移相器和微波转换论文汇编.pdf

810 %eeetransactions on microwave theory and techniques, august 1974 thelargestep discontinuitiesareappreciablyin error.errorsof this magnituderenderimpossiblethe accuratecomputerdesignof com- plexmicrostripmatchingnetworksformicrowavepowertransistor amplifiers.on the other hand,witha set of equationsapproximating thejunctionmodelcurvesincorporatedina microstripnetwork optimizationcomputerprogram,suchamplifiershavebeendevel- oped at the navalresearchlaboratoryon a “workthe firsttime” basis. the programdirectlygeneratescorrectedphysicaldimensions of the networks. vi.conclusions no attemptis made to generalizethe results presentedherein.the equivalentcircuithas been shownto be validforlargesteps from 50-q lines,in the frequencyrange from1 to 2 ghz,on 0.0635-cm- thickaluminasubstratematerial.cthertestshaveindicatedthat the curves are usable for steps betweenany two impedances,neither of whichis 50 !2. itshouldbe recognizedthatgreatprecisionis requiredinthe measurementof inputimpedancesand physicaldimensions,and in theknowledgeofsubstratedielectricconstant,inproducingthe parametersfor this junctionmodel.thisworkshows thatverylarge microstripstep effectscan be accountedfor, gives equivalentcircuit parametersfor a specificcase, and shows the utilityof the results. itis hopedthatthe presentationof thisinformationwillstimu- late furthertheoreticalworkon very large impedancesteps in micro- strip,so thatmore generalanalyticalexpressionscanbedeveloped toreplacethe specificresultspresentedherein. acknowledgment the authorswish to thankh. e. heddingsfor his expertfabrica- tionand measurementsupport. 1 2 3 4 5 6 7 i.introduction themostcommonlyused broad-bandwaveguidecirculatorin- corporatesa partialheightferritepostinthejunction.however, duetothecomplexityofthisconfiguration,noexacttheoryfor designingsuch a circulatorhas been obtained.theoriesfor onlythe fullheightferritepost have been attempted1,2.these analyses involvematchingthe dominantmode fields in the connectingwave- guidesto a summationof fieldsdue to modeswithinthe junction andthusrequireelaboratecomputerprograms.owenandbarnes 3proposedthatthepartialheightferritejunctioncirculator operatesin a turnstilefashionwithrotatingmodes propagatingalong the ferriteaxis. lateron, owen4measuredthe phase-frequency responsesof theeigenvaluesfromwhichthe principalfieldmodes couldbe experimentallyidentifiedandbuiltan x-bandcirculator based on these measurements.he couldadjustthe ferritegeometry toachievea 120 separationof theeigenvaluesovera broadfre- quencyrange. however,the instrumentationfor these measurements involvedmultiplephaseshifters,attenuators,couplers,a 3-way power-divider,and an hpnetworkanalyzer.thisequipmentis not readilyavailablefor devices operatingabove x-band. in this paper,approximateformulasare presentedwhichsimplify thedesignof partialheightwaveguidecirculators.theyapplyto boththesingleendedanddouble-endedconfigurationsoftheso- calledcompactturnstiledevice.the design is used to build38- and 60-ghzcirculators.goodcorrelationis achievedbetweenmeasured and predictedperformance. ii.theory thetwotypesof partialheightferritecirculatorsshownin fig. 1 (a) and(b)are the one-sidedcompactturnstiledevice,whichhas a shortcircuitat one end of the ferriterod, whilethe other is a double- sidedcompactturnstilewithdielectricspacers on bothends. with eithertype,twoofthethreeeigen excitationspropagateaxially alongtherodinrotatingmodeswhichare circularlypolarizedin oppositesenses.magnetizingtheferriteincreasesthepropagation constantof one of these modes and decreases the