COMPACT BANDPASS FILTERS UTILIZING DIELECTRIC FILLED WAVEGUIDES

Transcription

1 Progress In Electromagnetics Research B, Vol. 7, , 008 COMPACT BADPASS FILTERS UTILIZIG DIELECTRIC FILLED WAVEGUIDES H. Ghorbanineja an M. Khalaj-Amirhosseini College of Electrical Engineering Iran University of Science an Technology Tehran, Iran Abstract In this paper, a compact waveguie banpass filter is propose.the propose structure consists of some inuctive iaphragms in a rectangular waveguie an the regions between them have been fille fully by ielectrics.the relations between the physical an electrical parameters of the existe asymmetrical impeance invertors are obtaine.the usefulness of the propose structure an its performance are verifie by esigning an simulating an equal-ripple X-ban banpass filter. 1. ITRODUCTIO Waveguie banpass filters are one of the inevitable requirements of microwave circuits.the straightforwar approach to construct these filters is using inuctive elements such as irises, ros, iaphragms an posts as impeance invertors between transmission line resonators, which are realize with half wavelength hollow waveguies [1 4]. Although some other approaches such as using waveguies fille by multi-layer ielectrics [5] an substrate integrate waveguies (SIWs) [6] have been introuce as banpass filters by now.the long length of waveguie banpass filters, which is ue to hollow waveguie resonators, is a eficiency for them.in this paper, we propose to fill the region between two iaphragms fully by ielectrics to reuce the length of resulte filter.asymmetrical impeance invertors appear in the propose structure an we have to obtain the relations between their physical an electrical parameters.the usefulness of the propose structure an its performance are verifie by a comprehensive example an using HFSS software.

2 106 Ghorbanineja an Khalaj-Amirhosseini. DIELECTRIC FILLED WAVEGUIDE FILTER Figure 1 shows the propose waveguie banpass filter consisting of + 1 iaphragms an ielectric fille regions in a rectangular waveguie. The cross section of the waveguie has imensions of a an b. The n-th region (n =1,,..., ) has been fully fille by a ielectric with relative electric permittivity rn, where r0 = r, +1 = 1. The characteristic impeance an the phase constant of the n-th ielectric fille region are as the followings, respectively. Z n = β n = ω c η 0 rn (f c /f) (1) rn (f c /f) () where η 0 an c are the wave impeance an the velocity of the wave, respectively, in the free space. Also, f c is the cutoff frequency of the hollow waveguie. The iaphragms, which act as shunt inuctances, have an aperture of with g n, whose values are etermine in the next section. On the other han, Fig. shows a banpass filter consisting of series resonators an + 1 impeance invertors. The value of impeance invertors an the elements of resonators can be obtaine 1 b r0 r1 r r r, + 1 a 1 (a) t r0 r1 r r r, +1 β g1 g g 0 β 3 1 β g β g +1 β + 1 Z 0 Z1 Z Z Z +1 a (b) Figure 1. The propose ielectric fille waveguie banpass filter. (a) Three imensional view. (b) Top view.

3 Progress In Electromagnetics Research B, Vol.7, accoring to the type of filter transfer function, center frequency an the banwith of the filter [1 4]. L01 C01 L 0 C 0 R 0G K1 K K K + 1 R 0 L Figure. Typical banpass filter using series resonators an impeance invertors. ow, we want to moel the propose waveguie filter shown in Fig.1 as a banpass filter shown in Fig.. For this purpose, two following moelings are require: 1.Moeling series resonators by transmission lines of length half wavelength.equating the ABCD matrix an its erivative of a half wavelength waveguie transmission line with those of a series lumpe resonators gives us the characteristic impeance of the n-th region as follows r (f c /f 0 ) Z n =4f 0 L 0n (3) r.moeling the impeance invertors by shunt inuctances locate between two transmission lines of negative length as shown in Fig.3. φ 1n φ n K n Z 1 n X n Z n (a) (b) Figure 3. (a) An impeance invertor.(b) A circuit moel for impeance invertors. Using the above moelings, etermine, in which D n = λ gn /= π β n = the circuit shown in Fig.4 is λ 0 (4) rn (f c /f 0 )

