A Full-Wave Analysis of Millimeter Wave Microstrip Junction Circulator

Transcription

1 5 VOL. 2, NO., JANUARY 27 A Full-Wave Analysis of Millimete Wave Micostip Junction Ciculato F. Yang, H.C.Wu, W.B.Dou* State Key Lab of Millimete Waves, Southeast Univesit Naning, 296, P.R. China *Tel: , Fax: , wbdou@seu.edu.cn Abstact- In this pape millimete wave micostip unction ciculato is analyzed by a full wave method, which combines mode expansion and finite element method (FEM) based on Helmholtz equation weak fom. The scatteing paametes of the ciculato calculated ae pesented and compaed with that of expeiments, and ageement has been found. The loss of the micostip substate and feite disk is also analyzed. Fo the fist time, the electic field distibution in the feite disk is calculated to depict the ciculating pocess of the micostip unction ciculato. Index Tems- Millimete wave, Micostip unction ciculato, Finite element method, Helmholtz equation weak fom, Mode expansion I. INTRODUCTION Ciculato is an impotant component in micowave and millimete wave system. Micostip unction ciculatos at millimete wavelength wee desied fo its good compatibility with the integated system. So fa as we know, the development of the micostip unction ciculato is based on to some extent appoximation analysis []-[2]. Howeve, at millimete wave band, the suface wave and dispesive effect and the adiation at discontinuities of micostip inceases, which is not included in the appoximation analysis, so a -dimensional full wave analysis is essentially equied to analyze micostip unction ciculato exactly at millimete waves so as the ciculato can be designed accuately. Finite diffeence time domain method (FDTD) is a useful full wave method. In 2, FDTD has been used in the analysis of micostip unction ciculato with a feite sphee at Ka-band [24]. Howeve, FDTD is moe suitable fo analyzing the stuctue which coincides with the shape of the gid. Staicase appoximation fo cuved bounday will esult in some numeical eos. Recentl a hybid full-wave method, which combine mode expansion and finite element method (FEM) based on Helmholtz equation weak fom, has been pesented to analyze the waveguide multi-pots discontinuities [25]. This hybid method is adopted and extended hee to deal with the shielded micostip unction ciculato, which is a model of integated ciculato used in millimete wave integated systems. Because FEM gid can appoximate the cuve bounday of feite disk and iegula shape of micostip unction accuatel the accuate numeical esults can be obtained. With this method, the scatteing matix paametes of the shielded micostip ciculato ae computed in two steps. Fistl the field distibution in the shielded micostip is obtained using 2-dimensional FEM pogam, then - dimensional FEM is used to model the inhomogeneous iegula stuctue of micostip

2 6 VOL. 2, NO., JANUARY 27 unction, and finally the FEM field in the unction is matched with the field of micostip at the thee intefaces, so a spase matix equation is obtained. Solving the matix equation with symmetic successive ove-elaxation bi- conugate gadient algoithms (SSOR- BICG) can get the scatteing paametes of the ciculato. II. FORMULATION A). 2-D Finite Element Method Analysis of Modes b a w Fig. Coss-section of a shielded micostip line The coss section of the shielded micostip line is shown in Fig., accoding to the Maxwell s Equations, all of the popagation modes within the inhomogeneous stuctue ae hybid. In ode to obtain the electic field distibution of the inhomogeneous stuctue, following bounday value poblem has to be solved [26] [27] 2 ( E) k ε E = in S () μ Whee ε and μ ae the elative pemittivity and pemeability espectivel and k is the fee-space wave-numbe. S is the coss section of the stuctue whose bounday is electic wall Γ. On electic wall Γ, the field satisfies the standad bounday condition n ˆ E =. It is an eigenvalue poblem. When the eigenvalues (coesponding to popagating constants) and eigenvectos on the coss section S h ae obtained, the electic field distibution of each mode can be known. B). Hybid mode expansion and finite element method The configuation of shielded micostip unction ciculato is shown in Fig.2. Pot I,Pot II and Pot III ae the intefaces between the unction ciculato and shielded micostip. Pot I is the incidence pot. Pot III Pot I Fig.2 Schematic dawing of the ciculato Fom the Maxwell s equation, the following equation is easily obtained, 2 ( μ E) = k ε E (2) with the assumption of time hamonic field. By applying some vecto identities, Helmholtz equation weak fom can be obtained fom equation (2) as follows, [ T ( 2 μ E) k T ε E dv Ω = k = Sk Feite Junction ] T [ nˆ μ ( E)] ds () Whee T is test function. Eq.() will be solved by FEM and mode expansion method. That is, the electic field E in the volume integal in the left side of Eq.() is expessed with FEM vecto basic function, and the electic field E in the suface integal in the ight side of Eq.() is expessed by Pot II IMOT ISRAMT

