular Wafer
Wafer ___ --


Figure 2-5


I..... |I (b)

Actual-size drawing of vacuum ring showing (a) wafer placement and (b)
cross section.


2.2 Electrical Design Considerations


2.2.1 Antenna Chamber


The antenna chamber was designed so that the signal would take only one path,

the line-of-sight (LOS) path, to propagate from transmitter to receiver. Appropriate

absorbing material had to be placed inside the antenna chamber to absorb any reflected






12

signals. The absorber is shown in Figure 2-6, a 0.5-inch thick flat absorber was used for

all of the internal surfaces of the antenna chamber. As discussed in Section 2.2.2, it was

determined by experimental means that this absorber was a better choice for absorption at

23.7 GHz, the resonant frequency of the transmitting antenna.
Wafer
\ Vacuum Ring


Figure 2-6


Antenna chamber with absorber.


2.2.2 Electromagnetic Absorber

Electromagnetic radiation absorption can best be understood on a fundamental

level using plane-wave theory. This plane-wave radiation can be defined by the form seen

in Equation (2.1) in terms of the electric field intensity (E) or magnetic field intensity (H)

quantities as functions of position (x,y,z) and time (t).









E(x,y,z,t) E (kzot) (2.1)
tH(x,y,z,t)J Ho

Here the wave has been chosen to propagate in the z-direction which represents toward

the wafer in Figure 2-6, where the plane wave is defined by its polarized amplitude (Eo or

Ho), wave vector (k), and angular frequency (co). Also the convention of using bold-faced

type to indicate a vector quantity has been utilized. Partial absorption this propagating

wave is allowed by the complex k inside the absorbing material.

In other words, it was thought that there could be divergent direct-path rays from

the gaussian optics horn transmitter. Thus, the convoluted form (egg-crate absorber)

should be an ideal shape which allows for a more efficient production of currents inside

the polyurethane absorber. This can be directly observed from the maxwell boundary con-

ditions for the H field, given by [Wan88]

(Hchamber Habsorber) x n = K. (2.2)

The tangential magnetic fields in the chamber just outside the absorber are related to the

magnetic fields just inside the absorber (Habsorber) by a surface current launched just

inside the absorber (K). The absorbed energy is then carried by the current through the

absorber to ground via the conductive antenna chamber walls. Note the unit vector (n) is

directed out of the absorber.

Experiments were conducted to verify the convoluted absorber as the initial choice

to coat the inside of the transmitter platform. A 1.5-inch thick convoluted absorber was

specified by the Cumings Corporation, the supplier of the absorber, to have a -40 dB

reflectivity at the frequency of 30 GHz in the far-field of an antenna. This absorber was

compared to low-profile 0.5-inch thick flat absorber of the same polyurethan-based mate-






14

rial. To check these specifications for the UCATS, a near- to intermediate-field antenna

range, measurements were conducted with the set-up seen in Figure 2-7. The results of the

corresponding measurements are shown seen in Figures 2-8(a) and 2-8(b). As a bench-

mark for this experiment, these results were compared to the laboratory free-space mea-

surement of 2-7(c), which was performed in the laboratory by pointing the transmitter in a

direction with no LOS reflection path.


__ (a)


Tx


Aluminum




Absorber-Under-Test
(b)

Tx







(c)
Laboratory
Free space

Tx




Figure 2-7 Absorber attenuation experiments: (a) control, (b) experiment, and (c)
laboratory free space (no absorber or aluminum).










(a) 0.0












t G- Flat Absorber
1 z A- Aluminum
S-. v...v" Laboratory
-20.0 Free Space


-25.0
23.0 23.5 24.0 24.5 25.0
S-5.0










0)








S-10.0 Aluminum

"-..... 7 Laboratory Free Space
-25.0





Frequency (GHz)


Figure 2-8 Absorber experiments in the measurement bandwidth of the UCATS
using (a) flat absorber and (b) convoluted absorber as the

absorber-under-test.
23.0 23.5 24.0 24.5 25.0





















Frequency (GHz)


Figure 2-8 Absorber experiments in the measurement bandwidth of the UCATS
using (a) flat absorber and (b) convoluted absorber as the
absorber-under-test.









A comparison between these two plots shows that the flat absorber is better for the

antenna's resonant frequency of 23.7 GHz, attenuating the signal at least 15 dB better than

the convoluted absorber and about 5 dB better than the free-space measurement. In fact,

the convoluted absorber had even worse attenuation than the Aluminum control experi-

ment. As a result of these experiments, the flat absorber was chosen as the default

absorber in the UCATS.

Actual application of the flat absorber to the antenna chamber only increases its

capability of attenuating reflected waves, as the experiments performed above sought to

examine the worst-case scenario. These experiments measured reflectivity at normal inci-

dence, a situation which never occurs in the actual UCATS since the transmitter's effec-

tive beam aligns with the wafer and vacuum ring aperture. Thus, the UCATS uses the

absorber to attenuate rays diverging from the LOS path, and scattered rays, which have

oblique incidence to the absorbers in the UCATS.

2.2.3 Expected Level Adjustment Performance

The specification for minimum range of motion for level adjustment had a basis in

the system expectations for clock skew in an inter-chip clock distribution system. Even

though the industry standard [SIA01] has set the global clock skew tolerance at 10% of

the system clock period, optimal system performance often requires a tighter skew toler-

ance. Therefore, skew added by the measurement setup should be negligible, preferably

less than 0.5%.

In order to have a global skew of less than 0.5%, it has been determined that the

interchip clock distribution system should contain less than 10 degrees of phase error over

a 4 cm2 area at 24 GHz. In line with these initial performance benchmarks, it must be









required of the system level adjustment to be at least 20x more sensitive, accounting for a

phase difference of 10/20=0.5 degrees at 24 GHz.

The level adjustment criterion can be directly determined using first-principle

electromagnetic wave propagation theory. For a resolution of 20x greater than the speci-

fied phase error, the level adjustment must be able to correct for a phase error of 0.5

degrees at 24 GHz. Using the principle of optical path difference [Ped93], nominally 0.5

degrees for this case, the alignment must be able to correct for a difference in height (A =

RI-R2) as seen by plane waves propagating through opposite sides of the 2 cm wide wafer

as indicated in Figure 2-9,
silicon wafer








Figure 2-9 Optical path difference and level adjustment of wafer.


showing two different waves propagating with two different path lengths (R1 and R2). By

looking at this picture, Equation (2.3) can then immediately be written down.


0.5 (R2- R) A (2.3)


Here the left hand side can be seen to represent the optical path difference, while the right

hand side has expressed that phase difference in terms of an electromagnetic wave's phase

argument as a function of vertical misalignment (A), frequency (/), and speed of light (c).

In this way the equation was solved for A at 24 GHz, and equated with its expectation

over the 4 cm2 area. Thus, the minimum tolerable alignment resolution was found to be









0.0035 cm-vertical over a 2 cm width horizontal, a ratio of 2850 tol horizontal to vertical

length units.

2.2.4 Probe Isolation Module

The probe isolation module, a separate piece which is positioned over the wafer

and RF probes, is responsible for isolating the probes and wafer from errant signals. The

user places the module, an aluminum-tin alloy, half-pillbox structure lined on the inside

with the same flat absorber as the antenna chamber. The module is placed in position after

making connections to the antennas such that the circular top surface of the module is par-

allel to the vacuum ring. In position, the module looks like the rendering in Figure 2-10.

RF Probes Al-Sb
Exterior
Shell


0.5"
Flat
Absorber





Si Wafer Vacuum Ring

Figure 2-10 Probe isolation module cross-section.


The importance of this module can be best seen by measurements taken with, and

without the probe isolation module in place in Figure 2-11. The module in these measure-

ments has effectively reduced the variance of the measurements by 1-3 dB depending on

how close the measurements were to the noise floor. This picture has indicated that the

laboratory area around the UCATS presents a non-negligible multipath environment.The

probe shield can be used to provide a degree of isolation from this type of environment.







19

2.3 Data Extraction

2.3.1 S-Parameters

Like most microwave measurement tools, the UCATS measures the microwave

scattering parameters (s-parameters) of the device-under-test, or DUT. Acting as the con-

trol center of the UCATS, the HP 8510C Vector Network Analyzer, connecting to both the

receive and transmit antennas, directly administers the measurement of the two-port scat-

tering parameters [Poz98]. The 8510C sweeps the RF power at each port in frequency and

measures the resulting power level at each port. Association of the measured signal in

each port to its parent signal in ratio form gives the s-parameters. Equation (2.4) gives the

explicit form of how the s-parameters are expressed in terms of incident and reflected

powers for ports of equal characteristic impedance.

b.
S.. (2.1)
aI a .
a. O
1

Here the i orj index represent either port one or port two. When i andj are the same, Sii

represents a reflection coefficient with bi representing the reflected voltage wave. When

the indices are different, Sij becomes a transmission coefficient, meaning that bi is now the

transmitted voltage wave [Poz98]. In either case, portj sends the incident voltage wave,

aj. The network analyzer does not perform measurements with both port sources active at

the same time. Therefore, it becomes necessary to have the inactive port matched and its

source turned off. This is represented mathematically in equation (2.4) by setting ai equal

to zero.

A priori information about the DUT gives additional insights about its associated

scattering parameters. In the case of passive DUT's, the network does not generate any









signal. Therefore, the maximum value of any scattering parameter is one. If the DUT is a

symmetric and bilateral network, such as a passive filter, ideal measurement of S12 and

S2] yields the same value. Finally, if there is knowledge that the DUT is a lossless net-

work, this means that a power balance may be applied to either port, giving equation (2.5)

below for measurements using the port one source.


S112+ S21 2 1 (2.2)

This just means that the power that the network analyzer sends to the DUT is either

reflected back to port one, or transmitted without loss to port two.

2.3.2 Equipment Hierarchy

The UCATs uses a chain of equipment in order to extract the s-parameters out of

the DUT, each one serving a particular function.Figure 2-11 shows the block diagram of

the measurement setup. The setup has two branches of equipment flow, one flow going

through the transmission side of the UCATS, the other is the receive side. The vector net-

work analyzer (VNA) forms the head of the equipment hierarchy, controlling the flow

through each measurement branch. Chapter 3 gives more information on the transmit side

of the set-up, while Chapter 4 contains the details on the receive side.


Figure 2-11 Block diagram of equipment hierarchy.