4 108 Ghorbanineja an Khalaj-Amirhosseini 11 1 D 1 D = λ / 1 = λ / g1, g 1, + 1, + 1 Z11 X1 Z 1 Z1 X Z Z, 1, + 1 X + 1 Z Z, Figure 4. Transmission line realization of a ielectric fille waveguie banpass filter. where λ 0 is the wavelength of the free space at center frequency.also, comparing Figs. an 4 with each other results the following relations for n =1,,...,. n =,n + D n + 1,n+1 (5) Z,n = Z 1,n+1 = Z n (6) β,n = β 1,n+1 = β n (7) Z,+1 = Z +1 = R 0G = R 0L = Z 0 (8) Furthermore, accoring to Figs.3 an 4, the lengths 1n an n, which are negative, are obtaine from the following relations for n = 1,,..., +1. 1n = 1 φ 1n (9) β 1n n = 1 φ n (10) β n 3. IMPEDACE IVERTORS The values of parameters of the circuit shown in Fig.3(b) are known in the literature if Z 1n = Z n (shunt inuctance between two ientical transmission lines).however, this equality is not existe in Fig.4 especially at two ene impeance invertors (shunt inuctance between two ifferent transmission lines).so, we have to obtain the parameters of general moel shown in Fig.3, by equating the ABCD matrices of two circuits with each other as follows [ ][ cos(φ 1n/) jz 1nsin(φ 1n/) j/z 1nsin(φ 1n/) cos(φ 1n/) [ ] 0 jk = n j/k n j/x n 1 ][ ] cos(φ n/) jz nsin(φ n/) j/z nsin(φ n/) cos(φ n/) (11)

5 Progress In Electromagnetics Research B, Vol.7, After some mathematical manipulations one can obtaine three following relations ( ) φ1n + φ n tan = (Z 1n + Z n ) X n (1) Z 1n Z n ( ) φ1n φ n tan = (Z 1n Z n ) X n (13) Z 1n Z n 4K n X n = (14) K 4 n (p n q n ) 8Kn(p n + q n )+16 where p n an q n are real values efine as follows p n = (Z 1n + Z n ) Z1n Z n q n = (Z 1n Z n ) Z1n Z n (15) (16) The formulas (1) an (13) can be arrange as the followings ( ) ( ) φ 1n = tan 1 (Z1n Z n )X n tan 1 (Z1n + Z n )X n <0 (17) Z 1n Z n Z 1n Z n φ n = tan 1 ( (Zn Z 1n )X n Z 1n Z n ) tan 1 ( (Z1n + Z n )X n Z 1n Z n ) <0 (18) 4. THE IDUCTIVE DIAPHRAGMS One of iaphragms existe in Fig.1 an its equivalent circuit (shunt inuctance) are shown in Figs.5 an 6, respectively. The value of shunt y g b b 1 a (a) x Z 1 (b) Z Figure 5. (a) The cross sectional view of a iaphragm.(b) The sie view of a iaphragm.

6 110 Ghorbanineja an Khalaj-Amirhosseini inuctance of this iaphragm is known in the literature if Z 1 = Z (iaphragm between two ientical meiums).however, this equality is not existe in Fig.1 especially at two ene iaphragms (iaphragm between two ifferent meiums).so, we have to obtain the value of shunt inuctance of the circuit shown in Fig.6. Z 1 X Z Figure 6. The equivalent circuit of a iaphragm. It is assume that only ominant moe TE 10 can be propagate non-evanescently in the waveguie, i.e., a/3 <λ 0 < a.the incient fiel TE 10 will set up reflecte an transmitte higher orer moes. So we can write the transverse electric an magnetic fiels as follows (e jβ1z +Re jβ1z ) sin(πx/a)+ R m e γ1mz sin(mπx/a) z<0 E y = m= Te jβz sin(πx/a)+ T m e γmz sin(mπx/a) z>0 m= (19) H x = β 1 ωµ (e jβ 1z Re jβ1z ) sin(πx/a) + j γ 1m R m e γ1mz sin(mπx/a) ωµ β m= ωµ Te jβ z sin(πx/a) j γ m T m e γmz sin(mπx/a) ωµ m= z<0 z>0 (0) where γ 1m = ω (mfc /f) c r1 (1) γ m = ω (mfc /f) c r () The transverse electric fiel E y on the iaphragm must be continuous on the aperture an must be zero out of the aperture.

7 Progress In Electromagnetics Research B, Vol.7, Assuming E y (x, y, 0) = f(x) on the aperture an using Fourier analysis, we can obtain the following relations 1+R = T = a (a+g)/ (a g)/ f(x) sin(πx/a)x (3) R m = T m = a (a+g)/ f(x) sin(mπx/a)x for m =, 3,... (4) (a g)/ Moreover, the transverse magnetic fiel H x must be continuous on the aperture that gives the following relation jβ 1 (1 R) sin(πx/a)+ R m γ 1m sin(mπx/a) = jβ T sin(πx/a) m= T m γ m sin(mπx/a) (5) m= Using (3) an (4) in (5), we obtain the following relation gives us the following relation ( β1 + β T m= β 1 β 1 ) (a+g)/ sin(πx/a) (a g)/ f(x ) sin(πx /a)x = ( ) (a+g)/ γ1m + γ m j sin(mπx/a) f(x ) sin(mπx /a)x (6) (a g)/ where x is over the iaphragm aperture.it is known that the normalize susceptance B = BZ 1 = Z 1 /X = B/Y 1 causes a reflection R given by R 1+R =1 j B Z 1 Z (7) Accoring to (3) an (7), (6) turns to the following m= (a+g)/ B sin(πx/a) f(x ) sin(πx /a)x = (a g)/ [ ( γ ] 1m + γ (a+g)/ m ) sin(mπx/a) f(x ) sin(mπx /a)x (8) β 1 (a g)/

