EXPERIMENTALSTUDIESOFMICROWAVEPROPAGATIONTHROUGHFIRESFOR THROUGH-WALL,SEARCH-AND-RESCUERADARINFIREFIGHTING ByAndrewKennethGerkenTemme ADISSERTATION Submittedto MichiganStateUniversity inpartialfulÞllmentoftherequirements forthedegreeof ElectricalEngineeringÑDoctorofPhilosophy 2015 ABSTRACT EXPERIMENTALSTUDIESOFMICROWAVEPROPAGATIONTHROUGHFIRESFOR THROUGH-WALL,SEARCH-AND-RESCUERADARINFIREFIGHTING ByAndrewK.Temme FindingpeopletrappedinsideofaburninghouseisextremelydifÞcult,dangerous,andtime consuming.Smoke,heat,unfamiliarßoorplans,andpossiblestructuralcollapseallcombineto challengeaÞreÞghterÕsabilitytoÞndaperson.Thermalimagingcameras,themostadvanced technologyavailabletoÞreÞghterstoday,areabletoseethroughsmokebutareunabletosee throughwallsandhouseholditems.Through-wallradarandvital-signdetectionradarofferan imagingmodalitythatmaybeabletohelpÞreÞghtersÞndvictimsfromoutsideofaroomor evenahouse. Flamescaninteractwithelectromagnetic(radar)wavesbecausetheßamescreateaweakly- ionizedplasma.Previousworkhaslookedatsmallßamesfueledbypuregasesorßamesfrom wildÞres.Combustableitemsinahousearetypicallypetroleum-basedproductsthathavedif- ferentcombustionreactionscomparedtopreviouslystudiedßamesandÞre-inducedplasmas. Becauseofthis,itisunknownhowelectromagneticwavesinteractwithßamesfoundinahouse Þre. Thisdissertationinvestigatesthequestionofhowelectromagneticwavesinteractwith ßamesinahouseÞre.Thisisanopenproblem,withmanyvariables,thatposesasubtleand difÞcultmeasurementtask.Thisworkfocusesoncreatingexperimentaltechniquestoexplore thisproblem.Fromanelectromagneticmetrologyperspective,thephysicalphenomenaofin- terestaredifÞculttomeasureduetoill-deÞnedphysicalboundaries,characteristicslengthsof varyingmagnitude,inhomogeneity,andvaryingtimescales.Theexperimentalmethodsstud- iedhereprimarilyfocusontransmissionmeasurementsthroughßamesafewfeetinheight. Additionally,thisworkpresentsaproof-of-concepttwo-wiretransmissionlineforbench-scale, material-characterizationofsolids,liquids,gases,andßames. Resultsfromthisworkprovideametrologicalfoundationforfuturestudiesinthisarea.An experimentalsetupthatcanwithstanddirectexposuretoßameswasdevelopedandprelimi- narymeasurementsrecorded.Datatakenduringthedevelopmentofthissetupshowedatime- dependancethatcorrespondedtotransmissionsthroughtheßameandthesolidfuelbeing consumed.Calibrationprocedureswereusedtoverifymeasurementsofstandardmaterials; thecalibrationprocedureshouldbereÞnedforlargerßamemeasurements.Transmitterswere placedinsideofaburninghouseandsignalpropagationwasmeasured,whichrequiredthe designofÞre-proofenclosuresforthetransmitters.Measuredresultsdemonstratedthattrans- missionsmaynotbeaffectedwhensentfromaÞreÞghterinsideofahousewithÞreconditions suitableforanoffensive,interiorattack.Itisunknownifsevereconditions,suchasaßashover, wouldaffecttransmissions.Plasmaswereobservedininterferometricmeasurementsoflive- Þreexperimentsperformedinthelaboratory. Thisworkhasexploredanopenprobleminelectromagneticswithlive-savingapplications totheÞreservice.Resultsfromthisworkwarrantadditionalstudyinthisareatoimprovetech- niques,withthegoalofputtingsearch-and-rescueradarsintothehandsofÞreÞghters. Copyrightby ANDREWKENNETHGERKENTEMME 2015 ThisworkisdedicatedtothosewholosttheirlifeduetotheearthquakeonJanuary12,2010in Port-au-Prince,Haiti. vACKNOWLEDGMENTS IknowthatÞnishingmydissertationandreceivingaPhDwasnotfullymyowndoing.Many peopleandorganizationshavehelpedmealongtheway.Ihavemadeeveryefforttoacknowl- edgethosewhohavehelpedmeduringthisprocess.PleaseacceptmysincereapologyifIhave somehowmissedyou.IfIhave,pleaseletmeknow.Ilivetohelpothersandtrulyappreciate whenothershelpme.Thankyoutoeveryonewhohashelpedmeinthisendeavour. Firstandforemoest,IthankandpraiseGodforthetalents,intelligence,andheartthatHe hasgivenme.Ipraythatmyworkwillbehelpfultoothers.Hehasgivenmethisamazing opportunityandblessedmethroughout. People Dr.Rothwell hasbeenmyadvisorÑeitheracademicand/orresearchÑsincefreshmanyear atMSU.Thankyouforalltheadviceovertheyears.Youhaveguidedmedownawindingpath andhelpedmetoexplorenumerousareasofengineering.Yourloveofteachingandwriting inspiremetostriveforthehighestqualityinallthatIdo.Thankyouforbriningmeintothe ElectromagneticResearchGroup. Mydissertationcommitteehasbeenencouragingaswellasexcitedbymyworkthrough- out.IwouldliketothankDrs. EdwardRothwell ,PremChahal ,JohnVerboncoeur ,and Indrek Wichman fortheirsupportandguidance.Ihaveenjoyedworkingwithyou. Thankyouto Dr.RaoulOuedraogo formentoringmewhenIÞrstenteredtheElectro- magneticsGroup.Hisguidanceandexcitementhaveinspiredmeandshownjusthowmuch onecanaccomplishwhilelovinglife.Specialthanksto Dr.AlejandroDiaz forworkingwithand fundingmewhileIworkedonmetamaterialresearchwithRaoul. Dr.XiaboTan broughtmeintohislabasafreshmanandsophomore.Heturnedmelooseon myownprojectswhilementoringme.Thankyouforthisintroductiontoresearchandsetting medownthispath. DrewKim wasinßuentialinconnectingmewithDr.Tanaswellasinvolving meincollegeKÐ12outreachactivities.ThankyouDrew. viIwouldalsoliketothankallofmy teachers overstheyears.Somanyofyouencouragedme toexplorenewtopicsandpushmyselfbeyondtheregularassignment,strivingtolearnmore. Thankyouforstartingmedownthispath. Myfamily hasbeenasourceofencouragementandguidance.Atsomeofthelowestpoints, youhaveprovidedreasonsforcontinuingandadvice.Seeingwhatyouhaveaccomplishedis inspiration.Myparents, KennethandMiriamTemme ,havealwaysgoneoutoftheirwayto makesurethatmysiblingsandIhadthebestpossibleeducationandexperiences.Thankyou forallthetimeyouhavespentdrivingusaroundtodifferentschoolsandprograms.Youhave givensomuchforus.Thankyou Karsten foralwaysbeingthereasanolderbrotherwithadvice fromhavinggonedownmanyofthesameroads.IÕvealwayslookeduptoyou. Marliese has helpedsomuchalongtheway.Yourexperienceoutsideofengineeringhasgivenmeperspec- tivesthattheourothersiblingscouldnot.Thankyouforalwaysofferingmeaplacetostay andfoodwhenIleavecampustogetabreak.Goodluckwiththerestofyourprogram. Jacob hasbeenagreatbrotherandfriendthroughoutallofmylife.YouÕvetaughtmesomuchand answeredsomanyannoyingquestionsÑyouhavebeenespeciallyhelpfulwithmycombustion questions.Thanksforspendingallthetimeplayinggameswithme. Throughoutmytimeasagraduatestudentandevenbefore, Hanna hasalwaysbeenthere fromdiscussingnewideas,tosmilingandnodding,toconsolingmewhenIÕvefallenapart,to makingmeworkattimeswhenIhavenÕtwantedto.IamnotsurehowIwouldhaveÞnished withoutyou.IknowIprobablywouldhavetakenalittlebitlongerormaybenothaveeven Þnished.Youpushedmeandmademesticktoit.Ithankyouforeverything.Throughoutitwe havegonefromjustdatingtobeingmarried.ThosearesigniÞcantlifeexperiencesevenoutside ofgraduateschool.Thetravelandtimeaparthasbeenhard.Thankyouforputtingupwithall ofitandhelpingmetoÞnish.Nowitsyourturntograduate. Iwouldliketothank KathrynBonnen forhersupportandamazingcookingabilities throughoutmygraduateandundergraduatecareer.ThankyouforalwaysbeingthereforHanna andI,andwehopewecandothesameforyou. vii InadditiontoDr.Rothwell,Iwouldliketothank Dr.ShankerBalasubramaniam forhiring methatÞrstsummer.Hehassupportedmethroughoutandalwayslookedoutforme,even squirrelingawaysomefundstohelpneartheendofmyprogram. RoxannePeacock hasbeenagreathelpthroughoutmyresearchinplacingordersand assistinginmeobtainingnecessaryequipment.Morethanonceshehasgoneoutofherway toassistwhenIcameinatthelastmoment.Roxannehasalsobeenonewhoiseasytotalkto aboutlifeinschoolandout.Ihaveenjoyedourmanyconversations. GreggMulder and BrianWright oftheElectricalandComputerEngineering(ECE)Shop havebeencrucialtomecompletingmyPhD.Theycontinuallyoffertheirknowledge,equip- ment,andguidance.IcannotexpressenoughhowthankfulIamforallthetimesyouhavebent overbackwardstohelpme.GregghasbeenanamazinghamradioelmerÑkeepitup! KoredeOladimeji and Dr.JunyanTang havebeenindispensableinlabwork.Thesetwo haveansweredquestions,retrieveddata,anddonesomanyothertaskstoassistwhenIwason oroffcampus.TheyhavehelpedmakeitpossibleformetospendtimeinMinnesota. Manyotherpeoplehavealsodonatedtheirknowledge,skill,andtimetoassistme.Myother labmatesincluding JonathanFrasch ,JenniferByford and Dr.BenjaminCrowgey .The ECE departmentsecretaries including MeaganKroll ,LaurieRashid ,PaulineVandyke ,Michelle Stewart ,and JennierWoods havealwaysbeenhelpfulandresolvedsomanyissuesforme. KatyLuchiniColbry hasbeenimmenselyhelpfulsincemyfreshmanyear.Thankyouforall thehelp,advice,andfoodyouhaveprovidedtomeandtheotherstudents.Youcontributeso muchtoMSUandtheCollege. RafmagCabrera and Dr.NelsonSepœlveda offeredtheirassistanceinplacingwirebonds ontomybaluncircuitboards. Somuchofthisworkhasdependedoninspiration.Thiswasprovidedagainandagainbymy involvementwiththe BathTownship(MI)FireDepartment (BTFD).Callaftercallremainedme ofwhyIamanengineertryingtosolveproblemstohelpothers.Thedepartmentandespecially ChiefArthurHosford tookachancebyhiringsomekidfromWyomingandastudentatMSUto viii beonthedepartment.Ihopethetownshiphasfoundtheirinvestmentinmeandmytraining tobeworthwhile.Ihavelearnedsomuchwhileoncallsthathasimpactedmyresearch.The experiencegainedfrombeingaBTFDÞreÞghterwillguidemyworkforyearstocome.Allof theÞreÞghtersonthedepartmenthavebeensupportiveofmywork.Aspecialthanksto Kevin Douglas whohaspickedupmenumeroustimesfromtheairportaswellasbeingagoodfriend andpartnerontoomanycallswhenitwasjustus. DaveSnider and HaslettTrueValue havebeenatremendoushelpthroughout.Daveis knowledgeableandhelpfultoallthestudentswhocomein.Bestofluckwiththestore.Dave hasalsobeenagreatleaderontheÞredepartmentandsupportedmyworkthereandthiswork. Iwishtothank RickTaylor forhelpingmebarrowneededpartsandequipmentfromthe MSUphysicalplant.Additionally,thankyouforyourmentoringontheÞredepartment.Iwill alwaysrememberthetruecareandconcernyouexpressforeverypatient.MayGodblessyour ministry. DanaandMaryScherer havebeenkindenoughtohaveallowmetostaywiththemwhen IreturnedtoEastLansingduringthelastyearandahalfofmyprogram.Theyhavebeenvery easygoingandwonderfulhosts.Thanksforprovidingmeabed,aroof,andgreatcompany. Iwishtothankthoseat NISTand UnderwritersLaboratories whohavetakentime todiscussmyresearchandevengivenmetours,especially BobBackstrom and Daniel Madrzykowski .Thankyouto Dr.Ross forhisassistanceandadvicealongthewayandonpersonalside projects.HehasalsoallowedtheElectromagneticsResearchGrouptousehisWaveCalcpro- gram.Thishasbeenusefuloverandover. GregoryCharvat hasbeenagreatsoundingboard,especiallyasIwasbeginningmyre- search.Iappreciatehisinvitationtoworkwithhimalongwith HishamBedri and Dr.Ramesh Raskar oftheMITMediaLabonnewradarimagingtechniques.Thisprojecthasbeenexciting andpromising,aswellasprovidingapeakintotheanotherinstitution. ixFunding Attendingandcompletinggraduateschoolisacostlyendeavor.Iwishtoacknowledgethose whohavecontributedÞnancially. Iwassupportedona NationalScienceFoundation(NSF)GraduateResearchFellowship (GRFP)formuchofmytimeingraduateschool.Iwasselectedinthespringof2010asafel- low.IpostponedmyÞrstyearandusedotherfundingfromMichiganStateUniversityandthe ElectricalandComputerEngineeringDepartment.Mysecondthroughfourthyearsofgradu- ateschoolweredirectlycoveredbytheGRFP.IremainedafellowformyÞnaltimeingraduate schoolinordertocontinueinteractionswithNSF.AsrequestedbyNSF,thefollowingisaformal acknowledgementoftheirsupport: ThismaterialisbaseduponworksupportedbytheNationalScienceFoundation GraduateResearchFellowshipunderGrantNo.0802267.Anyopinion,Þndings,and conclusionsorrecommendationsexpressedinthismaterialarethoseoftheauthor anddonotnecessarilyreßecttheviewsoftheNationalScienceFoundation. Partofmyworkhasbeensupportedbythe IEEEAntennasandPropagationSociety throughaDoctoralResearchAwardfromtheNovember2012fundingcycle.Pleaselookinup- comingissuesoftheAntennasandPropagationSocietyMagazineforawriteupaboutmywork andmyfutureplans. Iwassupportedinthesummerof2014bya DepartmentofElectricalandComputerEngi- neeringGraduateExcellenceFellowship aswellasaresearchassistancepositionfrom Dr.Ed- wardRothwell .IreceivedaDissertationCompletionFellowshipfromthe MSUGraduateSchool .Thank youforsupportingmeandallowingmetoÞnish.TheGraduateSchoolhasalsoawardedme travelfundsforattendingthe2014IEEEInternationalSymposiumonAntennasandPropaga- tionandUSNC-URSIRadioScienceMeetingheldjointlyJuly6Ð11,2014,attheMemphisCook ConventionCenterinMemphis,Tennessee.Travelwasalsosupportedbythe DeanÕsOfÞce xoftheCollegeofEngineering .Othertravelhasbeensupportedfromthe Dr.DennisNyquist Fellowship .MaterialsandEquipment Alargeamountofmyresearchhasbeenconductedduetothekindnessofothersasmy budgetforequipmentandmaterialswaslimited. The LansingFireDepartment(LFD) hasbeenveryhelpfulwithmyexperimentsincluding allowingtheuseoftheirtrainingfacility.LFDhasbeensupportiveofthisworksincetheywere approachedinthelatesummerof2012.Specialthanksgoesto ChiefofTrainingDanOberst ,FireMarshalBradDrury ,and CaptainMarshaunBlake oftheFireMarshalÕsOfÞce(ranksat thetimeoftheexperiments). Iwouldliketothank TheClubatChandlerCrossings fordonatingfurniturewhichIused inÞreexperiments.The MerdianTownshipFireDepartment hasbeengraciousenoughto lendmetheirburnpanonmultipleoccasionsallowingmetoconductmeasurements.The MSUPhysicalPlant donatedsheetmetalforconstructionofaradarcornerreßector. DeLau FireServices allowedmetotakemeasurementsoftheirburnpanattheFireSafetyWeekOpen HouseonOctober10,2012atLansingFireStation8. The MSUEngineeringMachineShop hasbeenhelpfulthroughout.Theyhavehelpedwith manufacturingofnumerousdevices,alwayswillingtoanswermyquestionsandofferadvice. The MSUEngineeringDivisionofEngineeringComputingServices (DECS)hasbeenex- traordinary.Aftertalkingwithstudentsatotheruniversities,Iamamazedbythesupportthat wereceivefromDECS.RarelyhaveIeverreceivedanegativeanswerfromDECSandIhavehad manyout-thererequests. Manyofmyexperimentshavereliedonequipmentonloanfromthemanufacturer.Ihave usedaFieldFoxanalyzerfrom Agilent aswellasahandheldZVHfrom RohdeandSchwarz .Someofthishasbeensuppliedthrough ElectroRent .The MSUSurplusStore hasbeenhelpfulthroughoutmyresearch.Ithasalsoleadtomepur- chasingvarious,non-essentialitems.Whenpossible,theSurplusStoreallowedmetopickup xisamplesandothermaterialsneededforexperimentsatlittleornocost.Thiswasextremely importantbecauseofthelimitedfundingforexperiments. ElvitPotter fromMSUEnvironmentalHealthandSafety(EHS)assistedinaliveburnex- perimentearlyoninthiswork.Hewaskindaenoughtotaketimeoutofhisdaytosetupand runtheBullexFireExtinguisherTrainer.TangwasassistingmethatdayandreceivedabriefÞre extinguishertrainingfromElvitaftermyexperiment. JoanFettyfromUnifrax generouslydonatedFiberfraxDuraboardtoassistinmyresearch. ThisdonationwascrucialandIamverygrateful.Thankyou. Software Ihaveusednumerouspiecesofsoftwarealongtheway.Myinterestinprogrammingand laboratorytechniqueshasledmetocreatemanynewanddifferentprogramsfordatacollection andanalysis. Throughoutmywork,the MSUHighPerformanceComputingCenter (HPCC)hasbeenan importantresource. Dr.DirkColbry and Dr.BenjaminOng havebeeninvaluableinmaking theHPCCusefultomeandotherelectromagneticstudents. Iwishtothank AlexArsenovic forhisworkonScikit-RF 1,anopensourceRFengineering packagewritteninPython. Thisdissertationwastypesetusingaclassderivedfrom AlexandraDiemÕs dissertationstyle 2whichsheadaptedfrom MatthiasLiebisch ofDBIS-LehrstuhlatFriedrichSchillerUniversityin Jena,Germany. 1http://www.scikit-rf.org/ 2https://bitbucket.org/akdiem/dissertation_template and http://akdiem.wordpress.com/other/latex-template-for-dissertations/ xiiPREFACE Anycorrections,updates,orneweditionswillbepostedonlineandwillbelistedinthe errataonthefollowingpages. Duetouniversitydeadlinesfordegreecompletion,itwasnotpossibletoincludeallancillary informationinthisversionwhichhasbeensubmittedtotheuniversity.Atleastoneadditional version,tobereleasedin2016,isplanned. Aswebsiteaddressescanchangeovertime,adeÞnitiveURLcannotbegivenhere.Iwill attempttomaintainalinktothemostup-to-dateversionofthisdissertationatanyorallofmy followingpages: ¥ORCID:orcid.org/0000-0001-9259-4579 ¥GoogleScholar:scholar.google.com/citations?user=eK4xvf8AAAAJ ¥LinkedIn:linkedin.com/in/atemme ¥Github:github.com/temmeand ¥Bitbucket:bitbucket.com/temmeand ¥MichiganStateUniversityGitlab:gitlab.msu.edu/temmeand Ifthesesiteareinactive,pleaseperformaninternetsearchformynameandthetitleofthis dissertation.ThereadermayalsotrycontactingtheElectromagneticResearchGroupand/or theGraduateSchoolatMichiganStateUniversitytorequestanup-to-dateversionifitisnot availableelsewhere. Atthetimeofwriting,validemailaddressesformeare temmeand@msu.edu and temmeand@gmail.com .xiiiERRATA December2015 ¥Githash:gradSchool:fbff463 ¥Initialpublication xivTABLEOFCONTENTS LISTOFTABLES xxLISTOFFIGURESxxii PartIMotivation,Objective,andBackground1 Chapter1MotivationandObjectiveofthisWork2 1.1Motivation........................................2 1.2Objective.........................................4 Chapter2BasicTheoryofFieldsandPlasmas5 2.1ElectromagneticFieldsandWaves..........................6 2.2Plasmas..........................................14 2.2.1CharacteristicLength.............................15 2.2.2DebyeSphere..................................16 2.2.3ChargeNeutrality................................16 2.2.4CollisionDampening..............................16 2.3PlasmaModelforElectromagneticFields......................17 Chapter3LiteratureReview20 3.1EarlyWork........................................20 3.2WildlandFirePapers..................................22 3.3LossesinWildlandFiresInvestigatedbyBoan...................22 3.3.1LossMechanisms................................23 3.3.2FDTDSimulations...............................24 3.4ExperimentalMeasurementsConductedbyMphale................28 3.5Conclusion........................................31 PartIILarge-scaleFireExperiments32 Chapter4RadioWaveTransmissionThroughFurnitureCushionFlames33 4.1ExperimentalMethods.................................34 4.2GeneralMeasurementProcedure...........................41 4.3SafetyPrecautions....................................41 4.4Go/No-GoCriteria....................................42 4.5Results...........................................42 4.6Discussion........................................51 4.7ExperimentDesignObservationsandSuggestions.................53 4.8Conclusion........................................61 xvChapter5ExperimentsUsingaPropaneBurnPan62 5.1ExperimentatEHS....................................64 5.1.1ExperimentalSetup..............................64 5.1.2ExperimentalProcedureandDataProcessing...............68 5.1.3ResultsandDiscussion.............................69 5.2ExperimentatBTFD...................................75 5.2.1DuraboardInsulationandBurnChamberDesign.............75 5.2.2ExperimentalSetup..............................78 5.2.3ExperimentalProcedureandDataProcessing...............78 5.2.4ResultsandDiscussion.............................79 5.3Conclusion........................................82 Chapter6Interferometry83 6.1MicrowaveInterferometerTheory..........................84 6.2ExperimentalSetup...................................88 6.3Results...........................................99 6.3.1ECEHoodExperimentResults........................99 6.3.2CalorimeterExperimentResults.......................102 6.3.3ShutterExperimentResults..........................106 6.3.4MeshExperimentResults...........................111 6.4Discussion........................................115 6.5Conclusion........................................116 Chapter7TransmissionsfromInsideofaHouseFire117 7.1Transmitters.......................................118 7.1.1Insulation....................................119 7.1.2144MHzCWTransmitter...........................121 7.1.3440MHzCWTransmitter...........................123 7.1.4900MHzXBeeTransmitter..........................123 7.1.52.4GHzand5GHzWi-FiTransmitter....................125 7.1.6TransmitterPlacement.............................128 7.2Receivers.........................................132 7.3VideoRecordings....................................135 7.4ResultsandDiscussion.................................137 7.5Conclusion........................................148 PartIIIBench-ScaleDiagnosticsusingaTwo-WireTransmission Line149 Chapter8TransmissionLineCharacteristics153 8.1ElectricPotential.....................................156 8.1.1PotentialofSingleLineCharge........................157 8.1.2PotentialofTwoLineCharges........................158 8.1.3EquipotentialSurfaces.............................159 8.1.4ApplicationtoTwo-WireTransmissionLine................166 xvi8.1.5VisualizationofthePotential.........................170 8.2ElectricandMagneticFields..............................171 8.3RadiationResistance..................................177 8.3.1CloselySpacedWires..............................179 8.3.2DiscussionandRecommendations.....................180 8.4DistributedCircuitModel...............................181 8.4.1Capacitance...................................184 8.4.2Conductance..................................185 8.4.3Inductance....................................187 8.4.4Resistance....................................188 8.4.5SummaryofParameters............................191 Chapter9ThreeShortCalibrationMethod193 9.1Introduction.......................................193 9.2CalibrationTheory....................................194 9.2.1One-PortCalibration..............................195 9.2.2Two-PortCalibration..............................199 Chapter10Double-YBalun204 10.1Introduction.......................................204 10.2DesignOverview.....................................207 10.3CPSandCPWDesignEquations............................211 10.3.1CoplanarStrip..................................211 10.3.2CoplanarWaveguide..............................212 10.4DesignSoftwareTools..................................213 10.5BalunHolder.......................................215 10.6High-TemperatureModiÞcations...........................223 10.6.1DesignModiÞcations..............................223 10.6.2HeatTransferAnalysis.............................225 10.7AffectsofAirBridges...................................227 10.7.1FullTwo-wiretransmissionlineSystem...................228 10.7.2Back-to-BackBalun..............................238 10.7.3Summary.....................................247 10.8FinalBalunDesign....................................247 Chapter11Bench-ScaleExperimentResults254 11.1SolidMaterialMeasurement..............................254 11.1.1Calibration....................................256 11.1.2POMMeasurement...............................259 11.2LiquidCalibration....................................262 Chapter12ConclusionandFutureWork276 xvii PartIVFutureWorkandConclusions278 Chapter13FutureWork279 13.1NextIteration.......................................279 13.2OutstandingChallengesandQuestions.......................280 13.3FutureDirections....................................280 Chapter14Conclusion282 14.1FireExperiments.....................................282 14.2Two-WireTransmissionLine..............................283 14.3Summary.........................................284 APPENDICES285 AppendixANetworkParameters286 AppendixBCableandConnectorInformation291 AppendixCFurtherdetailsonSampleTrough296 AppendixDWeatherRecords299 AppendixESiteSafetyPlan301 AppendixFSelectedPagesfromLaboratoryNotebook00010303 AppendixGSelectedPagesfromLaboratoryNotebook00011316 AppendixHVNADataCollectionCode333 AppendixIWavecalcMacros342 AppendixJArchRange345 AppendixKIPythonnotebook:Single-Layer349 AppendixLIPythonnotebook:Bullex-at-ORCBS-2013-08-08359 AppendixMIPythonnotebook:Bullex-at-BTFD-2013-12-06371 AppendixNIPythonnotebook:analysis-of-2015-02-15382 AppendixOIPythonnotebook:AR8200-data-Þt397 AppendixPIPythonnotebook:CPW-CPS-Impedance400 AppendixQIPythonnotebook:WireTemperature443 xviii AppendixRIPythonnotebook:T-lineCalibration-diss451 AppendixSIPythonnotebook:T-lineCalibration-With-Water-diss486 BIBLIOGRAPHY508 xixLISTOFTABLES Table3.1:Summaryof neand !effresultspublishedbyMphale.............30 Table4.1:ExperimentconÞgurationforeachsample...................40 Table5.1:MeasurementsinEHSreplicatesetsandzero-Þlltime............68 Table6.1:Minimumthicknesstomeettheslabapproximationcriterionforselect frequencies.....................................85 Table6.2:Theoreticalphasedifferencesforvariousparameters............86 Table6.3:Summaryofinterferometricexperiments...................88 Table7.1:Lookuptablefor LMvaluestodBm.......................134 Table8.1:Summaryofequationsforthecalculationofthecircuitparametersofa two-wiretransmissionline............................192 Table9.1:SummaryofequationstocalculatetheS-parametersofatransitionofa 1-portcalibration.................................200 Table9.2:SummaryofequationstocalculatetheS-parametersoftransitionsfora 2-portcalibration.................................202 Table9.3:RelationsbetweenS-parametersandT-parameters.ReprintofTableA.1203 Table11.1:Foaminsertlabelsandthicknesses.......................256 TableA.1:RelationsbetweenS-parametersandT-parameters[3,p.541]and[123].289 TableB.1:Cablenumberingscheme,lengths,connectortype,gender,andlabel...292 TableB.2:Resultsfromgagingtheassortedconnectorsinthelab...........293 TableB.3:ResultsofgagingthecablesprovidedwiththeSatimosystem.......294 xxTableB.4:Resultsofgagingthe85052Dcalibrationkit..................295 TableD.1:Observedtemperatureandhumidityatthesiteoftheexperiment.....300 TableD.2:WeatherobservationsfromNOAA/NWSatCapitolCityAirportinLans- ingforMay30,2013................................300 xxiLISTOFFIGURES Figure2.1:Genericdispersion( "-#)diagram......................14 Figure2.2:Dispersion( "-#)diagramforacollisionlessplasma............18 Figure2.3:Dispersion( "-#)diagramforaplasmawithcollisions..........19 Figure4.1:Materialsampleburningduringanexperiment..............33 Figure4.2:Diagramofexperimentallayoutwhentheantennaswere(a)25.5ft and(b)9.5ftawayfromtheshelf.......................35 Figure4.3:Schematicofexperimentalsetup,(a)sideview(b)topview.......35 Figure4.4:Photographoftheexperimentalsetupshowingthelaserlevel,an- tennas,burningsample,wireshelf,sand,cablemats,windindicator, videotripod,andinstrumentationtable...................36 Figure4.5:Metalholderusedformetalplates,Plexiglassamples,andotherpla- narsamples....................................38 Figure4.6:Materialsamplesfortheexperiment.....................39 Figure4.7:Apurplesamplewithignitionsampleremovedanddisplayed......39 Figure4.8:Ignitionsampleinaluminumfoiltray....................40 Figure4.9:Exampleexperimentalsetupinalaboratorysetting............43 Figure4.10:Plexiglascontrolmeasurements(S 21)comparedtotheoreticalvalues foralosslessmaterialwithpermittivityof2.5.Eachmaterialis1in thick........................................44 Figure4.11:Processeddatafromburn1.Thetwocurvesatthefrontareforthe Plexiglasstandard................................45 Figure4.12:Processeddatafromburn2.Thetwocurvesatthefrontareforthe Plexiglasstandard................................46 Figure4.13:Processeddatafromburn3.Thetwocurvesatthefrontareforthe Plexiglasstandard................................47 xxiiFigure4.14:Processeddatafromburn4.Thetwocurvesatthefrontareforthe Plexiglasstandard................................48 Figure4.15:Processeddatafromburn5.Thetwocurvesatthefrontareforthe Plexiglasstandard................................49 Figure4.16:Videostillsfromburn4.Thetimestampsshowthesynchronizedtime foreachcamera.................................50 Figure4.17:Cardboardusedtoignitecushionsforsamplesb5andb6........53 Figure5.1:ExampleÞreextinguishertrainingusingtheBullexIntelligentTrain- ingSystem....................................63 Figure5.2:ExperimentalsetupatMSUEHSshowingtheBullexsystemandwire shelf........................................65 Figure5.3:IgnitedsystemduringexperimentsatMSUEHS..............66 Figure5.4:SchematicoftheEHSexperimentallayout.................67 Figure5.5:Dimensionsoftheburner...........................67 Figure5.6:AveragemeasuredtransmissionthroughaoneinchthickPlexiglas sample......................................71 Figure5.7:Unwrappedphaseoftheaveragemeasuredtransmissionthrougha oneinchthickPlexiglassample........................72 Figure5.8:AveragemeasuredtransmissionthroughanignitedBullexsystem...73 Figure5.9:Unwrappedphaseoftheaveragemeasuredtransmissionthroughan ignitedBullexsystem..............................74 Figure5.10:LabelforthedonatedUnifraxFiberfraxDuraboardLD..........76 Figure5.11:PhotosfromaburnusingaBullexsysteminaburnchamber......77 Figure5.12:Averagemeasuredtransmissionthroughaburnchamberwiththe Bullexsystemignited..............................80 Figure5.13:Unwrappedphaseoftheaveragemeasuredtransmissionthrougha burnchamberwiththeBullexsystemignited................81 xxiiiFigure6.1:Normalizedphasedifferenceversusfrequencyforaconstantelectron density.......................................85 Figure6.2:Minimumthicknesstomeettheslabapproximationcriterionversus frequencywithreferencelinesfor1,6,9.5,and20GHz..........86 Figure6.3:Minimumthicknesstomeettheslabapproximationcriterionversus frequencywithreferencelinesfor1,6,9.5,and20GHz..........87 Figure6.4:Schematicdrawingofinterferometerdimensions.............88 Figure6.5:ExperimentalsetupintheECEhoodforinterferometermeasurements.90 Figure6.6:Experimentalsetupintheconecalorimeterforinterferometermea- surements.....................................91 Figure6.7:ConÞgurationofthemetalshutter......................92 Figure6.8:ConÞgurationofthemetalshutterasseenfromtheside.........93 Figure6.9:Photoofaßamebeingdrawnintothesideoftheshutter.........94 Figure6.10:Experimentalsetupforthemeshinterferometermeasurements.....95 Figure6.11:Transmissionmeasurementsinthemeshexperimentalsetupinvari- ousconÞgurationswithnoÞredemonstratingthefrequencylimitsof themeshforshielding,panel1........................96 Figure6.12:Transmissionmeasurementsinthemeshexperimentalsetupinvari- ousconÞgurationswithnoÞredemonstratingthefrequencylimitsof themeshforshielding,panel2........................97 Figure6.13:Transmissionmeasurementsinthemeshexperimentalsetupinvari- ousconÞgurationswithnoÞredemonstratingthefrequencylimitsof themeshforshielding,panel3........................98 Figure6.14:Phasedifferencein3DfromburningmethanolfortheECEhooodex- periment.....................................99 Figure6.15:PhasedifferencefromburningmethanolfortheECEhoodexperiment.100 Figure6.16:Phasedifferencein3Dfromburningsodiumchloridesolutionforthe ECEhoodexperiment..............................100 xxivFigure6.17:PhasedifferencefromburningsodiumchloridesolutionfortheECE hoodexperiment................................101 Figure6.18:Phasedifferencein3Dfromburningmethanolintheconecalorime- terexperiment..................................102 Figure6.19:Phasedifferencefromburningmethanolintheconecalorimeterex- periment.....................................103 Figure6.20:Phasedifferencefromburningsodiumchloridesolutioninthecone calorimeterexperiment.............................103 Figure6.21:Phasedifferencefromburningsaltintheconecalorimeterexperiment.104 Figure6.22:Phasedifference3DfromburningPlexiglasintheconecalorimeter experiment....................................104 Figure6.23:PhasedifferencefromburningPlexiglasintheconecalorimeterex- periment.....................................105 Figure6.24:Phasedifference3Dfromburningmethanolintheshutterexperiment.106 Figure6.25:Phasedifferencefromburningmethanolintheshutterexperiment..107 Figure6.26:Phasedifference3Dfromburningasecondsampleofmethanolinthe shutterexperiment...............................107 Figure6.27:Phasedifferencefromburningasecondsampleofmethanolinthe shutterexperiment...............................108 Figure6.28:Phasedifference3Dfromburningsodiumchloridesolutioninthe shutterexperiment...............................108 Figure6.29:Phasedifferencefromburningsodiumchloridesolutionintheshut- terexperiment..................................109 Figure6.30:Phasedifference3DfromburningPlexiglasintheshutterexperiment.109 Figure6.31:PhasedifferencefromburningPlexiglasintheshutterexperiment...110 Figure6.32:Phasedifference3Dfromburningmethanolinthemeshexperiment.111 Figure6.33:Phasedifferencefromburningmethanolinthemeshexperiment...112 xxvFigure6.34:Phasedifference3Dfromburningsodiumchloridesolutioninthe meshexperiment................................112 Figure6.35:Phasedifferencefromburningsodiumchloridesolutioninthemesh experiment....................................113 Figure6.36:Summarypanelofinterferometricmeasurements,eachwithown colorscale....................................113 Figure6.37:Summarypanelofinterferometricmeasurementsnormalizedtothe samecolorscale.................................114 Figure7.1:PlanviewoftheÞrststoryoftheburnhouse................120 Figure7.2:Transmitterfor144MHz............................122 Figure7.3:Transmitterfor440MHz............................124 Figure7.4:900MHZtransmittersetup..........................125 Figure7.5:TransmittersforWi-Fiand900MHzXBee..................127 Figure7.6:Placementofthe144MHztransmitter....................129 Figure7.7:Placementofthe440MHztransmitter....................130 Figure7.8:Placementofthe900MHzXBeeandWi-Fitransmitters..........131 Figure7.9:Receiversaspositionedformeasurements.................132 Figure7.10:Photoshowingthereceiverlocationrelativetothehouseincluding vehiclesinbetweenthetwo..........................133 Figure7.11:BestÞtcurvefortheAR8200..........................135 Figure7.12:Receiving900MHzXBeemodule.......................136 Figure7.13:MeasurementlaptopsandWi-Fireceiveradapter(arrow)........137 Figure7.14:Post-Þreconditionsforthe144MHztransmitter..............139 Figure7.15:Post-Þreconditionsinthe440MHztransmitterroom...........140 Figure7.16:Post-ÞreconditionsfortheXBeeandWi-Fitransmitter..........141 xxviFigure7.17:Post-Þreconditionofthe144MHztransmitterroom...........142 Figure7.18:Post-Þreconditionoftheceilingsinthe144MHzand440MHztrans- mitterrooms...................................143 Figure7.19:Post-Þreconditionsinthelivingroom....................144 Figure7.20:Measuredsignalstrengthsbefore,during,andafterthehouseburn..146 Figure7.21:MeasuredsignalstrengthsnearthetimeoftheÞre.............147 Figure7.22:TemperatureversustimefromtheXBeemodules.............147 Figure7.23:Exampleofatwo-wiretransmissionlinewithanattachedshortcircuit (right)andbalun(left)manufacturedforthiswork............151 Figure7.24:Generalnotationusedforatwo-wiretransmissionline..........152 Figure8.1:Asinglelinecharge...............................157 Figure8.2:Geometryoftwolinecharges.........................158 Figure8.3:Examplesofequipotentialsurfacessurroundingtwolinecharges....163 Figure8.4:Thegeometryofatwo-wiretransmissionline...............167 Figure8.5:Electricpotentialofatwo-wiretransmissionlinesystem.........172 Figure8.6:Electricpotentialofatwo-wiretransmissionlinesystem.........172 Figure8.7:ElectricandmagneticÞeldsofatwo-wiretransmissionline.......175 Figure8.8:MagnitudeofelectricÞeld...........................175 Figure8.9:Magnitudeof Ex.................................176 Figure8.10:Magnitudeof Ey.................................176 Figure8.11:Radiationresistanceforatwo-wiretransmissionwithlineopen, short,orpurelyreactive(resonantline);matched(non-resonantline); and Z0/2loads..................................180 Figure8.12:Circuitmodelforadifferentiallengthoftransmissionline........181 xxviiFigure9.1:Blockdiagramsandsignalßowgraphsfor(a)aone-portnetworkand (b)atwo-portnetwork.............................194 Figure9.2:Blockdiagramshowingthetransitionthatistoberemovedandthe one-portnetworkthatistobemeasured..................195 Figure9.3:Illustrationofcalibrationmeasurementsshowingthethreedifferent distancesforaone-portcalibration.....................198 Figure9.4:Blockdiagramshowingthetransitionsthataretoberemovedandthe two-portnetworkthatistobemeasured..................200 Figure9.5:Illustrationofcalibrationmeasurementsshowingthesixdifferentdis- tancesforatwo-portcalibration.......................200 Figure10.1:Illustrationofthelayoutoftransmissionstructuresinadouble-ybalun.207 Figure10.2:SchematicofCPWandCPSlineswithcommondimensions.......208 Figure10.3:ACPWtoCPSdouble-ybalun.........................208 Figure10.4:SampleoutputfromtheIPythondesignnotebookusedtoassistin conveyingtheoptimizeddesign........................214 Figure10.5:Assemblydrawingforthebalunsupportstructure.............217 Figure10.6:DrawingforthemainPlexiglassupportstructure.............218 Figure10.7:Drawingformanufacturingashortingplate................219 Figure10.8:Drawingshowingcriticaldimensionsforsamples.............220 Figure10.9:DrawingsforplasticpiecesthatclampthecablewhenitÞrstenters theholder.....................................221 Figure10.10:Drawingforthepiecesthatclampthecircuitboard............222 Figure10.11:Anexampleofthemetalrodsliftingthetracesoffofthebalun......225 Figure10.12:Temperatureatthetipofa20AWG,copper/tungstenwireversusthe distancefromtheßametothetip.......................226 Figure10.13:Positioningoftheairbridges(blacklines)atthecenterofthebalun..227 xxviii Figure10.14:Experimentalsetupsimilartothatusedformeasuringtheeffective- nessofairbridges................................228 Figure10.15:Measurementsetuptotesttheairbridges..................230 Figure10.16:Zoomed-inviewoftherightbalunfromFigure10.15...........231 Figure10.17:Two-wiretransmissionlinesystemS-parameterswithnoairbridges installed......................................232 Figure10.18:Two-wiretransmissionlinesystemS-parameterswithairbridgesin- stalledonlyattheÒYÓs.............................233 Figure10.19:Two-wiretransmissionlinesystemS-parameterswithallairbridges installed......................................234 Figure10.20:Reßectionmeasurement(S 11)ofatwo-wiretransmissionlinesystem withvariousairbridgesinstalled.......................235 Figure10.21:Transmissionmeasurement(S 21)ofatwo-wiretransmissionlinesys- temwithvariousairbridgesinstalled....................236 Figure10.22:Powerbalanceforatwo-wiretransmissionlinesystemwithvarious airbridgesinstalled...............................237 Figure10.23:Back-to-backbalunwithallairbridgesinstalled..............239 Figure10.24:Back-to-backbalunS-parameterswithnoairbridgesinstalled.....240 Figure10.25:Back-to-backbalunS-parameterswithairbridgesinstalledonlyatthe ÒYÓs........................................241 Figure10.26:Back-to-backbalunS-parameterswithallairbridgesinstalled.....242 Figure10.27:Reßectionmeasurement(S 11)ofaback-to-backbalunwithvarious airbridgesinstalled...............................243 Figure10.28:Transmissionmeasurement(S 21)ofaback-to-backbalunwithvari- ousairbridgesinstalled............................244 Figure10.29:Powerbalanceforaback-to-backbalunwithvariousairbridgesin- stalled.......................................245 Figure10.30:Powerbalanceofallairbridgesinstallforthetransmissionlinesystem andtheback-to-backbalun..........................246 xxixFigure10.31:Manufactureddouble-ybaluns........................248 Figure10.32:Double-Ydimensionaldrawing,page1...................250 Figure10.33:Double-Ydimensionaldrawing,page2...................251 Figure10.34:Double-Ydimensionaldrawing,page3...................252 Figure10.35:CPWandCPSdimensionsfortheÞnaldouble-ybalundesign......253 Figure11.1:Two-wiretransmissionlineexperimentalsetups..............255 Figure11.2:Foamspacersusedincalibrationmeasurements..............256 Figure11.3:Shortcircuitbuiltforthetwo-wiretransmissionline...........257 Figure11.4:One-portS-parametersofashortcircuitlocatedinfourdifferentpo- sitionsalongatwo-wiretransmissionline..................258 Figure11.5:One-portS-parametersofashortcircuitlocated13.6mmfromthe PlexiglasholderbythefoamIspacer.....................260 Figure11.6:MeasurementsofaPOMsamplelayeredbetweentwofoamspacers onalineterminatedbyashortcircuit....................261 Figure11.7:Balunwithcopperrodsandcoppershort..................262 Figure11.8:Liquidmeasurementexperimentalsetup..................263 Figure11.9:Calibratedone-portS-parametersforatransmissionlinewithashort circuitindistilledwater.............................265 Figure11.10:Liquidmeasurementcontainer,page1...................268 Figure11.11:Liquidmeasurementcontainer,page2...................269 Figure11.12:Liquidmeasurementcontainer,page3...................270 Figure11.13:Liquidmeasurementcontainer,page4...................271 Figure11.14:Liquidmeasurementcontainer,page5...................272 Figure11.15:Liquidmeasurementcontainer,page6...................273 xxxFigure11.16:Liquidmeasurementcontainer,page7...................274 Figure11.17:Liquidmeasurementcontainer,page8...................275 FigureA.1:S-parameterblockdiagramandsignalßowgraphforatwo-portnet- work........................................287 FigureC.1:Metaltroughusedtoholdsamples......................297 FigureC.2:Sideviewofthemetaltrough.........................297 FigureC.3:Centerviewofthetroughshowingalignmentcue.............297 FigureC.4:Top-downviewofthetroughshowingalignmentmarks.........298 FigureF.1:LaboratoryNotebook00011:7........................304 FigureF.2:LaboratoryNotebook00011:14........................305 FigureF.3:LaboratoryNotebook00011:15........................306 FigureF.4:LaboratoryNotebook00011:16........................307 FigureF.5:LaboratoryNotebook00011:111.......................308 FigureF.6:LaboratoryNotebook00011:112.......................309 FigureF.7:LaboratoryNotebook00011:114.......................310 FigureF.8:LaboratoryNotebook00011:126.......................311 FigureF.9:LaboratoryNotebook00011:127.......................312 FigureF.10:LaboratoryNotebook00011:128.......................313 FigureF.11:LaboratoryNotebook00011:129.......................314 FigureF.12:LaboratoryNotebook00011:130.......................315 FigureG.1:LaboratoryNotebook00011:3........................317 FigureG.2:LaboratoryNotebook00011:4........................318 xxxiFigureG.3:LaboratoryNotebook00011:5........................319 FigureG.4:LaboratoryNotebook00011:7........................320 FigureG.5:LaboratoryNotebook00011:8........................321 FigureG.6:LaboratoryNotebook00011:9........................322 FigureG.7:LaboratoryNotebook00011:10........................323 FigureG.8:LaboratoryNotebook00011:11........................324 FigureG.9:LaboratoryNotebook00011:12........................325 FigureG.10:LaboratoryNotebook00011:13........................326 FigureG.11:LaboratoryNotebook00011:14........................327 FigureG.12:LaboratoryNotebook00011:30........................328 FigureG.13:LaboratoryNotebook00011:31........................329 FigureG.14:LaboratoryNotebook00011:32........................330 FigureG.15:LaboratoryNotebook00011:78........................331 FigureG.16:LaboratoryNotebook00011:79........................332 FigureJ.1:Archrangerailshowingthedegreemarkings................346 FigureJ.2:Dimensionaldrawingoftherulerusedtomarkangulardistancealong therailofthearchrange............................347 FigureJ.3:Rulerusedtomarkangulardistancetherailofthearchrange......348 FigureP.1:notebookÞgure.................................415 FigureP.2:notebookÞgure.................................416 FigureP.3:notebookÞgure.................................426 FigureP.4:notebookÞgure.................................427 xxxiiFigureP.5:notebookÞgure.................................429 FigureP.6:notebookÞgure.................................430 FigureP.7:notebookÞgure.................................435 FigureP.8:notebookÞgure.................................438 FigureQ.1:notebookÞgure.................................446 FigureQ.2:notebookÞgure.................................448 FigureQ.3:notebookÞgure.................................450 FigureR.1:notebookÞgure.................................458 FigureR.2:notebookÞgure.................................460 FigureR.3:notebookÞgure.................................461 FigureR.4:notebookÞgure.................................462 FigureR.5:notebookÞgure.................................465 FigureR.6:notebookÞgure.................................466 FigureR.7:notebookÞgure.................................469 FigureR.8:notebookÞgure.................................470 FigureR.9:notebookÞgure.................................474 FigureR.10:notebookÞgure.................................476 FigureR.11:notebookÞgure.................................477 FigureR.12:notebookÞgure.................................479 FigureR.13:notebookÞgure.................................480 FigureR.14:notebookÞgure.................................481 FigureR.15:notebookÞgure.................................482 xxxiiiFigureR.16:notebookÞgure.................................483 FigureR.17:notebookÞgure.................................484 FigureR.18:notebookÞgure.................................485 FigureS.1:notebookÞgure.................................494 FigureS.2:notebookÞgure.................................495 FigureS.3:notebookÞgure.................................496 FigureS.4:notebookÞgure.................................497 FigureS.5:notebookÞgure.................................498 FigureS.6:notebookÞgure.................................499 FigureS.7:notebookÞgure.................................501 FigureS.8:notebookÞgure.................................502 FigureS.9:notebookÞgure.................................504 FigureS.10:notebookÞgure.................................505 xxxivPartI Motivation,Objective,andBackground 1Chapter1 MotivationandObjectiveofthisWork 1.1Motivation WhenÞghtingahouseÞre,theprimarygoalofÞreÞghtersistosavelives;inaddition,Þre- Þghtersareconcernedwithprotectingpropertyandtheenvironment[1].Knowingwhether thereissomeoneinsideofaburninghousedictateshowthesegoalsarereached.Currently therearenotoolstotellÞreÞghtersifsomeoneisstillinsideofaburninghouse.Instead,Þre- ÞghtersrelyonbystandersforinformationaboutoccupantsandusecluessuchaschildrenÕs toysoutside,carsinthedriveway,andthetimeofdaytodeterminethelikelihoodofsomeone beinginside.Noneofthisinformation,however,tellsaÞreÞghterwhereavictimisactually located.Radaroffersapossiblesolutiontothisproblem,allowingforfasterrescuesandfewer Þrefatalities.ProvidingÞreÞghterswithmoredeÞnitiveknowledgeofthevictimsÕwhereabouts insideofaÞrewillenableÞreÞghterstobetterassessrisks,planactions,andprotectthelivesof bothoccupantsandÞreÞghters. SearchingaÞrestructureforatrappedvictimisatedious,time-consuming,anddanger- ousprocess.Smokecauseslimitedvisibility;hightemperaturesmakesomeareasinaccessible; andÞreÞghtersmustwatchforstructuralfailures.FireÞghtersmaybeabletostandandlook 2througharoomifthereisnosmoke,heat,orÞre.Moreoften,though,theymustcrawlunder heavysmokeandsearchthehouseusingonlytheirsensesoftouchandhearing.Searchesare doneinanorderedmannerthatemphasizescoveringallareasinathoroughbuttimeconsum- ingprocess.AlthoughÞreÞghtersaretrainedtoworkwithspeedandefÞciency,thecurrent methodsforÞndingandrescuingvictimsofhouseÞresareslowandinefÞcient. Thermalimagingcameras(commonlycalledthermalimagersorTICs)arethemostad- vancedpiecesoftechnologyavailabletodayforÞreÞghterstoconductsearch-and-rescueop- erationsfortrappedvictims.Thesehandhelddevicesuseinfrared(IR)emissionstodisplaya thermalimageonasmallscreen.Smokedoesnottypicallyobscurethisimage;however,many commonhouseholditems,suchasßoors,windows,mirrors,orfurniture,doobscureorcreate falsethermalimages. Theidealsearch-and-rescueequipmentwouldallowaÞreÞghtertoaccesscriticalinforma- tionaboutaburningbuilding,suchasthebuildinglayout,structuralhealth/stability,statusof utilities(electricity,gas,water),Þrelocationandspread,airmovement,andvictimlocations. ForÞrecommanders,theequipmentwouldbeabletotrackÞreÞghtersastheymovewithinthe building.AfterthemainÞreisout,ÞreÞghtersperformÒoverhaulÓtoidentifywheresmallÞres andhotspotsremaininthestructure;theidealequipmentwouldallowÞreÞghterstocomplete thisoverhaulprocesswithouthavingtotearapartwalls,ceilings,andßoors. RadaroffersanimagingmodalitythatmayprovideÞreÞghterswiththeiridealsolution.In thelastdecade,militaryapplicationshavedrivenresearchprioritiesforthrough-wallradar. Dopplershiftsandmovementdetectionaretwotechniquesusedbythrough-wallradartolo- catepeoplebehindanobstacle.ThistypeofradarcouldhelpÞreÞghterslocatevictimsinstruc- tures,butßamescangenerateaplasmathatcanbeproblematicforcurrentradartechnologies. Whileitisknownthatradiowavesinteractwithplasmasdifferentlythanothermedia[2], therehasbeenlimitedresearchonunderstandingÞre-inducedplasmasandevenlessworkto understandhowradarinteractswithÞre-inducedplasmas.Theoverarchinggoalofthework 3describedhereistoimprovetheunderstandingofhowÞre-inducedplasmasandradarinteract, withthelonger-termgoalofimprovingimagingtechniquesforÞreÞghters. Inadditiontoimprovingsearch-and-rescueoperations,thereareotherpotentialapplica- tionsandusesofthrough-wallradarforÞreÞghtingsuchas: ¥locatingÞresofdifferentsizes(rangingfromindividualhotspotstofullyinvolvedrooms), ¥detectinghazardscausedbyaÞresuchasbackdraft,whichisadangerousexplosion,or ßashover,whenanentireroominstantlyignites,and ¥detectingßowpathsofairthataffectÞrebehavior. Far-reachingusesthatwouldrequiresigniÞcantresearchanddevelopmentincludeÞreextin- guishmentandassistinginon-scenetrackingofresponders Itiseasytoseethatthrough-wallradarofferssigniÞcantpotentialbeneÞtstoÞrevictims andtoÞreÞghtersconductingasearch-and-rescueoperationfortrappedvictims,yetthereare manyyearsofresearchanddevelopmentaheadinordertobringradartechnologiestotheÞre ground. 1.2Objective ThebroadergoalofthisresearchistoassistÞreÞghtersinminimizingthetimethatittakesto Þndatrappedvictim,thusimprovingÞrevictimsÕchancesofsurvival.Inanarrowerscope, theobjectiveofthisworkistoinvestigatetheinteractionbetweenelectromagneticwavesand Þre-inducedplasmasusingbasiclaboratoryequipmentandexistingradarsystems.Thisisnot intendedtobeadevelopmentofaradarsystem. 4Chapter2 BasicTheoryofFieldsandPlasmas InordertounderstandtheinteractionbetweenelectromagneticÞeldsandÞre-inducedplas- mas,thischapterlaysoutthebasicsofelectromagneticÞelds,waves,andplasmas.Thisgen- eral,mathematicaldiscussionisthefoundationfortheexperimentaldesignandresultanalysis laterinthisdissertation. Assumption Thefocusofthischapterwillbeunmagnetizedplasmasintheformofahomogeneous slabthatisinÞniteintwodimensionsandtransverseelectromagnetic(TEM)waves. Forthesetypesofplasmasandwaves,theinteractionbetweenÞeldsandplasmasdepends onfrequencyandparametersoftheplasma.Thismeansthatbelowsomefrequency,essentially noradarwaveswillpropagatethroughtheÞre-inducedplasma.Atahighenoughfrequency,the Þrewillhavenoeffectontheradarwaves.Thequestionsinvestigatedhereinarewhatarethe particularfrequencyrangesofinterestandtowhatextentaretheradarwavesaffected? 52.1ElectromagneticFieldsandWaves ElectricandmagneticÞeldstogetherconstituteelectromagneticÞelds.Theymaybeindepen- dentofoneanother;however,theyarecoupledtooneanotheriftheychangeintime.Thisis shownbyMaxwellÕsequationswhicharethegoverningequationsforelectromagneticÞelds. MaxwellÕsequationsindifferentialformare[3,¤3.6] !á!D=$!á!B=0!"!E=#%!B%t!"!H=!J+%!D%t(2.1) where !Distheelectricßuxdensity, $istheelectricchargedensity, !Bisthemagneticßuxdensity, !EistheelectricÞeld, !HisthemagneticÞeld, !Jistheelectriccurrentdensity, tistime,and %isthepartialdifferential. AnimportantcaseiswhentheelectricandmagneticÞeldsvarysinusoidallyintime.In thiscase,theÞeldsmaybeexpressedintermsofthecomplexexponential ej"twhere j=$#1representsacomplexnumber,whichisoftenexpressedas iinotherdisciplines;and "=2&fistheangularfrequencyand fthefrequencyinHertz.Multiplyingaquantity,calledaphasor, byej"tandtakingtherealpartgivesthetime-varyingformofthequantity.Appendix4of[3] coversphasorsinmoredetail. Assumption Thetimeconvention e+j"tisusedthroughoutthiswork. 6MaxwellÕsequationsmaybeexpressedusingphasorsas[3,¤3.8] !á!D=$!á!B=0!"!E=#j"!B!"!H=!J+j"!D.(2.2) WhiletheÞeldsaredenotedinthesamewayinbothoftheaboveforms,thoseinEquation(2.1) areforinstantaneousvalueswhiletheÞeldsinEquation(2.2)representphasors.Thetimeand positionaldependenceoftheÞeldsaboveandelsewhereareimplicit,asiscommonintheliter- ature. TostudytheinteractionsbetweenÞeldsandplasmas,theplasmaisexpressedasregular matter,referredtoasamediuminelectromagnetics,andaspecialmodelforthepermittivity, ',oftheplasmaisused.InteractionsbetweenÞeldsandlinear,isotropicmediarequirethe followingconstitutiverelations[3,¤3.6]: !J=(!E(2.3) !D='!E(2.4) !B=µ!H(2.5) where (istheconductivity, 'isthepermittivity,and µisthepermeabilityofthematerial.Regu- lardielectricshavearelativepermittivitygreaterthanone;however,plasmascanhavearelative 7permittivitylessthanoneaswillbeshownlater.Itiscommontoexpresspermittivityandper- meabilityasrelativevalues,denotedbythesubscript r,'='0'r(2.6) µ=µ0µr(2.7) where '0and µ0representthepermittivityandpermeabilityoffreespace,respectively.The speedoflightinfreespaceisdeÞnedas c0=299,792,458m/s %3"108m/s(2.8) =1$µ0'0(2.9) andwillbeusedlatertosimplifyequations.ThepermeabilityoffreespaceisdeÞnedas µ0=4&"10#7H/m.(2.10) Thisgivesthevalueofthepermittivityoffreespaceas '0=1µ0c20=8.854187817620389 "10#12F/m(2.11) Foragivenmaterial,thepermittivitymaybeexpressedas '='&#j'&&.(2.12) Theimaginaryportion, '&&,captureslossesinthematerial.Theselossesarecommonlyex- pressedthrougheithertheconductivity, (,orthelosstangent,tan ),dependingonwhether 8thematerialisconsideredaconductororadielectric,respectively.Thesethreeparametersare relatedby '&&=(/"='0'rtan ).(2.13) Permittivitymayalsobeexpressedas '='!1#j("'".(2.14) Othermodelsexisttorepresentthepermittivityofamaterial,suchasthemodelpresentedlater inthischapterforaplasma. Anotherusefulconstantistheintrinsicimpedanceofamedium, *=#µ'(2.15) Inthecaseoffreespace[3,p.276], *0=#µ0'0=367.73 %120 &".(2.16) TheintrinsicimpedancerepresentstheratiooftheelectricÞeldtothemagneticÞeld.Given theelectricÞeld,themagneticÞeldmaybecalculatedusing !H=ök"!E*.(2.17) Thequantity kisthecomplexwavenumber.Itisusedheretorepresentthedirectionofpropa- gationforawave.FurtherdiscussionappearswithEquation(2.25). Energyistransferredfrompointtopointbyelectromagneticwaves.Thesewavesconsist ofcoupledelectricandmagneticÞeldsthatvaryinspaceandtime,andaresolutionstothe 9waveequation.InSections3.8Ð3.11oftheirbook[3],Ramo,Whinnery,andVanDuzerprovide aderivationfromMaxwellÕsequationstothewaveequation, !2!E=µ'%2!E%t2.(2.18) Theabovethree-dimensionalwaveequationreducestotheone-dimensionalcase, %2Ex%z2=µ'%2Ex%t2,(2.19) inrectangularcoordinatesthatisknownastheone-dimensionalHelmholtzequation.TheE- ÞeldinEquation(2.19)isdirectedinthe xdirectionasdenotedbythesubscript.Theformsare similarfor yand zdirectedelectricÞelds.Inphasornotation,thewaveequationis %2Ex%z2=#"2µ'Ex.(2.20) Onepossiblerepresentationofthesolutionistheplane-wavesolution[3,¤3.10], Ex=c1e#jkz +c2e+jkz ,(2.21) where c1and c2arerealconstants.Thetime-varyingformofEquation(2.21)is Ex(z,t)=Re$Exej"t%(2.22) =Re$c1e#jkz ej"t+c2e+jkz ej"t%(2.23) =c1cos("t#kz)+c2cos("t+kz).(2.24) 10Here kisthecomplexwavenumberdeÞnedas k=##j+.(2.25) Theparameters #and +canbefrequencydependent,therebymaking kfrequencydependent. Thewavenumberisalsomediumdependentandiscalculatedusinganyofthefollowingrela- tions: k="±$µ'(2.26) ="$µ0'0±$µr'r(2.27) ="c0±$µr'r.(2.28) The ±onthesquarerootfunctionhasbeenusedtoremindthereadertoselecttheappropriate signforthephysicsoftheproblemsinceplasmasbehavedifferentlythanmorecommonmedia andmayrequirespecialcases.Inthiswork #and +shouldbothbepositive.Thephysical meaningof +and #isseenwhen k=##j+issubstitutedintoEquation(2.24). Ex(z,t)=Re$c1e#j(##j+)zej"t+c2e+j(##j+)zej"t%(2.29) =Re$c1e#+ze#j#zej"t+c2e++ze+j#zej"t%(2.30) =c1e#+zcos("t##z)+c2e++zcos("t+#z).(2.31) Itiscommontoreferencesomeconstantpointonasinusoidwhenlookingatthebehaviorof theargument,forexamplethemaximumorthezerocrossing.Astime tincreases,theposition zofthereferencepointmustalsoincrease.The c1sinusoidisthereforeawavetravelinginthe positive zdirectionandthe c2sinusoidistravelinginthenegative zdirection.Thephaseof thewaveiskeptconstantby #,hence #isnamedthephaseconstant.Theparameter +isonly 11intheexponentialtermsofEquation(2.31)andhencedetermineshowquicklythesinusoid attenuates(decays)orgrows,hencethenameattenuationconstant.Asthe c1wavepropagates inthepositive zdirection,itdecays.The c2wavealsodecaysasitpropagateseventhoughthe exponentiallookstobegrowing.Sincethewaveispropagatinginthenegative zdirection, zdecreasesandtheexponentialtermdecays. Inthewave,theargumentofthecosineshouldbeconstant.Inorderforthistooccur,the positionalterm #zmustbeproportionaltothetimeterm "t.Theratio "/#determinesthis relationship.Since "=2&fhasunitsofradianspersecondsand #hasunitsofradiansper meter,theratiohasunitsofmeterspersecond.Itisthereforeavelocityandisknownasthe phasevelocityofthewave, vph="#=1$µ'=c0$µr'r.(2.32) Thephasevelocitymayalsobeexpressedas vp=f,where ,isthewavelength.Thewave- lengthisthedistancebetweentwosuccessivepointswiththesamephase,e.g.thepeakofthe Þrstwavetothepeakofthesecondwave.Rearrangingthisexpressionaswellasmakingsubsti- tutionsprovidesvariousformsforthecalculationofthewavelength[4,p.51], ,=vpf=2&#.(2.33) Because #canbefrequencydependent,thephasevelocitycanvarywithfrequency.This meansthatwavesofdifferentfrequencieswilltravelatdifferentrates.Ifthewavestogether carryinformation,suchastheenvelopeinanAMradiobroadcast,thenthisinformationmay bedistorted,aneffectcalleddispersion,bythedifferencesinphasevelocity.Amediumthat 12causesdispersionissaidtobedispersive.Theinformationitselftravelsataratethatisdifferent thanthephasevelocityandknownasthegroupvelocity, vg=d"d#(2.34) =vp1#("/vp)(dvp/d").