21

2.3.3 Balun and Semi-Rigid Cable Assembly

The 180 degree hybrid couplers act as baluns, converting the signal from balanced

to unbalanced transmission lines with minimal loss. The need for the balun comes from

the fact that the VNA operates on a coaxial-based system, a transmission line with unbal-

anced center and outer conductors; and the integrated antennas typically used in the inte-

grated clock receivers possess a balanced pair of transmission lines [KimOO, Flo00]. One

cannot simply connect the balanced lines to the unbalanced lines without deleterious

effects [Bal97] These effects in the worst case could amount to a net current flow to

ground, reflecting all power sent to the antenna. Therefore, the balun assembly becomes

necessary to transition between balanced and unbalanced transmission lines.

The balun used in the UCATS was of the same type of device used in previous

works [KimOO] except that it operates over a broader frequency range. The design of the

balun, shown as a black-box in Figure 2-12, has been specified to split power between

ports 2 and 3 equally in magnitude, all the while maintaining a phase difference of 180

degrees between the center conductors of these same two ports. The specifications that the


A -3dB
To Network 180 Degree
Analyzer 180 Degree RF
Hybrid Semi-
Cou r Rigid Probes
Coupler Cables
(Balun)

50 2-1 B c -3dBdi

Figure 2-12 Balun connection diagram.






22

coupler should have less than 1 dB amplitude mismatch and 10 degrees phase mismatch

between ports 2 and 3 were given to the vendor, Krytar.

To verify the specifications, measurements were made on each of the 2 baluns pur-

chased from the vendor, each with varying results. The best of the two baluns was used

throughout this work as the default balun. The mismatch in transmission coefficient mag-

nitude and phase for this balun with its semi-rigid cables may be seen in Figures 2-13(a)

and 2-13(b). Minimum amplitude mismatch is more desirable, since the phase difference

between the two different cables was used to compensate for excessive phase mismatch.
(a) 0.80
S21-S31 =Mismatch
0.60

-c 0.40

E
0.20
(b)
0.00
14.0 19.0 24.0
W 182.0
( S21-S31=Mismatch
( 180.0

2 178.0



E
5 176.0 -

174.0
S 14.0 19.0 24.0
Frequency (GHz)
Figure 2-13 Difference (mismatch) between balun ports 2 and 3 in terms of (a)
magnitude and (b) phase.


The semi-rigid cables in the UCATS have a wider function than just connecting

the probes to a balun. As previously mentioned, the phase delay difference in between the

cables are used to compensate for the phase mismatch of the balun. Thus, each balun has






23

its own "assembly" of semi-rigid cables. Figures 2-13(a) and 2-13(b) show both the defi-

nition of mismatch and the measured mismatch using the scattering parameters of the

default balun assembly.

2.4 Calibration

2.4.1 Introduction

When using a vector network analyzer, measurement apparatuses such as coaxial

cables, probes, and transmission line transitions are often needed to connect the DUT to

the VNA. These extraneous devices add error to the measurements due in part to internal

mismatches, phase delays, and signal attenuation. Calibration is then needed to de-embed

the DUT's s-parameters from the measured data. A typical calibration procedure involves

measuring standardized loads with the extraneous equipment, and then comparing the

load's measured s-parameters with their factory-measured definitions (standard defini-

tions). In this manner the s-parameters of the extraneous devices are determined and then

de-coupled from the s-parameters of the DUT.

An example of two-port calibration method is the .\/,, t, Open, Load, Through

(SOLT). A SOLT calibration is widely used for measurements involving 3.5 mm coaxial

cables. It is performed by first measuring a .\l,N t, Open and 500 Load termination at the

end of each cable. Next, the ports are connected together through their respective cable

assemblies in the Through measurement.

2.4.2 Calibration in the UCATS

For any two-port calibration procedure, it is vital to make a Through measure-

ment. The problem with the UCATS is that it uses two different types of transmission line

antenna feeds: waveguide on the transmission side and RF Signal-Signal (SS) probes on






24

the receive side. Currently, a calibration kit (standards and their definitions) exists for

either the SS probes or the waveguide. However, no kit is commercially available for a

two-port calibration using both transmission lines.

As a result, all measurements performed in this work used the 3.5 mm SOLT

method using the HP 85052A calibration kit. A reliable Through calibration was obtained

using this method at the expense of de-embedding the effects of the baluns, probes, and

waveguides. The resulting DUT is shown in Figure 2-14.
Port
2
180deg.- RF
Couple Probes







Port

Waveguide ,Mode
Assembly Launc



Figure 2-14 S-parameter reference planes in the UCATS (effective DUT).

Due to the inclusion of the mismatch associated with using the baluns, probes, and

waveguide assembly, the gain and S21 magnitude measurements taken in the UCATS were

lower than the actual case by at least 1 dB. Some of the reasons for this degradation

include attenuation in the waveguides and probes, and leakage radiation out of the probes

and cable interfaces. Although the absolute gain measurements will be in error due to this

calibration, the UCATS will still be able to accurately measure the relative gain across the






25

wafer surface. These types of measurement issues are discussed in more detail in Chap-

ters 4 and 5.

The absolute S21 phase measurements were also be affected by this calibration.

Propagation delay through the waveguides, baluns, semi-rigid cables, and probes added to

a measured phase delay much higher than the true phase delay for the clock distribution

system. However, only the phase differences across the wafer surface, not the absolute S21

phase, are needed to determine the clock skew.

2.4.3 Left- versus Right-Hand Side Probe Stations

Another calibration issue arises when measuring a wafer using both the left and

right hand side probe stations and then comparing the data taken from each probe station.

For these types of measurements, the same probe assembly (baluns, semi-rigid cables,

and probes) is used to characterize antennas. When taking measurements on opposite

sides of the wafer, the probe assembly must be taken off the probe arms, rotated 180

degrees, and then re-mounted on the opposing probe station (Figure 2-15).Because the

differential-mode SS probes have been rotated in the process, measurements performed

with opposite-handed probe stations will be 180 degrees out-of-phase from one another.

Therefore, in order to compare measurements across the wafer's center line, 180 degrees

must be added to the lowest set of S21 phase data of either the left-or right-hand side.



Left-handedght-handed
SS Probes-.. + A--SS Probes

Safer center line

Figure 2-15 Left- and right-hand side measurements across a wafer's center-line.















CHAPTER 3
INTEGRATED RECEIVE ANTENNAS

The application of integrated dipole and loop antennas to wireless links for clock

distribution has been successfully demonstrated [KimOO, Flo00, and 098]. Accordingly,

these antennas have been exclusively used as the receive antennas in the first testchip for

use in evaluating the UCATS. The use of these integrated antennas has been continued

here because of their small size, a fundamental consideration in microelectronic applica-

tions, and their balanced transmission line configuration. Thus, these antennas, particu-

larly the dipole antenna, are examined in order to understand measurement results of the

inter-chip clock distribution system presented in this work.

3.1 Infinitesimal Dipole Antennas

From the beginnings of antenna theory, the infinitesimal dipole, or Hertzian

dipole, has been used as a benchmark for antenna design and an introduction to antenna

theory in general [Bal97]. Furthermore, analysis of integrated dipole antennas follows

directly from the analysis of this fundamental antenna. The Hertzian dipole is physically

z

(R, ,9)


d IR y

x


Figure 3-1 Cartesian and spherical coordinate description of an infinitesimal
dipole antenna.









an infinitely thin rod of perfectly conducting material, which measures in electrical length

much smaller than a wavelength of its exciting current. In terms of excitation, it is fed at

the center of the rod, such that one arm of the dipole is 180 degrees out of phase with the

other arm as in Figure 3-1.

Starting the analysis, the vector potential can be used to define the magnetic

potential. The first goal is to write down the vector potential in terms of the currents trav-

eling along the dipole. This is shown in (3.1).

V.B = 0 B = VxA (3.1)

The next step in the analysis process is to start with the description of the antenna as a

source of electromagnetic fields. Application of a sinusoidally-varying current of angular

frequency (co), the angular global clock frequency, to the dipole antenna allows analysis

to proceed with a well-known equation (3.2) for the vector potential resulting from this

current density [Jac99]. Here the primed position vector describes the distance from the

origin to the source, while the un-primed vector locates the point of observation.


PO ej(k (R R'))
A(R, t) J(R) dv (3.2)
47r IR R'|
V

Also in this equation, the wave vector (k) replaces the scalar wave number (k). The direc-

tion of k is the direction of propagation and its magnitude is equal to the wave number.

This potential is more commonly known as the time-retarded potential [Ula99]. In

this equation, the vector potential as a function of position vector and time A(R,t), is

determined by integrating the current density, written in terms of its constant spatial dis-

tribution Io on the antenna, over the volume of the source. Also in the equation, R repre-

sents the relative distance from the dipole to the analysis point, k is the wave number, and






28

po is the permeability of free space, the medium for this analysis. This dipole's small size

allows the integral to be easily solved for in the form seen in (3.3).

j(kR at)
.A(R, t) = R Iod (3.3)
4 7R 0

Next the equation is converted to spherical coordinates, and then (3.4) is used to deter-

mine the E and B fields. Here, c is the velocity of light in free space.

2
E(R, t) = cVx B(R, t) (3.4)
JCo

Now the field equations for all space and time can be written down in terms of spherical

coordinates [Ula99], they have been recorded in (3.5), (3.6), and (3.7).


Iodk j(kR -ot) 1 j_
ER(R, t) 2T e 3 (k])3 cos (3.5)
odkR 2KO4To) 1 j3


ER, 0 j(kR L- + s in (3.6)
4L (kR)2 (kR)
4 7r IRe( k ) 23


S(R, t) =je(kR ot) J 1 2+ ] sin (3.7)
B4(Rtr) I--(kR) (kR)Z


The zero-valued x and y components of A have forced the 0 component of E, and both the

R and 0 components of B to vanish. Also, ro has been used to denote the free-space wave

impedance of 377 Q.

