三路威尔金森功分器设计 3 way wilkinsonWord格式.docx

三路威尔金森功分器设计 3 way wilkinsonWord格式.docx

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togotoourmainpageonWilkinsonsplitters

togotoourpageonN-waysplitters

togotoourpageontheKouzoujiansplitter,agreatalternativetotheconventionalN-wayWilkinson

NewforJune2010!

Thispagewillprovideabasicanalysisofplanar,three-wayWilkinsonsplittersin50ohmsystemimpedance.Thisissplitterisimperfect,becauseitismissinganisolationresistorbetweenthetwoouterports,however,thisiswhatmakesiteasytolayout.Wedividedtheanalysisintothree"

types"

whicharedescribedbelow,andrankedaccordingtobandwidthpotential.

Type1splitter

TheType1splitteristhesimplestnetworkpossible.Thethreearmseachemployasingle 

quarter-waveimpedancetransformer. 

Ifyouweretoimpedancematchport1atcenterfrequency,thetransformerswouldallbe86.6ohms（transformseach50ohmlegto150ohms,andthree150ohmsinparallelis50ohms）.Sorryaboutthecrummyschematic,you'

dthinkbynowAgilentwouldprovideameansforgraphiccapturebeyondtheusualcopy-and-pastintoPowerpoint,thenshrinkimagewithPaintShop...

ThevariablesR1andZ1wereallowedtooptimizetoprovidethemaximum"

-15dBbandwidth"

inotherwords,itwasrequiredthatreflectioncoefficientsS11,S22andS33andisolationtermsS23andS24werelessthan-15dB.Notethatbysymmetry,itisnotnecessarytooptimize（ormonitor）S44,andS43.

Thechoiceof-15dBasthegoalisarbitrary.However,intheplanarthree-wayWilkinson,youcan'

texpectperfectisolationofthesplitports,andwithoutperfectisolation,youwon'

tgetperfectreturnlossesforS22,S33andS44.

Thetransmissionlineimpedancevalueswererestrictedtonomorethan100ohms（inallthreetypes）,tomakethecircuitrealizableinmicrostrip.Itmightbebettertorestricttoalowervaluedependingonwhatsubstrateischosen,andyieldconsiderations.Thesubjectforanotherday!

ForType1,Z1wasfoundtobe91.4ohmsandR1was83.6ohms,resultingin-15dBbandwidthof39%.

Belowisthetransmissioncoefficient,showingthenear-idealvalueof4.78dB 

[-10*log（1/3）].Allthreetransmissioncoefficientsareequalinthissimplifiedanalysis,inpracticetheouterbrancheswillbehaveslightlydifferentlyfromthecenterbranch.

Herearethereturnlossesandisolation.Notethatallparametersaresomewhatcompromised,asexpected.Thisisthepricethatispaidforaplanardesignwithonlytwoisolationresistors.

Type2

InType2weaddedanothertransformersection,inthiscaseasingletransformerattheinput,andcomponentvalueswerereoptimizedformaximum-15dBbandwidth.

Theoptimizedresultsareshownbelow.Wedidn'

tbothertoplotthetransmissioncoefficient,itissimilartothatofType1.Here,Z1wasfoundtobe41.9ohms,Z2was91.4ohms,andR1was76.9ohms,resultingin-15dBbandwidthof75%.

Type3

InType3,thesecondtransformersectionwasmovedtotheoutputports,andcomponentvalueswerereoptimizedformaximum-15dBbandwidth.

Theoptimizedresultsareshownbelow.Here,Z1wasfoundtobe99.3ohms,Z2was54.7ohms,andR1was98.6ohms,resultingin-15dBbandwidthof53%.

Inconclusion,Type2offersthebestbandwidthofthethreesplittersweexamined.Notethatifyouneededmorebandwidth,youcouldaddmoresectionsandasecond（orthird）setofdumpresistors.Planardividershavebeenmadethatspan2-18GHzinthisfashion,andpeoplehavebeenhappytospend$1000onthem!

Afurtherexample

Thisexampleisofatwo-stagethree-wayWilkinsonwithtwosetsofisolationresistors.ItwasEM-analyzedbysomestudentsfromIndia.Bravo!

Belowisthelinearschematic.Weaccidentallycroppedoutthemicrostripparameters.ThemicrostripsubstratehasER4.4,andis1.5millimetersinheight.WelefttheconductivityasaPEC（perfectelectricalconductor）.

Andbelowistheoptimizationgoalsandconstraintsweputonthenetwork.Herewedidn'

tdemand15dBfortheisolationandreturnlosses.Weaskedfor20dB,butdidn'

ttrytocalculatetheexactbandwidththatitwascapableof,over65%bandwidth.

Hereistheresultafteroptimization（thefinalvaluesaregiveninontheschematic）.WeputaconstraintonZ2,itwasnotallowedtoexceed100ohms（itisoftendifficulttorealizeveryhighimpedances）.Theparameterthathastheleast20-dBbandwidthisS33,whichisthereturnlossofthecenterleg.Whoops,lookslikewealsoconstrainedR2to150ohms,therewasnoreasontoputanyconstraintsontheisolationresistors'

values.

Whathappenswhenyoudon'

thaveanyresistorsinthenetwork?

Intheschematicbelowtheresistorshaveallbeendeactivated.

Theinputmatch（S11）looksthesame,whiletheoutputmatchesandisolationshavebeenseverelydegraded.Thisisobv