(2.35) TheideathatthegroupvelocityrepresentstheÒvelocityofenergytravelÓisappropriateforthis dissertationbutisnotalwaystrue;seeRamo etal. [3,pp.260Ð264]andtheirreferencesof[5, pp.330Ð340]and[6].If vgisconstant,thennodispersionoccurs.Thisisakintosayingthat thephasevelocityisequalforallfrequencies.Normaldispersionoccursif vgvph,thenthedispersionisknownasanomalousdispersion[7,p.269].Abackwardpropagatingwave occursif vg<0.Thegroupvelocityisalwayslessthanorequaltothespeedoflight,while vphisgreaterthanorequaltothespeedoflightinavacuum, c0.Thephasevelocityisabletobe greaterthanthespeedoflightwithoutviolatingthetheoryofrelativitybecausenophysical quantity(massorenergy)ismovingatthisspeed[3,p.303]. Acommonwaytoconceptualizethefrequencydependenceofamediaistocreateadis- persiondiagram,whichisalsoknownasan "-#diagram.Whilefrequencyisusuallytheinde- pendentvariableinÞguresandisplacedonthehorizontalaxis,adispersiondiagramconven- tionallymakesfrequencythedependentvariableandplots "alongtheverticalaxisversus +or#.Figure2.1showsageneric "-#plot.First,thedotted,bluelineisthedispersionrelationfor freespace,i.e. "=c0#0,andisknownasthelightline.Theslopeofthelightlineisconstant, thereforethereisnodispersioninfreespace.Thesolid,redlineisthefrequencyresponseof #.Shownarereferencelinesforgroupandphasevelocities.Weseethatthegroupvelocityis theslopeof #andthatthephasevelocityistheslopeofthelinegoingfromtheoriginto #.Be- causetheslopeof #inFigure2.1isnotconstant,thegenericmediumrepresentedisdispersive. Finallythedashed,greenlineisthefrequencyresponseof +.When #goestozero,thegroup 13Figure2.1:Genericdispersion( "-#)diagram. velocitybecomeszerowhichmeansnoinformationiscarriedbyawaveinthemediumandthe phasevelocityisinÞnity.Thisfrequencyisknownasthecut-offfrequencybecausepropagation iscutoffatfrequenciesbelowit.Atthispointitiseasytoseethesevelocitiesifweexaminethe behaviorofthereferencevelocitylinesatthispoint.Thegroupvelocitylinewouldbehorizontal andthephasevelocitylinewouldbeverticalgivingtheaforementionedvelocityvalues. 2.2Plasmas Plasmasaregenerallyknownasthefourthstateofmatter;insimpleterms,plasmasarehot,ion- izedgases.Moreprecisely,plasmasareÒmacroscopicallyneutralsubstancescontainingmany interactingfreeelectronsandionizedatomsormolecules,whichexhibitcollective[effects]due 14tolong-rangeCoulombforces...[Theypossess]enoughkineticenergytoovercome,bycolli- sions,thebindingenergyoftheoutermostorbitalelectronsÓ[2,pp.1Ð2]. ThefollowingfourcriteriamustbesatisÞedformattertobeinaplasmastate[2,chap.1]: 1.theoverallsizemustbelargecomparedtothecharacteristiclength, 2.theelectrondensityinsideaDebyesphere(describedbelow)mustbelarge, 3.itmustbemacroscopicallychargeneutral,and 4.electronoscillationsshouldnotbeoverlydampedbycollisions. Assumption Todiscussthesecriteriaforaplasma,valueswillbeusedthatrepresentaßamefroma plant-basedfuel,suchasgrassesorpineneedles.Thesevalueswereselectedfromthe literaturereviewinChapter3andarediscussedfurtherthere.Theelectrondensityis ne=1"1016m#3,thecollisionfrequencyis !eff=1"1010collisionspersecond,andthe temperatureisaround866K(1000¡F). 2.2.1CharacteristicLength TheDebyeLength, ,D,isthecharacteristiclengthforaplasmagivenby ,D=&'0kBTnee2(2.36) where kB=1.3806488 "10#23J/KistheBoltzmannconstant, TisthetemperatureinKelvin, neistheelectrondensity,and e=1.6021766208 "10#19Cistheelementarycharge.TheDebye lengthdescribesthedistanceoverwhichtheelectricÞeldfromonechargedparticleaffects otherchargedparticles.Giventheabovevaluesforaßame,theDebyelengthisapproximately 0.02mm.Almostallßamesarelargecomparedtothislength,especiallythosefoundinahouse Þre. 152.2.2DebyeSphere ADebyesphereisthespheresurroundingaparticlethathasaradiusof ,D.Toshieldthe chargedparticleatthecenterofthespherefromtheeffectsofelectrostaticÞeldsoutsideof thesphere,theremustbealargenumberofchargedparticlesinsidethesphere.Effectively,a particleonlyinteractswiththoseparticlesthatarecontainedinsideitsownDebyesphere.This shieldingofthecenterparticleisknownascollectiveshieldingorDebyeshielding,andisan importantcharacteristicofallplasmas.Theexpression ne,2D'1(2.37) shouldbetrueinorderforcollectiveshieldingtobeeffectiveinaDebyesphere.Thelefthand sideisroughly80fortheselectedßamevalues,therebysatisfyingthiscriterion. 2.2.3ChargeNeutrality AsaconsequenceofthecollectiveshieldingobservedinaDebyesphere,theplasmaonthe wholeshouldbechargeneutral. 2.2.4CollisionDampening Inorderforaplasmatonotloseenergyandbecomeaneutralgas,thecollisionfrequency, !eff,mustbelessthantheplasmafrequency, 1"pe,i.e. !eff<"pe,[2,p.10].Theplasmafrequency, "pe=&nee2me'0(2.38) 1Inanopensystemwithanenergyinput,i.e.non-adiabatic,thecollisionfrequencymaybegreaterthanthe plasmafrequencyifthenetenergygainrateisgreaterthanthecollisionallosses. 16where meisthemassofanelectron,istheangularfrequencyatwhichelectronsoscillateinside theplasmainordertoremainneutrallychargedonaverageafterhavingbeendisplacedbysmall disturbingforces.Thecollisionfrequencyistherateatwhichfreeelectronscollidewithand transferenergytoheavier,relatively-stationaryparticles. Forthegenericßame-plasmaparameters, !pe="pe/2&%9"109.Earlier !effwasselected tobe1 "1010.Weseethatthesetwovaluesarecomparable.Becauseofthis,ßame-plasmasare sometimesclassiÞedasweakly-ionizedplasmas. 2.3PlasmaModelforElectromagneticFields Assumption Asstatedearlier,thefocushereisonunmagnetizedplasmas. Ofinterestforthisdissertationishowelectromagneticwavesinteractwithplasmas. MaxwellÕsequationsandtheconstitutiveequationspresentedinSection2.1governhowthe Þeldswillinteractwiththeplasmaifitismodeledasadielectric.Anacceptablemodelforthe permittivityofanunmagnetizedplasmais[2,p.412],[7,p.216], 'r=''0='1#"2pe"2+!2eff(#j"2pe!eff")"2+!2eff*.(2.39) Usingthisasthepermittivityoftheplasma,weareabletotreattheplasmaasaregularmedium andcarryouttraditionalanalysissuchaspropagationstudies,materialcharacterization,or transmissionlineproblems.Aconsequenceoftheconditionthattheplasmaisunmagnetized isthattheplasmaisisotropic,meaningthatthetransmissionthroughtheplasmawillbethe sameregardlessofthedirectionoftravelthroughtheplasma. First,wenoticethat 'risacomplexvaluedependentnotonlyuponplasmaparameters,but alsofrequency.Asfrequencyincreases,therealpartapproachesoneandtheimaginarypart approacheszero.ThusatsufÞcientlyhighfrequencies,determinedbytheplasmaproperties, 17Figure2.2:Dispersion( "-#)diagramforacollisionlessplasma. theplasmaappearstobefreespace.Thisisreasonablegiventhatatextremelyhighfrequencies, theparticlescannotoscillatequicklyenoughtokeepupwiththechangingÞelds[2,p.407].At lowerfrequencies,therealportionwillbelessthanone,evennegative.Atypicaldielectrichas arealpartgreaterthanone.Theimaginarypartofthemodelwillalwaysbenegativesignifying thattheplasmaislossy.Inacollisionlessplasmatheimaginarypartisequaltozeroandthe plasmaislosslesssince !eff=0.InFigure2.2weseethecut-offandfree-spacebehaviordiscussedabove.Atthelowestfre- quencies,absorptionishighest.Itdecreasestozeroattheplasmafrequency,atwhichpointthe phaseconstantbeginstoincrease.Athigherfrequencies,thephaseconstantapproachesthe lightlinemeaningthattheplasmahaslessofaneffectontheelectromagneticÞelds. Figure2.3showsthecaseforaplasmawithcollisions.Weseethatboth +and #arezero atzerofrequency.Atlowfrequencies,bothbegintogrow.Againatthehigherfrequencies, 18Figure2.3:Dispersion( "-#)diagramforaplasmawithcollisions. theplasmaapproachesfree-spacebehavior(lossestendtowardszeroandthephaseconstant approachesthatoffreespace, #0).Unlikethecollisionlesscase,thereisnoabruptcut-offbe- havior.Theattenuationisverylarge,however,anditisreasonablefortheretobesomeregion wherethewaveisÒcutoffÓbecausetheattenuationisrelativelylarge. Itwasassumedintheabovediscussionthattheplasmawassemi-inÞnite,homogeneous slab.Iftheplasmaisnothomogeneousandthereexistdensitygradients,thepropertiesofthe plasmawillchangespatial.Inthiscase,dispersionandgradualreßectionwilloccur. 19Chapter3 LiteratureReview Thefollowingliteraturereviewshowsthatßamescanaffectelectromagneticwavesatalabora- toryscaleandforcertainfuels.Italsoreviewsworkonelectromagneticwavesinteractingwith plant-fueledÞresofvarioussizes.Throughthisreview,nopriorworkwasfoundstudyinghow electromagneticwavesandßamesfromcommonhouseholditemsinteract.Understanding thisbackgroundinformationisimportantinordertoÞndpeopletrappedbyahouseÞreusing radar.Belowisareviewofthecurrentliteratureontheinteractionbetweenelectromagnetic wavesandßames. 3.1EarlyWork Researchintoelectromagneticpropagationthroughßamesbeganinthe1940sbySugdenatthe UniversityofCambridge[8].Inthispaper,a10GHzwavewasattenuatedby0.6dB/cmbythe ßameproducedattheendofarißebarrelwhentherißewasÞred. Followingthisinitialpaper,aseriesoffourpaperswereauthoredbySugdenandhisstu- dentsintheearly1950s[9Ð12].Workbeganbystudyingtheattenuationofacoal-gas/airßame between3GHzand37.5GHz[9].Theßamewas1.45cmwideandwasartiÞciallyseededwith ThischapterbeganasaclassprojectforBE820duringtheFall2012semester. 20alkali-metalsalts.Theßametemperaturewasroughly2200K.Throughattenuationmeasure- ments,itwasfoundthattheßamehadanelectronnumberdensityof ne=2.0 "1017m#3and acollisionfrequencyof !eff=8.8 "1010s#1.LaterworkbySugdenfoundtheelectronnum- berdensitytobe ne=0.8Ð1.5 "1017m#3forahydrogen-airßameseededwithalkalisalts[11]. Flametemperaturesinthiscasewerebetween1900Kand2000K.Itisimportantthattheßames wereseededwithalkali-metalsalts.Thisgroupofelementshasrelativelylowionizationener- gies,whichallowsfortheelectronstobeeasilyremovedandensuresthataplasmawouldform intheßame.Additionally,weknowthattheionizationistheresultoftheßametemperature andnotthecombustionreactionsincethealkalimetalsarenotresponsibleforcombustionin thesetypesofßames. In1954Adlerstudiedclean,unseededßamesfrompurejetfuel.Flametemperatureswere around1920K.Usingpropagationtheory,itwasfoundthattheelectronnumberdensitywas ne=1.9 "1012m#3andthatthecollisionfrequencywas !eff=6.5 "108s#1[13].Thisshows thatunseededßamescreateaweakerplasmathanseededßames(asexpected).Theimpor- tanceofthisresultisthatitisnotnecessarilythefuelthatdictatesthatplasmaparameters butotherconstitutivematerialsthatmaybebroughtintothecombustionregionthroughsome masstransportmechanism. Alsoin1954,Shulerstudiedunseededhydrogen-oxygenandacetylene-oxygenßamesfor variousfuel-airratios[14].Hefoundthattheelectronnumberdensityvariedbetween2.3Ð 6.3 "108cm#3forhydrogen-oxygenßames,1.42Ð1.66 "1010cm#3forleanacetylene-oxygen ßames,and0.644Ð3.47 "1010cm#3forrichacetylene-oxygenßames.Intheacetylene-oxygen ßames,thehighestelectronnumberdensityoccurredwhentheßamewasthehottestat3285K. Thislastresultisexpectedbecausethechargedparticleswouldhavehigheraveragekinetic speedsandenergiesleadingtomoreionizedparticles. 21Thereislittlepublishedliteratureonthistopicfromthelate1950Õstothe2000Õs.Otherwork thatissomewhatrelated(refraction,plasmas,atmosphericpropagation)wenton;however,no oneseemedtopickupSugdenÕswork,whichisnothighlycited. 3.2WildlandFirePapers Themostrecentresearchrelatingtoelectromagneticwavepropagationthroughßameshas comefromDr.JohnathanBoanattheUniversityofAdelaide[15Ð19]andDrs.MphaleandHeron atJamesCookUniversityinAustralia[20Ð33].TheworkatJamesCookUniversitywasdonein collaborationwiththeUniversityofBotswana.Collectivelytheseworksinvestigatedhowelec- tromagneticwavespropagatethroughÞresfueledbyorganicmatterspeciÞcallyrelatedtoAus- tralianwildlandÞres.Thesepapersarediscussedinthefollowingsections. 3.3LossesinWildlandFiresInvestigatedbyBoan JonathanBoan,astudentofAssociateProfessorChrisColeman,submittedhisPhDthesistitled RadioPropagationinFireEnvironments in2009totheUniversityofAdelaide,Australia[19]. Duringhistimeasastudent,BoanhadaWorkshopontheApplicationsofRadioScience beststudentpaper[16],twoIEEEAntennasandPropagationSociety(AP-S)Symposiumpa- pers[15,18],andanIEEEAntennasandWirelessPropagationLetter[17]accordingtohisper- sonalbibliographylistedatthefrontofhisthesis[19].Allofthesepapersfocusedonpropaga- tionthroughÞreandincludebothsimulationsandexperiments.BoanÕsworkinvestigatedthe lossmechanismsassociatedwithawildlandÞreßamefront.Hebreaksdownwavepropagation intorefraction,scattering,andplasmaeffectsasdescribednext. 223.3.1LossMechanisms Refractionisthephysicalphenomenathatchangesthedirectionoftravelofawavewhenitpass fromonemediumtoasecondmediumthathasadifferentindexofrefraction, n=$µr'rfor realvaluesof µrand 'r[3,p.278].RefractionisnumericallycalculatedusingSnellÕslawthat describestherelationshipbetweentheincidentangle, -1,inmedium1withtherealindexof refraction n1andtherefractedangle, -2,inmedium2withtherealindexofrefraction n2andis givenby[34] sin-1sin-2=n2n1.(3.1) Forgasesthismayalsobeexpressedintermsoftemperature,pressure,andtheconcentrations ofconstitutivesubstancesofthegas.AllofthesehavelargegradientsaroundaÞreresulting invaryingindicesofrefractionasonemovestowardsthecenteroftheßame.Movinginward, subrefractiveconditionscanoccurthatleadtowavesbeingbentupwardsandawayfroma receivingantennain-linewiththetransmittingantenna[16].Subrefractioncauseswavesto bendawayfromthegroundinsteadofbeingbentdowntowardsit,orbeingductedthrough theatmosphere.Bothsubrefractionandductingarenonstandardmeansofpropagation[35]. Subrefractionoccurswhentheindexofrefractionincreaseswithheightratherthandecreases, whichoccursundernormalatmosphericconditions. Scatteringoccurswhenawaveisdeßectedinoneormultipledirectionsdifferentthanthe original.DuringaÞre,wavesareprimarilyscatteredthroughtwomechanisms[16].TheÞrstis scatteringfromsmokeparticulatesandsmallparticlesentrainedintheÞreplume.Thesecond isscatteringduetochangesintheindexofrefraction.Notallenergycarriedinawaveistrans- ferredthroughaninterfacebetweenmediawhenitisrefracted;someoftheenergyisreßected fromtheinterface.Airturbulenceisalsoincludedinthissecondcauseofscattering.Swirling andmixingairaroundtheÞrewillresultinadditionalscattering[36Ð43].Boandoesnotinclude 23scatteringinanyofhisanalyses,insteadnotingthisasanareaoffuturework[19].Healsoover- looksthescatteringfromentrainedparticles,writingthatÒthechangesintherefractiveindex areknowntobesmallandthereforestrongscatteringisnotexpected[16].Ó Duringcombustion,chargedparticlesarecreatedthroughchemicalionizationaspartof thechemicalreactionofcombustionandthroughthermalionization[19,20,44].According toBoan,thermalionizationistheprimarycauseofchargedparticlesinaÞre[19].Thepri- maryspeciesionizedduringcombustionofplantbasedÞresisthoughttobealkali-metalsand graphiticcarbon[25].Thisthermalionizationmaybeduetotherelativelylowionizationener- giesofalkalimetals[45]. 3.3.2FDTDSimulations BoanbeganhisworkbystudyingÞnite-difference,time-domain[46](FDTD)simulationsof electromagneticpropagationthroughßames.BoanhadidentiÞedrefraction,scattering,and combustion-inducedplasmaasthethreeprimarylossmechanismsatthebeginningof[16].In ordertosimplifytheworkatthisstageofhisresearch,Boandidnotconsiderscatteringfrom theßameorsmokeparticlesin[15]or[16]. FDTDsimulationstypicallyrequireagreatdealofmemoryandtimetosolvelarge(interms ofwavelength)simulationdomains.Numericaldispersioniscommonwhenthesimulatedtime scaleisrelativelylong.WildlandÞresarephysicallylargeevents,spanningfromtensoffeetto tensofmiles.FlameheightcanrangefrominchestooverÞftyfeet.Thesephysicallylarge,and evenlargerintermsofwavelengths,dimensionsmakesimulationofwildlandÞresdifÞcult. BoanhasusedtheworkofAklemanandSevgirelatedtotroposphericpropagationtoman- agethelargedomain[47].AklemanandSevgipresenta2-D,FDTDtechniquethatmaybeused forpropagationproblemsoverlongdistances.Thistechniqueusesabroad-bandpulsethatis tracedoverthelengthofthesimulationdomainbyaspatialwindowsothattheentiresimula- tiondomaindoesnotneedtobeheldinmemoryforthedurationofthesimulation. 24Sincecombustioncreatesaweakly-ionizedgas,BoancombinestheaboveFDTDtechnique withtheworkofNickischandFranke[48]toaddacoldplasmamodelto[47].Boanfurther enhanceshisFDTDsimulationsbyaddingworkfromYoung[49]toproperlysimulatetheex- pecteddispersioncausedbytheßamebeingalossymedium.ThisisdonebyÒevaluatingthe polarizationcurrentofthemedium[15]ÓbyalteringthestandardformsofMaxwellÕsequations to'%!E%t=!"!H#(!E#!Jp(3.2) µ%!H%t=#!" !E(3.3) toincludeatermforthepolarizationcurrent, %!Jp%t=#!eff!Jp+'0"2p!E.(3.4) In[15]and[16],BoanconsidersTE zpolarizationandmodelsthegroundasaperfectelectrical conductor.BoanÕscodeusestheFDTDapproachofLan[50]withahigherorderalgorithmfrom Zygiridis[51]andartiÞcialanisotropy[15]tohandledispersion. Boanalsonotesthatthesettlingtimeofthesimulationmediummustbetakenintoaccount. HestatesthatthepolarizationcurrentwillhaveshortsettlingtimesbecauseÒthecollisionfre- quency[ !eff]underatmosphericpressuresisnormallyveryhigh (1011sec#1[15]Óaccordingto datapublishedbyItikawa[52]. Theeffectsofrefractionandhowitisimplementedinthesesimulationsisdiscussedin[16, 19]andisoriginallypresentedin[34]and[53].Foragas,theLorentz-Lorenzrelationis[34] +=34&nmol'#1'+2=34&nmoln2#1n2+2(3.5) 25where +istheelectricpolarizabilityofthegas, nmolisthenumberdensityofthemoleculesin thegas,and nistherefractiveindexforthegas.Valuesfortheelectricpolarizabilitymaybe foundinreferencetextsuchasthe CRCHandbook [45].Thiscanbewrittenas L1=n2#1n2+2=4&nmol3+=4&3$NAM+(3.6) where L1denotestheLorentz-LorenzcoefÞcient, $isthedensityofthegas, NAisAvagadroÕs number,and Misthemolecularweightofthegas 1.Forahomogenousgasmixtureinaknown, referencestate(denotedbythesuperscript ))theLorentz-LorenzcoefÞcientisgivenas[53] L)=+i(n)i)2#1(n)i)2+2=+i$)i,4&NA+i3Mi-(3.7) wherethesumisoverthevaluesforeachgasinthemixture.Ciddor[53]thengivestheLorentz- LorenzcoefÞcientforamixtureatanunknownstate L=+i$i$)i(n)i)2#1(n)i)2+2.(3.8) Theindexofrefractionforthegasmixtureinthisunknownstateistherefore n=.(1+2L)/(1#L).(3.9) TheidealgaslawmaybeusedtoexpresstheLorentz-LorenzcoefÞcientasafunctionofvari- ablesbesidespressure.BoanusesEquation(3.8)andEquation(3.9)tocalculatetheindexof refractioninsimulationsforaircomposedofnitrogen,oxygen,andcarbondioxide[16]. 1In[19]Equation(3.6)insteadhastheterm +#1.Thisisbelievedtobeamistakeprobablymadeduringtypeset- tingasdimensionalanalysisand[34]reachtheexpressiongivenhere. 26Asimplenumericalsimulationiscarriedoutin[15]thatusesa2DGaussiantemperature distribution T=300 +1050exp ,#,x#100 20-2#!y15"2-(3.10) where TisthetemperatureinKelvinwhile xand yarepositionvariablesinmeters.Boanuses alkali-metalconcentrationsof0.57%forpotassium,0.58%forcalcium,and0.43%formagne- siumforsimulations.Hereferences[20]foradescriptiononhowthesevaluesareusedtocalcu- lateelectrondensityintheßame.ThiscalculationisfurtherdevelopedinlaterworkbyMphale anddiscussedinSection3.4. ResultsfromthisGaussiantemperaturedistributionshowthatatthemaximumtempera- ture,whichwouldbethecenteroftheßame,attenuationistemperaturedependentnearthe ground.Abovethetemperaturedistributionlittleattenuationisobserved.Asonemovesfur- therawayfromthemaximumtemperature,signalstrengthbeginstorecover.Asimulationwas conductedwithnoplasmaeffectswhichBoanusestosuggestthatrefractionalonehasonly minoreffectsonthewavewhenpropagatingthroughthetemperaturedistribution.Givena spatiallylongertemperaturedistribution,andhencealongerpropagationpath,Boansuggests thatrefractioneffectswouldbemoreinßuential. Amorecomplexsimulationwascarriedoutin[16].HeredatafromanactualÞreinJarrah- dale,WesternAustralia,publishedin[54],wasusedtocreateaFireDynamicsSimulator[55] (FDS)simulation.Treeswere8minheight.BoanusedapilotÞreforignitionoftheentire simulationandincludeda3m ás-1wind. ResultsconcerningtheeffectofrefractioncausedbytheÞresuggestthatrefractionhasonly asmalleffectonpropagation;Boanpositsthatthewaveispushedupwardsbyrefraction.The signalstrengthdoesappeartowidenorriseasitpropagates;however,thiscouldsimplybedue 27tothewaveexpandingoritcouldbecausedbytheantennapattern.Itcouldalsobecausedby numericaldispersionthathasnotbeenproperlycorrected. EffectsofÞre-inducedplasmasseemmoredeÞnitive,buthowBoanseparatedtheeffectsis notdescribedinthetext.Assumingthatplasmaandrefractiveeffectsmaybeseparated,wecan concludedthataÞre-inducedplasmaaffectssignalpropagation.InthepublishedÞguresfora radiofrequencyof150MHz,plasmaeffectsaregreatestinwhatappeartothebehighesttem- peratureregionsoftheÞre.Below1200Kthereappearstobelittlereductioninsignalstrength. Astemperatureincreases,signalstrengthdecreases.AssumingthatBoanÕssimulationhasbeen codedtoonlyaddplasmaeffects(andonesthataredependentonßametemperature),itis plausiblethatelectromagneticwavesareeffectedbyÞres,albeitonlyinthehottestregionsof theßame.Thisisexpectediftheplasmaisprimarilygeneratedbythermalionizationassug- gestedbyBoan.Moleculeswouldonlybeionizedinthehottestregionsoftheßamebecause thisistheonlyareainwhichsigniÞcantenergyexists. OneofBoanÕscontributionistheintegrationofFDSdataintotheFDTDsimulationssothat amorerealistictemperatureproÞlefromaÞremaybesimulated.Itdoesnotappearthatthese simulationsincludescatteringordielectriceffectsofthefuel. 3.4ExperimentalMeasurementsConductedbyMphale AlargebodyofworkonthetopicofelectromagneticwavepropagationthroughÞrehasbeen producedbyDr.KgakgamatsoMphaleandhisadvisorDr.MalHeron.MphalewasaPhDstu- dentatJamesCookUniversity,Australia,andalsoassociatedwiththeUniversityofBotswana. HewassupportedbytheStaffDevelopmentOfÞceoftheUniversityofBotswanaandbyEmer- gencyManagementAustralia(EMA)underprojectnumber60/2001.OneofMphaleÕsearliest workswastheprojectreportforEMA[20]. 28Mphalecarriedoutnumerousstudiesusinganexperimentalburner.Thehexagonalwood framewaslinedwith20.3cm(8in)thickFiberfraxinsulationtocreatea50cm(19.69in)di- ameter,circularburnchamber.CutoutsforX-bandhornantennas(8.0Ð12.0GHz)wereplaced onoppositesidestofacilitatetransmissionandreßectionRFmeasurements.Ontheotherfour sides,two25mm(1in)holesweredrilledtoallowairßowintotheburner[21,24,25,29Ð32]. Fuelsfortheseburnsweregroundlitterthathadfallenfrom Eucalyptusplatyphylla (poplar gumoreucalyptus)and PinusCaribea (pine)treesalongwith Panicummaximum (Guinea grass).Samplesweredriedinthelaboratoryforatleasttendays.Thesefuelswereselected becauseoftheirprevalenceinAustralia.Somesampleswerewashed,driedandpreparedfor inductivelycoupledplasma-atomicemissionanalysistodeterminethealkaliandalkalinecon- tent[30].Eachfuelwasburnedindividuallyintheconstructedburnerandarrangedsothat ßameswouldfullycoverthebottomsurfaceoftheburner.Aswasnotedin[17,19],wavespropa- gatingaboveaÞresufferrelativelylittledegradationÑinsteadpropagationneedstobethrough theßametoobserveaninteraction.Theburnerwasconstructedandfuelwasloadedsothat forthemajorityofthetimethatfuelwasburning,wavespropagatedthroughtheßame[30]. ResultsfromMphaleÕsexperimentsarepresentedassignallosses,electrondensities,and collisionfrequencies.Intermediatedataisnotreported.Thisisprimarilyduetoobservation thattheabsorptionofaplasmaisrelatedto neand !eff,hencethosearetheimportantfactors toreport[56].AsummaryofresultsfromMphaleÕsexperimentsandthreesimulationsarepre- sentedinTable3.1.Thebottomrowsummarizestherangesseeninallexperimentaldataonly, i.e.thesummaryrowdoesnotincludesimulations). TheÞrsttworesultsarefromsimulationswherethefuelhad0.5%and3.0%potassium,re- spectively,torepresentgeneric,plant-basedfuel.Theobjectiveof[27]wastodemonstratea varianceinplasmacharacteristicsbasedonpotassiumcontent,whichisimportantinwildland Þresbecausetracealkalimetalsinplantsaretheprimarycontributortoplasmasforthisfuel 29Table3.1:Summaryof neand !effresultspublishedbyMphale. ne/m-3!eff/s-1FuelRef. 6.3 "1015-0.5%PotassiumSimulation[27] 1.5 "1016-3.0%PotassiumSimulation[27] 0.51 #1.35 "10163.43 #5.97 "1010Pine[24,25] 0.76 #3.21 "10161.11 #2.44 "1010Pine[30] 2.63 "1016-GuineaGrass[29] 0.32 #1.18 "10162.80 #3.95 "1010GuineaGrass[30] 5.061 "10151.0 "1011PrescribedGrassÞre[33] 2.26 "10165.84 "1010Eucalyptus[21] 2.19 "10166.18 "1010Eucalyptus[21] 3.40 "1016-EucalyptusSimulation[26] 1.46 "1016-Eucalyptus[29] 0.77 #1.47 "10161.47 #3.52 "1010Eucalyptus[30] 0.5061 #3.40 "10161.11 #6.18 "1010--type.Thetabulatedresultsshowthataspotassiumcontentincreases,electronnumber-density increasesaswell. TheprescribedgrassÞrein[33]wasaplotoflandontheJamesCookUniversitycampusthat hadaperimeterof393mandaRFpropagationpathofroughly44m.Raytracingwasused in[26]tocalculatepathlosses.Allotherresultslistedinthetablearefromexperimentscarried outinthehexagonalburnchamber. Table3.1showsthattheexpectedelectronnumberforawildlandÞreisontheorder of10 16m-3andthatthecollisionfrequencyisontheorderof10 10s-1.Mphalehasdevelopedatheoreticalbackgroundandanexperimentalsetupthatallowsfor anaccurateanalysisofelectromagneticpropagationthroughßames.Heallowsforvariability indataandthoughtfullyanalyzestheresults. 303.5Conclusion Initialworkinthe1950ÕsdemonstratedthatÞre-inducedplasmascanhaveaneffectonpropa- gatingelectromagneticwaves.Recentworkhasshownthatplant-basedfuelsburnedduringa Þrecanproduceweaklyionizedplasmas.Theseplasmashavesomewhatlocalizedeffects,pri- marilyinthemostintensecombustionzones.Recentresearchhasfocusedontheeffectthat largewildlandÞresmayhaveonhandheldradiocommunications.Ofinteresttothisreview istheeffectthatÞre-inducedplasmascouldhaveonsearch-and-rescueradarduringahouse Þre.CertainlyafullyengulfedcompartmentÞrewillreachsufÞcienttemperaturestocreatea plasmatosomeextent.FurtherresearchisneededinordertodeterminehowcompartmentÞre behaviorandcommonhouseholdfuelscreateÞre-inducedplasmasandaffectwavepropaga- tion.Thisliteraturereviewhasfoundnoresearchthataddressestheseissuestodate. 31PartII Large-scaleFireExperiments 32Chapter4 RadioWaveTransmissionThrough FurnitureCushionFlames Figure4.1:Materialsampleburningduringanexperiment. 33Thisresearchbeganwithanexperimentdesignedtoevaluateideasabouthowtomeasure andstudytheinteractionbetweenelectromagneticwavesandÞre-inducedplasmas.Todothis, anoutdoormeasurementrangewassetupattheCityofLansing(MI)FireDepartmentÕs(LFD) trainingsitethatconsistedoftwoantennaswithaburningsampleinbetweenthem.Thispro- ducedaßamethatdirectlyinterferedwiththetransmissionpath.Sofacushionswereusedfor samplesastheycouldbereadilyobtainedwhilebeingsimilartooneanotherforreplication purposes.Thegoalwastoevaluatetheexperimentalsetup,experimentaltechniques,andthe analyticaltechniqueswhichwouldbeusedinlaterwork. 4.1ExperimentalMethods Thesetupanddesignofthisexperimentwasbasedonexperiencewithothertransmissionmea- surementsinalaboratorysetting,ÞreÞghtingexperience,androughestimates.Equipment constraintsdictatedsomeofthesetupwhilecautionarystepstoprotecttheequipmentdictated otheraspects.Themainexperimentalsetupconsistedoftwotripod-mountedantennas,awire shelfonwhichsampleswereburned,andameasurementunit.Ancillaryequipmentincludeda laserlevelandvideocameras.AdiagramofthelayoutisshowninFigure4.2,aschematicofthe measurementsetupisshowninFigure4.3,andaphotooftheexperimentisshowninFigure4.4 Sampleswereplacedonawireshelfinthemiddleofanasphalt-coveredarea.Awireshelf wasusedbecauseitcouldwithstanddirectcontactwithßames,wasacquiredforalowcost, couldbeeasilycleaned,andhadanadjustableheight.Whileitwasexpectedthatthemetalshelf woulditselfaffectthetransmissions,weplannedtoremovetheeffectsthroughpost-processing ofthedata. Twoantennaswereplacedapproximately9.5ftor25.5ftfromtheshelf,dependingonthe datasetinaroughlynorth-southline.TherewerenospeciÞcreasonsforthesedistancesother thantryingtolimittheÞredangertotheantennasandthattheasphaltwasindecentcondi- 34Figure4.2:Diagramofexperimentallayoutwhentheantennaswere(a)25.5ftand(b)9.5ftawayfromtheshelf. Figure4.3:Schematicofexperimentalsetup,(a)sideview(b)topview. 35Figure4.4:Photographoftheexperimentalsetupshowingthelaserlevel,antennas,burningsample,wireshelf, sand,cablemats,windindicator,videotripod,andinstrumentationtable. tionatthosespots.TheantennaswereAmericanElectronicLaboratoriesH-1498broadband hornantennascoveringthefrequencyrangeof2GHzto18GHz.Theantennasandshelfwere squaredtooneanotheralongthemeasurementlineusingalaserlevel,whichemittedvertical andhorizontallines.Sandwasspreadunderneaththeshelfinordertocaptureslagfromthe burnedsamplesandtoprotecttheasphalt. Ameasurementunit(HP8753DVectorNetworkAnalyzer(VNA)connectedtoalaptopusing aUSB-GPIB)waslocatedeastoftheshelfonafoldingtabledesignatedastheinstrumentation table.Cableswererunfromeachantennatothemeasurementunitunderneathcableprotec- tors/mats 1.Atarpwassetupsothattheinstrumentscouldbeeasilycoveredintheeventof rain.CardboardwasusedtocovertheVNAandthelaptopfromthesuntoallowforeasierread- ingofthedisplaysandtohelpkeepinstrumenttemperaturesmoreconstant.Transmission properties(S 21)wererecordedduringtheexperimentasquicklyastheVNAcouldacquiredata usingthePythoncodefoundinAppendixH.Afull-twoportcalibrationusinganAgilent85052D 1Extendingfromport1oftheVNAtothenorthernantennawerecablesnumbered013,039,and038withap- propriateadapters.Extendingfromport2oftheVNAtothesouthernantennawerecablesnumbered040,037, and046withappropriateadapters.InformationaboutindividualcablescanbefoundinAppendixB. 363.5mmeconomymechanicalcalibrationkitwasperformedattheendofthecablessothatthe measurementreferenceplanesweretheportsoftheantennas. Datawasfurthercalibratedthroughpost-processingwhichusedmeasurementsofanes- sentiallyemptymeasurementrangeandofametalplate,placednormaltothedirectionof propagationinthesamelocationwheresampleswouldbe.Post-processingcorrectionused thefollowinggeneralformula: Scorr 21=Smeas 21#Splate 21Sempty 21#Splate 21(4.1) where corr isthecorrecteddataset, meas isthedatasettobecorrected, plate isthedataset foraplatecalibrationstandard,and empty isthedatasetforatransmissionpathwithnosam- ple[57,58].Theobjectsthatwereinthe empty rangemeasurementwerethosethatwouldbe therewhenthesamplewasburned,e.g.thewireshelf.APlexiglassample,2ftby2ftby1in thick,wasmeasuredasanexperimentalcontrolbeforeeachsamplewasburned.Thissample hasbeenmeasuredinthelabmultipletimesovertheyearsbyotherstudentsandalsobefore thisexperiment.Thisdatawasprocessedinthesamewayasotherdataandwasusedtocheck theperformanceofthemeasurementsystembycomparingittolaboratorymeasurementsand publisheddata. InordertokeepthemetalplateandthePlexiglassamplesvertical,theywereplacedintoa metaltroughasshowninFigure4.5.WoodshimswereusedtoholdthemetalorPlexiglasin placeandensurethattheplatewasvertical.The empty measurementusedforPlexiglassam- plescontainedthemetaltroughwhichwasnotinthe empty forthesamples.Byincludingthe troughinthePlexiglas empty measurements,wecouldaccountforitseffectsintheappropri- atemeasurements.Theburningsampleswerenotaffectedsincethatpaired empty didnot includethetrough.AdditionaldetailsaboutthetroughareinAppendixC. 37Figure4.5:Metalholderusedformetalplates,Plexiglassamples,andotherplanarsamples. Weatherobservationsweremadebecausetheambienttemperaturecanhaveaneffecton equipmentstability,likewise,windcaneffecttheÞrebehavior.Acombinationdigitalther- mometerandhygrometerwasplacedontheinstrumentationtable.Observedweatherand ofÞcialNOAA/NWSobservationsfromtheLansingairportarerecordedinAppendixD.1.Black andyellowstripedsurveyingtapewasattachedtoaÞberglasspoleandplacedSSWofthemea- surementlineasawindindicator.Thiswindindicatorisvisibleinsomevideoandphotographs. Videocameraswereplacedontripodsjustnorthoftheinstrumentationtableandtothe SSEofthemeasurementline.Videosweremanuallystartedandstoppedbeforeandaftereach sample. SamplesforthisexperimentwerefurniturecushionsobtainedfromtheMSUSurplusStore asindividualcushionsatnocost.Noinformationaboutthecushionmaterialorßameretar- dantswasavailable.ThereweretwodifferentstylesofcushionasseeninFigure4.6;Þvewereof asmallersizewithpurpleandblueupholstery,whichwillbereferredtoaspurplesamples,and twowereofalargersizewithorangeupholstery,whichwillbereferredtoasorangesamples. 38Figure4.6:Materialsamplesfortheexperiment. Figure4.7:Apurplesamplewithignitionsampleremovedanddisplayed. ABernzOmaticTS3000propanetorchwasusedtoignitesamples.Priortotheexperiment dayapiecewascutoutofapurplesample,Figure4.7,placedinanaluminumfoiltray,and ignitedusingthetorch,Figure4.8.Thesmallsampleignitedrelativelyeasilyoncethetorch burnedthroughtheupholsteryandthefoamhaddirectßamecontact.Asustainedßamewas observeduntilthesolidfoamwascombustedormeltedatwhichpointapoolÞreremained.It appearedthatthesampleshadsomesortofßameretardantbutthatignitionfortheexperiment wouldnotbeproblematic.IgnitiononthedayoftheexperimentturnedouttobemoredifÞcult thanexpected,asdiscussedlater. 39Figure4.8:Ignitionsampleinaluminumfoiltray. Table4.1:ExperimentconÞgurationforeachsample. BurnSampleAntennaDistStartStopNumPtsIFBWAvgFactPower FtGHzGHzHzdBm B1Purple25.52616013000410 B2Purple25.52616013000410 B3Orange9.52616013000410 B4Orange9.52616013000410 B5Purple9.52616013000410 B6Purple9.526263000410 Atotalofsixsamplesweremeasured.Theseventhsamplewaskeptforfuturesmall-scale testsandasareference 2.Thissamplewastheoneusedintheignitioninvestigation.Thecon- ÞgurationforeachsampleisshowninTable4.1. 2ItturnsouttheprimaryuseforthisremainingsamplehasbeenasashockabsorberfortheVNAduringtrans- portation.TheVNAisplacedontopofthecushionwhentransportedtofurtherdampenroadvibrationsthatmay damagetheVNA. 404.2GeneralMeasurementProcedure Thegeneralexperimentprocedurewasasfollows: 1.Measurewithonlymetalsampletrayonwireshelf 2.Measureametalplate 3.MeasureaknownPlexiglassample 4.Measureonlythewireshelf 5.Measurethesample 6.Ignitesample 7.Measurethroughouttheburn 8.(Self)Extinguish 9.Removesample 10. Repeat1Ð7forremainingsamples 11. Repeat1Ð2afterallsamplesburned 4.3SafetyPrecautions Thefollowingsafetyprecautionswereobserved: ¥AsafetybrieÞnguponMSUÕsarrivalinthemorningandbeforetheÞrstburn ¥EveryonewasmadeawareoftheRFcablesandtoldnotstepon,driveover,impact,nor loadanycable 41¥Appropriatepersonalprotectiveequipment(PPE)waswornwhenneeded ¥Asitesafetyplanwaspreparedforthisexperiment.ThiscanbefoundinAppendixE.1. AhandlinewasstretchedandchargedfromtheÞrehydrantinthesouthwestcornerofthe LFDfacility.AdditionallyaÞreextinguisherwasattheinstrumentationtablereadyforuse. LFDpersonnelwerepresentinthemorningtoassistwithsettingupthefacilityandtogive thego-aheadfortheexperiment. 4.4Go/No-GoCriteria Thefollowingcriteriawereusedtodetermineiftheexperimentcouldbeginorwastobeinter- rupted: ¥Unsafewindconditions(Nogo) ¥Imminentrain(Nogo) ¥FinalapprovalofLFDpersonnel(Go) 4.5Results Datafromtheexperimentwerepost-processedbytimegatingandnormalizingusingEqua- tion(4.1).Arectangularwindowwasusedtotimegatethedatato40nsforburns1and2,and to17nsfortheotherburnsusingtheprogramWaveCalcprovidedbyDr.RossofJohnRossand Associates.Thelengthoftimeforthewindowwasselectedtoblockoutanyreceivedsignals afterthedirectsignalwasreceived.Figure4.9showsacalibrationplatebeingmeasuredinthe labtoillustratetheexperimentalsetup.Platesandemptymeasurementsweretakenbefore burns1,2,3,and6.Burns4and5wereprocessedusingthecalibrationmeasurementsfrom burn3. 42Figure4.9:Exampleexperimentalsetupinalaboratorysetting. DataforsampleB6werenotanalyzedbecausethisdatasetwastakenattwenty-sixfre- quencypointsinsteadof1601points.Thenumberofpointswasreducedtotrytodecrease thetimebetweendatasets;however,thisresultedinloweringthetimeresolution(requiredfor gating)toanunusablelevel. Aone-inchthicksampleofPlexiglaswasusedasacontrolmaterial.Plexiglashasapermit- tivityofabout 'r=2.5[59].Datatakenjustbeforeburningsamples1,2,and3wereanalyzed andcomparedtothetheoreticalresultsforPlexiglasusingtheIPythonnotebookinAppendixK .Figure4.10showstheresultsforsample3. Figure4.11throughFigure4.15showthedataforeachoftheÞrstÞveexperiments.Thefront axisisfrequencyinGHz,therightaxisisthedatasamplenumberandrepresentsincreasing time,andtheverticalaxisisphaseindegrees.ThefronttwocurvesineachÞgurearetheresults fortheknownPlexiglassample.Thisprovidesacontrolmeasurementforcomparison. Figure4.16showsvideostillsfromburn4.Videowastakenofallexperiments.Thetwo camerasweresynchronizedaftertheexperiments. 43Figure4.10:Plexiglascontrolmeasurements(S 21)comparedtotheoreticalvaluesforalosslessmaterialwithper- mittivityof2.5.Eachmaterialis1inthick. 44Figure4.11:Processeddatafromburn1.ThetwocurvesatthefrontareforthePlexiglasstandard. 45Figure4.12:Processeddatafromburn2.ThetwocurvesatthefrontareforthePlexiglasstandard. 46Figure4.13:Processeddatafromburn3.ThetwocurvesatthefrontareforthePlexiglasstandard. 47Figure4.14:Processeddatafromburn4.ThetwocurvesatthefrontareforthePlexiglasstandard. 48Figure4.15:Processeddatafromburn5.ThetwocurvesatthefrontareforthePlexiglasstandard. 49Figure4.16:Videostillsfromburn4.Thetimestampsshowthesynchronizedtimeforeachcamera. 504.6Discussion Theresultsabovewereverypromising.Themostimpressiveaspectoftheaboveresultsisthat atimedependenttrendisobserved.Suchatrendsuggeststhatthemeasurementprocedure worksinanoutdoorrangewithoutmeansoffocusingtheantennabeams.Itdemonstratesthat somephysicalphenomenonisbeingmeasured,mostlikelythecushionmaterialgettingsmaller combinedwithveryslighteffectsoftheactualßame. Theobservedtrendisanon-linearincreaseinphaseastimeprogresses.Thischangein- creasesasfrequencyincreases.Thephaseapproacheszeroastimegoesonwhichiswhenthe Þreself-extinguishes.Itisbelievedthatthephaseapproacheszerobecausethemeasurement systemisessentiallybeingreturnedtoanemptystateasthereisnocushionleftontheshelf.At thistime,though,itisdifÞculttosayhowmuchofthetime-dependenttrendiscausedbythe cushionchangingandhowmuchiscausedbytheÞre. Whentheexperimentwasdesigned,wedidnotexpectthecushionmaterialtointeractwith thetransmissionsverymuchbecausethecushionismostlyfoam.Foamscanbetransparentat radiofrequenciesandisoftenusedtofabricatesupportstructuresinlaboratoryexperiments. Thereare,however,manytypesoffoamandnotallfallintothistransparentcategory. Inareal-worldusecase,measuringfurnitureorbuildingmaterialsthatareburningshould notbeaproblem.ThetimescaleofthismassreductionissigniÞcantlylargerthanthetimescale ofhumanmotionthatwouldbedetectedbyaradarsystem.Inthecaseofthisexperiment,I measuredoveraverylongtimescalehencewhythismeasurementofthecushionisobservable. TheseobservationsmeantthatfutureexperimentswereneededsothattheeffectoftheÞre couldbemeasuredmoreaccurately.Ascreenenclosurecouldbeusedtopreventtheelectro- magneticwavesfrominteractingwiththefuel.Ascreenwouldallowair,gases,andßamesto enterandexitwhileelectromagneticallyisolatingthecushion. 51DuringtheexperimentitwasnoticedthatthecushionsweredifÞculttolightanditwashard tocreateasustainedßame.Thiswasincontrasttotheignitiontestthatwasdonebeforethe experiment.ItisbelievedthatlightingthecushionswasdifÞcultbecauseoftheslightwind andtheßameretardantsinthecushion.Ithasbeendemonstratedthatmodernfurniturepri- marilyconstructedwithfoamburnsfasterandhotter,evenwithßameretardants,thanlegacy furniturethatismadeusingsolidwoodandcottonbatting[60,61].Thepeaktemperatureis aboutthesameforbothtypesoffurniture;however,thetimetoreachthispeakislessandthe heatreleaserateishigherformodernfurniture.Thisisduetofoambeingmadeofenergy-rich hydrocarbonswhichleadstohighertemperatureßameswhencomparedtocottonorother naturalbattingmaterial.HeatbuildsduringacompartmentÞrewhichhelpstoovercomethe ßameretardantspresentinmostfurniture.Therewasnoenclosureinwhichtobuildheatdur- ingthisexperiment.ThismadeitmoredifÞculttocreateasustainedßame.Theeffectofwind onßamemovement,andtosomeextentheatescapingfromtheßame,wastheprimaryreason whyfutureexperimentsusedsomemannerofÞre-resistiveenclosure. TheÞrstsample,B1,wasignitedonthewindwardside.SampleB2wasignitedonthethree non-windwardsides.SampleB3wasignitedfromunderneathinonecornerandthebottom center.SampleB4wasplacedontopofasheetofcardboard.Thecardboardandcushionwere ignitedfromunderneathatthecenter.SamplesB5andB6hadcardboardpiecesarrangedas showninFigure4.17.Thesewerelitfromthebottomcenter. Itwasfoundthatignitionfromunderneathallowedtheheattobuildinsmallpocketslead- ingtoasustainedßamewhicheventuallybrokethroughthetopofthecushion.Oncethrough thetop,thecushionquicklybecamefullyinvolved.Placingcardboardunderneathprovideda materialthatwaseasilylit,reducingthetimerequiredforignition. 52Figure4.17:Cardboardusedtoignitecushionsforsamplesb5andb6. 4.7ExperimentDesignObservationsandSuggestions ThediscussionsectionaboveidentiÞessomeoutcomesandchallenges,aswellasremaining questions.ThissectionidentiÞestouchesonthesepreviousitemsandaddsadditionalout- comesandchallengesthatexperimentalworkneedstoaddress. First,letusconsiderthemainÞndingabove:aburningcushioneffectsthepropagation ofEMwavesasitburns.Thisresultwasobservedmultipletimes.Thepropagationwasini- tiallydifferentthanpropagationthroughunobstructedspaceandthenwouldgraduallyreturn toneartheunobstructedstate.Thistimedependenceisimportantandhastwopossibleexpla- nations.OneisthattheÞreiseffectingthewavepropagation.Thesecondisthatthecushion itselfiseffectingthewavepropagation.Bothofthesemaybeoccurringatthesametime.The validityofeitherexplanationiswhatneedstobeinvestigatedandthetwoneedtobemade 53experimentallyindependent.Thisisthemainconclusionandchallengewhichisfurtherinves- tigatedinthefollowingchapters. Theexperimentalsohelpedtoidentifyothermethodologicalandproceduralchallenges. Thesearelistedbelow. ¥Equipment ÐPower Powerisrequiredattheexperimentsite.Theprimaryconcernispowerforthe measurementequipment.Additionalequipmenttoconsiderwhenassessingpower needsincludescameras(effectedbystandingby,temperature,etc.),laptops,andig- nitionsystems.Electronicignitionsystemsmayrequirealargepowerinputwhich mustbeconsideredintheexperimentaldesign.Batterybackupsoruninterruptible powersuppliesshouldbeused,especiallyfornetworkanalyzersorothercriticaltest equipment. Ifageneratorisused,itshouldbetestedwithmeasurementequipmentpriortouse. Portablegeneratorsmaynotproducethecleanpowerneededbylaboratoryquality equipment. ÐTimerequiredtosetupequipmentandexperiment Fromalogisticalperspective,setuptimeisimportant.Combustionexperiments aredifÞculttoperforminsidealaboratory.Thismeanstransportationandsetup ofequipmentmustnowbeincorporatedintotheplans.Additionalpersonnelare required. ÐEquipmentwarm-uptime Theexperimentscheduleshouldallowenoughtimeforinstrumentationtowarmup andstabilize. 54ÐCalibrationofequipment Calibrationoftheequipmentischallengingformultiplereasons.First,itistime consuming.Ifproblemsariseorthecalibrationisfoundtobeinaccurate,itwillneed tobere-performed.Whenothersarewaitingtohelpandexpectasetschedule,this canbeproblematic. Duetotheseexperimentsbeingperformedoutside,environmentalfactorswill changeandcaneffectthiscalibration.Thismayincludespuriousemissions,un- controlledtransmitters,andweather/temperature. Calibrationalsoeffectsthedurationofafrequencysweep.Itcanslowdownthe actualdwelltimeateachindividualfrequency.Moreimportantly,itslowsdownthe overalltimebetweensuccessivesweepsfortworeasons.First,allfourS-parameters needtobemeasured(inmostcases)inordertocompensateforallerrors.Secondly, calculationsmustbeperformedtocompensatefortheerrorsandtoproduceorsave calibrateddata. ÐIgnitionofsample Ignitionofasampleisnotalwaysstraightforward.Testignitionsshouldbeper- formedpriortoanactualexperiment.Oneshouldconsiderusingapilotßame,small amountsofaccelerants,ortinder/kindling.Itmaybenecessarytoprovideanextra windbreakaroundtheignitionsource.Aremotely-operatedignitionispreferred, butoftenunrealisticduetocostorcomplexity. ÐSampleacquisitiontime Acquisitiontimeisdependentonmanythingsincludingaveragingfactor,calibra- tion,numberofpoints,andintermediatefrequencybandwidth(IFBW).Aduplicate experimentshouldbesetup(inthelaboratoryifpossible)priortotheexperiment inordertodeterminetheacquisitiontimeandothertimingissues. 55ÐDynamicßame Fireisadynamicphenomenon.Themotionofaßameisßuidtotheeye,meaning thatonecanconsiderittobeafastmotioncomparedtothespeedoftheequipment usedtotakeelectromagneticwavemeasurements.Thismeansthatitcanbechal- lengingtomeasuretheßameinonestateforanentirefrequencysweep.Further,the ßamewillnotbeconsistentbetweensamplesorsweeps. ÐSynchronizationofstillimages,video,andannotationstosampleusingeithersam- plenumberortimestamp ThisisasigniÞcantchallengefacedwhenprocessingthedata.Itisveryimportantto knowwhatwasoccurringatthetimeof(andduring)aparticularsample.Recording oftheexperimentsusingwrittennotes,digitalphotography,andvideosisessential inidentifyingwhatischangingbetweenorduringameasureddatapoint.When multiplecamerasareinuse,synchronizationofthecamerasischallengingbutes- sential. ÐCableandconnectorintegrity,protection,andrelatedsitesafety Testcablesareexpensiveandrelativelyfragilecomparedtocableswithwhichmost peoplearefamiliarsuchasextensioncords.Theyarealsosusceptibletodamage fromtheenvironment.Careneedstobetakentoprotectthecableswhenoutsideof thelaboratoryincludingduringtransportation. Thesameistrueforconnectors.Dropping,throwing,andotherphysicalabusewill damageRFconnectors.Anythingtowhichtheymaybeconnectedcouldbedam- agedaswell.Dirtandotherforeignbodiesmaygetintoorontheconnectorand ruinotherconnectorswhenattached.Again,connectorsshouldbecarefullyhan- dledandprotectedoutsideofthelaboratory(andinthelaboratoryforthatmatter). 56Whileprobablynotamajorproblem,noisefrompowercablesmaybetransferredto measurementcables.Keepthisinmindwhensettingupcablesandtrytohavethem crossatrightangles. Testcablesaswellasothercablescreateasitesafetyhazard.Itisrelativelyeasyto re-routepowercables.Testcablesareharderbecauseanyaddedlengthincreases attenuation.Cablesshouldbeclearlymarkedandprotected.Regularcablemats withbuiltintraysorPVCpipescanbeusedtocover,protect,androutetestcables andregularcables. ÐWaterdangertoequipment Testequipmentisjustassusceptibletowaterdamageasotherelectronics(unless youareluckyenoughtohaveaFieldFoxnetworkanalyzer,inwhichcase,Iwould lovetouseit).Themaindifferencebetweenthetwoisthattestequipmentissignif- icantlymoreexpensivetoÞx.Becareful! ÐDurability Equipmentandexperimentalsetupsaremovedagreatdealwhenexperimentsare doneoutsideofthelaboratory.Durabilityaswellasproperhandlingneedtobe includedfromtheinitialexperimentdesignstage.Theexperimentalsetupmustbe durabletoensurethatsuccessiveexperimentshavethesameenvironment.Itisalso importanttoensurethatthemeasurementoccursinthesameenvironmentasthe calibration. ÐInfrastructureprotection Theinfrastructureoftheexperimentalenvironment,e.g.asphalt,extensioncords, buildings,andwatersupply,needtobeprotectedfromtheheat,ßame,andsmokeof experiments.Sandand/orsheetrockcanbeusedforgroundprotection.Duraboard fromFiberfraxorotherÞre-ratedinsulationcanbeusedtoprotectbuildingsand 57otherlargeobjects.Tripprotectionsuchasmatsmayprotectcables.PVCpipesmay beusedalsotocoverandprotectcables. ÐAmbientheatdangertoequipment Testequipment,andtosomeextentregularelectronics,haveenvironmentaltem- peraturelimits.Propercooling(orheating)mayberequired. ÐFiredangertoequipment TheßamebeingmeasuredobviouslypossesaÞredangertoallnearbyobjects.Test equipmentisparticularlyofconcernmainlyduetoitscost.Ensureallobjectsare Þreresistiveorproperlyinsulated. ÐFiresuppression Duringlive-Þreexperiments,itiscriticalthattheÞrecanbeputoutifneedbe.If possible,thereshouldbetwoindependentsuppressionmethods.AÞreextinguisher andachargedhoselinewerenormallyusedfortheexperimentsinthisdissertation. ¥Environment ÐWeather Weathermustbewatchedandconsidered.NeitherÞrenorelectronicequipmentdo wellinrain.WindcanhavevariouseffectsonÞreandcreateveryanimatedßames. Burningmaynotbepermittedifthereareredßagwarningsduetodryconditions. Transportationandsetupalsorequiredecentweather.Fluctuatingtemperaturesaf- fectequipmentcalibrationsandmeasurements. ÐAirßow(ventilation)causesmovingßame Formeasurementpurposes,itwouldbeidealiftheßamedidnotmove.Airßow causedbytheßame,aswellasbyoutsidesourceslikewind,willcausetheßameto moveanddance.ThismakesmeasuringtheßamepropertiesdifÞcult. 58ÐMovementintheareaoftheexperiment MovementwithintheÞeldofviewoftheantennaswillcausemeasurementerrors.It canbedifÞculttoconveythistothosewhoarenotexperiencedwithelectromagnetic experiments.Aquietzoneneedstobeestablishedaroundtheßameandantennas. WaterfromÞrehoseswillinterferewithelectromagneticwavepropagation.Other suppressionmethodssuchasÞreextinguishersorsandforsmotheringalongwith thepeopleinvolved,willalterpropagationaswell. ¥Systematic ÐUnabletodistinguishbetweenmeasurementsofthesampleandoftheßame Amajorsystematicchallengeisseparatingthefuelfromtheßamesothatonlythe ßameismeasured.Thisitemisdiscussedabove. ÐRepeatabilityoffuelorßamesize ItisdifÞculttorepeatthebehaviorofaßame.Numerousoutsidefactorseffectthis behaviorincludingventilation. ÐFlamesizecomparedtoantennaÞeldofview;ßamesizevswavelength ItisdifÞculttocreateßameslargeenoughcomparedtotheantennaÞeldofview. Theßamemustbelargeenoughtoimpactdirecttransmissionofwaveswhilelimit- ingothermodesofpropagationsuchasdiffraction. ÐDistancefromßame Flamesandantennasshouldbeincloseproximitytoensureobservationoftheef- fectsondirectpropagation.Thismustbebalancedwiththermalriskstoequipment. ÐValidityofplanewaveorplasmaslabapproximations 59Whensizeofanddistancetotheßameareconsidered,oneshouldalsoconsiderthe shapeofthewavefrontrelativetotheshapeoftheßame.Ideally,onewouldbeable toassumeaplanewaveincidentonaslabofplasma. ÐFlameduration Equipmentrequiresasetamountoftimetomakeameasurement.Flamesneedto haveenoughfuelandbehaveinthesamemannerforalongenoughperiodoftime soastoallowforthedesirednumberofmeasurementstobetaken. ÐFlamevs.soot/smoke Itisknownfromweatherandotherradarresearchthatsmokeandsootarede- tectable[36Ð43].Theaimofthisresearchisnottomeasurethesebyproductsbutto measuretheßameitself.Theeffectsshouldbeseparated,hopefullythroughcare- fulexperimentaldesignsothatthesmokeisnotevenmeasured.Futureresearch shouldstudybothßamesandsmoke. ÐNoiseduetono,orlimited,calibrationinformation Non-laboratorysetupsmaynotlendthemselvestosystemcalibration.Insomein- stances,apartialcalibrationmaybeperformed.Calibrationattemptsarealsohin- deredbytheoverallenvironmentchangingduringanexperimentsothattheinitial stateisdifferentthantheÞnalstateorthestateatanytimeduringtheÞre. ÐMasstransport Thesampleisbeingconsumedandthemeasuredmaterialisbeingremovedfrom themeasurementspacethroughmasstransportmechanismsincludingcombustion andrisingair. 604.8Conclusion ThisexperimentwasdesignedtoanalyzehowaÞreaffectsradiowavestransmittedthrough it.Theresultsdidnotprovideanyinsightsintohowradarmightbeusedinanactualhouse Þrebutsuggestedthatfutureexperimentsshouldbecompleted.Thisexperimentshowedthat theexperimentalsetupandprocedureareusablebutrequireimprovement.Thisexperiment alsoshowedthatthereexistssometemporaleffectontransmissionproperties.Observedtime- dependentchangescouldbeduetotheÞreortheeliminationofthecushion;atthistimethe twophysicalprocessescannotbeseparated.Experimentsconductedlaterinthisdissertation attemptedtoisolatethesetwoprocessesasdescribedinthesubsequentchapters.Inaddition, laterexperimentsutilizesomesortofcompartmentinordertoincreasetheheataroundthe cushionsandeliminatewind. 61Chapter5 ExperimentsUsingaPropaneBurnPan OneobservationfromtheexperimentinChapter4attheLFDtrainingcenterwasthatitwas difÞculttoknowifthemeasurementswereoftheßameorofthecushion.Apropane-fueledÞre extinguishertrainingsystemwasusedtotrytoisolatethefuelsourcefromtheÞre.Onedown sidetothisapproachisthatpropaneisarelativelycleanburningfuel,whichisundesirable becausetheimpuritiesandtracemoleculesinthefuelsourcearethoughttobetheparticles primarilyresponsibleforcreatingaÞre-inducedplasma. ThepropanesystemwasusedforexperimentsatMSUÕsEnvironmental,Health,andSafety (EHS)ofÞceandattheBathTownship(MI)FireDepartment(BTFD)station.AttheEHSofÞce, theunitwasopentothesurroundingsbutattheBTFDstationitwasenclosedbyaÞreproof chamber.NotesfromtheEHSburnwererecordedinalaboratorynotebookandareprovided inAppendixFforreference.Unfortunately,therewerenonotesrecordedfortheBTFDexperi- ment. Thankyou... ElvetA.PotterfromMSUEHSandDr.JunyanTangassistedwiththeexperimentatthe EHSofÞce.Lansing(MI)FireDepartmentloanedtheBullexsystemusedfortheBTFD experimentwithwhichKoredeOladimejiassisted. 62Figure5.1:ExampleÞreextinguishertrainingusingtheBullexIntelligentTrainingSystem. 635.1ExperimentatEHS 5.1.1ExperimentalSetup Twoexperimentswerecarriedouttomeasurethepropagationthroughaßameproducedbya BullexIntelligentTrainingSystem.ThissystemisapropanefueledburnerusedforÞreextin- guishertrainingasdemonstratedinFigure5.1.Propanefuelissplitintotwopipesthateach formanalmost-closedsquare.ThesepipesarevisibleinFigure5.2.Waterisaddedtothetray beneaththepipestoactasaheatsinkandkeeptheunitfromoverheating.Anoverßowdrainin therightandleftsidewallkeepthewaterfromßoodingthepropanepiping(leftcutoutvisiblein Fig.5.2).Powerissuppliedfroma12VDC,vehiclecigarettelighterstyleplug.TheÞreisstarted usingaremotecontrollerthatalsoconÞguresvarioussettingssuchasthedifÞcultyofthetrain- ing.Thepropanesupplyhose,powersupply,andcontrolcableareseendisconnectedonthe leftinFigure5.2.Oncetheunitisremotelyignitedbyaninstructor,astudentusesareÞllable waterextinguishertosimulateputtingouttheÞrebysprayingfoursensorsonthefrontofthe unit(visibleinFig.5.3) 1.IfthestudentdoesnotextinguishtheÞreinthirtyseconds,thesystem willturnofftopreventitselffromoverheating. TheoverallexperimentallayoutcanbeseeninFigure5.3aandissketchedinFigure5.4. Theantennaswerespaced13feetand1inchapartandalignedalongthecrackintheconcrete. ThetrayforholdingthemetalcalibrationplateandPlexiglassamplewas44inchesfromthe upperrightantennainFigure5.3a.Thisantennawasconnectedtoport1ofanHP8753DVNA bycablesnumbered003and039,andtheotherantennawasconnectedviacablesnumbered 040and037toport2(seeAppendixB).Fromtheport1antennatothenearestedgeofthe burnerwas56.5inches.ThedimensionsoftheburneraregiveninFigure5.5.Theaverage dimensionisprovidedbecauseitrepresentstheapproximatesizeoftheßamesincetheßame 1ThesensorsareonthefrontoftheunitbecausethesprayfromaÞreextinguishershouldbeaimedinfrontof theÞreandmovedintothebaseoftheÞreusingaside-to-sidesweepingmotion.Untraineduserswillnormally spraytheßamesabovethebaseoftheÞrewhichdoeslittletoextinguishaÞre. 64Figure5.2:ExperimentalsetupatMSUEHSshowingtheBullexsystemandwireshelf. islargerthanthepipingbutdoesnotcompletelyÞlltheburnpanarea.Alaptopconnectedto theHP8753DVNA,calibratedtotheportsoftheantennasusingan3.5mmcalibrationkit,was usedtomeasure1601,S 21datapointsbetween2GHzand6GHz. 65(a)ViewalongthepathofpropagationoftheEHSsetupwiththesystemlit. (b)FrontviewoftheEHSsetupwiththesystemlit. Figure5.3:IgnitedsystemduringexperimentsatMSUEHS. 66Figure5.4:SchematicoftheEHSexperimentallayout. Thissketchisfrompage14,whichmaybefoundinitsentirety inFigureF.2ofAppendixF,ofLaboratoryNotebook00010 Figure5.5:Dimensionsoftheburner. 67Table5.1:MeasurementsinEHSreplicatesetsandzero-Þlltime. Set1Set2Set3 Ptssettozero emptyemptyempty plateplateplate Plexi.Plexi.Plexi. 2Ð390ns burn1burn1burn1 5Ð390ns burn2burn2burn2 5Ð390ns burn3burn3burn3 5Ð390ns burn4 5Ð390ns 5.1.2ExperimentalProcedureandDataProcessing Threereplicatesetsofdataweremeasuredwitheachreplicatesetconsistingofmeasurements usedforcalibrationÑanÒemptyÓ,metalplate,andPlexiglasÑandeitherthreeorfourmeasure- mentswiththeburnerlitaslistedinTable5.1.Theemptymeasurementconsistedoftheshelf, metaltray,andburner.ThemetalplateandPlexiglasmeasurementswereof2feetby2feetby either1/4inchthickmetalplateor1inchthickpieceofPlexiglas,respectively.Thetrayand shelfwereleftinplaceforthelitburnermeasurements(seeFig.5.3b).Onedatasettookap- proximately18secondstobemeasuredandsavedfortheVNAconÞgurationused.Asnoted earlier,theburnerwillonlyrunforthirtysecondsbeforeitshutsitselfdown;therefore,onlyone datasetcouldbetakeneverytimetheburnerwaslit. Aftertheexperiment,datawascalibratedandtimegatedtoremovenoiseandtoshiftthe measurementplaneusinganIPythonnotebook(App.L)andWavecalc[62].DatawasÞrst calibratedusingtheformula Scorr 21=Smeas 21#Splate 21Sempty 21#Splate 21e#jk0dx(5.1) where corr isthecorrecteddata, meas isthesamplemeasurement, plate and empty corre- spondtotherespectivemeasurements, k0isthefreespacewavenumber,and dxisthethick- nessofthesampleÑforPlexiglas, dxis1inchandforfortheburner dxis27.94inches.Next,the 68datawastimegatedusingWavecalc[62]byapplyingacosinetaper(exponent k=2,fractionof bandwidth r=10)weightingfunctiontothefrequencydomaindata,performinganIFFT(exact, 4096datapoints),settingthetimepointslistedinTable5.1tozero(zeroÞlling),performingan FFT(exact,8192datapoints),andtruncatingthedatatothefrequencyrange2.5GHzÐ5.5GHz. TheÞnalfrequencyrangeissmallerthantheoriginalbecausethecosinetaperweightingmakes theedgesofthesignaltapertozero.FromthedocumentationforWavecalc,thecosingtaper weightingiscalculatedfrom: wCT(n#)=/0010021for r(N#1)*n*(1#r)(N#1)sink!&rn2(N#1)"otherwise (5.2) where Nisthenumberofpoints, #isthesamplinginterval, kisanexponentwithavalue greaterthanone,and risthefractionofthewidthtowhichthetaperedportionoftheweight- ingfunctionisapplied.ThisWavecalcprocessingwasautomatedusingthemacrotemplate inListingI.1andListingI.2inAppendixI.GateddatawasimportantbackintotheIPython notebookwhereitwasaveragedandplottedagainstatheoreticalcurve. 5.1.3ResultsandDiscussion TheaveragetransmissionofallthreePlexiglasmeasurementsisplottedinFigure5.6alongwith theoreticalcurvesforaslabofPlexiglas( 'r=2.5)surroundedbyfreespaceandthetheoretical curveforfreespace.Anareathatmayconcernsomesincethisisnotanactivesystemisthepeak over0dBfoundaround3GHzinthemeasuredmagnitude.Thisismostlikelycausedbythelow- lossnatureofPlexiglas.Itisreasonableforexperimentaldatalikethistobeslightlygreaterthan 0dBforalow-lossmaterialbeingmeasuredinanunreÞnedsystemwithprobablediffraction andthewidebeamwidthsoftheunfocusedantennas.Thephaseshowsgoodagreementwith thetheoreticalPlexiglascurve.AbestÞtline,having r=#0.997,ofthemeanPlexiglasphase 69isplottedalongwiththeunwrappedphasesinFigure5.7.ThetheoreticalandbestÞtlines arealmostontopofoneanother.ConsideringthatthepermittivityofPlexiglasvariesinthe literaturebetween 'r=2.4and 'r=2.8[59,63],thiscloseofameasuredvalueisveryacceptable. ThetransmissionsthroughthelitburnerexhibitbehaviorsimilartothePlexiglasmeasure- ments.Themagnitudeoscillatesaround0dB,probablybecauseoflow-lossesasinthePlexiglas case.Nocut-offbehaviourisobservedinthismeasuredmagnitudewhichsuggeststhat,ifthere isaÞre-inducedplasma,eithertheplasmafrequencyissigniÞcantlylowerthanthemeasured frequenciesorthesystemdoesnotaccuratelymeasuretheplasmabecausetheplasmaregion occupiesarelativelysmallvolumeofthemeasuredspace. ThephaseinFigure5.8isslightlyshiftedfromthefreespacetheoreticalcurveandFigure5.9 showstheunwrappedphases.Themeanphasesfromallthreeburnsareessentiallythesame andjustbarelydifferfromthefreespacecurve.Slightchangesinthepermittivitycouldhave causedthisaswelldifferencesinthedistancetraveled.Windduringtheexperimentcaused theßamestobeverydynamicwhichmakesdeterminingtheactualsizeoftheßamesvirtually impossiblesincetherearenocleanlydeÞnedboundariesordimensions. TheseresultssuggestthattheeffectsofanyplasmacreatedbytheÞreareminimalover thisfrequencybandforthissetup.Onereasonforthismaybetherelativelysmallsizeofthe ßame.Thedirectpathbetweentheantennasgoesthroughtheverytopoftheßame,oreven overtheßameifthewindisdeßectingtheßameresultinginlittleenergyisinteractingwith theßame,especiallythehigher-energyportionsinthecombustionzonenearthefuelsource thataremostlikelytocreateaplasma.Additionally,theßamepresentsasmallcross-section comparedtoitsdepthwhichlimitsthetotalamountofenergythatpropagatesthroughthe ßame.Theburnerwasorientedthiswaysothatthepropagatingwavewouldtravelthrough anyplasmaforthemaximumpossibledistance.Atheoreticalanalysisoftheorientationforthis unfocusedsystemremainstobecompleted.Finally,theremaybefewplasmaeffectsobserved becauseofthefuelusedinthisexperiment.Propaneisacleanburningfuelandnoadditional 70Figure5.6:AveragemeasuredtransmissionthroughaoneinchthickPlexiglassample. 