The field expressions for the Hertzian dipole over all space and time were solved

analytically from the above integral expressions. This type of success is rarely paralleled

for actual antennas. Often, the integrals are too complex to evaluate in closed form if the






29

same method of finding the retarded potential is used. In any case, simpler expressions are

always found when the distance to the receiver (R) moves very far away, fulfilling the con-

dition of kR>> 1 in (3.5), (3.6), and (3.7). Exactly how far depends on the antenna. For the

Hertzian dipole, this asymptotic far-field form can be directly observed as the terms of

order R-2 and R-3 get vanishingly small. The resultant far-field expressions for the electric

and magnetic fields can be seen in (3.8) and (3.9).


jdl0kl0e j(kR cot) sin (38)
E(R, t) 4R e s (3.8)


PE6
B (R, t) = = B(R, t) (3.9)
110

In the near- and intermediate-field regions, the radiation characteristics of the

infinitesimal dipole contrasts with that for the far-field limit. Looking at (3.5),(3.6), and

(3.7), and taking the limit as R goes to zero, we see that for the condition of kR<<1, the

R-1 terms vanish in significance next to the R-3 term. It is convention to call this region the

near-field region. The region between these two asymptotes at kR-1, forcing the inclusion

of all terms, is called the intermediate-field region.

As the radiated electromagnetic fields by the dipole are vector fields, they contain

a fundamental direction, or polarization [Wan88]. It is convention to refer to the electric

field polarization of the antenna as the polarization, since given an outward radiation

direction [see (3.8)and (3.9)], the polarization of B follows. Thus, the polarization of the

dipole antenna is in the z direction, parallel to the length of the antenna. The radiation in

the far-field region is linearly-polarized, since the E and B fields are in phase with one

another.






30

In the far-field region, the electric and magnetic fields are perpendicular to the R

direction, which is the direction of power flow and the wave vector. In (3.10), the Poynt-

ing vector (S) has units of power density. Its time-averaged form gives a real power flow

towards infinity or radiation.

S(R,t) = ExH (3.10)

It should be noted that liberties may quite often be successfully taken using these

limits. In approximating propagation in the intermediate-field region, invocation of either

the near- or far-field limit is sometimes justified for rough predictions if either limit is

almost met. Such approximations were successfully taken in the past in clock distribution

system analyses[Kim01]. These approximations will also be used in this work when cal-

culating the radiated E-field from the prototype transmitter of the UCATS at the wafer

surface. This discussion is presented in Chapter 5.

3.2 Radiated vs. Input Power

As time averaging of (3.10) gives the real power density at a distance R away from

the antenna. Integrating over the area of the sphere formed by R yields the total power

radiated. For the ideal case of a Hertzian dipole formed by perfect conductors, this power

radiated is the same as the power input to the terminals of the antenna. However, imper-

fections in the conductors and application of the dipole to a silicon substrate complicate

this situation. The power sent to the terminals of the antenna is, in general, not equal to

the power radiated.

A lumped-circuit model may be used to simulate the power flow into and out of

the antenna from an impedance standpoint. Power sent into free space via radiation can be

modeled by a resistor, Rrad, the radiation resistance. The power dissipated by the substrate









or conductors is similarly represented by a resistor with its value the same as the total

power dissipated by the antenna. The circuit transformations shown in Figure 3-2 can be

used to illustrate how the dipole antenna's input impedance models may be derived.



V (a)
Rrad



Rloss

(b)




Figure 3-2 Various levels of small dipole circuit models: (a) ideal case and (b) finite
conductivity dipole.


Knowledge of the radiation resistance, dissipative resistance, and the spatial distri-

bution of the radiated power as a function of R translates directly to information on the

radiation efficiency, directivity, and antenna gain. The typical engineering definition of

efficiency is simply the power radiated divided by the power supplied to the two resis-

tances in Figure 3-2(b). Using the I2R definition of power, one can use the formula in

(3.11) to represent the radiation efficiency for the simple series circuit in Figure 3-2(b).


rad
arad (3.11)
rad diss

The antenna directivity is determined by the fields description of the radiation.

The directivity is a measure of the antenna's ability to focus radiated energy, as a conse-

quence, this value is a pure number often expressed in the (dB). The mathematical defini-









tions of the directivity are given in (3.12) and (3.13). Here, the average power density

radiated (S,) at R, normalizes the maximum power density at the same distance (S,,m).

S
max
D ma (3.12)
S
av


D(O, ) S() (3.13)
S
av

It is also typical to define a directivity pattern, which results from using the spa-

tially-dependent power density (3.13) instead of the maximum power density in (3.12).

The normalization of S(0,0) versus its maximum value is customarily called the radiation

pattern of an antenna.

The antenna parameter which most directly relates to the measurements per-

formed in the UCATS is the antenna gain, which is just the directivity of an antenna

scaled by the radiation efficiency. The physical definition is the power radiated over the

power input to the antenna. These definitions are given in (3.14) and (3.15). The top equa-

tion shows how an antenna gain applies to an antenna operating in signal transmission

mode with etx representing the transmitter's radiation efficiency. The abbreviation of tx

and rx in subscripts will be used to denote parameters of the transmitter and receiver,

respectively.


Grad
tx txDtx p (3.14)
in


G e D o- (3.15)
rx rx tx p .
17C








Equation (3.15) depicts how to describe the gain of the antenna operating in receive mode.

The power radiated is replaced by the power detected by the receiver at its terminals, and

here the power input to the antenna is the incident radiation. Also, the receiver's radiation

efficiency has been represented by ex.

For the purposes of describing an RF-link, dependent on both a transmitting and a

receiving antenna, a different description of gain may be used. In this case, the receiver

antenna gain, transmitter antenna gain and the attenuation due to the spherical spreading

of the free-space radiation are combined in (3.16) to form the system antenna gain (Gsys).


G =G G (GxI (3.16)
sys rx tx 4 R

This equation describes the gain of an antenna system, which is perfectly matched at both

the receive and transmit ports. In this special case, the system gain would be equal to

IS212.

Transmitter Receiver

S(1- |S112) 2(1 |S22l2)


Iin



RI RL



S1 R i P t2R
F figure 3-3 Schematic for transmitter-receiver link visualization.
Figure 3-3 Schematic for transmitter-receiver link visualization.






34

As a practical system of antennas with a finite amount of power reflection at either

port, the UCATS must still be able to extract the system antenna gain out of the measured

s-parameters. These mismatch losses can be taken into consideration by revising (3.16)

into the version seen in (3.17). This equation is illustrated in Figure 3-3 and represents the

power traversing the reflection boundaries at the input or output ports.


S21 2 = (1- S11 2)(1 S22 2)Gsys (3.17)

This equation is called the Friis transmission formula (3.17), and has been widely

utilized in the field of electromagnetic measurements to find an unknown antenna gain

using a transmitting antenna whose gain pattern is known a priori. For the UCATS, the

system gain without the extraction of the individual antenna gains is extensively used. In

this work, the system antenna gain will be called the "gain".


3.3 Integrated Antennas in the UCATS

The set of integrated antennas used in the UCATS represents the success of past

research results [Kim00].[Kin91], and [Kat83]. Thus, the loop antenna was used along

with linear, zig-zag, and folded dipole antennas on a 20 Q-cm substrate measuring 0.5

mm in thickness. These antennas have been photographed and shown in Figure 3-4.

For a comparison between the antennas, the two-port s-parameters were measured

in the range of 23-25 GHz, which is the default measurement frequency bandwidth of the

UCATS. From the S]] data, the input impedance may be extracted using the formula

given in (3.18), with Zo being the 50 Q characteristic impedance of the s-parameters.

(1 +S11)
Z. = Z 1-11(3.18)
in 0 1-S



































Figure 3-4 Wafer photograph showing the integrated antennas used as the
receiver in the UCATS.


1 -100 L
.3.5 24.0 24.5 25.0 23.0 23.5 24.0 24.5
Frequency (GHz) (b) Frequency (GHz)


25.0


-Folded Dipole
Input resistance (a) and reactance (b) for various .--Long Dipole
'Loop
integrated antennas. Small Dipole
-.Zig-Zag Dipole


150


U)
c100
0



.L 50
U)
v,


Figure 3-5









The input resistance and reactance have been plotted versus frequency in Figures

3-5(a) and 3-5(b), respectively.Periodic resonances every 0.5 GHz can be observed in

these plots. These resonances could be due in part to high coupling between the antennas

on the test chip, or inaccuracies associated with the calibration [Bal89]. These plots also

show that, for each antenna, the resistance peaks at the reactance zero crossings, corre-

sponding to resonance points. Over this bandwidth, the resistance of the folded dipole

appears closer to the 100 Q characteristic impedance of the differential-mode probes and

clock receivers.

The same 2-port s-parameter data can be used to compare the gains among the dif-

ferent integrated antennas when using equation (3.17). These data were taken in the

UCATS with a spacing of 3 inches between the transmitter and receiver. In Figure 3-6, it

can be seen that the folded and zig-zag dipole have the highest gain, depending on the fre-

quency of observation. Since its radiation pattern null is in the direction of the transmitter,

the loop antenna had the lowest gain of all the measured integrated antennas. It was the

gain data of Figure 3-6 which has led to the selection of the folded dipole as the prototype

receive antenna used in the initial characterization of the UCATS.
-35.0

-40.0

-45.0

0- Folded Dipole
-50.0 L- Linear Dipole (2 mm)
Loop
--- -Linear Dipole (1 mm) Zig Zag Dipole-
-55.03.
-5. 23.5 24.0 24.5 25.0
Frequency (GHz)
Figure 3-6 Comparison of the system gain using different integrated antennas
as the receive antennas, taken at R= 3 inches.















CHAPTER 4
PROTOTYPE TRANSMITTER AND WAVEGUIDE ASSEMBLY

This chapter describes the prototype transmitting antenna used in the UCATS. As

the antenna in question is a gaussian optics antenna (GOA), possessing a waveguide feed

structure, this chapter also provides a quick guide to the applicable waveguide theory. The

discourse then broaches the topic of GOAs and the type of fields they radiate.

4.1 Waveguide Assembly

4.1.1 Basic Waveguide Theory

As the feed to the prototype transmitter is a waveguide, it becomes immediately neces-

sary to understand the characteristics of the electromagnetic fields inside a waveguide.

Instead of a general treatment using an arbitrary waveguide, found in such sources as

[Bal89], [Jac99], or [Col60], only the structure of interest to the measurement system, the

rectangular waveguide (RWG) is considered. The coordinate system used for the discus-

sion is shown in Figure 4-1









-- -I -
z- a a I
Figure 4-1 Rectangular waveguide: coordinates, dimensions, and cross-section.

Figure 4-1 Rectangular waveguide: coordinates, dimensions, and cross-section.









This drawing replicates the cross-section of the type WR-42 waveguide used in the

UCATS, with the large lateral dimension (a) measuring 0.42 inches and the small lateral

dimension (b) equal to 0.17 inches.

