电磁场与微波技术论文汇编.pdf

ieeetransactionsonmicrowavetheoryandtechniques,vol.ml”r22,no.6,june1974641 microwavecharacterizationofpartiallymagnetizedferrites jeromej.green,senior member,ieee,and franksandy (invitedpaper) iibsfracf-inorderto assistthemicrowaveengineerin predicthig theperformanceofpartiallymagnetizeddevices,wehavecharac- terizedthemicrowaveperxiieabwyof partiallymagnetizedmaterials. therealpartof thetenssrpermeabilityelements, k, andp,de- pendsprimarilyon theparametersy4tm/tiandt4tm./o.empirical foirnulashavebeendevelopedwhichshowthedependence.atfre- quenciessufficientlybeloww =m4m,thelosscan be characterized by thevalueof p“at 4um=o. ij,k,andp, dependweaklyon com- position,whereas“(4mm=o) doesdependuponthechemical composition. i.introduction w iththecontinuedevolutioninmicrowavedesign theoryandcomputertechnology,computer-aided designplaysan importantrole in the designof microwave ferritedevices.computeroptimizationas a functionof geometricdimensionsandmaterialparametersisnow commonpractice.inorderto fullyutilizetheseadvances, itis necessarytohavea microwavecharacterizationof theferritematerial,andifone is concernedwithferrite phaseshifters,thenthischaracterizationshoulddescribe thepartiallymagnetizedstateof theferrite.sincephase- shiftercalculationsbeginwiththewaveequationwhich involvesthepermeabilityofthematerial,wehaveat- temptedtocharacterizethepermeabilityas a function of suchparametersas saturationmagnetization,location on the hysteresisloop(averagemagnetizationor stateof partialmagnetization),frequenty, and chemicalcomposi- tion:noattemptwas madetocharacterizetheperme- abilityas a functionofporosityor grainsize, sincethe requirementof a highremanenceanda lowcoerciveforce dictatematerialsof highdensityand moderategrainsize. ii.experimentalprocedure measurementsofthetransversepermeabilitycom- ponentsp, “,ti, andk“were madeon rods in cylindrical 4-porttmiiocavitiessimilartothatoflecrawand spencer1.thepermeabilityof therodswas calculated fromthechangein frequencyandq of thetwocircularly polarizedmodesof lowestfrequency.therodswere 0.075 in in diameterand approximately3 in long.thepole faces of an electromagnetwere closed ontothe ends of the rod to imp-eveuniformityof themagnetizationof therod.the manuscriptreceivedseptember22,1973;reviseddecember14, 1973.thkworkwassupportedinpartbytheu.s.alrforce systemscommand,romeakdevelopmentcenter,griffissair forcebase,rome,n.y.,undercontractf30602-68-c-0005. theauthorsarewiththeraytheonresearchdivision,waltham, mass.02154. magnetizationof the rod was monitoredby a pairof coils one of whichsurroundedtherodjustoutsidethecavity theotherwas nextto thefirstandwas used to subtract out the componentbdue to the appliedfield.thisenabled a directmeasurementof thepermeabilityas a function of thestateof magnetizationof therod. measurementsof theparallelpermeabilitycomponents .and.”weremadeon spheresplacedat thecenterof arectangulartei02reflectioncavityusingwell-known methods2.themagnetizationof thespherewas meas- uredseparatelyas a functionof dc fieldon a magnetom- eter. thedetailsof all of theexperimentalprocedurescan be foundin3. 