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Compact printed microwave filters for wireless communication applications
Pacific Science Review A: Natural Science and Engineering xxx (2016) 1e5
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Pacific Science Review A: Natural Science and Engineering j o u r n a l h o m e p a g e : w w w . j o u r n a l s . e l s e v i e r . c o m / p a c i fi c - s c i e n c e review-a-natural-science-and-engineering/
Compact printed microwave filters for wireless communication applications V.V. Atuchin a, b, c, d, *, D.A. Buhtiyarov e, A.P. Gorbachev e a
Laboratory of Optical Materials and Structures, Institute of Semiconductor Physics, SB RAS, Novosibirsk 630090, Russia Functional Electronics Laboratory, Tomsk State University, Tomsk 634050, Russia c Laboratory of Semiconductor and Dielectric Materials, Novosibirsk State University, Novosibirsk 630090, Russia d Institute of Chemistry, Tyumen State University, Tyumen 625003, Russia e Department of Radio Engineering and Electronics, Novosibirsk State Technical University, Novosibirsk 630073, Russia b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 19 August 2016 Accepted 13 September 2016 Available online xxx
A novel coupled-line-free wideband bandpass/bandstop filter configuration is designed and tested. The filter is based on a reentrant structure with unequal dielectric constants for the internal and external fillings. As a result, additional symmetrical transmission zeros are generated in the lower and upper stop bands of the bandpass filter; this leads to an elliptic function response and improvement of the pass band and selectivity. Similar conclusions are made about the bandstop filter in terms of the return loss. The general TEM circuit model, in terms of the two-port series connection, is presented for the proposed filters, and then, it is used to determine its electrical parameters. The experimental prototype was fabricated using conventional printed circuit board technology. The measured S-parameters show acceptable agreement with the analytical and full-wave simulations, showing promising potential for different applications. Copyright © 2016, Far Eastern Federal University, Kangnam University, Dalian University of Technology, Kokushikan University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Keywords: Bandpass filter Bandstop filter Wideband filter Reentrant structure Multilayer implementation
1. Introduction Microwave filters are extensively used components in many communication systems for different purposes. Recently, multilayer structures have become a hot research topic in microwave component design for size reduction, including low-temperaturefired ceramic (LTCC) technology. With this trend, the reentrant coupling section can be used to produce filters formed from single transmission line segments with internal elements shielded from the ground by a solid conductor. This complete shielding can intensify the line interaction, and it has been used for wideband coupled-line-free four-port directional filter design [1,2]. The twoport filters, on the base of the reentrant structure, are the focus of the investigation. As will be demonstrated, such a structure can be a base of the novel elliptic bandpass/bandstop (BPF/BSF) filter without lumped components or hairpin and open-loop resonators.
* Corresponding author. Institute of Semiconductor Physics, Novosibirsk 630090, Russia. Fax: þ7 (383) 3332771. E-mail address: [email protected] (V.V. Atuchin). Peer review under responsibility of Far Eastern Federal University, Kangnam University, Dalian University of Technology, Kokushikan University.
The filter possesses a broad band symmetric insertion-loss-versusfrequency response around the pass or stop band, an acceptable frequency range and a compact planar structure that is suitable for multilayer implementation. The elliptic filter can be designed based on comb line, stepped digital and cross-coupled filter configurations [1,3e5]. Recently, these configurations have been further developed in many studies, and some results can be found elsewhere [6e9]. However, the capacitive (inductive) loading of an open-end resonator complicates a marked size reduction, and additionally, designing a broad band planar structure that has lumped-element-free requirements is difficult. In the present study, a novel approach for the design of reentrant elliptic filters using well-known multilayer technology is proposed. As a result, a bandpass filter with two transmission zeros is designed, fabricated and tested. The simulated and measured results are reported, and they show good agreement. 2. Formulation of the problem The basic reentrant coaxial section consists of three conductors, A, B, and C, as shown in Fig. 1 [10]. The A and B conductors are coaxial transmission line centre conductors with a characteristic
http://dx.doi.org/10.1016/j.psra.2016.09.003 2405-8823/Copyright © 2016, Far Eastern Federal University, Kangnam University, Dalian University of Technology, Kokushikan University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Please cite this article in press as: V.V. Atuchin, et al., Compact printed microwave filters for wireless communication applications, Pacific Science Review A: Natural Science and Engineering (2016), http://dx.doi.org/10.1016/j.psra.2016.09.003
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V.V. Atuchin et al. / Pacific Science Review A: Natural Science and Engineering xxx (2016) 1e5
Fig. 1. Basic four-port reentrant coaxial/bar structure.