Referring still to Figure 4-1, the four side walls together form the surface S, the

transverse boundary. While the fields are confined transversely, the solution in the z-direc-

tion resembles that of plane wave propagation. Thus the functional dependence of the vec-

tor field expressions takes the form [Jac99]:


E(x, y, z, t) E(x, y) j+(kz cot)
H(x, y, z, t) = H(x,y) (4.2)

Here the constant amplitude terms of the plane-wave field expressions become trans-

versely dependent functions [E(x,y) and H(x,y)].

By assuming steady-state, sinusoidal sources, Maxwell's boundary conditions, and

the source-free forms of Maxwell's equations, the field expressions in Equation (4.2) can

be solved for using the partial differential equation eigenmode-eigenfunction technique

[Sni99]. The equation to be solved is of the form:


V2 + k2 = 0 (4.3)

Here y could be taken as the z-component of either E or H, depending on the mode of

propagation. The transverse solutions are found by substituting the eigenfunctions into

Maxwell's equations (B.4).

As this solution is described in a vast number of microwave and advanced electro-

magnetics sources [Jac99], [Poz98], [Col66], [Bal89], the eigensolutions are just quoted

here. The solutions can be classified into two forms: TE, where the E-field is expressed as

being completely transverse to the direction of propagation, the z-direction and TM,









where the H-field is purely transverse to the z-direction. The eigenfunctions can be

expressed as functions of constrained wave vector (kc) and cross-sectional geometry (a, b):


(mx'\ (ny1
z(x, y, z) Emnsinma b )s y) I Jk c(44)

[H(XY,z ) H cos m7x Cos ny
mn a eb


In this above equation, the TM eigenfunction is represented by the top eigenfunction (Ez),

while the TE eigenfunction (Hz) is displayed in the bottom entry. The eigenfunctions are

in turn linked to their respective eigenvalues by the indices m and n, and the corresponding

arbitrary constants (Amn and Bmn). The transverse vector component solutions and the dual

field expression, can then be determined from the eigenfunctions using expressions

derived directly from Maxwell's Equations [Jac99] (Appendix B). It should be particularly

noted that only the TE eigenfunction can be non-zero for zero-valued modal indices, and

even then, only one index can be zero at a time.

The eigenvalues become evident when substituting the previously-listed eigen-

functions into the original wave equation, (4.3). The constrained wave vector then relates

the free-space wave vector (k) and the modal indices as

kc= k2 k2 2r (4.5)

k-^

This expression reduces easily to the cutoff mode expression when evanescent

modes are excluded [Col60]. This means that the square root argument must be greater

than or equal to zero in (4.5). Now the expression for the lowest frequency that a mode can

propagate down the wave guide, the cutoff frequency (fcmn), can be derived:










jnn 1 (mn n
f +ifAn I If(4.6)


Here pL and e are respectively the relative permeability and relative permittivity. A signifi-

cant observation is that the TE mode can propagate at lower frequencies than the TM

mode, since only the TE can have zero-valued m or n.

When this result is applied directly to the measurement spectrum, 0.045-26.5 GHz,

of the UCATS, key statements can be made. First, only the TElo mode can be detected

propagating inside this frequency band. The TE10 cutoff frequency was calculated at 14.05

GHz, while the cutoff for the next mode, TE20 was found to be 28.10 GHz. The word,

"ideally", must be inserted in the above statements with the cutoff frequency value since

all of the equations were derived for a section of waveguide with infinitely conducting

walls. Also fabrication process variation, and measurement resolution can also be labeled

as reasons for deviation from this ideal cutoff frequency calculation.

If a waveguide is finite in length, capped by metal ends in the z direction, it

becomes a resonant cavity. This means that the waveguide eigensolutions must include

another indexed term in the z-direction, and the eigenspectrum becomes more complicated

than before. However this represents a worst-case scenario, and since ideally both ends of

the waveguide are matched in the UCATS, the eigenspectrum more resembles that of a

waveguide than that of a resonant cavity.

4.1.2 Coax-Waveguide Transition

The coax-waveguide transition was used to transform the signal from the 3.5 mm

coaxial test cables to the WR-42 waveguide propagation environment required by the

horn. This is conceptually illustrated in Figure 4-2. The particular coupling mechanism









used in the assembly was a monopole probe. This device was selected for its efficient cou-

pling to the TElo mode [Pozar]. The complete analysis of this structure can be quite com-

plex, and is covered in such works as [Col60] and [Mar48], and is beyond the scope of this


S > 3.5 mm
Coax


h Monopole Probe






Figure 4-2 Simplified drawing of coax-waveguide transition.

work. The assumption that only the TElo mode has been excited greatly simplifies the

analysis [Poz98] and a first order expression for the input resistance is given by the (4.7).


-R. k (k2-k2)-1/2 (4.7)
in a f0 c

Here, the height of the probe has been approximated to the first order of b. Also we have

continued to use the free-space wave vector k, the permeability [go, and permittivity e0 of

free-space, and the waveguide transverse dimensions (a and b).

From (4.7) the scattering parameters can then be directly determined using basic

microwave relations. SiI can be expressed as a function of characteristic and input imped-

ance. Furthermore, (2.5) can be invoked to find an equation for the transferred power,

IS21 2, shown in (4.8). However, for the purposes of calculating the path gain in terms of

S21 2 = 1- S 112 (4.8)









the Friis formula, it has sufficed to simply measure the attenuation on the network ana-

lyzer, the results can be seen in Figure 4-3.

The s-parameters were measured by connecting two coaxial-WG transitions

together in cascade with the port reference planes located at the coaxial input of each tran-

sition. The attenuation through one coax-RWG transition was measured at 0.37 dB, this

means that the attenuation through one transition would be about 0.2 dB. Return loss

should be greater than 10 dB for one-transition, since the antenna is close to a matched

load.
0.0


-5.0


J -10.0
U0


-15.0
14.0 19.0 24.0
0.0


-10.0


S-20.0


-30.0
14.0 19.0 24.0
Frequency (GHz)
Figure 4-3 Scattering parameters for two cascaded coax-RWG transitions

4.2 Prototype Transmitter

The prototype transmitter consists of an abrupt junction mode launcher and the

GOA. The mode launcher converts the modes from the TElo modes propagating in the

rectangular waveguide to the TE11 and TM11 modes. The latter modes are needed by the









GOA to launch gaussian waves, which resemble plane waves at sufficiently large dis-

tances.

4.2.1 Abrupt Junction

An abrupt rectangular-circular waveguide transition has been built into the horn,

mating directly to the rectangular waveguide described in the previous section. The abrupt

junction first broadens its rectangular cross-section before abruptly changing to a circular

waveguide cross-section. In terms of modes, this junction has been shown to excite the

HE11 mode, a combination of the TE11 and TM11 modes, in the circular wave guide sec-

tion of the junction [Eng73]. This mode has been thoroughly researched in the past an effi-

cient mode for the production of gaussian beams [Cla69, Cla71].

4.2.2 Circular Waveguide

The transition to the circular waveguide necessitates the need to know the type of

modes allowed by this structure. Like the previous section, the development of the field

theory involves finding the eigensolutions which satisfy both the wave equation and the

boundary conditions on the edge of the circular waveguide cross-section. As the detailed

and complete solution may be found in most graduate electromagnetics textbooks, such as

those listed in the previous section, here simply the solutions, showing first the eigenfunc-

tions in (4.9) in cylindrical coordinates (p,4,z) are summarized.



E (p, t) A J(mnP
Ez(, t) mnn m a eJ (kz cot)4.9)
[Hz(p, z, t) = J '(mnpn
Z(PB J '
mn m( a I

The J(...) is the Bessel function of the first kind of order m, using the radius, a, of the cir-

cular waveguide in the argument forces the function to meet the boundary conditions at









the n-th zero (mn) of the Bessel function. Similarly, J'(...) is the derivative of the Bessel

function of the first kind of order m. The ,n term is the n-th zero for the same m-th order

derivative of the Bessel function.

Linked to the eigenfunctions by the modal indices, the equations for the eigenval-

ues dictate the modes propagating above cutoff in the transmitting antenna. Following

again the procedure outlined in 4.1.1, the TE eigenvalue equation is



k = 2 (4.10)
_2
k-^


Thus, from the above expressions the modes propagating in the feed of the GOA are deter-

mined. The cutoff frequency can be found using the same procedure as in the rectangular

waveguide case.

4.2.3 Gaussian Optics Horn Antenna

The GOA consists of two main parts: the conical horn with tapered corrugation, or

scalar horn, and the spherical lens which covers the scalar horn's aperture. The GOA and

its components are shown in Figure 4-4. The horn antenna is, by itself, already a highly

directive antenna, the addition of the lens only increases its ability to focus RF power. The

ability of the horn to launch gaussian waves even in the near field is what has led to its

selection as the prototype transmit antenna.

The internal geometry which causes the HE11 spherical modes to expand to a gaus-

sian mode is the corrugation on the inside surface of the horn. Its corrugation teeth are lin-

early tapered from length (L1) to the shorter length (L2) located near the aperture of the

horn. Also, the thicknesses of the teeth (tj) and gaps (wl) increase to t2 and w2 as the cor-

rugation approaches the aperture of the horn (Figure 4-5).












Corrugated


RWG
Feed


Abrupt Junction

Dielectric Lens


Figure 4-4 Gaussian lens-horn antenna shown with source and source impedance
(Zs).

---Iti t1^
Lw1



->: t1 .- Horn
Lrt2 Aperture

Circular WG
Feed

Figure 4-5 Tapered corrugation on one half of the conical horn antenna.

The spherical modes propagating across the corrugation surface are readily

expandable in terms of a Gaussian-Hermite series. The radiated fields are also of this

form, allowing the fields to be expressed in terms of gaussian modes even in the near to

intermediate-field region [Pad87, Gol82].

From a geometric optics perspective, the gaussian-spreading power in the far-field

region can be represented by a gaussian beam of rays [Ped93]. The application of the lens


Antenna









to the antenna limits the divergence of the beam, increasing both the directivity and gain of

the antenna. The application of geometric optics to submillimeter wave antenna design is

termed quasi-optical analysis.

