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A tutorial on designing a FSS in CST MWS
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FSS: Simulation of Resonator Array
Tutorials
ABSTRACT
AFrequencySelectiveSurface(FSS)isaperiodicassemblyofone-ortwo-dimensionalresonantstructures,eitherasaperturesinathinconductingsheetorasmetallicpatchesonasubstrate,whichmayhaveaband-passorband-stopfunction respectively. The increasing interestwithin the high-frequency community in this sortof structure has alsomade itsaccuratesimulation increasingly important.This tutorialdescribeshowanFSSstructuremaybesimulatedefficiently using CST MICROWAVE STUDIO (CST MWS). A simple unit cell of a ring resonator band-stop infinitearrayisconsideredasanexample.
Contents
Introduction
Physicaldescription
CSTMICROWAVESTUDIOModel
Simulationresults
Parametersweepanalysis
Conclusion
Introduction
Physical description
Frequency selective surfaces are increasingly used for the frequency filtering of plane waves in radar orcommunicationssystems.Aone-ortwo-dimensionalperiodicarrayofresonantstructuresonabackingmaterial,eitherapertures inametallic sheet ormetallic patchesona substrate,actsasa filter fora planewavearriving from anyangleof incidence. In thisexampleanarrayoffullwavelengthresonantconductingringsonadielectricsubstrate issimulated.SincetheFSSwouldbeusedoncurvedstructureslikeradomes,itisdesirablethattheFSShavethesameresonantfrequencyforallincidentplanewaveangles.Foragivenpolarisation,ringresonatorsareknowntobestablewiththescanangle.CSTMICROWAVESTUDIO(CSTMWS)canbeusedtoestablishtheangulardependenceoftheresonantfrequency.
CST MICROWAVE STUDIO Model: Parameter definition and preliminary settings
The simulationofanentirearrayof resonant ringswouldbeprohibitively timeandmemoryconsuming.TheuseofCSTMWSsunitcellboundaryconditionsinthedirectionsofperiodicityallowsarapidbutnolessaccuratesimulationoflargesurfaces.SettingupthesimulationmaybegreatlyeasedbyusingtheFSS-UnitCell(FD)template,whichautomaticallyappliesunitcellboundaryconditionsinthex-andy-directionsandsetsupFloquetportexcitationsinthepositive and negative z-directions. There is no need to define master and slave boundary conditions; the phaserelationoftheopposingboundariesisautomaticallysetbyspecifyingtheincidentangleoftheinwardtravellingplanewave.
CreateaNewProject
AfterlaunchingtheCSTSTUDIOSUITEyouwillenterthestartscreenshowingyoualistofrecentlyopenedprojectsandallowingyou to specify theapplicationwhichsuits your requirementsbest.Theeasiestway togetstarted is toconfigureaprojecttemplatewhichdefinesthebasicsettingsthataremeaningfulforyourtypicalapplication.Therefore
clickontheCreate Projectbutton intheNew Projectsection.
Nextyoushouldchoosetheapplicationarea,whichis Microwaves & RFfortheexampleinthistutorialandthenselecttheworkflowbydouble-clickingonthecorrespondingentry.
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For the frequency selective surface, please select Periodic Structures FSS, Metamaterial - Unit cell
FrequencyDomainSolver .
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Atlastyouarerequestedtoselecttheunitswhichfityourapplicationbest.Forthefrequencyselectivesurface,pleaseleavethesettingsasfollows:
Forthespecificapplicationin this tutorialtheothersettingscanbeleftunchanged.In thenextstepofsettinguptheprojecttemplateyouareaskedtoenterthefrequencyrangeofinterestanddefinefieldmonitors.Intheparticularcaseofourmodelwesettheminimumfrequencyto10GHzandthemaximumfrequencyto20GHz.AfterclickingtheNextbutton,youcangivetheprojecttemplateanameandreviewasummaryofyourinitialsettings:
FinallyclicktheFinishbuttontosavetheprojecttemplateandtocreateanewprojectwithappropriatesettings.CSTMICROWAVESTUDIOwillbelaunchedautomaticallyduetothechoiceoftheapplicationareaMicrowaves & RF.
Createstructure
Itisonlynecessarytoconstructasingleringonitsbackingsubstrate.Constructionofthegeometryitselfissimple:asubstrate is defined using a brick primitive object, and then a hollow cylinder can be used to create the ring. Theconductingringisalossymetaltypecopper,andthesubstrateisArlonAD300witharelativepermittivityof3.
Dimensions: mm
Frequency: GHz
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TheincidentangleoftheincomingplanewavemaybespecifiedbysettinganglesThetaandPhi,bothofwhichhavealreadybeenparameterizedby the template.Theperiodicityof theFSS isalso freelyconfigurableasshownbelow.Differentperiodicitiescanbeassigned in thex-andy-directions,andtheuseofaskewedlattice isalsopossiblebyspecifyingthegridangle(thiscanbeusefulforsimulatingcompactcloselycoupledarrays).
