Design of unequal Wilkinson power divider for dual-band operation with isolation stubs

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DesignofunequalWilkinsonpowerdividerfordual-bandoperationwithisolationstubs

X.Li,Y.-J.Yang,L.Yang,S.-X.Gong,T.Hong,X.ChenandY.-J.Zhang

ThedesignofanovelunequalWilkinsonpowerdividerfordual-bandoperationispresented.Theisolationstubsareintroducedtoreducetheparasiticeffectsbetweenthetwostubsthatareconnectedbytheiso-lationresistor.Closed-formdesignequationsarederivedbasedonnetworktheory.Thevalidityofthisanalysisiscon rmedthroughthedesign,simulationandexperimentalresultsforapowerdividerfor1and2.5GHz.

Introduction:Powerdividersarefrequentlyusedinthedesignofmicro-wavecircuits.Owingtothetrendofdual-bandormultibandcommuni-cations,wecanseeaworldwideefforttodevelopdual-bandormultibandpowerdividers[1–3].However,mostofthesecannotsatisfytheunequalpowerdividingratio.FortheproposedunequalWilkinsonpowerdivider[4],thesingle-frequencypropertyisstillade ciency.Moreover,themediatransmissionlinesinthesepowerdivi-dersareplacedclosetoeachother,andasaresult,theparasiticeffectsbetweentransmissionlineswillbeincreasedwhentheoperatingfre-quencybecomeshigher[5].Isolationstubsareintroducedtodealwithequalpowerdividersin[6].

InthisLetter,anovelunequalpowerdividercircuitfordual-bandoperationisintroduced.Itsmainadvantagesinclude:(a)noextralumpedelementsareneededforthedual-bandoperationotherthanasingleresistor.Astructureconsistingofisolationstubsis rstintroducedintheunequalpowerdivider,whichmeansthatthepowerdividercanbefabricatedeasilyandtheparasiticeffectscanbegreatlyreduced.(b)Openstubsandshortstubscanbechosen exibly.Forveri cation,bothsimulatedandexperimentalresultsofadual-bandpowerdivideraregiven.

Theoryanddesignequations:ThecircuitconstructionisillustratedinFig.1.Threetransmissionlinesectionsofdifferentcharacteristicimpe-dances(ZA,ZBandZC),twoisolationstubs(ZDandZE)andanisolationresistor(R)composethewholecircuit.Sincethepower-dividingratioisunequalinthisstructure,worktheoryisinvolvedtoprovidetheanalyticalsolutions.

Mathematically,theABCD-parametersofnetworks1and2canbeexpressedas

A1B1j2ZAsinucosu

¼

C1D1jsinu=2ZAcosu

jZBsinucosu

Â

jsinu=ZBcosu 10Âð3Þ;

jY11

A2B2j2ZAsinucosu

¼

C2D2jsinu=2ZAcosu

cosujZCsinu10Â

jsinu=ZCcosujY21Theinputimpedancescanbewrittenas

Zin2¼

A1Z0þB1A2Z0þB2

;Zin3¼

C1Z0þD1C2Z0þD2

ð4Þ

Aftersomealgebraicmanipulation,theaboveequationscanbesolved

analyticallyandtheresultscanbeexpressedas

p 2pf2=f1À1Z0ctg;ZA¼21 p pf2=f1À12ZB¼kð1þkÞZ0tan;ð5Þ2f2=f1þ1

s

Z0ð1þk2Þpf2=f1À1

tanZC¼

kk2f2=f1þ1Foropenstubs,uo¼2u

ZOD

f2=f1À1 Z0p 2pf2=f1À12kð1þkÞtanptan;¼

f2=f1þ142f2=f1þ1

s

Z0ð1þk2Þf2=f1À1ZOE¼tanp

kf2=f1þ14k

pf2=f1À1

Âtan2

2f2=f1þ1 Z0p f=fÀ1pf=fÀ12121

kð1þk2Þtan2p¼tan;42f2=f1þ1f2=f1þ1

s

Z0ð1þk2Þ2f2=f1À1

tanpZSE¼

kf2=f1þ14k

pf2=f1À1Âtan

2f2=f1þ1

ð6Þ

Forshortstubs,us¼u

Z0 = ZSD

ð7Þ

Fig.1Circuitofproposeddual-bandunequalWilkinsonpowerdivider

Toful lthepowerdividingratioP3/P2¼k2,wecanobtainZin2¼k2Zin3.Tomatchport1,Z0mustbethen

Zin2Zin3k2

¼Zin3

Zin2þZin31þkTheopenstubsandtheshortstubsmeanthestatusofthestubsintheequivalentcircuitoftheproposedpowerdivider.TheyarejY1andjY2intheABCD-parametersofnetworks1and2,andcanbetreatedasopenstubsorshortstubs.

Solutionsareassignedtothetwofrequenciesf1andf2(f1,f2),andtheycanbeputinthefollowingformatthelowerfrequency:

u2f2f2u2pÀu1p¼)¼¼)u1¼1111121

ThevalueofresistorRcanbeobtainedas

R¼

1þk2

Z0k

ð8Þ

Z0¼

ð1Þ

ð9Þ

So,Zin2andZin3canbewrittenas:

1þk2

Z0;Zin2¼ð1þk2ÞZ0k2

Zin3¼

ð2Þ

Fig.2showsthattheimpedancesoftransmissionlinesandstubsvarywiththefrequencyratio(f2/f1).Theseresultssuggestthat,whenavail-ableimpedancevaluesoftransmissionlinesliebetween7and150V,thepowerdividercanoperateatafrequencyratiorangingfromp 1.98to2.69foropenstubsaccordingto(5)and(6)whenk¼2,andfrom1.73to2.3forshortstubsaccordingto(5)and(7).