111. thepermeabilitytensor fora materialmagnetizedto saturationin thez direc- tion,thelow-powermicrowavepermeabilityis a tensor of the form where (1)oo.,/ =fl_jpl! =ki _ “kjl pz = pa jp.f. 1. thkformof the permeabilitytensorfor saturationy. = impliesrotationalsymmetryin the transverseplanewhich is thecase forpolycrystallinematerials.iftheapplied fielddropsbelowthe demagnetizingfield(n,47rm.),where nzisthedemagnetizingfactorinthez direction,the sampledemagnetizesto a valuebetweeno and the satura- tionmagnetization(4mm.)dependinguponthesample shapeandthevalueoftheappliedfield.thisstateof partialmagnetizationcan also be characterizedbya per- meability ytensorof theformgivenby(1)providedwe takethez directionas thatof theaveragemagnetization (4rm),therebymaintainingtherotationalsymmetry aboutz and also allowp. #1. ananalysisof tforthepartiallymagnetizedstate, was madebyrado4.usingaveragingtechniques,rado proposedthatthe real partof the off-diagonalcomponent k1be givenby 642ieeetransactionsonmicrowavetheoryandtechniques,june1974 k =y41rm/u(2) whereti/2risthesignalfrequencyandyisthegyro- magneticratio.lecrawand spencerlshowedthatthis relationshipis a reasonablygoodapproximationforktas a functionof +britf.someof ourownresultsare givenin figs.land2. theratioy4rm,/uwasvariedinflg.lby changingfrequencyandinfig.2 bychangitigsample temperature.thett1-390(transtechmagnesium manganeseferrite)exhibiteda hysteresiseffect,namely thevalueofkwas nota uniquefunctionof 4?rikf/wbut ratherdependedon whichside of thehysteresisloopone 10. redotheory 09- k= 74tmium g113 0s 4.m, =1t50 gauss t2yc .=92g“,.lrf.l,.=om . . 06- . . 05-. k . 04- x . # 03 radotheory- 04 x - 03 x. . 4.m, =2800 gauss : -02 .f=92gh, x xf=120gm, . . 0020436os10 +kl,f” fig.1.kversus-ymm/01ong-113at5.5and9.2ghzandon tt1-2800at 9.2and12.0ghz. 1.01 0.8 -redotheoryk, = 4miw 0.6- tti-390 0.4- f=55ghz t=53c 0,2- 47+1,= 1950gauss 747rm*/w=lo o - -0.2- d 100,” .po.(i-p,o) 6skindepth; dlengthof thecavity. inthesamemannera relativeq factorcanbe definedintheform q,= 1 +ocd/4a 1 +moreover, theyareexactwavefunctionsforanydeformedconventionalrec- tangularorcircularwaveguideso thatnoapproximatemethodof solutionshastobetaken.further,ithasbeenshownthatwave- guidesandcavitiessynthesizedwithnonseparablesolutionshave betterattenuationandklgherq factorthancomparableconven- tionalwaveguidesshapes. further,it is clearthattheyhaveinterestingpropertiesformicro- wavemeasurementandpowerapplications.allcalculationswere doneon thecomputerof therekencentrumof thecatholicuniver- sit y of louvain. references 1 p. m.morseandh.fesbach,methodsoftheoreticalphusics.new york:mcgraw-hill,1953,pp.753757. 2 d.s.moseley, nonseparablesolutionsofthehelmholtzwave equation,”quart.app1.math.,vol.22,pp.356357,1965. 3 p. j. luypaertandd. h.schoonaert,in1974proc.microwavepower stimp.,pp.135-1/l-135-l/3andb5-4/lb5-4/3. 4 p. lagasseandj. vanbladel,“squareandrectangularwaveguidas withroundedcorners, ”ieeetrans.microwauetheorfjtech.,vol. mtt-20,pp.331337,may1972. taperedasymmetricmicrostripmagictee m.h.arainandn.w.spencer,member,ieee absfractthedesign,development,andconstructionofa very compactdecade-(1-1 o-ghz)bendwidthmicrostrip8.34-dbcou- pleraredescribed.calculationsaregivenforthevoltagecoupling coefficientandthelow-frequencycutoff,andthemethodofdeter- gthephysicaldimensionsof thecircuitisdescribed.also,the feasibilityof a decade-bandwidthmicrostripmagicteebycascading two 8.34-dbcouplersis demonstratedby comparingtheactualand theoreticalresultsof a coupler. manuscriptreceivedapril21, 1975;revisedaugust26, 1975. theauthorsarewiththeautoneticsgroup,rockwellinternational, auaheim,calif.92803. shortpapers introduction thkshortpaperdescribesthedesignofanasymmetricbroad- bandmagictee.thehigh-passnatureofthiscouplermakesit inherentlybroadband,andsucha componentis applicableforuse in manybroad-bandmicrowaveassembliesincludlngbalancedmixers andbeamformingnetworks.alternatemagicteeswhichhavebeen