The GOA was designed, fabricated and tested by Milltech, LLC. Using the draw-

ings supplied by the manufacturer, the antenna was simulated using Ansoft HFSS, a

finite-elements simulator. The results are summarized in Table 4-1. The maximum antenna

gain measured by Millitech in their full-anechoic chamber was 17.7 dBi, given in decibels

with respect to an isotropic radiators, while the finite element program calculated a gain of

18.5 dBi. For definitions of these far-field antenna parameters, [Bal89] or [Ula99] can be

consulted. The Antenna Gain Pattern (AGP) in units of decibels with respect to an isotro-

pic radiator (dBi) is defined by (4.11). AGP is often plotted versus spatial 0 and 0. Figure

B-2 shows the AGP of the horn antenna as simulated in HFSS. In such a plot, Half-Power

Beam Width (HPBW) can be directly determined by finding the amount of cross-sectional

angle in degrees the main lobe covers between the 3 dB points.


AGP(O,) = lOlog( G( -) (4.11)
iso

Here G(0,4) is defined to be the transmitter's spatially-dependent antenna gain, measured

at an arbitrary R value in the far-field. This gain is normalized by the gain of an isotropic

point radiator (Giso) for the same distance.

This difference between the simulated and calculated values of the GOAs maxi-

mum gain and HPBW's is considered acceptable in terms of a first order approximation.

The difference stems mainly from the boundary conditions imposed on the finite element

model of the horn and the exclusion of the corrugation. For reasons of convergence and









simulation size in terms of a good aspect ratio [Sad91], corrugation inside the horn has

been left out of the model. Keeping the corrugation in the model would cause simulation

size to exceed available computer resource. Also, for simplicity the walls of the horn

antenna have been defined as perfect electric conductors, or E-walls.

The finite element model has proven itself to be an acceptable computer model in

approximating the far-field radiation of the GOA. The results of the far-field comparison

can be seen in Table 4-1 below. This data tend to support the statement that the lens char-

acteristics tend to dominate the far-field characteristics of the GOA, which becomes

important later in making gaussian-beam approximations.

Table 4-1 Finite Element Model (FEM) vs. Measured Antenna Parameters for the GOA

Parameter FEM Measured Difference
Azimuthal HPBW 21 25.17 3.88
(Degrees)
Elevational HPBW 24 27.23 3.23
(Degrees)
Azimuthal Peak Gain 18.5 17.7 0.8
(dBi)
Elevational Peak Gain 18.5 17.8 0.7
(dBi)


The fields in the far-field region are much easier to calculate than the fields in the

near-field region for the GOA. Unfortunately, the UCATS operation is not in the far-field

of the antenna, as per optical gaussian beam theory [Ped93]. Equation (4.12) shows the

calculation of the far-field limit, RFF, The gaussian beam waist (see Figure 4-6), is the

minimum width (wo) of the gaussian beam, and ) is still the wavelength.The beam waist

212
RFF k (4.12)









in turn was found by using the far-field measurement data supplied by the manufacturer

using (4.13). Here 0 is the same as the measured HPBW.

2h
w0 (4.13)


In summary, for a 1.25 cm wavelength and 1.81 cm beam waist, far-field measure-

ments should be taken at distances much larger than 8.23 cm, or 3.24 inches [Gol82].

Since measurements in the UCATS are limited in receiver-transmitter separation to 7.5

inches, measurements taken using this system are in the intermediate- to near-field region.

For approximation purposes, propagation in the intermediate- to near-field regions

for a conical lens-horn with tapered corrugation can be put into gaussian mode

form[Gol82]. For simplicity, coupling to higher order modes has been neglected. Using

these approximations, the complex electric field solution can be written in the form of

equations (4.14), the equation for the fundamental gaussian mode (TEMoo).

EOWO jkz )z jkp2) x p2 2
E(p,z) e exp -jatan exp ( exp 2
w(z) 2 2R(z) w(z)


where: w(z) = w0+f 2


R(z) = z 1+ (4.14)
(Az (4.14)

It should be observed that both the phase and amplitude of the above expression have

gaussian distributions. Therefore, both the phase and amplitude approach a uniform distri-

bution for large distances from the transmitter, as depicted in Figure 4-6. This approxima-

tion also involves placing the location of the beam waist at the beginning of the lens

[Gol82]. The location of the beam waist determines the origin of the coordinate system.











wafer
GOA Origin




Wo






y z
Figure 4-6 Gaussian mode radiation from the GOA.


Using the knowledge that the GOAs radiation can be described according to gaus-

sian beam theory, an expression for power can be derived. Equation (4.15) is the result of

using the time-averaged Poynting vector relationship of (3.10) and Maxwell's equations

(B.5). The E-field in this equation is the same as (4.14). This equation is the power in a

plane wave (Ppw), where Zo is the wave impedance of free space. The results of these cal-

culations were used to compare with the measured data in Chapter 5.


P (4.15)
pw 2 Z

With the gaussian mode equations of the GOA, it is then convenient to predict the

measured power for two different transmitter-receiver spacings. Using Equations (4.13)

and (4.14), spatial distributions can be plotted for both power magnitude and E-field phase

with x and y as the dependent parameters for each constant-z surface. These equations,

however, should not be used to calculate the absolute gain between the transmitter and

receiver. They do not account for the transmission through the wafer, standing waves

between the wafer and lens, diffraction through the measurement aperture, or reflected






50


waves inside the antenna chamber. However, the gaussian mode equations are useful to

predict the power and phase differences across the wafer surface. Conveniently, this type

of difference analysis is what is most important for analyses of clock skew in a clock dis-

tribution system. Chapter 5 contains the results of the gaussian mode calculations the in

the context of UCATS measurements.















CHAPTER 5
PROTOTYPE SYSTEM MEASUREMENTS

Utilizing the ultra-compact antenna test system, measurements were performed

using a testchip designed to characterize the planar quality of the wave form incident upon

the chip in the context of wireless clock distribution. In addition, the data were taken in

order to verify the measurement consistency of the UCATS.

5.1 Testchip Design

The testchip used in this chapter was designed so that the spatial distribution of

power across the wafer surface could be determined. The chip contained a 13 x 13 array of

antenna cells. Each cell contained a collection of 6 different integrated antennas. The pres-

ence of the vacuum ring limited the total number of measurable antennas. Since portions

of the wafer were covered by the vacuum ring (Figure 2-5), there were antennas which

either fully or partially blocked by the vacuum ring. These antennas had impedance and


'- I" iZ 1- '- ~ -



-- \ "' __--1"1~~ ~ 7





-- -- -.. .- Measurement
\. 7--/-- Aperture
,- ,- Footprint
S. -

Figure 5-1 Testchip layout showing measurement aperture.



51






52

radiation characteristics much different than those antennas in the more central cells and

were omitted in the statistical analyses. The total array along with the footprint of the mea-

surement aperture, as shown in Figure 5-1. Note that each cell has been labeled by row and

column in the array using a matrix-style notation.

5.2 Spatial Wavefront Uniformity Measurements

5.2.1 Wavefront Uniformity Mapping at 3-Inch Separation

In order to verify the uniformity of the transmitted waveform, a critical parameter

for clock applications, measurements were made on the folded dipole element in each cell.

The collection of cells was chosen to be a 7x9 set of cells away from the edge of the vac-

uum ring. For comparison purposes, four antennas lying on the edge of the measurement

aperture were included in some of the plots. Also, two sets of data were gathered: one with

a receiver-transmitter spacing of 3 inches, and the other at the UCATS' maximum spacing

of 7.5 inches.

The data were assembled into a series of spatial distribution plots of relative gain

and phase in order to better visualize the uniformity. The spatial gain plots were extracted

using equation (3.12) and the relative phase distributions were plotted directly as the phase

of S21. All the data used in these plots have been normalized to the center cell, #66, and

analyzed at 23.7 GHz, where the S]] of the transmitter is a minimum.

Correspondingly, the phase also had to be normalized. Phase data on the right-side

of the wafer was consistently 180 degrees out-of-phase with data on the left-side of the

wafer due to the probing issues discussed in Section 2.4.3. The relative gain and phase

data for a receiver-transmitter spacing of 3 inches were collected and plotted in Figures

5-2 and 5-3. The gain from this center cell, was observed to be considerably higher in

value than that of adjacent cells, by about 6.8 dB. The antennas lying over the edge of























































Figure 5-2 Spatial distribution of relative gain from center for 3-inch separation
(mean= -7.52 dB, standard deviation= 2.85 dB).























































Spatial distribution of relative phase for 3-inch separation
(mean = -30 degrees, standard deviation= 18.5 degrees).


Figure 5-3






55

the vacuum ring, seen as the four corer points in Figures 5-2 and 5-3, were measured to

have gain lower than the center by approximately 25 dB. Overall the average gain relative

to the peak value at the center was -7.52 dB with a standard deviation of 2.85 dB exclud-

ing the four corner points.

The phase distribution for the 3-inch separation measurements varied in both the

positive and negative directions from the central datum. However, the points which varied

in the positive direction from the center were cell locations 64, 65, and 67. Again, the cor-

ner points deviated significantly at an average of -77 degrees from the center value. Alto-

gether the measurement statistics for the phase data amounted to an average relative phase

shift of -30 degrees from cell #66 with a standard deviation of 18.5 degrees.

5.2.2 Wavefront Uniformity Mapping at 7.5-Inch Separation

Even though practical application of the wireless clock distribution requires the

receiver and transmitter to be placed at a minimum distance from one another, for compar-

ison it was useful to perform the same measurements at a distance closer to the far-field of

the transmitter. The distance of 7.5 inches was chosen because it coincides with the maxi-

mum range possible in the UCATS. However, the low S21 measured at this spacing, from

the range of (between -45 and -58 dB), meant more variance in the measurements due to

the closer proximity to the -75 dB noise floor of the measurement system. The spatial dis-

tribution pattern of the gain (Figure 5-4), like its 3-inch separation counterpart, was

peaked at the center cell of the measurement array. However, the rest of the distribution

did not fall off in the same monotonic manner as the data set in Figure 5-2. Instead, there

was a set of peaks and nulls located just outside the center, varying about 3 dB from crest

to trough. Nevertheless, excluding the edge points located on the edge of the measurement

























































Figure 5-4 Spatial distribution of relative gain for 7.5-inch separation
(mean= -3.77 dB, standard deviation= 2.90 dB).
























































Figure 5-5 Spatial distribution of relative phase for 7.5-inch separation
(mean= -15.6 degrees, standard deviation= 10.5 degrees).









aperture, the data did have less variance than the 3-inch data with a mean relative gain of

-3.77 dB and a standard deviation of 2.90 dB. Interestingly enough, the corner points var-

ied less from the center than the first set of data, ranging from -10 to -20 dB down from the

center.