propagationcon- stantof the othersince these modes experiencedifferentpermeabili- ties. thethirdeigen-excitationdoes notcoupleintothe ferriterod alongthe symmetryaxis. itsimplyuses the rod as a dielectricreso- natorwithitscenterfrequencyandphaseq a functionofthe effectivedielectricconstantof the dielectricferritecombinationand theeffectiveradius(includingtheeffectof fringingfields)of the resonator.withthe ferritemagnetized,a phase displacementof 2mr “i= symmetryaxis references a.a.oliner,“equivalentcircuitsfordiscontinuitiesinbalanced striptransmissionline, ”iretrans.microwavetheorytech.(special 3qmposiumissue onmicrowavestripcircuits).vo1. mtt-3.dp. 134143,mar.1955. a.farraranda.t.adams,“matrixmethodsformicrostripthres- dimensionalproblems,”ieeetrans.microwavetheorytech.,vol. iwtt-20,pp.497504,aug.1972. v.nalbandianandw.steenaart, discontinuitiesinsymmetric striplinesduetoimpedancestepsandtheircompensations,”ieee trans.mtcrowaoetheorytech.,tel.mtt-20,pp.57357s,sept. . -m 18(4. b. aianco.,m.grana,ands. ridella,“commentson theexistence of transmissionzeros m microstripdiscontinuities,”alta.freg.,vol. -j ,( l-.1 designof partialheightferritewaveguidecirculators e.j.denlinger,member,ieee abstractthisshortpaperpresentsa designprocedureforthe widelyused three-portwaveguidecirculatorthat has a partialheight ferritepost in the junctionregion.designformulasand curvesare derivedfor two configurationsof partialheightcirculators:one has a shortcircuitat one end of the ferritepost,whiletheotherhas di- electricspacers at bothends. the designmethodwas used to build twocirculatorsforoperationat 38 ghzand 60 ghz,respectively. excellentagreementbetweentheoryand experimentwas obtained in predictingthe centerfrequencyand requiredmatchingstructure of thesedevices. manuscriptreceiveddecember26,1973;revisedmarch11,1974. theauthoris withthercacorporation,princeton,n. j. 0s540. (a) hext jd,z /,/,/, , axis spacer dielectricspacer (b) fig.1.(a)one-sidedcompactturnstilecirculator.(b)double-sided compactturnstilecirculator. shortpapers ill is desiredbetweentheaveragephaseof therotatingmodeswith phases pl and p, and the so-calledin-phasedielectricresonatormode. usingtheone-sidedunit,theshortcircuitcontributesa +-radian phase shiftand the lengthand diameterof the ferriterod is adjusted togiveanadditionalaveragephase shiftof(2n l)rrplusa phase advancementandretardationof 2rr/3radiansof thetworotating modes, respectively.withthe double-sidedunit,the rotatingmodes propagateonlyonce throughtherod.-therradiansof phase shift are obtainedby couplingmodes intoand out of the ferritewhilethe remainingrequiredphaseshiftof(2n l)mwecanthen findthe requiredferriterod diameterby using fig.3 and the corre- spondingvalueof f?e/1918. 7miller,blichfeldt,anddickson,op.cit.,p.19. 1956t1395 proceedingsoftheire 4-portcirculator,exceptforthefactthat negativef operators,whicharepermissible,alsosatisfy(9).there- fore,thecompleteandmathematicallyexhaustivelist ofsymmetriesofthe4-portcirculatoriscontainedin thefollowinggroupwhoseorderis8. f1,f2, f3,i,-f1,-f2,-f3,-i.(14) ifastructurepossessesasymmetrynotcontainedin thisgroup,thenitcannotbeacirculator. flectionthroughthexzplane,port1andport3remain unchangedwhereasport2andport4havetheirpolarities reversed.thereflectionoperatorwhichspecifiesthis operationisgivenbyf:2in(16)below. 