realizedinmicrostriphavenothadtheinherentbandwidthcapa- bility.boththeslotline/microstripmagictee1andthemagic teeusingcascade-tandemconnectionof directionalcouplers2are limitedto 2:1frequencybandwidths. tovalidatethedesignapproach,a testcircuitwasmadewhich requiredthedevelopmentofafine-linedelineationprocessand specialpackagingtechniquestosupprewspuriousmodes.theactual resultscorrespondwiththetheoryexceptforthephaseshtitbelow theminimumfrequencyofoperation.thkeffecthasnotbeenex- plained.whiletheresultsobtainedatthistimeindicate-further workis required,thefeasibilityof sucha networkhas beendemon- strated. thetheoryforasymmetriccouplershasbeendescribedbyarndt 3andtresselt4.also,duhamelandarmstrong5demon- stratedthismagictee inlowdielectricstriplinetransmissionmedia. however,priorto thisworkthefeasibdityof producingthiscoupler ina microstripconfigurationhadnotbeendemonstrated.thkwas duetoseverallimitations.first,theplanarstructurewithedge couplingmadeitdmiculttoobtaintherequiredtightcoupling. second,thefabricationtechniquesforachievingrepeatable0.0002-in gapswerenotavailableforathickmetallizationlayer(=0.0005in). third,theinhomogeneoustransmissionmedlawithahlghdlelectric constantsubstratedegradedthedlrectivityof suchcoupler+because theeven-andodd-modevelocitiesofpropagationwerenotequal. thepotentialsolutionstotheseproblemsaredescribed. theasymmetricmicrostripmagicteeconsistsoftwo8.34-db couplerscascadedintandemtoforma3-dbcoupler6.reference linesareaddedtoeachsideofthecouplertocompensateforthe frequency-dependentlengthandto givea transmissionphasecliff er- enceof180 andooattheoutputportswhenfedfromthemainport andisolatedport,respectively.the8.34-dbcouplingwasselected becausetheedgecouplingrequiredat thetightcouplingregionwas consideredwithinreason;subsequentprocessingdevelopmentre- sultedinanadditiveprocesswhichachievedtherequiredcoupling. improveddirectivitywasachievedbypositioningthetopground planeveryclosetothedielectricsubstrate;fromtheliterature7 0.025inwasselectedas thespacing.however,itwasdetermined empiricallythat0.015in wassuperiorforourcouplerdimensions. analysisof8.34-dbcoupler theschematicsof theasymmetrichgh-pass8.34-dbdkectional couplerareshowninfig.1. theyconsistoftwotransmissionlines whicharecouplednonuniformlyalongthecouplingsection1. the voltagecouplingcoefficientk(z)changescontinuouslyalongthe longitudinaldirectionz.itis definedbyeven-andodd-modeim- pedanceszo. andzoo in(1)as ,%(2/1)= zoe(z/l)20.(2/1) 208(2/1)+200(2/1)“ (1) wuplingsecrion outpu7-.-.-f-w-=l- 1 i ?6i%p=*qfur:fwuwr: ,-l-l-.!- isii -a-:.-.-4- iti +-.-b-.b-.z,.=;.(34) 84 ieeetransactionsonmicrowavetheoryandtechniques,february1968 tablei elementvaluesforbutterworthbranch-guidecouplersforn =3to9branches ii b7wwhouide11.?.utcances ii main linslwittaxces vsm alaza3a4a5 b1 b2.b3b4 . ,-3 m 10.0501u,lw81.0039 15lij.61.181.u1 o.m960.1s24 1.0128 109.5?1.171.030. 163 0,34501.0445 87.6o1.161.cx!(1. 260.46071,0757 65.601,151.07 0.2.5870,6448 1.1342 54.701.141,09 0.30780.7874 43.70553ii. 9974 1.1s33 1.9573 32.691.141.$9 0.41491,3432 1.3n4 !.2 0.45131.61881.4693 21.7111ltns1witt,4nces is2coupcoupdir .vsm (db)(db)db) al2 “3a4bl“% b3b4 . .1 1,2 i .3 lem%rx- l1-.l 1,00491.03931.0653 1.owo1.(35281.1126 1.01701.1oli91.2316 1.(e411.14441.3392 1.03521.21461.5239 1.0537,1.33911.8861 1.86821.44262.2214 1.cs931.68202.8004_ dl- t 1.0002t.00141. w39.1.m15 1.00071.0c481.01371.019 1.00271.01881.0532l.m4 1.w491.03421.c975.i.137 1.00951.06621.1919:1.274 1.01361.09511.2817/1.4w 1.02011.14191.4357!1.648 1.03111.22451.73542.147 1,03991,29282.01052.639 1.0530t .39772.48113.55o elementvaluesforchebyshevbranch-guidecouplersforn =3to 8branches n=3 2u19.936.81.wc 0.05090.09931.0039 15,jj. $1 35.91.w1 0.091t0.1795 1.0130 109.8634.41. cob0.1656“.33851.0451 87.3533.51.007 0.21240. jj5121. 