3 7 modes fields in shielded micostip line, which has been obtained in Pat A. This pocedue is simila to that given in Ref.[25]. It is descibed as follows. In the volume integal of equation (), we have N E = E N, = N is the numbe of vecto basic functions; is fist-ode tetahedal N n element in vecto finite element; In the suface integal of equation (), L in in s s E = e δ e + e e z, k kl kl ) l = k=,2, ; Whee, e kl is nomalized electic field of the l mode in the micostip line at k pot; e kl is magnitude of e kl to be detemined. Supescipt in denotes incidence wave and s denotes the scatteing wave. δ lk =, k = l, k l Test function T is also the vecto basic function, that is T = N i. Substitute all these above into (), we obtain N N 2 [ Ni ( μ E N ) k N ( ε E N )] dv i Ω = = L s s + N ˆ i [ n μ ( ( eklekl ( x k = S l = k = k = S k i k, )] ds in in N [ nˆ μ ( ( e δ e )] ds (4) If test function N i, i =,2,..., N is adopted, we can get N linea equations. Howeve, unknowns ae N+L. L is numbe of modes in micostip line at each pot. VOL. 2, NO., JANUARY 27 Next, fields matching on the inteface S k ( k =,2, ) between unction and each pot ae done. This yields L in in s s e δ e + e e z k kl kl ) l= M = k m= E W m m, k=, 2, (5) Whee W is the field function in unction that on the intefaces. By multiplying e kl, l =,2...L on both sides of (5), then doing suface integal on intefaces S k, k =, 2, espectivel L linea equations can be obtained s s E W e ds e e e ds m m kl k s k s k kl kl kl = e e e s k in in δ k kl k (6) Finall a ( N + L) ( N + L) matix linea equations ae obtained: AN N AN L E N BN = s s (7) A L N A L L el BL In matix A, left side of (4), left side of (4), side of (6), N N AN L A L N k ds A is the volume integal at the A L L is the suface integal at the is the fist pat of the left is the second pat. In matix B, BN is the ight side of (4), B s L N side of (6). N is the ight E is the electic field value at edge e of gid in the volume, s L is the electic field values at the pots. Thus, scatteing paametes of the unction ciculato can be obtained by solving the matix equation (7) with the SSOR-BICG algoithm. III. NUMERICAL AND EXPERIMENTAL RESULTS

4 8 VOL. 2, NO., JANUARY 27 A compute pogam has been developed to calculate the shielded micostip unction ciculato using the hybid method mentioned above. We pesent numeical esult of a typical Y-unction ciculato fistly. And then, we pesent both the numeical and the expeiment esults of a T-Y unction ciculato we designed and fabicated. Finall the field stuctue in feite disk is depicted to show the ciculating pocess. A) Y unction ciculato Inteface II (a) -D model of the ciculato a b Inteface III The model is shown in Fig.. The thee symmetical ams of the ciculato have a width a=7.2mm, height b=.56mm, and length l=7mm. The micostip line has a weight w=.2mm, w2=.8mm; and thick of micostip h=.254mm. The substate is Duoid withε = The feite disk has height equal to that of substate and adius, which is a changing facto. The paametes of the feite disk used ae 4π M s = 5 Gauss, H i = 2Oe, ε f =. 5. Cell mesh used to epesent the Y- unction is shown in Fig.(c). Fo the micostip and feite disk small mesh is used to epesent the field distibution accuately. Fo the egion above micostip the field is weak and has little vaiation, mesh size may be inceased. The cente fequency of the ciculato was found to have a dependence on the adius of the feite disk in the ciculato (see Fig.4). The highe cente fequency can obtained when educing the feite adius, the lowe cente fequency can obtained when inceasing the feite adius. l w l w2 Inteface I (b) Top view of the ciculato (c) Cell mesh of Y unction S S2 S f / GHz (a) =.8mm Fig. Ciculato stuctue

