《Coupled-mode design of ferrite-loaded coupled-microstrip-lines section.pdf》由会员分享，可在线阅读，更多相关《Coupled-mode design of ferrite-loaded coupled-microstrip-lines section.pdf（8页珍藏版）》请在三一文库上搜索。
1、IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 50, NO. 6, JUNE 20021487 Coupled-Mode Design of Ferrite-Loaded Coupled-Microstrip-Lines Section Jerzy Mazur, Mateusz Mazur, and Jerzy Michalski AbstractA coupled-mode approach is applied to a microstrip circulator with a distributed section
2、of axially magnetized ferrite coupled lines (FCLs). The equivalent model of the FCL junction is found, which includes gyromagnetic interaction between prop- agated and evanescent isotropic modes. On the basis of the cou- pling process, the ferrite modes in the FCL are defined. From the decomposition
3、 of these modes, the waves in each line of the struc- ture are determined. The mode matching is applied at the junction ports, which allows one to obtain the scattering matrix of the mi- crostrip FCL. Validity of the approach is verified by checking the scattering parameters of the FCL section and c
4、omparing the nu- merical results with available measurements. The proposed model gives the properties with regards to the impedance matching and ferrite section dimensions, which can help the design of the FCL nonreciprocaldevices.Asanexample,the-parametersofanFCL circulator are presented. Index Ter
5、msCirculators, ferrite-coupled-lines junction, scat- tering matrix. I. INTRODUCTION T HE distributed circulators and isolators, which make use of the coupled slot-lines sections with an axially magne- tized ferrite, were discovered in 1. The operation principle of thesedeviceshasbeenexplainedin2and3
6、usingthebimode coupled-mode (CM) model employing the Faradays rotation phenomenon appearing in the ferrite coupled lines (FCLs). It was found that although the Faradays effect assured only the nonreciprocal phase shift, the section of FCL demonstrated full nonreciprocal properties when the structure
7、 was fed by even or odd excitations. Thus, these requirements are satisfied in FCL devices 3, which are constructed as a cascade of an FCL sec- tion with 0 /180 hybrid junction.One shouldnote here that the overall performance of these nonreciprocal devices depends on the appropriate scattering chara
8、cteristics of the individual com- ponents. Using the CM model of FCL lines, the scattering ma- trixoftheFCLsectionhasbeenderivedin2and3.However, there is no analysis of the matching conditions without which the proper compact of the FCL with external sections cannot be designed. Teoh and Davis have
9、presented in 4 and 5 the different attempts to solve the problem in terms of superposi- tion of the dominant ferrite modes propagating along the FCL. Manuscript received October 17, 2000. This work was supported in part by the Telecommunications Research Institute under Grant DN-24204. J.Mazuriswith
10、theTechnicalUniversityofGdan skandTelecommunications Research Institute, 81-952 Gdan sk, Poland (e-mail: jempg.gda.pl). M.MazurandJ.MichalskiarewiththeTelecommunications ResearchInstitute,81-952Gdan sk,Poland(e-mail:mefispit.gda.pl; MichalskiJprokom.pl). Publisher Item Identifier S 0018-9480(02)0520
11、3-1. Their normal mode approach confirmed the CM operation con- ditions of the FCL. However, the matching problem was also neglected. Therefore, the satisfactory design procedure of FCL junctions in principle has not been achieved. Recently, Xie and Davis6haveexaminedthereflectionandpowertransferoft
12、he even and odd isotropic modes at the interface between the cou- pled isotropic and ferrite lines. They solved the problem using the mode-matching approach where the dominant modes of the cascaded dielectric and ferrite lines were applied in the field ex- pansion. However, their solution has omitte
13、d the excitation of the interface by the ferrite modes so that the scattering problem at the considered interface has been only partially analyzed. Hence,theirtheoreticalpredictionisapplicabletothecasewhen thesecondinterfaceoftheFCLsectionisperfectlymatched.We can conclude, therefore, that the scatt
14、ering problem of the mag- netized FCL section has not yet been solved sufficiently. In this paper, the mode-matching approach is also applied to define, for the first time, the scattering matrix of the FCL sec- tion. The problem is solved by matching the fields of isotropic and ferrite modes at both
15、 of the interfaces of the section. The ferrite modes are defined using the CM model of the ferrite mi- crostrip lines 9, where these modes are performed by gyro- magnetic coupling of the propagating and evanescent isotropic modes. The fields at the ferrite region are defined by two for- ward and bac
16、kward traveling dominant and evanescent higher order ferrite modes. The two dominant and two higher order evanescent isotropic modes are taken into account as input and output waves at the isotropic regions of the structure. The de- composition of these modes into the waves, appearing at the microst