077u 65.2432.51.of50.2761li.6301 1.1369 54.8331.91.0210.31740.76861.1874 43.8331.21.03u0.36810.97291.2641 32.3330.41.o450.43301.31o31.3899 2019.524.51.0(!40.0531(l llg481.w41 157jj.523.51. w90.0957“, 171j31,0134 10. 4.2,.9, ,024 “.,76,“m, 1.m71 87.3821.01.0400.2280u.4207 1.0808 6j.3419.9q. u730.3w8 0.58301.1454 54.3219.31.1opu.34990.70871.2011 43.3018.51.150u.413u0.89581.288o 32.2917.71.236“,”? 7.2,56 1.4391 201“.916.91.013 0.05730, “864 1.w43 1513.815.91.029 0 .10430.1532 1.0142 lcq.6514.27.075 “. j g6p“. 2786 1 .q 5c4 rr,wcn083deiwitmnces 070.25510.6249 32.5060.01.0020,06030,30980.9059 201.953.41.0000.w890.03340.0583 1513.951,81.(3w0.0165v.06c40.1c41 108.9549.01.c+m0.03170.11180.1936 86.8347.41.0020.24140.14560.2579 64.8143.51.0040.05420.19400.3656 53.8244.31.w60. l!6190.22780.4561 42. !3342.81.o1o0.07050.27280.6038 1 31.87 18.1 151.o 107,87 8s.63 63.82 52.m7 41.01.016 39.71.001 37.91.003 34.91.0043 33.21.014 31.11.026 29.71.038 k%l%ka- 0.02150.1%210. w74 0.c4240.11530.1797 0.0566u.15070.2387 0,07650.20270.3387 0.88950.2401c.4248 mltlt 41.8828.1f.0590.1w30.29220.5702 31.w26.11.0990.12530.37390.8714 1511.726.41.0130.03080.c6230.0880 106.4823.21.0380.06400.11430.1597 bs.6321.21.w560.w*0.14890.2106 62.4618.81.1290.12720.19770.2982 e 51.%17.31.199.t5590.2332.3757 15so8“.;1;0.98531,18901.69342.55493.31 201;.129,51 .“0(%“.”1”3“.”2”“.”3,6“.0387,.w,l.”w1.”42l.w 159.9527. ij 1 .c1140.02120.0363o.cl%l0.06721.00421.01u91.0181t.o?ll 104. ,22.61.047“.”4920.c”:y; .307 1 111 .0s4typ “393 yp-+-l1-+”323 coupling(db) 75808.5909.5 10010.5 frequency(ghz) dir ectiwty(d b) 7.58,0s.59.0 9,510.010.5 frequency(g hz) vswr 0-0experiment theory 7580 8.59.095100105 frequency(g hz) fig.11.theoreticalcurves and experimentalresults for the couplerof fig.10. .091typ .296typ 11i j- .478typ ?r t 1“ 1- 1.922typ .029typ fig.12.planviewofbutterworth3-branch3 dbcouplerinair- spaced stripline,withground-planespacing0.3125 inchand strip thickness0.0625 inch. fig.10.cross section of butterworth4-branch6 db couplerin wr90(wg16)waveguide. levyandlind: synthesisofdirectionalcouplers 89 coupling(db) a 3.5 % 3.0 -x. 2 e, 2.5 1.301.40l501,601,701,80 directivity(db) frequency(ghzi 4 1.301.401.501,60.70 frequency(qhz) vswr 1! +-+experiment 125, theory l20 1.15 1.10 1,05 1.00 119 1,301.401.501,60i.m 1.80 / p ! 1.80 frequency(q hz) fig.13.theoreticalcurves and experimentalresults for the coupler of fig.12. coupling(db) : 5 11 ,1, 7.58.08.59,09.5100i0.5 iio frequency(g hz) oirectivity(db) 50t 40 pz,(experiments,partii), thelociofrarelikeopeneccentricspirals aboutthecenter.thelociofsinusoidal tapersinfig.2 appearsimilarto a reduced concentricspiralaboutthecenter;theseare typicalforthecases of z, z*.theposition ofralsosweepsalmostone cycleeveryhalf- wavelength.thelocationsinthek-plane andtheformsof theselociare almostidenti- cal forseveralsurgeimpedanceratios;hence thesetwofiguresdepicttypicalcharacter- isticsforthegeneralcases.moreover,re- gardingthelimitingcasesof t=o forlinear tapers,i haveobtainedreasonabledatafor thebehaviorofr. k.matsumaru elec.comm.lab. kichijoji,tokyo,japan b=mh(3) wheretheusualapproximationsofsmall signaltheorylhavebeenused.onemayob- servethatthiscompletelygeneralpermeabil- itymatrixstillpreserveshermitianchar- acteras longas lossesareneglected;and,of course,itreducestosimplewell-known