5 9 VOL. 2, NO., JANUARY S S2 S f / GHz (b) =.82mm (a) Configuation of the ciculato Inteface II Inteface III - S S2 S f / GHz (c) =.85mm Fig. 4 Pedicated pefomance of ciculato with this hybid method Inteface I (b) Top view of the ciculato A shap spike at highe band (on the insetion (c) Cell mesh of T-Y unction loss line, see Fig. 4) may be due to the paasitical modes which is exiting in the shield shell. Fig. 5 Ciculato stuctue Numeical expeiments have shown that by elements in integated systems. It is analyzed and adusting shielded stuctue paametes can shift expeiment is also done to veify the validity of this spike to be out of the woking ange. analysis. The paametes of the expeimental configuation shown in Fig. 5 ae: shielded B) T-Y unction ciculato waveguide width a=7.2mm, height b=.56mm, T-Y unction ciculato (an expeimental model and length L=4mm. The shield box has a width is shown in Fig.5) is moe convenience than Y W=2mm, length equal to width, and the height unction ciculato fo connecting with othe H=mm. The micostip line has a width w=.2mm, w2=.8mm and height h=.254mm,

6 VOL. 2, NO., JANUARY 27 the pemittivity of substate is ε = The feite disk has height equal to that of substate and adius =.8mm. The paametes of the feite disk used ae ε =. 5 4πM s = 5 Gauss, H i = 2Oe. The expeimental ciculato is fabicated by dop-in techniques. Calculated esults ae given in Fig.6, expeimental esults in Fig.7. S2 - S Fequency /GHz Fig.6 Calculated pefomance of Ciculato - -2 S S Fequency / GHz Fig.7 Measued pefomance of ciculato Fig.8 Photogaph of the micostip ciculato Good pefomance has been obtained as shown in Fig.6 and Fig.7. Both esults show the n=2 Chebyshev esponse, which had been mentioned in [9][28]. Fig. 8 shows the ciculatos used in expeiment, whee a tansition fom micostip to waveguide is used so as it can be measued in standad measue set. Because of the tansition between micostip and waveguide and some toleance in the ciculato, thee is some diffeence between computed esults and measued esults. Howeve, when the ciculato is used in integated millimete wave system, the tansition fom micostip to waveguide is not needed. The ciculato and othe cicuits of integated system will be designed and fabicated togethe. Theefoe, the calculated esults above ae vey useful fo millimete wave integated system design. C) Effect of mateial with loss Above, the mateials ae assumed to be lossless. In fact, the micostip substate and feite ae lossy. It is needed to know the influence of the loss on the pefomance of the ciculato. The loss is also elated to the pefomance of millimete wave integated system. The teatment on the loss is convenient with the method, we only need changing the pemittivity and pemeability of mateial fom eal numbe into complex numbe, othe pocedue is same. The loss tangent of the substate used hee -4 is tan δ = 2.5 ; electic loss of the feite is -4 tan δ = 2.5 and the magnetic loss is ΔH = 9Oe. It has been found that the loss of substate and feite has little effect on the etun loss and isolation of the ciculato. Howeve, it has effect on the insetion loss of the ciculato.

7 VOL. 2, NO., JANUARY 27 Table. S2 paametes of diffeent loss consideed Fequency (GH Lossless () Magnetic Loss only() Electic Loss only() Electic&Magnetic Loss() Table shows the calculated esults of insetion loss (S2) of the ciculato at diffeent fequency points fo diffeent losses. In the ciculato, the dielectic substate has a volume lage than that of the feite disk, so the electic loss caused by the dielectic substate is geate than the magnetic loss caused by the feite disk. The electical loss is dominant of the whole loss. D) The electic field distibution in the feite disk The electic field distibution in the feite disk when ciculato is ciculating will show how the ciculato is woking. It is also analyzed hee (c) t =8/T (d) t =/T (a) t = T Fig. 9 (a)-(e) (e) t =4/T E in the feite disk duing z peiod (5GH half (b) t = 4/T Fig.9 depicts the electic field distibution in the feite disk at ciculating fequency 5GHz, whee T is time peiod.