ELECTRONICSLETTERS19thNovember2009Vol.45No.24

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160140120line impedance, 1008060402001.0

ZAZBZCZO DZO E

160140120100806040200

ZAZBZCZS DZS E

2.02.12.2

2. 3f2/f1

2.42.52.62.71.71.81.9

2.0f

2/f1

2. 1

2.22.3

ab

p

Fig.2Circuitparametersagainstfrequency

ratiowhenk¼2aOpenstubsbShortstubs

Experiment:Thedual-bandWilkinsonpowerdividerhasbeenfabri-catedonasubstratewiththicknessof1mmandrelativedielectriccon-stantof2.65.Thepowerdividerhasbeendesignedforf1¼1GHzandf2¼2.5GHz.Thedesignparameterswerecalculated rst.Accordingto(8),u¼51.48atthelowerfrequency(f1).Using(5),thelineimpedancevaluesareZA¼44V,ZB¼82VandZC¼41V.From(6),ZD¼72VandZE¼36Vforopenstubs.Fig.3showsaphotoofthefabricatedpowerdivider,whichoccupiesasizeof145Â60mm.ThemeasuredS-parameterdatacollectedfromaWILTRON37269AnetworkanalyseralongwithsimulatedresultsusingHFSSarepresentedinFig.4.Thereisagoodagreementbetweenthesimulatedandmeasuredresultswiththedual-bandoperationat1and2.5GHz.Thereturnlossis225.22dBat1GHzand218.03dBat2.5GHz.ThemeasuredS21is24.35dBat1GHzand24.99dBat2.5GHz,S31is21.93dBat1GHzand21.94dBat2.5GHz.Theisolationbetweenports2and3is17.35dBat1GHzand15.02dBat2.5GHz,respectively.Itisfoundthatthetransmissionvaluesarenotideal3dB.Thissmalldifferenceismainlyduetotheneglectofsubstratelossesandtheapproximatevaluesofcomponents.

Conclusions:Thedesignandanalysisofadual-bandunequalWilkinsonpowerdividerarepresented.Theisolationstubsareintro-ducedinordertoreducetheparasiticeffects.Furthermore,openstubsandshortstubscanbechosen exibly.Theformulasusedtodeterminethedesignparametersaregiven.Thetheoreticaldesignisveri edthroughmeasurementontherealcircuit.

#TheInstitutionofEngineeringandTechnology200930July2009

doi:10.1049/el.2009.2137

Fig.3Photographoffabricatedpowerdivider

0input return loss and isolation, dB

–5–10–15–20–25–300.5

stimulated S11stimulated S32measured S11measured

S32

0–5transmission,

dB–10–15–20–25–300.5

stimulated S21stimulated S31measured S21measured S31

X.Li,Y.-J.Yang,L.Yang,S.-X.Gong,T.Hong,X.ChenandY.-J.Zhang(NationalKeyLaboratoryofAntennasandMicrowaveTechnology,XidianUniversity,Xi’an,Shaanxi710071,People’sRepublicofChina)E-mail:xixi1928@References

1Cameron,R.J.,Yu,M.,andWang,Y.:‘Direct-couplermicrowave lterswithsingleanddualstopbands’,IEEETrans.Microw.TheoryTech.,2005,53,pp.3288–3297

2Park,M.J.,andLee,B.:‘Adual-bandWilkinsonpowerdivider’,pon.Lett.,2008,18,pp.85–87

3Cheng,K.K.M.,andLaw,C.:‘Anovelapproachtothedesignandimplementationofdual-bandpowerdivider’,IEEETrans.Microw.TheoryTech.,2008,56,pp.487–492

4Chen,J.X.,andXue,Q.:‘Novel5:1unequalWilkinsonpowerdividerusingoffsetdouble-sidedparallel-striplines’,pon.Lett.,2007,17,pp.175–177

5Horst,S.,Bairavasubramanian,R.,Tentzeris,M.M.,andPapapolymerou,J.:‘Modi edWilkinsonpowerdividersformillimeter-waveintegratedcircuits’,pon.Lett.,2007,55,pp.2439–24466Wu,Y.,Liu,Y.,andLiu,X.:‘Dual-frequencypowerdividerwithisolationstubs’,Electron.Lett.,2008,44,pp.1407–1408

1.0

1.52.0frequency, GHz

2.53.01.0

1.52.0frequency, GHz

2.53.0

a

0–5output return loss, dB–10–15–20–25–300.5

stimulated S22stimulated S33

measured S22measured S33

b

1.0

1.52.0frequency, GHz

2.53.0

c

Fig.4Frequencyresponseofdesigneddual-bandpowerdivideraSimulatedandmeasuredinputreturnlossbTransmission

cSimulatedandmeasuredoutputreturnloss

ELECTRONICSLETTERS19thNovember2009Vol.45No.24

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