formsincaseswhenho isalonganyofthe axesof themicrowavecarrier. itmaybesometimesdesirableto express therelationbetweenthevectorsbandhin a canonicalform,thiscanbe accomplished byfindingtheprincipalaxesof themedium or,toputitdifferently-byfindinga co- ordinatesystemin whichthereexistsa rela- tionof theform , (ba)=(aaa)(i?a)(4) wherebaandhaare the componentsof the magnrjicinductionandmagneticintensity alongtheaxes of thenewcoordinatesystem, and(xjis a diagonalmatrixcomposedof theeigenvaluesofthepermeabilitymatrix of(2).theprocedureoffindingthecom- ponentsofthematrix( one in whichtheappliedmagnetostaticfield is atananglearbitrarytotheaxesofthe microwavecarrier. ifthegeometryoffig.1,whereho standsfortheappliedmagnetostaticfield andthecarrieraxesarex,yandz, isas- sumed,then,usingtheequationforthemo- tionof themagnetization am =-ymxh at (1) thefollowingrelationbetweenthevectorb andhresults: techniquesjanuary tensityfromtheoriginaltothenewcoordi- natesystemare =pb h= ph.(6) tofindthematrixp we solvetheeigenvalue equation (m ia)u=o(7) whereu isamatrixcomposedof threerow vectorsfromwhichthematrixpcan be con- structedbymeansof an orthonormalization process.jeq.(7)has a uniquesolutiononly if thedeterminant im-ia(=0,(8) whichyieldstheresults hl,z =n*k a3=po.(9) theeigenvaluesof(9) areexactlythesame astheywouldbeiftheappliedmagneto- staticfieldwerealonganyone of thecoordi- nateaxesof fig.1. thisfactmaybe some- whatsurprising. theamountof algebrainvolvedinfind- ingthematrixpcorrespondingtotheper- meabilitymatrixof(2)isprohibitive.we shalltrya simplerbutstillgeneralenough caseinwhichtheappliedmagnetostatic fieldisinthex yplane,i.e.,f?=t/2in fig.1. insucha case thepermeabilityy ma- trixbecomes (10) z .+, .h. 1949. addison-weseleypublishingco.,inc,p.119,1956,8 h.goldstein,ibid.,p.328. 1959 correspondence 177 tablei originalcoordinatenewcoordinate system system dbf vxev$xe1.-. atat vxh.j+? tid vixhi*.j,+ atat v.b=0 i v.b=o v.d=pv.dt=p b=mhb= (xti,jh d= jpd wecannowtransformtheentiresetof maxwellsequationstothenewcoordinate systemwhich,wehope,willbesimplerto workwith.tablei showstheresults. itis indeedthecasethatthemaxwell equationsincludingtherelationsbetween themagneticinductionandmagneticin- tensity,andelectricdisplacementandelec- tricintensityaremuchsimplerinthe primedthanintheunprimedform.itmay beanadvantageinaparticularproblem involvingarbitraryangleofmagnetization of a ferriteto workin theprimedsystemas faras possiblebeforeswitchingbacktothe originalone. georgetyras boeingairplaneco. pilotlessaircraftdiv. seattle,wash. resistive-filmcalorimetersfor microwavepowermeasurement* twopapersl.zpublishedrecentlyin these ransactionshavedescribedcalorimetric techniquesforthemeasurementofmicro- wavepoweratthemilliwattlevelwhichare freefromthelimitationsinherentin existing methodsusingresistance-typemilliwatt- meters. astheauthorspointout,thedevelop- mentofimprovedtechniquesisespecially importantat frequenciesoftheorderof104 mcandabove.somewhatsimilarworkhas recentlybeencarriedoutintheunited kingdomattheradioresearchstation, slough,andthisnotesummarizesthees- sentialfeaturesof thetechniquesused. a 3-cmbandcalorimeterintheformof a differentialairthermometerhasbeende- velopedforthepowerrange10-100mw. thisconsistsof twoidenticaltaperedresis- tivefilmslocatedinsidethinglass cells which are connectedby a capillarytubecontaining a movableliquidindex.onefilmabsorbsthe inputmicrowavepowerandtheotherserves as a controlagainstvariationsinambient temperature.ameasurementismadein termsof theequivalentdcpowerbya null technique.thein