FSS CST Tutorial

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.

Page 1 of 10FSS: Simulation of Resonator Array

4/5/2015file://D:\Installed Programs\CST Studio Suite 2014\Online Help\mergedprojects\exampl...

For the frequency selective surface, please select Periodic Structures FSS, Metamaterial - Unit cell

FrequencyDomainSolver .



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



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.



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.



TM(0,0)mode,electricfield.

HigherorderorcircularlypolarizedFloquetmodesmaybedefined.

SolverSetup



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.



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



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.



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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FSS CST Tutorial