8 11 Ghorbanineja an Khalaj-Amirhosseini Using an analytical metho ientical to the approach introuce in [7], in which only two evanescent moes have been consiere, the following relation is obtaine for the susceptance of the iaphragm shown in Fig.5. B = λ g a { 1 s 1 (1 s ) 1 δ 3 s 6 [3δ 3+ 5δ 5 [ s 1+δ 3 s 6 (s ) ] (1 δ 3 s 6 )(1 δ 5 s 10 ) 15s 6 (1 s ) δ 5 ]} (9) where s = sin(πg/a) an δ m = (δ 1m + δ m )/, in which δ 1m = 1 1 r1 (f/mf c ) an δ m =1 1 r (f/mf c ). 5. EXAMPLE AD RESULTS In this section a compact banpass filter is esigne utilizing a WR- 90 waveguie (a =0.9 inches an b =0.4 inches).we woul like to esign a 3-orer chebyshev type banpass filter with center frequency 10 GHz, the relative banwith 9 percent an equal ripples 0.5 B. It is assume that all three transmission line resonators have the same relative electric permittivity r1 = r = r3 =3.5 (ielectric-fille filter) or r1 = r = r3 =1.0 (air-fille filter).using the relevant relations, the physical parameters of both filters are calculate as shown in Tables 1 an.after calculating these values, we shoul optimize them to have a better frequency response with attention to the effects of some factors such as the thickness of iaphragms an the coupling between contiguous iaphragms.the simulation an optimization of the filters are one using full-wave software HFSS, which is base on the finite element metho (FEM) [8].Simulation results of both air-fille an ielectric-fille structures are plotte in Figs.7 an 8. It is seen that the performance of the ielectric-fille filter is ientical to that of the air-fille filter while the length of former one is 1.57 mm an that of the latter one is mm. Therefore, the ielectric-fille filter has more than 57% compactness compare to the conventional air-fille filter.from the above example one may satisfy about the goo performance an compactness of ielectric-fille waveguie banpass filter.moreover, it is obvious that the avantages of the propose filter coul be mentione as the followings: 1.It has a significant compactness compare to the conventional airfille waveguie filters..the fabrication is easy because the metals of iaphragms coul

9 Progress In Electromagnetics Research B, Vol.7, Table 1. The physical parameters of esigne air-fille waveguie banpass filter. Lengths an Withs [mm] Before Optimization After Optimization 1 3 g 1 g g 3 g Table. The physical parameters of esigne ielectric-fille waveguie banpass filter. Lengths an Withs [mm] Before Optimization After Optimization 1 3 g 1 g g 3 g Figure 7. The simulation results of esigne air-fille waveguie banpass filter.

10 114 Ghorbanineja an Khalaj-Amirhosseini glue to the ielectrics an consequently the waveguie coul be mae monolithic instea of multi-sectional. 3.The mechanical stability is goo because the iaphragms lean to the ielectrics. 4.It is suitable for high power microwave circuits because the breakown voltage of ielectrics is higher than that of the air. Of course, the above superiorities are in front of the losses of ielectrics an so we have to use low loss ielectrics. Figure 8. The simulation results of esigne ielectric-fille waveguie banpass filter. 6. COCLUSIO A compact waveguie banpass filter was propose.the propose structure consists of + 1 inuctive iaphragms in a rectangular waveguie an the regions between them have been fille fully by ielectrics.the relations between the physical an electrical parameters of the existe asymmetrical impeance invertors were obtaine.the usefulness of the propose structure an its performance are verifie by esigning an simulating an equal-ripple X-ban banpass filter.the esigne filter has 57% compactness compare to the conventional filters.moreover, the propose filter has the avantages of easy fabrication, mechanical stability an capability of using in high power applications.

11 Progress In Electromagnetics Research B, Vol.7, REFERECES 1. Matthaei, G.L., L.Young, an E.M.T.Jones, Microwave Filters, Impeance-Matching etworks an Coupling Structures, Artech House, Deham, Mass., Pozar, D.M., Microwave Engineering, Aison-Wesley, Collin, R.E., Founations for Microwave Engineering, McGraw- Hill, ew York, Levy, R., R.V.Snyer, an G.Matthaei, Design of microwave filters, IEEE Trans. Microwave Theory Tech., Vol.50, , Khalaj-Amirhosseini, M., Microwave filters using waveguies fille by multi-layer ielectric, Progress In Electromagnetics Research, PIER 66, , Sotooeh, Z., B.Beglarbegian, F.H.Kashani, an H.Ameri, A novel banpass waveguie filter structure on SIW technology, Progress In Electromagnetics Research Letters, Vol., , Lewin, L., Theory of Waveguies, Butterworth & Co, Lt., HFSS Release 9.0, Ansoft Corp., 003.