17、rip ports of the junction, makes it possible to incorpo- rate their eigenfields into a matching process at each ports in- terface. In this way, the complete scattering matrix of the FCL structure is finally formulated. The usefulness of the developed theoryisdemonstratedbythecomparisonofthescatterin
18、gchar- acteristics calculated for the FCL microstrip section with exper- imental ones presented by Davis et al. in 7. The overall scat- tering characteristics of the microstrip circulator comprising the investigated FCL section in cascade with a microstrip T-junc- tion are also presented. II. CM MOD
19、EL OFFCL The investigated guide is assumed to be a symmetrical struc- ture of lossless coupled lines with a slab of an axially magne- tized ferrite, as shown in Fig. 1. The transverse fieldsand in the guide are expressed in terms of eigenfunctionsof a second base isotropic waveguide. According to th
20、e CM proce- dure 8, the Maxwells equations of both guides are combined 0018-9480/02$17.00 2002 IEEE 1488IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 50, NO. 6, JUNE 2002 (a)(b) Fig. 1.Coupled lines loaded with a slab of an axially magnetized ferrite. (a) Ferrite guide. (b) Correspondin
21、g dielectric basis guide. together andintegratedoverthe crosssection of theinvestigated structure. Due to the orthogonality of the base eigenfunctions, the inte- gral equations are reduced to a matrix eigenvalue problem, and solutions correspond to the modal fields and propagation con- stants of the
22、 ferrite guide. The resulting system of linear equa- tions has the ordinary form 9 written as (1) where (2) (3) anddenote the wavenumber and intrinsic impedance in vacuum, andandare the propagation constant, wave impedance, and the wave admittance of theth isotropic mode, respectively.are diagonal e
23、lements andis the off-di- agonal element in the relative permeability tensor of the ferrite. The coefficientdefines the perturbation of theth isotropic mode, while the coefficientdetermines the gyromagnetic coupling between theth andth isotropic modes. The cou- pling occurs in the ferrite regionwher
24、e the transverse andvectors are perpendicular to each other. Moreover, the followingconditionforthecouplingcoefficientsissatisfied,i.e., . Theunknownvoltageandcurrentcoeffi- cients are functions ofonly, withdependence, where is propagation constant. III. SCATTERINGMATRIX OFMICROSTRIPFCL Following th
25、e above outlined model, the coupled ferrite mi- crostrips shown in Fig. 2 arefirst investigated. It is assumed that the ferrite is weakly magnetized, thus,and coef- ficientin (1). Additionally, it was found in 9 that at least four isotropic modes sufficiently define the CM model of the microstrip FC
26、L. There are two dominant evenand odd quasi-TEM modes and two higher modes, which correspond to the evenand oddquasi-waves, and only these modes are used in the field expansion. Applying the distribution of the magnetic-field vectorsof isotropic modes, shown in Fig. 3, Fig. 2.Structure of microstrip
27、 FCLs. (a)(b) (c)(d) Fig. 3.Schematic distribution of the transverse electric and magnetic fields of isotropic modes in the cross section of the FCL. (a) Even dominant mode?. (b) Odd dominant odd?. (c) Higher order even mode?. (d) Higher order odd mode?. Symmetry plane: magnetic wall for even modes
28、and electric wall for odd modes. to(3), we expectthat thecouplingof dominant modes aswell as of the higher ones can appear only in the ferrite region situated near the slot between the strips. Moreover, the additional cou- pling of the dominant even (odd) mode and higher odd (even) mode can occur in
29、 the ferrite regions beneath the strips. If we include the above assumptions into CM equations and assume the wave propagation along the ferrite guide as, then (1) can be reduced to the following matrix forms: (4a) and (4b) whereandare known propagation constants of the dominant and higher isotropic
30、 modes, respectively. Their wave admittance is defined as follows, i.e.,and . The quantitiesare coupling coefficients of isotropic modes. The propagation con- stantof the CMs is found by equating the determinant of the coefficient matrix of (4a) to zero. It yields the four eigen- values of (4a) defi
31、ning propagation constantsof funda- mental andof higher order ferrite modes for both propagation directions. On the other hand, if the propagation MAZUR et al.: CM DESIGN OF FERRITE-LOADED COUPLED-MICROSTRIP-LINES SECTION1489 constantsare known, then the characteristic equation of (4a) can be turned
32、 on to yield the coupling coefficients. The re- quirement that the determinant of (4a) is zero for each value ofyields the set of four nonlinear algebraic equations for, which can be solved numer- ically. To verify the solutions, we need the approximate values of the coupling coefficients. It can be
33、 found using (2) or the ef- fective mode formulation proposed in 9. The eigenfunctions of (4a) corresponding to the eigenvaluesde- fine the completedependence of the modal voltages of the ferrite modes given by (5) where and In addition,are unknown con- stants. Suppose we apply the eigenfunction of