0010 0001 fz= 1000 0100 (15) and 10 0-1 fxz= 00 00 (ca) (b) fig.1-structureshavingnonpermissiblesymmetries. infig.1,twoexamplesof4-portstructuresaregiven which,fromexperiencewithsimilarstructures,looklike theymightpossiblybecirculators.thesymbol (7r/2)-indicatesa900nonreciprocalphaseshift.how- ever,itwillbeseenthatthestructureoffig.1(a)is symmetricalaboutthezaxis.therefore,byrotatingthe structure1800aboutthezaxisport1replacesport3 andport2replacesport4withnochangeinpolarityof theports.thesymmetryoperatorwhichdescribesthis operationisgivenbyf2belowin(15).infig.1(b),the structureissymmetricalaboutthexzplane.inare- 0o 00 10 0-1 (16) neitheroneofthesefoperatorsmaybefoundinthe groupofthecirculatorgivenin(10)to(14).hence, withoutgoingthroughanyfurtheranalysis,itisknown thatthesestructurescannotbecirculators. topologicaldefinitionofcirculators acommonlyusedsymbolforacirculatorisshown infig.2(a).thesymbolillustratesinarathergraphical waythatenergywhichentersport1emergesatport2, etc.thepurposeofthesymbolismerelytoprovidea notationwhichcanberecognizedasdesignatinga circulator.itservesthispurposeverywell,butthereits utilityends.inthissection,anattemptwillbemadeto formalizethissymbolicrepresentation,bymeansofthe preciselanguageoftopology,intoanalternativedefini- tionofthecirculator. iffig.2(b)beobserved,therewillbeseentwopoints withadirectedpathbetweenthem.intopological language,thisisanoriented1-cellhavingthe0-cellaas theinitialpointandthe0-cellbastheterminalpoint.8 ifitisagreedthatthe0-cellsrepresentportsandthe oriented1-cellthepathanddirectionofenergyflow, thenacirculatormaybedefinedasanystructurewhich mayberepresentedbyan“oriented1-circuit.“(theword “circuit“isusedinadifferentsensethantheordinary electriccircuit.)itstopologicaldefinitionismathe- maticallypreciseandit isgiveninveblen.9however, aninformaldefinitionofanoriented1-circuitwouldnot beamisshereanditisaccordinglygivenbelow. topologically,thenotionofanncircuitinvolvesits behavioratitsintersections.iftwoandonlytwoncells intersectwithone(n-1)cell,thesystemiscalleda circuit.underthisdefinition,thefigureoffig.2(d)is alsoacircuitinthetopologicalsense,althoughitisnot whatisgenerallythoughtofasacircuitinelectricnet- 80. veblen,“analysissitus,“americanmathematicalsociety; 1931. 9ibid.,p.24. 1396 october treuhaft:networkpropertiesofcirculators worktheory.fig.2(d)isa2-circuitsincetwoandonly twoofits2-cells(thefaces),intersectwitheach1-cell. itservestoillustratethedifferencebetweentheprecise topologicalmeaningoftheterm“circuit“ascompared withitsordinaryusage.a1-circuitisthenasystemof 1-cellsand0-cellssuchthattwo1-cellsintersectwith each0-cell.anoriented1-circuitsimplymeansthatif arrowsareusedtoindicatetheorientationofthe1-cells, allthearrowswillbepointedinthesamedirection. 4 3 ca- (a)(b) formerandtheopencircuitareclassifiedascirculators andfig.2(e)andfig.2(f)arerespectivelytheirgraphi- calrepresentations. topologicalcombinationandinterconnection ofcirculators inordertostudytheresultofinterconnectingthe portsofcirculators,itisnecessarytosetupaformal rulewhichaccuratelydescribesthephysicalsituation. infig.3(a),twoportsbandbareshownwhichareto beconnected.afterconnection,theenergyflowing alongthedirectedpathabemergesatbandflowsalong thedirectedpathbc.similarly,theenergyflowing alongthepathabwillcontinuealongpathbc.this situationcanbedescribedformallybymeansofatopo- logicalconcept0calledtheproductoftwooriented 1-cells.anillustrationofthisproductisshowninfig. 