71Figure5.7:UnwrappedphaseoftheaveragemeasuredtransmissionthroughaoneinchthickPlexiglassample. compoundsweremixedintotheßame.InthepreviousworkexaminedinChapter3,theßames withobservedplasmaseitherhadsaltaddedtothemorwerefueledbycomplexsourcesthat hadsmallconcentrationsofeasilyionizedparticles. 72Figure5.8:AveragemeasuredtransmissionthroughanignitedBullexsystem. 73Figure5.9:UnwrappedphaseoftheaveragemeasuredtransmissionthroughanignitedBullexsystem. 745.2ExperimentatBTFD ThisexperimentwasdesignedtoaddressissuesobservedintheEHSexperimentbytryingto protecttheburnerfromthewindwithachamber,rotatingtheburnertoincreasethecross- sectionalareapresentedtoapropagatingwave,anddecreasingthedistancebetweenantennas. Thechamber,builtusingDuraboardÞreinsulation,alsoprotectsmeasurementequipment, suchastheantennas,fromtheÞre. 5.2.1DuraboardInsulationandBurnChamberDesign Thankyou... UnifraxgenerouslydonatedtheDuraboardinsulationforthisresearch. FiberfraxDuraboardLDinsulationismanufacturedbyUnifraxandisarigidceramicÞber boardwiththermalstabilityupto3000 )Candcanwithstanddirectßamecontact.Thedonated boardswere4feetby2feetand1inchthick.Additionalproductinformationisavailablefrom thelabelinFigure5.10.Whiletheboardisrigid,ithaslittleabrasionresistanceasaholecould quicklyandeasilyberubbedthroughtheboard.Theboardiseasilycutwithautilityknifeor drilledwithregularbits;infact,aboltcanbepushedthroughtheboardalthoughthiswould causepiecestocomeofffromthebackside.Whencutting,itwasimportanttocutthroughthe entirethicknessoftheboardtoensureacleanÞnishunlikesheetrockthatmaybescoredand snapped.Notcuttingthroughtheentireboardresultsinpiecesßakingoffandjaggededges beingleft.WhenworkingwithDuraboard,aparticlemask,eyeprotection,gloves,andalab coatshouldbeworn;theMSDSsheetforDuraboardisavailablefromUnifrax. Thechamberconsistedof4feetby4feetwallsthatwereconnectedtooneanotherand raisedoffoftheground;noroof/ceilingwasused.Squaresofsteelperforatedsheetjoined theDurabooardpanelsusingfourbolts.Solid90 )anglesteelstockwasusedatthebottom corners.Inadditiontothroughboltholes,thestockhadtappedholesforattachingperforated 75Figure5.10:LabelforthedonatedUnifraxFiberfraxDuraboardLD. 90)anglestockaslegs,whichallowedthegroundclearanceofthechambertobeadjusted. Allboltholeswerepre-drilledusingahanddrillandthena1inchpieceofcoppertubingwas insertedthroughthehole.ThetubbingprotectedtheDuraboardfromabrasioncausedbythe threadsofthebolts.Onthebolts,ßatwasherswereusedagainsttheDuraboardandasplitlock washerwasusedbetweenthenutandßatwasher.Theinsideoftheburnchamberisseenin Figure5.11aalongwithtwooftheperforatedsquares. Thisdesignevolvedasitwasused.AssemblyofthechamberwasdifÞcultforonlyoneper- sonandriskedsnappingtheinsulationifimproperlyliftedorsupported.Thiswasespecially truewheninstallingtheboltssincetheinsulationwasnotcompletelysecuredandcouldeasily sway;however,oncefullyassembled,thechamberwassturdy.ThelegsweredifÞculttoat- tachandendedupnotbeingusedforexperiments.Instead,thechamberwaseitherplaced onblocksorplaceddirectlyontheground.Theoriginaldesignaimedtoreducetheamount ofmetalusedsincethiscouldinterferewithmeasurements.Amechanicallyimproveddesign woulduseametalframeontowhichtheinsulationisattachedandacalibrationprocedure wouldbeusedtoaccountforanyeffectsofthemetalframe. 76(a)Burnchamberpriortoignition. (b)Phototakenduringaburn. Figure5.11:PhotosfromaburnusingaBullexsysteminaburnchamber. 775.2.2ExperimentalSetup TheburnchamberdescribedintheprevioussectionwasplacedaroundtheBullexburneras seeninFigure5.11a.Thetroughforholdingthecalibrationplateisseeninfrontoftheburner. Thetroughisalignedtoaparkingstripeontheasphaltwhichservedtoaligntherestofthe setup.OnehornantennaisseenontherightofthephotoÑtheotherantennaisbehindthe wallontheupperleft.Relativetothetransmissionpathbetweenthetwoantennas,theburner wasrotatedbyninetydegreescomparedtotheEHSexperiment.Thiswasdonesothatthe ßamewouldpresentalargercrosssectioninsteadofappearingdeeper.Theantennasareonly aboutfourfeetapartcomparedto13feetattheEHSexperiment.Thegapinthewallseenon theleftwasrequiredtoignitetheburnerusingapropanetorchsincethebuilt-instarterwas notfunctioning.DatawasagaincapturedusingtheHP8753DVNAandlaptop. 5.2.3ExperimentalProcedureandDataProcessing MeasurementswerelessextensiveinthisexperimentthantheEHSexperimentbecauseoffac- torswhichaffectedthetimeavailabletotakemeasurementsincludingassemblingtheburn chamber,troubleshootingtheigniter,respondingtoemergencycalls,andtheearlysunsetin December.First,twoemptymeasurementsweretaken,followedbyaplatemeasurement,and thenÞveburnsweremeasured(Fig.5.11b).Becauseofthelimitedburntimeoftheburnerand thelongdataacquisitiontimeoftheVNA,onlyonemeasurementfortheÞrsttwoburnsand twomeasurementsforthelastthreeburnswerecaptured.Itwaspossibletocapturetwomea- surementsforthelatterexperimentsbecausethetimingbetweentheignitionsequenceand dataacquisitionwasreÞned.NoPlexiglasmeasurementsweretaken.Datawasprocessedus- ingthestepsgiveninSection5.1.2withpointsbetween3nsand380nssetequaltozero(zero Þlled)usingthemacroinListingI.3.AppendixMistheIPythonnotebookforthisexperiment. 785.2.4ResultsandDiscussion ThemeantransmissionforallmeasurementsisshowninFigure5.12alongwiththetheoretical transmissionthroughfreespace.TheresultsaresimilartothosefortheEHSburn.Themag- nitudevariesaround0dBoverthemeasuredfrequencyrangemeaningthatthereisessentially noloss.Theaveragemeasuredphaseisoffsetfromthetheoreticalphasealthoughtheslopes arenearlythesameasseeninFigure5.13meaningthatnoplasmaeffectsweremeasured.Pos- siblereasonsfortheseresultsaresimilartothoseoftheEHSexperimentincludingpropagation throughthetoporabovetheßameandthefuelsource.Flamemovementwasgreatlyreduced bythechamber,andwhilestillpresent,itshouldnotplayassigniÞcantaroleasintheprevious experiment. 79Figure5.12:AveragemeasuredtransmissionthroughaburnchamberwiththeBullexsystemignited. 80Figure5.13:UnwrappedphaseoftheaveragemeasuredtransmissionthroughaburnchamberwiththeBullex systemignited. 815.3Conclusion Theexperimentsinthischapterusedapropaneburnertoremovethefuelsourcefromthe measurementdomain,leavingonlytheßametobemeasured.Achamberwasconstructedto reducetheeffectsofwindontheßame.Theresultsinthischaptersuggestthatthetransmitted wavesprimarilytraveledthroughairandwithlittle,ifany,interactionwithaplasma.While theexperimentalsetupwasimprovedbetweenexperiments,furtherimprovementscouldbe made.Thisincludesbringingthebaseoftheßameandthedirecttransmissionpathcloserto oneanother,increasingthetemporaldurationoftheburnsomoredatacanbecaptured,and usingafuelsourcethatismorelikelytocreateaplasma.Further,beamwidthcomparedto ßamesizeshouldbeinvestigated. 82Chapter6 Interferometry Amicrowaveinterferometersetupwasusedtoinvestigatetheinteractionbetweenelectromag- neticwavesandßamesatalaboratoryscale,andexploredasamethodtocharacterizeÞre- inducedplasmasfromvariousfuelsources.Samplesofmethanol(CH 3OH),methanolandsat- uratedsodiumchloride(NaCl)solution,andPlexiglaswereburntbetweentwohornantennas. Ameasurementwastakenbeforeignitiontouseasareferenceandthephasedifferencewas determinedinthepost-processingstage. Thankyou... MostoftheseexperimentswerecarriedoutusingthecalorimeterinDr.WichmanÕslabo- ratoryorinthefumehoodoftheElectricalandComputerEngineering(ECE)Shop. 836.1MicrowaveInterferometerTheory Tudiscoetal.discusscriteriaforandlimitsofmicrowaveinterferometryin[64]wherethey describeaninterferometerat75GHztomeasureaplasmathrusterforspaceßights.Thephase shiftinradiansisgivenby #.=!Ssample 21#!Sref 21(6.1) =2&,03D0!1#41#"2p/"20"dl(6.2) where "pistheplasmafrequency, "o=2&f0isthemicrowavefrequency, ,0isthefree-space wavelengthofthemicrowave,and Distheplasmathickness.Forlowdensityplasmas( "0'"p),theabovebecomes #.=e24&c20'0me,03D0nedl(6.3) =2.82 "10#15,0Dne(6.4) where eand mearethechargeandmassofanelectron, c0isthespeedoflightinfree-space, '0isthepermittivityoffree-space,and neistheaverageelectrondensityoftheplasmainm #3.ThephasedifferenceasafunctionofrelativepermittivityforadielectricisshowninFig- ure6.1.Apositivephasedifferencecorrespondstoarelativepermittivitylessthanonewhilea negativephasedifferencecorrespondstoarelativepermittivitygreaterthanone. Tolimittheeffectsofdiffractionandtoallowtheapplicationofaslabapproximation,the ratiooftheplasmadiametertothewavelength( D/,0)shouldbelarge.HealdandWharton showin[65]thattheslabapproximationmaybeusedwhen D/,0>3forcylindricallydense plasmasofconstantdensitymeasuredusingoptimized,coupledhorns.Thislineisplottedin Figure6.2withreferencelinesfor1,6,9.5and20GHz,where6GHzand20GHzcorrespondto 84Figure6.1:Normalizedphasedifferenceversusfrequencyforaconstantelectrondensity. Table6.1:Minimumthicknesstomeettheslabapproximationcriterionforselectfrequencies. Freq(GHz)D(mm)D(in) 1.000899.3835.41 6.000149.905.90 9.50094.673.73 20.00044.971.77 themaximumfrequenciesofanHP8753VNAandanHP8720VNA,respectively,and9.5GHz correspondstoanupperfrequencylimitforthemeshexperimentinSection6.2.Thesemini- mumdistancesarealsotabulatedinTable6.1. FromtheliteraturereviewinChapter3,theelectrondensityisexpectedtobeintherangeof 0.5Ð3.4 "1016m-3andthecollisionfrequencytobeintherangeof1Ð6 "1010collisionspersec- ond.Table6.2givestheexpectedphasedifferenceacrosstheminimumslabthicknessforthis electrondensityrangeatthereferencefrequenciesascalculatedbyEquation6.4.ItisdifÞcult 85Figure6.2:Minimumthicknesstomeettheslabapproximationcriterionversusfrequencywithreferencelinesfor 1,6,9.5,and20GHz. Table6.2:Theoreticalphasedifferencesforvariousparameters. Freq(GHz) D(mm)ne(m-3)#.(deg)19005 "1015217.974 19003.4 "10161482.22 61505 "10156.05484 61503.4 "101641.1729 9.5955 "10152.42193 9.5953.4 "101616.4692 20455 "10150.544935 20453.4 "10163.70556 tomeasurealargephasedifferencethatisover360 )suchasat1GHz;likewise,itisdifÞcultto measurethesmallphasedifferencesat20GHzduetoinstrumentaccuracy. Tovisualizesystemlimitationsandcriteria,electrondensityversusfrequencyhasbeenplot- tedinFigure6.3forÞvephasedifferences.Toassistwithapplyingthisinformationtopractical 86Figure6.3:Minimumthicknesstomeettheslabapproximationcriterionversusfrequencywithreferencelinesfor 1,6,9.5,and20GHz. systems,verticallinesatthefrequenciesofinterestareplottedandtheupperhorizontalaxisis labeledwiththeminimumplasmathicknessfortheslabapproximationtobevalid.Thelow- estlinecorrespondsaphasedifferenceofonedegreeandrepresentstheminimum,practically measurableelectrondensityatagivenfrequency.Aselectrondensityincreases,eachcurvecor- respondstoaprogressivelylargerphasedifference.Theupperlimitofasystemisdetermined byitsabilitytomeasurephasedifferencesover360 )withoutambiguity.DifÞcultieswithphase ambiguitymayleadtoproblemsinterpretingmeasureddata. 87Table6.3:Summaryofinterferometricexperiments. NameVNAFreq.(GHz) x(in)€y(in)àDescription ECEHoodHP87532Ð610.744.5Initialexperimentsinhood CalorimeterHP87532Ð6264Basicsetupincalorimeter ShutterHP87532Ð6264Shuttersetupatlowerfrequencies MeshcoveredHP87202Ð18184.5Meshcoveroverdish €Frontofhorntofrontofhorn àDistancebetweenbottomofdishtomid-lineofantennas,seeFig.6.4 xyFigure6.4:Schematicdrawingofinterferometerdimensions. 6.2ExperimentalSetup AmicrowaveinterferometerwassetupinfourdifferentconÞgurationsaslistedinTable6.3.The experimentalsetupwasdesignedaroundexistingandlow-costsolutionsasthisworkwasin- vestigatoryinnatureandalargecapitaloutlaycouldnotbesupported.Ingeneral,twohorn antennaswereplacedroughlytwofeet(Fig.6.4)apartwitha150mmdiameterglasspetridish placedmid-waybetweenthehornsoneitheracinderblockorapieceofDuraboardinsula- tion.InoneexperimentalconÞguration,piecesofsheetmetalwereplacedaroundthepetri dishtocreateashuttersothattheonlydirectcouplingbetweentheantennaswasthroughthe ßame.Threedifferentfuelswereburnedindependently:1)methanol,2)methanolwithsatu- ratedsodiumchloride,or3)Plexiglassamples.Areferencemeasurementwastakenbeforethe samplewasignited.Whilethesamplewasburning,measurementswereacquiredasquickly aspossibleusingeitheranHP8753DoranHP8720,whichwerecalibratedtotheantennatest ports. 88ECEHood ThiswastheÞrstinterferometricsetup.Thepetridishwasplacedontopofacinder blockintheECEfumehoodasshowninFigure6.5. Calorimeter Aninterferometricsetupwasplacedaroundtheconecalorimeter(mfg.FireTest- ingTechnology)inDr.WichmanÕslaboratoryasshowninFigure6.6byplacingthepetridishon apieceofDuraboardinsulationwhichreplacedtheoriginalcalorimeterburner. Shutter Fourpiecesofsheetmetalwereplacedaroundthepetridish(Figs.6.7and6.8)tocreate ashutter.Besidesaffectingtheelectromagnetictransmissions,thebehavioroftheßamewas alsoaffected(Fig.6.9).Thepiecesofsheetmetalwere12.25inchestallby7.5incheswideand wereseparatedby4inchesatthebasewithanopeningof5inchesfortheßame. Mesh Thepetridishwasplacedbetweenwiremeshandapieceofsheetmetal(Fig.6.10)that wasthenplacedontopofacinderblock.Thegoalofthemeshistoelectricallyshieldthefuel fromtheelectromagneticwaveswhileallowingtheßamethrough.Aruleofthumbformesh electricalshieldsisthattheopeningsshouldbelessthanatenthofawavelengthatthehighest frequency.Themeshthatwasusedhad0.125inchopeningswhichcorrespondstoatenthof awavelengthat9.5GHz.Datawascapturedupto18GHzinthisexperiment;however,only resultsoverasmallerbandareusedbecauseofthelimitsofthemesh.Figures6.11through6.12 showthetransmissionmagnitudeupto17GHz(truncatedfrom18GHzduetocosinetapering) forthesetupinvariousconÞgurationswithoutanyÞretodemonstratetheshieldingeffective- nessofthemeshversusfrequency.Asfrequencyincreases,theresponsesvarymoreshowing thatthemeshbecomeslesseffective. 89Figure6.5:ExperimentalsetupintheECEhoodforinterferometermeasurements. 90Figure6.6:Experimentalsetupintheconecalorimeterforinterferometermeasurements. 91Figure6.7:ConÞgurationofthemetalshutter. 92Figure6.8:ConÞgurationofthemetalshutterasseenfromtheside. 93Figure6.9:Photoofaßamebeingdrawnintothesideoftheshutter. 94Figure6.10:Experimentalsetupforthemeshinterferometermeasurements. 95Figure6.11:TransmissionmeasurementsinthemeshexperimentalsetupinvariousconÞgurationswithnoÞre demonstratingthefrequencylimitsofthemeshforshielding,panel1 96Figure6.12:TransmissionmeasurementsinthemeshexperimentalsetupinvariousconÞgurationswithnoÞre demonstratingthefrequencylimitsofthemeshforshielding,panel2 97Figure6.13:TransmissionmeasurementsinthemeshexperimentalsetupinvariousconÞgurationswithnoÞre demonstratingthefrequencylimitsofthemeshforshielding,panel3 98Figure6.14:Phasedifferencein3DfromburningmethanolfortheECEhooodexperiment. 6.3Results Datafromtheexperimentsarepresentedinthefollowingsections.Datawereprocessedusing IPythonnotebookssimilartotheoneinAppendixN.ThedatawastimegatedasinSection5.1.2 usingWavecalcmacrosgeneratedbytheIPythonnotebooks.Mostresultsaretruncatedtothe rangeof2.5GHzto5.5GHzduetothecosineweightingappliedduringprocessing.Inthe resultspresentedbelow,timeisindicatedbyincreasingsamplenumber.AÞnalsummarypanel ispresentedattheendofthechapterinFigure6.37. 6.3.1ECEHoodExperimentResults ResultsfromtheinitialinterferometricexperimentareshowninFigure6.14through6.17.For boththemethanolandthesodiumchlorideburn,thephaseisnegativebelowandpositive aboveabout3GHzatthebeginningoftheburn.Astimeprogressesandtheßamediminishes, thephasedifferenceapproacheszero.Thegreatestelectrondensityisaround2.5 "1017and 3.2 "1017formethanolandsodiumchloride,respectively,bothofwhichoccurnear6GHz. 99Figure6.15:PhasedifferencefromburningmethanolfortheECEhoodexperiment. Figure6.16:Phasedifferencein3DfromburningsodiumchloridesolutionfortheECEhoodexperiment. 100 Figure6.17:PhasedifferencefromburningsodiumchloridesolutionfortheECEhoodexperiment. 101 Figure6.18:Phasedifferencein3Dfromburningmethanolintheconecalorimeterexperiment. 6.3.2CalorimeterExperimentResults Figures6.18through6.23showthemeasuredphasedifferenceandcalculatedelectronden- sitiesformeasurementsmadeintheconecalorimeterwithnoshutterinstalled.Thephase differenceispositiveatfrequenciesbelowabout2.75GHzandbecomesmorenegativeasfre- quencyincreases,whichisoppositethebehaviorseenintheECEhoodexperiments.Asthefuel isconsumed,thephasedifferenceapproacheszero.Thistimedependentbehavior,however,is notobservedinthePlexiglasburnforwhichtheßamesizeandbehaviorvariedthemostdue tothesurfaceareachanging.Incontrast,poolÞres,likethemethanolorsodiumchlorideones, haveessentiallyaconstantsurfaceareaoverwhichtoburnandshouldhaverelativelyconstant resultsuntiltheend.Thegreatestcalculatedelectrondensitiespercubicmeterwerearound 7"1017,8"1017,and1.3 "1018formethanol,sodiumchloride,andPlexiglasÞres,respectively. 102 Figure6.19:Phasedifferencefromburningmethanolintheconecalorimeterexperiment. Figure6.20:Phasedifferencefromburningsodiumchloridesolutionintheconecalorimeterexperiment. 103 Figure6.21:Phasedifferencefromburningsaltintheconecalorimeterexperiment. Figure6.22:Phasedifference3DfromburningPlexiglasintheconecalorimeterexperiment. 104 Figure6.23:PhasedifferencefromburningPlexiglasintheconecalorimeterexperiment. 105 Figure6.24:Phasedifference3Dfromburningmethanolintheshutterexperiment. 6.3.3ShutterExperimentResults Figures6.24through6.31showthemeasuredphasedifferenceandcalculatedelectrondensi- tieswhenashutterwasinstalledaroundtheßame.Forthisexperiment,amethanolÞrewas measuredtwodifferenttimes.Thephasedifferenceisnearzerountilbetween4.5GHzand 5GHzintheseÞres,atwhichpointthephasedifferenceincreases.Aswasseenintheearlier experiments,thephasedifferenceapproacheszeroastheßameextinguishes.Thegreatestelec- trondensitypercubicmeterformethanol(1stand2ndburns),sodiumchloride,andPlexiglas wereapproximately1 "1018,1"1018,8"1017,and5 "1017,respectively.Samplenumber7was notplottedbecauseitwasover30 )differentthanallothersamples. 106 Figure6.25:Phasedifferencefromburningmethanolintheshutterexperiment. Figure6.26:Phasedifference3Dfromburningasecondsampleofmethanolintheshutterexperiment. 107 Figure6.27:Phasedifferencefromburningasecondsampleofmethanolintheshutterexperiment. Figure6.28:Phasedifference3Dfromburningsodiumchloridesolutionintheshutterexperiment. 108 Figure6.29:Phasedifferencefromburningsodiumchloridesolutionintheshutterexperiment. Figure6.30:Phasedifference3DfromburningPlexiglasintheshutterexperiment. 109 Figure6.31:PhasedifferencefromburningPlexiglasintheshutterexperiment. 110 Figure6.32:Phasedifference3Dfromburningmethanolinthemeshexperiment. 6.3.4MeshExperimentResults ResultsfortheexperimentsinwhichthepetridishwascoveredbywiremeshareshowninFig- ure6.32through6.35.Thephasedifferencepeaksaround6GHzandisnegativeateitherend ofthemeasuredfrequencyband.Atimedependenceisnotobservedasinthepreviousexper- iments.Peakelectrondensitieswerecalculatedasapproximately2.4 "1017forbothmethanol andsodiumchloride.Sample23fromthemethanolburnandsamples9,10,and38fromthe saltburnwerenotplottedastheygrosslydeviatedfromtheothersamples. 111 Figure6.33:Phasedifferencefromburningmethanolinthemeshexperiment. Figure6.34:Phasedifference3Dfromburningsodiumchloridesolutioninthemeshexperiment. 112 Figure6.35:Phasedifferencefromburningsodiumchloridesolutioninthemeshexperiment. (a)ECEhood,CH 3OH(b)ECEhood,NaCl (c)Calorim.,CH 3OH(d)Calorimeter,NaCl (e)Calorimeter,Plexi. (f)Shutter,CH 3OH(g)Shutter,2,CH 3OH(h)Shutter,NaCl (i)Shutter,Plexi. (j)Mesh,CH 3OH(k)Mesh,NaCl Figure6.36:Summarypanelofinterferometricmeasurements,eachwithowncolorscale. 113 (a)ECEhood,CH 3OH(b)ECEhood,NaCl (c)Calorim.,CH 3OH(d)Calorimeter,NaCl (e)Calorimeter,Plexi. (f)Shutter,CH 3OH(g)Shutter,2,CH 3OH(h)Shutter,NaCl (i)Shutter,Plexi. (j)Mesh,CH 3OH(k)Mesh,NaCl Figure6.37:Summarypanelofinterferometricmeasurementsnormalizedtothesamecolorscale. 114 6.4Discussion Theresultspresentedintheprevioussectionprovideaninitialstudyonhowinterferometry maybeusedtocharacterizeÞre-inducedplasmas.TheÞrstitemtonoteisthattheresultsfrom theECEhoodandthecalorimeterexperimentsaresimilarbutwithasigndifference.Thesetup ofthesetwoexperimentswerethemostsimilarofalltheinterferometrysetups;therefore,closer agreementisexpected.Anexactcauseforthissigndifferenceisnotknown;however,phase ambiguityfromunwrappingthephaseisalikelysourceoferror.Futureworkshouldlookto developarobustalgorithmforthesetypesofmeasurements. Thepeakelectrondensitymeasuredisonetotwoordersofmagnitudelargerthantheob- servedvaluesinwildlandÞres.Acrossallsamplesininterferometerburns,theelectronden- sityvariedwithfrequency.Theslabapproximationusedtoderivethiselectrondensityneed aminimumplasmathicknessinordertobevalid.Measurementsweretakenacrossaswidea frequencybandaspossibleÑeventhoughtheslabapproximationmaybeinvalidforportions ofthebandÑsincetheobjectivewastoinvestigatethetechniqueandevaluateperformanceof interferometry.Furthertheorycouldbedeveloped,especiallyincombinationwithcomputa- tionalsimulationsinthefuturetoextendtheusablefrequencyrange.Thismayalsogiveinsight intotheobservedvariability.Phaseambiguityisanotherconcernhereasinthelastitemand shouldbefurtherinvestigatedwhenadditionaltheoryisdeveloped. Manyofresultsshowatimedependencebyreturningtoanearlyzerophasedifferenceat theendofthemeasurement.Duetotherelativelylongtimerequiredtomeasureonesample (usuallybetween10secondsand30seconds),itisthoughtthatthistimedependencemaybe partiallyduetothefuelconsumption.Thisledtothemeshexperimentbeingconducted,for whichtheonlytimevarianceobservedshouldbethetransitionatignitionandextinguishment. Thisexpectedtimevarianceisnotobservedinthemeshexperiments;instead,theresponse wastimeinvariant.Thiscounter-physicalresultrequiresfurtherinvestigationtoexplain. 115 Themostpromisingresultsarethosefromthesetupwhichusedashutter.Atlowerfre- quencieswheretheslabapproximationsarenotvalid,thereislittlephasedifference.Arela- tivelylarge,positivephasedifferenceoccursathigherfrequenciesforwhichtheslabapproxi- mationisacceptable.ThissuggeststhatthereisaÞre-inducedplasma.Theelectrondensity acrossonesamplehaslessvariationcomparedtomeasurementsfromotherexperimentalset- upssuggestingthattheshutterhelpstoeliminateotherpropagationpaths,therebyimproving measurementaccuracy. Overall,theseexperimentsprovideusefulinitial,exploratoryresultsthatcanhelpfuture experimentsbedeveloped.Setupsmakinguseofwiremeshforshieldingaswellasshutters shouldbefurtherinvestigated.Itwouldbeworthwhiletocombinethetwointoonesetup.A squarefueldishmaybeusedwithasinglewalloneithersideofit. 6.5Conclusion ThischapterhasinvestigatedusinginterferometrictechniquestocharacterizeÞre-induced plasmasinthelaboratory.Experimentswereconductedusingvarioussetupsandmultiplefuels toevaluatethistechnique.Preliminaryresultssuggestthatplasmasmaybeformed,andthat theseplasmasmaybemeasuredusinginterferometry.Futureworkshouldlooktoreducephase ambiguities,increasefrequencyÑinitiallytoX-band(8Ð12GHz)Ñandimprovetheshutterand mesh/shieldingsetup. 116 Chapter7 TransmissionsfromInsideofaHouseFire Whileotherexperimentshavelocatedboththetransmittingandreceivingantennasoutsideof theÞre,anexperimentwasconductedwiththetransmittersplacedinsideofaburninghouse. PlacingtransmittersinsideofaÞremeansthatthetransmittedsignalmustpropagatethrough theÞre.Negativeeffectsfromdiffraction,focusing,andotherproblemsassociatedwithtrans- missionmeasurementsinarangesetup(asinpreviouschapters)aremitigated. ThishousewasburnedaspartoftheMichiganStatePoliceDepartmentÕsFireInvestiga- tionClassattheendofOctober2014.Thestatepolicewelcomedthisworkandlookedtoac- commodateitwheretheycould.Sincethemainobjectiveofthisburnwasnotthisresearch, thisexperimentworkedaroundtheconstraintsandneedsoftheinvestigationclass.Insulated transmitterswereplacedinthreeseparatelocationstotransmitÞvefrequencies.Signalstrength wasmeasuredbefore,during,andafterthehouseburned.ForthisÞreinvestigationclass,Þre ÞghtersandlawenforcementpersonnelfromaroundthestatelearnedhowtoinvestigateÞres, howarsonÞresareset,aboutÞregrowthandbehavior,andotherrelatedtopics.Toconclude theclass,instructorsstartedmultipleÞresinsideofahouse.FireÞghtersfromareaÞredepart- ments,usingthisasatrainingexercise,enteredthehouseandextinguishedtheÞre.First,Þres weresetontheÞrstßoorandextinguished,thenÞresweresetonthesecondßoorandextin- 117 guished.Thenextmorning,thestudentsinvestigatedthisÞre.Oncetheirinvestigationwas completed,anotherÞrewassetandthehouseburntdown. Further,thisexperimentsimulateshowahouseÞrecouldeffectthetransmissionsfromÞre- Þghtersinsideofahousetothoseoutsideofthehouse.OftheÞreÞghterlineofdutydeaths thatoccurwhentheÞreÞghterisinsideofaburningstructure,manyinvolveaßashoveror otherheavyÞreconditions.Radiocommunicationfailuresbetweenincidentcommandersor ofÞcersandtheÞreÞghterarecommoninthesecases.Whilemanyreasonsforthesefailures exist,onepossibilityisthattheÞreblocksoratleastdegradestransmissions.This,combined withthedegradationalreadycausedbythestructure,couldrendercommunicationsuseless. Suchascenarioismademorelikelyduetomoderntrunkedand/ordigitalsystemswhichdo notworkwellinverylowsignalenvironments 1.Thishypothesisisonlysupportedbywhatboth BoanandMphalesayisanecdotalevidencefoundin[66]and[67].Thesetwoworkscouldnot beobtainedatthetimeofwritingforreview.Thesetworeferencesreportedlysaythatthera- diotransmissionsbetweenwildlandÞreÞghtersthatweretransmittedthroughawildÞrefront (wherethelargest,mostintenseßamesare)werecut-offsometimes.Additionally,areviewof lineofdutydeathreportshasnotbeenconductedtodeterminehowlikelythisscenarioisor ifthereareotherobviouscausesforradiofailures.Muchofthistheoryisbaseduponpersonal ÞreÞghtingandelectromagneticengineeringexperience. 7.1Transmitters Itwasimpracticaltoplaceawidebandtransmitterandantennainthehouseduetothehigh riskofdamagingtheinstrument.Instead,Þvefrequenciesthatarecommonlyusedforcommu- 1AcommontactictaughttoÞreÞghterswhoareintroubleandcannotmakesuccessfulcommunicationwith anyoneistoswitchtheirradiotoasimplex,analogchannelthatdoesnotgothroughanytrunkingsystem,butin- steadtransmitsdirectlytootherradios.Thereasoningisthatthelow-levelsignalmaybereceivedbythosenearby whereasitcouldnotbereceivedbythetrunked/digitalsystemcontrollerlocatedatatowersitesomedistance away. 118 nicationsandforwhichlow-costtransmittersareavailablewereselected.Differenttransmis- sionmodeswereusedatdifferentfrequenciesbasedontransmitteravailability.Thefrequency bandsandmodeswere: ¥144MHzbandtransmittingacontinuoussignal ¥440MHzbandtransmittingacontinuoussignal ¥900MHzbandZigBeetransmitter ¥2.4GHzIEEE802.11g/n(Wi-Fi) ¥5GHzIEEE802.11g/n(Wi-Fi) TheÞreignitionpointsontheÞrstßoorandthetransmitterlocationsareshowninFig- ure7.1.AsnotedintheÞgure,thereceiverswereapproximately150ftawayfromthehouse. Thelocationwasselectedbasedonactivitiesandpersonnelpositionfortheclass.Notransmit- terswereplacedonthesecondßoor,therefore,thelayoutforthesecondßoorisnotprovided. 7.1.1Insulation TransmitterswereplacedinsideofplasticenclosuresthathadÞberglassbattinsulationeither insideoforaroundthebox.Theplasticenclosuresweremeanttokeeptheelectronicssafe fromminorwaterdamageandimpacts;therefore,theywereselectedbaseduponavailability, crushresistance,andwaterresistance.TheplasticenclosuresandÞberglassinsulationwere thenplacedinsideofaboxmadefromDuraboardinsulation(seeSection5.2.1).TheÞberglass insulationisusedtoinsulatetheelectronicsfromanyheatthatmaybetransferredthrough theDuraboardbox,whichismeanttoprotectfromdirectßameexposure.Tomaketheboxes, Duraboardwascuttopiecesandjoinedusingtwisttiesofsteelpicture-hangingwirethatwas pushedthroughadjoiningpieces. 119 !"#$%&''( 4' 7"3' 2"4' 7"12' 4"2' 11"5'2' 11"2' 3"1' 6"5' 3"2' 11"3' 11 3/4"3' 7"7' 6 3/4"3' 7"5' 6 1/4"9' 2"5'3' 4"5' 2"13' 6"3' 11"4' 4"2' 11"11' 2"2' 3"3'8' 4"5' 2"2'3' 3 1/4"2' 8"3' 10"16' 11 1/4" 3' 10"5' 6 3/4"9' 5 1/4"13' 9"KITCHEN 166 sq ft (13' 6" ! 12' 4") KITCHEN 166 sq ft (13' 6" ! 12' 4") KITCHEN 166 sq ft (13' 6" ! 12' 4") KITCHEN 166 sq ft (13' 6" ! 12' 4") KITCHEN 166 sq ft (13' 6" ! 12' 4") KITCHEN 166 sq ft (13' 6" ! 12' 4") KITCHEN 166 sq ft (13' 6" ! 12' 4") KITCHEN 166 sq ft (13' 6" ! 12' 4") KITCHEN 166 sq ft (13' 6" ! 12' 4") KITCHEN 166 sq ft (13' 6" ! 12' 4") KITCHEN 166 sq ft (13' 6" ! 12' 4") KITCHEN 166 sq ft (13' 6" ! 12' 4") KITCHEN 166 sq ft (13' 6" ! 12' 4") KITCHEN 166 sq ft (13' 6" ! 12' 4") KITCHEN 166 sq ft (13' 6" ! 12' 4") KITCHEN 166 sq ft (13' 6" ! 12' 4") KITCHEN 166 sq ft (13' 6" ! 12' 4") KITCHEN 166 sq ft (13' 6" ! 12' 4") KITCHEN 166 sq ft (13' 6" ! 12' 4") KITCHEN 166 sq ft (13' 6" ! 12' 4") KITCHEN 166 sq ft (13' 6" ! 12' 4") KITCHEN 166 sq ft (13' 6" ! 12' 4") KITCHEN 166 sq ft (13' 6" ! 12' 4") KITCHEN 166 sq ft (13' 6" ! 12' 4") KITCHEN 166 sq ft (13' 6" ! 12' 4") LIVING ROOM 207 sq ft (15' 4" ! 13' 6") ENTRY 24 sq ft4' 7" ! 5' 3"ENTRY 24 sq ft4' 7" ! 5' 3"ENTRY 24 sq ft4' 7" ! 5' 3"ENTRY 24 sq ft4' 7" ! 5' 3"ENTRY 24 sq ft4' 7" ! 5' 3"ENTRY 24 sq ft4' 7" ! 5' 3"ENTRY 24 sq ft4' 7" ! 5' 3"ENTRY 24 sq ft4' 7" ! 5' 3"ENTRY 24 sq ft4' 7" ! 5' 3"ENTRY 24 sq ft4' 7" ! 5' 3"ENTRY 24 sq ft4' 7" ! 5' 3"ENTRY 24 sq ft4' 7" ! 5' 3"ENTRY 24 sq ft4' 7" ! 5' 3"ENTRY 24 sq ft4' 7" ! 5' 3"ENTRY 24 sq ft4' 7" ! 5' 3"ENTRY 24 sq ft4' 7" ! 5' 3"ENTRY 24 sq ft4' 7" ! 5' 3"ENTRY 24 sq ft4' 7" ! 5' 3"ENTRY 24 sq ft4' 7" ! 5' 3"ENTRY 24 sq ft4' 7" ! 5' 3"ENTRY 24 sq ft4' 7" ! 5' 3"ENTRY 24 sq ft4' 7" ! 5' 3"ENTRY 24 sq ft4' 7" ! 5' 3"ENTRY 24 sq ft4' 7" ! 5' 3"ENTRY 24 sq ft4' 7" ! 5' 3"CLOSET 13 sq ft2' 11" ! 4' 6 1/4"BEDROOM 1 102 sq ft13' 5 1/2" ! 7' 6 3/4"BEDROOM 2 124 sq ft (13' 6" ! 9' 2") BEDROOM 3 103 sq ft11' 2" ! 10' 2"CLOSET BATHROOM 55 sq ft8' 3" ! 6' 8"BATHROOM 55 sq ft8' 3" ! 6' 8"BATHROOM 55 sq ft8' 3" ! 6' 8"BATHROOM 55 sq ft8' 3" ! 6' 8"BATHROOM 55 sq ft8' 3" ! 6' 8"BATHROOM 55 sq ft8' 3" ! 6' 8"BATHROOM 55 sq ft8' 3" ! 6' 8"BATHROOM 55 sq ft8' 3" ! 6' 8"BATHROOM 55 sq ft8' 3" ! 6' 8"BATHROOM 55 sq ft8' 3" ! 6' 8"BATHROOM 55 sq ft8' 3" ! 6' 8"BATHROOM 55 sq ft8' 3" ! 6' 8"BATHROOM 55 sq ft8' 3" ! 6' 8"BATHROOM 55 sq ft8' 3" ! 6' 8"BATHROOM 55 sq ft8' 3" ! 6' 8"BATHROOM 55 sq ft8' 3" ! 6' 8"BATHROOM 55 sq ft8' 3" ! 6' 8"BATHROOM 55 sq ft8' 3" ! 6' 8"BATHROOM 55 sq ft8' 3" ! 6' 8"BATHROOM 55 sq ft8' 3" ! 6' 8"BATHROOM 55 sq ft8' 3" ! 6' 8"BATHROOM 55 sq ft8' 3" ! 6' 8"BATHROOM 55 sq ft8' 3" ! 6' 8"BATHROOM 55 sq ft8' 3" ! 6' 8"BATHROOM 55 sq ft8' 3" ! 6' 8"MUD ROOM 142 sq ft8' 4 1/2" ! 16' 11"MUD ROOM 142 sq ft8' 4 1/2" ! 16' 11"MUD ROOM 142 sq ft8' 4 1/2" ! 16' 11"MUD ROOM 142 sq ft8' 4 1/2" ! 16' 11"MUD ROOM 142 sq ft8' 4 1/2" ! 16' 11"MUD ROOM 142 sq ft8' 4 1/2" ! 16' 11"MUD ROOM 142 sq ft8' 4 1/2" ! 16' 11"MUD ROOM 142 sq ft8' 4 1/2" ! 16' 11"MUD ROOM 142 sq ft8' 4 1/2" ! 16' 11"MUD ROOM 142 sq ft8' 4 1/2" ! 16' 11"MUD ROOM 142 sq ft8' 4 1/2" ! 16' 11"MUD ROOM 142 sq ft8' 4 1/2" ! 16' 11"MUD ROOM 142 sq ft8' 4 1/2" ! 16' 11"MUD ROOM 142 sq ft8' 4 1/2" ! 16' 11"MUD ROOM 142 sq ft8' 4 1/2" ! 16' 11"MUD ROOM 142 sq ft8' 4 1/2" ! 16' 11"MUD ROOM 142 sq ft8' 4 1/2" ! 16' 11"MUD ROOM 142 sq ft8' 4 1/2" ! 16' 11"MUD ROOM 142 sq ft8' 4 1/2" ! 16' 11"MUD ROOM 142 sq ft8' 4 1/2" ! 16' 11"MUD ROOM 142 sq ft8' 4 1/2" ! 16' 11"MUD ROOM 142 sq ft8' 4 1/2" ! 16' 11"MUD ROOM 142 sq ft8' 4 1/2" ! 16' 11"MUD ROOM 142 sq ft8' 4 1/2" ! 16' 11"MUD ROOM 142 sq ft8' 4 1/2" ! 16' 11"DECK 129 sq ft (13' 9" ! 9' 5 1/4") )*+"$(,-'(#$./"$0(,/#,1$23$#*,$4+0*+5/6$7#/#,$8'&+0,$%+(,$96:,"#+5/#+'6$;6+#<$)*+"$1'0=>,6#$./"$0(,/#,1$#'$5+:,$#*,$:+,.,($/6$':,(:+,.$'?$#*,$"0,6,<$$)*+"$1'0=>,6#$./"$6'#$0(,/#,1$#'$"0/&,< @ABACA!DA !ECB !"#$%$%&'()"%'*+),- CB@$F/&,$G1H$I/#'6$G/-+1"H$49H$;6+#,1$7#/#,"$BCCJB 7-&K75#$)'11$L$8,&&,#+,( 4+0*+5/6$7#/#,$8'&+0, MN#*$O/"+0$%+(,$70*''& D@!BP@NP@N$!@ED@ 8QFI$RSE$! 140MHz 440MHz WiFi &900MHz FFFFReceiver ~150 ft Figure7.1:PlanviewoftheÞrststoryoftheburnhouse. Bluetextboxesindicatetransmitterlocationsandredtext boxesindicateignitionpoints.OriginaldiagramcourtesyofMichiganStatePolice. 120 Theeffectsoftheinsulationandplasticenclosuresonthetransmissionsisnotamajorcon- cern.ThetransmissionpropertiesshouldnotchangeduringtheÞre,althoughtheymaychange whenwater,usedtoextinguishtheÞre,isabsorbedintotheinsulation.Sinceextinguishment isnotthetimeperiodofinterest,thisisacceptable.Themainconcernfortheenclosuresisthat asigniÞcantlystrongsignalisreceived.Thiseliminatesusingmetalenclosures(althoughthese couldbeusedifthetransmittingantennawasoutsideoftheenclosurewiththetransmitter, batteries,etc.inside). 7.1.2144MHzCWTransmitter AMicro-Fox15transmitter(Fig.7.2a)fromByonics,LLC[68]wasusedforthe144MHztrans- mitter.Thisisasmalltransmitterdesignedtotransmitacontinuoustonesothatamateur(ham) radiooperatorscantrytolocatethetransmitter.Thisactivityisknownasfoxhunting.The transmitterhasanoutputpowerof10Ð15mW.TheMicro-FoxwasconÞguredtotransmitat 146.565MHz.Thisisanamateurradiofrequency,sothetransmitterwasprogrammedwiththe authorÕsamateurcallsignofÒKE7ESDÓ.TheMicro-Foxisasmallcircuitboardwithamicrocon- troller,RFchip,andSMAconnector.Itrunsoffofasingle9Vbatteryandhasatoggleswitch. Thetransmitterisprogrammedthrougha2.5mmTRS(headphone)jack.Thecircuitboardand 9Vbatteryareslidintoaplastictubethathasacrosssectionjustlargeenoughforthebattery. Oneendcapofthetubehascut-outsfortheSMAconnectorandtoggleswitch. AprojectboxwasfoundthatÞttheMicro-Foxandthenasmallholewascutinthesidefor theantennaandtoggleswitch(Fig.7.2a).Arubberbandaroundtheprojectboxalloweditto beeasilyopenedandclosed.TheprojectboxwasplacedinsideofaDuraboardbox,which waslargeenoughfortheprojectboxandantenna,andsurroundedbyÞberglassinsulation (Fig.7.2c).ThelidoftheDuraboardboxwasheldonusingpiecesofanaluminumstreetsignso thatitcouldbeeasilyopenedtoturnthetransmitteronandoff.Figure7.2bshowstheclosed DuraboardboxaftertheÞre. 121 (a)Transmitterfor144MHzinplasticproject box. (b)Closed144MHztransmitterboxafterthe Þre. (c)Plasticprojectboxfor144MHztransmitterplacedininsulation. Totheleft isapieceofÞberglassinsulationtobeplacedontopofthetransmitter.The Duraboardpieceofinsulationontherightisthenusedtoclosethebox. Figure7.2:Transmitterfor144MHz. 122 7.1.3440MHzCWTransmitter ARadioShackHTX-204VHF/UHFDualBandTransceiver(Fig.7.3a,left)servedasthe440MHz transmitter.Itwastunedto442.125MHzandcontrolledbyanArduinoUno-R3(Fig.7.3a,top right).TheArduinokeyedtheradiototransmittheauthorÕscallsignandthenkeptthera- diokeyedup.ThecallsignwastransmittedeverytenminutesasrequiredbyFCCregulations. Low(0.35W),medium(2.5W),andhigh(5W)transmitpowerscouldbeselectedontheradio. Whichpowerlevelwasusedwasnotrecordedattheexperiment;however,themedium2.5W powerlevelwasmostlikelyselectedduetobatteryconstraints.TheHTXwaspoweredbyalead acidbattery(Fig.7.3a,bottomright)througharegulatorsincetheoriginalbatteryfortheradio wasdead. Likethe144MHztransmitter,theHTXwasplacedinsideofaprojectboxwhichwasthen placedinsideofaDuraboardboxandsurroundedbyÞberglassinsulation,seeFigure7.3c.The Duraboardbox(Fig.7.3b)wassecuredclosedbytwistingthesteelwiresinsteadofusingpieces ofastreetsign.AllofthephotographsinFigure7.3weretakenaftertheburn. 7.1.4900MHzXBeeTransmitter ADigiXBee-PROXSCS3B900MHzwithawireantenna(DigiPartNo.XBP9B-XCWT-001)was usedastheZigBeetransmitter.Itiscantransmitupto250mW.ASparkFunXBeeshieldcon- nectedtheXBeetoanArduinoUno.TheUnocontrolledtheXBeeaswellassamplingenviron- mentaldata.TheSparkFunTutorialÒInternetDataloggingWithArduinoandXBeeWiFiÓ[69] describeshowtosamplecarbonmonoxide,methane,ambientlight,andtemperature 2.The circuitwasbuiltwiththesesensors;however,onlytemperaturewasmeasuredduringtheex- periment.TemperaturereadingsfromtheXBeeÕsbuilt-insensorwerealsorecorded.Thelight sensorwasbrokenduringtesting.Gasreadingscouldnotbetakenbecausethecurrentdraw 2Partnumbersarenotprovidedsincethepartswereorderedthroughthetutorial.Itisexpectedthatthistutorial willeitherbearchivedorupdatedtoreßectSparkFuninventory. 123 (a)Openprojectboxshowingthe440MHztrans- mitter,battery,andArduinomicrocontroller. (b)Closed440MHztransmitterbox. (c)Open440MHztransmitterboxshowingplasticprojectboxand Þberglassinsulation(pink). Figure7.3:Transmitterfor440MHz. 124 Figure7.4:900MHZtransmittersetup. TheXBeemoduleandwireantennaarebarelyvisibleinthetoprightbecause theyarecoveredbytheArduinoshield(red)andtheArduinoUno(blueboardwithelectricaltape).Thesystemis poweredbya9Vbattery(center).Fromtheleft,themethane,carbonmonoxide,temperature,andlightsensorsare visibleonanothercircuitboard. foreachsensorwastoohighandwouldhavedrainedthebatterytooquickly.TheXBeemodule washousedinthesamecontainerastheWi-Firouterdescribedinthenextsection. 7.1.52.4GHzand5GHzWi-FiTransmitter Totransmitat2.4GHzand5GHz,aNetgearWNDR3400router(Fig.7.5a)wassetuptobroad- casttwoSSIDÕs.Channels6and153wereusedforthe2.4GHzand5GHznetworks,respectively. Alead-acidbatteryprovidedpowertotherouterthrougharegulator. Thankyou... Dr.JohnRossdonatedtherouterforthisexperiment. Therouter,battery,andregulatorwereplacedinsideofanoldelectricpowertoolcase.Also placedinsideofthistoolcasewerethe900MHzXBeemoduleandaccessories.Fiberglassinsu- lationlinedtheinsideofthetoolcasetoholdallpartsinplaceinadditiontoprovidingthermal 125 insulation(Fig.7.5a).Thisisdifferentfromthe144MHzand440MHztransmittersthathadthe Þberglassinsulationoutsideoftheprojectbox.ThetoolcasewasplacedinsideofaDuraboard box(Fig.7.5b).TheDuraboardboxisshownclosedaftertheÞreinFigure7.5c. 126 (a)OpentoolcaseshowingÞberglassinsulation(pink),Wi-Firouter(2.4GHzand5GHz),battery(center-bottom), and900MHzXBeeandsensors(right). (b)Opentransmitterboxshowingthetoolcaseen- closingthetransmitters. (c)ClosedtransmitterboxforWi-Fiand900MHz XBee. Figure7.5:TransmittersforWi-Fiand900MHzXBee. 127 7.1.6TransmitterPlacement Thetransmitterswereplacedintothehouseandturnedonshortlybeforethetimeofignition. ThelocationofeachDuraboardboxisindicatedinFigure7.1.Theselocationswereselectedso thatatleastoneÞrewouldbebetweenthetransmitterandthereceiver.IntheÞguresbelow,a solid,whiteorblackarrowpointstoaDuraboardboxorwheretheboxisifobscured.Abroken, redarrowindicatesanignitionpoint. The140MHztransmitterwasplacedinthesouth-eastroom(Bedroom2inFig.7.1)ofthe houseagainstthenorthwalloftheroom.Itwasplacedwiththeantennaverticalunderasmall deskasshowninFigure7.6a.Anignitionpointwasonthesouthwallofthisroomunderthe window(Fig.7.6b).Anopendoorwaytothe440MHztransmitterroomisinthenorth-east corneroftheroom(immediatelytotherightofthephotographerinFig.7.6b). Ontheoppositesideofthewallfromthe144MHztransmitterandslightlytotheeastwasthe 440MHztransmitter(Bedroom1inFig.7.1).AsseeninFigure7.7a,thetransmitterisagainst thewallbetweenadresserandachair.TheblackarrowontherightofFigure7.7aindicates theapproximatelocationofthe144MHztransmitter.Inthenorthwestcornerofthisroomis anadditionalignitionpoint(brokenredarrowinFig.7.7b).Directlynorthfromthe440MHz transmitterisawideopeningtothelivingroom. ThetoolcasewithWi-FirouterandXBeewasplacedunderatableinthelivingroom (Fig.7.8)nexttothedoortothekitchen(seeFig.7.1).Anignitionpointisnorthofthetransmit- tersunderthewindow. 128 (a)144MHztransmitterinplaceunderthedesk. (b)Theroomcontainingthe144MHztransmitter. Theviewislook- ingSW.Thetransmitterislocatedunderthedeskintheupperrightof thephoto.Anignitionpointisseenunderthewindowontheleft.The 440MHztransmitterislocatedontheothersideoftherightwall. Figure7.6:Placementofthe144MHztransmitter. 129 (a)Placementofthe440MHztransmitter. Theblackarrowonthe rightindicatestheapproximatelocationofthe144MHztransmitter ontheoppositesideofthewall. (b)Theroomcontainingthe440MHztransmitter. Theviewislook- ingSW.Thetransmitterislocatedbehindthedresser.The144MHz transmitterisontheoppositesideofthewall.Anignitionpointis seenintheupperrightcornerofthephoto.Thedoortotheroomcon- tainingthe144MHztransmitterisimmediatelytotheleftofthepho- tographerandthedoortothelivingroomisontherightsideofthe photo. Figure7.7:Placementofthe440MHztransmitter. 130 Figure7.8:Placementofthe900MHzXBeeandWi-Fitransmitters. TheDuraboardboxisinthetable.Atthetopof thephotoisanignitionpoint.Thekitchenisimmediatelyleftofthephotographer. 131 Figure7.9:Receiversaspositionedformeasurements. Thereceiverswerepoweredbythegenerator(right)andcon- trolledbythelaptops(rightarrow).TheXBeereceiveriselevatedonthesparetire(leftarrow)andthe144/440MHz receiverisnexttothelaptops(middlearow). 7.2Receivers Thereceiverswereplacedapproximately150ftnorthofthehouseasindicatedinFigure7.1.All receiverswereplacedinthebackofajeepwiththetailgateopen(Fig.7.9).Othervehicleswere betweenthereceiversandthehouse(Fig.7.10).Duringtheburn,peopleweremovingaround thisarea.Noneofthevehiclesbetweenthereceiversandtherehouseweremovedduringmea- surements.Vehiclesdidtravelalongthenorth-southroadtotheeastofthereceivers. Thereceiverswerepoweredbyaportablegeneratorandtwolaptopswereusedforsampling (Fig.7.9).Onelaptopwasusedforthe144MHzand440MHzreceiverandtheotherwasforthe 900MHzXBeeandWi-Fi.AnAR8200WideRangeReceiverfromAORwasusedtomeasurethe signalstrengthofthe144MHzand440MHztransmissions.Thereceiverwasplacedintoadual 132 Figure7.10:Photoshowingthereceiverlocationrelativetothehouseincludingvehiclesinbetweenthetwo. frequencymodeandmonitoredbothfrequenciesatthesametime.The LMcommandforthe AR8200wasusedtologthesignalstrengthmeterreadingsoftheunit.Thetimewaslogged foreachvalue.Atableisprovidedin[70]thatrelatesthevaluereturnedbythe LMcommand fortheAR8200Series-2withablackcabinettodBmvalues.ThistableisrepeatedinTable7.1. Theoriginaltableincludesvaluesbelow #115dBmwhichreturna0valueandvaluesabove #20dBmwhichreturnavalueof139.Thedatainthetableexceptforthe #20dBmpointwere Þttoa6 th-orderpolynomialcurveusingtheIPythonnotebookinAppendixO.Theresulting curveis y(x)=(3.24612295 "10#10)x6+(#5.49175302 "10#8)x5+(1.17145927 "10#6)x4+(2.61296036 "10#4)x3+(#0.0167315124) x2+(0.636706423) x#114.993119(7.1) 133 Table7.1:Lookuptablefor LMvaluestodBm. LMdBm 0-115 10-110 27-105 42-100 55-95 68-90 86-80 97-70 103-60 106-50 109-40 112-30 139-20 whichisshowninFigure7.11Thisequationwasusedtomaptherecorded LMvaluestodBm values.The #20dBmvaluewasnotincludedinthecurveÞttingbecauseawell-Þtlinecould notbefoundthatincludedthispoint,andbecausenovaluesgreaterthan107wererecordedat theburn. The900MHzXBeereceiverwasaZigBeemoduleidenticaltothetransmitter.ASparkFun XBeeExplorerUSBboard(SparkFunPartNo.WRL-11812)wasusedtointerfacethecomputer totheXBee.NotethattheparticularXBeemodulesuseddonotfunctioncorrectlyiftheRSSI pinhasanythingconnectedtoit.AsolderjumpermustberemovedontheUSBinterfaceboard inorderforthismoduletowork.TheXBeeandtheUSBboardareshowninFigure7.12.The laptoploggedthecomputertime,theup-timeoftheArduino,thetemperaturefromtheon- boardsensorofthetransmittingXBee,thetemperaturefromtheoff-boardtemperaturesensor, thetemperaturefromtheon-boardtemperaturesensorofthereceivingXBee,andthereceived signalstrength(RSSI).Valueswererecordedforthelight,CO,andmethanesensors;however, thesesensorswerenotoperationalduringtheexperimentasnotedearlier.Therearetimes whenthereceivingXBeereturnedanerrorornon-standardresponsetothecomputer.These 134 Figure7.11:BestÞtcurvefortheAR8200. valueswereloggedandareincludedinthedataÞles.Theseerrorsdonoteffectotherdata points. TheprogramNetSurveyorfromNutsAboutNets[71]wasusedtorecordtheWi-Fibeacon signalstrengthsforbothchannels.AcertiÞedrefurbishedLinksysWirelessMiniUSBAdapter AC580DualBand(AE6000)waspurchasedthroughAmazon(ASIN:B00LV87XD2)toallowthe laptoptomonitorthe5GHzchannel.Figure7.13showsthemeasurementlaptops,andthe Wi-Fiadapterisindicatedbythewhitearrowatthecenteroftheimage. 7.3VideoRecordings VideoswererecordedtoshowÞreconditionsandtohelpwiththeinterpretationofdata.Video wasonlyrecordedfortheÞrstßoorÞressincetransmitterswereonlylocatedonthatlevel.One 135 Figure7.12:Receiving900MHzXBeemodule. camerawasplacedeastofthehouse,lookingintothewindowsoftheroomsforthe144/440 transmitters.AlsointheÞeldofviewwasoneoftheentrancesusedbyÞreÞghters.Thiscamera isconsideredthemaincamerasinceitwasusedtopiecetogetheratimeline,matchingdata timestampstoevents.Thetimeonthecomputerrecordingthe900MHzXBeeandWi-Fisignal strengthswasselectedasthestandard,orreference,time.Theotherlaptopwasonesecond aheadofthistime,meaningthattimestampsforthe144MHzand440MHzdatashouldbe shiftedbackbyonesecond.Theclockonthemainvideocamerawas57secondsaheadof thereferencetime.Digitalphotoswereapproximately11.5minutesbehindthereferencetime. Anothercamerawasplacedtothenorthwestofthehouse;however,thecameradiedbeforethe Þrewasignited.Areplacementcamerawasstartedapproximately14secondsafterignition. 136 Figure7.13:MeasurementlaptopsandWi-Fireceiveradapter(arrow). 7.4ResultsandDiscussion MembersoftheMichiganStatePoliceBombSquadignitedtheÞresremotelyusingÒsquibÓ detonators.Allfourignitionpointsweresetoffatthesametime.Asimilarprocedurewasused toignitethesecondßoorÞresaftertheÞrstßoorwasextinguished. Datarecordingswerestartedafterthetransmitterswereturnedon,butbeforetheignition time.RecordingofXBeedatawasstartedlastat2.5minutespriortoignition.Datawasrecorded untilthetransmitterswererecoveredfromthehouse(afterthesecondßoorwasextinguished andbreathingapparatusnotrequired)andturnedoff. TheÞrewasallowedtoburnforapproximately3.5minutes.Atthispoint,Þrecrewsentered thehouseandbegantoextinguishtheÞres,startinginthelivingroomandthenmovingtothe 144/440rooms.Anothercrewenteredthekitchenonthewestsideofthehousetoextinguish theÞrethere. 137 Figures7.14through7.19showpost-Þreconditionsfortheroomsandtransmitters.TheÞrst thingtonoteisthattheÞrewasmuchmoreintenseinthelivingroomwiththeXBeeandWi- Fitransmitters(Fig.7.16).Thefurnitureischarredwithmostofthecushioningburnedaway (Fig.7.19).ThisisdifferentthantheothertworoomsthatshowlittleÞredamage(Figs7.14 and7.15).Smokedamageisnoticeableonthewallsintheserooms(Fig.7.18).Thefurnitureim- mediatelynexttoeachoftheseignitionpointsishardlyburnedordamaged(Fig.7.15and7.17). Inthesepictures,someoftheceilinghasbeenpulleddownduringoverhaultosearchforhidden Þre.Fromtheseobservations,wecanconcludethatthereweresigniÞcantßamesintheliving roomwiththeXBeeandWi-Fitransmitters,whiletheroomswiththe144MHzand440MHz transmittersweremostlysmokeÞlledwithveryfewßames.Thisobservationissupportedby thevideorecordingsaswell.Noßamesarevisibleinthewindowsfromthe144/440roomson thevideoexceptfortheinitialßashfromtheignition. 138 (a)The144MHztransmitterandroomaftertheÞre. Therightarrowindicatesthe positionofthe440MHztransmitterontheothersideofthewall. (b)Aclose-upviewofthe144MHztransmitteraftertheÞre. Figure7.14:Post-Þreconditionsforthe144MHztransmitter. 139 Figure7.15:Post-Þreconditionsinthe440MHztransmitterroom. Notethatthesofaandotherfurnituresustained littleÞredamagingdemonstratingthattheÞreconditionswerenotseverinthisarea. 140 (a)Post-ÞreconditionofthelivingroomwithXBeeandWi-Fitransmitters. (b)XBeeandWi-FiDuraboardboxpost-Þre. Theboxisinatleastoneinchofstanding watersincethebottomlayerofDuraboardisnotvisible.Alsonotethecharringonthe table. Figure7.16:Post-ÞreconditionsfortheXBeeandWi-Fitransmitter. 141 Figure7.17:Post-Þreconditionofthe144MHztransmitterroom. Notethatthechairandtableinparticularhave sustainedverylittledamage. 142 Figure7.18:Post-Þreconditionoftheceilingsinthe144MHzand440MHztransmitterrooms. The2x4studswere exposedduringoverhaulanddidnotsuffersmokeorÞredamage.Comparetheconditionsofthestudstothedrywall stillattachedtoitinthebottomofthephoto. 143 Figure7.19:Post-Þreconditionsinthelivingroom. TheÞrewasmuchmoresevereinthisroomcomparedtothe 144/440rooms.Almostallofthecushioningonthefurniturehasbeenburnedandthewoodischarred.Thewhitish piecesontopoffurnitureareceilingthatwerepulleddownduringoverhaul. 144 ThemeasuredsignalstrengthsareplottedinFigure7.20fortheentiredurationandinFig- ure7.21forashortertimeperiodcontainingtheÞre.ThedurationofÞreisoutlinedinaver- ticalbox.ThedataisverynoisyanddifÞculttoanalyze.Ingeneral,however,nosigniÞcant signaldegradationoccursduringtheÞre.Post-Þresignalstrengthtendstobelowerthanpre- Þrestrengths.Thisismostlikelyduetowaterandotherdebrisbeinginadvertentlyplacednear thetransmitters.Thesharpdecreaseinsignalstrengthforthe440MHztransmitterimmedi- atelyafterÞrecrewsenteredthehousesuggeststhatdebrisandwatereffectedthistransmitter drastically.ThistransmitterwouldhavebeentheÞrsttransmittertobehitbyÞrecrewsen- teringthehouse.Thegraphshowsthatallofthesignallevelsincreasedoncethetransmitters wereremovedfromthehouse,andwasreducedwhentheywereturnedoff.Thisshowsthatthe measurementsystemwasoperatingcorrectly. Thegraphshowsthatthe5GHzWi-Fichannelwasnotdetecteduntilafterthetransmitters wereretrievedfromthehouse.Italsoshows17minutesafterÞrecrewsenteredthehouse,the 2.4GHzWi-Fisignalwaslost.TheDuraboardboxfortheWi-Fitransmittersabsorbedalarge amountofwaterwhichcouldhaveactedtoshieldthe2.4GHzsignal.Itisreasonablethatittook 17minutesforenoughwatertobeabsorbedbecauseofthetimerequiredforoverhaulaftera ÞreandfortheDuraboardtoabsorbenoughwatertoimpactthesignal. Thetemperatureinsideofthetoolcase,whichcontainedtheXBeeandtheWi-Firouter, andthetemperatureatthereceiversareplottedinFigure7.22.Thetemperaturesensoronthe XBeeishotterthanthediscrete,off-boardsensorinthetoolcase.Thiscouldeitherbefroma calibration/referenceerror,oritcouldbeduetotheexhaustfromtherouter.TheXBeemod- ulewasrightnexttotherouterwhiletheoff-boardsensorwasnearthebattery(seeFig.7.5a). Thesemeasurementsshowthatthetoolcaseheatedupbecauseoftheelectronicsandnotbe- causeoftheÞre.Futureexperimentswillneedtoensurethatthetransmittersdonotoverheat themselves.TheDuraboardandÞberglassinsulationprovidedsufÞcientprotectionforthein- 145 !"#$%!""$%!"$$%!&$%!'$%!($%!)$%!*$%!+$%$&,*$,#+%"$,$+,+'%"$,"&,"#%"$,--,-)%"$,+',$$%"",$#,#+%"","),+'%"",-","#%"",+*,-)%"++%./0% ++$%.10% &$$%.10%2344% #5+%610% *%610% 7894%:;9<=>?% Figure7.20:Measuredsignalstrengthsbefore,during,andafterthehouseburn. struments.ThetemperatureatthereceivingXBeeshowsthattheoutsidetemperaturewasfairly constantthroughouttheburnanddataacquisitiontime. 146 !"#$%!""$%!"$$%!&$%!'$%!($%!)$%!*$%!+$%"$,$(,$$%"$,$&,*-%"$,"#,+)%"$,"*,-&%"$,"',-"%"++%./0% ++$%.10% &$$%.10%2344% #5+%610% 7894%:;9<=>?% Figure7.21:MeasuredsignalstrengthsnearthetimeoftheÞre. !"#""#$"#%"#&"#'"#()"#(("#)'*")*+!#()*)!*!&#()*('*(+#()*,,*,$#()*!&*))#((*)+*+!#((*($*!&#((*,(*(+#((*!"*,$#-.#/0#12345#6278# -.#-9:;#6278# <.#-9:;#6278# 7=49# Figure7.22:TemperatureversustimefromtheXBeemodules. Eachmodulehasatemperaturesensoronboard.A discrete,off-boardtemperaturesensorwasalsoplacedinsidethetoolcasewiththeXBeeandWi-Firouter. 147 ThemeasuredsignalstrengthsdolittletoshowtheeffectsofÞreonradiotransmissions. Numerousexperimentalfactorsledtotheselow-quality,andhenceinconclusive,results.The receiversshouldhavebeenplacedmuchclosertothetransmitters.Thiswouldhaveincreased theabsolutestrengthaswellaslimitingnegativeeffectsfrompeopleandotherenvironmental factors.Anareashouldbesetupintowhichnooneisallowedtogoduringtheexperiment. Additionally,numeroussamplesshouldbetakenimmediatelypriortoignitiontoestablisha baseline.Finally,Þregrowthshouldhavebeenallowedtoprogressmuchfurtherthanitdid inordertoallowforsufÞcientinteractionbetweenthewavesandßames.Thesethingswere unabletobedoneinthisexperimentbecauseoftheneedsandtimelineoftheÞreinvestigation class. 7.5Conclusion ThisexperimentenableddatatobecollectedduringastructureÞreonascalelargerthanany otherexperimentinthisdissertation.TheMichiganStatePoliceandtheclassinstructorsac- commodatedtheexperimentwell,whichisgreatlyappreciated.Foranexperimentalist,this burnedprovidesusefulknowledgeonthedesign,construction,andplacementofÞre-proof containersfortransmitters.ThetemperatureproÞleobtainedshowedthatheatfromthein- strumentsthemselvesistheprimaryconcerninsideoftheseboxes.Thereceiversshouldbe closertothetransmittersandtheeffectofoutsideobjects,suchaspeople,shouldbemitigated. Finally,Þregrowthshouldbeallowedtoprogresstolaterstages.Balancingobjectivesofother agenciesandexperimentsisdifÞcultandshouldbeexaminedfurtherforfuturejointwork.The resultsofthisexperimentdemonstratethatthereislittleeffectonÞreÞghtercommunications forÞresoflimitedgrowth.SeverÞreconditionswerepreventedinthisexperiment;therefore,it ispossiblethatcommunicationscouldbeaffectedinlargerÞres.StudyofsuchÞreconditions isanitemforfuturework. 148 PartIII Bench-ScaleDiagnosticsusingaTwo-Wire TransmissionLine 149 Bench-ScaleDiagnosticsusingaTwo-WireTransmissionLine Thesystemandexperimentspresentedearlierrelyonantennastotransmitandreceivesignals thatinteractwithaßame.Wemustconsiderthepatterninwhichthewavesareemittedor receivedbytheantennasandhowthispatternintersectswiththeßame.Overall,thesystem utilizesalargevolumeofspace.ThevariousÞresizesandlargefuelsourcesrequiredforthese previoussystemsforceexperimentstobeconductedoutsidewithextrasafetyprecautions.This isnotconducivetoscientiÞcresearch. Theobjectiveofthispartofthisdissertationistodescribeamethodforbench-scale,low- cost,controllableßamecharacterizationmeasurements.Overallweareabletooperateina muchmorecontrolledenvironmentthatoffersrepeatableconditions.Inaddition,bench-scale experimentsarelowercostthanfull-scaleoutdoorexperiments. Afterbrainstormingvariousbench-scalemeasurementsetups,wedecidedtouseatwo- wiretransmissionlinetomeasureßamecharacteristics.Figure7.23showsanexampletwo-wire transmissionlinewithanattachedshortcircuit(right)andabalun(left).Aßametobemea- suredwouldbeplacedontherightsideofthisÞgurebetweenthetwowires.ItwouldfullyÞll thespacebetweenthewiresandwouldcomearoundtheoutsidesaswell.Ifone-portmeasure- mentsweretobemade,theßamewouldbebetweenthebalunandtheshort(seenontheright ofFigure7.23);fortwo-portmeasurementstheßamecouldbeatanypointalongthetwo-wire line.Thistransmissionstructureisopentotheenvironmentwhichallowstheßametointeract withthelocalizedandrelativelyconcentratedÞelds.Differentsizedtransmissionlinesofferthe possibilityofvaryingthevolumeofspaceandßameinterrogatedofferingsomespatialreso- lution.Analysisofsuchameasurementsystemcanbeaccomplishedusingtransmissionline equations.Suchequationsareeasytoimplementanalyticallyandcomputationally. Furthermore,atwo-wiretransmissionsystemoffersopportunitiesinotherareasofmaterial characterization.Theopennatureofthistransmissionlineenablesthematerialorenviron- 150 Figure7.23:Exampleofatwo-wiretransmissionlinewithanattachedshortcircuit(right)andbalun(left)manu- facturedforthiswork. menttocompletelysurroundandencompasstheconductors.Suitablemeasurementmedia includeliquids,gases,andsoftsolids.Thismeasurementsystemcaneasilybeaddedtopipes orvats. Insitu measurementsofthecontainedsubstancecouldthenbemade.This insitu mea-surementisveryadvantageousasmanyelectromagneticmaterialcharacterizationtechniques requiresamplestobetakenandmeasured exsitu .Suchmeasurementsaretypicallycostlyand destructive.Bothone-ortwo-portmeasurementscanbemadewhichoffersadditionalinfor- mationforproblemswithmultipleunknowns.Additionally,atwo-wiretransmissionsystemis relativelylowcostcomparedtocoaxialorwaveguidesystems. Atwo-wiretransmissionlinesystemhassomelimitationsasdoothercharacterization methods.Sincethesystemisopen,itisunshieldedandsusceptibletonoise.Fieldcontain- mentreliesuponhavingbalancedcurrents 3ontheconductors.Performancecansufferifthe conductorsaretoofarapartorcommonmodecurrentsexist.Sinceatwo-wiretransmissionline isabalancedsystem,abalun(balanced-unbalanced)isrequiredtoconnecttoanunbalanced 3Balancedcurrentmeansthatcurrentononeconductorisequalinamplitudeandoppositeindirectioncom- paredtothecurrentontheotherconductor.Thisisknownasdifferentialmodecurrent.Currentsßowinginthe samedirectiononbothconductorsisknownascommonmodecurrent 151 aa',µ(c,µc(c,µcsFigure7.24:Generalnotationusedforatwo-wiretransmissionline. systemlikeacoaxialcable.Abalunisrequireinmostimplementationssincemostmeasure- mentequipmentutilizescoaxialconnectors,e.g.type-N,SMA,or3.5mm. Aninputimpedanceof50 "isthemostcommonimpedanceseenonmeasurementequip- ment.Achievingthislowofanimpedanceforatwo-wiretransmissionlineisdifÞcultandre- sultsinhighsensitivitytoerrorsinthetransmissionlinedimensions.Animpedancetrans- formeristhereforerequiredinmostapplications.Thisisnormallyincorporatedwiththebalun. Theworkinthispartofthedissertationcoversthetheoreticalanalysisofatwo-wiretrans- missionline,designofabalun,manufacturingofanexperimentalsetup,calibrationtheory,and somematerialcharacterizations.Atthetimeofwriting,thissystemhadnotbeentriedwitha ßameduetopoorcalibrationandperformanceissues.Challengeswiththissystemincludethe balundesign,widebandperformance,andtrade-offsbetweenheatthresholdsandconductiv- ity. Figure7.24showsthegeometryandnotationusedforatwo-wiretransmissionlineinthe followingchapters.Theparameter sisthecenter-to-centerdistanceofthewireswitharadius ofa,conductivityof µc,andapermeabilityof µc.Inmostcases, µcwillbe µ0.Ifthewiresare ferrous,thismaynotbetrue.Thesurroundingmediahasapermittivityof 'andapermeability ofµ.152 Chapter8 TransmissionLineCharacteristics Atwo-wiretransmissionlineisatransmissionstructuremadeupoftwoparallel,non- concentricconductors.Thediameteroftheconductorsmaybedifferent. Assumption Inthiswork,theconductorsaredeÞnedtobeofcircularcross-sectionwithequaldiame- ter. Figure7.23showsanexampleofatwo-wiretransmissionline.Beinganopensystemmeans nopartofthetransmissionlineenclosesanyotherpart.Thisallowsforthesurrounding mediumtochange,movingthroughandaroundthetransmissionlinestructure.Thisdiffers frombothwaveguidesandcoaxialcables;inthesetwostructurestheinternaldielectricisen- closedbysomepartofthetransmissionline.Inorderforthemediumofthetransmissionlineto change,theseclosedstructuresmustphysicallybeopenedinsomemanner,havethemedium changed,andthenbeclosedagain. Inanopenstructure,ßuids(liquidsorgases)maymovearoundthesystemandchangewith time.Suchastructurealsoallowsforsolidstoeasilybeplacedaroundthesystemandchanged. Inthecaseofatwo-wiretransmissionline,asolidmaybeclampedaroundtheconductorsor thetransmissionlineinsertedintoasolid. 