Correspondingly, the phase data also saw a set of minima and maxima, distributed

around the center point. Also following in the same trend as the 3-inch separation data, the

positive deviation was clustered around the center, with cell #67 having a value of 12

degrees above the center point. The mean for this set of data was -15.6 degrees phase

delay relative to the center, while the standard deviation was 10.5 degrees.

5.2.3 Estimated Clock Skew from the Uniformity Data

One of the defining metrics in the analysis of clock distribution systems is the

clock skew. Therefore, it is desirable to be able to determine the total clock skew of the

transmitter-receiver system under test inside the UCATS. Finding a conservative estimate

for clock skew of the prototype GOA/folded dipole combination involves simply deter-

mining the range of deviation, dividing by 8, and then dividing by 360 degrees to find the

clock skew as a percent of the period. The factor of 8 in the denominator is due to the fact

that the current wireless clock distribution receivers feature a divide-by-8 counting archi-

tecture.

Using the data from the uniformity measurements in the previous sections and the

formula for clock skew, explicitly written in equation (5.1).


Skew (Max-Min\ 0 (5.1)
8 -360 J









Clock skew for the prototype system may now be determined. Equation (5.1) only calcu-

lates skew based on phase data, the fact that skew may also be dependent on the signal

amplitude deviation across the wafer is also concern. This, however, is left for future work,

as it is currently believed that the skew is much more sensitive to phase mismatches.

The result of the skew calculation at 3 GHz has been tabulated in Table 5-1. A

clock skew of 1.7% of the period found for the 7.5-inch separation data and 3% clock

skew was calculated for the 3-inch case. Both are well within the current skew tolerance

limits for microprocessors. In addition, these skew values represented synchronization

over a 3.8 cm x 3.1 cm area at 3 GHz, which is a much larger area than previously thought

possible.

Table 5-1Clock skew for prototype external clock distribution system

Measurement Mean Range Skew
Set (Degrees) (Degrees) (% Period)
3 inch -15.6 75 3.0
7.5 inch -10.6 50 1.7


5.2.4 Comparison with Gaussian Beam Theory and FEM Simulations

The gaussian mode equations of the lens-horn antenna (4.14) can be used with

varying success to predict the measured wave fronts detected when the folded dipoles are

probed. The varied success may be particularly seen when the data collected during the

previously described uniformity measurement sets at 23.7 GHz are organized by rows and

compared with the plots according to equation (4.15) using the coordinate system defined

in Figure 4-5. The results of this comparison between the gaussian optics (GO) and FEM

calculations and the measured data for row 6, gain and phase, have been plotted in Figures

5-6(a) and 5-6(b), respectively. There were two sets of measured data, corresponding to
























-5.0




10.0


15.


Figu


60

the data taken from probe stations on opposite sides of the wafer. For these two plots the

measured data correlated more with the calculated towards the edge of the wafer, and the

correlation was the worst when the distance from the wafer center (p) ranged between 0.5

to 1 cm.


a) (b)
10.0
5.0
0.0
-5.0
-10.0
-15.0
-20.0
-25.0
-30.0
GO -35.0 GO
Right-Side Probe -40.0 -e Right-Side Pro
Left-Side Probe Left-Side Probe
FEM -45.0 FEM
-50.0
2.0 -1'.0 0.0 1.0 2.0 55.2.U -1.U UU 1.U 2
Distance from Center (cm)
ire 5-6 Center row comparison between GO calculated, FEM simulated, and
measured (a) gain and (b) phase at 3-inch transmitter-receiver spacing.


In addition, these plots show that the FEM simulations agreed much better with the

measured phase data than the gaussian optics calculations with the exception of the p=1.9

cm points. The FEM phase simulations on the edge of the wafer were possibly affected by

edge currents, which were caused by edge diffraction in the FEM model (Figure B-4).

Conversely, the GO calculations were largely in error for the middle three data points, but

more closely matched the measured data at the edge points. (This disagreement between

the GO calculations and the measured data was expected since the gaussian-beam calcula-

tions did not account for any reflected signals or standing waves between the wafer and

lens.)


0.S









The rest of the rows are plotted against their respective GO and FEM calculations

in Figures 5-7(a) and 5-7(b). The difference between the measured curves and the GO cal-

culations is smaller as cell rows farther from the center are plotted. The GO calculations

shown in these figures were slightly better at predicting the measurements since the stand-

ing wave magnitude has decreased in this region. However in each set of plots, the differ-

ence between the GO calculated and measured phase was always much higher than the

gain differences.Overall, the FEM calculations were better than the GO calculations at

predicting the measured gain and phase variations across the wafer.
a) 0 10




~5~-10



-30

--5
-108 FE -40 2.0




.-5
-20 -10 0.0 1.0 20 -2.0 -1.0 0.0 1.0 2.0


-10 -5 -51
c4 / GO Calculated (D
(D0-6- Right Side Probe -25
Left Side Probe \ -
-8- -FEM Y -35
-10__________________ -45
-2.0 -1.0 0.0 1.0 2.0 -2.0 -1.0 0.0 1.0 2.0
Distance from Center (cm) Distance from Center (cm)
Figure 5-7 Measured versus GO-predicted gain and S21 phase values at (a) row 7
and (b) row 8 at R=3 inches.






62

The data for the R=7.5-inch separation measurements appeared to be less con-

forming to calculations, possibly suggesting other interfering phenomena, such as

reflected waves in the isolation chamber, or diffraction through the measurement aperture

(Figure 5-8). In addition, due to computer resource limitations and convergence difficul-

ties, the 7.5-inch separation case could not be simulated by FEM.
(a) 0 20

-2 10



S -6 --10

-8 -20 -
(b)
-1.0 -1.0 0.0 1.0 2.0 -3.0 -1.0 0.0 1.0 2.0
4 .40

2 20

0 0 -

-2 a -20


-42.0 -1.0 0.0 1.0 2.0 -42.0 -1.0 0.0 1.0 2.0
5 35

-25 -
0 m 15


1-5 \- -5
E-15
-10
-25
-2.0 -1.0 0.0 1.0 2.0 -2.0 -1.0 0.0 1.0 2.0
Distance from Center (cm) Distance from Center (cm)
Figure 5-8 Gaussian calculation comparisons -Cal
-Calculated
for R=7.5 inches: (a) row 6, (b) -Right Side Probe
row 7, (c) row 8. Left Side Probe









The diffraction could come from the currents excited around edge of the measure-

ment aperture by the transmitted wavefront. At the R=3-inch separation, this was not a

problem, since the transmitted beam did not sufficiently spread from its beam waist diam-

eter to excite these edge currents. At R=7.5-inches a wider, more plane wave beam is

transmitted by the GOA, inducing edge currents in the absorber around the measurement

aperture. From electromagnetic theory [Jac99], significant currents circulating around the

edge of an aperture on an opaque screen (transmitter platform) are sources for diffraction.

However, more work is needed to fully understand the differences between the measured

and simulated data.

5.2.5 Standing Waves

When R= 3 inches (Figures 5-6 and 5-7), the disagreement between the GO calcu-

lations and measured data can be reconciled when one assumes the existence of a spa-

tially-confined standing wave. This standing wave, thoroughly researched in laser

resonators [Ver89], is created between the wafer and the lens inside the UCATS (Figure

B-4). Due to the curvature of the lens and the planar boundary formed by the wafer,

E-field waves incident upon the center of the lens are gradually guided with each

lens-reflection away from p=0, towards the absorbing walls in the antenna chamber. Inter-

ference with other waves, including the direct path, is limited to only a few passes. Thus,

the standing wave is confined in space, and is responsible for a series of minima and max-

ima across the wafer surface.

Since the GO calculations assume only one-way propagation along the LOS path,

only the FEM simulations were of use in describing this effect. The simulations for the

3-inch separation case showed that there is a variation in power and phase over the surface









of the wafer in agreement with the measured data (Figure 5-5). However, for the

R=7.5-inch case, due to computer resource limitations, the standing wave could not be

simulated using finite elements.

5.2.6 Right- versus Left-Hand-Side Measurements

In order for the UCATS to be a useful measurement platform, the measurement

offsets using the right- versus left-hand side (RHS versus LHS) probe stations, which

allows mapping of a 3.8 cm x 3.1 cm area, must be analyzed. This analysis can be per-

formed by checking the center row. Since a probe mounted on one of the two opposing

probe stations can reach exactly half of the wafer plus the center row, measurement offset

may be studied by performing center row measurements from probes mounted on each

side. As the measurements from each side are performed at different times, under different

calibrations, and with different probe landings, this can also be seen as a way to gauge

measurement robustness in the UCATS. The data for the maximum and average gain and

phase differences across the rows for both separation distances have been included in

Table 5-2.

Table 5-2 Center-row reliability check data

Max. Mean
Separation/ Max Ma.
Diff e Location Difference
Parameter Difference
(cell #) (Offset)
3"/ 2.55 #62 1.35
Gain (dB)
3"/ 13 #63 5.5
Phase (deg.)
7.5"/ 3.05 #67 1.2
Gain (dB)
7.5"/ 31 #68 13
Phase (deg.)






65

5.3 Frequency-Dependent Measurements

5.3.1 Measurement Dependence on Probes

For an acceptable measurement set across the wafer surface, the impedance of the

transmitter should not be changed upon varying the location of the probes on the wafer

surface [Rep88] and [Pet93]. The S11 has been measured for various probe locations

across the wafer at the two separations used in the uniformity measurements. This can be

used to investigate the probe-transmitter coupling effect (Figure 5-9). The transmitter's
0.0

-5.0

-10.0

-15.0

-20.0
0.023.0 23.5 24.0 24.5 25.0


-- -10.0
CO

cE -20.0


-30.
230 .0 23.5 24.0 24.5 25.0
0.---
R= 3 inch
-5.0 -...-- R= 7.5 inch


-10.0


-15.0 -

-2002 Uo 2..5b 24.0 24.5 25.0
Frequency(GHz)

Figure 5-9 SII stability for various same-row cell locations: (a) R = 3 inches, (b) R =
7.5 inches, (c) no wafer.