3(b).theoriented1-cellgl,g2istheproductofthetwo oriented1-cellsglandg2since,accordingtothedefini- tionofthe product,itcontainsallthepointsofgland g2andhasthesameinitialpointasgiandthesame terminalpointasg2. aa /abc bb cpc cc (a)(b) (c)(d) (e)(f) fig.2-thetopologicalncircuit. ifincidentvoltagesarethoughtofasenteringthe portsor0-cellsofanoriented1-circuitandemergingat thesucceedingportsasreflectedvoltages,thenitwill beseenthatthetopologicaldefinitionofthecirculator isineverywayequivalenttothecyclicsubstitution definition.theoriented1-circuitismoreorlessapre- cisegraphicalrepresentationofacyclicsubstitution.it isinterestingtonotehere,asinthecaseofcyclicsub- stitutions,whatoccursasthenumberofportsisbrought downtotwoandthentoone.againtheidealtrans- cc (c)(d) fig.3-interconnectionbymeansofmultiplicatioin. nowtheoperationofinterconnectionshowninfig. 3(a)maybedescribedbyaformalrule,asfollows. ruleforinterconnection-superimposethetwo0-cells whichrepresentthetwoportstobeinterconnected.formthe productofanoriented1-cellwhoseterminalpointisoneof the0-cellsthathavebeensuperimposedandanotherori- ented1-cellwhoseinitialpointistheother0-cellthathas beensuperimposed.replacethetwooriented1-cellsbythe product.thenreplacethetworemainingoriented1-cells, atthejunction,withtheirproduct. 10ibid.,p.139. 19561397 , proceedingsoftheire toillustratethisruletheinterconnectionofbandb infig.3(a)willbeshown.fig.3(c)representsthefirst stepwherebandbhavebeensuperimposedandthe oriented1-cellsa1anda2havebeenreplacedbya,la2. thenextstepistoreplacea,anda2bya1a2asshown infig.3(d). theinterconinectionltechniqueisnowinformtobe appliedtoactualcirculators.fig.4showsseveralin- terestingcases.inthefirstcolumnareshowntheoriginal circulatorsthataretobeinterconinected.therefollows, inthesucceedingcolumnsthestepsnecessarytomake theinterconiiections.infig.4(a),theconnectioniofa 3-portanda4-portcirculatorisshown.theresultisa anotherresult,whichisalsopracticallyobviousby topologicalmeans,isthefactthatanyhigherorder circulatorcanbeconstructedbyinterconnecting4-port circulators.fig.4(b)showshowa3-portcirculatormay berealizedfroma4-port.theinterconnectionofthis 3-portwithsuccessive4-portswillgivecirculatorsof oddorder5,7,9,etc.,andtheinterconnectioinof4-ports willgiveevenordercirculators6,8,10,etc.thisisa ratherimportantconsiderationifoneisititerestedin constructinghigherordercirculatorssincemuchis knownabouttheconstructionof4-portcirculators whereas,withtheexceptionofcarlin,1“therehasbeei verylittleworkonhigherordercirculators. fig.4-someexamplesoftheinterconnectiontechnique. 5-portcirculator.fig.4(b)illustrateshowtohandlethe sinigularcasewheretheinitialanidterminalpointsofg3 coincide.iftheruleforinterconnectionisfollowedcare- fully,thentheresultisa3-portcirculator.fig.4(c) showswhathappenswhentwocirculatorsareinter- connectedattwoports.(thisisequivalenttocascading thesecirculators.)theresultistwothroughconinec- tions.thisresultmayalsobeshowntobetrueby matrixmethods,butcertainlynotassimply.bytopo- logicalmethods,theresultispracticallyobvious.fig. 4(d)illustrateshowthesingularcasemaybeencoun- teredinthecourseofinterconnectioiialthoughneither oftheoriginalcirculatorswassingular. cascadingofcirculators intheprevioussectionsomegeneralruleswerede- finedfortheinterconnectionofcirculators.therewas norealrestrictiononthetypeofinterconnectioncon- sidered.inthissection,aspecial,butimportant,type interconnectionwillbeinvestigated,namely,thecascade connection.theverynatureofthecascadeconnectionas- sumesthatthereareanequalnumberofinputportsand outputportssothat,immediately,thestudyislimitedto 11 h.j.carlin,“principlesofgyratornetworks,“proceedingsof symposiumonmicrowavetechniques,polytechnicinst.ofbrooklyn, n.y.,p.197;november,1954. 