153 Assumption Atthistimeallworkhasbeencarriedoutundertheassumptionthatthesurroundingme- diacompletelyencompassandtouchbothconductors.Thisassumptionmeansthatno gapsexistbetweentheconductorsandthemedia. CreatingsuchasituationinpracticeisdifÞcultduetomanufacturingtolerances.Forßuids theßowspeedmustbelowenoughthattheßuidisabletocompletelyencircletheconductors. Additionallytheconductorsshouldnotinduceturbulenceintheßuid. Giventhatthetwo-wiretransmissionlineisanopensystem,materialscanreadilybeprobed orsampled.Potentialapplicationscouldbefoundinareassuchasshipping,materialstor- age,geology,healthcare,andmanufacturing.Onecanenvisionaddingorplacingatwo-wire transmissionlineintostoragevats,pipes,gels,soilsamples,meat,vegetables,softsolids,fume hoods,smokestacks,furnaces,combustionchambers,andÞrealarmsystem.Atwo-wiretrans- missionlinecouldeasilyberetroÞttedtoexistingpipes,vats,otherholdingcontainers,ortrans- portationvessels.Thetransmissionlinecouldbesetupaseitheraone-portoratwo-portde- vice.Thisallowsformountingandsensingoptionstomeetcustomerneeds. Whilecurrentexperimentshavebeencarriedoutusingvectornetworkanalyzers(VNA), othersimpler,cheaper,andlowerbandwidthdevicescouldbeused.Thisallowsbudgets, equipment,anddesiredmeasuredparameterstobematched. Analytically,themeasuredresponseofthetwo-wiretransmissionlinesystemisdependent uponthepermittivity, ',andpermeability, µ,ofthemediasurroundingthetransmissionline. Assumption Thisbodyofworkassumesthatthepermeabilityisunchanged,i.e. µ=µ0orµr=1.Fromamaterialsstandpoint,materialsarenottypicallydeÞnedordesignedbytheirrel- ativepermittivityorpermeability.InsteadothermaterialparametersdeÞnethesevalues.For exampleinradarabsorbingmaterial,themixingfractionofferrousparticleshelpstodeÞne 'rand µr.Inplasmasitistheelectrondensity, ne,andthecollisionfrequency, !eff;Inliquidsitcan 154 bethetemperatureandconductivity.Inallcases 'rand µraredependentvariablesoftenonly consideredforRFdesignpurposes.Correlatingmeasurementsof 'rand µrtootherparameters isimportantfortheaforementionedsensingapplications.PropermodelselectionandÞtting mustbecarriedoutinorderforthesensorstobeusefultonon-RFengineersandtechnicians. WebeginthischapterbyÞndingtheelectricpotential(voltage)ofthetwo-wiretransmis- sionline.Usingthis,weareabletoÞndtheelectricandmagneticÞelds.ByknowingtheÞeld structure,weareabletopredictsomebehaviorsofthetwo-wiretransmissionlineaswellas gaindesigninsightsforthematerialmeasurementsystem.Tobetterunderstandlossesinthis system,wealsoexaminetheradiationresistanceofthetransmissionline.WeÞnishbycreat- ingadistributedcircuitmodelofthetwo-wiretransmissionlinethatisbaseduponmaterial characteristicsinordertopredictsystembehaviorandinthefutureassistincharacterizingthe material. Manytextswereusedtodevelopthischapter.Perhapsthemoststraight-forwardtextfor ÞndingtheelectricpotentialisbyCheng[72].Section4-4.2coversÞndingtheelectricpotential andthecapacitance-per-unit-lengthforatwo-wiretransmissionline.Chapter9,andSection9- 3inparticular,coverthedistributedcircuitmodel.Thistextishighlyrecommendedasthe startingpointforanyonebeginningtoworkinthisarea.PlonseyandCollin[73,pp.63Ð72, 361Ð370]isasecondtextthatishighlyrecommended.Next,thetextbyBewley[74,pp.43Ð46] hasanothertakeontheelectricpotentialandexpressescertainequationsinformsnotused elsewhere.WewouldberemissnottomentionthetextbyRamo,Whinnery,andVanDuzer[3] asitwasanexcellentresourcesusedtopiecetogetheralltheotherparts.Finally,King[75, pp.13Ð19,23Ð31,487Ð492]providesaveryin-depthdiscussionoftransmissionlinesinhistext. ThishasnicediscussionsonradiationresistancespeciÞctotwo-wiretransmissionlinethatis notfoundinothertexts.ThenotationandmathematicalderivationscanbedifÞculttofollow. Themathematicalderivationsinthischapterareveryverbosewithfewstepsomitted.This isforthebeneÞtofallreaderssincenotallhavethesamemathematicalability.Whileonestep 155 isevidentandtrivialtoonereader,anotherreadermayÞndthesteptobearoadblock.The aforementionedtextsallleaveoutderivationsthatarenotobviousorrequiresigniÞcantwork andinsights.Thegoalhereistoassistallreaderssothatnonespendminutes,hours,ordays stuckinthemath. 8.1ElectricPotential Theelectricpotentialforatwo-wiretransmissionlineisusedforÞndingtheÞeldstructureof thetransmissionlineandfordevelopingthecircuitmodel.WeÞrstÞndtheelectricpotentialof oneandtwolinecharges,thenextendthistothecaseofatwo-wiretransmissionline. Assumption Weassumethatthepotentialisequaleverywhereonaconductor(althoughnotnecessar- ilyequaltothepotentialonanotherconductor). ElectricpotentialistheworkdonebyanelectricÞeldtomoveachargefromonepointto anotherandhasunitsofvolts.ItisaconservativeÞeldmeaningthatonlythebeginningand Þnalpointsareimportantbutnotthepathtakenbetweenthetwopoints.Thepotentialisalso relativemeaningthatsomepointmustbemadeareferenceandthepotentialforallotherpoints arerelativetothisreferencepoint[3,pp.17Ð22].Thetermelectricpotentialisusuallyused whendescribingtheÞeldwhilethetermvoltageisusuallyusedtodescribethepotentialina circuit.OtherpotentialÞeldsexistssuchasthevectormagneticpotential;however,whenused byitself,thetermpotentialusuallyreferstotheelectricpotential. 156 xy+$lpp0rr0Figure8.1:Asinglelinecharge. Shownarethereferencepointp 0atradiusr 0,andanobservationpointpatradiusr. 8.1.1PotentialofSingleLineCharge Theelectricpotential, V,atthepoint pwithrespecttothereferencepoint p0forasingle, inÞnitely-longlinechargewithdensity $l,asshowninFigure8.1,isgivenby Vs(r)=#3pp0!Eád!l(8.1) wherethesubscript sdenotessinglelinecharge.Thepoint p0hasaradiusof r0andthepoint phasaradiusof r.TheelectricÞeldisfoundusingGaussÕslaw, 5!Eád!S=Qenc '(8.2) where 'isthepermittivityofthemediumsurroundingthetransmissionline, Qenc istheamount ofchargeenclosedbythevolumeofintegration,and !E=örErforthisproblem.Integratingthe electricÞeldoveracylindergives 3L032&0Errd.dz=ErLr2&=$lL'(8.3) +Er=$l2&r'(8.4) 157 xy#$l+$lpr+r#bbFigure8.2:Geometryoftwolinecharges. ThisissubstitutedintoEquation(8.1)andtheorderofintegrationreversedtoremovetheneg- ativesign.BecausetheelectricpotentialisaconservativeÞeldandtheelectricÞeldhasonlya radialcomponent,weareonlyconcernedwiththechangeinradius.Thelimitsofintegration aretherefore rtor0.Theelectricpotentialforasinglelinechargeisthen Vs(r)=3r0r$l2&r'drVs(r)=$l2&'ln!r0r"(8.5) Thereferencepoint p0isnotspeciÞedatthistime;itmaynotbeplacedatinÞnityorthepoten- tialwouldbeinÞnityatallotherpoints[72,p.163].Wewillseethatitisinfactcanceledinlater equations. 8.1.2PotentialofTwoLineCharges Thetotalpotentialfromtwolinechargesisfoundthroughthesumofthepotentialsofeachline charge,whichisknownastheprincipleofsuperposition.Thetwolinecharges,withdensityof ±$l,areplacedat( ±b,0),respectively,asshowninFigure8.2.Thelengths r#and r+are r#=4(x+b)2+y2and r+=4(x#b)2+y2(8.6) 158 where xand yarethecoordinateof p.Thecombinedpotentialat pisthesumofEquation8.5 evaluatedoncefor r+andoncefor r#.Vd(p)=Vs(r+)+Vs(r#)=+$l2&'ln,r0r#-+#$l2&'ln,r0r#-(8.7) wherethesubscript ddenotesdoublelinecharge.Thecommontermsmaybefactoredoutand thelogarithmscombinedtoreachtheÞnalexpression: Vd(p)=$l2&'6ln,r0r+-#ln,r0r#-7(8.8) =$l2&'6ln,r0r#r+r0-7(8.9) Vd(p)=$l2&'ln,r#r+-(8.10) Equation8.10istheelectricpotentialoftwolinecharges. 8.1.3EquipotentialSurfaces Weseeherethatthepotentialisconstantwhenever r#/r+isaconstant.Thesurfacesoverwhich thepotentialisconstantarecalledequipotentialsurfaces.ÒSincethepotentialissingle-valued, surfacesfordifferentvaluesofpotentialdonotintersectÓ[3,pp.20Ð21].Wewillshowthatthe equipotentiallinesofEquation8.10arecirclesbyre-writingitinthestandardformofacircle. First,wewrite r+and r#inCartesiancoordinates: Vd=$l2&'ln8&(x+b)2+y2(x#b)2+y29(8.11) 159 wherewehavedroppedthefunctionalnotationfor Vd.Thelogarithmisremovedbysolvingfor itandraisinganexponentialtoeachside, Vd2&'$l=ln8&(x+b)2+y2(x#b)2+y29(8.12) +exp,2&'Vd$l-=&(x+b)2+y2(x#b)2+y2(8.13) Squaringeachsidegives exp,2&'Vd$l-2=(x+b)2+y2(x#b)2+y2(8.14) +exp,4&'Vd$l-=(x+b)2+y2(x#b)2+y2(8.15) Forsimplicity,let g=exp,4&'Vd$l-.(8.16) Wethenhave g=(x+b)2+y2(x#b)2+y2.(8.17) Multiplyingeachsidebythedenominatorgives g)(x#b)2+y2*=(x+b)2+y2.(8.18) The( x±b)2termsareexpandedandtherightsidemovedtotheleftside, g)x2#2bx+b2+y2*#(x2+2bx+b2)#y2=0,(8.19) 160 sothatitmaybewrittenintheform x2a1+xa2+a3=0,x2(g#1)#x2b(g+1)+b2(g#1)+y2(g#1)=0.(8.20) Wenowmultiplybynegativeone, x2(1#g)+2bx(1+g)+b2(1#g)+y2(1#g)=0,(8.21) anddividebythe x2coefÞcient(1 #g),x2+2bx(1+g)(1#g)+b2+y2=0.(8.22) Next,the b2termismovedtotherightsideandtheexpression b2,(1+g)(1#g)-2(8.23) isaddedtobothsides, x2+2bx(1+g)(1#g)+y2+b2,(1+g)(1#g)-2=#b2+b2,(1+g)(1#g)-2.(8.24) Weseeonthelefthandsidethatthe xand btermscomefrom( x+bc)2.Factoringtheseterms onthelefthandside,andfactoringthe b2termontherighthandsidegives ,x+b,1+g1#g--2+y2=,,1+g1#g-2#1-b2.(8.25) Thisisthestandardformforacircle. 161 Wecansimplifythisequationfurtherifthefullofexpressionfor gisreturnedtoit, :;x+b:;1+e4&'Vd$l1#e4&'Vd$l<=<=2+y2=:>;:;1+e4&'Vd$l1#e4&'Vd$l<=2#10.They-axiscorrespondstoapotentialof Vd=0.163 Twoimportantequationsmaybederivedfromtheradiusandcenterlocation.Firstwe squaretheradius, a2=,bsinh(2 &'Vd/$l)-2(8.36) =b2sinh2(2&'Vd/$l),(8.37) whichmayalsobewrittenas a2=b2csch 2(2&'Vd/$l).(8.38) Theidentity csch 2=coth 2#1(8.39) isusedtowritetheradiussquaredas a2=b2(coth 2(2&'Vd/$l)#1).(8.40) Equation(8.34)isnowsquared, s2c=b2coth 2,2&'Vd$l-,(8.41) andsolvedfor coth 2,coth 2,2&'Vd$l-=s2c/b2.(8.42) 164 ThiscannowbesubstitutedintoEquation(8.40)toget a2=b2(s2c/b2#1)(8.43) a2=s2c#b2(8.44) ThisistheÞrstofthetworelationsthatwelookedtoderive.Equation(8.44)isusedtoÞnd bwhenthecenterandradiusoftheequipotentialsurfaceisknown.Itisalsousedtoderivethe potentialforgivenequipotentialsurfacewhichwedonext. Equation(8.37),solvedfor b2,issubstitutedintoEquation(8.44), a2=s2c#a2sinh2(2&'Vw/$l).(8.45) Thesubscriptfor Vhasbeenswitchedto wtodenotewire.Thereasonforthiswillexplained afterthederivation.Wenowcollectthe a2terms, a2(1+sinh2(2&'Vw/$l))=s2c,(8.46) andapplytheidentity cosh 2(x)=1+sinh 2(x),a2cosh2(2&'Vw/$l)=s2c.(8.47) Solvingfor cosh (x)gives cosh2(2&'Vw/$l)=s2ca2(8.48) cosh(2 &'Vw/$l)=sca.(8.49) 165 Wenowapply cosh #1(x)tobothsides, 2&'Vw$l=cosh#1!sca",(8.50) andsolvefor Vwtoget Vw=$l2&'cosh#1!sca"(8.51) Equation(8.51)isthepotentialfortheequipotentialcircleofradius acenteredat scforaline chargeofdensity $l.Wenotethatthisisnotexpresslyafunctionofwherethelinechargeis placed;instead,thatpositionisimplicitinthecenterandradiusoftheequipotentialsurface. Thisisimportantbecausewenowhaveanequationthatcanbeappliedtothetwo-wiretrans- missionlineproblemsinceweassumedthatthewireshaveacircularcrosssectionandthat thepotentialisequaleverywhereonawire.Equation(8.51)isthereforethepotentialofawire, hencethesubscript w.8.1.4ApplicationtoTwo-WireTransmissionLine Wenowwishtoapplytheaboveequationstothetwo-wiretransmissionlinesystem.While theactualsystemusedinthisworkhasconductorsofequalradii,webeginwithtwowiresof unequalradiiwhosegeometryisshowninFigure8.4. ToÞndthecentersofthewires, s#and s+,westartwithEquation(8.44)foreachwire, b2=s2##a2#(8.52) b2=s2+#a2+.(8.53) 166 xy#$l+$lV+V#a#a+bbs#s+sFigure8.4:Thegeometryofatwo-wiretransmissionline. Theparameter bisthesameinbothequationssowemaywrite s2+#a2+=s2##a2#(8.54) +s2+#s2#=a2+#a2#.(8.55) Thetotaldistancebetweencentersisthesumofthetwodistances, s=s++s#.(8.56) Equations(8.55)and(8.56)aresolvedfor s#and s+.FromEquation(8.56), s#=s#s+(8.57) whichissubstitutedintoEquation(8.55), s2+#(s#s+)2=a2+#a2#.(8.58) 167 Completingthesquareandcollectingliketermsgives s2+#(s2#2s+s+s2+)=a2+#a2#(8.59) 2s+s=s2+a2+#a2#.(8.60) Dividingeachsideby2 sgivesthecenterlocationforthepotentialchargedwire, s+=s2+a2+#a2#2s(8.61) ThisisnowsubstitutedbackintoEquation(8.57) s#=s#s2+a2+#a2#2s.(8.62) The stermontherighthandsideismultipliedby2 s/2sandliketermscollectedtogive s#=2s2#s2#a2++a2#2s(8.63) s#=s2#a2++a2#2s(8.64) whichisthecenterofthenegativelypotentialwire. Caution Sincethewirescannotoverlapandshouldnottouch, s#+s+>a#+a+ThepotentialoneachwireisgivenbyEquation(8.51): V#=#$l2&'cosh#1,s#a#-(8.65) V+=+$l2&'cosh#1,s+a+-.(8.66) 168 Thepotentialdifference(voltage)betweenthetwowiresofunequalradiusis V=V+#V#,which simpliÞesto: V=+$l2&'cosh#1,s+a+-##$l2&'cosh#1,s#a#-(8.67) =$l2&'6cosh#1,s+a+-#cosh#1,s#a#-7(8.68) Inthiswork,however,thewireshaveequalradii, a=a+=a#.Thecentersarethereforelocated ats#=s2#a2+a22s=s2(8.69) s+=s2+a2#a22s=s2.(8.70) Since s#=s+thecentersarethesamedistancefromthey-axis.Equation(8.68)canbesimpli- Þedaswell.Substituting s/2for s#and s+,and afor a#and a+gives V#=$l2&'Acosh#1!s2a"#cosh#1!s2a"B(8.71) V#=$l&'cosh#1!s2a"(8.72) Equation(8.72)isthepotentialdifferencebetweenthewireswithequalradiiinatwo-wire transmissionline.BecausethevoltageisusuallyspeciÞed,thisequationmaybeusedtoÞndthe equivalentlinecharge.ThisisneededinordertoÞndthepotentialanywherearoundthewires usingEquation(8.11)whichisrepeatedhereforconveniencewithanewsubscripttodenote two-wiretransmissionline, V2w=$l2&'ln8&(x+b)2+y2(x#b)2+y29.(8.73) 169 Wemaysubstituteinexpressionsfor $land bfromEquations(8.72)and(8.44),respectively. FromEquation(8.70) sc=s/2,and bistherefore b=.(s/2)2#a2.(8.74) ThepotentialÞeldforatwo-wiretransmissionlineis V2w=&'V#2&'cosh#1(s/2a)ln:>>;CDDDDE!x+.(s/2)2#a2"2+y2!x#.(s/2)2#a2"2+y2>;CDDDDE!x+.(s/2)2#a2"2+y2!x#.(s/2)2#a2"2+y23andthelineislowloss,i.e. +lissmall.The Þrstconditionmeansthatthelineisessentiallymatched.For Z0=50",thismeansthat 49.75 3.Ifthetransmissionlineislongoramultipleofawavelength,2 #1l=n&,then Rrad match =*12s2=60#21s2.(8.94) 178 Whentheloadisanopen,short,orispurelyreactive, Rrad becomesinÞnitebecause I0inthedenominatorofEquation(8.91)iszerofor #1l+$&L=(2n+1)&/2.Forsuchloads,the maximumcurrent, Im,ischosenasareference.Theradiationresistanceisthen Rrad res =2PI2m=*14s2,1#sin(2#1l)2#1l-.(8.95) Assumption Equation(8.95)holdsif( +l+2$L)<0.1.Thismeansthatthelinehaslittlelossandthat theloadisclosetoanopenorshortcircuit. ThisisknownastheresonantcasebecausethereßectioncoefÞcientapproaches ±1whichsets upapurestandingwaveontheline.Foralonglineoramultipleofawavelengthwehave Rrad res =*14s2=30#21s2.(8.96) TheaboveequationsareplottedinFigure8.11.Acurvefor ZL=Z0/2isalsoplottedtodemon- stratethebehavioroftheradiationresistanceforcasesbesidestheresonantandnon-resonant cases. Weseethatcomparedtothematchedcase,theresonantlinehashalftheradiationresis- tance.Thismeansthatalinewithashortoropenloadwillradiatelesspowerthanonewitha matchedloadgivenidenticalcurrents. 8.3.1CloselySpacedWires Ifthewiresarecloselyspacedcomparedtoawavelength, a2/s2,aneffectivespacingparame- ter, se=b2HI1+&1#,2as-2JK,(8.97) 179 Figure8.11:Radiationresistanceforatwo-wiretransmissionwithlineopen,short,orpurelyreactive(resonant line);matched(non-resonantline);and Z0/2loads. shouldbeusedintheaboveequationsinplaceof s.8.3.2DiscussionandRecommendations Inhisdiscussion,Kingpointsoutthatthelossesduetoradiationarenotnecessarilynegligible comparedtoohmiclosses.HeevenpointstocaseswhereitmaybesigniÞcantlyhigher.Thisis easilyunderstoodsinceatwo-wiretransmissionlinecanbeusedasanantenna.Insuchacase, onewouldlike Rrad tobeaslargeaspossible. Ifthetransmissionlineisnotbalanced,radiationwillalsobeproduced.Thisisthemain reasonfortheuseofabalunasdiscussedelsewhereinthisdissertation.Kingcontinuesby furtherdiscussingexperimentalresultsrelatedtoradiationresistance. 180 Rdz Ldz Gdz Cdz z=lz=l+dzFigure8.12:Circuitmodelforadifferentiallengthoftransmissionline. Radiationresistanceshouldnotbeignoredinthedesignofthematerialmeasurementsys- tem.First,aone-portlinewithashortinsteadofatwo-portsystemshouldbeconsideredthe preferredmeasurementsetupifotherfactors(spacing,etc)leadtohigherradiationlosses.The two-portsystemwouldhavematchedloads(optimally)whichwouldresultinhigherradiative lossesthantheone-portsystem.Anotherconsiderationisthelengthoftheline.Weseefrom Figure8.11thatradiationresistanceoscillateswithlength.Thiscanbeadesignchallengeor beusedasanadvantage.Thelargestchallengemightactuallybeincreatingawidebandsys- temthathaslowloss.Thebeststartingpointmaybealong,one-porttransmissionlinewith closely-spacedwires. 8.4DistributedCircuitModel Thederivationpresentedbelowisbaseduponnumerousreferences.Thereaderisdirected to[3,72Ð75]formoreinformation.Ihavealsopresentedsomeofthisinformationatconfer- ences[76,77]. Atransmissionlinemaybemodeledasacircuitoflumpedelementsforadifferentiallength asshowninFigure8.12.Whenmodeledasacircuit,atransmissionlineconsistsofaseries resistance, R;aseriesinductance, L,thatincludesbothselfandexternalinductance;ashunt conductance, G;andashuntcapacitance, C,allbeingper-unit-lengthvalues.Thedifferential lengthcircuitthenhascircuitvaluesof Rdz ,Ldz ,Gdz ,and Cdz [3,pp.214Ð215,246Ð247]. 181 Thecharacteristicimpedanceofthetransmissionlineisgivenby[3,pp.246Ð247] Z0=&R+j"LG+j"C.(8.98) Notethatthisisthecharacteristicimpedanceofthetransmissionlineitselfanddoesnotac- countforanyloadsplacedontheline.Aloadimpedance ZListransformedbyatransmission lineandmayappearasadifferentimpedanceattheotherendoftheline.Thetransformed impedanceisgivenby Zin=Z06ZL+Z0tanh( /l)Z0+ZLtanh( /l)7(8.99) andisdependentuponlength l[3,pp.247].Theterm /isthepropagationconstant, /=++j#=.(R+j"L)(G+j"C),(8.100) asdeÞnedforthedistributedcircuitmodel[3,pp.246Ð247].Thecomplexwavenumber, k,whichwaspresentedinChapter2,foraTEMwaveisrelatedtothepropagationconstantby[3, p.399][78] k=#j/=##j+.(8.101) Thevoltagewavesforasinglefrequencyonthetransmissionlinearegivenby V=V+e#/z+V#e/z(8.102) 182 andthecurrentby I=1Z0FV+e#/z#V#e/zG(8.103) where V+exp(#/z)and V#exp(/z)representwavestravelinginthepositiveandnegative zdi-rection,respectively[3,p.246].Multi-frequencysignalsareexpressedasasumofindividual frequencywaves. Assumption Asnotedearlier,theequationsarewrittenascosine-basedphasorswiththe e+j"ttimefactorsuppressed. Theparameters R,L,C,and Gmustbedeterminedsothatthecharacteristicimpedanceand thepropagationconstantmaybecalculatedforthetwo-wiretransmissionline.Theequations derivedinthissectionhavecosh #1(x)terms.ItiscommontoÞndsimilarequationsintextbooks thatuse ln(x).If s2'a2,thatisthecenter-to-centerdistanceismuchlargerthanthewire diameter,then cosh #1(s/a)maybesimpliÞedto ln(s/a)andthecommonformisderived.The inversehyperboliccosinefunctioniskeptinthisworkasitisthemost-generalformandcanbe usedforall s2/a2ratios. 183 Assumption Theassumptionslistedbelowaremadeaboutthetwo-wiretransmissionlineconÞgura- tioninthefollowingderivations. ¥Thewireradiusissmallcomparedtoawavelength, a-,1.¥Thespacingissmallcomparedtoawavelength, s-,1.¥Thewiresdonottouch, s>2a.Thewavelengthhasasubscript1toemphasizethatthisisthewavelengthinthemedia surroundingthetransmissionlineandnotthefreespacewavelength.Thewiresarecon- sideredtobecloselyspacedif s2'a2doesnothold. 8.4.1Capacitance Theper-unit-lengthcapacitanceisgivenby C=Q/|V#|(8.104) where Qisthechargeononeconductorperunitlength.FromSection8.1,thelinecharge $Lisequivalenttothechargeontheconductor;therefore, Q=$L.Thedenominator V#isthe voltagepotentialbetweenthetwoconductorswhichisgivenbyEquation(8.72).Substituting theseintotheabovedeÞnitiongives C=$L$L/(&')cosh #1)s2a*(8.105) 184 whichsimpliÞesto C=&'cosh#1)s2a*(8.106) 8.4.2Conductance Theper-unit-lengthconductance, G,foratwo-wiretransmissionlineisderivedusingOhmÕs LawandthedeÞnitionforcapacitance.OhmÕsLawis 1G=R=VI=#LL!Eád!lMS!Jád!S.(8.107) Thecurrent JisrelatedtotheelectricÞeldthroughtheconstitutiverelation J=(!E(Eqn.(2.3)) where (istheconductivityofthemediasurroundingtheconductors.OhmÕslawcanthenbe writtenas 1G=#LL!Eád!lMS!(!Eád!S.(8.108) CapacitanceisdeÞnedas C=QV=MS!Dád!S#LL!Eád!l(8.109) =MS'!Eád!S#LL!Eád!l.(8.110) (8.111) 185 wheretheconstitutiverelation D='!E(Eqn.(2.4))hasbeenusedinthenumerator.Dividing capacitancebyconductancegives CG=MS'!Eád!S#LL!Eád!l#LL!Eád!lMS!(!Eád!S='((8.112) orG=C('.(8.113) Theconductanceofatwo-wiretransmissionlineperunitlengthisthen G=&(cosh#1)s2a*(8.114) whenEquation(8.106)issubstitutedfor C.MakinguseofEquation(2.13)allowstheconduc- tancetobeexpressedasanyofthefollowing: G=&(cosh#1)s2a*G=&"'&&cosh#1)s2a*G=&"'0'rtan )cosh#1)s2a*.(8.115) 186 8.4.3Inductance ToÞndtheper-unit-lengthinductance, L,foratwo-wiretransmissionline,webeginbyassum- ingthattheconductivityoftheconductorsissigniÞcantlylargesuchthat R%0.Thisallowsus toexpressthepropagationconstant(Eqn.(8.100))ofthetransmissionlineas /2=j"L(G+j"C).(8.116) Thiscanbeexpandedto /2=j"LG+j2"2LC(8.117) =j"LG#"2LC.(8.118) Factoring #"2LCgives /2=#"2LC,1#jG"C-(8.119) =#"2LC,1+Gj"C-(8.120) ThecomplexpropagationconstantforaTEMwaveinadielectricmediumis /2TEM =(jk)2=#k2.(8.121) Thewavenumbermaybewrittenas #k2=#"2µ',1+(j"'-(8.122) 187 fromEquation(2.14).Sincethedominantmodeofatwo-wiretransmissionlineistheTEM mode[72,pp.444Ð445],thesetwopropagationconstantsmaybecompared, #"2LC,1+Gj"C-=#"2µ',1+(j"'-.(8.123) giving LC=µ'(8.124) where µisthepermeabilityofthematerialsurroundingtheconductors.Onemaynowsolvefor L,makinguseofEquation(8.106),toÞndtheper-unit-lengthinductance L=µ&cosh#1!s2a".(8.125) Thissameexpressioncanbefoundusingeitherthemethodofimagesorconformalmapping asdiscussedinExample4.6bof[3]. 8.4.4Resistance Theresistanceperunitlength, R,isderivedbyÞndingtheelectricÞeld, Ez0,andthesurface current, Jsz,whichdeÞnethesurfaceimpedance Zs=Ez0Jsz=R+j"Li,(8.126) where Liistheinternalinductanceofthewire. 188 Assumption TheconductorsareassumedtobegoodconductorsasdeÞnedbythefollowingcriteria[3, pp.149-150]: 1.!J=(c!E,i.e.conductorssatisfyOhmÕslaw, 2."'-(csothat !"!H=(c!E,and 3.$=0,i.e.thenetchargedensityiszerobecauseoftheÞrstcondition. Here (cistheconductivityoftheconductor. Assumption Webeginbyassumingthatthecurrentisuniformlydistributedonthewiresasoccurs whenthecenter-to-centerdistanceissigniÞcantlylargerthanthewireradius, s2'a2.Whenthewiresarecloseandthisconditiondoesnothold,currentdensityincreasesclos- esttoanddecreasesawayfromtheotherconductor.AmodiÞcationintheformofan effectiveradiusisprovidedaftertheinitialderivationtoaccountforthisnon-uniformden- sity. WewillÞndthesurfaceimpedanceÞrstforaunitwidthofaconductorandthenapplythis tothewiresinourproblem.Thecurrentdensityintheconductorisgivenby[3,p.151] Jz(x)=J0e#x/)e#jx/)(8.127) where xisthedepthintotheconductorand )istheskindepthoftheconductor, )=1.&fµc(c(8.128) 189 with µcbeingthepermeabilityoftheconductor.Weintegratethecurrentdensityfromthe surfacetoaninÞnitedepthtoÞndthetotalcurrentßowingpastaunitwidth. Jsz=3.0J0e#x/)e#jx/)dx(8.129) =J0)1+j(8.130) Atthesurface,theelectricÞeldisrelatedtosurfacecurrentdensityby[3,p.154] Ez0=J0(c.(8.131) SubstitutingintoEquation(8.126)gives Zs=J0/(cJ0)/(1+j)(8.132) =1+j(c)(8.133) Forthecaseofawire,thecircumference,2 &a,isusedasthewidth.Theimpedanceforonewire istherefore Zi1=Zs2&a(8.134) =1+j2&a(c).(8.135) TheskindepthcanbeexpandedusingEquation(8.128),givingtheimpedanceas Zi1=1+j2&a#"µc2(c(8.136) 190 Fortwowires,theimpedanceis2 Zi1orZi=1+j&a#"µc2(c(8.137) Asnotedintheassumptionatthebeginningofthissubsection,Equation(8.137)isforuniform currentdensity.Ifthewiresareclose(thecondition s2'a2doesnothold),aneffectivewire radius ae=a.1#(2a/s)2(8.138) shouldbeusedinplaceofthenormalradius aasgivenbyKing[75,p.30]andderivedbyCar- son[79].Theeffectiveimpedanceistherefore Zie=1+j&a#"µc2(c(1#(2a/s)2).(8.139) Theresistanceperunitlengthistherealpartof Zi(Eqn.(8.126))[75,p.18], R=1&a#"µc2(c.(8.140) for s2'a2and R=1&a#"µc2(c(1#(2a/s)2).(8.141) forcloselyspacedwires. 8.4.5SummaryofParameters Table8.1summarizestheper-unit-lengthcircuitparametersofatwo-wiretransmissionline. 191 R=1&a#"µc2(c,use ae=a.1#(2a/s)2foraifcloselyspaced(8.140and8.141,repeated) L=µ&cosh#1!s2a"(8.125,repeated) G=&(cosh#1)s2a*=&"'&&cosh#1)s2a*=&"'0'rtan )cosh#1)s2a*(8.115repeated) C=&'cosh#1)s2a*(8.106,repeated) Table8.1:Summaryofequationsforthecalculationofthecircuitparametersofatwo-wiretransmissionline. 192 Chapter9 ThreeShortCalibrationMethod 9.1Introduction Thischapterpresentsacalibrationmethodthatplacesthemeasurementreferenceplaneata pointalongthetwo-wiretransmissionlineafterabalun(discussedinlaterchapters)transitions fromthecoaxialcableusedbytestequipmenttothetwo-wiretransmissionline.Thisallows forthedeviceundertest(DUT)tobemoreaccuratelymeasuredandtheeffectsofthebalun removedfromthemeasurements.Thiscalibrationprocedurehasbeenusedinthepastfor striplinemeasurements[80]. Avectornetworkanalyzer(VNA)withcoaxialtestcablesistypicallycalibratedtothecon- nectorattheendofthecableusingasetofknown,coaxialloads(e.g.short,open,matched load).Measurementsmadeusingthistraditionalcalibrationmethodwouldincludetheeffects ofanytransitionsfromthecoaxialcabletoatwo-wiretransmissionlineandthenanyeffectsof thetwo-wiretransmissionlineuntiltheDUT. Presentedhereisaone-portcalibrationmethodthatisthenextendedtoatwo-portcalibra- tionmethod,whichmaybeusedforalmostanytransmissionstructure.Itreliesonthemea- surementofashortcircuit(actuallyanyloadwithaknownreßectioncoefÞcientcanbeused) 193 [S]a1b1S11(a)One-portnetwork [S]a1b2b1a2S21S12S11S22(b)Two-portnetwork Figure9.1:Blockdiagramsandsignalßowgraphsfor(a)aone-portnetworkand(b)atwo-portnetwork. placedatthreedifferentpositionswithrespecttoareferencepointalongthetransmissionpath. Thetransmissionstructureleadinguptothereferencepointisremovedfrommeasurements basedonthesecalibrationmeasurements. Caution Intheinterestoftakingthemostaccuratemeasurementspossible,atraditionalcoaxial calibrationisstillexpectedatthecoaxialconnectorofthebalunbecausethefollowing proceduredoesnotprovidethefullerrorcorrectionmodelthatcompensatesforallerrors inthemeasurementequipment. 9.2CalibrationTheory Aone-portnetworkisillustratedinFigure9.1aasablockdiagramandasasignalßowgraph. Theinput/outputrelationshipofaone-portnetworkisgivenby [b1]=[S11][a1].(9.1) 194 FSAG[Sm11]FSDUT GTransition DeviceUnderTest am1bm1Figure9.2:Blockdiagramshowingthetransitionthatistoberemovedandtheone-portnetworkthatistobe measured. Figure9.1bshowstheblockdiagramandthesignalßowgraphofatwo-portnetwork.The input/outputrelationshipofatwo-portnetworkisgivenby 'b1b2(='S11S12S21S22('a1a2(.(9.2) Assumption Thefollowingassumptionsaremadeinthederivationsbelowandwhenthecalibrationis applied: ¥theDUTisapassive,reciprocalnetwork; ¥thesystemisisotropic; 9.2.1One-PortCalibration Thefollowingcalibrationprocedurerecoverstheone-portS-parametersoftheDUT,S DUT ,by ÞndingsomeoftheS-parametersofthetwo-porttransition,S A.Ablockdiagramofthemea- surementsetupisshowninFigure9.2. TheconventionaldeÞnitionforthereßectioncoefÞcientis %=ba.(9.3) 195 Intheone-portcase aDUT 1=bA2,(9.4) bDUT 1=aA2;(9.5) therefore, %DUT =bDUT 1aDUT 1=aA2bA2.(9.6) Equation(9.2)forthetransitionportionofacascadednetwork,asshowninFigure9.2,cannow beexpressedas 'bA1aA2/%DUT (='SA11SA12SA21SA22('aA1aA2((9.7) Solvingthesecondrowgives a2=SA21a11/%DUT #SA22,(9.8) whichinturngives b1=a18SA11+SA12SA211/%DUT #SA229(9.9) whensubstitutedbackintotheÞrstrow. Whenthecascadednetwork(consistingofthetransition,transmissionline,andcalibration standard),ismeasured,onlyS m11canbemeasured.Inthiscase am1=aA1and bm1=bA1,therefore Sm11=SA11+SA12SA211/%DUT #SA22(9.10) 196 and 1%DUT =SA22+SA12SA21Sm11#SA11.(9.11) Therearethreeunknowns(S A11,SA22,andS A12SA21)intheaboveequation.Thesevaluesmaybe foundmathematicallybyusingthreedifferentvaluesof %DUT .Experimentallythisisdoneby measuringthreestandardswithunique,knownvaluesof %DUT .Letthesubscripts1,2,and3 denotevaluesassociatedwiththethreedifferentstandards.Thesestandardsmaybeanydevice withaknownandrepeatablereßectioncoefÞcient.Onepossiblesetofstandardsisashort circuitlocatedatthreedifferentlocationsinthetransmissionsystem,resultingin %1=#1e#j2#d1%2=#1e#j2#d2(9.12) %3=#1e#j2#d3where diisthedistancefromthenewreferenceplanetotheshortcircuit.Figure9.3illustrates acalibrationsetupforthethreedistancesasusedinthecalibrationofatwo-wiretransmission lineforthisdissertation.ThesetofreßectioncoefÞcientsinEquation(9.12)isforthecaseofan idealshortcircuit.Theaccuracyofthiscalibrationschemereliesonhowwelltheshortcircuit standard(oranystandard)canberepresentedmathematically. Caution Atthetimeofwriting,anacceptablerangeof dhadnotbeenestablished.Basedupon othercalibrationandde-embeddingtechniques,oneexpectsthat dshouldprobablybe intherangeof0 #,min /4where ,min istheshortestwavelengthinthefrequencyrangeof interest. 197 Figure9.3:Illustrationofcalibrationmeasurementsshowingthethreedifferentdistancesforaone-portcalibra- tion. SubtractingthethreeversionsofEquation(9.10)where m=1,2,or3,onegets S111#S211=SA12SA21'11/%1#SA22#11/%2#SA22(=SA12SA21'1/%2#1/%1(1/%1#SA22)(1/%2#SA22)((9.13) and S111#S311=SA12SA21'11/%1#SA22#11/%3#SA22(=SA12SA21'1/%3#1/%1(1/%1#SA22)(1/%3#SA22)(.(9.14) DividingEquation(9.13)byEquation(9.14)gives S111#S211S111#S311=,1/%2#1/%11/%3#1/%1-81/%3#SA221/%2#SA229.(9.15) 198 AfterrearrangingwecandeÞnetheconstant K=,1/%3#1/%11/%2#1/%1-8S111#S211S111#S3119=1/%3#SA221/%2#SA22.(9.16) S22forthetransitionisgivenby SA22=1/%3#K(1/%2)1#K.(9.17) OnceS A22iscomputeditmaybeusedinEquation(9.13)toÞndS A12SA21,SA12SA21=S111#S2111/%2#1/%1,1%1#SA22-,1%2#SA22-.(9.18) ReturningnowtoEquation(9.10),S A11isfoundusing SA11=S111#SA12SA211/%1#SA22.(9.19) ThereßectioncoefÞcientofasamplemaynowbefoundusingEquation(9.11). Note TheS-parametersS A12andS A21arenotfoundindividuallysinceonlytheproductofthese twoS-parametersappearinEquation9.11. Table9.1providesasummaryoftheequationsusedintheone-portcalibrationprocedure. 9.2.2Two-PortCalibration ThefollowingcalibrationprocedureisusedwhentheDUTisatwo-portdeviceasshownin Figure9.4.Sixmeasurementsareneededtoperformthiscalibration.Inthecaseofatwo-wire transmissionline,onemaybeabletopositiontheshortonlythreetimesandmeasurebothS 11andS 22.Thissavesthetechnicianfromhavingtomovethecalibrationstandardsixtimes.The 199 %i=#1e#j2#di(9.12,repeated) K=,1/%3#1/%11/%2#1/%1-8S111#S211S111#S3119=1/%3#SA221/%2#SA22(9.16,repeated) SA22=1/%3#K(1/%2)1#K(9.17,repeated) SA12SA21=S111#S2111/%2#1/%1,1%1#SA22-,1%2#SA22-(9.18,repeated) SA11=S111#SA12SA211/%1#SA22(9.19,repeated) 1%DUT =SA22+SA12SA21Sm11#SA11(9.11,repeated) Table9.1:SummaryofequationstocalculatetheS-parametersofatransitionofa1-portcalibration. [SA]FSDUT G[SB]TransitionA DeviceUnderTest TransitionB Figure9.4:Blockdiagramshowingthetransitionsthataretoberemovedandthetwo-portnetworkthatistobe measured. Figure9.5:Illustrationofcalibrationmeasurementsshowingthesixdifferentdistancesforatwo-portcalibration. 200 distancefromeachporttothestandardmustbeknownsothatthelocationofthereference planeforeachportmaybedeÞned.Aschematicofthiscalibrationprocedureanddistancesis showninFigure9.5. TodeterminetheS-parametersofTransitionA,theprocedureandequationsgiveninthe previoussectionmaybeused(seeTable9.1).TransitionBisessentiallythesameasTransitionA exceptwithindicesforports1and2interchanged.TheequationsinTable9.1maybeusedif 1and2areswitchedinalloftheequations.Table9.2providesasummaryoftheequations neededtodeterminetheS-parametersofbothtransitions. OncetheS-parametersofthetwotransitionsareknown,theS-parametersoftheDUTcan berecoveredbycomputing FTDG=FTAG#1FTCGFTBG#1(9.26) where [T]aretheT-parameters,seeAppendixA.3.Thematrix FTCGrepresentstheT-parameters fortheentirecascadedsystemasmeasuredattheVNAtestports.Relationsforconvertingbe- tweenS-parametersandT-parametersaregiveninTableA.1andreprintedhereasTable9.3. 201 TransitionA %Ai=#1e#j2#dAi(9.12,repeated) K=,1/%3#1/%11/%2#1/%1-8S111#S211S111#S3119=1/%3#SA221/%2#SA22(9.16,repeated) SA22=1/%3#K(1/%2)1#K(9.17,repeated) SA12SA21=S111#S2111/%2#1/%1,1%1#SA22-,1%2#SA22-(9.18,repeated) SA11=S111#SA12SA211/%1#SA22(9.19,repeated) 1%DUT =SA22+SA12SA21Sm11#SA11(9.11,repeated) TransitionB %Bi=#1e#j2#dBi(9.20) K=,1/%6#1/%41/%5#1/%4-8S122#S222S122#S3229=1/%6#SB111/%5#SB11(9.21) SB11=1/%6#K(1/%5)1#K(9.22) SB12SB21=S122#S2221/%5#1/%4,1%4#SB11-,1%5#SB11-(9.23) SB22=S122#SB12SB211/%4#SB11(9.24) 1%m=SB11+SB12SB21Sm22#SB22(9.25) Table9.2:SummaryofequationstocalculatetheS-parametersoftransitionsfora2-portcalibration. 202 T11=S12S21#S11S22S21T12=S11S21T21=#S22S21(9.27) T22=1S21S11=T12T22S12=T11T22#T12T21T22S21=1T22(9.28) S22=#T21T22Table9.3:RelationsbetweenS-parametersandT-parameters.ReprintofTableA.1 203 Chapter10 Double-YBalun 10.1Introduction Thisgoalofthisworkistouseatwo-wiretransmissionlineformaterialcharacterization.In ordertodothis,thetwo-wiretransmissionlinemustbeconnectedtotestequipmentthathas coaxialconnectors.Adevicecalledabalun,forbalanced-unbalanced,isusedforthisconnec- tion.Sincewewouldliketoperformmaterialcharacterizationoveralargefrequencyspan,a widebandbalunisdesired.Thischapterdescribesawidebandbaluncalledadouble-ybalun. Abalunprovidesabalancedfeedfromanunbalancedstructuretoabalancedstructure.A balancedfeedhasonlydifferential-modecurrents,meaningthatcurrentsareequalinmagni- tudebutoppositeindirection.Thisisincontrasttocommon-modecurrentsthatareequalin magnitudeanddirection.Inabalancedstructure,eachconductorhasthesameimpedance withrespecttoground.Thisisnotthecaseinunbalancedstructurewheretheimpedancesare different.Oneoftheconductorsisoftenusedasgroundinanunbalancedstructure.Sometimes thetermbalancedstructureisusedtomeanthatonlydifferential-modecurrentsarepresent whilethetermunbalancedstructureisusedtodescribeastructurewithbothdifferential-and common-modecurrents.AbalancedstructureasdeÞnedaboveisabletocarrybothcommon- 204 anddifferential-modecurrents[81,pp.1Ð4],[82,p.460].Themostcommonexampleofabal- ancedtransmissionlineisatwistedpaircablelikethosefoundintelephonecordsorethernet cables.Manyantennas,suchasdipolesandspirals,arebalancedstructures.Themostcom- monunbalancedtransmissionlineisacoaxialtransmissionlineusedforcableTVandinternet service. Thefunctionofabalunistosuppressthecommon-modecurrentswhilepassingthe differential-modecurrentbetweenbalancedandunbalancedtransmissionstructures 1.Tran- sitioningfromanunbalancedtoabalancedtransmissionlinewithoutabaluncancause common-modecurrents;therefore,abalunnotonlysuppressesbutalsodoesnotcreate common-modecurrents[82,p.460].Common-modecurrentsareunwantedbecausethey causesigniÞcantlymoreradiationwhencomparedtothesameamountofdifferential-mode current[82,p.506].Inatransmissionsystem,thisleadstolossandinterference.Inanantenna system,theradiationcausedbythecommon-modecurrentcaninterferewiththedesiredradi- atedÞeldsfromthedifferential-mode,therebyalteringtheradiationpatternoftheantenna. Tounderstandwhycommon-modecurrentsareresponsibleforalargertotalelectricÞeld, considerthecurrentsonatwo-wiretransmissionline.ThetotalelectricÞeldisthesumofthe electricÞeldfromeachindividualcurrent.Inthecaseofdifferential-modecurrents,theelec- tricÞeldsaredirectedinoppositedirectionssincethecurrentsareoppositelydirected.When added,theÞeldswillmostlycancelÑtheydonotcancelfullysincethecurrentsarenotlocated inthesamespotbutareslightlyoffset.Forcommon-modecurrents,theelectricÞeldsaredi- rectedinthesamedirectionandthereforeproduceastrongerÞeldinsteadofcanceling[82, pp.346Ð349,¤8.1]. 1Acommonargumentfortheuseofcoaxialtransmissionlinesisthattheydonotradiatecomparedtoanopen systembecausetheÞeldsarecontainedwithintheouterconductor.Thisistrueforcoaxwithnocommon-mode currents.Thedifferential-modecurrentsareontheinnerconductorandtheinsideoftheouterconductor.Ifno balunisusedwhenconnectingtoacoax,even-modecurrentscanßowonthe outside oftheouterconductor. ThesearetheÞeldsthatusuallyradiatefromacoaxandcauseinterference[82,p.460]. 205 Asecondaryfunctionofabalunistomatchimpedancesoneithersideofthebalunsince theimpedancesofeachtransmissionlineareusuallynotequal.Thecombinationofreduc- ingeven-modecurrentsandimpedancematchinghelpstoensurethatthemaximumpossible powermaybedeliveredtoaload.Balunsmaybeeithernarrowbandorwideband.Examples ofnarrowbandbalunsarechokebalunsandbazookabaluns.Widebandbalunsincludethe Marchandanddouble-ybaluns. Abalunusedforthisworkshouldbewidebandsincewewishtocharacterizeamaterialover alargefrequencyspan.Interestinwidebanddevices,includingbaluns,hasgrownsincethe FCCopenedtheradiospectrumforultra-wideband(UWB)emissionsin2002.UWBdevices typicallyoperateinthefrequencyrangeof3.1GHzÐ10.6GHz,withotherrangessetforthfor speciÞcradarandimagingsystems.AnUWBtransmitterhasa10dBfractionalbandwidthof atleast0.20orabandwidthofatleast500MHz[83,84].Researchershavelookedtodevelop devicesthatcoverthisbandwidthandhavecontinuedtoincreasetheoperationalbandwidthof baluns.Kimetal.reportedabalunoperatingfrom0.5GHzto110GHzonaGaAssubstrate[85]. Whilenotachievingsuchalargebandwidth,double-ybalunscanprovidebandwidthsthat surpassthenormalUWBfrequencyrange[86].Adouble-ybalunisaplanarstructureconsisting oftwodifferenttypesoftransmissionstructures,e.g.acoplanarstripandacoplanarwaveguide. Figure10.1illustratesthelayoutofthetransmissionstructuresinadouble-ybalun.Thetwo structuresarelaidoutend-to-end,alongacommoncenterline,onthesamelayerofacircuit board.Eachlineisforkedintoashortedandanopenedstubwherethelinesmeet.Thisfork createsaÒYÓshapeandtheabutmentofthelinesmeansthesetwoÒYÓsoverlap.Theoverlap allowsforcouplingfromonetransmissionstructuretotheother.Double-Ybalunstypically providewiderbandwidthsthanMarchandbalunsbecausethetransmissionlinestubsusedin adouble-yareclosertoidealelementsathigherfrequencieswithfewerparasitics[87].The lowerfrequencylimitofadouble-ybalunisdeterminedbythelengthofthetransitionfromthe inputtotheÒYÓsatthemiddleofthebalunwhiletheupperfrequencylimitisdeterminedby 206 Figure10.1:Illustrationofthelayoutoftransmissionstructuresinadouble-ybalun. howsmalltheÒYÓsofthebaluncanbemade.Aruleofthumbistomakethetransitionabouta quarterofawavelengthatthelowestfrequencyandtomakethestubslessthanaquarterofa wavelengthatthehighestfrequency. Double-YbalunshavebeeninvestigatedbyvariouspeopleincludingTrifunovi«cand Jokanovi«cwhoÞrstpublishedtheirworkin1991[88].Theirworkhaslookedatthecreationof thebalunsusingdifferenttransmissionstructuresincludingmicrostriplines,coplanarwaveg- uides,andslotlinesaswellasresonancesofthestructures,operationalbandwidths,andbridg- ingmethods[86,89Ð92].Venkatesanhasmorerecentlystudiedthedouble-ybalundesign.His particularworkcloselyexaminedabalunusingunbalancedcoplanarwaveguidesandbalanced coplanarstrips,bothofwhichhaveimpedancematchingtapers[81,93,94].Inhisdisserta- tion[81],Venkatesanhasaverygood,moderndiscussionofbalunsandthedouble-ybalunin particular.AppendixGinthisworkcontainsexcerptsfromtheauthorÕslaboratorynotebook coveringtheinitialresearchandworkonthebalundesign. 10.2DesignOverview Thedouble-ybalundesigncanbeusedwithvarioustransmissionlinestructures.Manufactur- ingcapabilitiesandlimitationsdictatedselectionofthetransmissionstructuresforthisdisser- tation.In-housemillingbytheElectricalandComputerEngineering(ECE)shopwasselectedas themanufacturingmethodduetobetteravailabilityandturnaroundtimecomparedtoetch- ing.Aone-sidedbalunwasdesiredbecausealignmenterrorsbetweenlayerscouldoccurwhen millingadouble-sidedboard.ToÞtthisrequirement,acoplanarstrip(CPS)andaÞnite-width 207 CPW'rhabcCPS'rab2c2b2agWSWg'rh2b2aWSW'rFigure10.2:SchematicofCPWandCPSlineswithcommondimensions. Figure10.3:ACPWtoCPSdouble-ybalun. ground-planecoplanarwaveguide(CPW)wereselected.ACPSisabalancedlinetowhicha two-wiretransmissionlinecanbeconnectedandtheCPWisanunbalancedtransmissionline towhichaSMAconnectorcanbeconnected.Figure10.2isadiagramshowingexamplesof CPWandCPSlinesannotatedwithcommonnotationsfordimensions;Figure10.3showsa CPW-to-CPSdouble-ybalun. 208 Caution InorderfortheCPWtobehaveasdesired,thetwogroundplane(traces)mustbekeptat thesamepotential.Thisisaccomplishedusingairbridgeswhichareessentiallyjumper wiresthatbridgethecenterconductorandconnectthetwogroundplanes.Thisensures thatthecurrentsoneachgroundplanearematchedandaproperchangefromunbal- ancedtobalancedcanoccur.Theuseanddiscussionofairbridgesisnotcoveredinmany ofthereferencesandinsteadtheyareusuallymentionedinpassing.Section10.7discusses airbridgesmore. Note Thegroundplaneoneithersideofthecenterconductoriscomparableinwidthtothe centerconductor.AtrueCPWhasgroundplanesthataresigniÞcantlylargerthanthecen- terconductor.TheCPWimplementedhereiscalledaÞnite-width-ground-planecoplanar waveguide;however,itisreferredtoasaCPWforbrevity. Thankyou... Thebalunwasmadeonasingle-sided,FR-4boardmaterialasthiswasreadilyfabricated byECEshop. TheECEShopusuallymillscircuitboardsoutof60mil-thick,FR-4boardwith1oz/sq.ft copper(correspondstoathicknessof34.1 µm(1.34mil))onbothsides.FR-4hasaspeciÞed relativepermittivityof 'r=4.4andalosstangentoftan )=0.02;however,thesevaluescanvary frombatchtobatchandmanufacturertomanufacturer.Theminimumwidthofatraceforthe ECEShopmillingprocessis0.20mmÐ0.25mm(8milÐ10mil)andtheminimumwidthofagap is0.3mm(12mil).Theshopnotesthattracesnearthisminimumwidthareeasilyliftedoff thesubstrate,especiallywiththeapplicationofheat.Careshouldbeexercisedwhensoldering suchtraces.Alignmentofthetopandbottomtracesisestimatedtobearound10milduetothe ßippingoftheboard.Viascanbedrilledbytheshop,buttheyarenotplated.Becauseoftop-to- bottommis-alignmentandunplatedvias,asingle-sidedbalundesignwassoughtforthiswork 209 andthedouble-ywasagoodmatchforthis.Theneedforwirebondswasdiscoveredafterthe balundesignhadbeenselectedandsomedesignworkhadbeendone. Ifthebalunismanufacturedthroughaboardhousethatcanperformviaswork,itmaybe worthwhiletoinvestigateothertypesofbalun,suchasamicrostrip-to-slotlineormicrostrip- to-CPWbalun,thatcanimprovebandwidthand/orlowerlosses.The EncyclopediaofRFand MicrowaveEngineering [87]offerssummariesofdifferenttypes.Theworkpresentedin[95Ð97] isworthreviewingaswell. Thebalunforthisdissertationwasdesignedtomeetthefollowingcriteria: ¥wideband ¥easilyfabricated, ¥lowcost,and ¥durable. Thisworkrequiredabalunwithaslargeabandwidthaspossibleandalowcutofffrequency. AcutofffrequencyinthehundredsofmegaHertzwasdesirablebecausetheexpectedplasma frequencyoftheÞre-inducedplasmawasbetween500MHzand1GHz.Theupperfrequency wasdeterminedtobeatleast6GHzinordertobeabletousethefullbandwidthoftheHP8753D networkanalyzer. Thefollowingstepswereneededtosynthesizeadesign: ¥Determinecoplanarstripline(CPS)andcoplanarwaveguide(CPW)designequations. ¥ProgramandverifyCPSandCPWdesignequations. ¥ProgramanoptimizationroutinetomatchimpedancesofCPSsandCPWsgivencertain constraints. 210 10.3CPSandCPWDesignEquations TodesigntheCPSandCPWtransmissionstructuresusedonthebalun,theimpedancewas needed.TheCPWneededtomatcha50 "coaxialcableconnector.TheCPSneededtomatch theimpedanceofthetwo-wiretransmissionline.Theimpedanceofthetwo-wiretransmis- sionlineiscalculatedusingtheequationspresentedinSection8.4.Bothstructureshadtobe transitionedtothesameimpedanceatthecenterofthebalun.Thefollowingequationswere usedtocalculatetheimpedancesandcreatethebalundesign.Theequationspresentedhere arefrom MicrostripLinesandSlotlines .Therearethreeeditionsofthisbookatthetimeof writing.K.C.Guptawasanauthorofthe1979[98]and1996[99]editionsbutnotthethirdin 2013[100].Someequationnumbershavechangedbetweenallthreeversions.Equationsbelow aretakenfromthe2 ndedition[99].Thebasicdimensionsusedforcalculationsaredenotedin theschematicinFigure10.2. 10.3.1CoplanarStrip TheimpedanceofasymmetricCPSwithÞnitedielectricthicknessis[99,(7.75)] Zo,cps =120 &4'cps reK(k1)K&(k1).(10.1) Here 'cps reistheeffectiverelative-permittivityofaCPSwith h/b>1givenby[99,(7.17)] 'cps re=1+'r#12K(k2)K&(k2)K&(k1)K(k1),(10.2) where k1isgivenby[99,(7.7)] k1=ab=SS+2W(10.3) 211 (notethat a,=Sbut2 a=S,likewise2 b=S+2W),and k2isgivenby[99,(7.16)] k2=sinh( &a/2h)sinh( &b/2h).(10.4) Theparameter Sisthegapbetweenthestrips,and Wisthewidthofthestrip(Figure10.2).The functions K(k)and K&(k)arethecompleteellipticintegralsoftheÞrstkindanditscomplement, respectively, K&(k)=K!.1#k2"=K(k&).(10.5) 10.3.2CoplanarWaveguide TheimpedanceofaCPWwithaÞnite-widthground-planeis[99,(7.29)] Zo,cpw =30&4'cpw reK&(k3)K(k3).(10.6) Here 'cpw reistherelativepermittivityforaCPWgivenby[99,(7.28)] 'cpw re=1+'r#12K(k4)K&(k4)K&(k3)K(k3),(10.7) where k3isgivenby[99,(7.23)] k3=ab&1#b2/c21#a2/c2(10.8) 212 (notethat a,=Sbut2 a=S,likewise2 b=S+2W,and2 c=S+2W+2g),and k4isgivenby[99, (7.27)] k4=sinh( &a/2h)sinh( &b/2h)&1#sinh2(&b/2h)/sinh 2(&c/2h)1#sinh2(&a/2h)/sinh 2(&c/2h).(10.9) Theparameter Sisthewidthofthecenterconductor, Wisthewidthofthegap, gisthewidth ofthegroundstrip(seeFigure10.2),and Kand K&arethecompleteellipticintegralsoftheÞrst kindanditscomplement,respectively, K&(k)=K!.1#k2"=K(k&).(10.10) 10.4DesignSoftwareTools AnIPythonnotebookwasusedtodesignthedouble-ybalun.ItisreproducedinAppendixP 2.Toaidinreadingtheoutputdesign,thenotebookcandisplaythedesigninaformatsimilarto Figure10.4whichusesthecommonnotationdeÞnedinFigure10.2. Asindicatedinthenotebook,theprimaryreferencesusedincludedtheÞrstandsecond editionsof MicrostripLinesandSlotlines [98,99],JaikrishnaVenkatesanÕsPhDdissertation[81], and CoplanarWaveguideCircuits,Components,andSystems [101].Otherimportantresources includethe EncyclopediaofRFandMicrowaveEngineering [87]andtheonlinecalculatorspro- videdat http://www1.sphere.ne.jp/i-lab/ilab/index_e.htm [102].Othermaterialused indevelopingthebalunmaybefoundin[85,86,89,91Ð93,103Ð116]. 2ThenotebookwasrunusingSciPy0.11.0andNumPy1.6.1.Thisisbecausecertainminimizationroutinesare notincludedinearlierversionsofSciPy.Therewereproblemsingettingthenotebooktorunusinglaterversions ofSciPyandNumPy,sotheintermediate(intermsofage)versionswereused.TherewillprobablybesigniÞcantly newerversionsbythetimethisscriptgetsusedagain. 213 |-----------------2c------------------| |-----------2b------------| |---2a----||--g--|---W---|----S----|---W---|--g--| ___________________ ____|_____|_______|_________|_______|_____|_______ |\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\|| |\\\\\\\\\\\\\\\\\\\\eps_r\\\\\\\\\\\\\\\\\\\|h |\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\|| -------------------------------------------------- CoplanarWaveguide(cpw) |-------------2b--------------| |---2a----||----W----|----S----|----W----| __________________ ________|_________|_________|_________|___________ |\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\|| |\\\\\\\\\\\\\\\\\\\\eps_r\\\\\\\\\\\\\\\\\\\|h |\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\|| -------------------------------------------------- CoplanarStrips(cps) Figure10.4:SampleoutputfromtheIPythondesignnotebookusedtoassistinconveyingtheoptimizeddesign.. 214 10.5BalunHolder DuringtestingoftheÞrstbalundesigns,itwascommonforthecoppertracestoliftoffofthe board.Thiswascausedbymechanicalstressfromthefollowingitems: ¥ImproperinstallationofSMAconnectors TheSMAconnectorsusedintheinitialboarddesignshadtabsthatextendedaboveand belowtheboard.Theyareintendedtoprovidemechanicalsupporttotheboardaswell asenhancecouplingofthesignaltotheboard.Thetabsonthetopoftheconnectorwere removedfortheinitialprototypebecausetheboardswerethickerthanthespacebetween thetabs.Forlaterprototypes,properlysizedconnectorswerepurchased. ¥Unsolderingofconnectors SMAconnectorswerelimitedinquantitywhentheÞrstprototypeswerefabricated.The connectorswereunsolderedandmovedfromboardtoboard.Theheatofsolderingand thetorqueinadvertentlyappliedwouldsometimescausethetracestoliftoffoftheboard. ¥Cablestresses Cablesattachedtotheboardmechanicallystresstheboard,connectors,andtracesto whichtheconnectorsaresoldered.ASMAconnectorthatproperlyÞtstheboardshould compensateforstressesnormallyobservedinthelaboratorywithoutcausingcopper tracestoliftofftheboard.SinceinitialprototypesusedmodiÞedconnectors,theseca- blestressesimpactedtheprototypetraces. ¥Two-wiretransmissionline Thetwo-wiretransmissionlinethatwasattachedtothecircuitboardwasmadeofmetal rods.Thesewereoftenunsupportedwhichcausedstressonthetracesanddamaged some. 215 Aholderwascreatedtorelievethesestresses.TheÞnaldesignalsokeepsthecablesinplace duringcalibrationandelevatesthecircuitboardawayfromothermaterialswhichcouldinter- ferewiththeÞelds,i.e.ametalbenchtop. Furthermore,theholderhelpedwiththespacingofthetwo-wiretransmissionlinetoensure theimpedancematchedthedesignimpedance.Ajigwasusedtoproperlyspacetherodswhen solderingthemtotheboard.Becauseofthelengthsoftherods,however,therodsmayßexand thespacingcanchangeawayfromtheboardaftertherodsaresolderedandthejigremoved. Theholderensurestheproperspacingneartheboardforabettertransition. Figures10.5through10.10aredimensionaldrawingsoftheholder.Figure7.23showspic- turesoftheholder.Theholderwasdesignedtoallowforchangesinpositionandsize.Various lengths,widths,andthicknessesofcircuitboardareaccommodatedbytheadjustableclamp. Theelevationofthecircuitboardcanbechangedtoallowforthetwo-wiretransmissionlineto beproperlyaligned.Acableclampadjusttokeepthecablesofvariousdiametersin-linewith theboardaswellaskeepingthecableinthesameplaceforcalibrations.ApieceofPlexiglas wasbenttocreatethebaseandthesideoftheholder.Holesforthestandoffsandtwo-wire transmissionlineweredrilledbothbeforeandafterbending.Ifthemanufacturercancontrol thepreciselocationandradiusofthebend,thentheholesforthetwo-wiretransmissionline canbeproperlylocatedanddrilledbeforebending.ThismakesdrillingsigniÞcantlyeasier. Whentheholderwasused,mechanicalstresseswerereducedandmeasurementswereeasier toperformcomparedtoexperimentsthatdidnotusetheholder. 216 Figure10.5:Assemblydrawingforthebalunsupportstructure. 217 Figure10.6:DrawingforthemainPlexiglassupportstructure. 218 Figure10.7:Drawingformanufacturingashortingplate. 219 Figure10.8:Drawingshowingcriticaldimensionsforsamples. 220 Figure10.9:DrawingsforplasticpiecesthatclampthecablewhenitÞrstenterstheholder. 221 Figure10.10:Drawingforthepiecesthatclampthecircuitboard. 222 10.6High-TemperatureModiÞcations 10.6.1DesignModiÞcations Theoriginalmotivationforthebalunandtwo-wiretransmissionlinewereforbench-topßame experiments.Thetwo-wiretransmissionlinewouldbeplacedaboveafuelsourcesothatthe burningßamewouldburnbetweenandaroundthetwowires,allowingformaterialmeasure- mentstobemade.ThematerialsanddesignoftheaboveprototypeneededtobemodiÞedto withstandthehightemperaturesofaßame. Apieceof1/4inthickGarolitewaspurchasedfromMcMaster-Carr(No.8557K232Flame- RetardantGarolite(G-10/FR4),1/4ÓThick,2ÓWidth,2ÕLength).Garolite,alsocalledFR-4,was selectedbecauseitisrigid,non-metalic,easilymachined,andcanwithstandtheexpectedtem- peratures. Thankyou... RoxannePeacocktookcareofthisorderandalloftheotherordersforthisdissertation! Prototypebalunsandinitialexperimentswerecarriedoutusingcopperorsteelrodswhile tungstenwasselectedforÞreexperiments.Ashortliteraturesearchfoundthatplatingthetung- stenwithcopperistheeasiestwaytosoldertoatungstenrod[117Ð119].Chackett etal. provide themostcompleteinstructions[117]. Firstthetungstenrodshouldbecleaned.Chackett etal. suggestplacingthetungstenintoa sodiumhydroxidesolution(Ò5%causticsodasolution[117]Ó)andapplyingavoltageof12Vand currentof1Aforafewminutes.Thetungstenservesastheanodeandthecathodeshouldbe nickel.Thisisthenfurtherelectrolyticallywashedinnitricacidforafewminuteswiththepolar- izationswitchedoccasionally.Aftercleaning,copperiselectro-depositedforabout10minutes fromcoppersulfateusing2Vand10Ð20mA/cm 2.Chackett etal. suggestacoppersulfatecon- centrateof10gCuSO 4per100mlsolution.Thetimesandcurrentsusedarenotnecessarily optimalasnotedbyChackettetal.. 223 Thankyou... BrianWrightassistedmeinplatingtheendsof1/8indiameterby12inlongtung- stenweldingrodsobtainedfromDiamondGroundProducts(partnumberPT-1/8-12).A Caswellcopperelectroplatingkitwasusedthattheshopalreadyhad. ThestandardtungstenweldingrodfromDiamondGroundProductsis7inlongandhasthe endsmarkedwithgreenpaint.The1/8indiameterrodhasatoleranceof ±0.003inwhiletighter tolerancesmaybespecialordered.AcompanyrepresentativeinApril2014saiditwasnotun- commonforthemtohave12inandlongerlengthstockavailable,possiblyupto48in.Stan- dardqualityelectrodescomefromChinesemanufactureswhileDiamondGroundProductsÕ premiumelectrodesarefromaGermansupplier.Thegreenpaintisusedtoindicatethetypeof electrode.DiamondGroundProductsisablesupplyelectrodeswithorwithoutthepaint;the rodsusedforthisworkwereun-painted. Afterplating,Chackettetal.suggesttestingthecopperbyrubbingitwithoneÕsÞnger.In ourcase,thecopperremainedonthetungstenrodwhenrubbed;however,thecoppercame offwhenscratchedwithaÞngernailorothersharpobject.Afterbeingsolderedtothecircuit board,thecopperwasmoreÞrmlyafÞxedtothesolderandcoppertracethantothetungsten rod.Becauseofthemechanicaladvantagegivenbythelongrod,theplatingwouldberemoved iftherodwaspivotedawayfromtheboard.Thiswouldbeacommonissueinalaboratory setupbecausethesamplecausesadownwardforceattheendofthetwowireswhichwould liftthemawayfromtheboardÑanexampleofthisisseeninFigure10.11forabalunwithcop- perrods.Theplatingwouldholdtherod,however,whentheroadwasroatedaboutitscenter axis.Solderingwaseasilyaccomplishedandbehavedlikesolderingcoppertocopperaswould beexpected.Apossiblewaytoimprovetheadhesionwouldbetosolder(actuallyjusttin)the tungstenwithcopperandthensolderthecoppertothecircuitboard.PetruninandGrzhi- malÕskiiusedasolderingtemperatureof1120¡C[119]tosoldertungstenusingcopper.Plating wasusedherebecauseofresourceavailability. 224 Figure10.11:Anexampleofthemetalrodsliftingthetracesoffofthebalun. 10.6.2HeatTransferAnalysis Therewasalsoconcernthatthesolderbetweenthewiresandthebaluncouldmeltifheatfrom theßametraveleddownthewire.WecantreatthewireasaÞndesignedtodissipateheatto thesurroundingenvironmentinordertoÞndthetemperatureatthesolderjunction.Agood, introductoryreferencetoÞndesignisSection4.5of AHeatTransferTextbook byLienhardand Lienhard[120]whichisavailableforfreeonlineaspartoftheMITOpenCoursewareInterme- diateHeatandMassTransferclass[121].AppendixQisanIPythonnotebookusedtoperform thecalculations.Thetemperatureofthewireatthetipwasestimatedtogiveamaximumtem- peraturethatthesolderjunctioncouldreach.Therearevariousassumptionsandlimitstothis estimate;however,theseallpushtheresulttothehighside. Iassumedthatthewirewas2000¡Catthepointoftheßamethatwasplacedhalfwaydown thelengthofwire,andthatthetemperatureofthesurroundingroomwas25¡C.TheÞrstcalcu- lationsweredoneforwiresinsteadofrodsbecausetheinitialtwo-wiretransmissionlinedesign wastousewires.A45%copperand55%tungsten,20AWGwirewithathermalconductivity of2.4W/(cm¡C)wasused.AheattransfercoefÞcientforairof20W/(m 2¡C)wasused.The 225 Figure10.12:Temperatureatthetipofa20AWG,copper/tungstenwireversusthedistancefromtheßametothe tip. temperatureatthetipforthislong,thingwirewasfoundtobealmost25¡C.Figure10.12shows thetiptemperatureversuswirehalf-length(distancefromßametotip). Wecanseethatforthisgaugewire,thesolderjunctionwouldreachanacceptablelevel veryquickly.Solderusuallymeltssomewherebelow,butaround,200¡C.Weseethatthetip temperaturereachesthispointfora0.3mwireandreaches100¡Cforalengthofabout0.4m. Ifashorterlengthtransmissionsystemisdesired,asolderwithahighermeltingpointcouldbe used. Theimplementedcalculationsrelyonapproximationsthatcanbemadefor mL05.This conditiondoesnotholdforthetungstenweldingrodsobtained.Thecalculationsshouldbere- writtentousetheexactformoftheequationsinsteadofapproximationsandthentheproblem re-analyzedforthecorrectsizedrods. 226 Figure10.13:Positioningoftheairbridges(blacklines)atthecenterofthebalun. 10.7AffectsofAirBridges Asnotedearlier,airbridgesareimportanttoensurethecorrectelectrical-currentbehavior onthebalun.Thisgreatlyaffectstheperformanceofthebalunwithregardstosuppressing common-modecurrentsandreducingradiation. Theseairbridgescanbesmalljumperwires,wirebonds,ribbonbonds,ormoresigniÞcant metalconnections.Itisespeciallyimportanttouseairbridgeswherethetwolinescometo- getheratthecenterofthebalun.Thejumpersshouldbeasclosetothegapaspossiblesince thisiswheretheÞeldsareconcentrated.Figure10.13showsthepositioningoftheairbridges atthecenterofthebalun. Airbridgeswereimplementedusingtwodifferentmethods.TheÞrstwastodrillthru-holes asclosetotheoutsideedgeofthegroundplanesaspossible.Whilethejumpersshouldbeclose tothecenteredgeofthegroundplane,theholesweredrilledontheoutsidesoasnottodamage thetraces.A30AWGwirewaspassedthroughtheholesandacrossthebacksideoftheboard. Thewirewassolderedtothegroundplanewiththesoldernormallywickingacrosstheentire widthofthegroundplane. Thepreferredair-bridgemethodistousewirebonds.Notesfromthisprocedureincluding instrumentsettingsandmodelnumberappearonpages78and79oftheauthorÕslaboratory notebooknumber00011inAppendixG. 227 Figure10.14:Experimentalsetupsimilartothatusedformeasuringtheeffectivenessofairbridges. Thelaptop controllingthemeasurementispartiallyvisibleatthetop-left.BelowthelaptopistheHP8753DVNAthatisper- formingthemeasurements.Onebalunisdirectlyattachedtoport1oftheVNAwhileport2isconnectedviaashort cabletotheotherbalun.Thebalunsystemissupportedbyfoamblocks.Forthemeasurementspresentedinthis section,onlythebalunontheright(port2)wassupported. Thankyou... RafmagCabreraandDr.NelsonSepœlvedaassistedmeinplacingthesewirebonds. 10.7.1FullTwo-wiretransmissionlineSystem Toevaluatetheperformanceanddemonstratethenecessityoftheairbridges,measurements weretakenbefore,during,andaftertheairbridgeswereplacedonthebalunformanyofthe boards.Thesemeasurementscouldnotbedoneforthebalunswithwirebondsbecausethe networkanalyzerandwirebondingmachinewereindifferentbuildings.Anexamplemea- surementsetupisshowninFigure10.14.Themeasurementsofonesystemthatconsistedof 228 twobalunsconnectedbyasteel,two-wiretransmissionlinearepresentedinthissection.Fig- ure10.15showsthebalunasitwasbeingmeasured.Thesystemmeasurementsareshownin Figures10.17through10.22.TheSMAconnectorsweresolderedontotheboardsÞrstandthe two-wiretransmissionlineconnectedbetweenthebaluns.Thefulltwo-portS-parametersof thesystemwerethenmeasured(Figure10.15aandFigure10.17).Next,theairbridgesnearthe centerÒYÓswereinstallandthesystemre-measured(Figure10.18).Theremainingairbridges werethenaddedalongthelengthoftheCPWÕs(Figure10.15b,Figure10.15c,Figure10.19).No speciÞcinformationabouttheairbridgespacingwasfoundinthepreviouslyreferencedliter- aturesotheairbridgeswereplacedapproximately250milapartforatotaloftenairbridges alongthetaper.FinallythepowerbalanceofthesystemisshowninFigure10.22whennoair bridges,onlyÒYÓs,andallbridgeswereinstalled. 229 (a)Measuringwithnoairbridges. (b)Measuringwithallairbridgesplaces. (c)Viewoftheairbridgesfromthebottomofthebalun. Figure10.15:Measurementsetuptotesttheairbridges. 230 (a)Balunwithnoairbridges. (b)Balunwithallairbridgesinstalled. (c)Bottomviewofallairbridgesinstalled Figure10.16:Zoomed-inviewoftherightbalunfromFigure10.15. 