In the current article the concept of multi-resonator dual-band filter has been described. The dual-band filters based on three and four rectangular dielectric resonators have been synthesized that functionate in ТЕ01δ and ТЕ02δ modes. The proposed construction benefits since it doesn’t have additional coupling elements or DR shape complication. The analytical model of dual-band filter has been developed that accounts for two bands simultaneously. The accuracy of the proposed model is verified by the simulation results obtained by applying finite element method and shows insignificant disagreement. The proposed dual-band filter can be applied for satellite systems that require the transmission of several non-contiguous frequency channels in the one beam

Pidhurska, Tatyana V.

Electronic Archive of Kyiv Polytechnic Institute

29  ISSN 2312-4121, Information and Telecommunication Sciences, 2015, Volume 6, Number 1 © 2015, National Technical University of Ukraine “Kyiv Polytechnic Institute”   UDC 621.382  MULTI-RESONATOR DUAL-BAND FILTERS ON DIELECTRIC RESONATORS  Tatyana V. Pidhurska National Technical University of Ukraine “KPI”, Kyiv, Ukraine   In the current article the concept of multi-resonator dual-band filter has been described. The dual-band filters based on three and four rectangular dielectric resonators have been synthesized that functionate in  ТЕ01δ  and ТЕ02δ modes. The proposed construc-tion benefits since it doesn’t have additional coupling elements or DR shape complication. The analytical model of dual-band filter has been developed that accounts for two bands simultaneously. The accuracy of the proposed model is verified by the sim-ulation results obtained by applying finite element method and shows insignificant disagreement. The proposed dual-band filter can be applied for satellite systems that require the transmission of several non-contiguous frequency channels in the one beam.  Introduction With the movement to the mm-wave range [1], the high Q resonator filters are of great importance, particu-larly on dielectric resonators, since they pro-vide better in-band selectivity. In order to provide several frequency bands simulta-neously the multiband band-pass filters have got a growing attention for satellite and mobile communica-tions [2]. The actual importance of dual-band filter de-velopment on dielectric resonators (DR) is this three-dimensional cavity-type of resonators which ensure high unloaded quality factor and consequently lower in-band losses [3]. The drawbacks of the existing construc-tions include the complication shape of DR as well as additional coupling elements that generally complexify the analytical model of the filter [4], [5] as well as in-crease the weight and size parameters. In [6] the dual-band filter design has been re-searched, operating in lower mode ТЕ01δ as well as higher ТЕ02δ [7] mode of rectangular DR. The electro-magnetic field distribution of ТЕ02δ resembles two magnetic dipoles, exited in antiphase, thus providing higher unloaded quality factor.  Statement of the problem  The aim of the article is to synthesize multi-resonator dual-band filter, particularly on three and four resonators while applying the proposed concept [6], namely: by using elongated rectangular DRs with square cross-section, op-erating in ТЕ01δ  and ТЕ02δ oscillating modes with approx-imately equal coupling coefficients. The applied methods include: numerical, realized in the software HFSS [8], ana-lytical [9] that implies the development of analytical scat-tering model of the filter.  Main part  The construction of three-resonator filter consists of rectangular dielectric resonators, the coaxial lines that are connected to the central conductors, which excite the resonators in ТЕ01δ and ТЕ02δ modes. In fig.1 the simulation model of the filter has been illustrated solved by applying finite element method (FEM).   