1398 ocftober treuhaft:networkpropertiesofcirculators circulatorshavinganevennumberofports.also,there isanotherrestrictionthatfollowsquitenaturallyfrom practicewith4-portcirculatorswheretwodecoupled portsarepairedasinputportsandthe othertwode- coupledportsarepairedasoutputports.thisrestriction isthatnoinputportbedirectlycoupledtoanyother inputportandnooutputportbedirectlycoupledto anotheroutputport.severalcirculatorssatisfyingthese requirementsareshowninfig.5.itmaybeverifiedthat eachofthenetworksoffig.5isanoriented1-circuit anidthatnopairofinputoroutputportsaredirectly coupledbyanoriented1-cell. o(l) (ac) turnstileresonators( cf =15.0,r = 6.0 mm, r/l= 2.36,2,49,2.62, and3.06). theoperatingfrequencyof any junctionforwhichthe frequencyvariationof the in-phaseeigennetworkmaybe neglectedcomparedto thatof the degeneratecounterrotat- ing ones is usuallynot very differentfromthatof the latter eigennetworks.itmaybe experimentallydeducedby not- ingthatat whichthedevicedisplayseitherbandpassor bandstopcharacteristics.inthe formercase, the cotmter- rotatingeigenvaluesareoutofphasewiththein-phase one;inthelattercase, theyareinphasewithit.the situationin whichthe eigennetworksare commensurateis, althougha moredemandingrequirement,alwaysdesirable ina well-designeddevice.thestroctureinvestigatedhere infactexhibitsa bandpasscharacteristicinitsdemag- netizedstate. a higherorderbandpassresponsecirculating intheoppositedirectionhasalsobeennotedin7;a bandstopsolutionhas been describedin 9 and 10. fig.8 depictsthe experimentalmode chartof an e-plane circulatorin wr90for fourdifferentvalues ofr/l;three possiblesolutionsforthe designofa 9.o-ghzdeviceare noted.fig.9 indicatesthe same datain normalizedform. thediscrepancybetweenthislatterrelationshipandthe theoreticaloneillustratedinfig.7 is inpartduetothe faqtthatthe formercoincideswiththe frequencyat which thein-phaseandcounterrotatingeigennetworksarein antiphaseratherthancommensurate.theoptimumcircu- lationsolutionisthatforwhichthein-phaseandthe degeneratecounterrotatingeigenvaluesare commensurate, butthisproblemawaitsa solution.a morepreciseknowl- edge of the frequencyof the degenerateeigennetworksmay be derivedby constructinga familyof solutionsof the type indicatedin fig.4. 802 ieee transactions on microwave theory and techniques,vol.mtt-35, no. 9september1987 ,.w-3 /) l=l.96mm / )- l=2.29mm p 08 rn6.omrr iiiiii, 0020,4 0608i hmjgfactor,l/b fig.10.experimentalmodechartofe-planejunctionusingsingle h-planeheii:turnstileresonator(c,= 15.0,r = 6.0mm,r/1.= 2.36,2.62,and 3.06). theferritematerialutilizedinthisworkwas a garnet onewithasaturationmagnetization( lfo )toequalto 0.1600t and a relativedielectricconstant(ef ) of 15.0. the relativedielectricconstant(c ) of the regionbetweenthe tworesonatorswas unity.the radiusof the resonatorwas arbitrarilymadeequalto thatofthe junctionformedby the threewr90waveguides(r = 6 mm). someadditionalmeasurementsonthe frequencyofan e-planejunctionusinga singlehe ii;resonatorareil- lustratedinfig.10. itsoperatingfrequencyis obviously againrelatedto thatof a singledecoupledresonatorsup- portingtheheii;mode.nocorrelationbetweentheory andpracticehas, however,beenattempted.thequantity b, has the same meaninghere as in fig. 6, i.e., bl = (s + l). scrutinyofthe modechartof an idealizedopengarnet waveguidehavinga radialwavenumber(korfi)equalto thatoftheresonator(4.38),as is the case here,indicates thatthephaseconstantsofitstmii,teoi,andtm21 modesareequaltotio, 1.080and1.26 tio, respectively. thismeansthatthefractionalbandwidth(8)of suchan idealizedresonatoroperatingin the tmii modeis limited bytheonsetoftheteoi mode.thepacingbetween these frequenciesmayof coursebe widenedby employing aresonatorwitha somewhatsmallerradiusthanthat definedbythe junction.thechoicesemployedin 5 and 8 are kor.it may beinc