8 2 When t=t, the field in the zone of feite disk close to input pot is positive, the field in the zone of feite disk close to out pot 2 is negative. Powe fom pot is tansmitted into pot 2. At middle of pot, field appoximate zeo, one side is positive and anothe side is negative, so it can not excite basic mode of micostip, pot thus isolated. Fom t=t to t=8/t, the field has small vaiation, the zone of negative field is inceasing and positive field zeo is deceasing. Pot is still isolated. When t=/t, field in the feite disk is negative and field seems to be shifted to zone between pot and pot 2. In the zone close to pot, field is still zeo. When t=4/t, the field at pot 2 changes to positive and at pot field changes to negative. Fo t=5/t, the field distibution is same with t=t, except positive zone and negative zone is exchanged. Fom t= 6/T to t=t, the pocess is same with that of t=t to t=5/t, the only diffeence is that positive zone and negative zone is exchanged So fa as we know, the field distibution in the feite disk of micostip unction ciculato is fistly calculated with full wave method. It will be helpful fo pactical enginees to undestand the ciculating pocess of micostip unction ciculato. IV. CONCLUSION A hybid full-wave method, which combine mode expansion and finite element method (FEM) based on Helmholtz equation weak fom is adopted to deal with Ka-band micostip ciculatos. Two examples ae shown above. The influence of feite disk adius changing is pesented. Expeiments have been done to veify the validity of analysis, and ageement has been found. The ciculating pocess of micostip unction ciculato is depicted based on the calculated esults fo the fist time. The loss of the ciculato is also analyzed. This wok will be useful fo pactical enginee to design a millimete wave integated system. VOL. 2, NO., JANUARY 27 This full-wave method validated above may also be useful fo analyzing othe micostip stuctues. REFERENCES [] H.Bosma, On stipline Y-ciculation at UHF, IEEE Tans., MTT, 964, 2(): 6-72 [2] C.E.Fa R.L.Comstock, Opeation of the feite unction ciculato, IEEE Tans., MTT, 965, (): 5-27 [] B. Owen, The identification of modal esonances in feite loaded waveguide Y-unctions and thei adustment fo ciculation, Bell Syst. Tech. J., 97, 5: [4] Y.S Wu, F.J.Rosenbaum, Wideband opeation of micostip ciculatos, IEEE Tans., MTT, 974, 22(2): [5] T.Miyoshi,etc., Feite plana cicuits in micowave integated cicuits, IEEE Tans., MTT, 977, 25(7): 59-6 [6] Ronald W.Lyon, Joseph Helszan, A Finite Element Analysis of Plana Ciculatos Using Abitaily Shaped Resonatos, IEEE Tans.,MTT, 982, (): [7] J. Cendes and J-F Lee, The tansfinite element method fo modelling MMIC devices, IEEE Tans., MTT, 988, 6(2): [8] Andeson,B, Cendes,Z, Thee- dimensional finite element analysis of feite devices including spatial in- homogeneity of the pemeability tenso, IEEE AP-S. Digest, July 996, : 8 4. [9] H. Heshenov, X-band micostip ciculato, Poc. IEEE, 966, 54: [] Heshenov, B, All ganet substate micostip ciculatos, Poc. IEEE, 967, 55: [] D. Masse, Boadband micostip unction ciculatos, Poc. IEEE, 968, 56: [2] P. Bason Some poblems of mico- stip ciculatos, pesented at the Annu. Res. Inst. Telecommun., Budapest, Hunga 974. [] C. H. Oxle T. J. Bazil, J. J. Pucell, and R. Genme, Design and pefomance of J band feite micostip ciculatos, Poc. IEE., 978, 25(8). [4] J. Helszan and M. Powesland, Low-loss high powe micostip ciculatos, IEEE Tans. MTT, 98, 29(7): [5] N. Kause, Impoved micostip ciculato design by esonance components, in Poc. EuMC, Amstedam, The Nethelands, 98, [6] Chang.K, W-band (75G-G) Micostip Components, IEEE Tans., MTT, 985, (2): [7] W.B.Dou, Z.L.Sun, A Boadband Ka-Band Micostip Ciculato fo Integated Millimete

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