66

return loss data are affected by less than 0.5 dB for different probe locations. Also shown

in this figure is the shifting of the 24.5 GHz null as the distance is increased from R=3

inches to R= 7.5 inches. Figure 5-9 (c) shows how the S11 of the GOA decreases by about

4 dB when there is no wafer on the vacuum ring. This is a clear indication of the presence

of a standing wave, since with a wafer over the transmitter, there would be a significantly

larger amount of the power reflected back into the GOA.

5.3.2 Frequency Dependent Gain Data

As indicated in the wafer uniformity data, the frequency dependent gain of the

folded dipole varied significantly from one cell location to another. Going down a row on

the test chip, the gain towards the center of the wafer tended to be peaked at 23.7 GHz, the

frequency of uniformity analysis and the resonant frequency of the transmit antenna
(a) -30.0


--40.0 :


-50.0


-60.0
S 2-60.0 .0 28.5 24.0 24.5 2,.0
(b) _jn n I -- I


* -50.0
C0


-uu.23.0 23.5 24.0 24.5 25.0
Figure 5-10 Frequency-dependent gain plots for: (a) R = 3 inches, (b) R= 7.5 inches.









(Figure 5-10). Also in each plot, on every cell location, there are frequency-dependent

nulls.Furthermore, the location of the nulls changed for different cell locations. Finally, as

in the uniformity data, there was more gain variation across the frequency range when the

separation distance is increased to 7.5 inches.

The data for cell location 61, previously left out of the uniformity data, have been

included in Figure 5-10 for comparative purposes. Compared to cell locations not border-

ing on the aperture edge, it had the poorest gain over the frequency band, the steepest dip

of all the cell locations, and a much higher phase delay (Figure 5-11). The high phase

delay was observed due to its proximity to the vacuum ring. In order for the signal to be

(a)200





c -200
U)
C-

-400


-600
23.0 23.5 24.0
(b)


0-200
-
( -400 -Cell 61
Cell 62
-Cell 63
e.-600 .-- Cell 64
Cell 65

-803.0 23.5 24.0
Frequency (GHz)

Figure 5-11 Frequency-dependent S21 phase plots for: (a) R= 3 inches, (b) R=7.5
inches.






68

detected by this antenna, part of the signal had to propagate through the dielectric vacuum

ring with a higher permittivity.

The reasons for the significant variation in the gain-frequency plots could be a

combination of coupling between the antenna elements, measurement reliability, standing

wave effects, or resonance in the isolation chamber. Figure 5-12 shows another collection

of gain data, which further illustrates the gain variations. These plots contain the same

trend as both of the gain-versus-frequency plots in Figure 5-10: the gain decreases in over-

all magnitude for cell sites farther from the center. In Figure 5-12(b), both the gain and
(a)
-30.0



-40.0 _--



c -50.0



-60.0
23.0 23.5 24.0 24.5 25.0

(b) -40.0


-45.0


-50.0 Cell 62
", Cell 82
= Cell 63
-55.0 Cell 83
Cell 86
Cell 86
-60.0
23.0 23.5 24.0 24.5 25.0
Frequency (GHz)
Figure 5-12 Column-wise comparisons of frequency-dependent gain data for: (a) R=
inches, (b) R= 7.5 inches.









null magnitudes increase along all three columns as the row number changes from 6 to 8.

The relation between the data of Figures 5-12 and 5-10 further emphasizes the need to

identify the sources of the nulls at the 7.5-inch separation, since the null severity and gain

degradation increase with distance in any direction from the center cell.

5.4 Measurement Summary

5.4.1 Uniformity Measurements

As discussed earlier, spatial plots of relative gain and S21 phase at two different

receiver-transmitter separations were assembled with the purpose of determining the uni-

formity of the transmitted wavefront. The data were collected by individually probing the

folded dipole antennas in each cell over a 3.8 cm x 3.1 cm area on the test chip. The statis-

tics are summarized in Table 5-3 below along with the offset for RHS versus LHS probe

measurements. All data are referenced to the center cell measurement. The data indicate

that, when fit to a unimodal normal distribution, the shape of the gain distribution is

roughly the same for each separation value. However, measured gain for the 3-inch sepa-

ration varied more on average than the data for the 7.5-inch separation. For the phase data,

the uniformity improved in both shape and average deviation when the receiver is moved

from 3 inches to 7.5 inches away from the transmitter.

Table 5-1 Uniformity statistics for relative gain and phase

Separation/ Mean LHS/RHS Max-
a 30
Parameter Deviation Offset Min
3" -7.52 2.85 8.55 +/- 1.5 14.7
Gain
3" -30 18.5 55.5 +/- 5.5 97
Phase
7.5" -3.77 2.90 8.7 +/- 1.2 13.6
Gain
7.5" -16 10.5 31.5 +/- 13 51
Phase









From the phase data, the clock skew was calculated assuming a divide-by-8

receiver architecture. Measurements taken at R=3 inches yielded a skew of 3.0%, while.

measurements for full separation (R=7.5 inches) corresponded to a skew at 1.7%

5.4.2 Uniformity Measurements versus Predictions

There was only partial agreement of the above measured data with the theoretical

gaussian optics (GO) calculations at the 3-inch separation due to the proposed presence of

a standing wave confined to the center of the wafer. The data agreed better with the GO

calculations when the data were analyzed along row 8, the row farthest from the center

row. There was little agreement between the GO calculations and the data taken at row 6,

the center row of the wafer, except at the edges of the wafer. However, the simulations per-

formed using the finite element method (FEM) agreed better with the phase data in the

central region of this row. In fact, overall the FEM calculations agreed with the measured

data much better than the GO calculations. This can be seen when the measured gain and

phase are plotted with the two calculation methods along row 7 and row 8 (Figure 5-7).

The gaussian calculations did not have any correlation with the data when the sep-

aration was increased to 7.5 inches. Also, because of the prohibitive size, no FEM solution

could be generated at this separation. The lack of agreement between the GO calculations

and the data could possibly stem from diffraction through the vacuum ring aperture, or

reflected waves and resonances inside the antenna chamber.

5.4.3 Frequency Dependence

When the gain was analyzed versus frequency, the measured data between the two

different separations became even more disparate. In both row and column analysis, the

gain plots for R=7.5 inches showed that there were frequency-dependent nulls, which






71

became worse for increasing distance away from the center cell. For both separation plots

the gain magnitude over the entire bandwidth decreased as the distance from the center of

the wafer increased, in agreement with the uniformity data.

The measured S11 data for both separations showed how probing different loca-

tions minimally influenced these measurements. However, the Si1 was strongly influenced

by the separation distance.















CHAPTER 6
SUMMARY AND FUTURE WORK

6.1 Summary

An ultra-compact antenna test system (UCATS) has been developed for specific

application to externally-transmitted clock distribution systems (ECDS) operating at the

global clock frequency range of 14-26 GHz. Some of the user-friendly features included

continuously-variable receiver-transmitter (RX-TX) spacing, modular vacuum ring

design, and compatibility with standard vector network analyzers and RF probe stations.

The UCATS is also the first known near- to intermediate-field electromagnetic measure-

ment environment in terms of its small physical size relative to frequency bandwidth, the

use of a densely-packed (spacing<
[Wan88, Pet94, and Rep88].

In order to characterize the measurement system and to provide a benchmark for

future designs, a prototype ECDS was also designed as part of this work. A gaussian

optics horn antenna (GOA) was used as the transmitter due to its capability of emitting

gaussian waves, which closely approximate plane waves. An array of integrated antennas

typically used in wireless clock receivers were used as the receive antennas. From initial

measurement results, the folded dipole was chosen as the default antenna for characteriza-

tion of the UCATS.

Measurement results using the UCATS showed promising results for the measure-

ment set collected at a spacing of 3 inches. To facilitate usefulness to clock distribution









development, data were expressed as relative gain and phase to those of the wafer center.

The measurements along array rows showed agreement with the gaussian beam theory.

However, the agreement was better for data from the cell rows away from the middle of

the wafer, particularly along row 8. Data from the center row was largely different than the

GO-calculated data, suggesting a standing wave between the wafer and lens. Finite ele-

ment simulations confirmed these assumptions, and overall agreed better with the mea-

surements at the center row than the GO calculations. Measurements at this range showed

a clock skew of 3% at 3 GHz over a 3.4 x 3.1 cm. This was well within the suggested 10%

global skew tolerance over an area well beyond the current or projected size of micropro-

cessors [SIA01].

The measurements performed at an RX-TX spacing of 7.5 inches, the maximum

separation allowed in the UCATS, were both promising and surprising. Unlike the results

for the 3-inch case, the measurements strongly disagreed with gaussian beam predictions.

However, even with this variation, the results yielded a measured clock skew of 1.7% over

a 3.4 x 3.1 cm area.

In conclusion, the UCATS proved to be a reliable platform for ECDS characteriza-

tion. The fact that the antenna measurements agreed better with the underlying theory for

decreasing receiver-transmitter spacing, should not mitigate its usefulness to the micro-

processor industry. In fact, in a practical ECDS, the transmitter should be placed at a min-

imum distance from the receiver for compactness, making decreased spacing desirable.

Measurements taken with a prototype inter-chip clock distribution system suggest that it

may be possible to increase the size of multi-GHz synchronous systems well beyond what

is currently believed possible









6.2 Future Work

There is much work which could improve the performance of wireless clock distri-

bution using the UCATS. Such efforts could include an improved vacuum ring design to

eliminate multipath, numerical algorithms such as wavelets to increase standing-wave

analysis capabilities, and investigation using further wavefront uniformity mappings at a

wider range of RX-TX distances. Finally, the inclusion of a matching layer below the

wafer could effectively take out the dependence on the spatially-confined standing wave.

In addition, the task of developing the transmitter and receiver for the interchip

clock distribution systems is also a critical area for future development work. Fitting a

longer electrical-length antenna into a smaller area is still an open task. Possible antenna

structures include log-periodic and fractal antennas.

Likewise, further work studying the feasibility of the ECDS could prove to be

technically challenging. Such work would eventually involve the insertion of the heatsink

and packaging between the receiver and transmitter link. The continued development of

external clock transmitters should proceed in line with the feasibility studies. Practical

transmitters should be more planar in structure than the lens-horn combination prototype

used in this work, making their size easier to fit inside a computer system. Such structures

could include microstrip arrays, which could give the freedom of aligning gain maxima

with receivers.















APPENDIX A
DRAWINGS FOR THE ULTRA-COMPACT ANTENNA TEST SYSTEM

A. 1 Engineering Drawings for the UCATS

The assembly drawings are shown here as they were sent out to the machine shop.