231 Figure10.17:Two-wiretransmissionlinesystemS-parameterswithnoairbridgesinstalled. NocurveforS 12(red) isvisiblebecauseS 21(green)coversit. 232 Figure10.18:Two-wiretransmissionlinesystemS-parameterswithairbridgesinstalledonlyattheÒYÓs. Nocurve forS 12(red)isvisiblebecauseS 21(green)coversit. 233 Figure10.19:Two-wiretransmissionlinesystemS-parameterswithallairbridgesinstalled. NocurveforS 12(red) isvisiblebecauseS 21(green)coversit. 234 Figure10.20:Reßectionmeasurement(S 11)ofatwo-wiretransmissionlinesystemwithvariousairbridgesin- stalled. 235 Figure10.21:Transmissionmeasurement(S 21)ofatwo-wiretransmissionlinesystemwithvariousairbridges installed. 236 Figure10.22:Powerbalanceforatwo-wiretransmissionlinesystemwithvariousairbridgesinstalled. Powerlosses increaseasthepowerbalancedecreasestowardszero. 237 Weseethatsystemperformanceisimprovedwhenairbridgesareinstalled,evenifonlyat theÒYÓs.First,considerFigure10.22.Apowerbalanceequaltoonemeansthatallpowersent outoftheVNAisreturnedtoitthrougheitherport.Asthepowerbalancedecreasestowards zero,moreandmorepowerislostsomewhereinthesystem.Forthecurrentsystemdesign, powerlossismostlikelyduetoradiation.Ohmiclossesarelikelypresentbecauseofthetwo- wiretransmissionlinebeingmadeofsteelinthesemeasurements;however,theoverallbehav- iorofthepowerbalancesuggestsradiationasthemainlossfactor.Forexample,weseeareas thatareverylossy,e.g.around3GHz,wherethepowerlossdecreaseasairbridgesareinstalled. Thissuggeststhattheairbridgesarealteringthecurrentsandhelpingtoreducecommonmode currentsandtherebyradiation.WenotefromFigure10.22thattheÞrstinstalledairbridgescre- ateneworshiftexistingareasofhighloss.Theseareas,however,aremorenarrow-bandedthan whennoairbridgeswereinstalled.Oncealloftheairbridgesareinstalled,theseareasofloss aresmoothedout.Weseeafairlylinearpowerlossnowthatincreases(downwardslope)with frequency.Thissuggeststhatthetwo-wiretransmissionlineitselfisradiatingcombinedwith someamountofohmiclosses. ThesameanalysiscanbemadeusingeitherFigure10.20or10.21.InthecaseofS 11,less powerisreßectedbacktoport1astheairbridgesareinstalled.Thismeansthatmorepoweris transferredintothebalunsystem.ThechangeinS 21showsthatmorepowermakesitthrough thebalunsystemasairbridgesareinstalled. 10.7.2Back-to-BackBalun Inadditiontothetwo-wiretransmissionlinesystemmeasuredintheprevioussection,two balunsweremanufacturedback-to-backasoneunitwiththeCPStracesconnectedasshownin Figure10.23.Thisremovesthetwo-wiretransmissionlinefromthesystemandonlymeasures thebalunperformance.Asinthelastsection,thebalunwasmeasuredbeforeanyairbridges wereinstalled,whenonlytheÒYÓswereinstalled,andafterallairbridgeswereinstalled.Air 238 (a)Frontsideoftheback-to-backbalun. (b)Backsideoftheback-to-backbalun. Figure10.23:Back-to-backbalunwithallairbridgesinstalled. bridgeswereinstalledusingthesameprocedureasthelastsection.Figures10.24through10.29 showtheresultsofthesemeasurements.Weagainseethattheairbridgesimprovesystemper- formance. Figure10.30showsthepowerbalanceforthefulltwo-wiretransmissionlinesystemmea- suredinthelastsectionandtheback-to-backbalunofthissection.Acrossalmosttheentirefre- quencybandtheback-to-backbalunhaslesslossthanthetwo-wiretransmissionlinesystem. Thissuggeststhattheactualtransmissionlinescontributesomelosses,presumablythrough radiationandohmiclosses.Onlyonemeasurementofeachdevicewastaken,therefore,addi- tionalmeasurementswouldhelptodeterminemoreaccuratelyhowthelossesofthedevices compare. 239 Figure10.24:Back-to-backbalunS-parameterswithnoairbridgesinstalled. NocurveforS 12(red)isvisiblebecause S21(green)coversit. 240 Figure10.25:Back-to-backbalunS-parameterswithairbridgesinstalledonlyattheÒYÓs. NocurveforS 12(red)is visiblebecauseS 21(green)coversit. 241 Figure10.26:Back-to-backbalunS-parameterswithallairbridgesinstalled. NocurveforS 12(red)isvisiblebecause S21(green)coversit. 242 Figure10.27:Reßectionmeasurement(S 11)ofaback-to-backbalunwithvariousairbridgesinstalled. 243 Figure10.28:Transmissionmeasurement(S 21)ofaback-to-backbalunwithvariousairbridgesinstalled. 244 Figure10.29:Powerbalanceforaback-to-backbalunwithvariousairbridgesinstalled. Powerlossesincreaseasthe powerbalancedecreasestowardszero. 245 Figure10.30:Powerbalanceofallairbridgesinstallforthetransmissionlinesystemandtheback-to-backbalun. 246 10.7.3Summary Insummary,themeasurementsshowthatevenaddingairbridgesattheÒYÓsimprovethesys- temfromsomethingthatisessentiallyunusableduetoanunpredictableresponsetoareason- ableperformingsystem.Byinstallingalloftheairbridges,thesystemresponseisimproved evenmore. 10.8FinalBalunDesign Duringthedesignprocess,thebalundesignwasiteratedthroughthreedesigns.Allthreede- signsareshowninFigure10.31.Weseethatsomeofthetracesareliftedofftheboards.Also seenonmostoftheboardsarereferencemarksforthesolderjointsoftheairbridges.Onthese boards,theairbridgesarejumperwiressolderedonthebacksideoftheboardasnotedearlier inthechapter. TheÞnaldouble-ybalundesignhasthefollowingcharacteristicsanddimensionswhichare alsoillustratedinFigures10.32Ñ10.35: ¥TheSMAconnectorattachestoaCPWthathasa154.11milcenterconductor,a12mil gap,and125milgroundtraces.ThisCPWis250millongfromtheedgeoftheboardto thestartofthetaper. ¥Overalengthof2500mil,theCPWtapersdowntoacenterconductorof10.31milin width,agapof17.09mil,and10milgroundtraces.Thetaperisonalledgesofthetraces andusesthefollowingequation: x(y)=x0,xfx0-y/len (10.11) 247 Figure10.31:Manufactureddouble-ybaluns. 248 where yisthelineardistancealongthecenter-lineofthetaper(notthetapercurveitself), xisthedistanceawayfromabaseline, x0isthestartingdistancefromthebaseline, xfistheÞnaldistancefromthebaseline,and len isthetotallinearlengthofthetaper. ¥FromtheendofthetapertothecenteroftheÒYÓis300mil.TheCPWsplitsintotwo, 105millongstubs.Thestubsareßared45 )awayfromthecenterlineoftheCPW. ¥TheCPSßaresatthesamepointintostubsatthesameangleandofthesamelengthas theCPW.Thecentergaphasawidthof15.23milandtraceshavewidthsof24.63mil. ¥A300milCPSgoesfromthecenteroftheÒYÓtothebeginningofthetaper. ¥TheCPStaperfollowsEquation(10.11)overalengthof1500mil. ¥TheÞnalgapofthetaperis125milwith149.724milwidetraces. ¥Thereisa75milstraightsectiontowhichthetwo-wiretransmissionlineissoldered. TheÞleversioningsystemGitwasusedtotrackthedevelopmentofthisdesign.Thisdesignis referredtoas 0d96092becausethiswasthehashofthedesignÞleinGit. 249 Figure10.32:Double-Ydimensionaldrawing,page1. 250 Figure10.33:Double-Ydimensionaldrawing,page2. 251 Figure10.34:Double-Ydimensionaldrawing,page3. 252 EndsofBalun 'r60125 12154.11 'r149.724 125 MiddleofBalun 1017.09 10.31 'r6024.63 15.23 'rUNITS:mils ÑNottoScaleÑ Figure10.35:CPWandCPSdimensionsfortheÞnaldouble-ybalundesign. 253 Chapter11 Bench-ScaleExperimentResults Twoexperimentsarepresentedinthischaptertodemonstratehowatwo-wiretransmission linemaybeusedformaterialcharacterizationandhowthecalibrationprocessfromChap- ter9isused.First,asampleofpolyoxymethylene(POM,manufacturedbyDuPontunderthe nameDelrin)wasmeasuredalongwithashortcircuitinfourdifferentpositions.Second,the two-wiretransmissionlinewasplacedverticallyintoabeaker.Asdistilledwaterwasadded, measurementsweretaken.Theseexperimentsservetodemonstratesolidandliquidmaterial measurements. 11.1SolidMaterialMeasurement Forthisexperiment,a12.9mmthickpieceofPOMwasplacedontothetwo-wiretransmission linewithfoamoneithersideofthesample.Onepieceoffoamwascompressedbetweenthe PlexiglasholderandthePOMsamplewhiletheotherfoampiecewascompressedbetweenthe shortcircuitandthesample.ThebalunusedwasthesameasinSection10.7withsteelrods. ThisexperimentalsetupisshowninFigure11.1a.Thephotosinthissectionarefromanearlier experimentthanthedatabecausenophotosweretakenatthesametimeasthedata. 254 (a)MaterialmeasurementofaPOMsample. (b)Threeshortcalibrationsetup. Anexamplesetupshowingtheshortcircuitplacedonatwo-wiretransmission linewithapieceoffoamusedasaspacer. Figure11.1:Two-wiretransmissionlineexperimentalsetups. 255 Figure11.2:Foamspacersusedincalibrationmeasurements. Thenumberswrittenonthespacersarethethick- nessesinmillimetersofthefoamwhennotcompressed.Thedistanceusedincalculationswasmeasuredafterthe foamwasinstalledandcompressed. Table11.1:Foaminsertlabelsandthicknesses. Thetableisarrangedbythicknessandnotalphabetically.Itjust happenedthatIwasthinnerthanHandthetableorderisnotanerror. LabelThickness/ mmF5.9 G9.7 I13.6 H17.7 11.1.1Calibration BeforethePOMsamplecouldbemeasured,thetwo-wiretransmissionlinesystemneededtobe calibrated.Thecalibrationprocedurerequiresthatthreemeasurementsbemadeofaloadwith aknownreßectioncoefÞcient.AnidealshortcircuithasareßectioncoefÞcientwithmagnitude equaltooneandaphaseshiftproportionaltotheelectricallengthofthetransmissionline. Forthisexperiment,ashortcircuitwasmeasuredinfourdifferentpositionssothatthreemea- surementscouldbeusedtocalibratethefourthmeasurementinordertocheckperformance. Piecesoffoam(Figure11.2)wereusedasspacersbetweenthePlexiglasbalunholderandthe shortcircuit(Figure11.3)asshowninFigure11.1b.Foamwaschosenbecauseithasarela- tivepermittivityclosetoonesoitapproximatesairinelectromagneticexperiments.Table11.1 showsthelabelsforthepiecesoffoamandthethicknessofeachpiecewhenitwascompressed intheexperimentalsetup.Theone-portS-parametersoftheshortcircuitinthefourdifferent positionsareshowninFigure11.4. 256 Figure11.3:Shortcircuitbuiltforthetwo-wiretransmissionline. Coppertapehasbeenaddedinanattemptto removeairgapsbetweenthetwo-wiretransmissionlineandtheshortcircuitblock. Asthefoamthicknessincreases,theshortcircuitismovedfurtherdowntheline.This increasesthedistancethatawavetravelsalongthetransmissionlineandtherelativephase changeofthewaveincreases.Numericallytheslopeofthephasebecomesmorenegativeas distanceincreases.WeobservethistrendinFigure11.4whichmeansthatthemeasurements arereasonable. Totestthecalibration,threeofthefourmeasurementswereusedtocalibratethefourth measurement.FoamspacersF,G,andHwereusedasstandardsandthesampledatawasfor thefoamspacerI.Theoriginalsampledataset,thecorrecteddata,andatheoreticalcurveare showninFigure11.5.Weseethattheoriginalsampleismuchlongerelectricallybecausethe phasewrapsnumeroustimeswhilethecalibrateddatadoesnotwraps.Alsonotedisthatthere islesslossintheoriginaldatathaninthetheoreticalorcorrecteddata.Thecorrecteddatais signiÞcantlyimprovedcomparedtotheoriginal;however,itdoesnotcompletelymatchthethe- oreticalcurve.Weposittwomainreasonsforthis.First,thetheoreticalmodelofthetwo-wire transmissionlineisnotnecessarilycompleteatthistimesotheremaybeeffectsnotcurrently computed.Notalllossesareaccountedforsincethecalibrateddataislessthanthetheoret- icaldata.Perhapsdimensionsvaryenoughthroughoutthemanufacturedsetupcomparedto 257 Figure11.4:One-portS-parametersofashortcircuitlocatedinfourdifferentpositionsalongatwo-wiretransmis- sionline. 258 themodel,ormaybethetheoreticalvalueusedforthecalibrationstandarddoesnotcapture alllosses.Secondly,non-idealeffectsarepresentasshownbytheripplesinthecorrecteddata, e.g.below1GHzandabove4GHz).Therecouldbemultiplecausesfortheseeffectssuchasair gapsaroundtheshortcircuitorunevenwiresinthetwo-wiretransmissionline. 11.1.2POMMeasurement Oncethecalibrationmeasurementswerechecked,the12.9mmthickPOMsamplewasplaced ontothetransmissionlinewithfoamspacerF(6.0mm)onthebalunsideofitandfoamspacer G(9.8mm)ontheshortcircuitsideofit.Themeasurementwascalibratedusingthesame measurementsasintheprevioussection.Figure11.6showstheoriginalandcalibratedmea- surementaswellasthetheoreticalresponseforanair-line,i.e.atwo-wiretransmissionlineof thesamelength(28.7mm)withneitherfoamnormaterialsample. Weseethatbelow1GHzthemagnitudehasspikesabove0dBwhichdoesnotmakephysical sense.Thisissimilartocalibratedshortcircuitmeasurementalthoughinthatcasethespikes didnotsurpass0dB.Sincetheoriginalmeasurementstaysbelow0dB,theerrorisprobablyin thecalibrationmeasurementsandcausedbynon-idealeffectssuchasairgaps.Withstanding thiserror,wenoticethatthephasehasbeencorrectedtoanelectrically-shortertransmission line.Becausetheslopeismorenegativethantheair-linecase,weknowthatsomeportionof thetransmissionlineissurroundedbyamediumwith 'r>1.Insummary,weseethatthetwo-wiretransmissionlinesystemcanbecalibratedandre- spondstomaterialsamplesbeingplacedin-line.Thecalibrationprocedurerequiresadditional workatthistimeinordertoimproveaccuracyandreduceunwantedeffects,suchasairgaps, thatcancausetroublesomeartifactsintheprocesseddata. 259 Figure11.5:One-portS-parametersofashortcircuitlocated13.6mmfromthePlexiglasholderbythefoamI spacer. 260 Figure11.6:MeasurementsofaPOMsamplelayeredbetweentwofoamspacersonalineterminatedbyashort circuit. 261 Figure11.7:Balunwithcopperrodsandcoppershort. 11.2LiquidCalibration Forthisexperiment,atwo-wiretransmissionlinewascalibratedusingdistilledwater.Copper rodswereattachedtoabalunofdesign 0d96092presentedinSection10.8withwire-bondair bridges.Acopperplatewassolderedontotheotherendofthecopperrods.Theassembled systemisshowninFigure11.7. Agrooveforthebalunwascutabouthalf-waythroughtwo,oneinchbyoneinch,square plastictubes.Thesetubesweresetontopofa1000mLPyrexbeakerandthetwo-wiretrans- missionlinesystemsuspendeddown,intothebeakerasshowninFigure11.8.Alsoshownin thisÞgureisaverticalcaliper.Aslotwascutintheuppersurfaceofoneoftheplastictubesfor thefullbeamofthecaliperandasmallerslotwascutinthebottomsurfaceforthedepthbar ofthecaliper.Thisallowedthecalipertorestonthebottomofthetubeandthedepthbarto extenddownintothebeaker.Hotgluewasusedtosecurethecaliperinaverticalposition.The plastictubesaresecuredtothebeakerandthebeakersecuredtothetableusingpainterstape. Nexttothebeakerisanantennastand,securedtothetableagainwithtape,thatservesasa 262 Figure11.8:Liquidmeasurementexperimentalsetup. 263 cablestand.ASMAcable 1witharight-angleadapterissecuredtothestandusingzipties.An HP8510VNAiscalibratedtotheright-angleadapterusingastandard3.5mmcalkit.Theforce ofthecableonthebalunisusedtopositionthebalunverticallyascheckedbyalaserlevel. DistilledwaterwaspurchasedinagallonjugfromMSUStores.Thedistilledwaterwas addedtothebeaker,thedepthmeasured,andameasurementtaken.Therewasnotacon- sistentamountofwateraddedeachtimesincethecalibrationprocedurecanuseanydistance. Thedepthwasmeasuredbyloweringthedepthbardownuntilthesurfacetensionofthewater wasbrokenandwaterwickedontothedepthbar.Thesurfacetensionwasbrokenbyasmall dropofwaterthatremainedontheendofthedepthbarwhenitwasraisedup. ThesystemiscalibratedusingtheprocedureinChapter9;however,theprocedureisslightly differentthanforthepreviousexperiment.Earlier,theshortcircuitwasmovedalongthelength ofthelineinordertocreatethreedifferentreßectioncoefÞcientsandthetwo-wiretransmission linewasonlysurroundedbyair.Inthisexperiment,theshortcircuitdoesnotmovebutthe mediumsurroundingthetwo-wiretransmissionlinechanges.Eachcalibrationmeasurement hasadifferentlengthofairandwater.ThiscreatesdifferentreßectioncoefÞcientsbecausethe electricallengthchangeseventhoughthephysicallengthdoesnot. ThetheoreticalreßectioncoefÞcientsarecalculatedbaseduponthetwo-wiretransmission linegoingthroughairandthenwater.Tocalculatethetransmissionlinecircuitparametersfor thewatersection,therelativepermittivityofthedistilledwateriscalculatedusingtheDebye Equation[45,p.6-14],[7], '='&#j'&&(11.1) '&='.+'s#'.1+"202(11.2) '&&=#('s#'.)"01+"202.(11.3) 1Cablenumber 2013-05-17-009264 Figure11.9:Calibratedone-portS-parametersforatransmissionlinewithashortcircuitindistilledwater. 265 TheDebyeEquationisusedtomodeldielectricsbasedonthefollowingparameters: ¥staticpermittivity, 's;¥highfrequencylimit, '.;and ¥relaxationtime, 0.Fordistilledwaterat25 )C,'s=78.408, '.=5.2and 0=8.27ps[45,pp.6-1&6-14]. Figure11.9showsonemeasurement(54.31mm)thathasbeencalibratedusingthreeother measurements(51.39mm,57.34mm,and60.02mm).Weseebehaviorsimilartotheprevious experimentsuchasareductionintheelectricallengthofthesystemandregionswithobvi- ouslyerroneousdataÑinthiscasearound1.5GHzto3GHz.Ofparticularconcernisbetween 2GHzand3GHzwerethecalibratedmagnituderaisesabove0dB.Overall,however,wesee thattherawdatahasbeencorrectedtowardsthetheoreticaldataandrepresentsasigniÞcant improvement. Unlikethepreviousexperiment,therearenoexpectedairgapsasthewatercompletelysur- roundsthetwo-wiretransmissionline.Onepossiblesourceoferroristhedistilledwater.It isunknownhowthewaterusedactuallymatchestheparametersusedintheDebyeEquation. Theliteraturesimplyliststheparametersasbeingforwaterbutdoesnotstatewhetheritisdis- tilledwater,deionizedwater,orhowitisÞltered.Thismaycausesomeerrors,however,itdoes notexplainoscillations.Apossiblecauseofthelargesterrorsintheregionbetween2GHzand 3GHzisthenaturalresonancefrequencyofwater. Inthisexperiment,asimplebeakerwasusedasthecontainer.Alonger-termsolutionwould beaspeciÞcpurposecontainer.Figures11.10through11.17aredrawingsforacontainerthat submergesthebalunverticallyinaliquid.Thereisasmallholethroughwhichtheliquidis added.Awedgeisusedtosecurelyholdthebalunwhileallowingfornewdesigns.Thedrawings aretheÞrstdesigniterationofthecontainer.Ithasnotbeenmanufacturedandispresented heresolelyasaconcept. 266 Insummary,weagainseethatthetwo-wiretransmissionlinesystemcanbecalibratedand weseethatitcanbeusedtomeasurealiquidsample.Thecalibrationprocedurerequiresaddi- tionalworkatthistimeinordertoimproveaccuracysuchasdeterminingacceptablefrequency rangesforcalibrationliquids. 267 Figure11.10:Liquidmeasurementcontainer,page1. 268 Figure11.11:Liquidmeasurementcontainer,page2. 269 Figure11.12:Liquidmeasurementcontainer,page3. 270 Figure11.13:Liquidmeasurementcontainer,page4. 271 Figure11.14:Liquidmeasurementcontainer,page5. 272 Figure11.15:Liquidmeasurementcontainer,page6. 273 Figure11.16:Liquidmeasurementcontainer,page7. 274 Figure11.17:Liquidmeasurementcontainer,page8. 275 Chapter12 ConclusionandFutureWork PartIIIhasfocusedonatwo-wiretransmissionlinematerialmeasurementsystemdesignedfor bench-topexperiments.ThetheoryofthesystemwasÞrstdevelopedthenadesigndeveloped andpresented.Finallyexperimentalresultswerepresentedtodemonstratethefeasibilityand currentcapabilitiesofthesystem.Thepresentedsystemenablesbench-scaleexperimentsfor measuringthepropertiesofßames. TobeginPartIII,theelectricpotentialandÞeldswerederivedforatwo-wiretransmission line.Next,adistributedcircuitmodelwasderivedandtheparameterssummarizedinTable8.1 followedbyadiscussiononhowtocalibrateatwo-wiretransmissionlineandremovetheeffects ofabalun.Adouble-ybalundesignwasthenpresentedasawaytoconnectthemeasurement systemtotestequipment.Detailsaboutdesigningthebalunandancillaryequipmentsuchas astandandashortcircuitwerealsoprovided.Becausethegoalofthesystemistomeasure ßames,high-temperaturemodiÞcationstothedesignwerediscussed.Finally,measurements ofsolidandliquidmaterialswerepresentedtodemonstratethecapabilitiesofthetwo-wire transmissionlinesystem. Thetwo-wiretransmissionlinesystemwasdemonstratedtobeareasonablematerialmea- surementsystemforsolidandliquidmaterials.Actualmeasurementsofßameswerenotable 276 tobeconducted.Beforetheseareconducted,thereareafewitemsthatshouldbeaddressedas illustratedbytheinitialexperiments.Firsttheprecisionandaccuracyofthecalibrationtech- niqueshouldbeimproved.Thiscanbedonebyimprovingthemanufacturingaccuracyofthe shortcircuitorothercalibrationstandard.Improvedmanufacturingwillhelptoeliminateair gaps,lowertolerances,andresultinanimprovementoftheoverallsystemperformance.The theoreticalreßectioncoefÞcientusedinthecalibrationcalculationsneedstobereÞnedtobet- termatchthestandardused.Thisshoulddecreasesomeoftheproblemsinaccuracyofthe currentcalibrations.Secondarevisiontothebalundesignshouldbeconsidered.Thegoals ofthisnewbalunshouldbelowerlossesandtonotrequireairbridges.Atrade-offforanar- rowerbandwidthbalunshouldbeconsidered.Finallyworkpresentedin[77]basedontheory foundin[75]shouldbecontinuedinordertodeterminetheminimumneededsizeofamaterial sampleandtheshortcircuitforcalibration. Additionalworkthatshouldbeinvestigatedlaterincludesusingwaterforthecalibration standard.OneshouldverifytheDebyemodelorestablishamodiÞedmodelforthewaterused. Resonancesofthewatershouldbefurtherinvestigatedincludinghowtheseaffectthecalibra- tionprocess.Additionalworkistoinvestigatelimitsontheelectricallengthofthesystem. Inshort,PartIIIhasprovidedaproof-of-conceptforamaterialmeasurementsystemthat couldbeusedtomeasuresolids,liquids,orgasesthatmeritsfurtherinvestigation. 277 PartIV FutureWorkandConclusions 278 Chapter13 FutureWork 13.1NextIteration Resultsfromthisdissertationarepromisingandcontinuedresearchismerited.Forlive-Þre experimentsoutsideofthelab,workshouldlooktoreÞnetransmissionmeasurementtech- niques.Initiallythisshouldinvolveafurtherstudyofantennas,reßectors,andlensesrelativeto Þresize.Setupsshouldlooktoutilizegasburnersandwindprotectioninordertocreatelarge, repeatableßames.Optionstocreatepre-mixedßamesandtoseedthefuelwithtraceamounts ofothermaterials,suchasalkalisalts,shouldbeinvestigated.Measurementequipmentthat reducesthetimerequiredfortomeasureonesampleshouldbeselected. ThenextsetofinterferometricmeasurementsofßamesshouldreÞnethemeshandshutter designs.ConsiderationshouldbegiventomeasuringatX-bandandusingsomesortoflensfor focusing. Anewbalunforthetwo-wiretransmissionlineexperimentalsetupshouldbecreatedand thecalibrationmethodshouldthenbeveriÞedfurther. 279 13.2OutstandingChallengesandQuestions Severalimportantquestionsbasedonthisresearchremainunanswered.Futureworkshould aimtoanswerthese. ¥Thisresearchhasfocusedonplasmasinßameswithonlyminimalworkthataccounted forsoot,smoke,andotherparticulates.SpeciÞcstudiesareneededtoanswer:howdo soot,smoke,andotherparticulatesaffectelectromagneticwaveswhencombinedwith Þre-inducedplasmasinahouseÞre?Isthisbehaviorchangediftheparticulatesbecome negativelychargedbymobileelectronsattachingtotheparticulates? ¥Airßowandturbulencecanaffectelectromagneticwaves.Howdoesairßowarounda Þre-inducedplasmaaffectsignalpropagation? ¥HowdoÞre-inducedplasmasvarybetweendifferentfuels? ¥AtwhatsizedoesaÞre-inducedplasmabecomesigniÞcantenoughtoaffectpropagation? ¥Howdonon-ionizingthermaleffectscontributetoaltersignalpropagation? ¥Forthemeasurementtechniquesused,whataretherequiredminimumsystemspeciÞ- cationsandsensitivities? ¥Towhatextentisactualmessagecontentfromcommonlyusedtransmissionmodes,e.g. P25,conventionaltrunkedradiosystems,orBluetooth,actuallyaffectedbyÞre-induced plasmas? 13.3FutureDirections Thisworkandotherfutureworkmayleadtoapplicationsbeyondlocatingpeopletrappedina house.Potentialapplicationsincludeusingelectromagneticwavesfordetectingorextinguish- 280 ingÞres,andevaluatingstructuralstabilityandÞreimpingement.Forradarunitstobecome standardontheÞreground,prototypeswillneedtodemonstrateareliableeffectiveness.Next, usabilitystudiesofunitsareneededandstandardsshouldbedeveloped.Safetyoftheunitsfor ÞreÞghtersandforvictimsthatmaybescannedbytheunitiscritical;absorptionrates(SAR) andintrinsicsafetyshouldbeconsidered.Thermalimagingcameraswillnotbereplacedby radarunitsintheforeseeablefuture;therefore,integrationofthesetwounitsisimportantso thattheymaybeusedeffectivelytogether. 281 Chapter14 Conclusion FindingpeopletrappedinsideofaburninghouseisextremelydifÞcult,dangerous,andtime consuming.Smoke,heat,unfamiliarßoorplans,andpossiblestructuralcollapseallcombine tochallengeaÞreÞghterÕsabilitytoÞndaperson.Through-wallradarandvital-signdetection radarofferanimagingmodalitythatmaybeabletohelpÞreÞghtersÞndvictimsfromout- sideofaroomorevenahouse;however,electromagnetic(radar)wavescanbeaffectedbythe weakly-ionizedplasmacreatedbyaßame.Fundamentalunderstandingoftheinteractionsbe- tweenelectromagneticwavesandÞre-inducedplasmasisfoundationaltodevelopingtheselife savingÞreÞghtingtechnologies.Thisdissertationdescribestheinvestigationoftheseinterac- tionsthroughbasictheory,small-andlarge-scaleÞreexperiments,andmaterialmeasurement setups.ResultsfromthisresearchidentiÞedÞre-inducedplasmasfromßamesusinginterfero- metricmeasurements. 14.1FireExperiments ExperimentsperformedattheLansing(MI)FireDepartmenttrainingcentermeasuredtrans- missionsthroughburningcushions.ResultsshowedasigniÞcantdifferenceintransmissionas 282 thecushionburnedcomparedtoanunlitstate.Thetransmissionshadalargedifferenceini- tiallyandgraduallyreturnedtotheunlitstateasthecushionwasburned.Theseresultsare likelyduetoacombinationofÞre-inducedplasmasandmaterialmeasurementsofthesolid massofthecushion. Experimentswerecarriedoutusingpropaneburnerstoreducethepossibleinteractionbe- tweenelectromagneticwavesandthefuel.Plasma-likebehaviorwasnotobservedinthese measurementsmostlikelyduetotheexperimentalsetup.ReÞnementofcalibrationmethods shouldimprovefutureresults. ResultsfrominterferometricmeasurementsofßamesÞndplasmaelectrondensitiesone totwoordersofmagnitudelargerthanthosefoundinwildlandÞre.Measuredßamesfrom methanol,sodiumchloridesolution,orPlexiglassaremorerepresentativeofhouseÞresthan wildlandÞres.TheseresultsthereforerepresentÞre-inducedplasmaswhichcouldaffectÞre- Þghtingsearch-and-rescueradars. Anadditionallive-ÞreexperimentwasperformedtoevaluatetheeffectsofÞreontransmis- sionsfrominsideofaburninghouse.AseriesofÞreswereignitedinsideofahouseandthen extinguished.Transmittersatmultiplefrequencieswereplacedinsideofthehouseandtrans- mittedthroughtheÞre.NosigniÞcanteffectsonthetransmissionstrengthwereobservedfor thetestedÞreconditionswhichwereslighttomoderate.Thismeansthatthetransmissions fromaÞreÞghterinsideofahousewithsuchconditionsmaynotbeaffected.BecausetheÞre conditionsweremoderate,itisunknownifsevereconditions,suchasaßashover,wouldaffect transmissions. 14.2Two-WireTransmissionLine Atwo-wiretransmissionlineandbalunwereinvestigatedformaterialmeasurementpurposes. Theinitialmotivationforthisdesignwastomeasureandcharacterizeßamesinthelaboratory. 283 Amodelofthetwo-wiretransmissionlinewaspresentedaswellasacalibrationprocedureand anexperimentaldesign.Acalibrationmethodwasdevelopedwhichshowedmoderatesuccess inexperiments.CalibrationstandardsandthemodelsforthesestandardscanbereÞnedand improvedusingthemeasuredresults. 14.3Summary Thisworkpresentedlive-Þreexperimentswhichinvestigatedtheinteractionbetweenelectro- magneticwavesandÞre-inducedplasmas.Plasmaswereobservedininterferometricmeasure- mentsoflive-Þreexperiments.ContinuedreÞnementofexperimentaldesignscouldprovide additionaldatainthisarea.Aproof-of-concept,two-wiretransmissionlineusedformate- rialmeasurementsshowedpromisingresultsthatcouldbeimprovedwithareÞnedcalibration technique.Thisworkhasexploredanopenprobleminelectromagneticswithlive-savingap- plicationstotheÞreservice.Resultsfromthisworkwarrantadditionalstudyinthisareato improvetechniques,withthegoalofputtingsearch-and-rescueradarsintothehandsofÞre- Þghters. 284 APPENDICES 285 AppendixA NetworkParameters Ametricisneededtoevaluatetheperformanceofadeviceortocompareittosimilardevices. Asimple,linearcircuitmayhaveavoltage-currentcurveforthispurpose.ItisdifÞculttodeÞne thesevaluesfortheÞeldsencounteredinmicrowavedevices.Differenttypesofparametersare deÞnedformicrowavedevicestosolvethisproblem.Theseincludescattering(S),transmission (Torscattering-transfer),ABCD,impedance(Z),andadmittance(Y)parameters. Foramorein-depthdiscussionthanwhatispresentedbelow,thereaderisdirectedtoRamo, Whinnery,andVanDuzer[3,chap.11];Pozar[4,chap.4];Hewlett-PackardApplicationNote AN-154[122]andWikipedia[123]. A.1BasicDeÞnitions Acollectionofinter-connecteddevicesorcomponentsiscommonlycalledanetwork.Tochar- acterizetheperformanceofthenetwork,wemaydescribetheinput-outputrelationshipin termsofwaves(incidentandreßected)orintermsofvoltagesandcurrentsforalumped,equiv- alentcircuit[3]. Regardlessofwhichdescriptionmethodwechoose,wewishtorepresenttherelationship betweeninputsandoutputs,whichisdeÞnedatorbetweenports.Aportisaplacethrough whichelectricalenergyentersorleavesacircuitornetwork.Examplesincludeawaveguide aperture,batteryterminals,leadsofaresistor,andanSMAconnector. Toanalyzeanetwork,westartbydeÞningthenetworkaccordingtotherulesbelow[3, p.532]: 1.voltage, V,andcurrent, I,areproportionallydeÞnedtothetransverseelectricandmag- neticÞeldsofthemode,respectively; 2.theaveragepowerisRe{ VI1/2};3.AcharacteristicimpedanceforthemodeoftheincidentwaveisdeÞnedas Z0=V/I.286 V1=V+1+V#1V2=V+2+V#2V+1V#1V+2V#2a1b2b1a2S21S12S11S22FigureA.1:S-parameterblockdiagramandsignalßowgraphforatwo-portnetwork. Note Rememberthatvoltage, V,andcurrent, I,arecomplexvaluesandhencequantitiesde- rivedfromthesearealsocomplex. Withthisunderstanding,wecandeÞnethevariousparametersusedtodescribeandchar- acterizeanetwork. A.2S-Parameters Scatteringparameters,usuallyreferredtoasS-parameters,representthepropertiesofami- crowavenetworkintermsofwaves.ThevoltageatagivenportisdeÞnedasthesumofan incidentandareßectedwave,i.e. V=V++V#(A.1) asshowninFigureA.1wherethe +subscriptdenotestheincidentwaveandthe #subscriptde- notesthereßectedwave.Theincidentandreßectedwavesarenormalizedbythecharacteristic impedance Z0,whichisthesameforallports,to a=V+$Z0,and(A.2) b=V#$Z0,(A.3) respectively[3,pp.539Ð541].WedeÞneanS-parameteras Sij=bjai(A.4) where iistheinputportand jistheoutputportwhenallportsareterminatedbyaloadequal tothecharacteristicimpedance.Theindices iand jmaybeforthesameport,andarelessthan orequaltothenumberofports, n,ofthenetwork.Wemaywritethisrelationforthen-port networkasasystemof nequations, FbG=FSG[a].(A.5) 287 Thecommontwo-portnetworkisthereforedescribedbythesystem[3,pp.539Ð541] Ab1b2B=AS11S12S21S22BAa1a2B.(A.6) Caution S-parametersdependuponthecharacteristicimpedance, Z0,usedfornormalization.It isimportanttoknowwhatthisvalueissincetheincorrectvaluecandrasticallychange interpretationofwhattheS-parameterrepresents. A.3T-Parameters Transmissionparameters,alsoknownasscattering-transferparametersorT-parameters,ex- pressthewavequantitiesatoneportasalinearrelationshiptothewavequantitiesattheother port.Ramo,Whinnery,VanDuzerdeÞnethesystemas[3,p.541] Ab2a2B=AT11T12T21T22BAa1b1B.(A.7) Iftheportnumbersareswitched,thissystembecomes Aa1b1B=AT11T12T21T22BAb2a2B.(A.8) asdonefortheRFToolboxinMATALB[124,see s2t() ].WemayalsodeÞneitas Ab1a1B=AT11T12T21T22BAa2b2B.(A.9) ThissystemisusedintheHewlett-Packard(Agilent/Keysight)ApplicationnotenumberAN- 154[122],Wikipedia[123],andScikit-RF[125]. Caution BeawareofthedifferentdeÞnitionsofT-parametersandunderstandwhichoneyou are(oryoursoftwareis)using.ItisprobablybettertosharenetworkinformationasS- parametersandconvertto/fromT-parametersforintermediarycalculations. RelationsforconvertingbetweenS-parametersandT-parametersaregiveninTableA.1. A.4OtherParameters BesidesS-andT-parameters,onemayencounterZ-,Y-,andABCDparameters.Z-parameters orimpedanceparametersaredeÞnedas [V]=[Z][I].(A.16) 288 UsingEqn.(A.7)deÞnition [T]=HIS12S21#S11S22S12S22S12#S11S121S12JK(A.10) [S]='#T21T221T22T11T22#T12T21T22T12T22((A.11) UsingEqn.(A.8)deÞnition [T]=HI1S21#S22S21S11S21S12S21#S11S22S21JK(A.12) [S]='T21T11T11T22#T12T21T111T11#T12T11((A.13) UsingEqn.(A.9)deÞnition [T]=HIS12S21#S11S22S21S11S21#S22S211S21JK(A.14) [S]='T12T22T11T22#T12T21T221T22#T21T22((A.15) TableA.1:RelationsbetweenS-parametersandT-parameters[3,p.541]and[123]. 289 ThesecoefÞcientsrepresenttheimpedancerelationshipatandbetweenports.Similarly,Y- parametersoradmittanceparametersrepresenttheadmittancerelationshipatandbetween ports.ThesearedeÞnedbythesystem [I]=[Y][V].(A.17) Finally,ABCDparametersprovidearelationshipbetweentheinputsandoutputsofatwo-port network, AV1I1B=AABCDBAV2#I2B(A.18) Relativelysimpleexpressionsexisttotransformdatafromonetypeofparameterstothe other.Atableisgivenonpage192ofPozar[4]whileexpressionsarescatteredthroughoutChap- ter11ofRamo,Winnery,andVanDuzer[3]. 290 AppendixB CableandConnectorInformation 291 TableB.1:Cablenumberingscheme,lengths,connectortype,gender,andlabel. !"#$ %$&'"( )"*$($+ ,-.$ %$/ )$01#2 ,-.$ %$/ )'0$34 )'0$35 !!"#!"$%!&%"'()* +,$'-.()* +,#!"$%!&%"'%!!"()*%+,%$'%()*%+, !!##!"$%!&%"'()* +"#!-.()* +#!"$%!&%"'%!!#()*%+%"#!%()*%+ !!$#!"$%!&%"'()* +"#!-.()* +#!"$%!&%"'%!!$()*%+%"#!%()*%+ !!/#!"$%!&%"'()* +"#!-.()* +#!"$%!&%"'%!!/()*%+%"#!%()*%+ !!&#!"$%!&%"'()* +/0-.()* +#!"$%!&%"'%!!&()*%+%/0%()*%+ !!1#!"$%!&%"'()* +/0-.()* +#!"$%!&%"'%!!1()*%+%/0%()*%+ !!'#!"$%!&%"'()* +/0-.()* +#!"$%!&%"'%!!'()*%+%/0%()*%+ !!0#!"$%!&%"'()* +/0-.()* +#!"$%!&%"'%!!0()*%+%/0%()*%+ !!2#!"$%!&%"'()* +/0-.()* +#!"$%!&%"'%!!2()*%+%/0%()*%+ !"!#!"$%!&%"'()* +/0-.()* +#!"$%!&%"'%!"!()*%+%/0%()*%+ !""#!"$%!&%"'()* +/0-.()* +#!"$%!&%"'%!""()*%+%/0%()*%+ !"##!"$%!&%"'()* +/0-.()* +#!"$%!&%"'%!"#()*%+%/0%()*%+ !"$#!"$%!&%"'()* +"#34()* +#!"$%!&%"'%!"$()*%+%"#%()*%+ !"/#!"$%!&%"'()* +$1-.()* +#!"$%!&%"'%!"/()*%+%$1%()*%+ !"&#!"$%!&%"05+21-.5+#!"$%!&%"0%!"&5%+%21%5%+ !"1#!"$%!&%"05+"#345+#!"$%!&%"0%!"15%+%"#%5%+ !"'#!"$%!&%"05+$!345+#!"$%!&%"0%!"'5%+%$!%5%+ !"0#!"$%!&%"05+"#345+#!"$%!&%"0%!"05%+%"#%5%+ !"2#!"$%!&%"05+"&345+#!"$%!&%"0%!"25%+%"&%5%+ !#!#!"$%!&%"05+1!345+#!"$%!&%"0%!#!5%+%1!%5%+ !#"#!"$%!&%"05+"/-.5+#!"$%!&%"0%!#"5%+%"/%5%+ !###!"$%!&%"05+#/-.5+#!"$%!&%"0%!##5%+%#/%5%+ !#$#!"$%!&%"05+#'-.5+#!"$%!&%"0%!#$5%+%#'%5%+ !#/#!"$%!&%"05+#1-.5+#!"$%!&%"0%!#/5%+%#1%5%+ !#&#!"$%!&%"05+/!-.5+#!"$%!&%"0%!#&5%+%/!%5%+ !#1#!"$%!&%"05+#'-.5+#!"$%!&%"0%!#15%+%#'%5%+ !#'#!"$%!&%"05+$2345+#!"$%!&%"0%!#'5%+%$2%5%+ !#0#!"$%!&%"05+1!-.5+#!"$%!&%"0%!#05%+%1!%5%+ !#2#!"$%!&%"05+'#-.5+#!"$%!&%"0%!#25%+%'#%5%+ !$!#!"$%!&%"05+'#-.5+#!"$%!&%"0%!$!5%+%'#%5%+ !$"#!"$%!&%"05+'#-.5+#!"$%!&%"0%!$"5%+%'#%5%+ !$##!"$%!&%"05+'#-.5+#!"$%!&%"0%!$#5%+%'#%5%+ !$$#!"$%!&%"05+'#-.5+#!"$%!&%"0%!$$5%+%'#%5%+ !$/#!"$%!&%"05+'#-.5+#!"$%!&%"0%!$/5%+%'#%5%+ !$&#!"$%!&%"05+'#-.5+#!"$%!&%"0%!$&5%+%'#%5%+ !$1#!"$%!&%"05+"#345+#!"$%!&%"0%!$15%+%"#%5%+ !$'#!"$%!&%"0()* +"#!-.()* +#!"$%!&%"0%!$'()*%+%"#!%()*%+ !$0#!"$%!&%"0()* +"#!-.()* +#!"$%!&%"0%!$0()*%+%"#!%()*%+ !$2#!"$%!&%"0()* +"#!-.()* +#!"$%!&%"0%!$2()*%+%"#!%()*%+ !/!#!"$%!&%"0()* +'#-.()* +#!"$%!&%"0%!/!()*%+%'#%()*%+ !/"#!"$%!&%"0()* +1!-.()* 3#!"$%!&%"0%!/"()*%+%1!%()*%3 !/##!"$%!&%"0'6/0-.'6#!"$%!&%"0%!/#'%6%/0%'%6 !/$#!"$%!&%"0'6/0-.'6#!"$%!&%"0%!/$'%6%/0%'%6 !//#!"$%!&%"0'6#/-.'6#!"$%!&%"0%!//'%6%#/%'%6 !/&#!"$%!&%"0'6#/-.'6#!"$%!&%"0%!/&'%6%#/%'%6 !/1#!"$%!&%#'()* +"#!-.()* +#!"$%!&%#'%!/1()*%+%"#!%()*%+ 60+3460+35)"*$( 292 TableB.2:Resultsfromgagingtheassortedconnectorsinthelab. NumberType123 Average x0.0001"Male Color 1,2 Female Inspection Female Color 3,4 1SMA-8-8-8-8.00GREENGOODGREEN 2SMA-15-15-15-15.00GREENTALLRED 3SMA-26.5-26.5-26.5-26.50GREENGOODGREEN 4SMA-36-36-36.5-36.17REDSPACERED 53.5-11-11-11-11.00GREENGOODGREEN 63.5-18-17-20 -18-18-19-18.33GREENGOODGREEN 7SMA-26.5-27-27 -27-26.88GREENGOODGREEN 8SMA-40-40-39.5-39.83REDGOODGREEN 9SMA-49-48.5-48-48.50REDSPACERED 10SMA-29-30-30-29.67GREENGOODGREEN 11SMA-32-32-32-32.00REDBADRED 12SMA-30-30-30-30.00GREENGOODGREEN 13SMA-50-50<-50.00REDGOODGREEN 14SMA-14-14-14-14.00GREENGOODGREEN 15SMA-34.5-35-34-34.50REDGOODGREEN 16SMA-5-7-4-5.33GREENn/a SMA89109.00REDn/a 17SMA>>REDn/a SMA32-32-32-10.67GREENn/a 183.542-43-43-14.67GREENn/a 193.5 to 714-15-15-5.33GREENn/a HP3.511-10-10-3.00GREENn/a 3.54-4-4-1.33GREENn/a Notes 1. Green is assigned if the connector has a recessi on between 0.0" and 0.0030" 2. Red is assigned if the connector protudes at all or has a recession greater than 0.0030" 3. Green is assigned if the female connector appear s to be in good condition with no defects 4. Red is assigned if there are any defects in the female connector #4 Already Marked #1-#4 were from the red gage box #5, #6 were new from the bag #1 is a 10dB attenuator #10 is a 20dB attenuator #14 is an right angle connector 5. If a connector takes more than one line but only has one average, more than 3 measurements were made 6. If a connector takes up more than one line but h as multple averages, has multple male ends 293 TableB.3:ResultsofgagingthecablesprovidedwiththeSatimosystem. NumberType123 Average x0.0001"Male Color 1,2 Marked 50 ohmSMA-100-100-100-100.00RED 3LSMA-100-100-100-100.00RED 3RSMA-48-48-48-48.00RED 4LSMA-100-100-100-100.00RED 4RSMA-49-49-49-49.00RED 5LSMA-47-46-46-46.33RED 5RSMA-100-100-100-100.00RED 6LSMA15151515.00REDx 6RSMA-37-35-35-35.67RED 7LSMA-46-47-47-46.67RED 7RSMA-25-26-26-25.67GREENx 8LSMA-5-6-6-5.67GREENx 8RSMA41424241.67REDx Notes Measured by: Date: 1. Green is assigned if the connector has a recessi on between 0.0" and 0.0030" 2. Red is assigned if the connector protudes at all or has a recession greater than 0.0030"3. A measurement of -100 signifies that the length is less than -50, the lowest value on the gage Andrew Temme 6/25/20124. L and R indicate the left or right end of the ca ble when holding the cable so that the label is properly oriented 294 TableB.4:Resultsofgagingthe85052Dcalibrationkit. 123Average Standard Sex Serial Num. x0.0001"OpenM14872-1.5 -2-1-1.50 Short M13864-1.5 -2-2-1.83 Broadband Load M11011 -1.5 -2-2-1.83 Male to Male, top 1M79839-4-4-4.5 -4.17 Male to Male, bottom M79839-4-3-4-3.67 Male to Femail M80251-7-6-6.5 -6.50 Notes 1. Top refers to the side on top when properly reading the serial number. 295 AppendixC FurtherdetailsonSampleTrough The57inlongmetaltrough(seeFigureC.1)wasfabricatedfromtwopiecesofaluminumthat werejoinedtogetherasshowninFigureC.2.Thesetwopieceswereusedbecausetheywere obtainedforlittlecostfromtheMSUSurplusstore.Theboltheadinthecenterofthepicture holdsthetwopiecestogether.Thebottomoftheboltandthenut(bothunshown)causethe troughtotiltwhenplacedonaßatsurface.Thiswasnotaproblemduringtheexperiment becausethetroughwasalwayslongerthananyshelfonwhichitwasset.Thegapbetweeneach verticalÞnontheindividualpartsis1inchoncenter;however,thewidthandÞlletoftheÞn meanthattheactualwidthissmaller.Thetwopiecesneededtobejoinedinordertocreate agaplargerthan1inch,hencetheinitialneedforshims.TheotherboltsvisibleinFigureC .2wereoriginallyusedforaligningsamplesusingstringsuntilalaserlevelwaspurchasedfor thelab.Aclose-upviewofthefront-centerofthetroughisshowninFigureC.3including thecenter-lineandvalueof28 1/2in.Markswereplaced12inoffcentertouseinaligningthe commonly-sized,24inby24insamples.Therightmarkisvisibleinthetop-downviewof FigureC.4. 296 FigureC.1:Metaltroughusedtoholdsamples. FigureC.2:Sideviewofthemetaltrough. FigureC.3:Centerviewofthetroughshowingalignmentcue. 297 FigureC.4:Top-downviewofthetroughshowingalignmentmarks. 298 AppendixD WeatherRecords Thisappendixcontainsweatherrecordsfromvariousexperiments. D.1May30,2013ÑExperimentatLFDTrainingFacility ThesedatacorrespondtotheexperimentdescribedinChapter4thatoccuredonMay30,2013 attheLansingFireDepartmentÕsTrainingFacility.TableD.1showstheobservedtemperature andhumidityaswasrecordedattheexperimentsite.TableD.2showstheweatherreported byNOAA/NWSattheCapitolCityAirportonthenorthsideofLansing.Noprecipitationwas recordedinthereportedperiod;therefore,thiscolumnhasbeenremovedfromthetable.The windchillandheatindexwerereportas NAandhavebeenremovedfromthetable. 299 TableD.1:Observedtemperatureandhumidityatthesiteoftheexperiment. TimeTemp/¡FHumidity/%Notes 9:4577.064 9:5377.861 10:0378.561cal 10:2580.159 10:3580.559 10:4681.557 10:5481.958thermometermovedtotopofanalyzer 10:5781.756 11:0081.757 11:0581.457plate,empty 11:1382.358plexi 11:2383.056beginningofburn1 11:3685.053endofburn1 11:5084.454empty 11:5885.352plate 12:0385.552beginningofburn2 12:2186.850endofburn2 12:5187.749calnear 12:5887.748plate 13:0287.848plexi 13:0787.748beginningofburn3 13:2088.647 13:2588.046endofburn3 13:3387.8483withcarboard 13:4987.349 13:5187.549endof3withcardboard 13:5387.549burn3withsmallcardboard 14:0088.448 14:0788.747 14:1588.945lastplate 14:2289.545 14:3490.044end 14:4189.144 TableD.2:WeatherobservationsfromNOAA/NWSatCapitolCityAirportinLansingforMay30,2013. Temperature(¡F)RelativePressure TimeWindVis.WeatherSkyCond.6hourHumidityaltimetersealevel (edt)(mph)(mi.)AirDwptMax.Min.(in)(mb) 6:53S710FairCLR696073%30.031016.4 7:53S910FairCLR7162716673%30.041016.7 8:53S1310PartlyCloudyFEW070SCT090746471%30.041016.8 9:53S9G1810FairCLR786462%30.031016.4 10:53S1210FairCLR806662%30.031016.3 11:53S1710PartlyCloudySCT039826658%30.021015.9 12:53SW16G2410PartlyCloudySCT041SCT110846757%30.011015.7 13:53SW16G2510PartlyCloudySCT0438467857157%301015.3 14:53SW15G2510AFewCloudsFEW047856551%29.981014.7 15:53S15G2610PartlyCloudySCT049856450%29.971014.4 300 AppendixE SiteSafetyPlan E.1LFDTrainingFacility SITESAFETYPLAN LFDTrainingAcademy3015AlphaStLansingMI LansingFireDepartment MichiganStateUniversityÑElectricalEngineering MSURadarExperiment May30,2013 RecognizedSafety&HealthHazards LiveFireExercise TripHazards RemediationMethod StandardFireOperations Protocols/FireÞghterPPE Hazardmarking EmergencyActionPlan Intheeventanemployeeorresearcherbecomesinjuredorincapacitatedthehighestrank- ingLFDofÞcerwillimmediatelytakecontroloftheoperationandsummontheappropriate assistancefrompublicsafetyagenciesnumber911orRadioChannelLFDMAIN. Injuries EmployeeswillfolloworganizationalÒworkplaceinjuriesÓproceduresforreportinganddocu- mentation.AllincidentsofinjuriesonLFDpropertywillbereportedtotheLFDChiefofTrain- ing517-230-3451assoonaspracticalandtoMSUifappropriate. 301 Authority ItistheresponsibilityoftheleadresearcherandhighestrankingLFDofÞcertobriefandenforce thisplanduringthedurationoftheexperiment. Preparedby:AndrewTemme,MSUÑElectricalEngineering,May15,2013 Approvedby: 302 AppendixF SelectedPagesfromLaboratory Notebook00010 303 FigureF.1:LaboratoryNotebook00011:7 304 FigureF.2:LaboratoryNotebook00011:14 305 FigureF.3:LaboratoryNotebook00011:15 306 FigureF.4:LaboratoryNotebook00011:16 307 FigureF.5:LaboratoryNotebook00011:111 308 FigureF.6:LaboratoryNotebook00011:112 309 FigureF.7:LaboratoryNotebook00011:114 310 FigureF.8:LaboratoryNotebook00011:126 311 FigureF.9:LaboratoryNotebook00011:127 312 FigureF.10:LaboratoryNotebook00011:128 313 FigureF.11:LaboratoryNotebook00011:129 314 FigureF.12:LaboratoryNotebook00011:130 315 AppendixG SelectedPagesfromLaboratory Notebook00011 316 FigureG.1:LaboratoryNotebook00011:3 317 FigureG.2:LaboratoryNotebook00011:4 318 FigureG.3:LaboratoryNotebook00011:5 319 FigureG.4:LaboratoryNotebook00011:7 320 FigureG.5:LaboratoryNotebook00011:8 321 FigureG.6:LaboratoryNotebook00011:9 322 FigureG.7:LaboratoryNotebook00011:10 323 FigureG.8:LaboratoryNotebook00011:11 324 FigureG.9:LaboratoryNotebook00011:12 325 FigureG.10:LaboratoryNotebook00011:13 326 FigureG.11:LaboratoryNotebook00011:14 327 FigureG.12:LaboratoryNotebook00011:30 328 FigureG.13:LaboratoryNotebook00011:31 329 FigureG.14:LaboratoryNotebook00011:32 330 FigureG.15:LaboratoryNotebook00011:78 331 FigureG.16:LaboratoryNotebook00011:79 332 AppendixH VNADataCollectionCode 8753, ListingH.1:Collectfull 1#Downloadareadingfromthenetworkanalyzer 23from__future__importdivision 45importvisa 6importnumpyasnp 7fromdatetimeimportdatetime 8fromosimportpath,makedirs 9importskrf 1011print"start" 12# ############################################################################## 13fileName=Õbtfd #kevin #sep25 #calOFFÕ 14# ############################################################################## 15numGrps=4 1617ena=visa.instrument(ÕGPIB::16Õ,timeout=120) 18idn=ena.ask(Õ *IDN?Õ) 19printidn 2021optLine="#HzSRIR50" 2223cmd8753D={\ 24ÕbasicInitÕ:ÕHOLD;DUACOFF;CHAN1;S11;LOGM;CONT;AUTOÕ,\ 25ÕcorrQÕ:ÕCORR?Õ,\ 26ÕfreqSpanQÕ:ÕSPAN?Õ,\ 27ÕfreqStartQÕ:ÕSTAR?Õ,\ 28ÕfreqStopQÕ:ÕSTOP?Õ,\ 29ÕgetImagÕ:ÕIMAG;OUTPFORMÕ,\ 30ÕgetLinMagÕ:ÕLINM;OUTPFORMÕ,\ 31ÕgetLogMagÕ:ÕLOGM;OUTPFORMÕ,\ 32ÕgetPhaseÕ:ÕPHAS;OUTPFORMÕ,\ 33ÕgetRealÕ:ÕREAL;OUTPFORMÕ,\ 333 34ÕholdÕ:ÕHOLDÕ,\ 35ÕIDStrÕ:ÕHEWLETTPACKARD,8753D,0,6.14Õ,\ 36ÕifbwQÕ:ÕIFBW?Õ,\ 37ÕnumPtsQÕ:ÕPOIN?Õ,\ 38ÕpowerQÕ:ÕPOWE?Õ,\ 39ÕpresetÕ:ÕPRESÕ,\ 40ÕnumGroupsÕ:ÕNUMGÕ,\ 41ÕpolarÕ:ÕPOLAÕ,\ 42Õs11Õ:ÕS11Õ,\ 43Õs21Õ:ÕS21Õ,\ 44Õs12Õ:ÕS12Õ,\ 45Õs22Õ:ÕS22Õ\ 46} 4748cmdDict=cmd8753D 495051# ############################################################################## 52ena.write(Õform4Õ) 53numPts=ena.ask_for_values(cmdDict[ÕnumPtsQÕ])[0] 54freqStart=ena.ask_for_values(cmdDict[ÕfreqStartQÕ])[0] 55freqStop=ena.ask_for_values(cmdDict[ÕfreqStopQÕ])[0] 56freq=np.linspace(freqStart,freqStop,num=numPts,endpoint=True) 57ifbw=ena.ask_for_values(cmdDict[ÕifbwQÕ])[0] 58pwr=ena.ask_for_values(cmdDict[ÕpowerQÕ])[0] 59corr=ena.ask(cmdDict[ÕcorrQÕ]) 6061dateString=datetime.now().strftime(" %Y#%m#%d") 62timeString=datetime.now().strftime(" %H:%M:%S") 6364dataDir=ÕData/Õ+dateString 65ifnotpath.exists(dataDir): 66makedirs(dataDir) 6768print"here" 69s11polar=np.array(ena.ask_for_values(cmdDict[Õs11Õ]+cmdDict[ÕpolarÕ]+Õ;Õ+cmdDict[Õ numGroupsÕ]+str(numGrps)+Õ;outpformÕ)) 70print"there" 71s11polReal=s11polar[::2]#realvaluesfromthepolardata 72s11polImag=s11polar[1::2]#imaginaryvaluesfromthepolardata 7374print"s21" 75s21polar=np.array(ena.ask_for_values(cmdDict[Õs21Õ]+cmdDict[ÕpolarÕ]+Õ;Õ+cmdDict[Õ numGroupsÕ]+str(numGrps)+Õ;outpformÕ)) 76s21polReal=s21polar[::2]#realvaluesfromthepolardata 77s21polImag=s21polar[1::2]#imaginaryvaluesfromthepolardata 7879print"s12" 80s12polar=np.array(ena.ask_for_values(cmdDict[Õs12Õ]+cmdDict[ÕpolarÕ]+Õ;Õ+cmdDict[Õ numGroupsÕ]+str(numGrps)+Õ;outpformÕ)) 81s12polReal=s12polar[::2]#realvaluesfromthepolardata 334 82s12polImag=s12polar[1::2]#imaginaryvaluesfromthepolardata 8384print"s22" 85s22polar=np.array(ena.ask_for_values(cmdDict[Õs22Õ]+cmdDict[ÕpolarÕ]+Õ;Õ+cmdDict[Õ numGroupsÕ]+str(numGrps)+Õ;outpformÕ)) 86s22polReal=s22polar[::2]#realvaluesfromthepolardata 87s22polImag=s22polar[1::2]#imaginaryvaluesfromthepolardata 8889visa.vpp43.gpib_control_ren(ena.vi,2) 90#saveData=s22polar 91saveData=np.concatenate(([freq], 92[s11polReal],[s11polImag], 93[s21polReal],[s21polImag], 94[s12polReal],[s12polImag], 95[s22polReal],[s22polImag])).T 969798touchFileName=dataDir+"/"+fileName+".s2p" 99printtouchFileName 100saveFile=open(touchFileName,"w") 101saveFile.write("!"+idn+"\n") 102saveFile.write("!Date:"+dateString+""+timeString+"\n") 103saveFile.write("!Data&CalibrationInformation:\n") 104ifcorr==Õ0Õ: 105saveFile.write("!FreqS11S21S12S22\n") 106elifcorr==Õ1Õ: 107saveFile.write("!FreqS11:Cal(ON)S21:Cal(ON)S12:Cal(ON)S22:Cal(ON)\n") 108 109saveFile.write("!PortZPort1:50+j0Port2:50+j0\n") 110saveFile.write(("!AbovePortZisportzconversionorsystemZ0" 111"settingwhensavingthedata.\n")) 112saveFile.write(("!Whenreading,referenceimpedancevalueatoption" 113"lineisalwaysused.\n")) 114saveFile.write("!\n") 115saveFile.write("! ##Configfileparameters\n") 116saveFile.write("!start="+str(freqStart)+"\n") 117saveFile.write("!stop="+str(freqStop)+"\n") 118saveFile.write("!numPts="+str(numPts)+"\n") 119saveFile.write("!avgFact="+str(numGrps)+"\n") 120saveFile.write("!power="+str(pwr)+"\n") 121saveFile.write("!ifbw="+str(ifbw)+"\n") 122saveFile.write("!\n") 123saveFile.write(optLine+"\n") 124np.savetxt(saveFile,saveData,delimiter="") 125saveFile.close() 126 127balun=skrf.Network(touchFileName) 128balun.plot_s_db() 129legend(loc=0) ListingH.2:CollectS 21continuouslyfromanHP8753 335 1#Downloadareadingfromthenetworkanalyzer 23from__future__importdivision 45importvisa 6importnumpyasnp 7fromdatetimeimportdatetime 8fromosimportpath,makedirs 9#importskrf 1011print"start" 12# ############################################################################## 13dataPrefix=Õcarpet #foamÕ 14# ############################################################################## 15numGrps=2 16ena=visa.instrument(ÕGPIB::16Õ,timeout=120) 17idn=ena.ask(Õ *IDN?Õ) 18printidn 1920optLine="#HzSRIR50" 2122cmd8753D={\ 23ÕbasicInitÕ:ÕHOLD;DUACOFF;CHAN1;S21;LOGM;CONT;AUTOÕ,\ 24ÕcorrQÕ:ÕCORR?Õ,\ 25ÕfreqSpanQÕ:ÕSPAN?Õ,\ 26ÕfreqStartQÕ:ÕSTAR?Õ,\ 27ÕfreqStopQÕ:ÕSTOP?Õ,\ 28ÕgetImagÕ:ÕIMAG;OUTPFORMÕ,\ 29ÕgetLinMagÕ:ÕLINM;OUTPFORMÕ,\ 30ÕgetLogMagÕ:ÕLOGM;OUTPFORMÕ,\ 31ÕgetPhaseÕ:ÕPHAS;OUTPFORMÕ,\ 32ÕgetRealÕ:ÕREAL;OUTPFORMÕ,\ 33ÕholdÕ:ÕHOLDÕ,\ 34ÕIDStrÕ:ÕHEWLETTPACKARD,8753D,0,6.14Õ,\ 35ÕifbwQÕ:ÕIFBW?Õ,\ 36ÕnumPtsQÕ:ÕPOIN?Õ,\ 37ÕpowerQÕ:ÕPOWE?Õ,\ 38ÕpresetÕ:ÕPRESÕ,\ 39ÕnumGroupsÕ:ÕNUMGÕ,\ 40ÕpolarÕ:ÕPOLAÕ,\ 41Õs11Õ:ÕS11Õ,\ 42Õs21Õ:ÕS21Õ,\ 43Õs12Õ:ÕS12Õ,\ 44Õs22Õ:ÕS22Õ\ 45} 4647cmdDict=cmd8753D 484950# ############################################################################## 51ena.write(Õform4Õ) 336 52ena.write(ÕPOIN1601Õ) 53numPts=ena.ask_for_values(cmdDict[ÕnumPtsQÕ])[0] 54freqStart=ena.ask_for_values(cmdDict[ÕfreqStartQÕ])[0] 55freqStop=ena.ask_for_values(cmdDict[ÕfreqStopQÕ])[0] 56freq=np.linspace(freqStart,freqStop,num=numPts,endpoint=True) 57ifbw=ena.ask_for_values(cmdDict[ÕifbwQÕ])[0] 58pwr=ena.ask_for_values(cmdDict[ÕpowerQÕ])[0] 59corr=ena.ask(cmdDict[ÕcorrQÕ]) 6061dateString=datetime.now().strftime(" %Y#%m#%d") 62timeString=datetime.now().strftime(" %H:%M:%S") 6364dataDir=ÕData/Õ+dateString 65ifnotpath.exists(dataDir): 66makedirs(dataDir) 6768i=0 69#saveMeas=True 70#foriinrange(numMeasurements): 71try: 72ena.write(Õpola;numgÕ+str(numGrps)) 73#whilesaveMeas: 74whileTrue: 75print(ÕStartingMeasurementNumber: %dÕ%i) 76s21polar=np.array(ena.ask_for_values(cmdDict[Õs21Õ]+cmdDict[ÕpolarÕ]+Õ;Õ+ cmdDict[ÕnumGroupsÕ]+str(numGrps)+Õ;outpformÕ)) 77s21polReal=s21polar[::2]#realvaluesfromthepolardata 78s21polImag=s21polar[1::2]#imaginaryvaluesfromthepolardata 798081saveData=np.concatenate(([freq], 82[s21polReal],[s21polImag])).T 838485timeAppend=datetime.now().strftime(" #%Y#%m#%d#%H%M%S") 86dataName=dataDir+Õ/Õ+dataPrefix+timeAppend 8788touchFileName=dataName+".s1p" 89printtouchFileName 90saveFile=open(touchFileName,"w") 91saveFile.write("!"+idn+"\n") 92saveFile.write("!Date:"+dateString+""+timeString+"\n") 93saveFile.write("!Data&CalibrationInformation:\n") 94ifcorr==Õ0Õ: 95saveFile.write("!FreqS21\n") 96elifcorr==Õ1Õ: 97saveFile.write("!FreqS21:Calsavedonanalyzer\n") 9899saveFile.write("!PortZPort1:50+j0\n") 100saveFile.write(("!AbovePortZisportzconversionorsystemZ0" 101"settingwhensavingthedata.\n")) 337 102saveFile.write(("!Whenreading,referenceimpedancevalueatoption" 103"lineisalwaysused.\n")) 104saveFile.write("!\n") 105saveFile.write("! ##Configfileparameters\n") 106saveFile.write("!start="+str(freqStart)+"\n") 107saveFile.write("!stop="+str(freqStop)+"\n") 108saveFile.write("!numPts="+str(numPts)+"\n") 109saveFile.write("!avgFact="+str(numGrps)+"\n") 110saveFile.write("!power="+str(pwr)+"\n") 111saveFile.write("!ifbw="+str(ifbw)+"\n") 112saveFile.write("!\n") 113saveFile.write(optLine+"\n") 114np.savetxt(saveFile,saveData,delimiter="") 115saveFile.close() 116 117i+=1 118#balun=skrf.Network(touchFileName) 119#balun.plot_s_db() 120#legend(loc=0) 121exceptKeyboardInterrupt: 122print(ÕCtrl #CInterruptÕ) 123 124finally: 125print(ÕFinallyÕ) 126 127 128 129visa.vpp43.gpib_control_ren(ena.vi,2) 130print("Done") 8510, ListingH.3:Collectfull 1#Downloadareadingfromthenetworkanalyzer 23from__future__importdivision 45importvisa 6importnumpyasnp 7fromdatetimeimportdatetime 8fromosimportpath,makedirs 9importskrf 1011print"start" 12# ############################################################################## 13fileName=ÕemptyÕ 14# ############################################################################## 15optLine="#HzSRIR50" 1617cmd8510C={\ 18ÕbasicInitÕ:ÕHOLD;CHAN1;S11;LOGM;CONT;AUTO;Õ,\ 19ÕcorrQÕ:ÕCORR?;Õ,\ 338 20ÕfreqSpanQÕ:ÕSPAN;OUTPACTI;Õ,\ 21ÕfreqStartQÕ:ÕSTAR;OUTPACTI;Õ,\ 22ÕfreqStopQÕ:ÕSTOP;OUTPACTI;Õ,\ 23ÕgetImagÕ:ÕIMAG;OUTPFORM;Õ,\ 24ÕgetLinMagÕ:ÕLINM;OUTPFORM;Õ,\ 25ÕgetLogMagÕ:ÕLOGM;OUTPFORM;Õ,\ 26ÕgetPhaseÕ:ÕPHAS;OUTPFORM;Õ,\ 27ÕgetRealÕ:ÕREAL;OUTPFORM;Õ,\ 28ÕholdÕ:ÕHOLD;Õ,\ 29ÕIdQÕ:ÕOUTPIDEN;Õ,\ 30ÕIDStrÕ:ÕHP8510C.07.10:Mar301995Õ,\ 31ÕifbwQÕ:ÕDETE?Õ,\ 32ÕnumPtsQÕ:ÕPOIN;OUTPACTI;Õ,\ 33ÕpowerQÕ:ÕPOWE;OUTPACTI;Õ,\ 34ÕpresetÕ:ÕPRES;Õ,\ 35ÕnumGroupsÕ:ÕNUMGÕ,\ 36ÕpolarÕ:ÕREIP;Õ,\ 37Õs11Õ:ÕS11;Õ,\ 38Õs21Õ:ÕS21;Õ,\ 39Õs12Õ:ÕS12;Õ,\ 40Õs22Õ:ÕS22;Õ\ 41} 4243cmdDict=cmd8510C 4445ena=visa.instrument(ÕGPIB::16Õ,timeout=120) 46idn=ena.ask(cmdDict[ÕIdQÕ]) 47printidn 4849numGrps=16 50# ############################################################################## 51ena.write(Õform4Õ) 52numPts=ena.ask_for_values(cmdDict[ÕnumPtsQÕ])[0] 53freqStart=ena.ask_for_values(cmdDict[ÕfreqStartQÕ])[0] 54freqStop=ena.ask_for_values(cmdDict[ÕfreqStopQÕ])[0] 55freq=np.linspace(freqStart,freqStop,num=numPts,endpoint=True) 5657#IFBWisdifferentforthe8510 58ifbw=ena.ask(cmdDict[ÕifbwQÕ]) 59# 6061pwr=ena.ask_for_values(cmdDict[ÕpowerQÕ])[0] 62corr=ena.ask(cmdDict[ÕcorrQÕ]) 6364dateString=datetime.now().strftime(" %Y#%m#%d") 65timeString=datetime.now().strftime(" %H:%M:%S") 6667dataDir=ÕData/Õ+dateString 68ifnotpath.exists(dataDir): 69makedirs(dataDir) 70339 71s11polar=np.array(ena.ask_for_values(cmdDict[Õs11Õ]+cmdDict[ÕpolarÕ]+cmdDict[Õ numGroupsÕ]+str(numGrps)+Õ;outpformÕ)) 72s11polReal=s11polar[::2]#realvaluesfromthepolardata 73s11polImag=s11polar[1::2]#imaginaryvaluesfromthepolardata 7475s22polar=np.array(ena.ask_for_values(cmdDict[Õs22Õ]+cmdDict[ÕpolarÕ]+cmdDict[Õ numGroupsÕ]+str(numGrps)+Õ;outpformÕ)) 76s22polReal=s22polar[::2]#realvaluesfromthepolardata 77s22polImag=s22polar[1::2]#imaginaryvaluesfromthepolardata 7879s12polar=np.array(ena.ask_for_values(cmdDict[Õs12Õ]+cmdDict[ÕpolarÕ]+cmdDict[Õ numGroupsÕ]+str(numGrps)+Õ;outpformÕ)) 80s12polReal=s12polar[::2]#realvaluesfromthepolardata 81s12polImag=s12polar[1::2]#imaginaryvaluesfromthepolardata 8283s21polar=np.array(ena.ask_for_values(cmdDict[Õs21Õ]+cmdDict[ÕpolarÕ]+cmdDict[Õ numGroupsÕ]+str(numGrps)+Õ;outpformÕ)) 84s21polReal=s21polar[::2]#realvaluesfromthepolardata 85s21polImag=s21polar[1::2]#imaginaryvaluesfromthepolardata 868788visa.vpp43.gpib_control_ren(ena.vi,2) 89saveData=np.concatenate(([freq], 90[s11polReal],[s11polImag], 91[s21polReal],[s21polImag], 92[s12polReal],[s12polImag], 93[s22polReal],[s22polImag])).T 949596touchFileName=dataDir+"/"+fileName+".s2p" 97printtouchFileName 98saveFile=open(touchFileName,"w") 99saveFile.write("!"+idn+"\n") 100saveFile.write("!Date:"+dateString+""+timeString+"\n") 101saveFile.write("!Data&CalibrationInformation:\n") 102ifcorr==Õ0Õ: 103saveFile.write("!FreqS11S21S12S22\n") 104elifcorr==Õ1Õ: 105saveFile.write("!FreqS11:Cal(ON)S21:Cal(ON)S12:Cal(ON)S22:Cal(ON)\n") 106 107saveFile.write("!PortZPort1:50+j0\n") 108saveFile.write(("!AbovePortZisportzconversionorsystemZ0" 109"settingwhensavingthedata.\n")) 110saveFile.write(("!Whenreading,referenceimpedancevalueatoption" 111"lineisalwaysused.\n")) 112saveFile.write("!\n") 113saveFile.write("! ##Configfileparameters\n") 114saveFile.write("!start="+str(freqStart)+"\n") 115saveFile.write("!stop="+str(freqStop)+"\n") 116saveFile.write("!numPts="+str(numPts)+"\n") 117saveFile.write("!avgFact="+str(numGrps)+"\n") 340 118saveFile.write("!power="+str(pwr)+"\n") 119saveFile.write("!ifbw="+str(ifbw)+"\n") 120saveFile.write("!\n") 121saveFile.write(optLine+"\n") 122np.savetxt(saveFile,saveData,delimiter="") 123saveFile.close() 124 125balun=skrf.Network(touchFileName) 126balun.plot_s_db() 127legend(loc=0) 341 AppendixI WavecalcMacros ListingI.1:EHSPlexiglassmacro 1"Open" 223"\\tsclient\Z\Documents\code\Data\2013 #08#08\c1x.odf" 4"1" 5"CT" 627"2" 8"10" 9"FFT" 106 11"800" 12"4096" 13"8192" 14"8192" 15"4.883409E #02"16"0" 17"ZF" 182 19"2" 20"390" 21"FFT" 226 23"0" 24"8192" 25"4096" 26"8192" 27"0.0025" 28"0" 29"Trc" 302 31"2.5" 32"5.5" 33"Save" 341 342 35"\\tsclient\Z\Documents\code\Data\2013 #08#08\gated2 #390 #c1x.ODF" ListingI.2:EHSburnmacro 1"Open" 223"\\tsclient\Z\Documents\code\Data\2013 #08#08\c11.odf" 4"1" 5"CT" 627"2" 8"10" 9"FFT" 106 11"800" 12"4096" 13"8192" 14"8192" 15"4.883409E #02"16"0" 17"ZF" 182 19"5" 20"390" 21"FFT" 226 23"0" 24"8192" 25"4096" 26"8192" 27"0.0025" 28"0" 29"Trc" 302 31"2.5" 32"5.5" 33"Save" 341 35"\\tsclient\Z\Documents\code\Data\2013 #08#08\gated5 #390 #c11.ODF" ListingI.3:BTFDBullexmacro 1"Open" 223"\\tsclient\Z\Documents\code\Data\2013 #12#06\c1a.odf" 4"1" 5"CT" 627"2" 8"10" 9"FFT" 106 343 11"800" 12"4096" 13"8192" 14"8192" 15"4.883409E #02"16"0" 17"ZF" 182 19"3" 20"380" 21"FFT" 226 23"0" 24"8192" 25"4096" 26"8192" 27"0.0025" 28"0" 29"Trc" 302 31"2.5" 32"5.5" 33"Save" 341 35"\\tsclient\Z\Documents\code\Data\2013 #12#06\gated3 #380 #c1a.ODF" 344 AppendixJ ArchRange WhenmakingmeasurementsusingthearchrangeintheElectromagneticResearchGrouplab- oratory,itisimportanttoknowtheangularpositionofthehornantennaswhentheyareonthe rail.Theangulardistancefromoneendwasmarkedusingthefollowingprocedure(seeFig.J .1): 1.PainterÕstapewasappliedtotherail 2.Alaserlevelwasplacedneartheoutsideoftherotatorwiththelasergoingthroughthe centeroftherotatorandtheangle180 )awayfromwherethelaserwasplaced. 3.Thelaserwasalignedtotheedgeoftherail. 4.Therotatorwasrepeatedlysteppedby3 )andthelaserlinemarkedonthetape 5.TherulerinFigureJ.3wasusedtomarkeveryquarterofadegreebyaligningtoeach markfromthelaser. Afewremarks: ¥Therotatorwassteppedby3 )becausethisisthesmallestintegerdegreethatcorresponds toaintegerstepvalueforthemotoroftherotator.Numerically,themotorhas50800 stepsandagearratioof1:6whichgives846 2/3stepsperdegreeor2540stepsper3 )(seeNotebook00010:130inFig.F.12). ¥PainterÕstapewasusedbecauseitwasunknownhowthemarkingswouldturnout.At somepointinthefuture,therailshouldbemarkedinamorepermanentmanner. ¥TherulerwasdrawnusingSolidWorks.TheoriginalsourceÞleisavailableinthedata archiveprovidedtoDr.Rothwellaswellasinmygitrepository.RefertotheErratasection formoreinformation. 345 FigureJ.1:Archrangerailshowingthedegreemarkings. 346 FigureJ.2:Dimensionaldrawingoftherulerusedtomarkangulardistancealongtherailofthearchrange. 347 FigureJ.3:Rulerusedtomarkangulardistancetherailofthearchrange. 