TheincidentplanewaveangleandunitcellperiodicityoftheFSSarefreelyconfigurable.
Foroff-normal incidentangles theFloquetportmodesensure that thereflectedwave is recorded in thedirectionofopticalreflection,whilethetransmissionisinthesamedirectionastheincidentwave.Thisiselucidatedbythefigurebelow.
IncidentandtransmitteddirectionsareautomaticallysetbytheFloquetmodes.
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Theperiodicitycanalsobespecified,asinthisexample,bysettingthesizeofthesubstratetothedesiredperiodicity,thencheckingtheFit unit cell to bounding boxcheckbox.
Unitcellboundaryconditionscanbesettofittheboundingbox.
ThedefaultFloquetportsettingsexcitetwoplanewaveswithorthogonalelectricfieldsasshownbelow(TE(0,0)andTM(0,0)modes),buthigherordermodesmayalsobespecified in theportpropertiesdialog (Details).Co-polarandcross-polarcouplingbetweenthemodes,bothreflectionandtransmission,arerepresentedintermsofS-parameters.The co-polarised reflection of mode 1 at port Zmin would thus, for example, be named SZmin(1),Zmin(1), and thecross-polarisedtransmissionbetweenmodes2and1SZmax(1),Zmin(2).
TE(0,0)mode,electricfield.
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TM(0,0)mode,electricfield.
HigherorderorcircularlypolarizedFloquetmodesmaybedefined.
SolverSetup
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Oncethegeometry isconstructed, thesimulationconditionsaresetup,andsome fieldmonitorshavebeendefined,thefrequencysolvercanbestarted(witheitherahexahedralortetrahedralmesh).
Themonitors'frequencyischosenasthesingleadaptivetetrahedralmeshrefinementfrequency:
Simulation results
Of primary interest in this case are the S-parameter results, which represent the reflection from and transmissionthroughtheFSS.Theco-polarreflectionsandtransmissionsofbothmodesarealmostidenticalduetothesymmetricalcircular rings(theslightdifference isdueto thetetrahedralmesh).The transmission isalmostcompletelyblockedat14.81 GHz, as seen from the SZmin(1),Zmax(1) of about -53 dB, and the reflection is almost complete (SZmax(1),Zmax(1)-0.02dB).
Pleasenote that theadaptive tetrahedralmesh refinementusually shouldbeperformed in thepassbandofa filterratherthaninthestopbandtofocusontheaccuracyofthetransmissionS-parameters.Astheadaptationfrequencywas forced to 15 GHz, the solver detects this situation and recommends to move the adaptation frequency.Alternatively,morethanonemeshadaptationfrequencycanbespecified.Seethefrequencydomainsolveroverviewfordetails.
ReflectionfromandtransmissionthroughtheFSS.
A view of the electric field magnitudes at 14.78 GHz (which can be calculated after the simulation by using theCalculate fieldsataxismarkeroption fromthe1Dplot'scontextmenu)reveals thetwofull-wavelengthresonancesduetothetwoFloquetportmodes.
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ElectricfieldsattheresonancewiththeplanewaveFloquetmodeTE(0,0)excited.
ElectricfieldsattheresonancewiththeplanewaveFloquetmodeTM(0,0)excited.
Parameter sweep analysis
Asmentionedpreviously,thedependenceoftheFSSresonantfrequencyontheangleoftheincidentplanewaveisofinterest.Aparametersweepcanbe setup to vary the incidentangle, in this case theta from0 to50degrees.Thereflectionandtransmissioncoefficientscanbeinvestigatedasapost-processingstep,eitherbyviewingtheparametric
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results for the S-parameters, or by extracting data with a result template. In the following here the transmissioncoefficientsofTEandTMmodewillbecompared.
AparametersweepcanbesetuptoobservetheeffectofscanangleontheFSStransmissioncharacteristics.
Thetransmissioncoefficientof theTEmodeshowsgreaterdependenceonvariationofthescanangleinthetathantheTMmodedoes.Thisistobeexpectedsincetheincidentwavesdirectionofincidencehasnotchangedrelativetothetopandbottomoftherings(asorientedinthefieldplotsabove),onlytotheleftandright.
EffectofvaryingthetaontransmissionoftheTEmodethroughtheFSS.
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EffectofvaryingthetaontransmissionoftheTMmodethroughtheFSS.
Conclusion
ThistutorialhasdescribedhowCSTMWSmaybeusedforthesimulationoffrequencyselectivesurfaces.Thesetupof the simulation may be greatly simplified by using a template which configures the simulation appropriately andgeneratesFloquetportmodeswithparameterizedincidentangleoftheplanewave.Oncethegeometryofasinglecellhasbeenconstructedtheperiodicitycanbesetupveryflexibly.ReflectionsfromandtransmissionsthroughtheFSScanbeobservedeasilyusingthefamiliarS-parameterrepresentation.Finally,aparametersweepoftheincidentwaveanglecanbeperformedtoinvestigateitseffectontheperformanceoftheFSS.
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