Fig.1. Construction of dual-band filter on three DR  The frequency offset between central frequencies can be tuned by varying the length of DR. By applying the numerical method to the EMW scat-tering problem on the system of three resonators the following wide-band amplitude-frequency response (AFR) of dual-band filter has been depicted in fig.2.   Fig.2 Wideband AFR of dual-band filter based on three DR with the dimensions: 33.926.426.4 ⋅⋅ mm, TELECOMMUNICATION SCIENCES  VOLUME 2  NUMBER 1  JANUARY ─ JUNE 2011  30manufactured from the material ,80=rε4105 −⋅=δtg and placed in metal cavity with dimensions  5.55026 ⋅⋅ mm  The analytical scattering model of the three-resonator filter has been developed, that accounts for the behavior of scattering parameters of the three-DR system (fig. 1) in the resonance region [9], enabling to calculate the frequency dependences of both transmis-sion ( )fT1  and reflection ( )fR1  coefficients in each band: ( ) ∑=×⋅−⋅⋅−=21 _3_12_1_121 442j jjjjDkkQfT λλ  ( )+⋅⋅×fQkkjjjj_1_1_12_11~2 λ ( ) −⋅⋅−⋅⋅+fQkkkkjjjjjjj_2_1_12_11_3_12_11~2~2 λλ ( ) ,~2_3_3_12_11⋅⋅−fQkkjjjj λ  (1) ( ) ∑=⋅−⋅⋅−−=21 _3_12_1_121 *4421j jjjjDkkQfR λλ  ( )+⋅⋅fQkkjjjj_1_1_12_112*λ ( ) −⋅⋅−⋅⋅+fQkkkkjjjjjjj_2_3_12_11_1_12_11 22 λλ( ) ,2_3_3_12_11⋅⋅−fQkkjjjj λ where DQ  - Q-factor of dielectric , jk _11~ – coupling coefficient between the trans-mission line and DR in j-th operating mode,  jk _12 , jk _13 – are the cross-coupling coeffi-cients between the first and second DR as well as first and third DR correspondingly in j-th operating mode. jf _0 – the resonance frequency of j-th operating mode; ( ) ,5.0~5.0_13_11_ dkki jjjm ⋅±+⋅⋅=λ  jjj kki _13_11_2~−⋅=λ- j-th eigenvalues of the coupling operator,  ;3,1=m ( ) 2_122_13_11 8~jjj kkkid ++⋅=, i – imaginary unit; ( )−−+=212 __0_0_jnjDjjn ffiQfffQλ, .3,2,1=n  The coupling coefficients have been calculated for each band according to the results, reported in [9], namely: ,1075.2~,1067.2~ 32_1131_11 −− ⋅=⋅= kk  71_1332_1231_12 105,1025.3,1041.4 −−− ⋅=⋅=⋅= kkk.105 72_13 −⋅=k  In [10] the coupling coefficients’ dependencies have been also researched, namely the coupling pa-rameters between DR and transmission line as well as the cross-coupling coefficients. Moreover, the optimal conditions for the equal alteration of coupling coeffi-cients have been determined that ensure the two bands of the filter. In fig.3 (a,b) the AFR of dual-band filter calcu-lated by applying two methods, namely FEM and ana-lytical one (1), have been depicted. The phase frequen-cy responses (PFR) have been also illustrated in fig.3 (c,d).  (а)    (b)  (c)    (d) Fig.3 AFR of 3-resonator dual-band filter in each band calculated according to analytical (1) and FEM [8] ap-proaches According to fig.2, the computed numerical and ana-lytical dependencies have modest disagreement in each band of the filter. This occurs due to the fact that HFSS software environment accounts for the boundary condi-tions of the construction as well as the effect of non-resonance propagation whilst the presented analytical model considers solely the resonant scattering of elec-tromagnetic wave (EMW) on the system of DR. From fig. 3 the -3dB level fractional bandwidth of T.V. PIDGURSKA; O.O. TRUBIN, B. M. SHELKOVNIKOV: «QUADRUPOLE» MODE DR FILTER FOR C-BAND APPLICATIONS   31the first passband (TE01δ mode) is 0.68% at the center frequency of 6.09 GHz with the insertion loss of 1.8 dB while the -3dB level fractional bandwidth of the second passband (TE02δ mode) is 0.5% at the center frequency of 6.58 GHz with the insertion loss of 2dB in the band. Out-of-band rejection between passbands is about 60dB. The spurious product is located at 7.41GHz. The four-resonator band-pass filter has been also synthesized. In fig.4 the simulation model of the filter has been illustrated solved by applying finite element method.   