348 AppendixK IPythonnotebook:Single-Layer In[ ]:fromscipyimportconstantsasconstimportnumpyasnp#adjustfontsizeforplots matplotlib.rcParams.update({Õfont.sizeÕ:16})eta_free=np.sqrt(const.mu_0/const.epsilon_0)eps_theory=2.7eta_plexi=1/np.sqrt(eps_theory)*eta_freeR=(eta_plexi -eta_free)/(eta_plexi+eta_free)T=R+1In[ ]:A11=(1-R**2*T**2)/((1-R**2)*T)A12=-R*(1-T**2)/((1-R**2)*T)A21=-A12A22=(T**2-R**2)/((1-R**2)*T)In[ ]:S11=A21/A11S12=(A11*A22 -A21*A12)/A11S21=1/A11S22=-A12/A11 print(S21)print(20*log10(S21)) In[ ]:eps_r=linspace(1,10,200)eta_free=np.sqrt(const.mu_0/const.epsilon_0)eta_r=1/np.sqrt(eps_r)*eta_freeR=(eta_r-eta_free)/(eta_r+eta_free) T=R+1A11=(1-R**2*T**2)/((1-R**2)*T)A12=-R*(1-T**2)/((1-R**2)*T)A21=-A12A22=(T**2-R**2)/((1-R**2)*T)S11=A21/A11 349 S12=(A11*A22 -A21*A12)/A11S21=1/A11S22=-A12/A11 In[ ]:fig,ax =subplots()ax.plot(eps_r,abs(S21)) right=ax.twinx() right.set_ylim(20*log10(ax .get_ylim()))ax.set_xlabel(r"$\epsilon_r$ ")ax.set_ylabel(r"$|S_{21}|$ ")right.set_ylabel(rÕ$|S_{21}|(dB)$ Õ)ComputetheSparametersofasinglelayerofamaterial.Plot S21In[ ]:freq=linspace(1e9,20e9,500)eps_rel=[1,2.7,2.7-.05J]mu_r=1L_in=1#lengthofsampleininches L=L_in*0.0254 Z_0=np.sqrt(const .mu_0/const.epsilon_0)fig,axes =subplots(ncols=2,nrows =1,figsize =(13,4))foreps_rineps_rel:Z_1=Z_0*np.sqrt(mu_r/eps_r)gamma=1j*2*pi*freq/const.c*np.sqrt(mu_r*eps_r)R=(Z_1-Z_0)/(Z_1+Z_0)P=exp(-gamma *L)S11=R*(1-P**2)/(1-R**2*P**2)S22=S11S21=P*(1-R**2)/(1-R**2*P**2)S12=S21axes[0].plot(freq/1e9,20*log10(abs(S21)),label=rÕ$\epsilon_r=$ Õ+str(eps_r))axes[0].set_xlabel(ÕFrequency(GHz) Õ)axes[0].set_ylabel(rÕ$|S_{21}|$(dB) Õ)axes[1].plot(freq/1e9,angle(P,deg=1))axes[1].set_xlabel(ÕFrequency(GHz) Õ)axes[1].set_ylabel(rÕ$\angleS_{21}$(deg) Õ)#axes[0].set_title(rÕ$\epsilon_r=$Õ+str(eps_r)) fig.subplots_adjust(left =-.05)#axes[0].legend(loc=0) 350 axes[0].legend(bbox_to_anchor =(0.,1.02,1.,.102),loc =3,ncol=2,mode ="expand ",borderaxespad =0.)In[ ]:cdÕE://controlexperiments//burn3 ÕIn[ ]:empty1=np.loadtxt(Õempty1-t40.odf Õ,delimiter=",")empty2=np.loadtxt(Õempty2-t40.odfÕ,delimiter=",")plate1=np.loadtxt(Õplate1-t40.odfÕ,delimiter=",")plate2=np.loadtxt(Õplate2-t40.odfÕ,delimiter=",")plexi1=np.loadtxt(Õplexi1-t40.odfÕ,delimiter=Õ,Õ)plexi2=np.loadtxt(Õplexi2-t40.odfÕ,delimiter=Õ,Õ)shelf1=np.loadtxt(Õshelf1-t40.odfÕ,delimiter=Õ,Õ)shelf2=np.loadtxt(Õshelf2-t40.odfÕ,delimiter=Õ,Õ)In[ ]:freqExp=empty1[:,0]cempty1=empty1[:, 1]+1j*empty1[:,2]cempty2=empty2[:, 1]+1j*empty2[:,2]cplate1=plate1[:, 1]+1j*plate1[:,2]cplate2=plate2[:, 1]+1j*plate2[:,2]cplexi1=plexi1[:, 1]+1j*plexi1[:,2]cplexi2=plexi2[:, 1]+1j*plexi2[:,2]cshelf1=shelf1[:, 1]+1j*shelf1[:,2]cshelf2=shelf2[:, 1]+1j*shelf2[:,2]In[ ]:burn=ÕBurn3: ÕIn[ ]:fromscipyimportconstantsconstants.mu_0constants.epsilon_0In[ ]:eps_r=2.5printeps_rfig,axes =subplots(ncols=2,nrows =1,figsize =(13,4))Z_1=Z_0*np.sqrt(mu_r/eps_r)gamma=1j*2*pi*freq/const.c*np.sqrt(mu_r*eps_r)R=(Z_1-Z_0)/(Z_1+Z_0)P=exp(-gamma *L)S11=R*(1-P**2)/(1-R**2*P**2)S22=S11S21=P*(1-R**2)/(1-R**2*P**2)S12=S21defplotit(plotData,titleString,saveName): printtitleStringf=pylab.gcf() f.clear()figsize(2,2)subplot(2,1,1)plot(freqExp,20*log10( abs(plotData)))351 plot(freq/1e9,20*log10( abs(S21)),label =rÕ$\epsilon_r=$ Õ+str(eps_r))title(titleString)ylabel(Õ|S21|(dB) Õ)xlim(2,6)subplot(2,1,2)#plot(freqExp,rad2deg(angle(plotData))) plot(freqExp,rad2deg(angle(plotData *np.exp(-1j*k_0*L))))plot(freq/1e9,angle(P,deg =1))ylabel(rÕ$\angle$S21(deg) Õ)xlabel("Frequency(GHz) ")xlim(2,6)#savefig(saveName+Õ.pdfÕ) L_in=1L=L_in*0.0254k_0=2*np.pi*freqExp*1e9*np.sqrt(constants.mu_0*constants .epsilon_0)plotit((cplexi1-cplate1) /(cempty1-cplate1),burn+Õ(Plexi1-Plate1)/(Empty1-Plate1) Õ,Õplexi1_cald Õ)#plotit((cplexi2-cplate1)/(cempty1-cplate1), #burn+Õ(Plexi2-Plate1)/(Empty1-Plate1)Õ,Õplexi2_caldÕ) #plotit((cshelf1-cplate1)/(cempty1-cplate1), #burn+Õ(Shelf1-Plate1)/(Empty1-Plate1)Õ,Õshelf1_caldÕ) #plotit((cshelf2-cplate1)/(cempty1-cplate1), #burn+Õ(Shelf2-Plate1)/(Empty1-Plate1)Õ,Õshelf2_caldÕ) In[ ]:empty1=np.loadtxt(Õempty1-t17.odf Õ,delimiter=",")empty2=np.loadtxt(Õempty2-t17.odfÕ,delimiter=",")plate1=np.loadtxt(Õplate1-t17.odfÕ,delimiter=",")plate2=np.loadtxt(Õplate2-t17.odfÕ,delimiter=",")plexi1=np.loadtxt(Õplexi1-t17.odfÕ,delimiter=Õ,Õ)plexi2=np.loadtxt(Õplexi2-t17.odfÕ,delimiter=Õ,Õ)shelf1=np.loadtxt(Õshelf1-t17.odfÕ,delimiter=Õ,Õ)shelf2=np.loadtxt(Õshelf2-t17.odfÕ,delimiter=Õ,Õ)freqExp=empty1[:, 0]cempty1=empty1[:, 1]+1j*empty1[:,2]cempty2=empty2[:, 1]+1j*empty2[:,2]cplate1=plate1[:, 1]+1j*plate1[:,2]cplate2=plate2[:, 1]+1j*plate2[:,2]cplexi1=plexi1[:, 1]+1j*plexi1[:,2]cplexi2=plexi2[:, 1]+1j*plexi2[:,2]cshelf1=shelf1[:, 1]+1j*shelf1[:,2]cshelf2=shelf2[:, 1]+1j*shelf2[:,2]eps_r=2.5-0.05jprinteps_rfig,axes =subplots(ncols=2,nrows =1,figsize =(13,4))Z_1=Z_0*np.sqrt(mu_r/eps_r)gamma=1j*2*pi*freq/const.c*np.sqrt(mu_r*eps_r)R=(Z_1-Z_0)/(Z_1+Z_0)P=exp(-gamma *L)352 S11=R*(1-P**2)/(1-R**2*P**2)S22=S11S21=P*(1-R**2)/(1-R**2*P**2)S12=S21defplotit(plotData,titleString,saveName): printtitleStringf=pylab.gcf() f.clear()figsize(2,2)subplot(2,1,1)plot(freqExp,20*log10( abs(plotData)))plot(freq/1e9,20*log10( abs(S21)),label =rÕ$\epsilon_r=$ Õ+str(eps_r))title(titleString)ylabel(Õ|S21|(dB) Õ)xlim(2,6)subplot(2,1,2)#plot(freqExp,rad2deg(angle(plotData))) plot(freqExp,rad2deg(angle(plotData *np.exp(-1j*k_0*L))))plot(freq/1e9,angle(P,deg =1))ylabel(rÕ$\angle$S21(deg) Õ)xlabel("Frequency(GHz) ")xlim(2,6)#savefig(saveName+Õ.pdfÕ) L_in=1L=L_in*0.0254k_0=2*np.pi*freqExp*1e9*np.sqrt(constants.mu_0*constants .epsilon_0)plotit((cplexi1-cplate1) /(cempty1-cplate1),burn+Õ(Plexi1-Plate1)/(Empty1-Plate1) Õ,Õplexi1_cald Õ)#plotit((cplexi2-cplate1)/(cempty1-cplate1), #burn+Õ(Plexi2-Plate1)/(Empty1-Plate1)Õ,Õplexi2_caldÕ) #plotit((cshelf1-cplate1)/(cempty1-cplate1), #burn+Õ(Shelf1-Plate1)/(Empty1-Plate1)Õ,Õshelf1_caldÕ) #plotit((cshelf2-cplate1)/(cempty1-cplate1), #burn+Õ(Shelf2-Plate1)/(Empty1-Plate1)Õ,Õshelf2_caldÕ) In[ ]:cdÕ..//burn2ÕIn[ ]:burn=ÕBurn1: Õempty1=np.loadtxt(Õempty-2013-05-30-110926-t40.odf Õ,delimiter=",")empty2=np.loadtxt(Õempty-2013-05-30-110945-t40.odf Õ,delimiter=",")plate1=np.loadtxt(Õplate-2013-05-30-110727-t40.odf Õ,delimiter=",")plate2=np.loadtxt(Õplate-2013-05-30-110745-t40.odf Õ,delimiter=",")plexi1=np.loadtxt(Õplexiglass-2013-05-30-111303-t40.odf Õ,delimiter=Õ,Õ)plexi2=np.loadtxt(Õplexiglass-2013-05-30-111321-t40.odf Õ,delimiter=Õ,Õ)shelf1=np.loadtxt(Õshelf-2013-05-30-111532-t40.odf Õ,delimiter=Õ,Õ)shelf2=np.loadtxt(Õshelf-2013-05-30-111551-t40.odf Õ,delimiter=Õ,Õ)353 freqExp=empty1[:, 0]cempty1=empty1[:, 1]+1j*empty1[:,2]cempty2=empty2[:, 1]+1j*empty2[:,2]cplate1=plate1[:, 1]+1j*plate1[:,2]cplate2=plate2[:, 1]+1j*plate2[:,2]cplexi1=plexi1[:, 1]+1j*plexi1[:,2]cplexi2=plexi2[:, 1]+1j*plexi2[:,2]cshelf1=shelf1[:, 1]+1j*shelf1[:,2]cshelf2=shelf2[:, 1]+1j*shelf2[:,2]eps_r=2.5-0.05jprinteps_rfig,axes =subplots(ncols=2,nrows =1,figsize =(13,4))Z_1=Z_0*np.sqrt(mu_r/eps_r)gamma=1j*2*pi*freq/const.c*np.sqrt(mu_r*eps_r)R=(Z_1-Z_0)/(Z_1+Z_0)P=exp(-gamma *L)S11=R*(1-P**2)/(1-R**2*P**2)S22=S11S21=P*(1-R**2)/(1-R**2*P**2)S12=S21defplotit(plotData,titleString,saveName): printtitleStringf=pylab.gcf() f.clear()figsize(2,2)subplot(2,1,1)plot(freqExp,20*log10( abs(plotData)))plot(freq/1e9,20*log10( abs(S21)),label =rÕ$\epsilon_r=$ Õ+str(eps_r))title(titleString)ylabel(Õ|S21|(dB) Õ)xlim(2,6)subplot(2,1,2)#plot(freqExp,rad2deg(angle(plotData))) plot(freqExp,rad2deg(angle(plotData *np.exp(-1j*k_0*L))))plot(freq/1e9,angle(P,deg =1))ylabel(rÕ$\angle$S21(deg) Õ)xlabel("Frequency(GHz) ")xlim(2,6)#savefig(saveName+Õ.pdfÕ) L_in=1L=L_in*0.0254k_0=2*np.pi*freqExp*1e9*np.sqrt(constants.mu_0*constants .epsilon_0)plotit((cplexi1-cplate1) /(cempty1-cplate1),burn+Õ(Plexi1-Plate1)/(Empty1-Plate1) Õ,Õplexi1_cald Õ)354 #plotit((cplexi2-cplate1)/(cempty1-cplate1), #burn+Õ(Plexi2-Plate1)/(Empty1-Plate1)Õ,Õplexi2_caldÕ) #plotit((cshelf1-cplate1)/(cempty1-cplate1), #burn+Õ(Shelf1-Plate1)/(Empty1-Plate1)Õ,Õshelf1_caldÕ) #plotit((cshelf2-cplate1)/(cempty1-cplate1), #burn+Õ(Shelf2-Plate1)/(Empty1-Plate1)Õ,Õshelf2_caldÕ) In[ ]:cdÕ../burn1ÕIn[ ]:cdÕ../burn3ÕIn[ ]:burn=ÕBurn3: Õempty1=np.loadtxt(Õempty1-t17.odfÕ,delimiter=",")empty2=np.loadtxt(Õempty2-t17.odfÕ,delimiter=",")plate1=np.loadtxt(Õplate1-t17.odfÕ,delimiter=",")plate2=np.loadtxt(Õplate2-t17.odfÕ,delimiter=",")#plexi1=np.loadtxt(Õplexi1-t17.odfÕ,delimiter=Õ,Õ) plexi1=np.loadtxt(Õburn3-t17.odfÕ,delimiter=Õ,Õ)plexi2=np.loadtxt(Õplexi2-t17.odfÕ,delimiter=Õ,Õ)shelf1=np.loadtxt(Õshelf1-t17.odfÕ,delimiter=Õ,Õ)shelf2=np.loadtxt(Õshelf2-t17.odfÕ,delimiter=Õ,Õ)freqExp=empty1[:, 0]cempty1=empty1[:, 1]+1j*empty1[:,2]cempty2=empty2[:, 1]+1j*empty2[:,2]cplate1=plate1[:, 1]+1j*plate1[:,2]cplate2=plate2[:, 1]+1j*plate2[:,2]cplexi1=plexi1[:, 1]+1j*plexi1[:,2]cplexi2=plexi2[:, 1]+1j*plexi2[:,2]cshelf1=shelf1[:, 1]+1j*shelf1[:,2]cshelf2=shelf2[:, 1]+1j*shelf2[:,2]eps_r=1.1-0.05jprinteps_rfig,axes =subplots(ncols=2,nrows =1,figsize =(13,4))Z_1=Z_0*np.sqrt(mu_r/eps_r)gamma=1j*2*pi*freq/const.c*np.sqrt(mu_r*eps_r)R=(Z_1-Z_0)/(Z_1+Z_0)P=exp(-gamma *L)S11=R*(1-P**2)/(1-R**2*P**2)S22=S11S21=P*(1-R**2)/(1-R**2*P**2)S12=S21defplotit(plotData,titleString,saveName): printtitleStringf=pylab.gcf() f.clear()figsize(2,2)355 subplot(2,1,1)plot(freqExp,20*log10( abs(plotData)))plot(freq/1e9,20*log10( abs(S21)),label =rÕ$\epsilon_r=$ Õ+str(eps_r))title(titleString)ylabel(Õ|S21|(dB) Õ)xlim(2,6)subplot(2,1,2)#plot(freqExp,rad2deg(angle(plotData))) plot(freqExp,rad2deg(angle(plotData *np.exp(-1j*k_0*L))))plot(freq/1e9,angle(P,deg =1))ylabel(rÕ$\angle$S21(deg) Õ)xlabel("Frequency(GHz) ")xlim(2,6)#savefig(saveName+Õ.pdfÕ) L_in=1L=L_in*0.0254k_0=2*np.pi*freqExp*1e9*np.sqrt(constants.mu_0*constants .epsilon_0)plotit((cplexi1-cplate1) /(cempty1-cplate1),burn+Õ(Plexi1-Plate1)/(Empty1-Plate1) Õ,Õplexi1_cald Õ)#plotit((cplexi2-cplate1)/(cempty1-cplate1), #burn+Õ(Plexi2-Plate1)/(Empty1-Plate1)Õ,Õplexi2_caldÕ) #plotit((cshelf1-cplate1)/(cempty1-cplate1), #burn+Õ(Shelf1-Plate1)/(Empty1-Plate1)Õ,Õshelf1_caldÕ) #plotit((cshelf2-cplate1)/(cempty1-cplate1), #burn+Õ(Shelf2-Plate1)/(Empty1-Plate1)Õ,Õshelf2_caldÕ) K.1ControlDatafortheLFDReport In[ ]:!pwdIn[ ]:!cd~/Documents/code/Data/2013-05-30/odf/control/burn3/ In[ ]:fromscipyimportconstantsasconstimportnumpyasnp#adjustfontsizeforplots matplotlib.rcParams.update({Õfont.sizeÕ:16})burn=ÕBurn3: Õ#loaddata empty1=np.loadtxt(Õempty1-t17.ODFÕ,delimiter=",")empty2=np.loadtxt(Õempty2-t17.ODFÕ,delimiter=",")plate1=np.loadtxt(Õplate1-t17.ODFÕ,delimiter=",")plate2=np.loadtxt(Õplate2-t17.ODFÕ,delimiter=",")plexi1=np.loadtxt(Õplexi1-t17.ODFÕ,delimiter=Õ,Õ)plexi2=np.loadtxt(Õplexi2-t17.ODFÕ,delimiter=Õ,Õ)shelf1=np.loadtxt(Õshelf1-t17.ODFÕ,delimiter=Õ,Õ)shelf2=np.loadtxt(Õshelf2-t17.ODFÕ,delimiter=Õ,Õ)#parsedataintocomplexvalues 356 freqExp=empty1[:, 0]cempty1=empty1[:, 1]+1j*empty1[:,2]cempty2=empty2[:, 1]+1j*empty2[:,2]cplate1=plate1[:, 1]+1j*plate1[:,2]cplate2=plate2[:, 1]+1j*plate2[:,2]cplexi1=plexi1[:, 1]+1j*plexi1[:,2]cplexi2=plexi2[:, 1]+1j*plexi2[:,2]cshelf1=shelf1[:, 1]+1j*shelf1[:,2]cshelf2=shelf2[:, 1]+1j*shelf2[:,2]#theoreticalcalculations eps_r=2.5printeps_reta_free=np.sqrt(const.mu_0/const.epsilon_0)mu_r=1freq=linspace( 1e9,20e9,500)L_in=1#lengthofsampleininches L=L_in*0.0254 Z_0=np.sqrt(const .mu_0/const.epsilon_0)Z_1=Z_0*np.sqrt(mu_r/eps_r)gamma=1j*2*pi*freq/const.c*np.sqrt(mu_r*eps_r)R=(Z_1-Z_0)/(Z_1+Z_0)P=exp(-gamma *L)S11=R*(1-P**2)/(1-R**2*P**2)S22=S11S21=P*(1-R**2)/(1-R**2*P**2)S12=S21#calculatehowmuchtoshiftthedata L_in=1L=L_in*0.0254k_0=2*np.pi*freqExp*1e9*np.sqrt(const.mu_0*const.epsilon_0)#functiontoplotresults fig,axes =subplots(ncols=2,nrows =1,figsize =(13,8))defplotit(plotData,titleString,saveName): printtitleStringf=pylab.gcf() f.clear()#figsize(2,2)subplot(2,1,1)plot(freqExp,20*log10( abs(plotData)),Õb-Õ,lw =2,label =ÕPlexiglassControl Õ)plot(freq/1e9,20*log10( abs(S21)),Õg-.Õ,lw =2,label=rÕ$\epsilon_r=$ Õ+str(eps_r))title(titleString)ylabel(ÕMagnitude(dB) Õ)357 xlim(2,6)#legend(loc=4,borderaxespad=0.) subplot(2,1,2)#plotunshifteddata #plot(freqExp,rad2deg(angle(plotData))) #plotshifteddata plot(freq/1e9,angle(S21,deg =1),Õg-.Õ,lw =2,label=rÕ$\epsilon_r=$ Õ+str(eps_r))plot(freqExp,rad2deg(angle(plotData *np.exp(-1j*k_0*L))),Õb-Õ,lw =2,label=ÕPlexiglassControl Õ)ylabel(ÕPhase(deg) Õ)xlabel("Frequency(GHz) ")xlim(2,6)legend(loc=4,borderaxespad =0.)#axes[0].legend(bbox_to_anchor=(0.,1.02,1.,.102),loc=3,ncol=2, #mode="expand",borderaxespad=0.) #axes[0].legend(loc=2) savefig(saveName+Õ.pngÕ)plotit((cplexi1-cplate1) /(cempty1-cplate1),ÕResultsforPlexiglassControlSample,Burn3data Õ,Õb3-plexi-ctrl-dissertation Õ)358 AppendixL IPythonnotebook: Bullex-at-ORCBS-2013-08-08 L.1ExperimentsatMSUEHSusingtheBullexFireExtin- guisherTrainer ¥ConductedatMSUEHSofÞceattheEngineeringResearchComplex ¥AssistedbyElvetA.PotterfromEHSandTang ¥2013-08-08 L.1.1Files In[ ]:!ls-1~/Documents/code/Data/2013-08-08/b [1,2,3]*.odfIn[ ]:!ls~/Documents/code/Data/2013-08-08/gated [2,5]*.ODFL.2Pre-ßight L.2.1Imports In[ ]:#Importbasicmodules #makesurethatdivisionisdoneasexpected from__future__importdivision#plottingsetup %matplotlibinline importmatplotlib.pyplot aspltplt.style.use(Õgray_back Õ)#gettheviridiscolormap #https://bids.github.io/colormap #itwillbeavailableascmaps.viridis 359 importcolormaps ascmaps#for3dgraphs #frommpl_toolkits.mplot3dimportaxes3d #forlegendsofcombinedfigtypes #importmatplotlib.linesasmlines #numericalfunctions importnumpyasnp#needsomeconstants fromscipyimport constantsfromnumpyimport pi#RFtools! importskrfasrf#versioninformation #%install_exthttp://raw.github.com/jrjohansson/version_information/ #master/version_information.py #%load_extversion_information #%reload_extversion_information #%version_informationnumpy,scipy,matplotlib In[ ]:fromscipyimportstatsfromscipy.constants importinchL.2.2Parameters,ConÞg,andConstants In[ ]:dataDir=Õ/mnt/home/temmeand/Documents/code/Data/2013-08-08/ ÕdoPlot=True doSave=True #doSave=False ifdoSave:doPlot =Trueplt.rcParams[Õaxes.ymargin Õ]=0In[ ]:fmin=2.5e9fmax=5.5e9fpts=201#Plexiglasparameters plexi={ÕepsrÕ:2.5,ÕmurÕ:1,ÕdÕ:1*constants.inch}#Freespaceparameters freeSpace={ÕepsrÕ:1360 ,ÕmurÕ:1}#FreespaceinPlexiglascase freePlexi=freeSpace.copy()freePlexi[ÕdÕ]=plexi[ÕdÕ]#FreespaceinBullexcase freeFire=freeSpace .copy()freeFire[ÕdÕ]=27.94*constants.inchL.2.3ErrorChecking In[ ]:#noneatthistime L.2.4PrelimCalculations In[ ]:freq=np.linspace(fmin,fmax,fpts) L.2.5FunctionDeÞnitions In[ ]:defntwk2odf(ntwk,m =1,n=0,fileName =None,EOL =Õ\r\nÕ):ÕÕÕSavesanskrfnetworkinODFformat Saveones-parameterfromanetworkasanodfformattedfile.In thefrequencydomain,eachlinecontainsthefrequency,real values,andimaginaryvaluesseperatedbycommas. ÔmÔandÔnÔallowyoutopickwhichSparametertosave Ifnofilenameisgiven,thenameofthenetworkisused DefaultendoflinecharacterisWindowscompatible(\\r\\n) Parameters----------ntwk:skrfNetworkobject Datatobesaved m,n:int SpecifiestheSparametertobesavedasS_m,n fileName:string Nameofthesavedfile.Ifnostringisprovided,the nameofthenetworkisused EOL:string Stringtobeusedattheendoftheline \\r\\n-Dos 361 \\n-Unix Returns-------NothingÕÕÕfileName=ntwk .nameiffileNameisNoneelsefileNamewithopen(fileName +Õ.odfÕ,ÕwÕ)asfo:data=np.vstack((ntwk .f/1e9,ntwk .s_re[:,m,n],ntwk .s_im[:,m,n])).Tnp.savetxt(fo,data,delimiter =Õ,Õ,newline=EOL)defodf2ntwk(fileName,name =""):ÕÕÕLoadODFfileasntwk Createaoneports-parameternetworkfromanodfformattedfile.In thefrequencydomain,eachlinecontainsthefrequency,real value,andimaginaryvalueseperatedbycommas. Parameters----------fileName:string Filetobeloaded Returns-------ntwk:skrfNetworkobject ÕÕÕ#fromnumpyimportloadtxt importskrfasrff=open(fileName, ÕrÕ)raw=np.loadtxt(f,delimiter =Õ,Õ)f.close()ifnameis"":name =fileNamefreq=raw[:,0]data=raw[:,1]+1j*raw[:,2]#ntwk=rf.Network(name=fileName,f=axis,f_unit=ÕGHzÕ,z0=50,s=data) ntwk=rf.Network(name =name,f=freq,f_unit=ÕGHzÕ,z0=50,s=data)returnntwkdefcalibrate(raw,empty,plate,thick): """Calibraterawdatausingemptyandplatemeasurement ForS21data: Cald=(raw-plate)/(empty-plate)*exp(-j*k_0*thick) 362 Parameters----------raw:skrfnetwork rawdatatobecalibrated empty:skrfnetwork emptyrangemeasurement plate:skrfnetwork measurementofplateatthepositionofthesample thick:number thicknessofmaterialsampleinmeters Returns-------cald:skrfnetwork Calibratedata """k=wavenumber(raw .f,1,1)cald=(raw-plate) /(empty-plate)*np.exp(-1j*k*thick)cald.name=cald .name+",cald "returncalddefanalyze(raw,empty,plate,thick,name ="",_doPlot =False,_doSave =False):"""Processthedata Calibratethedataandplot Parameters----------raw:skrfnetwork rawdatatobecalibrated empty:skrfnetwork emptyrangemeasurement plate:skrfnetwork measurementofplateatthepositionofthesample thick:number samplethicknessinmeters name:string labelornametouseongraphs _doPlot:boolean makeplots _doSave:boolean saveplots Returns-------cald:skrfnetwork 363 calibratednetwork """cald=calibrate(raw,empty,plate,thick) ifnameisnot"":cald.name=nameif_doPlot:fig,ax =plt.subplots(2,1)fig.set_figheight(7)ax[0].set_title(ÕDataset: Õ+name)raw.plot_s_db(ax=ax[ 0],label =ÕRawÕ)cald.plot_s_db(ax=ax[ 0],label =ÕCaldÕ)raw.plot_s_deg(ax=ax[ 1],show_legend =False)cald.plot_s_deg(ax=ax[1],show_legend =False)if_doSave:fig.savefig(name+Õ.pdf Õ)returncalddefwavenumber(f,epsr,mur): return2*pi*f*np.sqrt(constants.epsilon_0*epsr*constants.mu_0*mur) defpropFactor(k,d): returnnp.exp(-1j*k*d)defimpedance(epsr =1,mur =1):returnnp.sqrt(constants .mu_0*mur/(constants.epsilon_0*epsr)) defreflectionCoeff (eta,etaf): return(eta-etaf)/(eta+etaf)deftransmission (p,g): return(1-g**2)*p/(1-p**2*g**2)defslabTheory(f,d,epsr =1,mur =1):"""Theoreticalslabtransmission S21=(1-Gamma^2)P/(1-P^2*Gamma^2) P=exp(-jkd) k=omega*sqrt(mu*eps) d=thickness 364 Gamma=(Z-Z0)/(Z+Z0) Z=sqrt(mu/eps) Z0=sqrt(mu0/eps0) """k=wavenumber(f,epsr,mur) eta=impedance(epsr,mur) etaFree=impedance( 1,1)p=propFactor(k,d) g=reflectionCoeff(eta,etaFree) s21=transmission(p,g) name="Theory "f=f/1e9ntwk=rf.Network(name =name,f =f,f_unit =Õghz Õ,z0=50,s=s21)returnntwkL.3Theory Transmissionthroughadielectricslab.Normalincidence. S21=(1#%2)P/(1#P2%2)¥P=e#jkd ¥k="$µ'¥disslabthickness ¥%=(Z#Z0)/(Z+Z0)¥Z=.µ/'¥Z0=.µ0/'0L.3.1Plexiglas In[ ]:#calculateplexiglasstheory plexiThy=slabTheory(freq,plexi[ ÕdÕ],plexi[ ÕepsrÕ],plexi[ ÕmurÕ])plexiThy.name=ÕPlexiglastheory ÕfreeThy=slabTheory(freq,freePlexi[ ÕdÕ],freePlexi[ ÕepsrÕ],freePlexi[ ÕmurÕ])freeThy.name=ÕFreespacetheory Õ#ifdoPlot: #fig,ax=plt.subplots() #plexiThy.plot_s_db() #freeThy.plot_s_db(label=ÕFreespacetheory,d=1inÕ) 365 #fig,ax=plt.subplots() #plexiThy.plot_s_deg() #freeThy.plot_s_deg(label=ÕFreespacetheory,d=1inÕ) L.3.2FreeSpaceAcrossBullex In[ ]:#calculateBullextheory bullexThy=slabTheory(freq,freeFire[ ÕdÕ],freeFire[ ÕepsrÕ],freeFire[ ÕmurÕ])bullexThy.name="Theory"#ifdoPlot: #fig,ax=plt.subplots() #bullexThy.plot_s_db(label="FreespaceaboveBullex,theory,d=28in") #_=ax.set_ylim([-.8,0.1]) #fig,ax=plt.subplots() #bullexThy.plot_s_deg(label="FreespaceaboveBullex,theory,d=28in") L.4CalibrateDataandExportforTimeGating Originallyweimportedthedata,calibrateditusing Sc21=Sm21#Sp21Se21#Sp21e#jk0d¥ccald¥mmeasured ¥pplate ¥eempty ¥k0freespacewavenumber ¥dsamplethickness ThenitwassavedsothatWavecalccouldbeusedtotimegateit.Timegatingconsistedof applyingacosinetaperinthefreqdomain,applyinganinverseFFT,zeroÞllingbetweentwo timepoints,forwardFFT,andthentruncatingtooriginalfrequencyrange. Sincethisisdone,weskipthiscodenowandjustimportthegateddata. In[ ]:#originaldatamanip ##loadinODFfilesandmakethemntwks #b11=odf2ntwk(dataDir+Õb1-b1-2013-08-08-122942.odfÕ,name=Õsample1-1Õ) #b12=odf2ntwk(dataDir+Õb1-b2-2013-08-08-123035.odfÕ,name=Õsample1-2Õ) #b13=odf2ntwk(dataDir+Õb1-b3-2013-08-08-123123.odfÕ,name=Õsample1-3Õ) #b1e=odf2ntwk(dataDir+Õb1-empty-2013-08-08-122411.odfÕ,name=Õempty1Õ) #b1p=odf2ntwk(dataDir+Õb1-plate-2013-08-08-122638.odfÕ,name=Õplate1Õ) #b1x=odf2ntwk(dataDir+Õb1-plexi-2013-08-08-122819.odfÕ,name=ÕPlexiglas1Õ) #b21=odf2ntwk(dataDir+Õb2-b1-2013-08-08-124510.odfÕ,name=Õsample2-1Õ) 366 #b22=odf2ntwk(dataDir+Õb2-b2-2013-08-08-124557.odfÕ,name=Õsample2-2Õ) #b23=odf2ntwk(dataDir+Õb2-b3-2013-08-08-124654.odfÕ,name=Õsample2-3Õ) #b2e=odf2ntwk(dataDir+Õb2-empty-2013-08-08-124058.odfÕ,name=Õemtpy2Õ) #b2p=odf2ntwk(dataDir+Õb2-plate-2013-08-08-124332.odfÕ,name=Õplate2Õ) #b2x=odf2ntwk(dataDir+Õb2-plexi-2013-08-08-124156.odfÕ,name=ÕPlexiglas2Õ) #b31=odf2ntwk(dataDir+Õb3-b1-2013-08-08-130015.odfÕ,name=Õsample3-1Õ) #b32=odf2ntwk(dataDir+Õb3-b2-2013-08-08-130109.odfÕ,name=Õsample3-2Õ) #b33=odf2ntwk(dataDir+Õb3-b3-2013-08-08-130243.odfÕ,name=Õsample3-3Õ) #b34=odf2ntwk(dataDir+Õb3-b4-2013-08-08-130338.odfÕ,name=Õsample3-4Õ) #b3e=odf2ntwk(dataDir+Õb3-empty-2013-08-08-125919.odfÕ,name=Õemtpy3Õ) #b3p=odf2ntwk(dataDir+Õb3-plate-2013-08-08-125650.odfÕ,name=Õplate3Õ) #b3x=odf2ntwk(dataDir+Õb3-plexi-2013-08-08-125827.odfÕ,name=ÕPlexiglas3Õ) ##calibratealldata #c11=calibrate(b11,b1e,b1p,28.5*inch) #c12=calibrate(b12,b1e,b1p,28.5*inch) #c13=calibrate(b13,b1e,b1p,28.5*inch) #c21=calibrate(b21,b2e,b2p,28.5*inch) #c22=calibrate(b22,b2e,b2p,28.5*inch) #c23=calibrate(b23,b2e,b2p,28.5*inch) #c31=calibrate(b31,b3e,b3p,28.5*inch) #c32=calibrate(b32,b3e,b3p,28.5*inch) #c33=calibrate(b33,b3e,b3p,28.5*inch) #c34=calibrate(b34,b3e,b3p,28.5*inch) #c1x=calibrate(b1x,b1e,b1p,1*inch) #c2x=calibrate(b2x,b2e,b2p,1*inch) #c3x=calibrate(b3x,b3e,b3p,1*inch) ##savedatatobetimegated #ntwk2odf(c11,0,0,fileName=dataDir+Õc11Õ) #ntwk2odf(c12,0,0,fileName=dataDir+Õc12Õ) #ntwk2odf(c13,0,0,fileName=dataDir+Õc13Õ) #ntwk2odf(c21,0,0,fileName=dataDir+Õc21Õ) #ntwk2odf(c22,0,0,fileName=dataDir+Õc22Õ) #ntwk2odf(c23,0,0,fileName=dataDir+Õc23Õ) #ntwk2odf(c31,0,0,fileName=dataDir+Õc31Õ) #ntwk2odf(c32,0,0,fileName=dataDir+Õc32Õ) #ntwk2odf(c33,0,0,fileName=dataDir+Õc33Õ) #ntwk2odf(c34,0,0,fileName=dataDir+Õc34Õ) #ntwk2odf(c1x,0,0,fileName=dataDir+Õc1xÕ) #ntwk2odf(c2x,0,0,fileName=dataDir+Õc2xÕ) #ntwk2odf(c3x,0,0,fileName=dataDir+Õc3xÕ) L.5ImportTimeGatedDataandMakeUseable In[ ]:#loadinODFfilesandmakethemntwks c11=odf2ntwk(dataDir +Õgated5-390-c11.ODFÕ,name =Õcald1-1 Õ)367 c12=odf2ntwk(dataDir +Õgated5-390-c12.ODFÕ,name =Õcald1-2 Õ)c13=odf2ntwk(dataDir +Õgated5-390-c13.ODFÕ,name =Õcald1-3 Õ)c21=odf2ntwk(dataDir +Õgated5-390-c21.ODFÕ,name =Õcald2-1 Õ)c22=odf2ntwk(dataDir +Õgated5-390-c22.ODFÕ,name =Õcald2-2 Õ)c23=odf2ntwk(dataDir +Õgated5-390-c23.ODFÕ,name =Õcald2-3 Õ)c31=odf2ntwk(dataDir +Õgated5-390-c31.ODFÕ,name =Õcald3-1 Õ)c32=odf2ntwk(dataDir +Õgated5-390-c32.ODFÕ,name =Õcald3-2 Õ)c33=odf2ntwk(dataDir +Õgated5-390-c33.ODFÕ,name =Õcald3-3 Õ)c34=odf2ntwk(dataDir +Õgated5-390-c34.ODFÕ,name =Õcald3-4 Õ)c1x=odf2ntwk(dataDir +Õgated2-390-c1x.ODFÕ,name =ÕcaldPlexiglas1 Õ)c2x=odf2ntwk(dataDir +Õgated2-390-c2x.ODFÕ,name =ÕcaldPlexiglas2 Õ)c3x=odf2ntwk(dataDir +Õgated2-390-c3x.ODFÕ,name =ÕcaldPlexiglas3 Õ)MakeNetworkSets In[ ]:#makeadatasetforeachburn,uncaldandcald c1=rf.NetworkSet((c11,c12,c13),name =ÕBurn1 Õ)c2=rf.NetworkSet((c21,c22,c23),name =ÕBurn2 Õ)c3=rf.NetworkSet((c31,c32,c33),name =ÕBurn3 Õ)cx=rf.NetworkSet((c1x,c2x,c3x),name =ÕPlexiglas Õ)LinearRegressionofPlexiglasPhase In[ ]:m,b,r,p,sterr =stats.linregress(c1x.f/1e9,np.real(cx.mean_s_deg_unwrap .s[:,0,0]))xFit_unwrap=m*c1x.f/1e9+bxFit=(xFit_unwrap +180)%(360)-180printrL.6BurnResults In[ ]:#ifdoPlot: #fig,ax=plt.subplots(2,1) #fig.set_figheight(7) #c1.mean_s.plot_s_db(ax=ax[0],label=ÕBurn1meanÕ) #c2.mean_s.plot_s_db(ax=ax[0],label=ÕBurn2meanÕ) #c3.mean_s.plot_s_db(ax=ax[0],label=ÕBurn3meanÕ) #bullexThy.plot_s_db(ax=ax[0],c=ÕdimgrayÕ,ls=Õ--Õ,lw=0.5) #c1.mean_s.plot_s_deg(ax=ax[1],label=ÕBurn1meanÕ) #c2.mean_s.plot_s_deg(ax=ax[1],label=ÕBurn1meanÕ) #c3.mean_s.plot_s_deg(ax=ax[1],label=ÕBurn1meanÕ) #bullexThy.plot_s_deg(ax=ax[1],c=ÕdimgrayÕ,ls=Õ--Õ,lw=0.5) #_=ax[1].legend(loc=ÕlowerrightÕ) #fig,ax=plt.subplots(2,1) #fig.set_figheight(7) #c1x.plot_s_db(ax=ax[0],label=ÕPlexi1Õ) 368 #c2x.plot_s_db(ax=ax[0],label=ÕPlexi2Õ) #c3x.plot_s_db(ax=ax[0],label=ÕPlexi3Õ) #plexiThy.plot_s_db(ax=ax[0],label=ÕTheoryÕ,c=ÕdimgrayÕ,ls=Õ--Õ,lw=0.5) #freeThy.plot_s_db(ax=ax[0],label=ÕFreeSpaceÕ,c=ÕdimgrayÕ,ls=Õ:Õ,lw=0.5) #_=ax[0].legend(loc=ÕlowerleftÕ) #c1x.plot_s_deg(ax=ax[1],y_label=ÕTransmission(dB)Õ,label=ÕPlex1Õ) #c2x.plot_s_deg(ax=ax[1],y_label=ÕTransmission(dB)Õ,label=ÕPlex2Õ) #c3x.plot_s_deg(ax=ax[1],y_label=ÕTransmission(dB)Õ,label=ÕPlex3Õ) ##c1x.plot_s_deg(ax=ax[1],c=ÕkÕ,ls=Õ-Õ) ##c2x.plot_s_deg(ax=ax[1],c=ÕkÕ,ls=Õ--Õ) ##c3x.plot_s_deg(ax=ax[1],c=ÕkÕ,ls=Õ:Õ) #_=ax[1].plot(c1x.f/1e9,xFit, #label="Linearfit") #_=ax[1].annotate("r=%.3f\ny=(%.2f)x+(%.2f)" #%(np.real(r),np.real(m),np.real(b)),(2.6,-40)) #plexiThy.plot_s_deg(ax=ax[1],label=ÕTheoryÕ,c=ÕdimgrayÕ,ls=Õ--Õ,lw=0.5) #freeThy.plot_s_deg(ax=ax[1],label=ÕFreespaceÕ,c=ÕdimgrayÕ,ls=Õ:Õ,lw=0.5) ##_=ax[1].legend() #_=ax[1].legend(loc=ÕlowerrightÕ) ##_=ax[1].set_ylim([-180,0]) In[ ]:ifdoPlot:fig,ax =plt.subplots(2,1)fig.set_figheight(7)c1.mean_s.plot_s_db(ax =ax[0],label =ÕBurn1mean Õ)c2.mean_s.plot_s_db(ax =ax[0],ls =Õ-.Õ,label =ÕBurn2mean Õ)c3.mean_s.plot_s_db(ax =ax[0],ls =Õ--Õ,label =ÕBurn3mean Õ)bullexThy.plot_s_db(ax =ax[0],ls =Õ:Õ,c=ÕkÕ,label =ÕFreespace Õ)c1.mean_s.plot_s_deg(ax =ax[1],label =ÕBurn1mean Õ,show_legend =False)c2.mean_s.plot_s_deg(ax =ax[1],ls=Õ-.Õ,label=ÕBurn2mean Õ,show_legend=False)c3.mean_s.plot_s_deg(ax =ax[1],ls=Õ--Õ,label=ÕBurn3mean Õ,show_legend=False)bullexThy.plot_s_deg(ax =ax[1],ls =Õ:Õ,c=ÕkÕ,label=ÕFreespace Õ,show_legend =False)ifdoSave:fig.savefig(dataDir+Õ2013-08-08-burn.pdfÕ)#------------------------------------------------------------ #unwrappedburn fig,ax =plt.subplots()c1.mean_s.plot_s_deg_unwrap(ax =ax,label =ÕBurn1mean Õ)c2.mean_s.plot_s_deg_unwrap(ax =ax,ls =Õ-.Õ,label =ÕBurn2mean Õ)c3.mean_s.plot_s_deg_unwrap(ax =ax,ls =Õ--Õ,label =ÕBurn3mean Õ)bullexThy.plot_s_deg_unwrap(ax =ax,ls =Õ:Õ,c=ÕkÕ,label=ÕFreespace Õ)ifdoSave:fig.savefig(dataDir+Õ2013-08-08-burn-unwrap.pdfÕ)369 #------------------------------------------------------------ #Plexiglasmeasurements fig,ax =plt.subplots(2,1)fig.set_figheight(7)cx.mean_s.plot_s_db(ax =ax[0],label =ÕPlexiglas,mean Õ)plexiThy.plot_s_db(ax=ax[0],ls =Õ--Õ,label =rÕTheory,$ \epsilon_r=%.1f$Õ%plexi[ÕepsrÕ])freeThy.plot_s_db(ax=ax[0],ls =Õ-.Õ,c=ÕkÕ,label =ÕFreeSpace Õ)#_=ax[0].legend(loc=ÕlowerleftÕ) cx.mean_s.plot_s_deg(ax =ax[1],label =ÕPlexiglas,mean Õ,show_legend =False)plexiThy.plot_s_deg(ax =ax[1],ls =Õ--Õ,label =ÕTheoryÕ,show_legend =False)freeThy.plot_s_deg(ax=ax[1],ls =Õ-.Õ,c=ÕkÕ,label=ÕFreespace Õ,show_legend =False)ifdoSave:fig.savefig(dataDir+Õ2013-08-08-plexi.pdfÕ)#------------------------------------------------------------ #unwrappedplexiglass fig,ax =plt.subplots()cx.mean_s.plot_s_deg_unwrap(ax =ax,label =ÕPlexiglas,mean Õ)plexiThy.plot_s_deg_unwrap(ax =ax,ls =Õ--Õ,label=rÕTheory,$ \epsilon_r=%.1f$Õ%plexi[ÕepsrÕ])_=ax.plot(c1x.f/1e9,xFit_unwrap,label =ÕBestfitofmean Õ)freeThy.plot_s_deg_unwrap(ax =ax,ls =Õ-.Õ,c=ÕkÕ,label=ÕFreespace Õ)ifdoSave:fig.savefig(dataDir +Õ2013-08-08-plexi-unwrap.pdfÕ)370 AppendixM IPythonnotebook: Bullex-at-BTFD-2013-12-06 M.1ExperimentsatBTFDusingtheBullexFireExtinguisher Trainer ¥ConductedatBTFD ¥2013-12-06 M.1.1Files In[ ]:!ls-1~/Documents/code/Data/2013-12-06/ M.2Pre-ßight M.2.1Imports In[ ]:#Importbasicmodules #makesurethatdivisionisdoneasexpected from__future__importdivision#plottingsetup %matplotlibinline importmatplotlib.pyplot aspltplt.style.use(Õgray_back Õ)#gettheviridiscolormap #https://bids.github.io/colormap #itwillbeavailableascmaps.viridis importcolormapsascmaps#for3dgraphs 371 #frommpl_toolkits.mplot3dimportaxes3d #forlegendsofcombinedfigtypes #importmatplotlib.linesasmlines #numericalfunctions importnumpyasnp#needsomeconstants fromscipyimport constantsfromnumpyimport pi#RFtools! importskrfasrf#versioninformation #%install_exthttp://raw.github.com/jrjohansson/version_information/ #master/version_information.py #%load_extversion_information #%reload_extversion_information #%version_informationnumpy,scipy,matplotlib In[ ]:fromscipyimportstatsM.2.2Parameters,ConÞg,andConstants In[ ]:dataDir=Õ/mnt/home/temmeand/Documents/code/Data/2013-12-06/ ÕdoPlot=True #doSave=True doSave=False ifdoSave:doPlot =Trueplt.rcParams[Õaxes.ymargin Õ]=0In[ ]:fmin=2.5e9fmax=5.5e9fpts=201freeFire={ÕepsrÕ:1,ÕmurÕ:1,ÕdÕ:11.25*constants.inch#,ÕdÕ:12*constants.inch }M.2.3ErrorChecking In[ ]:#noneatthistime 372 M.2.4PrelimCalculations In[ ]:freq=np.linspace(fmin,fmax,fpts) M.2.5FunctionDeÞnitions In[ ]:defntwk2odf(ntwk,m =1,n=0,fileName =None,EOL =Õ\r\nÕ):ÕÕÕSavesanskrfnetworkinODFformat Saveones-parameterfromanetworkasanodfformattedfile.In thefrequencydomain,eachlinecontainsthefrequency,real values,andimaginaryvaluesseperatedbycommas. ÔmÔandÔnÔallowyoutopickwhichSparametertosave Ifnofilenameisgiven,thenameofthenetworkisused DefaultendoflinecharacterisWindowscompatible(\\r\\n) Parameters----------ntwk:skrfNetworkobject Datatobesaved m,n:int SpecifiestheSparametertobesavedasS_m,n fileName:string Nameofthesavedfile.Ifnostringisprovided,the nameofthenetworkisused EOL:string Stringtobeusedattheendoftheline \\r\\n-Dos \\n-Unix Returns-------NothingÕÕÕfileName=ntwk .nameiffileNameisNoneelsefileNamewithopen(fileName +Õ.odfÕ,ÕwÕ)asfo:data=np.vstack((ntwk .f/1e9,ntwk .s_re[:,m,n],ntwk .s_im[:,m,n])).Tnp.savetxt(fo,data,delimiter =Õ,Õ,newline=EOL)defodf2ntwk(fileName,name =""):ÕÕÕLoadODFfileasntwk 373 Createaoneports-parameternetworkfromanodfformattedfile.In thefrequencydomain,eachlinecontainsthefrequency,real value,andimaginaryvalueseperatedbycommas. Parameters----------fileName:string Filetobeloaded Returns-------ntwk:skrfNetworkobject ÕÕÕ#fromnumpyimportloadtxt importskrfasrff=open(fileName, ÕrÕ)raw=np.loadtxt(f,delimiter =Õ,Õ)f.close()ifnameis"":name =fileNamefreq=raw[:,0]data=raw[:,1]+1j*raw[:,2]#ntwk=rf.Network(name=fileName,f=axis,f_unit=ÕGHzÕ,z0=50,s=data) ntwk=rf.Network(name =name,f=freq,f_unit=ÕGHzÕ,z0=50,s=data)returnntwkdefcalibrate(raw,empty,plate,thick): """Calibraterawdatausingemptyandplatemeasurement ForS21data: Cald=(raw-plate)/(empty-plate)*exp(-j*k_0*thick) Parameters----------raw:skrfnetwork rawdatatobecalibrated empty:skrfnetwork emptyrangemeasurement plate:skrfnetwork measurementofplateatthepositionofthesample thick:number thicknessofmaterialsampleinmeters Returns-------cald:skrfnetwork Calibratedata 374 """k=wavenumber(raw .f,1,1)cald=(raw-plate) /(empty-plate)*np.exp(-1j*k*thick)cald.name=cald .name+",cald "returncalddefanalyze(raw,empty,plate,thick,name ="",_doPlot =False,_doSave =False):"""Processthedata Calibratethedataandplot Parameters----------raw:skrfnetwork rawdatatobecalibrated empty:skrfnetwork emptyrangemeasurement plate:skrfnetwork measurementofplateatthepositionofthesample thick:number samplethicknessinmeters name:string labelornametouseongraphs _doPlot:boolean makeplots _doSave:boolean saveplots Returns-------cald:skrfnetwork calibratednetwork """cald=calibrate(raw,empty,plate,thick) ifnameisnot"":cald.name=nameif_doPlot:fig,ax =plt.subplots(2,1)fig.set_figheight(7)ax[0].set_title(ÕDataset: Õ+name)raw.plot_s_db(ax=ax[ 0],label =ÕRawÕ)cald.plot_s_db(ax=ax[ 0],label =ÕCaldÕ)raw.plot_s_deg(ax=ax[ 1],show_legend =False)cald.plot_s_deg(ax=ax[1],show_legend =False)375 if_doSave:fig.savefig(name+Õ.pdf Õ)returncalddefwavenumber(f,epsr,mur): return2*pi*f*np.sqrt(constants.epsilon_0*epsr*constants.mu_0*mur) defpropFactor(k,d): returnnp.exp(-1j*k*d)defimpedance(epsr =1,mur =1):returnnp.sqrt(constants .mu_0*mur/(constants.epsilon_0*epsr)) defreflectionCoeff (eta,etaf): return(eta-etaf)/(eta+etaf)deftransmission (p,g): return(1-g**2)*p/(1-p**2*g**2)defslabTheory(f,d,epsr =1,mur =1):"""Theoreticalslabtransmission S21=(1-Gamma^2)P/(1-P^2*Gamma^2) P=exp(-jkd) k=omega*sqrt(mu*eps) d=thickness Gamma=(Z-Z0)/(Z+Z0) Z=sqrt(mu/eps) Z0=sqrt(mu0/eps0) """k=wavenumber(f,epsr,mur) eta=impedance(epsr,mur) etaFree=impedance( 1,1)p=propFactor(k,d) g=reflectionCoeff(eta,etaFree) s21=transmission(p,g) name="Theory "f=f/1e9ntwk=rf.Network(name =name,f =f,f_unit =Õghz Õ,z0=50,s=s21)376 returnntwkM.3Theory Transmissionthroughadielectricslab.Normalincidence. S21=(1#%2)P/(1#P2%2)¥P=e#jkd ¥k="$µ'¥disslabthickness ¥%=(Z#Z0)/(Z+Z0)¥Z=.µ/'¥Z0=.µ0/'0M.3.1FreeSpaceAcrossBullex In[ ]:#calculateBullextheory bullexThy=slabTheory(freq,freeFire[ ÕdÕ],freeFire[ ÕepsrÕ],freeFire[ ÕmurÕ])bullexThy.name="Theory"#ifdoPlot: #fig,ax=plt.subplots() #bullexThy.plot_s_db(label="FreespaceaboveBullex,theory,d=%.2fin" #%(freeFire[ÕdÕ]/constants.inch)) #_=ax.set_ylim([-.8,0.1]) #fig,ax=plt.subplots() #bullexThy.plot_s_deg(label="FreespaceaboveBullex,theory,d=%.2fin" #%(freeFire[ÕdÕ]/constants.inch)) M.4CalibrateDataandExportforTimeGating Originallyweimportedthedata,calibrateditusing Sc21=Sm21#Sp21Se21#Sp21e#jk0d¥ccald¥mmeasured ¥pplate ¥eempty ¥k0freespacewavenumber 377 ¥dsamplethickness ThenitwassavedsothatWavecalccouldbeusedtotimegateit.Timegatingconsistedof applyingacosinetaperinthefreqdomain,applyinganinverseFFT,zeroÞllingbetweentwo timepoints,forwardFFT,andthentruncatingtooriginalfrequencyrange. Sincethisisdone,weskipthiscodenowandjustimportthegateddata. In[ ]:##originaldatamanip ##loadinODFfilesandmakethemntwks #b1a=odf2ntwk(dataDir+Õburn1-2013-12-06-165943.odfÕ,name=Õburn1aÕ) #b2a=odf2ntwk(dataDir+Õburn2-2013-12-06-170045.odfÕ,name=Õburn2aÕ) #b3a=odf2ntwk(dataDir+Õburn3-2013-12-06-170139.odfÕ,name=Õburn3aÕ) #b3b=odf2ntwk(dataDir+Õburn3-2013-12-06-170155.odfÕ,name=Õburn3bÕ) #b4a=odf2ntwk(dataDir+Õburn4-2013-12-06-170414.odfÕ,name=Õburn4aÕ) #b4b=odf2ntwk(dataDir+Õburn4-2013-12-06-170426.odfÕ,name=Õburn4bÕ) #b5a=odf2ntwk(dataDir+Õburn5-2013-12-06-170546.odfÕ,name=Õburn5aÕ) #b5b=odf2ntwk(dataDir+Õburn5-2013-12-06-170558.odfÕ,name=Õburn5bÕ) #plate=odf2ntwk(dataDir+Õplate-2013-12-06-165331.odfÕ,name=ÕplateÕ) #thrua=odf2ntwk(dataDir+Õthrough-2013-12-06-164957.odfÕ,name=ÕthruaÕ) #thrub=odf2ntwk(dataDir+Õthrough-2013-12-06-165012.odfÕ,name=ÕthrubÕ) ##plotplatemeasurement #plate.plot_s_db(show_legend=False) #plt.figure() #plate.plot_s_deg(show_legend=False) ##plotthrumeasurements #ifdoPlot: #fig,ax=plt.subplots() #thrua.plot_s_db(ax=ax,label=ÕThruAÕ) #thrub.plot_s_db(ax=ax,label=ÕThruBÕ) #fig,ax=plt.subplots() #thrua.plot_s_deg(ax=ax,label=ÕThruAÕ) #thrub.plot_s_deg(ax=ax,label=ÕThruBÕ) ##diff=np.abs(thrua.s[:,0,0]-thrub.s[:,0,0]) #magDiff=np.abs(thrua.s_db[:,0,0]-thrub.s_db[:,0,0]) #degDiff=np.abs(thrua.s_deg_unwrap[:,0,0]-thrub.s_deg_unwrap[:,0,0]) #ifdoPlot: #fig,ax=plt.subplots() ##_=ax.plot(thrua.f,diff,label="diff") #_=ax.plot(thrua.f,magDiff,label="mag") #fig,ax=plt.subplots() #_=ax.plot(thrua.f,degDiff,label="deg") ##_=ax.legend() 378 ##calibratealldata #c1a=calibrate(b1a,thrua,plate,freeFire[ÕdÕ]) #c2a=calibrate(b2a,thrua,plate,freeFire[ÕdÕ]) #c3a=calibrate(b3a,thrua,plate,freeFire[ÕdÕ]) #c3b=calibrate(b3b,thrua,plate,freeFire[ÕdÕ]) #c4a=calibrate(b4a,thrua,plate,freeFire[ÕdÕ]) #c4b=calibrate(b4b,thrua,plate,freeFire[ÕdÕ]) #c5a=calibrate(b5a,thrua,plate,freeFire[ÕdÕ]) #c5b=calibrate(b5b,thrua,plate,freeFire[ÕdÕ]) #ifdoPlot: #fig,ax=plt.subplots() #c1a.plot_s_db() #c2a.plot_s_db() #c3a.plot_s_db() #c3b.plot_s_db() #c4a.plot_s_db() #c4b.plot_s_db() #c5a.plot_s_db() #c5b.plot_s_db() #ifdoPlot: #fig,ax=plt.subplots() #b1a.plot_s_deg() #b2a.plot_s_deg() #b3a.plot_s_deg() #b3b.plot_s_deg() #b4a.plot_s_deg() #b4b.plot_s_deg() #b5a.plot_s_deg() #b5b.plot_s_deg() #ifdoPlot: #fig,ax=plt.subplots() #c1a.plot_s_deg() #c2a.plot_s_deg() #c3a.plot_s_deg() #c3b.plot_s_deg() #c4a.plot_s_deg() #c4b.plot_s_deg() #c5a.plot_s_deg() #c5b.plot_s_deg() ##savedatatobetimegated #ntwk2odf(c1a,0,0,fileName=dataDir+Õc1aÕ) #ntwk2odf(c2a,0,0,fileName=dataDir+Õc2aÕ) #ntwk2odf(c3a,0,0,fileName=dataDir+Õc3aÕ) #ntwk2odf(c3b,0,0,fileName=dataDir+Õc3bÕ) #ntwk2odf(c4a,0,0,fileName=dataDir+Õc4aÕ) #ntwk2odf(c4b,0,0,fileName=dataDir+Õc4bÕ) 379 #ntwk2odf(c5a,0,0,fileName=dataDir+Õc5aÕ) #ntwk2odf(c5b,0,0,fileName=dataDir+Õc5bÕ) M.5ImportTimeGatedDataandMakeUseable In[ ]:#loadinODFfilesandmakethemntwks c1a=odf2ntwk(dataDir +Õgated3-380-c1a.ODFÕ,name =Õcald1a Õ)c2a=odf2ntwk(dataDir +Õgated3-380-c2a.ODFÕ,name =Õcald2a Õ)c3a=odf2ntwk(dataDir +Õgated3-380-c3a.ODFÕ,name =Õcald3a Õ)c3b=odf2ntwk(dataDir +Õgated3-380-c3b.ODFÕ,name =Õcald3b Õ)c4a=odf2ntwk(dataDir +Õgated3-380-c4a.ODFÕ,name =Õcald4a Õ)c4b=odf2ntwk(dataDir +Õgated3-380-c4b.ODFÕ,name =Õcald4b Õ)c5a=odf2ntwk(dataDir +Õgated3-380-c5a.ODFÕ,name =Õcald5a Õ)c5b=odf2ntwk(dataDir +Õgated3-380-c5b.ODFÕ,name =Õcald5b Õ)MakeNetworkSets In[ ]:#makeadatasetforeachburn,uncaldandcald c=rf.NetworkSet((c1a,c2a,c3a,c3b,c4a,c4b,c5a,c5b), name=ÕCald/Gatedburns Õ)LinearRegressionofPlexiglassPhase In[ ]:m,b,r,p,sterr =stats.linregress(c1a.f/1e9,np.real(c.mean_s_deg_unwrap .s[:,0,0]))xFit=m*c1a.f/1e9+bxFit=(xFit +180)%(360)-180printrM.6BurnResults In[ ]:#ifdoPlot: #fig,ax=plt.subplots(2,1) #fig.set_figheight(7) #c1a.plot_s_db(ax=ax[0],label=ÕCald1aÕ) #c2a.plot_s_db(ax=ax[0],label=ÕCald2aÕ) #c3a.plot_s_db(ax=ax[0],label=ÕCald3aÕ) #c3b.plot_s_db(ax=ax[0],label=ÕCald3bÕ) #c4a.plot_s_db(ax=ax[0],label=ÕCald4aÕ) #c4b.plot_s_db(ax=ax[0],label=ÕCald4bÕ) #c5a.plot_s_db(ax=ax[0],label=ÕCald5aÕ) #c5b.plot_s_db(ax=ax[0],label=ÕCald5bÕ) #bullexThy.plot_s_db(ax=ax[0],c=ÕdimgrayÕ,ls=Õ--Õ,lw=0.5) #c1a.plot_s_deg(ax=ax[1],label=ÕCald1aÕ,c=ÕkÕ,lw=Õ0.5Õ) #c2a.plot_s_deg(ax=ax[1],label=ÕCald2aÕ,c=ÕkÕ,lw=Õ0.5Õ) #c3a.plot_s_deg(ax=ax[1],label=ÕCald3aÕ,c=ÕkÕ,lw=Õ0.5Õ) #c3b.plot_s_deg(ax=ax[1],label=ÕCald3bÕ,c=ÕkÕ,lw=Õ0.5Õ) 380 #c4a.plot_s_deg(ax=ax[1],label=ÕCald4aÕ,c=ÕkÕ,lw=Õ0.5Õ) #c4b.plot_s_deg(ax=ax[1],label=ÕCald4bÕ,c=ÕkÕ,lw=Õ0.5Õ) #c5a.plot_s_deg(ax=ax[1],label=ÕCald5aÕ,c=ÕkÕ,lw=Õ0.5Õ) #c5b.plot_s_deg(ax=ax[1],label=ÕCald5bÕ,c=ÕkÕ,lw=Õ0.5Õ) #bullexThy.plot_s_deg(ax=ax[1],c=ÕdimgrayÕ,ls=Õ--Õ,lw=0.5) #_=ax[1].plot(c1a.f/1e9,xFit,c=plt.rcParams[Õaxes.color_cycleÕ][0], #label="Linearfit") #_=ax[1].legend() #_=ax[1].annotate("r=%.3f\ny=(%.2f)x+(%.2f)" #%(np.real(r),np.real(m),np.real(b)),(2.6,-40)) #_=ax[1].legend(loc=ÕupperrightÕ) #_=ax[1].set_ylim([-180,0]) In[ ]:ifdoPlot:fig,ax =plt.subplots(2,1)fig.set_figheight(7)c.mean_s.plot_s_db(ax=ax[0],label =ÕMeanofallburns Õ)bullexThy.plot_s_db(ax =ax[0],label =ÕFreespace Õ,ls =Õ--Õ)c.mean_s.plot_s_deg(ax =ax[1],show_legend =False)bullexThy.plot_s_deg(ax =ax[1],ls =Õ--Õ,show_legend =False)ifdoSave:fig.savefig(dataDir+Õ2013-12-06-burn.pdfÕ)#----------------------------------------------------------------- #unwrappedphase fig,ax =plt.subplots()c.mean_s.plot_s_deg_unwrap(ax =ax,label =ÕMeanofallburns Õ)bullexThy.plot_s_deg_unwrap(ax =ax,ls =Õ--Õ,label =ÕFreespace Õ)ifdoSave:fig.savefig(dataDir+Õ2013-12-06-burn-unwrap.pdfÕ)381 AppendixN IPythonnotebook:analysis-of-2015-02-15 N.1AnalysisofInterferometricMeasurementsfrom2015-02- 15Description Availabledatasetsare: DataSetName|Cat|NoFiles|Description -------------------------|-----|--------|----------- N.2Pre-ßight Thissectionsetsupthenotebook. N.2.1Imports In[ ]:#Importbasicmodules #makesurethatdivisionisdoneasexpected from__future__importdivision#plottingsetup %matplotlibinline importmatplotlib.pyplot aspltplt.style.use(Õgray_back Õ)plt.rcParams[Õaxes.ymargin Õ]=0#gettheviridiscolormap #https://bids.github.io/colormap #itwillbeavailableascmaps.viridis importcolormaps ascmaps#for3dgraphs frommpl_toolkits.mplot3d importaxes3d382 #forlegendsofcombinedfigtypes #importmatplotlib.linesasmlines #numericalfunctions importnumpyasnp#needsomeconstants fromscipyimport constantsfromnumpyimport pi#RFtools! importskrfasrf#versioninformation #%install_exthttp://raw.github.com/jrjohansson/ #version_information/master/version_information.py #%load_extversion_information #%reload_extversion_information #%version_informationnumpy,scipy,matplotlib In[ ]:frommatplotlibimportcolors,colorbar importosimportglobN.2.2Parameters,ConÞg,andConstants In[ ]:dataDir=Õ./wichman/Data/2015-02-15/ ÕcmapUse=cmaps .viridiscmapRel=plt .get_cmap(name=ÕPRGnÕ)normAll=78In[ ]:doPrint=TruedoPlot=True doLongPlot=True#doLongPlot=False doSave=True #doSave=False ifdoSave:doPlot =TrueN.2.3ErrorChecking In[ ]:#noneatthistime N.2.4PrelimCalculations In[ ]:#noneatthistime 383 N.2.5FunctionDeÞnitions In[ ]:defntwk2odf(ntwk,m =1,n=0,fileName =None,EOL =Õ\r\nÕ):ÕÕÕSavesanskrfnetworkinODFformat Saveones-parameterfromanetworkasanodfformattedfile.In thefrequencydomain,eachlinecontainsthefrequency,real values,andimaginaryvaluesseperatedbycommas. ÔmÔandÔnÔallowyoutopickwhichSparametertosave Ifnofilenameisgiven,thenameofthenetworkisused DefaultendoflinecharacterisWindowscompatible(\\r\\n) Parameters----------ntwk:skrfNetworkobject Datatobesaved m,n:int SpecifiestheSparametertobesavedasS_m,n fileName:string Nameofthesavedfile.Ifnostringisprovided,the nameofthenetworkisused EOL:string Stringtobeusedattheendoftheline \\r\\n-Dos \\n-Unix Returns-------NothingÕÕÕfileName=ntwk .nameiffileNameisNoneelsefileNamewithopen(fileName +Õ.odfÕ,ÕwÕ)asfo:data=np.vstack((ntwk .f/1e9,ntwk .s_re[:,m,n],ntwk .s_im[:,m,n])).Tnp.savetxt(fo,data,delimiter =Õ,Õ,newline=EOL)defodf2ntwk(fileName,name =""):ÕÕÕLoadODFfileasntwk Createaoneports-parameternetworkfromanodfformattedfile.In thefrequencydomain,eachlinecontainsthefrequency,real value,andimaginaryvalueseperatedbycommas. Parameters384 ----------fileName:string Filetobeloaded Returns-------ntwk:skrfNetworkobject ÕÕÕ#fromnumpyimportloadtxt importskrfasrff=open(fileName, ÕrÕ)raw=np.loadtxt(f,delimiter =Õ,Õ)f.close()ifnameis"":name =fileNamefreq=raw[:,0]data=raw[:,1]+1j*raw[:,2]#ntwk=rf.Network(name=fileName,f=axis,f_unit=ÕGHzÕ,z0=50,s=data) ntwk=rf.Network(name =name,f=freq,f_unit=ÕGHzÕ,z0=50,s=data)returnntwkdefprocessWichBurnODF (dataDir,emptyName,sampleName,D,fRange ="",figTitle="",skip =[],ntwkODF ="odf"):"""Dininches """fromscipy.constants importc,inch ifntwkODFis"odf":eList=[]sList=[]skip=[dataDir +sforsinskip]foroinglob.glob(dataDir+emptyName+"*.ODF"):ifonotinskip:n=odf2ntwk(o) iffRangeisnot"":n=n[fRange] #printn eList.append(n)else:print"removed%s"%oforoinglob.glob(dataDir+sampleName+"*.ODF"):ifonotinskip:n=odf2ntwk(o) iffRangeisnot"":385 n=n[fRange] #printn sList.append(n)else:print"removed%s"%o#printlen(eList) #printlen(sList) empty=rf.NetworkSet(eList)salt=rf.NetworkSet(sList) elifntwkODFis"ntwk":empty=rf.NetworkSet(rf.read_all(dataDir,contains=emptyName))salt=rf.NetworkSet(rf .read_all(dataDir,contains=sampleName))empty.sort()salt.sort()freq=salt[0].f/1e9phase=salt[0].s_deg_unwrap[:,0,0]forninsalt[1:]:phase=np.vstack([phase,n .s_deg_unwrap[:,0,0]])empty=empty.mean_semptyPhase=empty.s_deg_unwrap[:,0,0]diff=phase-emptyPhaseN=lambdap,f:np .deg2rad(p)/(2.82e-15*(c/f)*D*inch)Ne=N(diff,freq *1e9)diffMask=diff <0diffMasked=np.ma.array(diff,mask=diffMask)neMask=Ne<0NeMasked=np.ma.array(Ne,mask=neMask)diffSurf=diff .copy()diffLessZero=diffSurf<0diffSurf[diffLessZero] =0NeSurf=Ne.copy() NeLessZero=NeSurf<0NeSurf[NeLessZero]=0absMaxDiff=np.max([np.max(diff),abs(np.min(diff))]) absMaxNe=np.max([np.max(Ne),abs(np.min(Ne))])printabsMaxDiffprintabsMaxNe#frommpl_toolkits.mplot3dimportAxes3D #importmatplotlib.pyplotasplt 386 #--------------------------------------------------------------------------- #--------------------------------------------------------------------------- #fig=plt.figure() #ax=fig.gca(projection=Õ3dÕ) ##fori,ninenumerate(diff): #ax.plot(freq,n,i,zdir=ÕyÕ) ###ax.legend() #ax.set_xlim3d(min(freq),max(freq)) #ax.set_ylim3d(-1,diff.shape[0]) #ax.set_zlim3d(diff.min(),diff.max()) ##ax.set_xlabel(ÕFrequency(GHz)Õ) #ax.set_ylabel(ÕSampleNo.Õ) #ax.set_zlabel(ÕPhaseDifference(deg)Õ) ##iffigTitleisnot"": #ax.set_title(figTitle) ##plt.show() ###*********** ##plt.figure() #empty.plot_s_db(show_legend=False) #iffigTitleisnot"": #plt.title(figTitle) #plt.legend([ÕEmptyÕ]) ###*********** ##plt.figure() #salt.plot_s_db(show_legend=False) #iffigTitleisnot"": #plt.title(figTitle) #plt.legend([ÕSaltÕ]) ###*********** ##plt.figure() #empty.plot_s_deg(show_legend=False) #iffigTitleisnot"": #plt.title(figTitle) #plt.legend([ÕEmptyÕ]) ###*********** ##plt.figure() #salt.plot_s_deg(show_legend=False) 387 #iffigTitleisnot"": #plt.title(figTitle) #plt.legend([ÕSaltÕ]) ###*********** ##plt.figure() #forxindiff: #plt.plot(freq,x) #plt.xlabel(ÕFrequency(GHz)Õ) #plt.ylabel(ÕPhaseDifference(deg)Õ) #iffigTitleisnot"": #plt.title(figTitle) ##fromscipy.constantsimportc,inch ###*********** ##plt.figure() #forxinNe: #plt.plot(freq,x) ##plt.xlabel(ÕFrequency(GHz)Õ) #plt.ylabel(rÕElectronDensity,N(m$^{-3}$)Õ) #iffigTitleisnot"": #plt.title(figTitle) ###ax2=twinx() ###ax2.set_xscale(ÕlogÕ) ##grid(False,ÕbothÕ,ÕbothÕ) ###xlabel(ÕPlasmaThickness(mm)Õ) ###ax2.set_xlim([min(D),max(D)]) ###t=[30,50,100,200,300,500] ###ax2.set_xticks(t) ###ax2.set_xticklabels(t) ###ax2.invert_xaxis() ##plot(freq,empty.s_deg[:,0,0]) ###*********** ##fig=plt.figure() #ax=fig.gca(projection=Õ3dÕ) ##fori,ninenumerate(Ne): #ax.plot(freq,n,i,zdir=ÕyÕ) ###ax.legend() ##ax.set_xlim3d(min(freq),max(freq)) #ax.set_ylim3d(-1,Ne.shape[0]) #ax.set_zlim3d(Ne.min(),Ne.max()) 388 ##ax.set_xlabel(ÕFrequency(GHz)Õ) #ax.set_ylabel(ÕSampleNo.Õ) #ax.set_zlabel(rÕElectronDensity,N(m$^{-3}$)Õ) ##iffigTitleisnot"": #ax.set_title(figTitle) ##plt.show() ###-------------------------------------------------------------------------- ##-------------------------------------------------------------------------- ##-------------------------------------------------------------------------- ##-------------------------------------------------------------------------- ###3DgraphsofPhaseDifference ##----------------------------- #fig=plt.figure() #ax=fig.gca(projection=Õ3dÕ) ##X=freq #Y=np.arange(1,diff.shape[0]+1) #X,Y=np.meshgrid(X,Y) #Z=diffSurf #surf=ax.plot_surface(X,Y,Z,rstride=1,cstride=1,linewidth=0, #cmap=cmapUse)#,vmin=0,vmax=absMaxDiff) ###ax.legend() #ax.set_xlim3d(min(freq),max(freq)) #ax.set_ylim3d(-1,Z.shape[0]) #ax.set_zlim3d(Z.min(),Z.max()) ##ax.set_xlabel(ÕFrequency(GHz)Õ) #ax.set_ylabel(ÕSampleNo.Õ) #ax.set_zlabel(rÕPhaseDifference,$\angle_1-\angle_0$(deg)Õ) #iffigTitleisnot"": #ax.set_title(figTitle) ##plt.show() ###*********** ##plt.figure() #plt.imshow(diffMasked,interpolation=ÕnoneÕ,origin=ÕlowerÕ, #cmap=cmapUse,#vmin=0,vmax=absMaxDiff, #extent=[freq.min(),freq.max(),1,diff.shape[0]+1],aspect=ÕautoÕ) #plt.grid(ÕoffÕ) #cb=plt.colorbar() #cb.set_label(rÕPhaseDifference,$\angle_1-\angle_0$(deg)Õ) #plt.xlabel(ÕFrequency(GHz)Õ) #plt.ylabel(ÕSampleNumberÕ) 389 #iffigTitleisnot"": #plt.title(figTitle) ###-------------------------------------------------------------------------- ###3DgraphsofElectronDensity ##----------------------------- #fig=plt.figure() #ax=fig.gca(projection=Õ3dÕ) ##X=freq #Y=np.arange(1,Ne.shape[0]+1) #X,Y=np.meshgrid(X,Y) #Z=NeSurf #surf=ax.plot_surface(X,Y,Z,rstride=1,cstride=1,linewidth=0, #cmap=cmapUse)#,vmin=0,vmax=absMaxNe) ####ax.legend() #ax.set_xlim3d(min(freq),max(freq)) #ax.set_ylim3d(-1,Z.shape[0]) #ax.set_zlim3d(Z.min(),Z.max()) ##ax.set_xlabel(ÕFrequency(GHz)Õ) #ax.set_ylabel(ÕSampleNo.Õ) #ax.set_zlabel(rÕElectronDensity,N(m$^{-3}$)Õ) #iffigTitleisnot"": #ax.set_title(figTitle) ##plt.show() ###*********** ##plt.figure() #plt.imshow(NeMasked,interpolation=ÕnoneÕ,origin=ÕlowerÕ, #cmap=cmapUse,#vmin=0,vmax=absMaxNe, #extent=[freq.min(),freq.max(),1,Ne.shape[0]+1],aspect=ÕautoÕ) #plt.grid(ÕoffÕ) #cb=plt.colorbar() #cb.set_label(rÕElectronDensity,N(m$^{-3}$)Õ) #plt.xlabel(ÕFrequency(GHz)Õ) #plt.ylabel(ÕSampleNumberÕ) #iffigTitleisnot"": #plt.title(figTitle) ##-------------------------------------------------------------------------- ##-------------------------------------------------------------------------- ##-------------------------------------------------------------------------- ##-------------------------------------------------------------------------- ##RelativeColors ##-------------------------------------------------------------------------- #390 #3DgraphsofPhaseDifference #----------------------------- fig=plt.figure() ax=fig.gca(projection =Õ3dÕ)ax.set_axis_bgcolor(ÕwhiteÕ)X=freqY=np.arange( 1,diff.shape[0]+1)X,Y =np.meshgrid(X,Y) Z=diffsurf=ax.plot_surface(X,Y,Z,rstride =1,cstride =1,linewidth =0,cmap=cmapRel,vmin =-absMaxDiff,vmax =absMaxDiff)#ax.legend() ax.set_xlim3d(min(freq), max(freq))ax.set_ylim3d(-1,Z.shape[ 0])ax.set_zlim3d(Z.min(),Z .max())ax.set_xlabel(ÕFrequency(GHz) Õ)ax.set_ylabel(ÕSampleNo. Õ)ax.set_zlabel(rÕPhaseDifference,$ \angle_1-\angle_0$(deg) Õ)#iffigTitleisnot"": #ax.set_title(figTitle) plt.show()ifdoSave:fig.savefig(dataDir+figTitle+"-3d.pdf")fig.savefig(dataDir+figTitle+"-3d.jpg")#*********** #plt.figure() #plt.imshow(diff,interpolation=ÕnoneÕ,origin=ÕlowerÕ, #cmap=cmapRel,vmin=-absMaxDiff,vmax=absMaxDiff, #extent=[freq.min(),freq.max(),1,diff.shape[0]+1],aspect=ÕautoÕ) #plt.grid(ÕoffÕ) #cb=plt.colorbar() #cb.set_label(rÕPhaseDifference,$\angle_1-\angle_0$(deg)Õ) #plt.xlabel(ÕFrequency(GHz)Õ) #plt.ylabel(ÕSampleNumberÕ) #iffigTitleisnot"": #plt.title(figTitle) #ifdoSave: #plt.savefig(dataDir+figTitle+"-2d.pdf") #plt.savefig(dataDir+figTitle+"-2d.jpg") ####--------------------------------------------------------------------------- ###3DgraphsofElectronDensity 391 ##----------------------------- #fig=plt.figure() #ax=fig.gca(projection=Õ3dÕ) ##X=freq #Y=np.arange(1,Ne.shape[0]+1) #X,Y=np.meshgrid(X,Y) #Z=Ne #surf=ax.plot_surface(X,Y,Z,rstride=1,cstride=1,linewidth=0, #cmap=cmapRel,vmin=-absMaxNe,vmax=absMaxNe) ####ax.legend() #ax.set_xlim3d(min(freq),max(freq)) #ax.set_ylim3d(-1,Z.shape[0]) #ax.set_zlim3d(Z.min(),Z.max()) ##ax.set_xlabel(ÕFrequency(GHz)Õ) #ax.set_ylabel(ÕSampleNo.Õ) #ax.set_zlabel(rÕElectronDensity,N(m$^{-3}$)Õ) #iffigTitleisnot"": #ax.set_title(figTitle) ##plt.show() ###*********** ##plt.figure() #plt.imshow(Ne,interpolation=ÕnoneÕ,origin=ÕlowerÕ, #cmap=cmapRel,vmin=-absMaxNe,vmax=absMaxNe, #extent=[freq.min(),freq.max(),1,Ne.shape[0]+1],aspect=ÕautoÕ) #plt.grid(ÕoffÕ) #cb=plt.colorbar() #cb.set_label(rÕElectronDensity,N(m$^{-3}$)Õ) #plt.xlabel(ÕFrequency(GHz)Õ) #plt.ylabel(ÕSampleNumberÕ) #iffigTitleisnot"": #plt.title(figTitle) #------------------------------------------------------------------------- #2dfigurewith2colorbars fig=plt.figure(figsize =(6,4))ax=fig.add_axes([ 0.05,0.05,0.7,0.7])p=ax.imshow(diff,interpolation =ÕnoneÕ,origin=Õlower Õ,cmap=cmapRel,vmin =-absMaxDiff,vmax =absMaxDiff,extent=[freq.min(),freq .max(),1,diff.shape[0]+1],aspect=Õauto Õ)ax.grid(ÕoffÕ)plt.xlabel(ÕFrequency(GHz) Õ)plt.ylabel(ÕSampleNumber Õ)cb=plt.colorbar(p)392 cb.set_label(rÕPhaseDifference,$ \angle_1-\angle_0$(deg) Õ)axC=fig.add_axes([ 0.8,0.05,.02,.7])norm=colors.Normalize(vmin=-absMaxNe,vmax =absMaxNe) cb2=colorbar .ColorbarBase(axC,cmap =cmapRel,norm =norm)cb2.set_label(ÕElectronDensity,$m^{-3}$ Õ)#iffigTitleisnot"": #plt.title(figTitle) ifdoSave:plt.savefig(dataDir+figTitle+"-2d.pdf")plt.savefig(dataDir+figTitle+"-2d.jpg")#------------------------------------------------------------------------- #Normalized2dfigure plt.figure()plt.imshow(diff,interpolation =ÕnoneÕ,origin=ÕlowerÕ,cmap=cmapRel,vmin =-normAll,vmax =normAll,extent=[freq.min(),freq .max(),1,diff.shape[0]+1],aspect=Õauto Õ)plt.grid(ÕoffÕ)#cb=plt.colorbar() #cb.set_label(rÕPhaseDifference,$\angle_1-\angle_0$(deg)Õ) #plt.xlabel(ÕFrequency(GHz)Õ) #plt.ylabel(ÕSampleNumberÕ) plt.axis(ÕoffÕ)ifdoSave:plt.savefig(dataDir+figTitle+"-norm.pdf")plt.savefig(dataDir+figTitle+"-norm.jpg")#xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx #xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx #xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx #xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx #xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx #xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx defwavenumber(f,epsr,mur): return2*pi*f*np.sqrt(constants.epsilon_0*epsr*constants.mu_0*mur) defcalibrate(raw,empty,plate,thick): """Calibraterawdatausingemptyandplatemeasurement ForS21data: Cald=(raw-plate)/(empty-plate)*exp(-j*k_0*thick) 393 Parameters----------raw:skrfnetwork rawdatatobecalibrated empty:skrfnetwork emptyrangemeasurement plate:skrfnetwork measurementofplateatthepositionofthesample thick:number thicknessofmaterialsampleinmeters Returns-------cald:skrfnetwork Calibratedata """k=wavenumber(raw .f,1,1)cald=(raw-plate) /(empty-plate)*np.exp(-1j*k*thick)cald.name=cald .name+",cald "returncalddefwriteZFmacro (macroName,folder,zfStart,zfStop,trMin,trMax,prefix): withopen(macroName +Õ.MACÕ,ÕwÕ)asfo:forfinos.listdir(folder):iff[-3:]=="s1p":fName=f[:-4]fo.write("\"Open\"\r\n")fo.write("2\r\n")fo.write(("\"\\\\tsclient \\Z\\Documents\\plasmaInterferometer "+"\\wichman\\Data\\2015-02-15\\"+fName+".odf\"\r\n"))fo.write("\"1\"\r\n")fo.write("\"CT\"\r\n")fo.write("2\r\n")fo.write("\"2\"\r\n")fo.write("\"10\"\r\n")fo.write("\"FFT\"\r\n")fo.write("6\r\n")fo.write("\"200\"\r\n")fo.write("\"1024\"\r\n")fo.write("\"2048\"\r\n")fo.write("\"2048\"\r\n")fo.write("\"4.885198E-02 \"\r\n")fo.write("\"0\"\r\n")fo.write("\"ZF\"\r\n")fo.write("2\r\n")fo.write("\""+str(zfStart) +"\"\r\n")fo.write("\""+str(zfStop) +"\"\r\n")fo.write("\"FFT\"\r\n")fo.write("6\r\n")394 fo.write("\"0\"\r\n")fo.write("\"2048\"\r\n")fo.write("\"1024\"\r\n")fo.write("\"2048\"\r\n")fo.write("\"0.01\"\r\n")fo.write("\"0\"\r\n")fo.write("\"Trc\"\r\n")fo.write("2\r\n")fo.write("\""+str(trMin) +"\"\r\n")fo.write("\""+str(trMax) +"\"\r\n")fo.write("\"Save\"\r\n")fo.write("1\r\n")fo.write(("\"\\\\tsclient \\Z\\Documents\\plasmaInterferometer "+"\\wichman\\Data\\2015-02-15\\"+prefix+fName+".ODF\"\r\n"))defloadAll(ntwks): loaded={}forkey,val inntwks.items():loaded[key]=rf.NetworkSet(rf.read_all(dataDir,contains =val))#ntwk2odf(loaded[key].mean_s,m=0,n=0,fileName=dataDir+val+Õ-meanÕ) #ifdoPlot: #fig,ax=plt.subplots() #loaded[key].plot_uncertainty_bounds_s_deg(show_legend=False) #_=ax.set_title(val) ##ax2=ax.twinx() ##loaded[key].plot_uncertainty_bounds_s_deg(show_legend=False, ##c=plt.rcParams[Õaxes.color_cycleÕ][1]) #_=ax.set_ylim([-180,180]) returnloadeddefplotAll(cnt,ntwkNames,frange =""):forkey,val insorted(ntwkNames.items()):iffrangeisnot"":val.mean_s[frange].plot_s_db(ax =ax[cnt-1],c =ÕkÕ,lw =0.5,show_legend=False)else:val.mean_s.plot_s_db(ax =ax[cnt-1],c =ÕkÕ,lw =0.5,show_legend =False)N.3GateData In[ ]:#writeZFmacro(ÕzfMeÕ,dataDir,3.9,120,2,6,Õgated-3-9--Õ) In[ ]:#forfinos.listdir(dataDir): #iff[-3:]=="s1p": #ntwk2odf(rf.Network(dataDir+f),m=0,n=0,fileName=f[:-4]) 395 N.4CompareEmptyData In[ ]:#freqRange=Õ2-6ghzÕ ##names={Õ1foilDishÕ:Õempty-foil-lined-dish-2015Õ, #Õ2dishPlexiÕ:Õdish-with-plexi-meth-2015Õ, #Õ3preMethanolÕ:Õempty-methanol-pre-2015Õ, #Õ4betweenÕ:Õempty-between-meth-salt-2015Õ, #Õ5saltPostÕ:Õempty-salt-post-2015Õ, #Õ6plexiPostÕ:Õempty-plexi-2-post-2015Õ, #}##emptys=loadAll(names) ##num=len(names) #firstColor=plt.rcParams[Õaxes.color_cycleÕ][0] ##ifdoLongPlot: #fig,ax=plt.subplots(num,1) #fig.set_figheight(num*3) ##forkey,valinsorted(emptys.items()): #i=int(key[0]) #plotAll(i,emptys) ##val.mean_s[freqRange].plot_s_db(ax=ax[i-1],show_legend=False, ##c=firstColor) #val.mean_s.plot_s_db(ax=ax[i-1],show_legend=False, #c=firstColor) #_=ax[i-1].legend([names[key]]) N.5PlotBurns In[ ]:processWichBurnODF(dataDir,Õgated-3-9--empty-methanol-pre-2015 Õ,Õgated-3-9--methanol-pure-2015 Õ,D=6*constants.inch,fRange=Õ2.5-5.5ghzÕ,figTitle=Õ2015-02-15-meth Õ,ntwkODF=ÕodfÕ)In[ ]:processWichBurnODF(dataDir,Õgated-3-9--empty-methanol-pre-2015 Õ,Õgated-3-9--salt-250ml-2015 Õ,D=6*constants.inch,fRange=Õ2.5-5.5ghzÕ,figTitle=Õ2015-02-15-salt Õ,ntwkODF=ÕodfÕ)In[ ]:processWichBurnODF(dataDir,Õgated-3-9--empty-methanol-pre-2015 Õ,Õgated-3-9--plexi-2-flame-2015 Õ,D=6*constants.inch,fRange=Õ2.5-5.5ghzÕ,figTitle=Õ2015-02-15-plexi Õ,ntwkODF=ÕodfÕ)396 AppendixO IPythonnotebook:AR8200-data-Þt O.1FitLMValuestodBmValues S-meterreadingsareaccquiredoveraserialconnecitonusingthe LMcommandontheAR8200 scanner.OnepieceofdocumentationhasatablerelatingtheS-meterreadingstodBm.This Þtsacurvetothatdata. O.2Pre-ßight Thissectionsetsupthenotebook. O.2.1Imports In[ ]:#Importbasicmodules #makesurethatdivisionisdoneasexpected from__future__importdivision#plottingsetup %matplotlibinline importmatplotlib.pyplot aspltplt.style.use(Õgray_back Õ)plt.rcParams[Õaxes.ymargin Õ]=0#gettheviridiscolormap #https://bids.github.io/colormap #itwillbeavailableascmaps.viridis #importcolormapsascmaps #for3dgraphs #frommpl_toolkits.mplot3dimportaxes3d #forlegendsofcombinedfigtypes #importmatplotlib.linesasmlines #numericalfunctions 397 importnumpyasnp#needsomeconstants fromscipyimport constantsfromnumpyimport pi#RFtools! #importskrfasrf #versioninformation #%install_exthttp://raw.github.com/jrjohansson/version_information/ #master/version_information.py #%load_extversion_information #%reload_extversion_information #%version_informationnumpy,scipy,matplotlib O.2.2Parameters,ConÞg,andConstants In[ ]:doPrint=TruedoPlot=True doSave=True #doSave=False ifdoSave:doPlot =Trueplt.rcParams[Õlines.linewidth Õ]=2O.3FitCurve In[ ]:lm=np.array([0,10,27,42,55,68,86,97,103,106,109,112])dbm=np.array([ -115,-110,-105,-100,-95,-90,-80,-70,-60,-50,-40,-30])x=np.linspace( 0,120)z=np.polyfit(lm,dbm, 6,full =True)printzp=np.poly1d(z[ 0])ifdoPlot:fig,ax =plt.subplots()_=ax.plot(x,p(x),label =ÕBestfit Õ)_=ax.scatter(lm,dbm,s =35,marker =ÕsÕ,c=plt.rcParams[Õaxes.color_cycle Õ][1],label=ÕTabularvalue Õ)_=ax.set_xlabel(ÕLMvalue Õ)_=ax.set_ylabel(ÕdBmvalue Õ)_=ax.legend()398 ifdoSave:fig.savefig(Õar8200-curve.pdf Õ)399 AppendixP IPythonnotebook:CPW-CPS-Impedance P.1CoplanarLineImpedanceCalculations MostofthisworkcomesfromGupta,KC. MicrostripLinesandSlotlines ,2nded.Boston: ArtechHouse,1996,Venkatesan,Jaikrishna,2004.ÒInvestigationoftheDouble-YBalunfor FeedingPulsedAntennas,ÓDissertation.http://hdl.handle.net/1853/5036,orSimons,Rainee. 2001. CoplanarWaveguideCircuits,Components,andSystems .NewYork:JohnWiley. http://ieeexplore.ieee.org/xpl/bkabstractplus.jsp?bkn=5201692.AlsocheckouttheCPScalcu- latorathttp://www1.sphere.ne.jp/i-lab/ilab/tool/cps_e.htm In[ 1]:from__future__importdivisionimportscipy.constants asconstfromscipy.special importellipkfromscipy.optimize importfsolve,minimize,fminbound fromnumpyimport abs,log,sqrt fromIPython.core.display importImageimportgitrepo=git.Repo( "./")#a79-charruler: #234567891123456789212345678931234567894123456789512345678961234567897123456789 #a72-charruler: #23456789112345678921234567893123456789412345678951234567896123456789712 In[ 2]:print repo.head.commit.hexshadd2179db63cbbf351e47a02e76ea2404ee8b40b5 http://docs.python.org/2/tutorial/inputoutput.html ThisprogramrunswithSciPy0.11.0andNumPy1.6.1.Theminimizationroutineisnot availablein0.9.0andIwashavingproblemsgettingeverythingtoworkin0.13.0. 400 P.1.1MSUSubstratePropertiesandManufacturing TheMSUEMgrouptypicallyuses1.575mmthickRogersRT/duroid5870asasubstrate.The ECEShopusuallymillscircuitboardsoutof0.06inthickFR4with1oz/sq.ftcopperonboth sides. PropertiesofRogersRT/duroid5870include:
  • 1.575mm=62milsthickness
  • Relativepermittivity$\epsilon_r=2.33$
  • Relativepermeability$\mu_r=1$
  • Losstangent$\tan\delta=0.0012$
  • Smallestgappossible0.2mm=7.87mils
    • PropertiesoftheFR4inclde:
  • 0.06~in=60milsthickness