34、th mode as a partial voltage source. The response will then be the th partial field voltage of the th mode due to source. Hence, the coefficientsand are the nondimensional terms. Applying (5) in (4b), the vector of modal currents is defined as (6) In matrix, the elements are the partial transfer wav
35、e admittance forand the th mode wave admittance for. According to the mode expansion, the electric and magnetic fields in the ferrite section taken as the superposition of the four normal ferrite modes can be expressed as (7) whereandare eigenvectors of the transverse electric and magnetic fields of
36、 isotropic modes. Todecomposethefieldsandintotwolinesconstituting the FCL section, we consider the schematic distribution of anddepicted in Fig. 3. It is seen that the eigenfields of domi- nant evenand oddmodes haveandcomponents asso- ciated with each of the lines. Similar components of the higher e
37、venand oddmodes areand. The symmetry plane of the isotropic guide is defined as the magnetic and electric Fig. 4.Top view of the microstrip FCL junction consisting of input dielectric ?and ferrite?sections. This configuration was proposed by Davis et al. in 7. wall for the even and odd modes, respec
38、tively. Therefore, we can assume that the values of these components for the domi- nant modes, as well as for the higher order ones, are equal at the both lines. Moreover, the eigenfields of the dominant even and the higher odd modes are in-phase, while they are 180 out-of-phase for the dominant odd
39、 mode and higher even one. Making use of the above fields properties in (7), the distribution of the electricand magneticfields along both lines can be written as (8) where superscripts 1 and 2 denote the FCL lines, and andare the eigenfields at the both lines of the FCL. Let us now examine the four
40、-port section of the FCL shown in Fig. 4, where microstrip ports 1, 2 and 3, 4 are located at the interfacesand, respectively. The field expansion in the ports is limited only to the two modes. There are domi- nant quasi-TEMand higher quasi-modes of a single microstrip line. Note that their eigenfie
41、lds can be considered as close to the ones of the isotropic modes associated with the one of the FCL line. Therefore, it is possible to express the trans- verse fields components at the microstrip ports of the junction as follows: (9) wherereferstotheportnumber,andsuperscripts1 and 2 relate to the m
42、odes employed in the ports. Now we apply the continuity conditions for the tangential-field component of electric and magnetic fields at the interfacesand. It corresponds to the matching of the transversal field compo- nents(7)and(9)attheportinterfaceswhentheinfluenceoftheir transversedistributionso
43、ntheneighboringportscanbeomitted. Imposing the continuity conditions atyields the set of equations that are dot-multiplying by conjugate values of eigen- fieldsand,respectively,andintegratedoverthe -port interface. Hence, for, we obtain (10) 1490IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES,
44、VOL. 50, NO. 6, JUNE 2002 whereand the submatricesandare given as (11) and (12) It is conventionalto assume the oppositedirection of thecurrent vectors of ports placed at the interface. Hence, the trans- formations of the continuity conditions atyield (13) whereand. Now we wish to eliminate the vect
45、or of unknown coefficients . From (10), it is possible to relate thecoefficients to the voltages and currents at the ports of the plane, assuming that thehas an inverse (14) Applying (14) in (13), the voltages and currents at the ports of the planeare then given by (15) whereis a two modal transfer
46、matrix of the FCL section under test. Thematrix can be now converted into the scattering matrix, which gives the essential power relationsof thedevice in termsof wave amplitudes.First, we relate the voltages and currents to the wave amplitudes as (16) whereandrepresent an th input andoutput wave, re
47、spec- tively, at theth port.is the wave impedance of a th wave. We assume that this impedance at all ports is identical. Next, substituting (16) into (15) and after some of the mathematical rearrangement, the two-modal scattering matrixof the inves- tigated four-port FCL junction takes the form (17)
48、 (a)(b) Fig. 5.Schematic representation of an FCL junction magnetized: (a) axially and (b) transversely. whereandfor th waveare the four-element column vectors of the wave amplitudes at the ports, andfor is a complex 44 submatrices of the scattering ma- trix of interest. Furthermore, we have assumed
49、 that evanescent modes are sufficientlyattenuated near thetransition plane ofthe ports. The propagating dominant modes are then still referred to the transition planes and, for dominant mode propagation in the ports, the scattering matrix of the junction can be taken as sub- matrixof (17), which is read as (18) where (19) and the subscripts denote the junction ports. IV. PROPERTIES OFFCL JUNCTIONS Now let us consider the influence of the symmetry plane on the scattering properties of the FCL junctions shown in Fig. 5. This plane, as perpendicul