Fig.4. Construction of dual-band filter on four DR  As follows from the numerical solution of the EMW scattering from the four-resonator system the following wideband AFR of dual-band filter has been calculated as indicated in the fig.5.  Fig.5 Wideband AFR of dual-band filter based on four DR with the dimensions: 9.334.264.26 ⋅⋅  mm, manufac-tured from the material ,80=rε4105 −⋅=δtg and placed in metal cavity with dimensions  5.56220 ⋅⋅ mm As follows from [9] the analytical scattering model of the DRs’ system implies the successive determina-tion of both the eigenvalues and eigenvectors of  cou-pling operator, afterwards handling the scattering prob-lem of EMW on the DR system. In view of awkwardness of the four-resonator filter’s analytical model the scattering coefficients have been written in the matrix form through the eigenvectors of  coupling operator. The derived eigenvectors for the coupling operator matrix can be given for each band as: ( ) ( ) ( ) ( )( ) ( ) ( ) ( ) ,1111~~~~~~~~1111131214211131214411131214311131214111131214211131214411131214311131214111−−++−⋅−−−−⋅−−−−⋅−++−⋅−++−⋅−−−−⋅−−−−⋅−++−⋅−=kkkkikkkkikkkkikkkkikkkkikkkkikkkkikkkkiB λλλλλλλλ where eigenvalues of coupling operator are defined as: ( ) ( ) ( ) ( )( ),2~4~~ 2131214111221411121411122,1kkkkikkkikkkik +++⋅⋅−+⋅+±+⋅+=λ( ) ( ) ( ) ( )( )2~*4~~ 2131214111221411121411124,3kkkkikkkikkkik −+−⋅+−⋅+±−⋅+=λ14k -  the cross-coupling coefficient between the first and fourth DR. By providing summation for each operational band the scattering parameters of dual-band filter on four resonators can be found as: ( ) ( ) ,221412jj t ttDfQABQfT ∑ ∑= =⋅⋅−= ( ) ( ) ,2121412 ∑ ∑= =⋅⋅−=j jt ttDfQLBQfR  (3) where 4,3,2,1=t  since there are four resonators, matrices tA , tL  are defined through the elements of eigenvector matrix B: ,...0......0......0......~...3330232013100331100⋅=bbbbbbbbkbAtt=3330232013100301100...0......0......0......*~...bbbbbbbbkbLtt,  wherе ⋅000~311 tbk, ⋅000~011 tbk substitute  the t-th col-umn of the matrix tA correspondingly ( ) .1200−⋅⋅++⋅=ffQiffQfQ DDtt λ  The following coupling coefficients have been cal-culated for each band according to [9]: .101,101,101,101,1027.3,107.4,1077.2~,1036.3~62_1461_1442_1341_1332_1231_1232_1131_11−−−−−−−−⋅=⋅=⋅=⋅=⋅=⋅=⋅=⋅=kkkkkkkk According to the chosen coupling coefficients the AFR of dual-band filter by applying FEM has been compared with the AFR based on analytical model (3) in fig.6 (a,b). The PFR of |S21| in each band have been illustrated in fig.6 (c,d). TELECOMMUNICATION SCIENCES  VOLUME 2  NUMBER 1  JANUARY ─ JUNE 2011  32 (а)    (b)   (c)    (d) Fig.6 AFR of 4-resonator dual-band filter in each band calculated according to analytical (3) and FEM approaches [7]  According to fig.6, the computed numerical and analytical dependencies have modest disagreement in each band due to the effect of non-resonance scattering that is not accounted by the analytical model. Neverthe-less, the applied analytical method is considerably more accurate comparing with the well-known low-frequency prototype approach, since the first one addresses the resonant properties of the system more precisely. By summarizing the data from fig. 6, the -3dB level fractional bandwidth of the first passband (TE01δ mode) is 0.64% at the center frequency of 6.1 GHz with the insertion loss of 2.1dB, while the  -3dB level frac-tional bandwidth of the second passband (TE02δ mode) is 0.55% at the center frequency of 6.58 GHz with the insertion loss of 2.6 dB. Out-of-band rejection between passbands is about 80 dB. The spurious product is lo-cated at 7.57 GHz. The future work might be connected with the synthesis of three-band filter, since the four-resonator BPF has shown that there is one more possi-ble band (TE03δ mode) at 7.6 GHz, close to the spurious product.  