  • Copperthickness1oz/sq.ft=$34.1\\mu$m=1.34mill
  • Relativepermittivity$\epsilon_r=4.4$
  • Relativepermeability$\mu_r=1$
  • Losstangetn$\tan\delta=0.02$
  • smallestgappossible12mils=0.3mm
    • TheEMgroupusesphotolithographytocreatecircuitboards.PaststudentsÕexperience suggestthattheminimumtracewidthis1mm(~39mils),maybeeven0.75mm(~29.5mils), andthattheminimumgapis0.2mm(7.87mils). TheECEShopmanufacturingtolerancesarereportedly0.20Ð0.25mm(8-10mils)forthe minimumwidthofatraceand0.3mm(12mils)fortheminimumwidthofagapfortheirma- chiningprocess.Theshopnotesthattracesnearthisminimumwidthareeasilyliftedoffthe substratebytheapplicationofheat.Theengineershouldbecarefulwhensolderingsuchtraces. [FromemailswiththeECEShop] P.1.2Geometry ReferenceGeometry |-----------------2c------------------| |-----------2b------------| |---2a----||--g--|---W---|----S----|---W---|--g--| ___________________ ____|_____|_______|_________|_______|_____|_______ |\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\|| |\\\\\\\\\\\\\\\\\\\\eps_r\\\\\\\\\\\\\\\\\\\|h |\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\|| 401 -------------------------------------------------- CoplanarWaveguide(cpw) |-------------2b--------------| |---2a----||----W----|----S----|----W----| __________________ ________|_________|_________|_________|___________ |\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\|| |\\\\\\\\\\\\\\\\\\\\eps_r\\\\\\\\\\\\\\\\\\\|h |\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\|| -------------------------------------------------- CoplanarStrips(cps) P.1.3Equations CoplanarStrip Theimpedanceforacoplanarstripisgivenby Zo,cps =120 &$'cps reK(k1)K&(k1)Gupta(7.75) 'cps re=1+'r#12K(k2)K&(k2)K&(k1)K(k1)for h/b>1Gupta(7.17) k1=ab=SS+2WGupta(7.64).Notethat a,=Sbut2 a=S,likewise2 b=S+2W.k2=sinh( &a/2h)sinh( &b/2h)Gupta(7.16) where Sisthegapbetweenthestrips, Wisthewidthofthestrip,and Kand K&arethe completeellipticintegralsoftheÞrstkindanditscomplement K&(k)=K!$1#k2"=K(k&)CoplanarWaveguide Theimpedanceforacoplanarwaveguideisgivenby Zo,cpw =30&$'cpw reK&(k3)K(k3)Gupta(7.29) 'cpw re=1+'r#12K(k4)K&(k4)K&(k3)K(k3)Gupta(7.68) k3=ab41#b2/c21#a2/c2Gupta(7.23) where2 a=S,2b=S+2W,and2 c=S+2W+2gk4=sinh( &a/2h)sinh( &b/2h)#1#sinh2(&b/2h)/sinh 2(&c/2h)1#sinh2(&a/2h)/sinh 2(&c/2h)Gupta(7.27) where Sisthewidthofthecenterconductor, Wisthewidthofthegap, gisthewidthofthe groundstrip,and Kand K&arethecompleteellipticintegralsoftheÞrstkindanditscomple- ment K&(k)=K!$1#k2"=K(k&)402 P.1.4Computations Functions Notethattheelectircallengthandpermittivityfunctionshavenotbeentestedrigorouslyby themselves. In[ 3]:#23456789112345678921234567893123456789412345678951234567896123456789712 defKKPrime(k):"""AnapproximatecalculationofK(k)/KÕ(k) Usinganapproximation,calculatesacompleteellipticintegralofthe firstkindoveritscomplement.TheapproximationisgiveninGupta,1st ed.Parameters----------k:scalar argumentoftheellipticintegral Returns-------result:scalar AnapproximatevalueforK(k)/KÕ(k) """if0<=kandk<0.707:kp=sqrt(1-k**2)result=const .pi/log(2*(1+sqrt(kp))/(1-sqrt(kp))) elif0.707<=kandk<=1:result=log( 2*(1+sqrt(k))/(1-sqrt(k)))/const.pielse:printkraiseNameError(ÕEllipticArgumentoutofrange,k= Õ,k) returnresultdefKPrimeK(k):"""AnapproximatecalculationofKÕ(k)K(k) Usinganapproximation,calculatesacomplementarycompleteelliptic integralofthefirstkindovertheoriginalintegral.The approximationisgiveninGupta,1sted. Parameters----------k:scalar argumentoftheellipticintegral Returns-------403 result:scalar AnapproximatevalueforKÕ(k)K(k) """return1/KKPrime(k) deflenElectric(physicalL,freq,eps_eff): """Calculatestheelectricallengthofatransmissionline Parameters----------physicalL:scalar Thephysicallengthofthelineinmeters freq:scalar Frequency(Hz) eps_eff:scalar Effectivepermittivityofthetransmissionline Returns-------d:scalar Electricallengthindegrees """omega=2*pi*freqr=physicalL*omega*sqrt(eps_eff*const.mu_0*const.epsilon_0) d=r*180/pireturnddeflenPhysical(elecL,freq,eps_eff): """Convertselectriclength(deg)tophysicallength Parameters----------elecL:scalar,degrees Thephysicallengthofthelineinmeters freq:scalar Frequency(Hz) eps_eff:scalar Effectivepermittivityofthetransmissionline Returns-------p:scalar Physicallengthinmeters """omega=2*pi*freqr=elecL*pi/180p=r/(omega*sqrt(eps_eff*const.mu_0*const.epsilon_0)) returnp404 defunitsmmtomil (x):"""ConvertÕmmÕtoÕmilÕ """returnx/0.0254defunitsmiltomm (x):"""ConvertÕmilÕtoÕmmÕ """returnx*0.0254defzCPS(gap,trace,h,eps_r,approx =True ):"""Calctheimpedanceofasymmetriccoplanarstripline.Defaultapprox Calculatetheimpedanceofasymmetriccoplanarstripline(CPS)with agapofwidthÕgapÕandtracesÕtraceÕ,onasubstrateofheigth ÕhÕ,andrelativepermittivityÕeps_rÕ.Bydefault,itusesan approximatevalueforK/KÕorKÕ/K. Parameters----------gap:scalar Gapwidth trace:scalar Tracewidth(assumessymmetricCPS) h:scalar Substrateheigth eps_r:scalar Relativepermittivityofthesubstrate approx:bool,optional Iftrue,useanapproximationforK/KÕandKÕ/K,theelliptic integralsReturns-------z:scalar CalculatedimpedanceoftheCPS """a=gap/2b=gap/2+trace k1=a/b#notsurewhichversionofk2touse.Somebookshave #thesinhsquaredandsomedonÕt #k2=sinh(const.pi*a/(2*h))**2/sinh(const.pi*b/(2*h))**2 k2=sinh(const .pi*a/(2*h))/sinh(const.pi*b/(2*h))ifapprox:vecKKP=numpy .vectorize(KKPrime)405 vecKPK=numpy .vectorize(KPrimeK)eps_eff=1+(eps_r-1)/2*vecKKP(k2)*vecKPK(k1)z=120*const .pi/sqrt(eps_eff)*vecKKP(k1)else:k1Prime=sqrt( 1-k1**2)k2Prime=sqrt( 1-k2**2)eps_eff=(1+(eps_r-1)/2*ellipk(k2) /ellipk(k2Prime)*ellipk(k1Prime)/ellipk(k1)) z=120*const .pi/sqrt(eps_eff)*ellipk(k1)/ellipk(k1Prime) returnzdefepsCPS(gap,trace,h,eps_r,approx =True):"""Calceps_effofasymmetriccoplanarstripline.Defaultapprox Calculatetheeffictivepermittivityofasymmetriccoplanar stripline(CPS)withagapofwidthÕgapÕandtracesÕtraceÕ,ona substrateofheigthÕhÕ,andrelativepermittivityÕeps_rÕ.By default,itusesanapproximatevalueforK/KÕorKÕ/K. Parameters----------gap:scalar Gapwidth trace:scalar Tracewidth(assumessymmetricCPS) h:scalar Substrateheigth eps_r:scalar Relativepermittivityofthesubstrate approx:bool,optional Iftrue,useanapproximationforK/KÕandKÕ/K,theelliptic integralsReturns-------eps_eff:scalar CalculatedeffictivepermittivityoftheCPS """a=gap/2b=gap/2+trace k1=a/b#notsurewhichversionofk2touse.Somebookshave #thesinhsquaredandsomedonÕt #k2=sinh(const.pi*a/(2*h))**2/sinh(const.pi*b/(2*h))**2 k2=sinh(const .pi*a/(2*h))/sinh(const.pi*b/(2*h))ifapprox:vecKKP=numpy .vectorize(KKPrime)vecKPK=numpy .vectorize(KPrimeK)eps_eff=1+(eps_r-1)/2*vecKKP(k2)*vecKPK(k1)406 else:k1Prime=sqrt( 1-k1**2)k2Prime=sqrt( 1-k2**2)eps_eff=(1+(eps_r-1)/2*ellipk(k2) /ellipk(k2Prime)*ellipk(k1Prime)/ellipk(k1)) returneps_effdefepsCPW(cntr,gap,gnd,h,eps_r,approx =True):"""Calceps_effofasymmetriccoplanarwaveguide.Defaultapprox Calculatetheeffectivepermittivityofasymmetriccoplanr waveguide(CPW)withacentertraceofwidthÕcntrÕ,gapsofwidth ÕgapÕ,andgroundtracesofwidthÕgÕ,onasubstrateofheigthÕhÕ, andrelativepermittivityÕeps_rÕ.Bydefault,itusesan approximatevalueforK/KÕorKÕ/K. Parameters----------cntr:scalar Centertracewidth gap:scalar Gapwidth(assumessymmetricCPW) gnd:scalar Groundtracewidth(assumessymmetricCPW) h:scalar Substrateheigth eps_r:scalar Relativepermittivityofthesubstrate approx:bool,optional Iftrue,useanapproximationforK/KÕandKÕ/K,theelliptic integralsReturns-------eps_eff:scalar CalculatedeffictivepermittivityoftheCPW """a=cntr/2b=(cntr+2*gap) /2c=(cntr+2*gap +2*gnd)/2k3=a/b*sqrt(( 1-b**2/c**2)/(1-a**2/c**2))k4=(sinh(const .pi*a/(2*h))/sinh(const.pi*b/(2*h))*sqrt((1-sinh(const.pi*b/(2*h))**2/sinh(const.pi*c/(2*h))**2)/(1-sinh(const.pi*a/(2*h))**2/sinh(const.pi*c/(2*h))**2))) ifapprox:vecKKP=numpy .vectorize(KKPrime)vecKPK=numpy .vectorize(KPrimeK)eps_eff=1+(eps_r-1)/2*vecKKP(k4)*vecKPK(k3)407 else:k3Prime=sqrt( 1-k3**2)k4Prime=sqrt( 1-k4**2)eps_eff=(1+(eps_r-1)/2*ellipk(k4) /ellipk(k4Prime)*ellipk(k3Prime)/ellipk(k3)) returneps_effdefzCPW(cntr,gap,gnd,h,eps_r,approx =True):"""Calctheimpedanceofasymmetriccoplanarwaveguide.Defaultapprox Calculatetheimpedanceofasymmetriccoplanarwaveguide(CPW)with acentertraceofwidthÕcntrÕ,gapsofwidthÕgapÕ,andground tracesofwidthÕgÕ,onasubstrateofheigthÕhÕ,andrelative permittivityÕeps_rÕ.Bydefault,itusesanapproximatevaluefor K/KÕorKÕ/K. Parameters----------cntr:scalar Centertracewidth gap:scalar Gapwidth(assumessymmetricCPW) gnd:scalar Groundtracewidth(assumessymmetricCPW) h:scalar Substrateheigth eps_r:scalar Relativepermittivityofthesubstrate approx:bool,optional Iftrue,useanapproximationforK/KÕandKÕ/K,theelliptic integralsReturns-------z:scalar CalculatedimpedanceoftheCPW """a=cntr/2b=(cntr+2*gap) /2c=(cntr+2*gap +2*gnd)/2k3=a/b*sqrt(( 1-b**2/c**2)/(1-a**2/c**2))k4=(sinh(const .pi*a/(2*h))/sinh(const.pi*b/(2*h))*sqrt((1-sinh(const.pi*b/(2*h))**2/sinh(const.pi*c/(2*h))**2)/(1-sinh(const.pi*a/(2*h))**2/sinh(const.pi*c/(2*h))**2))) ifapprox:vecKKP=numpy .vectorize(KKPrime)vecKPK=numpy .vectorize(KPrimeK)eps_eff=1+(eps_r-1)/2*vecKKP(k4)*vecKPK(k3)z=30*pi/sqrt(eps_eff) *vecKPK(k3)408 else:k3Prime=sqrt( 1-k3**2)k4Prime=sqrt( 1-k4**2)eps_eff=(1+(eps_r-1)/2*ellipk(k4) /ellipk(k4Prime)*ellipk(k3Prime)/ellipk(k3)) z=30*pi/sqrt(eps_eff) *ellipk(k3Prime)/ellipk(k3)returnzdefzEqual(dims,gnd,h,eps_r,approx =True):"""CalculatestheimpedancedifferencesbetweenCPSandCPW Calculatestheimpedancedifferencebetweenacoplanarstirpanda coplanarwaveguide. Parameters----------dims:array AnarrayoftheCPSandCPWparameters. cpwCntr=dims[0] cpwGap=dims[1] cpsGap=dims[2] cpsTrace=dims[3] gnd:scalar Groundtracewidth(assumessymmetricCPW) h:scalar Substrateheigth eps_r:scalar Relativepermittivityofthesubstrate approx:bool,optional Iftrue,useanapproximationforK/KÕandKÕ/K,theelliptic integralsReturns-------zDiff:scalar TheabsolutedifferencebetweentheimpedanceofaCPS andaCPW """cpwCntr=dims[ 0]cpwGap=dims[ 1]cpsGap=dims[ 2]cpsTrace=dims[ 3]cpw=zCPW(cpwCntr,cpwGap,gnd,h,eps_r,approx) cps=zCPS(cpsGap,cpsTrace,h,eps_r,approx) zDiff=abs(cpw -cps)returnzDiffdefzEqualOutsideWidths (dims,cpwCntr,cpwGap,cpsGap,h,eps_r,approx =True):"""WrapperforzEqualwithadifferentorderofargs 409 Parameters----------dims:array AnarrayoftheoutsidewidthsofaCPWandCPS cpsTrace=dims[0] cpwGnd=dims[1] cpwCntr:scalar WidthoftheCPWcenterstrip cpwGap:scalar WidthoftheCPWgap cpsGap:scalar WidthoftheCPSgap h:scalar Substrateheigth eps_r:scalar Relativepermittivityofthesubstrate approx:bool,optional Iftrue,useanapproximationforK/KÕandKÕ/K,theelliptic integralsReturns-------zDiff:scalar TheabsolutedifferencebetweentheimpedanceofaCPS andaCPW """cpsTrace=dims[ 0]cpwGnd=dims[ 1]cpw=zCPW(cpwCntr,cpwGap,cpwGnd,h,eps_r,approx) cps=zCPS(cpsGap,cpsTrace,h,eps_r,approx) zDiff=abs(cpw -cps)returnzDiff#Wrapperfunctions defcpsS(S,W,h,eps_r,approx): return zCPS(S,W,h,eps_r,approx) defcpsW(W,S,h,eps_r,approx): return zCPS(S,W,h,eps_r,approx) defcpsh(h,S,W,eps_r,approx): return zCPS(S,W,h,eps_r,approx) defcpsEps_r(eps_r,S,W,h,approx): returnzCPS(S,W,h,eps_r,approx) defcpwS(S,W,g,h,eps_r,approx): returnzCPW(S,W,g,h,eps_r,approx) defcpwW(W,S,g,h,eps_r,approx): returnzCPW(S,W,g,h,eps_r,approx) defcpwh(h,S,W,g,eps_r,approx): returnzCPW(S,W,g,h,eps_r,approx) defcpwg(g,S,W,h,eps_r,approx): returnzCPW(S,W,g,h,eps_r,approx) defcpwEps_r(eps_r,S,W,g,h,approx): returnzCPW(S,W,g,h,eps_r,approx) defminimizeGivenGnd (minGap,minTrace,cpwGnd,eps_r,h,approxK, printResults=True):"""FindCPS/CPWdimensinosgivenminimumsandacpwgroundwidth 410 Thisfunctionfindsthedimensionsforacoplanrstripline(CPS)and acoplanarwaveguide(CPW),givenaminimumgapwidth,minimumtrace width,andawidthfortheCPWground(outside)traces.Thereturned solutionshouldhavelinesthatareequalintotalwidthandhave equalimpedances. Theinitialguessissimplytheminimumvalues Parameters----------minGap:scalar Minimumwidthofagap minTrace:scalar Minimumwidthofatrace cpwGnd:scalar Widthofthegroundtracesforthecoplanarwaveguide(CPW) eps_r:scalar Therelativepermittivityofthesubstrate h:scalar Heigthofthesubstrate approxK:bool Iftrue,useanapproximationforK/KÕandKÕ/K,theelliptic integralsprintResults:bool,optional Printresultsandotherinformationabouttheinputvaluesand thesoltuion Returns-------res:Result Theresultreturnedbyscipy.optimize.minimize.res.xhasthe solutionvalues. Notes-----SeedocumentationforÔÔscipy.optimize.minimizeÔÔformoreinfo. Thevariablesforsolvingaredefinedinthefollowingorder: x[-]*S_cpw *W_cpw *S_cpw *W_cps ConstraintsareeitherÕeqÕforequalityorÕineqÕforÔ>0Ô Thefollowingconstraintisusedsothatthelinesareofequal width:x[0]+2*x[1]+2*p[ÕcpwGndÕ]-x[2]-2*x[3] 411 Thatis S_cpw+2*W_cpw+2*g_cpw-(S_cps+2*W_cps)=0 """p={ÕminGapÕ:minGap, ÕminTraceÕ:minTrace, ÕcpwGndÕ:cpwGnd, Õeps_rÕ:eps_r, ÕhÕ:h, ÕapproxKÕ:approxK} #argumentorder: resOrder=(ÕcpwCntr(S) Õ,ÕcpwGap(W) Õ,ÕcpsGap(S) Õ,ÕcpsTrace(W) Õ)args=p[ÕcpwGnd Õ],p[ ÕhÕ],p[ Õeps_rÕ],p[ ÕapproxKÕ]initGuess=(p[ ÕminTraceÕ],p[ ÕminGapÕ],p[ ÕminGapÕ],p[ ÕminTraceÕ])#cpwCntr,cpwGap,cpsGap,cpsTrace bnds=((p[ÕminTrace Õ],200),(p[ ÕminGapÕ],200),(p[ ÕminGapÕ],200),(p[ÕminTraceÕ],200))cons=({Õtype Õ:ÕeqÕ,ÕfunÕ:lambdax:x[ 0]+2*x[1]+2*p[ÕcpwGnd Õ]-x[2]-2*x[3]})res=minimize(zEqual,initGuess,args,method =ÕSLSQPÕ,bounds =bnds,constraints=cons)ifprintResults:aCpwCntr,aCpwGap,aCpsGap,aCpsTrace =res.xaCpwGnd=cpwGnd cpwWidth=aCpwCntr+2*aCpwGap+2*aCpwGndcpsWidth=aCpsGap+2*aCpsTracecpsZ=zCPS(aCpsGap,aCpsTrace,h,eps_r,approxK) cpwZ=zCPW(aCpwCntr,aCpwGap,cpwGnd,h,eps_r,approxK) cpsEpsEff=epsCPS(aCpsGap,aCpsTrace,h,eps_r,approxK) cpwEpsEff=epsCPW(aCpwCntr,aCpwGap,cpwGnd,h,eps_r,approxK) FREQ=8e9cpsStub45=lenPhysical(45,FREQ,cpsEpsEff) cpwStub45=lenPhysical(45,FREQ,cpwEpsEff) checks={ÕWidth,CPW Õ:cpwWidth, ÕWidth,CPS Õ:cpsWidth, ÕWidth,|Diff| Õ:abs(cpwWidth-cpsWidth),ÕZ,CPS Õ:cpsZ, ÕZ,CPW Õ:cpwZ, ÕZ,|Diff| Õ:abs(cpsZ-cpwZ)}print"Command\n-------"print("minimizeGivenGnd(minGap={},minTrace={},cpwGnd={}, ""eps_r={}, ".format(minGap,minTrace,cpwGnd,eps_r)) print("\t\th={},approxK={},printResults={}) ".format(h,approxK,printResults)) print"\nResults \n-------\n",res 412 forainrange(4):printÕ{0:15}={1:15f} Õ.format(resOrder[a],res.x[a])print"\nParameters \n----------"print"{0:15}={1:15} ".format(ÕInitialguess Õ,initGuess) forit,val insorted(p.items()):printÕ{0:15}={1:15} Õ.format(it,val) print"\nChecks\n------"forit,val insorted(checks.items()):print"{0:15}={1:15f} ".format(it,val) print"\nEffectivePermittivity \n---------------------- "print"CPS={} ".format(cpsEpsEff)print"CPW={} ".format(cpwEpsEff)print("\n45degLengthinmil(mm)at{}GHz \n""----------------------------------- ".format(FREQ/1e9))print"CPS={}({}) ".format(unitsmmtomil(cpsStub45 /1e-3),cpsStub45/1e-3)print"CPW={}({}) ".format(unitsmmtomil(cpwStub45 /1e-3),cpsStub45/1e-3)print"\nCommit\n------"printrepo.head.commit.hexshareturnresVeriÞcation HeresomebasictestsaredonetotrythefunctionsdeÞnedabove.Firstwewilltestthat zEqualcomputesthedifferencecorrectly. In[ 4]:#MakesurethatZequalcomputesthedifferencecorrectly S_cps=15#milsW_cps=23.21#milsS_cpw=10#milsW_cpw=11.54#milsgtry=8#milshtry=62#milseps_rtry=2.33 printzEqual([S_cpw,W_cpw,S_cps,W_cps],gtry,htry,eps_rtry,approx =False)a=zCPW(S_cpw,W_cpw,gtry,htry,eps_rtry,approx =False)b=zCPS(S_cps,W_cps,htry,eps_rtry, False)printabs(a-b)#shouldbe16.635... 16.635405237716.6354052377NowcheckthecomputationoftheimpedanceforspeciÞclines.FromFigure29ofVenkate- sanÕsPhDdissertation,weexpectthattheimpedanceshouldbearound104 "whenanapprox- imateexpressionfortheEllipticalIntegralsisused.ThedimensionsfromtheÞgureare: 413 ¥CPSÐGap(S)=6 ÐTrace(W)=21.51 ÐHeigth(h)=58 ÐRel.Perm.(eps_r)=4.4 ¥CPWÐCenterTrace(S)=10 ÐGap(W)=11.54 ÐGroundTrace(g)=8 ÐHeigth(h)=58 ÐRel.Perm.(eps_r)=4.4 Atthistime,Idonotknowhaveasourcetowhichtocomparetheimpedanewhenapproxi- mationsarenotused. In[ 5]:print zCPS(6,21.51,58,4.4 ,False)printzCPS(6,21.51,58,4.4,True)#~104printzCPW(10,11.54,8,58,4.4,False )printzCPW(10,11.54,8,58,4.4,True )#~10497.6507742856104.134634884110.319293355104.131367052LetÕstrytomatchFigure7.9inGupta.ThisÞgureisaplotoftheÒ(a)Variationofthechar- acteristicimpedanceforaCPWwithÞnitewidthgroundplanesonGaAssubstrate( 'r=13, h=300 µm,and2 b=200 µm)and(b)variationoftheeffectivedielectricconstantforaCPW withÞnitewidthgroundplanesonGaAssusbstrate...(from[26]).Ó In[ 6]:b=200/2#micrometersabFrac=linspace( .01,.8,99)cbFrac=1.5a=b*abFracc=b*cbFracS=2*aW=b-ag=c-bh=300#micrometerseps_r=13plot(abFrac,zCPW(S,W,g,h,eps_r, False))Out[6]:[] TryingtomatchFigure7.15inGupta2nded. 414 FigureP.1:notebookÞgure In[ 7]:eps_r =13b=100h=2*babFrac=linspace( .01,.9,99)a=b*abFracS=2*aW=b-avfunc=numpy .vectorize(zCPS)z=vfunc(S,W,h,eps_r, True)semilogx(abFrac,z,abFrac,zCPS(S,W,h,eps_r, False))#semilogx(abFrac,z)#semilogx(abFrac,Z_0cps(S,W,h,eps_r,0)) Out[7]:[, ] P.1.5TestingSolving LetÕstryÞndingtheslotwidthofthetracesforaCPSgivenanimpedanceandtracewidth.These valuesarebasedonFigure29ofVenkatesanÕsdissertation. 415 FigureP.2:notebookÞgure 416 ¥CPSÐGap(S)=6 ÐTrace(W)=21.51 ÐHeigth(h)=58 ÐRel.Perm.(eps_r)=4.4 ¥CPWÐCenterTrace(S)=10 ÐGap(W)=11.54 ÐGroundTrace(g)=8 ÐHeigth(h)=58 ÐRel.Perm.(eps_r)=4.4 In[ 8]:cpsGap =6h=58eps_r=4.4approx=True ztarget=104 fargs=cpsGap,h,eps_r,approx defsol(W,S,h,eps_r,approx): return abs(cpsW(W,S,h,eps_r,approx) -ztarget)cpsTrace=fsolve(sol, 15,fargs)print"CPSTraceWidth(W)foundtobe:{} ".format(cpsTrace)print"Expected:21.51 "cpwCntr=10cpwGap=11.54 h=28eps_r=4.4approx=True ztarget=104 initGuess=10fargs=cpwCntr,cpwGap,h,eps_r,approx defsol(g,S,W,h,eps_r,approx): returnabs(cpwg(g,S,W,h,eps_r,approx) -ztarget)gcpw=fsolve(sol,initGuess,fargs) print"CPWgroundtracewidth(g)foundtobe:{} ".format(gcpw) print"Expected:8 "CPSTraceWidth(W)foundtobe:[21.62419289] Expected:21.51 CPWgroundtracewidth(g)foundtobe:[8.44234866] Expected:8 417 P.1.6SolvingfortheBalunDesign Minimization Seethedocumentationfor scipy.optimize.minimize foranexampleofsolvingaproblem withboundsandconstraints.TheproblemisExample16.4fromNocedal,J,andSJWright. 2006.NumericalOptimization.SpringerNewYork.Theoreticalsolutionis(1.4,17.7). CheckingoptimizationaroundVenkatesanÕsdesigninFigure29ofhisPhD.Again,hisdesign is¥CPSÐGap(S)=6 ÐTrace(W)=21.51 ÐHeigth(h)=58 ÐRel.Perm.(eps_r)=4.4 ¥CPWÐCenterTrace(S)=10 ÐGap(W)=11.54 ÐGroundTrace(g)=8 ÐHeigth(h)=58 ÐRel.Perm.(eps_r)=4.4 In[ 9]:ans=minimizeGivenGnd(minGap=5,minTrace =5,cpwGnd =8,eps_r =4.4 ,h=58,approxK =True,printResults =True)Command-------minimizeGivenGnd(minGap=5,minTrace=5,cpwGnd=8,eps_r=4.4, h=58,approxK=True,printResults=True) Results-------status:0 success:True njev:8 nfev:60 fun:5.3060588811604248e-08 x:array([5.56456239,8.18915459,5.19301774,16.37492691]) message:ÕOptimizationterminatedsuccessfully.Õ jac:array([-4.77325726,4.17049885,-5.38675499,1.65678978,0.]) nit:8 cpwCntr(S)=5.564562 cpwGap(W)=8.189155 cpsGap(S)=5.193018 cpsTrace(W)=16.374927 418 Parameters----------Initialguess=(5,5,5,5) approxK=1 cpwGnd=8 eps_r=4.4 h=58 minGap=5 minTrace=5 Checks------Width,CPS=37.942872 Width,CPW=37.942872 Width,|Diff|=0.000000 Z,CPS=107.357323 Z,CPW=107.357323 Z,|Diff|=0.000000 EffectivePermittivity ---------------------- CPS=2.67849405337 CPW=2.699593365 45degLengthinmil(mm)at8.0GHz ----------------------------------- CPS=112.683847983(2.86216973877) CPW=112.242630524(2.86216973877) Commit------dd2179db63cbbf351e47a02e76ea2404ee8b40b5 Twodifferentresultsbaseduponslightlydifferentinitialconditions. Firstsethasinitialparamatersof minGap=5 ,minTrace=5 ,and cpwGnd=8 .Results-------status:0 success:True njev:8 nfev:60 fun:5.3060588811604248e-08 x:array([5.56456239,8.18915459,5.19301774,16.37492691]) message:ÕOptimizationterminatedsuccessfully.Õ jac:array([-4.77325726,4.17049885,-5.38675499,1.65678978,0.]) nit:8 cpwCntr=5.564562 cpwGap=8.189155 419 cpsGap=5.193018 cpsTrace=16.374927 Parameters----------Initialguess=(5,5,5,5) approxK=1 cpwGnd=8 eps_r=4.4 h=58 minGap=5 minTrace=5 Checks------Width,CPS=37.942872 Width,CPW=37.942872 Width,|Diff|=0.000000 Z,CPS=107.357323 Z,CPW=107.357323 Z,|Diff|=0.000000 Thesecondsethasinitialparamatersof minGap=5.8 ,minTrace=7.5 ,and cpwGnd= 8.Results-------status:0 success:True njev:13 nfev:99 fun:2.3782860125720617e-07 x:array([8.39335319,11.27949445,6.45282611,20.24975799]) message:ÕOptimizationterminatedsuccessfully.Õ jac:array([3.04381466,-1.3562355,4.36965179,-1.3295393,0.]) nit:13 cpwCntr=8.393353 cpwGap=11.279494 cpsGap=6.452826 cpsTrace=20.249758 Parameters----------420 Initialguess=(7.5,5.8,5.8,7.5) approxK=1 cpwGnd=8 eps_r=4.4 h=58 minGap=5.8 minTrace=7.5 Checks------Width,CPS=46.952342 Width,CPW=46.952342 Width,|Diff|=0.000000 Z,CPS=107.714192 Z,CPW=107.714192 Z,|Diff|=0.000000 Theseresultssuggestthatthesolutionisverysensitivetotheinitialguess/inputparameters andalsothatmultiplesolutionsarepossible.Thisisplausiblebecauseofthenumerouspossible combinationsofdimensionsforthegeometry. BalunOptimization EtchingRogersSubstrateDesign WewanttoÞndtheparametersfortheCPWandCPSlines inthebalun.Weneedtheimpedancetobethesameformaximumpowertransferandtoavoid problemswiththelengthofthestubs. Afterdeterminingthebalundimensions,wecanÞndthedimensionsforthe50 "coaxfeed. Afterthatwedesignthedimensionsforthetwo-wiret-linefeed. IntheendwewanttheoveralwidthoftheCPWtobethesameastheCPS.Thismeansthat Scpw +2Wcpw +2gcpw =Scps +2Wcps .Ourboundsare: ¥Lineimpedancethesame,i.e. Z0,cpw =Z0,cps +Z0,cpw #Z0,cps =0¥Overalwidthequal,i.e. Scpw +2Wcpw +2gcpw =Scps +2Wcps +Scpw +2Wcpw +2gcpw #(Scps +2Wcps )=0¥Gapslargerthan10mils,i.e. Scps and$W_{cpw}>10$mils(fornowusingRogersand photoetch) ¥Traceslargerthan30mils,i.e. Scpw ,gcpw and$W_{cps}>30$mils(fornowusingRogers andphotoetch) Knownvaluesare: ¥h=62mils 421 ¥'r=2.33 Guptasuggestskeeping gcpw assmallaspossiblesotry gcpw =40mils. LetÕstryforadesignusingRogerÕsboardandMSUÕsphotoetchingtolerances. Fromabove: PropertiesofRogersRT/duroid5870include: ¥1.575mm=62milsthickness ¥Relativepermittivity 'r=2.33 ¥Relativepermeability µr=1¥Losstangenttan )=0.0012 ¥Smallestgappossible0.2mm=7.87mils TheEMgroupusesphotolithographytocreatecircuitboards.PaststudentsÕexperience suggestthattheminimumtracewidthis1mm(~39mils),maybeeven0.75mm(~29.5mils), andthattheminimumgapis0.2mm(7.87mils). In[ 10]:ans=minimizeGivenGnd(minGap=10,minTrace =30,cpwGnd =30,eps_r =2.33,h=62,approxK =True,printResults =True)Command-------minimizeGivenGnd(minGap=10,minTrace=30,cpwGnd=30,eps_r=2.33, h=62,approxK=True,printResults=True) Results-------status:0 success:True njev:13 nfev:102 fun:4.2085090967702854e-08 x:array([30.25031242,26.83738566,11.48377189,66.22065592]) message:ÕOptimizationterminatedsuccessfully.Õ jac:array([-0.95010185,1.48096275,-2.54771805,0.37209129,0.]) nit:13 cpwCntr(S)=30.250312 cpwGap(W)=26.837386 cpsGap(S)=11.483772 cpsTrace(W)=66.220656 Parameters----------Initialguess=(30,10,10,30) approxK=1 cpwGnd=30 eps_r=2.33 h=62 minGap=10 422 minTrace=30 Checks------Width,CPS=143.925084 Width,CPW=143.925084 Width,|Diff|=0.000000 Z,CPS=120.030812 Z,CPW=120.030812 Z,|Diff|=0.000000 EffectivePermittivity ---------------------- CPS=1.58958675438 CPW=1.64859004902 45degLengthinmil(mm)at8.0GHz ----------------------------------- CPS=146.273244525(3.71534041093) CPW=143.631823869(3.71534041093) Commit------dd2179db63cbbf351e47a02e76ea2404ee8b40b5 MillingFR4Design PropertiesoftheFR4inclde:
  • 0.06~in=60milsthickness
  • Copperthickness1oz/sq.ft=$34.1\\mu$m=1.34mill
  • Relativepermittivity$\epsilon_r=4.4$
  • Relativepermeability$\mu_r=1$
  • Losstangetn$\tan\delta=0.02$
  • smallestgappossible12mils=0.3mm
    • TheECEShopmanufacturingtolerancesarereportedly0.20Ð0.25mm(8-10mils)forthe minimumwidthofatraceand0.3mm(12mils)fortheminimumwidthofagapfortheirma- chiningprocess.Theshopnotesthattracesnearthisminimumwidthareeasilyliftedoffthe substratebytheapplicationofheat.Theengineershouldbecarefulwhensolderingsuchtraces. [FromemailswiththeECEShop] In[ 11]:ans=minimizeGivenGnd(minGap=15,minTrace =10,cpwGnd =10,eps_r =4.4,h=60,approxK =False,printResults =True)Command-------minimizeGivenGnd(minGap=15,minTrace=10,cpwGnd=10,eps_r=4.4, h=60,approxK=False,printResults=True) Results423 -------status:0 success:True njev:10 nfev:72 fun:6.2007970313970873e-08 x:array([10.31348856,17.08618148,15.23289466,24.62647843]) message:ÕOptimizationterminatedsuccessfully.Õ jac:array([2.85736275,-2.39193249,2.44193268,-1.38985634,0.]) nit:10 cpwCntr(S)=10.313489 cpwGap(W)=17.086181 cpsGap(S)=15.232895 cpsTrace(W)=24.626478 Parameters----------Initialguess=(10,15,15,10) approxK=0 cpwGnd=10 eps_r=4.4 h=60 minGap=15 minTrace=10 Checks------Width,CPS=64.485852 Width,CPW=64.485852 Width,|Diff|=0.000000 Z,CPS=122.488955 Z,CPW=122.488955 Z,|Diff|=0.000000 EffectivePermittivity ---------------------- CPS=2.63153917822 CPW=2.69632614237 45degLengthinmil(mm)at8.0GHz ----------------------------------- CPS=113.684718893(2.88759185988) CPW=112.310613887(2.88759185988) Commit------dd2179db63cbbf351e47a02e76ea2404ee8b40b5 Noideaifthisisactuallythe BEST design,butitworks.Checksaregood. 424 P.1.7TaperDesign Theabovesolutionneedstobematchedtoeitherthe50ohmcoaxorthetwo-wiretransmission line. LetÕsbeginwithmatchingtheCPWtoa50ohmcoaxcable.SincetheCPWimpedanceis greaterthan50ohms,wecandecreasethegaporincreasethewidthofthetraces. ApossibleCPWgeometrywasfoundinthedatasheetforthePasternackPE4542SMAFemale ConnectorSolderAttachment0.062inchEndLaunchPCB,.030inchDiameterafterlooking atvariouspossibleconnectors.Thisdatasheethappenedtohaveadrawingandtablefora connectortoCPWovergroundplanetomicrostriptransition.Foraboardthicknessof62mils, thecenterconductoris90milswide,agapwidthof80mils,andagroundtraceof95mils inwidth.ForaCPWwithÞnitewidthgroundplane,thesedimensionson60milsthickFR4 ('r=4.4)giveanimpedanceof In[ 12]:zCPW( 90,80,95,60,4.4)Out[12]:103.11657421385755 Thisimpedanceistoohigh.Pastexperience Pastexperiencesuggeststhat50ohmscannotbereachedbysimplyextendingtheground plane.Thisissupportedbythefollowinggraph. In[ 13]:gnd=linspace(50,500,201)vfunc=numpy .vectorize(zCPW)z=vfunc(90,80,gnd, 60,4.4)plot(gnd,z) Out[13]:[] Theimpedancedoesnotreach98ohmsevenwhentheCPWisoveroneinchintotalwidth. Trailanderrorforreducingthegapandincreasingthetracewidthsgivesthefollowingclose solutionfor50ohms: In[ 14]:zCPW( 190,15,200,60,4.4)Out[14]:50.083760262937176 Usingthisinformation,asolutionforthecenterwidthissought. In[ 15]:cpwGap =15cpwGnd=200h=60eps_r=4.4ztarget=50initGuess=200approx=(True ,False)forainapprox:fargs=cpwGap,cpwGnd,h,eps_r,a defsol(S,W,g,h,eps_r,a): return abs(cpwS(S,W,g,h,eps_r,a) -ztarget)scpw=fsolve(sol,initGuess,fargs) print("Approx:{} \nCPWcentertracewidth(S)foundtobe:{} ".format(a,scpw)) 425 FigureP.3:notebookÞgure Approx:True CPWcentertracewidth(S)foundtobe:[192.17178487] Approx:False CPWcentertracewidth(S)foundtobe:[173.91823265] HFSSresultssuggestthatthe173.91milswidecentertraceisabettermatchto50ohms becauseS11islower. VenusesanexponentialtaperfromPozar,(pg262,4thed).Theimpedanceatanypoint alongthetaperisgivenby Z(z)=Z0e+z,0*z*L,where +=1Lln,ZLZ0-,Listhelengthofthetaper, Z0isthesourceimpedance,and ZListheloadimpedance.This canalsobeexpressedas Z(z)=Z0,ZLZ0-z/L.426 Pozarnotes thatthelengthshouldbegreaterthan$\lambda/2\(\betaL> \pi)$tominimizethemismatchatlowfrequencies. (pg263)Alongerline,however, hasmoreloss;therefore,abalancemustbeselected. InHFSS,thisisenteredas (S/2+W+g)*((bS/2+bW+bg)/(S/2+W+g))ö(_t/L) foraequation basedcurve.HereapreÞxof bcorrespondstodimensionsonthebalunsideofthetaperwhile nopreÞxcorrespondstodimesnsionsonthecoaxsideofthetaper. In[ 16]:L=1Z_src=50Z_L=122.49z=linspace( 0,L,200)alpha=1/L*log(Z_L/Z_src)Zofz=Z_src*(Z_L/Z_src)**(z/L)plot(z,Zofz) Out[16]:[] FigureP.4:notebookÞgure Wearesimplygoingtoapplythissamecurvetothedimensionsofthetransmissionlines.In theend,wegetagradualtransistion,sohopefullyitworkswell. Todeterminelength,letususethe1GHzasourfrequencyandaneffectivepermittivityfrom thebalundesignabove. ,/2isthen In[ 17]:lenPhysical( 180,1e9,2.69)427 Out[17]:0.091393343832089732 meters.Thisisprettybig.Probablynotgoingtosatisfythiscriteria. Theabovedesignworks;however,thewidthofthecenterstripisprobablytoowide.Ihad Brianintheshopmeasurethedielectricofaconnectorandhesaid4.3mmindiameter.Thisis 169.29mils.Wewilltryadesignwithacenterstripwidthof150and125milstoseewhatthe groundplanesizesendupbeing. In[ 18]:cpwCntr =150cpwGap=15h=60eps_r=4.4ztarget=50initGuess=300approx=(True ,False)forainapprox:fargs=cpwCntr,cpwGap,h,eps_r,a defsol(g,S,W,h,eps_r,a): return abs(cpwg(g,S,W,h,eps_r,a) -ztarget)gcpw=fsolve(sol,initGuess,fargs) print("Approx:{} \nCPWgroundtracewidth(g)foundtobe:{} ".format(a,gcpw)) -c:291:RuntimeWarning:overflowencounteredinsquare -c:292:RuntimeWarning:overflowencounteredinsquare -c:291:RuntimeWarning:overflowencounteredinsinh -c:292:RuntimeWarning:overflowencounteredinsinh /opt/software/SciPy/0.11.0--GCC-4.4.5/lib/python2.7/site-packages/scipy/ optimize/minpack.py:221:RuntimeWarning:Theiterationisnotmakinggood progress,asmeasuredbythe improvementfromthelastteniterations. warnings.warn(msg,RuntimeWarning) Approx:True CPWgroundtracewidth(g)foundtobe:[10983888.26897169] Approx:False CPWgroundtracewidth(g)foundtobe:[17610084.44435658] ThatÕsnotreallyworking.Ifwevary g,whatistheasymptopicimpedance? In[ 19]:gnd=linspace(50,500,201)vfunc=numpy .vectorize(zCPW)z=vfunc(150 ,15,gnd, 60,4.4,False)plot(gnd,z) z=vfunc(125 ,15,gnd, 60,4.4,False)plot(gnd,z) z=vfunc(125 ,12,gnd, 60,4.4,False)plot(gnd,z) Out[19]:[] Oh.ThatÕswhyitisnotworking.CanÕtreallygetdownlowenough.Letustrytovarythegap sizewitha200milwidegroundtrace.Firstthough,whatistheimpedanceifwejustshrinkthe centrtrace? 428 FigureP.5:notebookÞgure 429 In[ 20]:print zCPW(173.92,15,200,60,4.4,False)printzCPW(150,15,200,60,4.4,False )printzCPW(125,15,200,60,4.4,False )49.999912862651.329078476453.1489813028Notbad.Certainlyuseable.LetÕstryvaryingthegapnow. In[ 21]:gap=linspace(8,15,201)vfunc=numpy .vectorize(zCPW)z=vfunc(125 ,gap, 200,60,4.4)plot(gap,z) Out[21]:[] FigureP.6:notebookÞgure Theshopsaysthattheminimumgapsizeis12mils.Thisgives In[ 22]:print zCPW(125,12,200,60,4.4,False)49.687145128LetÕsoptimizefor12then. 430 In[ 23]:cpwCntr =125cpwGap=12h=60eps_r=4.4ztarget=50initGuess=200approx=(True ,False)forainapprox:fargs=cpwCntr,cpwGap,h,eps_r,a defsol(g,S,W,h,eps_r,a): return abs(cpwg(g,S,W,h,eps_r,a) -ztarget)gcpw=fsolve(sol,initGuess,fargs) print("Approx:{} \nCPWGROUNDtracewidth(g)foundtobe:{} ".format(a,gcpw)) Approx:True CPWGROUNDtracewidth(g)foundtobe:[494.24149395] Approx:False CPWGROUNDtracewidth(g)foundtobe:[154.11046673] Hereisagoodtimetopointoutthedifferencebetweenusingatrueapproximationversus thefunctionsfor K/K'.Oneseesthatwhenusingtheapproximation,thetracewidthis494mils insteadof154.ThisisasigniÞcantdifference.Weshouldtrysimulatingthisandseewhatthe actualdifferenceis.Tonote,though,isthatwemaybeoperatinginthenormalboundsofthe CPWequations. Insummary,wehavethefollowingdimensions:: |CoaxFeedSide |154.1112125mil ||--g--|---W---|----S----|---W---|--g--| |___________________ |____|_____|_______|_________|_______|_____|_______ ||\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\|| ||\\\\\\\\\\\\\\\\\eps_r=4.4\\\\\\\\\\\\\\\\\|60mil ||\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\|| |-------------------------------------------------- |||BalunFeedSide |1017.0910.31mil ||--g--|---W---|----S----|---W---|--g--| |___________________ |____|_____|_______|_________|_______|_____|_______ ||\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\|| ||\\\\\\\\\\\\\\\\\eps_r=4.4\\\\\\\\\\\\\\\\\|60mil ||\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\|| |-------------------------------------------------- |431 ||BalunFeedSide |24.6315.23mil ||----W----|----S----|----W----| |__________________ |________|_________|_________|_________|___________ ||\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\|| ||\\\\\\\\\\\\\\\\\\eps_r=4.4\\\\\\\\\\\\\\\\|60mil ||\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\|| |-------------------------------------------------- |P.2Two-WireTransmissionLine Fromthecomprehensiveexam,thetransmissionlineparametersforatwo-wiretransmission lineare R=&"µc2&2a2(cF1#(2a/D)2GL=µ&cosh#1,D2a-G="&'&&cosh#1(D/2a)C=&'&cosh#1(D/2a)where Disthecenter-to-centerdistance, aistheradiusofthewire, (cistheconductivity ofthewire, µcisthepermeabilityofthewire(usually µc=µ0),andÞnally µand 'c='&#j'&&are thepermeabilityandpermittivity,respectively,ofthematerialsurroundingthewires. In[ 2]:#234567891123456789212345678931234567894123456789512345678961234567897123456789 #a72-charruler: #23456789112345678921234567893123456789412345678951234567896123456789712 deftwoWireParameters (freq,a,D,sigma_c =inf,mu_c =1,eps_r=1,tanDelta =0,mu_r =1,unitsScale=1):"""ReturnR,L,G,C,Z_0foratwo-wireline Calculatesandreturnstheresistance,impedance,conductance, andcapacitanceforatwo-wiretransmissionline.Geometricand electricalpropertiesaregivenforthewireandthemediain whichthewiresarelocated. 432 Parameters----------freq:scalar Frequencyatwhichtheparametersshouldbecalculated a:scalar Wireradius D:scalar center-to-centerdistanceofthewires sigma_c:scalar Conductivityofthewires mu_c:scalar,optional Relativepermeabilityofthewires.Defaultis1. eps_r:scalar,optional Relativepermittivityoftheenvironment.Usedas epsilon=eps_r*eps_0*(1-j*tanDelta).Defaultis1. tanDelta:scalar,optional Losstangentoftheenvironment.Usedas epsilon=eps_r*eps_0*(1-j*tanDelta).Defaultis0. mu_r:scalar,optional Relativepermeabilityoftheenvironment.Defaultis1 unitsScale:scalar,optionalifusingmeters Scalingfactorforunits.Formm,use1e-3,forinuse 0.0254.Returns-------R:scalar Resistanceofthetwo-wiretransmissionline L:scalar Impedanceofthetwo-wiretransmissionline G:scalar Conductanceofthetwo-wiretransmissionline C:scalar Capacitanceofthetwo-wiretransmissionline Z_0:scalar Compleximpedanceofthetwo-wiretransmissionline """#from__future__importdivision importscipy.constants asconst#Scaledimensions a=a*unitsScale D=D*unitsScale eps_sgl=const .epsilon_0*eps_reps_dbl=const .epsilon_0*eps_r*tanDeltaomega=2*pi*freq#delta_cond=1/np.sqrt(const.pi*freq*sigma_c) invCosh=np.arccosh(D/(2*a))433 #R=1/(const.pi*a*sigma_c*delta_cond) R=np.sqrt(omega *mu_c/(2*(const.pi*a)**2*sigma_c*(1-(2*a/D)**2)))G=(const.pi*omega*eps_dbl)/invCoshL=const.mu_0 /pi*invCoshC=pi*eps_sgl /invCoshZ_0=np.sqrt((R +1j*omega*L)/(G+1j*omega*C))returnR,L,G,C,Z_0 In[ 3]:foo=twoWireParameters(1e9,.125 /2,0.25,unitsScale =0.0254)twoWireParameters(printfoo(0.0,5.2678315876992667e-07,0.0,2.1121595053488982e-11,(157.92561800064058+0j)) impedance350 $beginÕPropertiesÕ VariableProp(ÕradiusÕ,ÕUDÕ,ÕÕ,Õ(.812/2)mmÕ) VariableProp(ÕlengthÕ,ÕUDÕ,ÕÕ,Õ(12*25.4)mmÕ) VariableProp(ÕspacingÕ,ÕUDÕ,ÕÕ,Õ7.5mmÕ) VariableProp(ÕportSizeÕ,ÕUDÕ,ÕÕ,Õspacing*66Õ)#.812 VariableProp(ÕlayerThicknessÕ,ÕUDÕ,ÕÕ,Õ5mmÕ) VariableProp(ÕlayerWidthÕ,ÕUDÕ,ÕÕ,Õ25mmÕ) VariableProp(ÕlayerLÕ,ÕUDÕ,ÕÕ,Õ25mmÕ) $endÕPropertiesÕ radius.812/2mm.406 length12*25.4mm304.8 spacing7.5mm portSizespacing*66495mm port1mm toprect3.5mm bottomrect3 20mmabsoluteoffset In[ 25]:a=1.0237e-3/2D=6.35e-3sigma_cond=5.96*10**7eps_r=np.linspace( 0.9,1.1,200)tanD=0.00015 freq=1e9#234567891123456789212345678931234567894123456789512345678961234567897123456789 434 R,G,L,C,Z_0 =twoWireParameters(freq,a,D,sigma_cond,eps_r =eps_r,tanDelta=tanD)fig,axes =subplots(ncols=2,nrows =1,figsize =(13,4))axes[0].plot(eps_r,Z_0 .real)axes[0].set_xlabel(rÕRelativePermittivity$ \epsilon_r$ Õ)axes[0].set_ylabel(rÕRe{$Z_0$}Õ)axes[0].set_title(rÕTwin-leadTheoreticalImpedance Õ)axes[1].plot(eps_r,Z_0 .imag)axes[1].set_xlabel(rÕRelativePermittivity$ \epsilon_r$ Õ)axes[1].set_ylabel(rÕIm{$Z_0$}Õ)fig.subplots_adjust(left =-.05)FigureP.7:notebookÞgure Trytestingthefunctionfora300ohmcable. In[ 26]:a=0.0625/2D=.375sigma_cond=5.96*10**7sigma_cond=infeps_r=1tanD=0freq=1e9R,G,L,C,Z_0 =twoWireParameters(freq,a,D,eps_r =eps_r,tanDelta=tanD,unitsScale =0.0254)printRprintGprintLprintCprintsqrt(L/C)zcalc=np.sqrt((R +1j*2*pi*freq*L)/(G+1j*2*pi*freq*C))printzcalcprintsqrt(L/C)print"Returnedimpedance:{} ".format(Z_0)435 print"Magnitudeofreturnedimpedance:{} ".format(abs(Z_0))print"Impedancecalculatedfromparameters:{} ".format(zcalc)printtype(L)printtype(C)omega=2*pi*freqprintnp.sqrt((R+1j*omega*L)/(G+1j*omega*C))0.09.91155492115e-070.01.12257871233e-110.00j0.0Returnedimpedance:(297.140941241+0j) Magnitudeofreturnedimpedance:297.140941241 Impedancecalculatedfromparameters:0j 0jP.2.1Problemabove Whydoes $L/Cgive0herebutnotbelow? Z0=&R+j"LG+j"CIn[ 27]:D=.375*0.0254a=0.0625/2*0.0254L=const.mu_0 /pi*arccosh(D/(2*a))C=pi*const.epsilon_0/arccosh(D/(2*a))R=0G=0Z=sqrt(L/C)printLprintCprintsqrt(L/C)printZprinttype(L)printtype(C)9.91155492115e-071.12257871233e-11297.140941241297.140941241 436 P.2.2TwoWireGeometryDesign Impedancesforvaryingseperationdistancesandwirediameters.Thisismeanttoreplicatethe tableathttp://www.qsl.net/co8tw/openline.htm In[ 28]:spacing =np.linspace(0.5,6,12)a=array([.128,.102,.081,.064,.051])/2units=0.0254 print"D|Impedancesforvaryingradii "print"|"+str(a)print"---|-------------------------------- "forelinspacing:_,_,_,_,Z0 =twoWireParameters(1e9 ,a,el,eps_r =1,unitsScale =units)pStr=str(el)+Õ|Õforvalinabs(Z0):pStr=pStr+Õ{:.1f}\tÕ.format(val)printpStrD|Impedancesforvaryingradii |[0.0640.0510.04050.0320.0255] ---|-------------------------------- 0.5|244.5272.5300.6329.1356.6 1.0|329.1356.6384.3412.6439.9 1.5|378.0405.3433.0461.3488.6 2.0|412.6439.9467.6495.8523.1 2.5|439.4466.7494.4522.6549.9 3.0|461.3488.6516.2544.5571.7 3.5|479.8507.1534.7563.0590.2 4.0|495.8523.1550.7579.0606.2 4.5|510.0537.2564.9593.1620.3 5.0|522.6549.9577.5605.8633.0 5.5|534.0561.3588.9617.2644.4 6.0|544.5571.7599.4627.6654.8 Theseimpedanesmatchforsomecombinationsbutnotothers.Needtocontinuetotryto verifymycalculations. WhatimpedancesarepossibleforaCPSgivenacertainspacingtomatchthatofthetwo wiret-line? In[ 29]:gnd=linspace(25,500,201)vfunc=numpy .vectorize(zCPS)spacing=np.linspace(50,150,5)forDinspacing:z=vfunc(D,gnd, 60,4.4,False)plot(gnd,z,label =D)legend()Out[29]: ACPSgeometryneedstobefoundthatmatchesoriscompatiblewithatwo-wiretransmis- sionlinegeometry.First, 2a+D*gap +2trace 437 FigureP.8:notebookÞgure In[ 30]:freq =2e9diam=0.122a=diam/2D=0.25units=0.0254 _,_,_,_,Z2wire =twoWireParameters(freq,a,D,unitsScale =units)print"Diameter:{}in ".format(diam)print"Center-CenterDist:{}in ".format(D)print"Gapbetween:{} ".format(D-diam)print"TotalWidth:{} ".format(D+diam)print"Two-wireimpedance:{} ".format(Z2wire)cpsGap=(50,75,100,125,150)h=60eps_r=4.4ztarget=abs (Z2wire)initGuess=25approx=False print""print"Gap\t|\tTrace \tImpedance\tSol.\tTot\tAccpets"print"\t|\tWidth \t\t\tAcc.\tWidth\t2Wire "print"----\t|\t-----\t---------\t----\t-----\t------"forgapincpsGap:fargs=gap,h,eps_r,approx 438 defsol(W,S,h,eps_r,aprox): return abs(zCPS(S,W,h,eps_r,approx)-ztarget) wCPS=fsolve(sol,initGuess,fargs) print"{}\t|\t{:.3f} \t{:.3f}\t\t{:.2}\t{:.3f}\t{}".format(gap,wCPS[ 0],zCPS(gap,wCPS,h,eps_r,approx)[ 0],sol(wCPS,*fargs)[0],gap +2*wCPS[0],gap+2*wCPS>(diam+D)*1000)#print"Gap:{}".format(gap) #print"CPStracewidth(W)foundtobe:{}".format(wCPS) #print"Impedance:{}".format(zCPS(gap,wCPS,h,eps_r,approx)) #print"SolutionAcc.:{}".format(sol(wCPS,*fargs)) #print"Totalwidth:{}".format(gap+2*wCPS) #print"Accepts2wire:{}".format(gap+2*wCPS>(diam+D)*1000) Diameter:0.122in Center-CenterDist:0.25in Gapbetween:0.128 TotalWidth:0.372 Two-wireimpedance:(161.276087605+0j) Gap|TraceImpedanceSol.TotAccpets |WidthAcc.Width2Wire ----|----------------------------- 50|37.143161.2765.7e-14124.286[False] 75|65.188161.2768.5e-14205.376[False] 100|102.736161.2761.1e-13305.472[False] 125|149.724161.2767.7e-13424.447[True] 150|205.014161.2763e-12560.028[True] Usingthesmallestgapthatacceptsthe2wiregeometrygives Gap|TraceImpedanceSol.TotAccpets |WidthAcc.Width2Wire ----|----------------------------- 125|149.724161.2767.7e-13424.447[True] WhenIgotomanufacturethis,thewiresmaybealignedanywhereonthe~150miltrace. WhatrangeofimpedancesshouldIexpectfromthispossiblemisalignment? Considerthewiresbeingclosesttogether.Thismeansthatthegapbetweenthewiresisthe sameasthegampbetweenthetraces,i.e.125mils.Thisgives 125 =D#2a+D=125 +2a+D=125 +122 In[ 31]:DSmall =125+122print"{}mils ".format(DSmall)247mils 439 Theimpedanceisthen In[ 32]:_,_,_,_,zSmall =twoWireParameters(freq,a,DSmall /1000,unitsScale =units)printzSmallprint"Difference:{} ".format(zSmall-Z2wire) (159.614310234+0j)Difference:(-1.66177737126+0j) Thisdifferenceshouldbeacceptable. Goingnowtothemaximumseperation,wewouldhavetheoutsidedimensionsofthetwo- wiretransmissionlineequalto424.447(readingfromtableabove).Thismeansthatthecenter- to-centerspacingis 424.447 =D+2a+D=424.447 #2a+D=424.447 #122 In[ 33]:DLarge =424.447-122print"{}mils ".format(DLarge)302.447mils Theimpedanceisthen In[ 34]:_,_,_,_,zLarge =twoWireParameters(freq,a,DLarge /1000,unitsScale =units)printzLargeprint"Difference:{} ".format(zLarge-Z2wire) (186.785145094+0j)Difference:(25.5090574891+0j) Thisislargerthanwhenthewiresarepushedtowardsthecenter. Fromthiswecanconcludethatitisbesttokeepthewiresmoretowardsthecenterthan towardstheoutside. P.2.3Summary Copyingfromabovewegetthefollowinggeometries |BalunSide |24.6315.23mil ||----W----|----S----|----W----| |__________________ |________|_________|_________|_________|___________ ||\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\|| ||\\\\\\\\\\\\\\\\\\eps_r=4.4\\\\\\\\\\\\\\\\|60mil ||\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\|| 440 |-------------------------------------------------- ||Two-WireSide |149.724125mil ||----W----|----S----|----W----| |__________________ |________|_________|_________|_________|___________ ||\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\|| ||\\\\\\\\\\\\\\\\\\eps_r=4.4\\\\\\\\\\\\\\\\|60mil ||\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\|| |-------------------------------------------------- ||Two-Wire ||**** |*122*** |*mil*** |*diam*** |**** |**** ||--128mil--| ||-------250mil-------| ||--------------372mil-------------| LetÕsdoublecheckthesenumbers: In[ 35]:cpsGap =125cpsGnd=149.724 h=60eps_r=4.4approx=False diam=122a=diam/2spacing=250 units=1e-3printzCPS(cpsGap,cpsGnd,h,eps_r,approx) _,_,_,_,z2Wire =twoWireParameters(1e9,a,spacing,unitsScale =units)printz2Wire161.275990587(161.276087605+0j)Thosematch.LetÕsbuildit...inasecond. LetÕschecksincestainlesssteelislossy.Thesteelbeingusedisgrade304accord- ingtothemanufacturerer.Thisgradesteelhasaresistivityof720 n"maccordingto http://www.azom.com/article.aspx?ArticleID=965.Thisgivesthefollowing: 441 In[ 36]:resist =720#nanoohmspermeter sigma=1/(resist *1e-9)print"Conductivity:{}S/m ".format(sigma)_,_,_,_,zLossy =twoWireParameters(1e9,a,spacing,sigma_c =sigma, unitsScale=units)print"Impedance:{} ".format(zLossy)print"ImpedanceMagnitude:{} ".format(abs(zLossy)) print"Losslessimpedancemag:{} ".format(abs (z2Wire))Conductivity:1388888.88889S/m Impedance:(161.41842333-6.77723816809j) ImpedanceMagnitude:161.560633657 Losslessimpedancemag:161.276087605 TheimpedancedoesnÕtreallychangemuchwhenweusealossycase.Thespacingeffects theimpedancemoreso.NowletÕsbuilditandgetthespacingcorrect. P.2.4ManufacturingNotes Manufacturedgapfortwo-wiresis138mils.Thisgivesanimpedanceof In[ 37]:manufacturedGap =138DSmall=122+manufacturedGapprint"{}mils ".format(DSmall)_,_,_,_,zSmall =twoWireParameters(freq,a,DSmall /1000,unitsScale =units)printzSmallprint"Difference:{} ".format(zSmall-Z2wire) 260mils (nan+nan*j)Difference:(nan+nan*j) -c:64:RuntimeWarning:invalidvalueencounteredinarccosh In[ 37]:442 AppendixQ IPythonnotebook:WireTemperature Q.1Introduction Wewishtomeasurepropertiesofaßameusingatwowiretransmissionline.Theßamewillbe atthecenterofthetransmissionline.Overtimethetemperatureofthewireswillincrease.At thecenteroftheline,weshallassumethatthewireisthesametemperatureastheßame.The entiretransmissionlinewouldreachthistemperatureiftherewerenolosses.Lossesatthistime willonlybeairatroomtemperature.Itisassumedthattheairtemperaturedoesnotincrease whereinrealityitwouldnearthewire.Webelievethatthisisnegligable.Wewouldliketo determinethetemperatureattheendsofthewiresothatweknowthemaximumtemperature thatthewirejunctionsmustbeabletowithstand. Tungstenhasthehighestmeltingpoint.Italsohasarelativelyhigherelectricalresistivity. Nickelshouldbeavoidedbecauseofitsmagneticproperties. Labnotebook00009:150Ð159. Q.2TungstenResources ¥http://hypertextbook.com/facts/2004/DeannaStewart.shtml ¥http://www.matweb.com/search/datasheettext.aspx?matguid= 4ec9eefceac0484c832b4fc6ee608345 ¥http://www.a-msystems.com/v-27-tungsten.aspx ¥http://www.mcmaster.com/#metal-wire/=nuhllt ¥googlesearchtungstencopperalloymeltingpoint ¥http://neon.mems.cmu.edu/laughlin/pdf/130.pdf ¥http://puhep1.princeton.edu/~mcdonald/e166/Walz/De- sign%20Manual%20WHA%20.doc ¥http://www.eaglealloys.com/c-16-tungstentungsten-alloys.html ¥http://eaglealloys.com/t-tungsalloyscopper.html ¥http://www.specialmetals.com/documents/Incoloy%20alloy%20825.pdf 443 Q.3HeatTransferBooks ¥http://site.ebrary.com.proxy1.cl.msu.edu/lib/michstate/docDe- tail.action?docID=10540860 ¥http://site.ebrary.com.proxy1.cl.msu.edu/lib/michstate/docDe- tail.action?docID=10503000 ¥http://site.ebrary.com.proxy1.cl.msu.edu/lib/michstate/docDe- tail.action?docID=10506157 ¥http://link.springer.com.proxy1.cl.msu.edu/book/10.1007/978-3-642-03932-4/page/1 ¥http://link.springer.com.proxy1.cl.msu.edu/book/10.1007/978-3-642-19183-1/page/1 Q.4OtherResources ¥http://tutorial.math.lamar.edu/Classes/DE/HeatEqnNonZero.aspx ¥http://en.wikipedia.org/wiki/Heat_equation ¥http://www.physics.miami.edu/~nearing/mathmethods/pde.pdf ¥http://ocw.mit.edu/courses/mechanical-engineering/2-51-intermediate-heat-and- mass-transfer-fall-2008/index.htm Q.5FinTemperatureatTip AÞnisaprojectionfromawallorotherbodyintoanenvironmentwiththepurposeoftransfer- ringheat.FinsarecommonlyseenonCPUheatsinksandotherheatsinksinelectronics.Fins arediscussedinmanyheattransfertextbooks.Themathematicspresentedbelowwerederived byfollowingthediscusiononÞnsinsection4.5ofAHeatTransferTextbook,4thed.byLien- hardandLienhard.ThisisthetextbookforMITOpenCourseWareÕsIntermediateHeatand MassTransferclass. AÞnhasacharacteristicdimensiongivenbytheratiooftheareatotheperimeteroftheÞn andalongitudinaldimesion,thelength. ForasmallsegmentofaÞntheenergybalanceisgivenas #kAdTdx@@@@x+)x+kAdTdx@@@@x+øh(P)x)(T#T.)@@x=0where kisthethermalconductivity(W/m áK),TisthetemperatureinKelvinasafunctionof position, T.istheambienttemperature, xisalineardistance, Aisthecross-sectionalarea, PistheperimeterdistanceoftheÞn, kisthethermalconductivityoftheÞn,and øhistheheat transfercoefÞcient.Itisassumedthat øhisconstantalongtheÞn.Thetemperatureatthebase oftheÞnisdenotedby T0.AtthetipoftheÞn,heatmayormaynotbeexchanged.Thisisgovernedbytheheattransfer coefÞcient øhL.ThisvalueisusallydifferentthantheheattransfercoefÞcientfortherestof thebar.Inmanycases øhLissmallenoughtobeneglected.ItisalsodifÞculttodeterminethis 444 value.Asthisvaluereducestheoverallheatexchange,when øhLisneglectedtheÞntipwillhave aslightlyhighertemperature(assuming T.$L_{wire}=1$m
  • $\bar{h}=20$W/(m^2K)
  • $k=2.40$W/(cmdegC)$=240$W/(mdegC)
  • $T_0=2000^\circ\text{C}$
  • $T_\infty=25^\circ\text{C}$
  • $d=0.81$mm
    • In[ 10]:#Importbasicmodules #makesurethatdivisionisdoneasexpected from__future__importdivision#plottingsetup %matplotlibinline importmatplotlib.pyplot aspltplt.style.use(Õwhite_back Õ)#for3dgraphs #frommpl_toolkits.mplot3dimportaxes3d #forlegendsofcombinedfigtypes #importmatplotlib.linesasmlines #numericalfunctions importnumpyasnp#needsomeconstants fromscipyimport constantsfromnumpyimport piIn[ 15]:Lwire =1L=Lwire/2h=20k=2.40*100T_0=2000+273 T_inf=25+273 d=0.81*10**-3P=pi*dA=pi*(d/2)**2T=T_inf+(T_0-T_inf)/(np.cosh(2*L*np.sqrt(h /(k*d))))print"Tempterauteattip: "+str(T-273)m=np.sqrt(h *P/(k*A))print"mL="+str(m*L)#LetÕsplotthisastempvslength Lwire=np.linspace( 0.05,1,200)L=Lwire/2#sinceflameisatthecenter 447 P=pi*dA=pi*(d/2)**2T=T_inf+(T_0-T_inf)/(np.cosh(2*L*np.sqrt(h /(k*d))))#semilogy(Lwire,T-273) fig,ax =plt.subplots()lin=ax.plot(L,T -273)_=ax.set_ylim([min(T)-273,max(T)-273])_=ax.set_xlabel( ÕWirehalf-length(m) Õ)_=ax.set_ylabel( rÕTemperature($^ \circ$C)Õ)_=ax.set_title(ÕTemperatureattheTipofaWirevsWireHalf-Length Õ)up=fig.add_axes([ .4,.4,.45,.45])lin=up.plot(L,T -273)_=up.axis([0.15,.5,0,200])#fig.savefig(ÕtipTemp-20awg.pdfÕ,transparent=True) Tempterauteattip:25.1554331617 mL=10.1430103242FigureQ.2:notebookÞgure 448 Q.8CalculationsforTungstenWeldingRod Apuretungstenweldingrod,1/8inby12inwaspurchasedfromDiamondGroundProducts. Tungstenhasathermalconductivityof174W/(mK)andanelectricalresistivityof5.3 "10#8"mAccordingtoWikipediatheheattransfercoefÞcientforairisbetween10and100W/(mö2 K).AccordingtoEngineeringToolboxitisbetween5and25W/(mö2K)forfreeconvection.We willuse20W/(mö2K). Letusdothemathwiththefollowingparameters:
  • $L_{wire}=12$in
  • $\bar{h}=20$W/(m^2K)
  • $k=174$W/(mdegK)
  • $T_0=2000^\circ\text{C}$
  • $T_\infty=25^\circ\text{C}$
  • $d=0.125$in
    • Q.8.1CAUTION Thecalculationsrelyontheassumptionthat mL05whichisnotthecaseforthisrod.This reallyshouldbere-donewiththeexactsolutionandnottheapproximations/simpliÞcations. In[ 5]:Lwire =12*constants.inchh=20k=174T_0=2000+273 T_inf=25+273 d=0.125*constants .inch#Definelengthashalftheactuallengthsince #theflamewillbeinthemiddleandwewantthe #tempattheend L=Lwire/2#perimeter P=pi*d#area A=pi*(d/2)**2#temperatureattip T=T_inf+(T_0-T_inf)/(np.cosh(2*L*np.sqrt(h /(k*d))))print"Tempterauteattip: "+str(T-273)+"C"#mLratio m=np.sqrt(h *P/(k*A))print"mL="+str(m*L)#LetÕsplotthisastempvslength L=np.linspace( 0.01,1,201)449 P=pi*dA=pi*(d/2)**2T=T_inf+(T_0-T_inf)/(np.cosh(2*L*np.sqrt(h /(k*d))))fig,ax =plt.subplots()lin=ax.plot(L,T -273)_=ax.set_ylim([ min(T)-273,max(T)-273])_=ax.set_xlabel( ÕFinlength(m) Õ)_=ax.set_ylabel( rÕTemperature($^ \circ$C)Õ)_=ax.set_title( ÕTemperatureattheTipofaWirevsFin(Wire)Length Õ)up=fig.add_axes([ .4,.4,.45,.45])lin=up.plot(L,T -273)_=up.axis([0.3,.5,0,200])Tempterauteattip:640.433814338C mL=1.83393302627FigureQ.3:notebookÞgure 450 AppendixR IPythonnotebook:T-lineCalibration-diss R.1CalibrationofaTransmissionLine Thepurposeofthisnotebookistoexaminetheone-andtwo-portcalibrationofatransmission line.Thiswilluseatwo-wiretransmissionlineandthemeasurementashortingplatelocated atthreedifferentlocationsalongtheline. R.1.1Derivation Dr.Rothwelldidthederivation.Additinhereatsomepoint. Belowrelatestotheone-portcalibrationofa2-portnetwork.Thiswouldbeusedtocalibrate outasinglecablesothatmeasurementscouldbemadeattheendofthecable. WecanÞndtheS-parametersofa2-portnetworkbymeasuringS11withthreeknownloads connectedindividuallytoport2ofthenetwork.Thisprovidesthreedifferentmeasured S11values, Si11(0indexingwillbeusedsincethatiswhatPythonuses).Theloadsusedforthis calibrationareshortslocatedatdifferentdistancesalongthetransmissionline.Themeasured responseashortedtransmissionlineistheoreticallyjust %i=#e#j2#di.Placingashortinthreedifferentlocationsgivesthreedifferentvaluesof %whichareknown (intheory). BeginbydeÞning K=1%2#1%01%1#1%0S011#S111S011#S211thentheS-parameterscanbecalculatedinthefollowingorder: S22=1%2#1%1K1#K451 S=S12S21=S011#S1111%1#1%0,1%0#S22-,1%1#S22-S11=S011#S1%0#S22R.2Preßight Beginwiththenecessaryimports In[ 3]:#Importbasicmodules #makesurethatdivisionisdoneasexpected from__future__importdivision#plottingsetup %matplotlibinline importmatplotlib.pyplot aspltplt.style.use(Õgray_back Õ)plt.rcParams[Õaxes.ymargin Õ]=0#gettheviridiscolormap #https://bids.github.io/colormap #itwillbeavailableascmaps.viridis #importcolormapsascmaps #for3dgraphs #frommpl_toolkits.mplot3dimportaxes3d #forlegendsofcombinedfigtypes #importmatplotlib.linesasmlines #numericalfunctions importnumpyasnp#needsomeconstants fromscipyimportconstantsfromnumpyimportpi#RFtools! importskrfasrf#versioninformation #%install_exthttp://raw.github.com/jrjohansson/ #version_information/master/version_information.py #%load_extversion_information #%reload_extversion_information #%version_informationnumpy,scipy,matplotlib In[ 4]:import os452 In[ 14]:doSave =True#doSave=False DeÞnitionoffunctionsthatwillbeneeded. In[ 6]:deftwoWireParameters(freq,a,D,sigma_c =np.inf,mu_c =1,eps_r=1,tanDelta =0,mu_r =1,unitsScale=1):"""ReturnR,L,G,Cforatwo-wireline Calculatesandreturnstheresistance,impedance,conductance, andcapacitanceforatwo-wiretransmissionline.Geometricand electricalpropertiesaregivenforthewireandthemediain whichthewiresarelocated. Parameters----------freq:scalar Frequencyatwhichtheparametersshouldbecalculated a:scalar Wireradius D:scalar center-to-centerdistanceofthewires sigma_c:scalar Conductivityofthewires mu_c:scalar,optional Relativepermeabilityofthewires.Defaultis1. eps_r:scalar,optional Relativepermittivityoftheenvironment.Usedas epsilon=eps_r*eps_0*(1-j*tanDelta).Defaultis1. tanDelta:scalar,optional Losstangentoftheenvironment.Usedas epsilon=eps_r*eps_0*(1-j*tanDelta).Defaultis0. mu_r:scalar,optional Relativepermeabilityoftheenvironment.Defaultis1 unitsScale:scalar,optionalifusingmeters Scalingfactorforunits.Formm,use1e-3,forinuse 0.0254.Returns-------R:scalar Resistanceofthetwo-wiretransmissionline L:scalar Impedanceofthetwo-wiretransmissionline G:scalar Conductanceofthetwo-wiretransmissionline C:scalar Capacitanceofthetwo-wiretransmissionline """#from__future__importdivision 453 importscipy.constants asconst#Scaledimensions a=a*unitsScale D=D*unitsScale eps_sgl=const .epsilon_0*eps_reps_dbl=const .epsilon_0*eps_r*tanDeltaomega=2*pi*freq#delta_cond=1/np.sqrt(const.pi*freq*sigma_c) invCosh=np.arccosh(D/(2*a))#R=1/(const.pi*a*sigma_c*delta_cond) R=np.sqrt(omega *mu_c/(2*(const.pi*a)**2*sigma_c*(1-(2*a/D)**2)))G=(const.pi*omega*eps_dbl)/invCoshL=const.mu_0 /pi*invCoshC=pi*eps_sgl /invCoshreturnR,L,G,C defreflectionCoeff (dist,beta): """Calculatethereflectioncoefficientofashort. Calculatethereflectioncoefficientofashortinagivenmediaat agivendistanceinmeters. gamma=-exp(2j*beta*dist) Parameters----------dist:array_like Distancetotheshortfromsomereferenceplane beta:array_like Propagationconstant,beta,forthemediacontainingtheshort Returns-------coeff:array_like Thereflectioncoefficientcalculatedas gamma=exp(-j*beta*dist) """coeff=-np.exp( 2j*beta*dist)returncoeffdeffind1PortTransition (beta,dist,shorts): #23456789112345678921234567893123456789412345678951234567896123456789712 """Calculated*SOME*oftheS-parametersforatransition.READDETAILS 454 CalculateS_11,S_22,andS_12*S_21foratransition.Thisisused whenyouwanttode-embedasamplefromthetransitionandthe sample.Thisrequiresscikit-rfversionwithsourceafterApril4,2014. Probablywillbeversion0.15.Youmightneedtogetthisfrom github(https://github.com/scikit-rf/scikit-rf). Parameters----------beta:array_like Thepropagationconstant,beta,usedtocalculatethereflection coefficientofeachshort.Thisshouldbethesameforall threeshorts. dist:ndarray ANumPyarraycontainingthedistancefromtherefenceplane toeachofthethreeshortsinmeters. Ex:array([1.3e-3,4e-3,7.87e-3]) shorts:list AlistofthefilenamesfortheTouchstonefiles,i.e.