All parts were fabricated in Aluminum, except for vacuum ring, which was fabricated in

polyethylene. Graphics may appear distorted, since they have been reshaped to fit the for-

mat of this document. In addition, photographs of the assembled UCATS are shown in the

final section, A.6.
/- - - -
/


6 4" 5"

1/4 I 1/4" 7" 6.125
2" 1
I I

14" l 25 6.12




2"

I 1.5" 3" 3" In 3.5"
1.5" I

13.25"
0.5"
Figure A-i Isolation chamber sidewalls.




























Figure A-2


II/
I11i


-


Back-panel of isolation chamber.



Top View


6"

I 4-


0.5"


Top view of back-panel.


Figure A-3



























<"


+ + +


Figure A-4 Front-panel of isolation chamber with access door.











1.25" (typical spacing)


2.75"
44 ow


0.75"spacing from edge
typicaF


12.25"


~ 9/16 smoot
bored hole


Figure A-5 Transmitter platform.


41 wo















1/8" diameter circular
groove


IXCB


holes drilled completely through part


Figure A-6 Vacuum ring.














7/16" 1
1/a6" diam. hL


1/8" diam. hemispherical groove (h. g. )
I i


1/16" diam. h. g.
- ( for O-ring)


1/8" diam. screw drilled


1/4 "sdwy (countersunk)


1/8" h. g.


5/16"
- -.


(note all measurements
on grooves
are the same as
XCA


Vacuum ring cross section.


0.5"


XCB


Figure A-7








1.5"
--


3/4"


I I


I


3/4" t


2"




3/4"


0.5"

Top View


to accommodate 6 1/2" diameter SHC screws


Figure A-8 Threaded "L" steps.


1.25"

I


2.5"


3/4'



























































.M


Figure A-9


Vacuum ring platform.
























3.5"

---,--, -/Ai"


0.5"

11


2.25" diameter hole
0-------------


4.125" diameter cut


-4---


C




ZI
0


rC



C)
*1-

Q

0
C)

00


I









A.2 Photographs of Assembled UCATS


The UCATS was photographed, and the results are shown below in Figure A-1.

The top panel of the antenna chamber has been taken off to reveal the GOA transmitter on


Figure A-11 Photographs of the assembled UCATS: (a) inside the antenna chamber
and (b) top-down view showing through the vacuum ring.






85

the transmitter platform, surrounded by absorber [Figure A-1 l(a)]. Figure A- l(b) shows

a top-down view of the UCATS. Here, the transmitter can be seen through the measure-

ment aperture in the white-colored polyethylene vacuum ring.















APPENDIX B
FINITE ELEMENT SIMULATIONS

B. 1 Electromagnetic Application of Finite Elements

B. 1.1 Introduction to the Theory of Finite Elements

The theory of finite elements was originally applied by civil engineers to the anal-

ysis of structures. However, this numerical technique for solving partial differential equa-

tions has been generalized to all engineering fields. In electrical engineering, this

technique is used to provide numerical solutions to Maxwell's Equations, (Eq. B.1), in

3-dimensional physical space. The sources, or particular solutions to the partial differen-

tial equation, are represented by p, the charge density in the medium, and the current den-

sity source, J.


VB = 0 VxE =
at

V D = p VxH= J+D
6t (B.1)

Now the constitutive equations (B.2) are used to express in terms of the H and E

fields. Here a has been taken as the conductivity of the domain being analyzed.

J = aE

D = eE B = pH (B.2)

Using this relation between J and E, assumption of a time-harmonic current density

source, the complex permittivity, C' in (B.4), and the time-harmonic field









= e+j (B.3)

expressions, Maxwell's equations may be expressed as (B.4). Note that p has disappeared.

It is assumed that our system is purely electrodynamic, or no initial charge exists prior to

source application.

V p-H = 0 VxE = -joctH

V. E = 0 VxH = jo'E (B4)

With this suggestive form, Maxwell's equations condense into the vector wave

equation, (B.5). In this equation, k is the same as o2pe. This is the partial differential

equation to which the software package, Ansoft's HFSS, now applies the finite element

method.


Vx(Vx E) -kE = 0 (B.5)

The finite element method starts by projecting the above equation over the domain

of analysis (Q) using a collection of weights (W,), for example, the lens-horn antenna, as

in (B.6). The domain discretizes into N small tetrahedron-shaped subdomains (Qi), or

finite elements.

N

Sf [Vx (Vx E) k2E] W = 0 (B.6)
i= li

The space spanned by the projecting basis functions is typically a piecewise poly-

nomial space [Bre94], and must adequately represent the variation of the fields over each

small tetrahedron. For a given, non-trivial, field distribution, the choice of a simple basis

function implies decomposition into a larger number of elements than a more complex









basis function. In other words, the solver must be able to write the E-field locally on each

subdomain in the form of(B.7).

N
E = x nW (B.7)
n= 1

In order to incorporate surface boundary conditions (BC) into the solution, (B.8)

can be written, with the help of Green's theorem, in the form of (B.8). The boundary inte-

gral is evaluated over the surface of the domain (8&).

(B.8)
(Vx W ) (Vx E) k2 (E- W )] d = BCdQ


The software then solves for the fields by using the expansion of E, with (B.7) in (B.8).

Equation (B.9) represents this development.

(B.9)

I x [(Vx W ).(Vx W -k2(WW W)]d d = BCdQa


This equation, summed over m and n, enables matrix formulation of the form: Ax=b with

x and b as column vectors. Solution of this equation is the E-field distribution over the

entire domain.

B. 1.2 Convergence by Error Analysis

Because the initial mesh, or decomposition of the domain into subdomains, might

not lead to an acceptably accurate solution, a mesh must be refined to obtain a more accu-

rate solution. The analysis of the error and re-meshing of the domain into smaller subdo-

mains allow this eventual convergence upon the desired solution. The software computes

the percent difference in power of the fields, AS, after each mesh. If the percent difference









in the fields is equal to or less than the user-defined stopping criterion, the re-meshing

stops and the field solution after the last mesh is the final solution to the problem.


B.2 Simulation of Prototype Transmitter

B.2.1 Model

The gaussian lens-horn antenna, in order to verify manufacturer specifications,

was drawn inside Ansoft HFSS using its CAD-style interface. Due to the symmetry of the

structure, and the resulting symmetry of the fields inside, it was necessary to draw only

half of the structure, and in fact it could also be done with a quarter of the system. Figure

B-l shows the simulated system.



Port (and origin) z omLens (Rexolite)
I Horn r= 1.25
1 (Perfect E) PMLxyz







PMLyz


The prototype transmitter, as drawn inside Ansoft HFSS.


Figure B-l









B.2.2 Sources and Boundaries

The model, drawn above in figure B-l, was then assigned a set of boundary condi-

tions. The cross-sectional plane of the model was given the H-symmetry boundary. When

this boundary condition is applied to a surface, HFSS assumes symmetry with respect to

the selected surface, keeping the H-fields tangentially continuous across either side. Next,

the inside of the horn was designated a Perfect E boundary, effectively making this surface

a perfect conductor and forcing the E-fields to be normal at this boundary. Also, the wall

framing the lens and horn aperture was also assigned a Perfect E boundary.

Around the lens, a bounding box of Perfectly Matched Layers (PMLs) were placed.

These boundaries, drawn and defined automatically using a macro inside HFSS, have been

developed by Ansoft to efficiently solve for radiated fields from an antenna. The notation,

xy,xyz,x, etc., has been used to designate the axis of anisotropy, as the PMLs are basically

a virtual anisotropic material.

Finally, the semi-circular cap at the end of the horn was assigned a port designa-

tion. This source has been defined as an ideal waveguide source, exciting the waveguide

feed of the horn, as if the waves were sent from an infinite distance away. In each simula-

tion, excitation control of the entire model is given to the port source.

B.2.3 Single Frequency Simulation at 23.7 GHz

A single frequency simulation at 23.7 GHz was performed in order to find an accu-

rate field solution at the UCATS frequency of analysis. A convergence value of 0.001 W/

m2 using 40,000 tetrahedra was achieved using this model. The results are summarized in

Table 4-1, but the phi and theta plots for the antenna gain pattern are shown in Figures in

Figure B-1.











20.0

15.0-

10.0

5.0

0.0

-5.0

-10.0

-15.0

-20.0

-25.0(


20.0


Phi (degrees)
Antenna Gain Pattern (AGP) plots for (a) 0=90 degrees, (b) 0= 90 degrees
in spherical coordinates.


Theta (degrees)


Figure B-2






92

B.3 Standing Wave Simulations

Instead of analysis using complicated special function theory, the standing wave

inside the UCATS was investigated using Ansoft HFSS. This was accomplished by the

inclusion of the wafer into the model used in Section B.3, and reduction to half of the

model size using symmetry. The new model has been defined as in Figure 5-2. However,
X .Z
Ix Surrounding PMLs
(Ideal Absorber) virtual boxes
(Iused to optimize
source meshing)
I


1,4 of
\\ afei


lens-horn symmetry
combination planes


Figure B-3


Impedance BC at wafer surface y

Finite element model used to simulate R=3-inch separation case inside
the UCATS.


due to its larger size compared to the previous model of only the lens-horn antenna, the

convergence criterion was relaxed to under 0.008 (W/m2) in order to prevent overflow of






93

computer resource. In Figure B-4, the phase and power of E is plotted versus the dis-

tance from the wafer. The increase in the gain around 2 cm is what was referred to as the

gain due to the diffraction-induced currents in Section 5.2.5


130.0


Figure B-4


Distance from Wafer Center (cm)

Plot of EO 's power and phase over lateral dimension of wafer.










Next, the spatial distribution of E-field strength across the simulated wafer is

shown in Figure B-5. Note, again, that the maximum shown at the edge of the wafer did

not corroborate with the measured data, and could be a simulation artifact resulting from

the fact that our wafer is "suspended" in free space in the model. Therefore, this area of

high field strength in the simulator could be due to the edge diffraction of the incident

radiation around the edge of the wafer. .




-. uII|.ECr'
m 3


















Figure B-5 Distribution of FEM-simulated E-field strength across the area of the
wafer.




Figure B-6 shows a spatial distribution on the x-z plane of the typical minima and

maxima associated with standing waves along the y-dimension between the wafer and

GOA. The power and phase of the standing wave are plotted single-dimensionally versus y

in Figure B-7.