Conclusion  The dual-band multi-resonator filter on rectan-gular DRs has been synthesized, that operates in TE01δ, TE02δ  oscillation modes. The analytical models based on Maxwell equations have been derived for both three- and four-resonator filters accounting for two frequency bands simultaneously as well as their phase-frequency properties. Compared with the finite element method application the scattering parameters derived by apply-ing analytical model, demonstrates insignificant dis-crepancy due to the fact that the analytical model doesn’t consider the effect of non-resonance propaga-tion. The proposed dual-band filter can be used for sat-ellite systems that require noncontiguous in frequency channels to be transmitted to the ground through one beam.   References 1. Kolomytsev M.A. Increase of geostationary orbit efficiency in the Ku band based on changes of ITU threshold values/ M.A. Kolomytsev, A. Lipatov, Y. Synepol-ski// Information and Telecommunication Sciences. — 2013. —№2(4). — С.42-46.   2. G.Macchiarella. Present and near future in the world of microwave filters: Proc. 22nd International Con-ference Radioelektronika. — Brno, Czech Republic, 2012. — 6 p. 3. Cameron R.J. Microwave Filters for Com-munication Systems Fundamentals, Design and Applications / R.J. Cameron, R.Mansour, C. M. Kudsia. — New York: Wiley, 2007.—804p. 4. Zhang R. Dual-band dielectric resonator filters / R.R. Mansour// IEEE Transactions on Microwave Theory and Techniques. — 2009. —№7(57). — P. 1760—1766. 5. Memarian M. Novel quadruple-mode, dual-mode and dual-band dielectric resonator filters and multi-plexers: Master Degree dissertation, Dept. Elect. Comp. Eng./ Mohammad Memarian. —  Univ. Waterloo, Ontario, Canada, 2009. —100 p. 6. T.V. Pidgurska, O. Trubin. Novel dual-band rectangular dielectric resonator filter: Proc. IEEE 2014 X International Symposium on Telecommunications (BI-HTEL). — Sarajevo, Bosnia and Herzegovina, 2014. — P. 1–5. 7. Pidgurska T.V. “Quadruple” mode of the rectangular dielectric resonators Scientific proceeding of Ukrainian research institute of communication// Scientific proceeding of Ukrainian research institute of communication. — 2014. —№2(30). — С.100-105. 8. HFSS full book. — 2005. — Режим доступу: http://ru.scribd.com/doc/17748492/Hfss-Full-Book (22.03.15). — Назва з екрану. 9. Trubin A. Scattering of infrared optical pulses on the band-stop filters on ring dielectric micro-resonators// Electronics and Communications. — 2013. —№6(1). — С.26-32.  10. Pidgurska, T. V. Coupling coefficients of dual-band filter on rectangular dielectric resonators// Scien-tific proceeding of Ukrainian research institute of communi-cation. — 2014. —№4(32). — PP. 72-78.  (Rus)   Received in final form on June 6, 2015 

Multi-Resonator Dual-Band Filters on Dielectric Resonators

In the current article the concept of multi-resonator dual-band filter has been described. The dual-band filters based on three and four rectangular dielectric resonators have been synthesized that functionate in  ТЕ01δ  and ТЕ02δ modes. The proposed construction benefits since it doesn’t have additional coupling elements or DR shape complication. The analytical model of dual-band filter has been developed that accounts for two bands simultaneously. The accuracy of the proposed model is verified by the simulation results obtained by applying finite element method and shows insignificant disagreement. The proposed dual-band filter can be applied for satellite systems that require the transmission of several non-contiguous frequency channels in the one beam

Multi-Resonator Dual-Band Filters on Dielectric Resonators

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