*.s*p, foreachshort.Theorderoffilesshouldmatchthedistances inÔdistÔ.OnlytheS11datawillbeusedsothesemaybe multi-portTouchstonefilesandalldonothavetobethesame numberofports. Returns-------ntwkS11,ntwkS22,ntwkS12S21:skrf.network.Network 1-portnetworksforthecalculatedS-parameterstobeusedfor de-embeddingasample. To-Do-----Shouldthrowinsomeerrorcheckingtomakesurethatthethree shortshavethesamenetworkproperties """#gis1/Gamma g=[1/reflectionCoeff(beta,d) fordindist]sc=[rf.Network(a) .s[:,0,0]forainshorts]tempNtwk=rf.Network(shorts[0]).s11freq=tempNtwk .fz0=tempNtwk.z0K=(g[2]-g[0])/(g[1]-g[0])*(sc[0]-sc[1])/(sc[0]-sc[2])s22=(g[2]-g[1]*K)/(1-K)s12s21=(sc[0]-sc[1])/(g[1]-g[0])*(g[0]-s22)*(g[1]-s22)s11=sc[0]-s12s21 /(g[0]-s22)ntwkS11=rf.Network(name="TransitionS11 ",f=freq,z0 =z0,s =s11)ntwkS22=rf.Network(name="TransitionS22 ",f=freq,z0 =z0,s =s22)455 ntwkS12S21=rf.Network(name="TransitionS12S21 ",f=freq,z0 =z0,s=s12s21)returnntwkS11,ntwkS22,ntwkS12S21 defdeembed(trans,raw): #23456789112345678921234567893123456789412345678951234567896123456789712 """De-embeda1-portsample. De-embeda1-portsamplefromatransitionthathasbeen characterizedusingathreeshortmethod. Parameters----------trans:tupleofskrf.network.Network Atupleofscikit-rf1-PortNetworksthatcorrespondtothe characterizedS-parametersofthetransition.Ordershouldbe S_11,S_22,S_12*S_21. raw:skrf.network.Network Therawdatameasurementthatincludesthesampleandthe transition.Thesamplewillbede-embeddedfromthisdata Returns-------sample:skrf.network.Network Thede-embeddedsample """b=[x.s[:,0,0]forxintrans]#printb[0] inv=b[1]+b[2]/(raw.s[:,0,0]-b[0])sample=trans[ 0]sample.s=1/invreturnsampleR.32014-08-05 R.4ComplexPropagationConstant ThisdatasetiswhenIrealizedthatthereßectioncoefÞcientwasnottakingintoaccountlosses ontheline. In[ 8]:#13-6mm-foam-I-short.s1p #17-2mm-foam-H-short.s1p #5-9mm-foam-F-short.s1p #9-7mm-foam-G-short.s1p #line.s1p#scratch.s1p#short-against-plexi.s1p #F,5.9,mm,white 456 #G,9.7,mm,white #H,17.2,mm,white #I,13.6,mm,white dataDir=os.path.join(os.path.expanduser("~"),"Documents ","plexiglass-holder-data ","Data","2014-08-05")rawSample=rf.Network(os.path.join(dataDir,"13-6mm-foam-I-short.s1p"))sampleDist=13.6*1e-3short1=os.path.join(dataDir,"5-9mm-foam-F-short.s1p ")short2=os.path.join(dataDir,"9-7mm-foam-G-short.s1p ")short3=os.path.join(dataDir,"17-2mm-foam-H-short.s1p ")shortDistances=np.array([5.9,9.7,17.2])*1e-3ntwkF=rf.Network(short1) ntwkG=rf.Network(short2) ntwkH=rf.Network(short3) ntwkI=rawSample freq=rawSample .fdiam=0.122radius=diam /2cntr2cntr=0.25sigma=1/(7.2e-7 )R,L,G,C =twoWireParameters(freq=freq,a =radius,D =cntr2cntr, sigma_c=sigma,unitsScale =0.0254)rRad=30*(2*pi*freq**2*constants.epsilon_0*constants .mu_0)*cntr2cntr**2R=R+rRadgamma=np.sqrt((R +1j*2*pi*freq*L)*(G+1j*2*pi*freq*C))rfFreq=rf.Frequency(freq[0],freq[ -1],freq .shape[0],ÕHzÕ)theory=rf.media.DistributedCircuit(rfFreq,C,L,R,G) .delay_short(sampleDist) shorts=[short1,short2,short3] balun=find1PortTransition( 1j*gamma,shortDistances,shorts) sample=deembed(balun,rawSample) fig,ax =plt.subplots(2,1)fig.set_figheight(7)_=rawSample.plot_s_db(ax =ax[0],ls =":",label =ÕOriginal-I Õ)_=sample.plot_s_db(ax =ax[0],label =ÕCalibratedusingF,G,H Õ)_=theory.plot_s_db(ax =ax[0],ls ="--",label =ÕTheoryÕ)_=rawSample.plot_s_deg(ax =ax[1],ls =":",label =ÕOriginalÕ,show_legend =False)_=sample.plot_s_deg(ax =ax[1],label =ÕCalibratedÕ,show_legend =False)_=theory.plot_s_deg(ax =ax[1],ls ="--",label =ÕTheoryÕ,show_legend =False)ifdoSave:fig.savefig(Õdeembed-I.pdf Õ)457 FigureR.1:notebookÞgure 458 In[ 9]:#plt.rcParams[Õaxes.ymarginÕ]=0 fig,ax =plt.subplots(2,1)fig.set_figheight(7)_=ntwkF.plot_s_db(ax =ax[0],label ="F5.9mm ")_=ntwkG.plot_s_db(ax =ax[0],label ="G9.7mm ")_=ntwkI.plot_s_db(ax =ax[0],label ="I13.6mm ")_=ntwkH.plot_s_db(ax =ax[0],label ="H17.2mm ")_=ntwkF.plot_s_deg(ax =ax[1],label ="F5.9mm ",show_legend =False)_=ntwkG.plot_s_deg(ax =ax[1],label ="G9.7mm ",show_legend =False)_=ntwkI.plot_s_deg(ax =ax[1],label ="I13.6mm ",show_legend =False)_=ntwkH.plot_s_deg(ax =ax[1],label ="H17.2mm ",show_legend =False)ifdoSave:fig.savefig(Õshort-s-param.pdf Õ)R.52014-08-07vs-05vs-11 In[ 11]:#compareshortsfromdifferentdays dataDir=os.path.join(os.path.expanduser("~"),"Documents ","plexiglass-holder-data ","Data","2014-08-05")I5=rf.Network(os .path.join(dataDir,"13-6mm-foam-I-short.s1p "),name =Õ5thÕ)dataDir=os.path.join(os.path.expanduser("~"),"Documents ","plexiglass-holder-data ","Data","2014-08-07")I7=rf.Network(os .path.join(dataDir,"13-6mm-foam-I-short.s1p "),name =Õ7thÕ)dataDir=os.path.join(os.path.expanduser("~"),"Documents ","plexiglass-holder-data ","Data","2014-08-11")I11=rf.Network(os .path.join(dataDir,"13-6mm-foam-I-short.s1p "),name =Õ11thÕ)#diff=np.abs(I5.s[:,0,0]-I7.s[:,0,0]) #magDiff=np.abs(I5.s_db[:,0,0]-I7.s_db[:,0,0]) #degDiff=np.abs(I5.s_deg_unwrap[:,0,0]-I7.s_deg_unwrap[:,0,0]) #fig,ax=plt.subplots() #_=ax.plot(I5.f,diff,label="diff") #_=ax.plot(I5.f,magDiff,label="mag") ##_=ax.plot(I5.f,degDiff,label="deg") #_=ax.legend() fig,ax =plt.subplots()_=I5.plot_s_db(ax =ax)_=I7.plot_s_db(ax =ax)_=I11.plot_s_db(ax =ax)fig,ax =plt.subplots()_=I5.plot_s_deg(ax =ax)_=I7.plot_s_deg(ax =ax)_=I11.plot_s_deg(ax =ax)459 FigureR.2:notebookÞgure 460 FigureR.3:notebookÞgure 461 FigureR.4:notebookÞgure 462 R.62014-08-11 In[ 12]:#Caldatafrom2014-08-05 #13-6mm-foam-I-short.s1p #17-2mm-foam-H-short.s1p #5-9mm-foam-F-short.s1p #9-7mm-foam-G-short.s1p #line.s1p#scratch.s1p#short-against-plexi.s1p #11-7mm-air-short.s1p #13-6mm-foam-I-short.s1p #5-9mm-foam-F-6-6mm-teflon-22-4mm-foamG-short.s1p #6-0mm-foam-F-12-9mm-delrin-28-7mm-foamG-short.s1p #F,5.9,mm,white #G,9.7,mm,white #H,17.2,mm,white #I,13.6,mm,white dataDir=os.path.join(os.path.expanduser("~"),"Documents ","plexiglass-holder-data ","Data","2014-08-05")rawDir=os.path.join(os.path.expanduser("~"),"Documents ","plexiglass-holder-data ","Data","2014-08-11")rawSample=rf.Network(os.path.join(rawDir,"6-0mm-foam-F-12-9mm-delrin-28-7mm-foamG-short.s1p "))sampleDist=28.7*1e-3short1=os.path.join(dataDir,"5-9mm-foam-F-short.s1p ")short2=os.path.join(dataDir,"9-7mm-foam-G-short.s1p ")short3=os.path.join(dataDir,"17-2mm-foam-H-short.s1p ")shortDistances=np.array([5.9,9.7,17.2])*1e-3freq=rawSample .fdiam=0.122radius=diam /2cntr2cntr=0.25sigma=1/(7.2e-7 )R,L,G,C =twoWireParameters(freq=freq,a =radius,D =cntr2cntr, sigma_c=sigma,unitsScale =0.0254)rRad=30*(2*pi*freq**2*constants.epsilon_0*constants .mu_0)*cntr2cntr**2R=R+rRadgamma=np.sqrt((R +1j*2*pi*freq*L)*(G+1j*2*pi*freq*C))rfFreq=rf.Frequency(freq[0],freq[ -1],freq .shape[0],ÕHzÕ)theory=rf.media.DistributedCircuit(rfFreq,C,L,R,G) .delay_short(sampleDist) shorts=[short1,short2,short3] balun=find1PortTransition( 1j*gamma,shortDistances,shorts) sample=deembed(balun,rawSample) 463 fig,ax =plt.subplots(2,1)fig.set_figheight(7)_=rawSample.plot_s_db(ax =ax[0],ls =":",label =ÕOriginalÕ)_=sample.plot_s_db(ax =ax[0],label =ÕCalibratedDelrinusingF,G,H Õ)_=theory.plot_s_db(ax =ax[0],ls ="--",label =ÕAirLine Õ)_=rawSample.plot_s_deg(ax =ax[1],ls =":",label =ÕOriginalÕ,show_legend =False)_=sample.plot_s_deg(ax =ax[1],label =ÕCalibratedDelrin Õ,show_legend =False)_=theory.plot_s_deg(ax =ax[1],ls ="--",label =ÕAirLine Õ,show_legend =False)ifdoSave:fig.savefig(Õdelrin-layered.pdf Õ)In[ 15]:fig,ax =plt.subplots(2,1)fig.set_figheight(7)_=rawSample.plot_s_db(ax =ax[0],ls =":",label =ÕOriginalÕ,lw =3)_=sample.plot_s_db(ax =ax[0],label =ÕCalibratedÕ,lw =3)_=theory.plot_s_db(ax =ax[0],ls ="--",label =ÕAirLine Õ,lw =3)_=rawSample.plot_s_deg(ax =ax[1],ls=":",label=ÕOriginal Õ,show_legend=False,lw=3)_=sample.plot_s_deg(ax =ax[1],label =ÕCalibratedÕ,show_legend =False,lw =3)_=theory.plot_s_deg(ax =ax[1],ls="--",label=ÕAirLine Õ,show_legend =False,lw =3)_=ax[0].legend(fontsize =16)_=ax[0].set_xlabel( ÕFrequency(Hz) Õ,fontsize =16)_=ax[0].set_ylabel( ÕMagnitudeÕ,fontsize =16)_=ax[1].set_xlabel( ÕFrequency(Hz) Õ,fontsize =16)_=ax[1].set_ylabel( ÕPhase(deg) Õ,fontsize =16)ifdoSave:fig.savefig(Õdelrin-layered-defense.pdf Õ)R.7LayeredDe-embedMeasurement In[ 9]:#Caldatafrom2014-08-05 #13-6mm-foam-I-short.s1p #17-2mm-foam-H-short.s1p #5-9mm-foam-F-short.s1p #9-7mm-foam-G-short.s1p #line.s1p#scratch.s1p#short-against-plexi.s1p #11-7mm-air-short.s1p #13-6mm-foam-I-short.s1p #5-9mm-foam-F-6-6mm-teflon-22-4mm-foamG-short.s1p #6-0mm-foam-F-12-9mm-delrin-28-7mm-foamG-short.s1p 464 FigureR.5:notebookÞgure 465 FigureR.6:notebookÞgure 466 dataDir=os.path.join(os.path.expanduser("~"),"hpcc ","plexiglass-holder-data ","Data","2014-08-05")rawDir=os.path.join(os.path.expanduser("~"),"hpcc ","plexiglass-holder-data ","Data","2014-08-11")rawSample=rf.Network(os.path.join(rawDir,"6-0mm-foam-F-12-9mm-delrin-28-7mm-foamG-short.s1p "))sampleDist=28.7*1e-3short1=os.path.join(dataDir,"5-9mm-foam-F-short.s1p ")short2=os.path.join(dataDir,"9-7mm-foam-G-short.s1p ")short3=os.path.join(dataDir,"17-2mm-foam-H-short.s1p ")shortDistances=np.array([5.9,9.7,17.2])*1e-3freq=rawSample .fdiam=0.122radius=diam /2cntr2cntr=0.25sigma=1/(7.2e-7 )R,L,G,C =twoWireParameters(freq=freq,a =radius,D =cntr2cntr, sigma_c=sigma,unitsScale =0.0254)rRad=30*(2*pi*freq**2*constants.epsilon_0*constants .mu_0)*cntr2cntr**2R=R+rRadgamma=np.sqrt((R +1j*2*pi*freq*L)*(G+1j*2*pi*freq*C))rfFreq=rf.Frequency(freq[0],freq[ -1],freq .shape[0],ÕHzÕ)airLine=rf.media.DistributedCircuit(rfFreq,C,L,R,G) .delay_short(sampleDist) #########Cascade########layerEps_r=np.array([1,3.7,1])tanDelta=1.5e-4 lengths=np.array([6,12.9,28.7-6-12.9])*1e-3R,L,G,C =twoWireParameters(freq,radius,cntr2cntr,sigma,eps_r =1,tanDelta=0,unitsScale=0.0254)R+=rRadZ=np.sqrt((R +1j*2*pi*freq*L)/(G+1j*2*pi*freq*C))Z_norm=Zsect1=rf.media .DistributedCircuit(rfFreq,C,L,R,G) .line(lengths[0])sect1.renormalize(Z_norm) #added10/31/2015 #foamandshortsection sect3=rf.media .DistributedCircuit(rfFreq,C,L,R,G) .delay_short(lengths[ -1])sect3.renormalize(Z_norm) #samplesection R,L,G,C =twoWireParameters(freq,radius,cntr2cntr,sigma, eps_r=layerEps_r[1],tanDelta =tanDelta,467 unitsScale=0.0254)R+=rRadsect2=rf.media .DistributedCircuit(rfFreq,C,L,R,G) .line(lengths[1])sect2.renormalize(Z_norm) totalLine=sect1**sect2**sect3##De-embed #shorts=[short1,short2,short3] balun=find1PortTransition( 1j*gamma,shortDistances,shorts) sample=deembed(balun,rawSample) #airLine.renormalize(50) #totalLine.renormalize(50) printsampleprintairLineprinttotalLine##Plotting ##sample.plot_s_db(show_legend=False) #airLine.plot_s_db(show_legend=False) #totalLine.plot_s_db(show_legend=False) ##rawSample.plot_s_db(show_legend=False) #plt.figure() #sample.plot_s_deg(show_legend=False) #airLine.plot_s_deg(show_legend=False) #totalLine.plot_s_deg(show_legend=False) fig,ax =plt.subplots()_=sample.plot_s_db(ax =ax,label =ÕDe-embeddedÕ)_=airLine.plot_s_db(ax =ax,label =ÕAirline Õ)_=totalLine.plot_s_db(ax =ax,label =ÕTheoryÕ)fig,ax =plt.subplots()_=sample.plot_s_deg(ax =ax,label =ÕDe-embeddedÕ)_=airLine.plot_s_deg(ax =ax,label =ÕAirline Õ)_=totalLine.plot_s_deg(ax =ax,label =ÕTheoryÕ)1-PortNetwork:ÕTransitionS11Õ,30000-6000000000GHz,1601pts,z0=[50.+0.j] 1-PortNetwork:ÕÕ,30000-6000000000Hz,1601pts,z0=[2806.49894742-2801.86123236j] 1-PortNetwork:ÕÕ,30000-6000000000Hz,1601pts,z0=[2806.49894742-2801.86123236j] R.8TheoryDoneManually In[ 10]:defABCD(gamma,length,Z): """468 FigureR.7:notebookÞgure 469 FigureR.8:notebookÞgure 470 CalculatetheABCDparametersforat-line A=cosh(gamma*length) B=Z*sinh(gamma*length) C=(1/Z)*singh(gamma*length) D=cosh(gamma*length) Parameters----------gamma:numpyarray-like Gammaforthetransmissionline,freq.dep. length:value lengthoftransmissionlinesegment Z:numparyarray-like Characteristicimpedanceoftransmissionline,freq.dep. Returns-------A:numpyarray Aparameter B:numpyarray Bparameter C:numpyarray Cparameter D:numpyarray Dparameter """A=np.cosh(gamma *length)B=Z*np.sinh(gamma *length)C=(1/Z)*np.sinh(gamma *length)D=np.cosh(gamma *length)returnA,B,C,D defa2s(A,B,C,D,Z): """ConvertABCDparamstoSparams S11=A+B/Z-C*Z-D -----------------A+B/Z+C*Z+D S12=2(A*D-B*C) -----------------A+B/Z+C*Z+D S21=2 -----------------A+B/Z+C*Z+D S11=-A+B/Z-C*Z+D -----------------471 A+B/Z+C*Z+D Parameters----------A,B,C,D:numpyarray A,B,C,Dparameters Returns-------s11,s12,s21,s22:numpyarray S-parameters"""denom=A+B/Z+C*Z+Ds11=(A+B/Z-C*Z-D)/denoms12=2*(A*D-B*C)/denoms21=2/denoms22=(-A+B/Z-C*Z+D)/denomreturns11,s12,s21,s22 In[ 11]:dataDir =os.path.join(os.path.expanduser( "~"),"hpcc","plexiglass-holder-data ","Data","2014-08-05")rawDir=os.path.join(os.path.expanduser("~"),"hpcc","plexiglass-holder-data ","Data","2014-08-11")rawSample=rf.Network(os.path.join(rawDir,"6-0mm-foam-F-12-9mm-delrin-28-7mm-foamG-short.s1p "))short1=os.path.join(dataDir,"5-9mm-foam-F-short.s1p ")short2=os.path.join(dataDir,"9-7mm-foam-G-short.s1p ")short3=os.path.join(dataDir,"17-2mm-foam-H-short.s1p ")shortDistances=np.array([5.9,9.7,17.2])*1e-3layerEps_r=np.array([1,3.7,1])tanDelta=1.5e-4 lengths=np.array([6,12.9,28.7-6-12.9])*1e-3totalLen=28.7 *1e-3freq=rawSample .fdiam=0.122radius=diam /2cntr2cntr=0.25sigma=1/(7.2e-7 )472 R.8.1AirLine Scikit-RF In[ 12]:R,L,G,C =twoWireParameters(freq =freq,a =radius,D =cntr2cntr,sigma_c=sigma,unitsScale =0.0254)rRad=30*(2*pi*freq**2*constants.epsilon_0*constants .mu_0)*cntr2cntr**2R=R+rRadgamma=np.sqrt((R +1j*2*pi*freq*L)*(G+1j*2*pi*freq*C))rfFreq=rf.Frequency(freq[0],freq[ -1],freq .shape[0],ÕHzÕ)#airLine=rf.media.DistributedCircuit(rfFreq,C,L,R,G).delay_short(sampleDist) airLine=rf.media.DistributedCircuit(rfFreq,C,L,R,G) .line(totalLen,ÕmÕ)airLine.renormalize(50)Manually In[ 13]:R,L,G,C =twoWireParameters(freq =freq,a =radius,D =cntr2cntr,sigma_c=sigma,unitsScale =0.0254)rRad=30*(2*pi*freq**2*constants.epsilon_0*constants .mu_0)*cntr2cntr**2R=R+rRadgamma=np.sqrt((R +1j*2*pi*freq*L)*(G+1j*2*pi*freq*C))Z=np.sqrt((R +1j*2*pi*freq*L)/(G+1j*2*pi*freq*C))rfFreq=rf.Frequency(freq[0],freq[ -1],freq .shape[0],ÕHzÕ)a,b,c,d=ABCD(gamma,totalLen,Z) s11,s12,s21,s22 =a2s(a,b,c,d,50)In[ 14]:#plt.rcParams[Õaxes.ymarginÕ]=0 fig,ax =plt.subplots(2,2)fig.set_figheight(7)fig.set_figwidth(10)_=airLine.plot_s_db(ax =ax[0,0])_=ax[0,1].plot(airLine .f,20*np.log10(s11),label ="thy11 ")_=ax[0,1].plot(airLine .f,20*np.log10(s12),label ="thy12 ")_=ax[0,1].plot(airLine .f,20*np.log10(s21),label ="thy21 ")_=ax[0,1].plot(airLine .f,20*np.log10(s22),label ="thy22 ")_=ax[0,1].legend() _=airLine.plot_s_deg(ax =ax[1,0])_=ax[1,1].plot(airLine .f,np .rad2deg(np.angle(s11)),label ="thy11 ")_=ax[1,1].plot(airLine .f,np .rad2deg(np.angle(s12)),label ="thy12 ")_=ax[1,1].plot(airLine .f,np .rad2deg(np.angle(s21)),label ="thy21 ")_=ax[1,1].plot(airLine .f,np .rad2deg(np.angle(s22)),label ="thy22 ")_=ax[1,1].legend() #ifdoSave: #fig.savefig(Õshort-s-param.pdfÕ) 473 //anaconda/lib/python2.7/site-packages/numpy/core/numeric.py:462: ComplexWarning:Castingcomplexvaluestorealdiscardstheimaginarypart returnarray(a,dtype,copy=False,order=order) FigureR.9:notebookÞgure R.8.2CascadedLine Scikit-RF In[ 15]:freq =rawSample.fdiam=0.122radius=diam /2cntr2cntr=0.25sigma=1/(7.2e-7 )R,L,G,C =twoWireParameters(freq=freq,a =radius,D =cntr2cntr, sigma_c=sigma,unitsScale =0.0254)rRad=30*(2*pi*freq**2*constants.epsilon_0*constants .mu_0)*cntr2cntr**2R=R+rRadgamma=np.sqrt((R +1j*2*pi*freq*L)*(G+1j*2*pi*freq*C))rfFreq=rf.Frequency(freq[0],freq[ -1],freq .shape[0],ÕHzÕ)airLine=rf.media.DistributedCircuit(rfFreq,C,L,R,G) .delay_short(sampleDist) 474 #########Cascade########R,L,G,C =twoWireParameters(freq,radius,cntr2cntr,sigma,eps_r =1,tanDelta=0,unitsScale=0.0254)R+=rRadZ=np.sqrt((R +1j*2*pi*freq*L)/(G+1j*2*pi*freq*C))Z_norm=Zsect1=rf.media .DistributedCircuit(rfFreq,C,L,R,G) .line(lengths[0])sect1.renormalize(Z_norm) #added10/31/2015 #foamandshortsection sect3=rf.media .DistributedCircuit(rfFreq,C,L,R,G) .delay_short(lengths[ -1])sect3.renormalize(Z_norm) #samplesection R,L,G,C =twoWireParameters(freq,radius,cntr2cntr,sigma, eps_r=layerEps_r[1],tanDelta =tanDelta,unitsScale=0.0254)R+=rRadsect2=rf.media .DistributedCircuit(rfFreq,C,L,R,G) .line(lengths[1])sect2.renormalize(Z_norm) totalLine=sect1**sect2**sect3##De-embed #shorts=[short1,short2,short3] balun=find1PortTransition( 1j*gamma,shortDistances,shorts) sample=deembed(balun,rawSample) #airLine.renormalize(50) #totalLine.renormalize(50) printsampleprintairLineprinttotalLine##Plotting ##sample.plot_s_db(show_legend=False) #airLine.plot_s_db(show_legend=False) #totalLine.plot_s_db(show_legend=False) ##rawSample.plot_s_db(show_legend=False) #plt.figure() #sample.plot_s_deg(show_legend=False) #airLine.plot_s_deg(show_legend=False) #totalLine.plot_s_deg(show_legend=False) 475 fig,ax =plt.subplots()_=sample.plot_s_db(ax =ax,label =ÕDe-embeddedÕ)_=airLine.plot_s_db(ax =ax,label =ÕAirline Õ)_=totalLine.plot_s_db(ax =ax,label =ÕTheoryÕ)fig,ax =plt.subplots()_=sample.plot_s_deg(ax =ax,label =ÕDe-embeddedÕ)_=airLine.plot_s_deg(ax =ax,label =ÕAirline Õ)_=totalLine.plot_s_deg(ax =ax,label =ÕTheoryÕ)1-PortNetwork:ÕTransitionS11Õ,30000-6000000000GHz,1601pts,z0=[50.+0.j] 1-PortNetwork:ÕÕ,30000-6000000000Hz,1601pts,z0=[2806.49894742-2801.86123236j] 1-PortNetwork:ÕÕ,30000-6000000000Hz,1601pts,z0=[2806.49894742-2801.86123236j] FigureR.10:notebookÞgure Manual In[ 16]:R,L,G,C =twoWireParameters(freq,radius,cntr2cntr,sigma,eps_r =1,tanDelta=0,unitsScale=0.0254)R+=rRadgamma=np.sqrt((R +1j*2*pi*freq*L)*(G+1j*2*pi*freq*C))Z=np.sqrt((R +1j*2*pi*freq*L)/(G+1j*2*pi*freq*C))476 FigureR.11:notebookÞgure 477 t1a,t1b,t1c,t1d =ABCD(gamma,lengths[ 0],Z) t1=np.array([[t1a,t1b],[t1c,t1d]]) #foamno.2 t3a,t3b,t3c,t3d =ABCD(gamma,lengths[ 2],Z) t3=np.array([[t3a,t3b],[t3c,t3d]]) #samplesection R,L,G,C =twoWireParameters(freq,radius,cntr2cntr,sigma, eps_r=layerEps_r[1],tanDelta =tanDelta,unitsScale=0.0254)R+=rRadgamma=np.sqrt((R +1j*2*pi*freq*L)*(G+1j*2*pi*freq*C))Z=np.sqrt((R +1j*2*pi*freq*L)/(G+1j*2*pi*freq*C))t2a,t2b,t2c,t2d =ABCD(gamma,lengths[ 2],Z) t2=np.array([[t2a,t2b],[t2c,t2d]]) t=t1*t2*t3s11,s12,s21,s22 =a2s(t[0,0],t[ 0,1],t[ 1,0],t[ 1,1],50)In[ 17]:foriin[t1,t2,t3]: s11,s12,s21,s22 =a2s(i[0,0],i[ 0,1],i[ 1,0],i[ 1,1],50)fig,ax =plt.subplots()_=ax.plot(airLine.f,20*np.log10(s11),label ="thy11 ")_=ax.plot(airLine.f,20*np.log10(s12),label ="thy12 ")_=ax.plot(airLine.f,20*np.log10(s21),label ="thy21 ")_=ax.plot(airLine.f,20*np.log10(s22),label ="thy22 ")_=ax.legend()fig,ax =plt.subplots()_=ax.plot(airLine.f,np .rad2deg(np.angle(s11)),label ="thy11 ")_=ax.plot(airLine.f,np .rad2deg(np.angle(s12)),label ="thy12 ")_=ax.plot(airLine.f,np .rad2deg(np.angle(s21)),label ="thy21 ")_=ax.plot(airLine.f,np .rad2deg(np.angle(s22)),label ="thy22 ")_=ax.legend()In[ 18]:#plt.rcParams[Õaxes.ymarginÕ]=0 fig,ax =plt.subplots(2,2)fig.set_figheight(7)fig.set_figwidth(10)#_=airLine.plot_s_db(ax=ax[0,0]) _=ax[0,1].plot(airLine .f,20*np.log10(s11),label ="thy11 ")_=ax[0,1].plot(airLine .f,20*np.log10(s12),label ="thy12 ")_=ax[0,1].plot(airLine .f,20*np.log10(s21),label ="thy21 ")_=ax[0,1].plot(airLine .f,20*np.log10(s22),label ="thy22 ")_=ax[0,1].legend() 478 FigureR.12:notebookÞgure 479 FigureR.13:notebookÞgure 480 FigureR.14:notebookÞgure 481 FigureR.15:notebookÞgure 482 FigureR.16:notebookÞgure 483 FigureR.17:notebookÞgure 484 #_=airLine.plot_s_deg(ax=ax[1,0]) _=ax[1,1].plot(airLine .f,np .rad2deg(np.angle(s11)),label ="thy11 ")_=ax[1,1].plot(airLine .f,np .rad2deg(np.angle(s12)),label ="thy12 ")_=ax[1,1].plot(airLine .f,np .rad2deg(np.angle(s21)),label ="thy21 ")_=ax[1,1].plot(airLine .f,np .rad2deg(np.angle(s22)),label ="thy22 ")_=ax[1,1].legend() #ifdoSave: #fig.savefig(Õshort-s-param.pdfÕ) FigureR.18:notebookÞgure In[ ]:485 AppendixS IPythonnotebook: T-lineCalibration-With-Water-diss S.1WaterCalibrationandDe-Embedding ThisnotebookisaÞrstattemptatcalibratingusingdeionizedwater.Itstarted asacopyofT-lineCalibration.OriginalandÞrstcommitareincommit 83bb869eac88fde4aa8976c2033b607d76d598fe. ThenewnotebookwascreatedsothatIwouldnÕtmessupfunctionsthatwereusedforthe solids. S.2BasicImports In[ 1]:#Importbasicmodules #makesurethatdivisionisdoneasexpected from__future__importdivision#plottingsetup %matplotlibinline importmatplotlib.pyplot aspltplt.style.use(Õgray_back Õ)#gettheviridiscolormap #https://bids.github.io/colormap #itwillbeavailableascmaps.viridis #importcolormapsascmaps #for3dgraphs #frommpl_toolkits.mplot3dimportaxes3d #forlegendsofcombinedfigtypes #importmatplotlib.linesasmlines #numericalfunctions 486 importnumpyasnp#needsomeconstants fromscipyimport constantsfromnumpyimport pi#RFtools! importskrfasrf#versioninformation #%install_exthttp://raw.github.com/jrjohansson/ #version_information/master/version_information.py #%load_extversion_information #%reload_extversion_information #%version_informationnumpy,scipy,matplotlib S.3Pre-ßight In[ 20]:import osplt.rcParams[Õaxes.ymargin Õ]=0doSave=True #doSave=False In[ 3]:#a79-charruler: #234567891123456789212345678931234567894123456789512345678961234567897123456789 #a72-charruler: #23456789112345678921234567893123456789412345678951234567896123456789712 deftwoWireParameters (freq,a,D,sigma_c =np.inf,mu_c =1,eps_r=1,tanDelta =0,mu_r =1,unitsScale=1):"""ReturnR,L,G,Cforatwo-wireline Calculatesandreturnstheresistance,impedance,conductance, andcapacitanceforatwo-wiretransmissionline.Geometricand electricalpropertiesaregivenforthewireandthemediain whichthewiresarelocated. Parameters----------freq:scalar Frequencyatwhichtheparametersshouldbecalculated a:scalar Wireradius D:scalar center-to-centerdistanceofthewires sigma_c:scalar 487 Conductivityofthewires mu_c:scalar,optional Relativepermeabilityofthewires.Defaultis1. eps_r:scalar,optional Relativepermittivityoftheenvironment.Usedas epsilon=eps_r*eps_0*(1-j*tanDelta).Defaultis1. tanDelta:scalar,optional Losstangentoftheenvironment.Usedas epsilon=eps_r*eps_0*(1-j*tanDelta).Defaultis0. mu_r:scalar,optional Relativepermeabilityoftheenvironment.Defaultis1 unitsScale:scalar,optionalifusingmeters Scalingfactorforunits.Formm,use1e-3,forinuse 0.0254.Returns-------R:scalar Resistanceofthetwo-wiretransmissionline L:scalar Impedanceofthetwo-wiretransmissionline G:scalar Conductanceofthetwo-wiretransmissionline C:scalar Capacitanceofthetwo-wiretransmissionline """#from__future__importdivision importscipy.constants asconst#Scaledimensions a=a*unitsScale D=D*unitsScale eps_sgl=constants .epsilon_0*eps_reps_dbl=constants .epsilon_0*eps_r*tanDeltaomega=2*pi*freq#delta_cond=1/np.sqrt(constants.pi*freq*sigma_c) invCosh=np.arccosh(D/(2*a))#R=1/(constants.pi*a*sigma_c*delta_cond) R=np.sqrt(omega *mu_c/(2*(constants.pi*a)**2*sigma_c*(1-(2*a/D)**2)))G=(constants .pi*omega*eps_dbl)/invCoshL=constants.mu_0/pi*invCoshC=pi*eps_sgl /invCoshreturnR,L,G,C deffind1PortTransitionWater (measured,theory): #23456789112345678921234567893123456789412345678951234567896123456789712 488 """Calculated*SOME*oftheS-parametersforatransition.READDETAILS CalculateS_11,S_22,andS_12*S_21foratransition.Thisisused whenyouwanttode-embedasamplefromthetransitionandthe sample.Thisrequiresscikit-rfversionwithsourceafterApril4,2014. Probablywillbeversion0.15.Youmightneedtogetthisfrom github(https://github.com/scikit-rf/scikit-rf). Parameters----------measured:listof1-portskrfNetworkobjects Alistofskrf.networksforthethreemeasuredstandardsused tode-embedthesample theory:listof1-portskrfNetworkobjects Alistofskrf.networksforthetheoreticalthreestandards usedtode-embedthesample.S11isusedasthereflection coefficient.Returns-------ntwkS11,ntwkS22,ntwkS12S21:skrfNetworkobject 1-portnetworksforthecalculatedS-parameterstobeusedfor de-embeddingasample. To-Do-----Shouldthrowinsomeerrorcheckingtomakesurethatthethree shortshavethesamenetworkproperties """#gis1/Gamma g=[1/t.s[:,0,0]fortintheory]sc=[m.s[:,0,0]forminmeasured]tempNtwk=measured[ 0].s11freq=tempNtwk .fz0=tempNtwk.z0K=(g[2]-g[0])/(g[1]-g[0])*(sc[0]-sc[1])/(sc[0]-sc[2])s22=(g[2]-g[1]*K)/(1-K)s12s21=(sc[0]-sc[1])/(g[1]-g[0])*(g[0]-s22)*(g[1]-s22)s11=sc[0]-s12s21 /(g[0]-s22)ntwkS11=rf.Network(name="TransitionS11 ",f=freq,z0 =z0,s =s11)ntwkS22=rf.Network(name="TransitionS22 ",f=freq,z0 =z0,s =s22)ntwkS12S21=rf.Network(name="TransitionS12S21 ",f=freq,z0=z0,s=s12s21)returnntwkS11,ntwkS22,ntwkS12S21 defdeembed(trans,raw): #23456789112345678921234567893123456789412345678951234567896123456789712 489 """De-embeda1-portsample. De-embeda1-portsamplefromatransitionthathasbeen characterizedusingathreeshortmethod. Parameters----------trans:tupleofskrf.network.Network Atupleofscikit-rf1-PortNetworksthatcorrespondtothe characterizedS-parametersofthetransition.Ordershouldbe S_11,S_22,S_12*S_21. raw:skrf.network.Network Therawdatameasurementthatincludesthesampleandthe transition.Thesamplewillbede-embeddedfromthisdata Returns-------sample:skrfNetworkobject Thede-embeddedsample """b=[x.s[:,0,0]forxintrans]#printb[0] inv=b[1]+b[2]/(raw.s[:,0,0]-b[0])sample=trans[ 0]sample.s=1/invreturnsampledefdebye(f):"""CalculatethecomplexpermittivityofpurewaterusingDebyeequation CalculatethecomplexpermittivityofpurewaterusingtheDebyeequation ..math:: \\epsilon=\epsilon^\prime+j\epsilon^{\prime\prime}\\ \\epsilon^\prime=\epsilon_\infty+ \frac{\epsilon_s-\epsilon_\infty}{1+\omega^2\tau^2}\\ \\epsilon^{\prime\prime}= \frac{(\epsilon_s-\epsilon_\infty)\omega\tau}{1+\omega^2\tau^2} At25degC$\\epsilon_s=78.408$,$\\epsilon_\\infty=5.2$and$\\tau=8.27$ps. Reference:CRCHandbookofChemistryandPhysics,95thEd.,2014-2015. Parameters----------f:array-like Frequencyarray Returns490 -------eps:array-like Complexrelativepermittivity,epsilon """omega=2*pi*fes=78.408einf=5.2tau=8.27e-12 ep=einf+(es-einf)/(1+omega**2*tau**2)edp=((es-einf) *omega*tau)/(1+omega**2*tau**2)eps=ep+1j*edp returnepsdefairWaterShort (water,short,paramAir,paramWater,rfFreq): """Returns1-portofaair,water,short2wiret-line A1-portnetworkiscreatedtosimulateashortcircuitedtwo-wire transmissionlinesubmergedinwaterwithanairgapbetweenthe balunandthewaterlevel. Thisactuallyignoresasmallportionoftheline(total-short).I didthisbecuaseonecanaddthisoffsetmanuallyifneeded.This keepsthingssimplier(fromprogramminganduniformityperspective). IfIwanttode-embedandusethelargestamountofwaterasmy referenceplane,Isetwater=0andshort=short_0-water_0where _0meanstheoriginalvalues. TheairsectioniscreatedusingtheRLGCparameterssuppliedin paramAir.AlinefromskrfÕsdistributedcircuitmediaiscreated. Thelengthofthislineis ..math:: length=water AdelayedshortiscreatedusingtheRLGCparameterssuppliedin paramWater.Theshortislocatedatadistanceof ..math:: length=short-water Thelineanddelayedshortarethencascadedtocreateasingle one-portnetworkwhichisreturned. HereÕsacoolpicturebecauseIfiguredouthowtouseVIMtomake ASCIIart(itsintheamazingVIMmanual:usr_25.txtEditing formattedtext). 491 ---------||+|+___ |-------------------------+-------------------|s| |+|h| balun|air+liquid|o| |<--total-short+water-->+<--short-water-->|r| |-------------------------+-------------------|t| |+--- |+---------||=========water====| |=========short========================| |==============total========================| Parameters----------water:number Distancemeasuredtothesurfaceofthewaterinmeters(m) short:number Distancemeasuredtotheshortinmeters(m) paramAir:tuple AtupleasreturnedbytwoWireParametersfortheairline paramWater:tuple AtupleasreturnedbytwoWireParametersforthewater freq:skrfFrequencyobject Returns-------ntwk:skrfNetworkobject """C,L,R,G =paramAir[3],paramAir[ 1],paramAir[ 0],paramAir[ 2]line=rf.media .DistributedCircuit(rfFreq,C,L,R,G) .line(water)C,L,R,G =paramWater[3],paramWater[ 1],paramWater[ 0],paramWater[ 2]short=rf.media .DistributedCircuit(rfFreq,C,L,R,G).delay_short(short-water)ntwk=line**shortreturnntwkS.3.1DebyeEquation '='&+j'&&'&='.+'s#'.1+"202'&&=('s#'.)"01+"202At25degC 's=78.408, '.=5.2and 0=8.27ps. In[ 4]:freq=np.array([0,1e3,1e6,10e6,100e6 ,200e6,500e6,1e9,2e9,3e9,4e9,5e9,10e9,20e9 ,30e9,40e9,50e9])foo=debye(freq) forxinfoo:printx492 (78.408+0j)(78.408+3.80402988584e-06j) (78.4079998023+0.00380402987556j) (78.4079802335+0.0380402885873j) (78.4060234055+0.380392717815j) (78.4000942625+0.760723817672j) (78.3586171384+1.90073192821j) (78.2108674842+3.79378649739j) (77.6257888874+7.52676935397j) (76.6712213609+11.1413504822j) (75.3763335831+14.5859944393j) (73.7788529053+17.8174520536j) (62.8438971946+29.9528887095j) (40.3958596401+36.5769046903j) (26.5431968048+33.271018948j) (18.9607223632+28.6013545624j) (14.6460610982+24.5417841774j) Thisisclosetomatching6-14ofCRCHandbookofChemistryandPhysics,95thEd.,2014- 2015butoffafterabouttheÞrstdecimalplace. S.4BalunTesting Iconnectedthebaluntothe8510testcablewithanapadter.Ishortedthebalunwithapieceof wireacrossthetwowireterminals.Thisgivesmeashortofjustthebalun.Ialsocaptureddata inthesameposition/setupwiththetransmissionlinesshortedusingthecopperplate.Results arebelow In[ 5]:dataDir =Õ../plexiglass-holder-data/Data/2014-08-15/ Õfig,ax =plt.subplots()rf.Network(dataDir+Õbalun-wire-short.s1pÕ).plot_s_db(ax=ax,lw =2,label =ÕBalunÕ)rf.Network(dataDir+Õbalun-tline-short.s1pÕ).plot_s_db(ax=ax,lw =2,linestyle=Õ-.Õ,label=Õ2WTLÕ)ax.legend(loc=Õlowerleft Õ)fig,ax =plt.subplots()rf.Network(dataDir+Õbalun-wire-short.s1pÕ).plot_s_deg(ax=ax,lw =2,label=ÕBalunÕ)rf.Network(dataDir+Õbalun-tline-short.s1pÕ).plot_s_deg(ax=ax,lw =2,linestyle=Õ-.Õ,label =Õ2WTLÕ)ax.legend(loc=Õlowerleft Õ)Out[5]: S.5TestingofairWaterShortFunction In[ 6]:generic =rf.Network(Õ../plexiglass-holder-data/Data/2014-08-15/ ÕÕbeaker-mm-51-39.s1pÕ)493 FigureS.1:notebookÞgure 494 FigureS.2:notebookÞgure shortDist=72.38e-3diam=0.126radius=diam /2cntr2cntr=0.25sigma=5.96e7 R,L,G,C =twoWireParameters(freq=generic.f,a =radius,D =cntr2cntr, sigma_c=sigma,unitsScale =0.0254)rRad=30*(2*pi*generic.f**2*constants.epsilon_0*constants .mu_0)*cntr2cntr**2R+=rRadparamAir=tuple ([R,L,G,C]) waterEps=debye(generic .f)tanD=waterEps .imag/waterEps.realR,L,G,C =twoWireParameters(freq=generic.f,a =radius,D =cntr2cntr, sigma_c=sigma,eps_r =waterEps.real,tanDelta=tanD,unitsScale =0.0254)rRad=30*(2*pi*generic.f**2*waterEps.real*constants .mu_0)*cntr2cntr**2R+=rRadparamWater=tuple([R,L,G,C]) theory=airWaterShort( 21.40e-3,shortDist,paramAir,paramWater,generic .frequency)theory.plot_s_db()495 plt.figure()theory.plot_s_deg()FigureS.3:notebookÞgure Seemsreasonable.LetÕstrysomemoretesting In[ 7]:generic =rf.Network(Õ../plexiglass-holder-data/Data/2014-08-15/ ÕÕbeaker-mm-51-39.s1pÕ)shortDist=21.4e-3diam=0.126radius=diam /2cntr2cntr=0.25sigma=5.96e7 R,L,G,C =twoWireParameters(freq=generic.f,a =radius,D =cntr2cntr, sigma_c=sigma,unitsScale =0.0254)rRad=30*(2*pi*generic.f**2*constants.epsilon_0*constants .mu_0)*cntr2cntr**2R+=rRadparamAir=tuple ([R,L,G,C]) airCompare=rf.media.DistributedCircuit(generic.frequency,C,L,R,G) .line(21.4e-3)waterEps=debye(generic .f)496 FigureS.4:notebookÞgure 497 tanD=waterEps .imag/waterEps.realR,L,G,C =twoWireParameters(freq=generic.f,a =radius,D =cntr2cntr, sigma_c=sigma,eps_r=waterEps .real,tanDelta=tanD,unitsScale =0.0254)rRad=30*(2*pi*generic.f**2*waterEps.real*constants .mu_0)*cntr2cntr**2R+=rRadparamWater=tuple([R,L,G,C]) theory=airWaterShort( 21.40e-3,shortDist,paramAir,paramWater,generic .frequency)theory.plot_s_db()#airCompare.plot_s_db(0) plt.figure()theory.plot_s_deg()#airCompare.plot_s_deg(0) FigureS.5:notebookÞgure S.6WaterCalibration Steps: ¥Calcwaterpermittivity 498 FigureS.6:notebookÞgure 499 ¥Createmediaofdifferentsections ÐairÐwaterÐshort ¥Calcs11=reßectioncoefÞcient ¥De-embedlikenormal In[ 8]:rawSample =rf.Network(Õ../plexiglass-holder-data/Data/2014-08-15/ ÕÕbeaker-mm-54-31.s1pÕ)standards=[rf.Network(Õ../plexiglass-holder-data/Data/2014-08-15/ ÕÕbeaker-mm-51-39.s1pÕ),rf.Network(Õ../plexiglass-holder-data/Data/2014-08-15/ ÕÕbeaker-mm-57-43.s1pÕ),rf.Network(Õ../plexiglass-holder-data/Data/2014-08-15/ ÕÕbeaker-mm-60-02.s1pÕ)]offset=-1*50e-3sampleDist=offset+54.31e-3stdDist=offset +np.array([51.39,57.43,60.02])*1e-3 shortDist=offset+72.38e-3freq=rawSample .frfFreq=rawSample .frequencydiam=0.126radius=diam /2cntr2cntr=0.25sigma=5.96e7 R,L,G,C =twoWireParameters(freq=freq,a =radius,D =cntr2cntr, sigma_c=sigma,unitsScale =0.0254)rRad=30*(2*pi*freq**2*constants.epsilon_0*constants .mu_0)*cntr2cntr**2R+=rRadparamAir=tuple([R,L,G,C]) waterEps=debye(freq)tanD=waterEps .imag/waterEps.realR,L,G,C =twoWireParameters(freq=freq,a =radius,D =cntr2cntr,sigma_c =sigma,eps_r=waterEps.real,tanDelta =tanD,unitsScale=0.0254)rRad=30*(2*pi*freq**2*waterEps.real*constants.mu_0) *cntr2cntr**2R+=rRadparamWater=tuple([R,L,G,C]) theory1=airWaterShort(stdDist[ 0],shortDist,paramAir,paramWater,rfFreq) theory2=airWaterShort(stdDist[ 1],shortDist,paramAir,paramWater,rfFreq) theory3=airWaterShort(stdDist[ 2],shortDist,paramAir,paramWater,rfFreq) 500 theory=airWaterShort(sampleDist,shortDist,paramAir,paramWater,rfFreq) balun=find1PortTransitionWater(standards,[theory1,theory2,theory3]) sample=deembed(balun,rawSample) fig,ax =plt.subplots()sample.plot_s_db(label ="Cald",show_legend=False)theory.plot_s_db(label ="Theory",show_legend=False)rawSample.plot_s_db(label ="Raw",show_legend=True)ax.set_title("Deionized:54.31c51.39-57.43-60.02 ")#ifdoSave: #fig.savefig("deionized-54.31c51.39-57.43-60.02-mag.png") fig,ax =plt.subplots()sample.plot_s_deg(label ="Cald",show_legend=False)theory.plot_s_deg(label ="Theory",show_legend=True)ax.set_title("Deionized:54.31c51.39-57.43-60.02 ")#ifdoSave: #fig.savefig("deionized-54.31c51.39-57.43-60.02-phase.png") Out[8]: FigureS.7:notebookÞgure In[ 9]:#compositefigure fig,ax =plt.subplots(2,1)501 FigureS.8:notebookÞgure 502 fig.set_figheight(7)rawSample.plot_s_db(ax =ax[0],label ="Original",ls =":",show_legend =True)sample.plot_s_db(ax=ax[0],label ="Calibrated",show_legend =True)theory.plot_s_db(ax=ax[0],label ="Theory",ls ="--",show_legend =True)#ax.set_title("Deionized:54.31c51.39-57.43-60.02") ax[0].annotate(ÕCaldist: \n51.39mm\n57.34mm\n60.02mmÕ,xy=(2.5e9,-33))ax[0].annotate(ÕSample \n54.31mm\n\nÕ,xy =(4e9,-33))rawSample.plot_s_deg(ax =ax[1],label ="Original",ls =":",show_legend =False)sample.plot_s_deg(ax =ax[1],label ="Cald",show_legend =False)theory.plot_s_deg(ax =ax[1],label ="Theory",ls="--",show_legend =False)ifdoSave:fig.savefig("deionized-cal.pdf ")In[ 22]:#compositefigure fig,ax =plt.subplots(2,1)fig.set_figheight(7)rawSample.plot_s_db(ax =ax[0],label ="Original",ls =":",show_legend =True,lw =3)sample.plot_s_db(ax=ax[0],label ="Calibrated",show_legend =True,lw =3)theory.plot_s_db(ax=ax[0],label ="Theory",ls ="--",show_legend =True,lw =3)_=ax[0].legend(fontsize =16)_=ax[0].set_xlabel( ÕFrequency(Hz) Õ,fontsize =16)_=ax[0].set_ylabel( ÕMagnitudeÕ,fontsize =16)#ax.set_title("Deionized:54.31c51.39-57.43-60.02") rawSample.plot_s_deg(ax =ax[1],label ="Original",ls =":",show_legend=False,lw =3)sample.plot_s_deg(ax=ax[1],label ="Cald",show_legend =False,lw =3)theory.plot_s_deg(ax=ax[1],label ="Theory",ls="--",show_legend =False,lw =3)_=ax[1].set_xlabel( ÕFrequency(Hz) Õ,fontsize =16)_=ax[1].set_ylabel( ÕPhase(deg) Õ,fontsize =16)ifdoSave:fig.savefig("deionized-cal-defense.pdf ")In[ ]:rawSample=rf.Network(Õ../plexiglass-holder-data/Data/2014-08-15/ ÕÕbeaker-mm-60-02.s1pÕ)standards=[rf.Network(Õ../plexiglass-holder-data/Data/2014-08-15/ ÕÕbeaker-mm-51-39.s1pÕ),rf.Network(Õ../plexiglass-holder-data/Data/2014-08-15/ ÕÕbeaker-mm-54-31.s1pÕ),rf.Network(Õ../plexiglass-holder-data/Data/2014-08-15/ ÕÕbeaker-mm-57-43.s1pÕ)]offset=-1*50e-3sampleDist=offset+60.02e-3503 FigureS.9:notebookÞgure 504 FigureS.10:notebookÞgure 505 stdDist=offset +np.array([51.39,54.31,57.43])*1e-3 shortDist=offset+72.38e-3freq=rawSample .frfFreq=rawSample .frequencydiam=0.126radius=diam /2cntr2cntr=0.25sigma=5.96e7 R,L,G,C =twoWireParameters(freq=freq,a =radius,D =cntr2cntr, sigma_c=sigma,unitsScale =0.0254)rRad=30*(2*pi*freq**2*constants.epsilon_0*constants .mu_0)*cntr2cntr**2R+=rRadparamAir=tuple ([R,L,G,C]) waterEps=debye(freq) tanD=waterEps .imag/waterEps.realR,L,G,C =twoWireParameters(freq=freq,a =radius,D =cntr2cntr,sigma_c =sigma,eps_r=waterEps.real,tanDelta =tanD,unitsScale=0.0254)rRad=30*(2*pi*freq**2*waterEps.real*constants.mu_0) *cntr2cntr**2R+=rRadparamWater=tuple([R,L,G,C]) theory1=airWaterShort(stdDist[ 0],shortDist,paramAir,paramWater,rfFreq) theory2=airWaterShort(stdDist[ 1],shortDist,paramAir,paramWater,rfFreq) theory3=airWaterShort(stdDist[ 2],shortDist,paramAir,paramWater,rfFreq) theory=airWaterShort(sampleDist,shortDist,paramAir,paramWater,rfFreq) balun=find1PortTransitionWater(standards,[theory1,theory2,theory3]) sample=deembed(balun,rawSample) fig,ax =plt.subplots()sample.plot_s_db(show_legend =False)theory.plot_s_db(show_legend =False)rawSample.plot_s_db(show_legend =False)fig,ax =plt.subplots()sample.plot_s_deg(show_legend =False)theory.plot_s_deg(show_legend =False)In[ ]:rawSample=rf.Network(Õ../plexiglass-holder-data/Data/2014-08-15/ ÕÕbeaker-mm-06-02.s1pÕ)standards=[rf.Network(Õ../plexiglass-holder-data/Data/2014-08-15/ ÕÕbeaker-mm-11-67.s1pÕ),rf.Network(Õ../plexiglass-holder-data/Data/2014-08-15/ ÕÕbeaker-mm-24-41.s1pÕ),rf.Network(Õ../plexiglass-holder-data/Data/2014-08-15/ ÕÕbeaker-mm-40-27.s1pÕ)]506 offset=-1*3e-3sampleDist=offset+6.02e-3stdDist=offset +np.array([11.67,24.41,40.27])*1e-3 shortDist=offset+72.38e-3freq=rawSample .frfFreq=rawSample .frequencydiam=0.126radius=diam /2cntr2cntr=0.25sigma=5.96e7 R,L,G,C =twoWireParameters(freq=freq,a =radius,D =cntr2cntr, sigma_c=sigma,unitsScale =0.0254)rRad=30*(2*pi*freq**2*constants.epsilon_0*constants .mu_0)*cntr2cntr**2R+=rRadrAir=rRadparamAir=tuple ([R,L,G,C]) waterEps=debye(freq) tanD=waterEps .imag/waterEps.realR,L,G,C =twoWireParameters(freq=freq,a =radius,D =cntr2cntr,sigma_c =sigma,eps_r=waterEps.real,tanDelta =tanD,unitsScale=0.0254)rRad=30*(2*pi*freq**2*waterEps.real*constants.mu_0) *cntr2cntr**2R+=rRadparamWater=tuple([R,L,G,C]) rWater=rRad theory1=airWaterShort(stdDist[ 0],shortDist,paramAir,paramWater,rfFreq) theory2=airWaterShort(stdDist[ 1],shortDist,paramAir,paramWater,rfFreq) theory3=airWaterShort(stdDist[ 2],shortDist,paramAir,paramWater,rfFreq) theory=airWaterShort(sampleDist,shortDist,paramAir,paramWater,rfFreq) balun=find1PortTransitionWater(standards,[theory1,theory2,theory3]) sample=deembed(balun,rawSample) sample.plot_s_db(show_legend =False)theory.plot_s_db(show_legend =False)rawSample.plot_s_db(show_legend =False)plt.figure()sample.plot_s_deg(show_legend =False)theory.plot_s_deg(show_legend =False)507 BIBLIOGRAPHY 508 BIBLIOGRAPHY [1] S.Ramo,J.R.Whinnery,andT.VanDuzer, FieldsandWavesinCommunicationElectron- ics ,3rded.NewYork:Wiley,1994. [2] ÒScatteringparameters,ÓNov.2014,pageVersionID:632781014.[URL]http://en. wikipedia.org/w/index.php?title=Scattering_parameters&oldid=632781014 [3] IFSTA, EssentialsofFireFightingandFireDepartmentOperations ,5thed.PrenticeHall, Jan.2008. [4] J.A.Bittencourt, Fundamentalsofplasmaphysics ,3rded.Springer,2004. [5] D.M.Pozar, MicrowaveEngineering ,4thed.Hoboken,NJ:Wiley,2012. [6] J.A.Stratton, Electromagnetictheory ,1sted.,ser.Internationalseriesinphysics.New York,London:McGraw-Hillbookcompany,inc,1941. [7] L.Brillouin, WavePropagationandGroupVelocity ,ser.PureandAppliedPhysics.New York:AcademicPress,1960. [8] E.J.RothwellandM.J.Cloud, Electromagnetics ,2nded.BocaRaton,Fla:CRCPress, 2009.[URL]https://catalog.loc.gov/vwebv/holdingsInfo?searchId=7961&recCount=25& recPointer=1&bibId=12227004 [9] E.R.Andrew,D.W.E.Axford,andT.M.Sugden,ÒThemeasurementofionisationina transientßame,Ó TransactionsoftheFaradaySociety ,vol.44,p.427,1948.[URL]http: //pubs.rsc.org.proxy2.cl.msu.edu/en/Content/ArticleLanding/1948/TF/tf9484400427 [10] H.BelcherandT.M.Sugden,ÒStudiesontheIonizationProducedbyMetallic SaltsinFlames.I.TheDeterminationoftheCollisionFrequencyofElectrons inCoal-Gas/AirFlames,Ó ProceedingsoftheRoyalSocietyofLondon.SeriesA, MathematicalandPhysicalSciences ,vol.201,no.1067,pp.480Ð488,May1950.[URL] http://www.jstor.org/stable/98501 [11] H.BelcherandT.M.Sugden,ÒStudiesontheIonizationProducedbyMetallic SaltsinFlamesII.ReactionsGovernedbyIonicEquilibriainCoal-Gas/AirFlames ContainingAlkaliMetalSalts,Ó ProceedingsoftheRoyalSocietyofLondon.SeriesA, MathematicalandPhysicalSciences ,vol.202,no.1068,pp.17Ð39,Jun.1950.[URL] http://www.jstor.org/stable/98512 [12] H.SmithandT.M.Sugden,ÒStudiesontheIonizationProducedbyMetallicSaltsin Flames.III.IonicEquilibriainHydrogen/AirFlamesContainingAlkaliMetalSalts,Ó ProceedingsoftheRoyalSocietyofLondon.SeriesA,MathematicalandPhysicalSciences ,vol.211,no.1104,pp.31Ð58,Feb.1952.[URL]http://www.jstor.org/stable/98839 509 [13] H.SmithandT.M.Sugden,ÒStudiesontheIonizationProducedbyMetallicSaltsin Flames.IV.TheStabilityofGaseousAlkaliHydroxidesinFlames,Ó Proceedingsofthe RoyalSocietyofLondon.SeriesA,MathematicalandPhysicalSciences ,vol.211,no.1104, pp.58Ð74,Feb.1952.[URL]http://www.jstor.org/stable/98840 [14] F.P.Adler,ÒMeasurementoftheConductivityofaJetFlame,Ó JournalofApplied Physics ,vol.25,no.7,pp.903Ð906,Jul.1954.[URL]http://jap.aip.org.proxy2.cl.msu.edu/ resource/1/japiau/v25/i7/p903_s1 [15] K.E.ShulerandJ.Weber,ÒAMicrowaveInvestigationoftheIonizationofHydrogen- OxygenandAcetylene-OxygenFlames,Ó TheJournalofChemicalPhysics ,vol.22,no.3, pp.491Ð502,Mar.1954.[URL]http://link.aip.org/link/JCPSA6/v22/i3/p491/s1&Agg=doi [16] J.Boan,ÒFDTDfortroposphericpropagationwithstrongcoldplasmaeffects,Óin IEEE AntennasandPropagationSocietyInternationalSymposium2006 ,Jul.2006,pp.3905Ð 3908,http://digital.library.adelaide.edu.au/dspace/displaystats?handle=2440/35259. [17] J.A.Boan,ÒRadioPropagationinFireEnvironments,Óin Work- shopontheApplicationsofRadioScience2006 ,Luera,Australia,Feb. 2006,http://www.ips.gov.au/IPSHosted/NCRS/wars/wars2006-meeting/index.html. [URL]http://www.ips.gov.au/IPSHosted/NCRS/wars/wars2006/proceedings/index.htm [18] J.J.Boan,ÒRadioExperimentsWithFire,Ó IEEEAntennasandWirelessPropagationLet- ters ,vol.6,pp.411Ð414,2007. [19] C.ColemanandJ.Boan,ÒAKirchhoffIntegralapproachtoradiowavepropagationin Þre,Óin 2007IEEEAntennasandPropagationSocietyInternationalSymposium .IEEE, 9-15June2007,pp.3752Ð3755. [20] J.A.Boan,ÒRadiopropagationinÞreenvironments,ÓThesis,UniversityofAdelaide, Adelaide,Australia,2009.[URL]http://digital.library.adelaide.edu.au/dspace/handle/ 2440/58684 [21] M.L.HeronandK.M.Mphale,ÒRadiowaveattenuationinbushÞres,tropicalcyclones andothersevereatmosphericconditions,ÓAustralianEmergencyManagement,Final ReportEMAProject60/2001,Apr.2004.[URL]http://www.em.gov.au/Documents/ EMA%20Project%2010-2001.PDF [22] K.M.Mphale,D.Letsholathebe,andM.L.Heron,ÒEffectivecomplexpermittivity ofaweaklyionizedvegetationlitterÞreatmicrowavefrequencies,Ó Journalof PhysicsD:AppliedPhysics ,vol.40,no.21,pp.6651Ð6656,Nov.2007.[URL] http://iopscience.iop.org/0022-3727/40/21/026 [23] K.MphaleandM.Heron,ÒAbsorptionandTransmissionPowerCoefÞcientsfor MillimeterWavesinaWeaklyIonisedVegetationFire,Ó InternationalJournalof InfraredandMillimeterWaves ,vol.28,no.10,pp.865Ð879,2007.[URL]http: //www.springerlink.com/content/n48v060420267w32/abstract/ 510 [24] K.Mphale,M.Heron,andT.Verma,ÒEffectofWildÞre-InducedThermalBubbleon RadioCommunication,Ó ProgressInElectromagneticsResearch ,vol.68,pp.197Ð228, 2007.[URL]http://www.jpier.org/PIER/pier.php?paper=06072202 [25] K.MphaleandM.Heron,ÒMicrowavemeasurementofelectrondensityandcollision frequencyofapineÞre,Ó JournalofPhysicsD:AppliedPhysics ,vol.40,no.9,pp. 2818Ð2825,May2007.[URL]http://eprints.jcu.edu.au/2587/ [26] K.Mphale,M.Jacob,andM.Heron,ÒPredictionandMeasurementofElectron DensityandCollisionFrequencyinaWeaklyIonisedPineFire,Ó InternationalJournal ofInfraredandMillimeterWaves ,vol.28,no.3,pp.251Ð262,Mar.2007.[URL] http://eprints.jcu.edu.au/2655/ [27] K.MphaleandM.Heron,ÒRayTracingRadioWavesinWildÞreEnvironments,Ó ProgressInElectromagneticsResearch ,vol.67,pp.153Ð172,2007.[URL]http: //www.jpier.org/PIER/pier.php?paper=06082302 [28] K.MphaleandM.Heron,ÒWildÞreplumeelectricalconductivity,Ó TellusB ,vol.59,no.4, pp.766Ð772,Sep.2007.[URL]http://www.tellusb.net/index.php/tellusb/article/view/ 17055 [29] K.M.MphaleandM.L.Heron,ÒPlantalkalicontentandradiowavecommunication efÞciencyinhighintensitysavannawildÞres,Ó JournalofAtmosphericandSolar- TerrestrialPhysics ,vol.69,no.4Ð5,pp.471Ð484,Apr.2007.[URL]http://www. sciencedirect.com/science/article/pii/S1364682606003063 [30] K.M.MphaleandM.Heron,ÒNonintrusivemeasurementofionisationinvegetation Þreplasma,Ó TheEuropeanPhysicalJournalAppliedPhysics ,vol.41,no.2,pp.157Ð 164,Feb.2008.[URL]http://www.epjap.org.proxy2.cl.msu.edu/action/displayAbstract? fromPage=online&aid=8015723 [31] K.Mphale,P.Luhanga,andM.Heron,ÒMicrowaveattenuationinforestfuel ßames,Ó CombustionandFlame ,vol.154,no.4,pp.728Ð739,Sep.2008.[URL] http://www.sciencedirect.com/science/article/pii/S0010218008002101 [32] K.MphaleandM.Heron,ÒMeasurementofElectricalConductivityforaBiomassFire,Ó InternationalJournalofMolecularSciences ,vol.9,no.8,pp.1416Ð1423,Aug.2008.[URL] http://www.mdpi.com/1422-0067/9/8/1416 [33] K.M.Mphale,ÒRadiowavepropagationmeasurementsandpredictioninbushÞres,Ó PhD,JamesCookUniversity,Australia,2008.[URL]http://eprints.jcu.edu.au/2028/ [34] K.Mphale,M.Heron,R.Ketlhwaafetse,D.Letsholathebe,andR.Casey,ÒInterferometric measurementofionizationinagrassÞre,Ó MeteorologyandAtmosphericPhysics ,vol.106,no.3,pp.191Ð203,2010.[URL]http://www.springerlink.com/content/ n4621420l5466177/abstract/ 511 [35] M.BornandE.Wolf, Principlesofoptics:electromagnetictheoryofpropagation,interfer- enceanddiffractionoflight ,6thed.Cambridge,UK;NewYork;CambridgeUniversity Press,1997. [36] M.Skolnik, IntroductiontoRadarSystems ,3rded.McGraw-HillScience/Engineering/- Math,Dec.2002. [37] A.C.Bemis,ÒWeatherradarresearchatMIT,Ó BulletinoftheAmericanMeteorological Society ,vol.28,no.3,pp.115Ð117,1947. [38] L.F.Radke,D.A.Hegg,P.V.Hobbs,J.D.Nance,J.H.Lyons,K.K.Laursen,R.E.Weiss, P.J.Riggan,andD.E.Ward,ÒParticulateandtracegasemissionsfromlargebiomass ÞresinNorthAmerica,Ó Globalbiomassburning:Atmospheric,climatic,andbiospheric implications ,pp.209Ð224,1991.[URL]http://www.fs.fed.us/psw/publications/riggan/ psw_1991_riggan001(radke).pdf? [39] R.M.Banta,L.D.Olivier,E.T.Holloway,R.A.Kropßi,B.W.Bartram,R.E.Cupp,and M.J.Post,ÒSmoke-ColumnObservationsfromTwoForestFiresUsingDopplerLidar andDopplerRadar,Ó JournalofAppliedMeteorology ,vol.31,no.11,pp.1328Ð1349, Nov.1992.[URL]http://journals.ametsoc.org/doi/abs/10.1175/1520-0450(1992)031% 3C1328:SCOFTF%3E2.0.CO;2 [40] R.R.RogersandW.O.J.Brown,ÒRadarObservationsofaMajorIndustrialFire,Ó Bulletin oftheAmericanMeteorologicalSociety ,vol.78,no.5,pp.803Ð814,May1997.[URL]http: //journals.ametsoc.org/doi/abs/10.1175/1520-0477(1997)078<0803:ROOAMI>2.0.CO;2 [41] V.M.Melnikov,D.S.Zrnic,andR.M.Rabin,ÒPolarimetricradarpropertiesofsmoke plumes:Amodel,Ó JournalofGeophysicalResearch:Atmospheres ,vol.114,no.D21, p.D21204,Nov.2009.[URL]http://onlinelibrary.wiley.com/doi/10.1029/2009JD012647/ abstract [42] T.A.Jones,S.A.Christopher,andW.Petersen,ÒDual-PolarizationRadarCharacteristics ofanApartmentFire,Ó JournalofAtmosphericandOceanicTechnology ,vol.26, no.10,pp.2257Ð2269,Oct.2009.[URL]http://journals.ametsoc.org/doi/abs/10.1175/ 2009JTECHA1290.1 [43] T.A.JonesandS.A.Christopher,ÒSatelliteandRadarRemoteSensingofSouthernPlains GrassFires:ACaseStudy,Ó JournalofAppliedMeteorologyandClimatology ,vol.49, no.10,pp.2133Ð2146,May2010.[URL]http://journals.ametsoc.org/doi/abs/10.1175/ 2010JAMC2472.1 [44] T.Baum,L.Thompson,andK.Ghorbani,ÒAComplexDielectricMixingLawModelfor ForestFireAshParticulates,Ó GeoscienceandRemoteSensingLetters,IEEE ,vol.9,no.5, pp.832Ð835,Sep.2012. [45] C.K.Law, CombustionPhysics ,1sted.CambridgeUniversityPress,Aug.2010. 512 [46] W.M.Haynes,Ed., CRCHandbookofChemistryandPhysics,92ndEdition(Internet Version2012) .CRCPress/TaylorandFrancis,BocaRaton,FL.,2012.[URL]http: //www.hbcpnetbase.com/ [47] K.Yee,ÒNumericalsolutionofinitialboundaryvalueproblemsinvolvingmaxwellÕsequa- tionsinisotropicmedia,Ó IEEETransactionsonAntennasandPropagation ,vol.14,no.3, pp.302Ð307,May1966. [48] F.AklemanandL.Sevgi,ÒAnovelÞnite-differencetime-domainwavepropagator,Ó IEEE TransactionsonAntennasandPropagation ,vol.48,no.5,pp.839Ð841,May2000. [49] L.NickischandP.Franke,ÒFinite-differencetime-domainsolutionofMaxwellÕsequations forthedispersiveionosphere,Ó IEEEAntennasandPropagationMagazine ,vol.34,no.5, pp.33Ð39,Oct.1992. [50] J.Young,ÒPropagationinlineardispersivemedia:Þnitedifferencetime-domainmethod- ologies,Ó IEEETransactionsonAntennasandPropagation ,vol.43,no.4,pp.422Ð426,Apr. 1995. [51] K.Lan,Y.Liu,andW.Lin,ÒAhigherorder(2,4)schemeforreducingdispersioninFDTD algorithm,Ó IEEETransactionsonElectromagneticCompatibility ,vol.41,no.2,pp.160 Ð165,May1999. [52] T.T.ZygiridisandT.D.Tsiboukis,ÒHigher-orderÞnite-differenceschemeswithreduced dispersionerrorsforaccuratetime-domainelectromagneticsimulations,Ó International JournalofNumericalModelling:ElectronicNetworks,DevicesandFields ,vol.17,no.5, pp.461Ð486,2004.[URL]http://onlinelibrary.wiley.com/doi/10.1002/jnm.551/abstract [53] Y.Itikawa,ÒEffectivecollisionfrequencyofelectronsingases,Ó PhysicsofFluids ,vol.16, no.6,pp.831Ð835,Jun.1973.[URL]http://pof.aip.org/resource/1/pßdas/v16/i6/p831_s1 [54] P.E.Ciddor,ÒRefractiveindexofair:newequationsforthevisibleandnear infrared,Ó AppliedOptics ,vol.35,no.9,pp.1566Ð1573,Mar.1996.[URL]http: //ao.osa.org/abstract.cfm?URI=ao-35-9-1566 [55] C.D.Grant,W.A.Loneragan,J.M.Koch,andD.T.Bell,ÒFuelcharacteristics,vegetation structureandÞrebehaviourof11-15year-oldrehabilitatedbauxiteminesinwesternaus- tralia,Ó AustralianForestry ,vol.60,no.3,pp.147Ð157,1997. [56] NationalInstituteofStandardsandTechnology(NIST),ÒFireDynamicsSimulator.Ó [URL]http://code.google.com/p/fds-smv/ [57] E.KoretzkyandS.P.Kuo,ÒCharacterizationofanatmosphericpressureplasma generatedbyaplasmatorcharray,Ó PhysicsofPlasmas ,vol.5,no.10,pp.3774Ð3780,Oct. 1998.[URL]http://pop.aip.org.proxy1.cl.msu.edu/resource/1/phpaen/v5/i10/p3774_s1 513 [58] A.Krutz,ÒElectromagneticMaterialCharacterizationUsingFree-FieldTransmission Measurements,ÓPh.D.dissertation,1997. [59] T.A.Zwietasch,ÒTransientReßectionofPlaneWavesfromaPlasmaHalf-Space,ÓDiplom Wirtschaftsingenieur,UniversityofKaiserslautern,Kaiserslautern,Germany,2006. [60] B.T.Perry,ÒNaturalresonancerepresentationofthetransientÞeldreßectedfromamulti- layeredmaterial,ÓPh.D.dissertation,MichiganStateUniversity,EastLansing,Michigan, UniteStatesofAmerica,2005. [61] S.Kerber,ÒAnalysisofChangingResidentialFireDynamicsandItsImplicationsonFire- ÞghterOperationalTimeframes,ÓUL,Tech.Rep.,2011.[URL]http://newscience.ul.com/ wp-content/uploads/2014/04/Analysis_of_Changing_Residential_Fire_Dynamics_and_ Its_Implications_on_FireÞghter_Operational_Timeframes.pdf [62] S.Kerber,ÒAnalysisofChangingResidentialFireDynamicsandItsImplicationson FireÞghterOperationalTimeframes,Ó FireTechnology ,vol.48,no.4,pp.865Ð891,Dec. 2011.[URL]http://link.springer.com/article/10.1007/s10694-011-0249-2 [63] J.Ross,ÒWavecalc,ÓMoab,UT.[URL]http://www.johnross.com/wavecalc.html [64] W.Gunn,Jr.,ÒApplicationoftheThreeShortCalibrationTechniqueinaLowFrequency FocusBeamSystem,ÓM.S.,AirForceInstituteofTechnology,Wright-PattersonAirForce Base,Ohio,Mar.2010.[URL]http://www.dtic.mil/dtic/tr/fulltext/u2/a518512.pdf [65] O.Tudisco,A.LuccaFabris,C.Falcetta,L.Accatino,R.DeAngelis,M.Manente, F.Ferri,M.Florean,C.Neri,C.Mazzotta,D.Pavarin,F.Pollastrone,G.Rocchi,A.Selmo, L.Tasinato,F.Trezzolani,andA.A.Tuccillo,ÒAmicrowaveinterferometerforsmall andtenuousplasmadensitymeasurements,Ó ReviewofScientiÞcInstruments ,vol.84, no.3,pp.033505Ð033505Ð7,Mar.2013.[URL]http://rsi.aip.org/resource/1/rsinak/v84/ i3/p033505_s1 [66] M.A.HealdandC.B.Wharton, PlasmaDiagnosticswithMicrowaves .Huntington,N.Y: R.E.KriegerPub.Co,1978. [67] D.W.Williams,J.S.Adams,J.J.Betten,G.F.Whitty,andG.T.Richardson,ÒOperation Euroka:AnAustralianMassFireExperiment,ÓAustraliaDefenseStandardsLaboratory, Maribyrnor,Victoria,Tech.Rep.386,1970. [68] J.E.Foster, BushÞre:history,preventionandcontrol .Sydney:Reed,1976. [69] ÒByonics-MicroTrak.Ó[URL]http://www.byonics.com/mf [70] ÒInternetDataloggingWithArduinoandXBeeWiFi.Ó[URL]https://learn.sparkfun.com/ tutorials/internet-datalogging-with-arduino-and-xbee-wiÞ 514 [71] ÒAR8200BulletinPage.Ó[URL]http://www.thiecom.de/ftp/aor/ar8200/information/ ar8200bul.pdf [72] ÒNetSurveyor802.11NetworkDiscoveryTool.Ó[URL]http://nutsaboutnets.com/ netsurveyor-wiÞ-scanner/ [73] D.K.Cheng, FieldandWaveElectromagnetics ,2nded.Reading,MA:Addison-Wesley, 1989. [74] R.PlonseyandR.E.Collin, PrinciplesandapplicationsofelectromagneticÞelds ,ser. McGraw-Hillseriesinelectricalengineering.Electromagnetics.NewYork:McGraw-Hill, 1961. [75] L.V.Bewley, Two-DimensionalFieldsinElectricalEngineering .DoverPublication,1963. [76] R.W.P.King, Transmission-LineTheory .NewYork:McGraw-Hill,1955. [77] A.TemmeandE.Rothwell,ÒMaterialcharacterizationusingatwo-wiretransmission line,Óin RadioScienceMeeting(JointwithAP-SSymposium),2014USNC-URSI ,Jul.2014, pp.11Ð11. [78] A.TemmeandE.Rothwell,ÒEvaluationofMaterialCharacterizationSystemsthat UtilizeaTwo-WireTransmissionLine,ÓVancouver,BC,Canada,Jul.2015.[URL] https://github.com/temmeand/Temme-and-Rothwell-URSI-2015 [79] IEEE,ÒIEEEStandardDeÞnitionsofTermsforRadioWavePropagation,Ó IEEEStd211- 1997 ,1998. [80] J.R.Carson,ÒWavepropagationoverparallelwires:Theproximityeffect,Ó Philosophical MagazineSeries6 ,vol.41,no.244,pp.607Ð633,1921.[URL]http://www.tandfonline. com/doi/abs/10.1080/14786442108636251 [81] D.J.Infante,ÒFull-waveintegral-operatordescriptionofpropagationmodesexcitedon striplinestructures,ÓPh.D.,MichiganStateUniversity,EastLansing,Michigan,Unite StatesofAmerica,1999. [82] J.Venkatesan,ÒInvestigationoftheDouble-YBalunforFeedingPulsedAntennas,Ó Dissertation,GeorgiaInstituteofTechnology,Jul.2004.[URL]https://smartech.gatech. edu/handle/1853/5036 [83] C.R.Paul, IntroductiontoElectromagneticCompatibility ,2nded.Hoboken,NewJersey: Wiley-Interscience,2006. [84] ÒTitle47:TelecommunicationPART15ÑRADIOFREQUENCYDEVICESSub- partFÑUltra-WidebandOperation.Ó[URL]http://www.ecfr.gov/cgi-bin/text-idx?SID= 6717b8161d802bc6e2caf2d6bc1e8fb7&mc=true&node=sp47.1.15.f&rgn=div6 515 [85] ÒFirstReportandOrder.RevisionofPart15oftheCommissionÕsRulesRegardingUltra WideBandTransmissionSystems.FFC02-48,ÓFeb.2002.[URL]https://transition.fcc. gov/Bureaus/Engineering_Technology/Orders/2002/fcc02048.pdf [86] S.Kim,S.Jeong,Y.-T.Lee,D.Kim,J.-S.Lim,K.-S.Seo,andS.Nam,ÒUltra-wideband(from DCto110GHz)CPWtoCPStransition,Ó ElectronicsLetters ,vol.38,no.13,pp.622Ð623, Jun.2002. [87] B.Jokanovi«c,V.Trifunovi«c,andB.Reljic,ÒBalancemeasurementsindouble-Ybaluns,Ó Microwaves,AntennasandPropagation,IEEProceedings ,vol.149,no.56,pp.257Ð260, Oct.2002. [88] K.Chang,Ed., EncyclopediaofRFandMicrowaveEngineering .Hoboken,N.J:John Wiley,2005.[URL]http://onlinelibrary.wiley.com/book/10.1002/0471654507 [89] V.Trifunovi«candB.Jokanovi«c,ÒNewuniplanarbalun,Ó ElectronicsLetters ,vol.27,no.10, pp.813Ð815,May1991. [90] V.Trifunovi«candB.Jokanovi«c,ÒFourdecadebandwidthuniplanarbalun,Ó ElectronicsLet- ters ,vol.28,no.6,pp.534Ð535,Mar.1992. [91] V.Trifunovi«candB.Jokanovi«c,ÒReviewofprintedMarchandanddoubleYbaluns:char- acteristicsandapplication,Ó IEEETransactionsonMicrowaveTheoryandTechniques ,vol.42,no.8,pp.1454Ð1462,Aug.1994. [92] B.Jokanovi«candV.Trifunovi«c,ÒDouble-YbalunsforMMICsandwirelessapplications,Ó MicrowaveJournal,Internationaled. ,vol.41,no.1,pp.70Ð92,Jan.1998.[URL]http:// search.proquest.com/docview/204946934/F7D291AB0403486EPQ/18?accountid=12598 [93] B.Jokanovi«c,A.Marinci«c,andB.Kolundzija,ÒAnalysisoftheparasiticeffectsindouble- Ybaluns,Ó Microwaves,AntennasandPropagation,IEEProceedings ,vol.148,no.4,pp. 239Ð245,Aug.2001. [94] J.B.VenkatesanandJ.Scott,WaymondR.,ÒInvestigationofthedouble-ybalunfor feedingpulsedantennas,Óin ProceedingsoftheSPIE ,vol.5089,2003,pp.830Ð840.[URL] http://dx.doi.org/10.1117/12.487372 [95] J.Venkatesan,ÒNovelVersionoftheDouble-YBalun:MicrostriptoCoplanarStripTran- sition,Ó IEEEAntennasandWirelessPropagationLetters ,vol.5,no.1,pp.172Ð174,Dec. 2006. [96] Y.-G.Kim,D.-S.Woo,K.W.Kim,andY.-K.Cho,ÒANewUltra-widebandMicrostrip-to- CPSTransition,Óin MicrowaveSymposium,2007.IEEE/MTT-SInternational ,Jun.2007, pp.1563Ð1566. 516 [97] D.S.Woo,Y.G.Kim,I.B.Kim,Y.K.Cho,andK.W.Kim,ÒBroadbandantennasusinga planarultra-widebandbalun,Óin 11thIEEEInternationalConferenceonCommunication Technology,2008.ICCT2008 ,Nov.2008,pp.305Ð308. [98] Y.-G.Kim,I.-B.Kim,D.-S.Woo,M.-G.Choi,Y.-K.Cho,andK.W.Kim,ÒUltra-wideband componentsusingamicrostrip-to-CPSbalun,Óin 34thInternationalConferenceonIn- frared,Millimeter,andTerahertzWaves,2009.IRMMW-THz2009 ,Sep.2009,pp.1Ð2. [99] K.C.Gupta,R.Garg,I.J.Bahl,andP.Bhartia, Microstriplinesandslotlines .Dedham, Mass:ArtechHouse,1979. [100] K.C.Gupta,R.Garg,andI.Bahl, Microstriplinesandslotlines ,2nded.,ser.TheArtech Housemicrowavelibrary.Boston:ArtechHouse,1996.[URL]http://www.scribd.com/ doc/112426565/Gupta-Et-Al-1996-Microstrip-Lines-and-Slotlines-2nd-Ed#scribd [101] R.Garg,I.J.Bahl,andM.Bozzi, Microstriplinesandslotlines ,3rded.,ser.ArtechHouse microwavelibrary.Boston:ArtechHouse,2013. [102] R.N.Simons, CoplanarWaveguideCircuits,Components,andSystems .NewYork,USA: JohnWiley&Sons,Inc.,Mar.2001.[URL]http://ieeexplore.ieee.org.proxy2.cl.msu.edu/ xpl/bkabstractplus.jsp?bkn=5201692 [103] Y.Ichikawa,ÒI-Laboratory[TOOL],ÓFeb.2014.[URL]http://www1.sphere.ne.jp/i-lab/ ilab/tool/tool_e.htm [104] J.W.DuncanandV.P.Minerva,Ò100:1BandwidthBalunTransformer,Ó Proceedingsofthe IRE,vol.48,no.2,pp.156Ð164,Feb.1960. [105] K.Hettak,N.Dib,A.Sheta,A.Omar,G.-Y.Delisle,M.Stubbs,andS.Toutain,ÒNewminia- turebroadbandCPW-to-slotlinetransitions,Ó IEEETransactionsonMicrowaveTheory andTechniques ,vol.48,no.1,pp.138Ð146,Jan.2000. [106] T.Hirota,Y.Tarusawa,andH.Ogawa,ÒUniplanarMMICHybridsÐAProposedNewMMIC Structure,Ó IEEETransactionsonMicrowaveTheoryandTechniques ,vol.35,no.6,pp. 576Ð581,Jun.1987. [107] C.-H.Ho,L.Fan,andK.Chang,ÒBroad-banduniplanarhybrid-ringandbranch-linecou- plers,Ó IEEETransactionsonMicrowaveTheoryandTechniques ,vol.41,no.12,pp.2116Ð 2125,Dec.1993. [108] P.A.R.Holder,ÒX-bandmicrowaveintegratedcircuitsusingslotlineandcoplanarwaveg- uide,Ó RadioandElectronicEngineer ,vol.48,no.1.2,pp.38Ð42,Jan.1978. [109] Y.-G.Kim,S.-Y.Song,andK.W.Kim,ÒAPairofUltra-WidebandPlanarTransitionsfor PhaseInversionApplications,Ó IEEEMicrowaveandWirelessComponentsLetters ,vol.20, no.9,pp.492Ð494,Sep.2010. 517 [110] G.A.Kouzaev,M.J.Deen,andN.K.Nikolova,ÒChapterTwo-Transmission LinesandPassiveComponents,Óin AdvancesinImagingandElectronPhysics ,ser. Silicon-BasedMillimeter-waveTechnologyMeasurement,ModelingandApplications, M.JamalDeen,Ed.Elsevier,2012,vol.Volume174,pp.119Ð222.[URL]http: //www.sciencedirect.com/science/article/pii/B9780123942982000028 [111] H.-Y.LeeandT.Itoh,ÒWidebandandlowreturnlosscoplanarstripfeedusinginterme- diatemicrostrip,Ó ElectronicsLetters ,vol.24,no.19,pp.1207Ð1208,Sep.1988. [112] M.Manohar,R.Kshetrimayum,andA.Gogoi,ÒPrintedmonopoleantennawithtapered feedline,feedregionandpatchforsuperwidebandapplications,Ó IETMicrowaves,An- tennasPropagation ,vol.8,no.1,pp.39Ð45,Jan.2014. [113] S.-G.Mao,C.-T.Hwang,R.-B.Wu,andC.H.Chen,ÒAnalysisofcoplanarwaveguide-to- coplanarstriplinetransitions,Ó IEEETransactionsonMicrowaveTheoryandTechniques ,vol.48,no.1,pp.23Ð29,Jan.2000. [114] H.Nakajima,T.Kosugi,andT.Enoki,ÒHyperbolictangenttaperedslotantenna,Ó Elec- tronicsLetters ,vol.46,no.21,pp.1422Ð1424,Oct.2010. [115] V.K.Tripp,ÒTapereddoublebalun,ÓU.S.PatentUS7994874B2,Aug.,2011,u.S.Clas- siÞcation333/26,343/821,333/34,343/859;InternationalClassiÞcationH01Q1/50, H03H7/42,H01Q9/16,H03H7/38;CooperativeClassiÞcationH01P5/10,H01Q9/27;Eu- ropeanClassiÞcationH01P5/10,H01Q9/27. [116] M.J.White,ÒBroadbandbalun,ÓU.S.PatentUS20120019333A1,Jan.,2012,u.S. ClassiÞcation333/26;InternationalClassiÞcationH01P5/10;CooperativeClassiÞcation H01P5/10,H01P5/12;EuropeanClassiÞcationH01P5/10,H01P5/12. [117] S.J.Zegelin,I.White,andD.R.Jenkins,ÒImprovedÞeldprobesforsoilwatercontentand electricalconductivitymeasurementusingtimedomainreßectometry,Ó WaterResources Research ,vol.25,no.11,pp.2367Ð2376,1989.[URL]http://onlinelibrary.wiley.com/doi/ 10.1029/WR025i011p02367/abstract [118] K.F.Chackett,P.Reasbeck,andD.G.Tuck,ÒAnoteonjoiningtungstenwiretoother metals,Ó JournalofScientiÞcInstruments ,vol.33,no.12,p.505,Dec.1956.[URL] http://iopscience.iop.org/0950-7671/33/12/417 [119] J.G.Dodd,G.Schwarz,andA.J.Bearden,ÒSoftSolderingtoTungstenWire,Ó AmericanJournalofPhysics ,vol.34,no.10,pp.xviÐxvi,Oct.1966.[URL]http: //scitation.aip.org/content/aapt/journal/ajp/34/10/10.1119/1.1972398 [120] I.E.PetruninandL.L.GrzhimalÕskii,ÒInteractionoftungstenwithcopper,manganese, silver,andtin,Ó MetalScienceandHeatTreatment ,vol.11,no.1,pp.24Ð26,Jan.1969. [URL]http://link.springer.com/article/10.1007/BF00655167 518 [121] J.H.Lienhard,IVandJ.H.Lienhard,V, AHeatTransferTextbook ,4thed.Cambridge, MA,USA:PhlogistonPress,2012.[URL]http://web.mit.edu/lienhard/www/ahtt.html [122] ÒIntermediateHeatandMassTransfer.Ó[URL]http://ocw.mit.edu/courses/ mechanical-engineering/2-51-intermediate-heat-and-mass-transfer-fall-2008/ [123] Hewlett-Packard,ÒS-ParameterDesign,ÓHewlett-Packard,ApplicationNoteAN154, 1990.[URL]http://cp.literature.agilent.com/litweb/pdf/5952-1087.pdf [124] ÒMATLAB,ÓTheMathWorks,Inc.,Natick,Massachusetts,UnitedStates. [125] ÒScikit-rf.Ó[URL]http://www.scikit-rf.org 519