pffiffiffiffiffiffi impedance ZB and electrical length qB ¼ 2pl εrB =l (in the following, it is designated as transmission line (ZB ; qB )) within intermediate conductor C, where C is the centre conductor of a strip (bar) transmission line with a characteristic impedance ZB and pffiffiffiffiffiffiffi electrical length qN ¼ 2pl εrN =l within ground conductor G, where l is the section length and εrB and εrN are the relative dielectric constants of the coaxial and bar transmission line fillings, respectively. It should be noted that a strip transmission line equivalent to the basic reentrant coaxial section was described in Ref. [11]. It is well known that, if εrB ¼ εrN , the section depicted in Fig. 1 behaves as a conventional quarter-wave directional coupler with corresponding even- and odd-mode characteristic impedances, Z0e and Z0o , respectively: Z0e ¼ ZB þ 2ZN , Z0o ¼ ZB [10]. Thus, if port 1 in Fig. 1 is the input port, port 2 is the coupled port and port 3 is the isolated port. Through classical consideration, the discontinuity reactances are neglected, and then, the isolation and input matching are perfect when theffi terminating line characteristic pffiffiffiffiffiffiffiffiffiffiffiffiffi impedance Z0 is equal to Z0e Z0o . The methods of its connection to conductors A and B, with appropriate design procedures, have been described previously [9e13]. Thus, the section depicted in Fig. 1 may be used as four-port, as well as two-port. However, more than ten two-ports can be obtained from the section shown in Fig. 1 by placing open or short circuits on various terminal pairs or by joining the ends of the A and B conductors. To determine the electrical parameters of the section formed as a twoport, a pertinent port condition application is necessary, as described elsewhere [5,14e17]. It is evident that the additional twoport number can be obtained from the section depicted in Fig. 1 by placing the short circuit on the end of conductor C or by the connection of the ends of conductors A and/or B and C together. In general, εrB sεrN ; this satisfies a multilayer strip line realization. Thus, it is necessary to describe the novel additional two-ports using adequate equivalent circuits that take the reentrant nature into account and may be used for the determination of electrical parameters ZB , qB , ZN and qN with the prescribed values of relative dielectric constants εrB and εrN . The values can be selected as appropriate initial properties to be used in full-wave simulation and the following optimization by a proper electromagnetic solver.
existence in the lines. This condition cannot be regarded as a limiting factor because new technological methods used for standard strip-line device implementation substantially expand the applications of this condition in microwave engineering. Subsequent full-wave simulations and experimental results agree with this explanation. Let us consider the filter element formed from the reentrant circuit shown in Fig. 1 when ports 3 and 4 of coaxial transmission line centre conductors A and B are short-circuited to the butt-end of shielding bar line conductor C, as depicted in Fig. 2. In other words, in this case, the cable conductors are short-circuited to the cable armours. It is clear that, if the filter two-port element was formed when conductors A and B were short-circuited to ground conductor G, it could be analysed by adding boundary condition U3 ¼ U4 ¼ 0 and using known analysis methods [15e17]. However, in the case under consideration, the boundary condition for the structure shown in Fig. 2 is U3 ¼ U4 s0 and the filter element can be represented by the model depicted in Fig. 3a and then as a two two-ports series connection shown in Fig. 3b with the corresponding impedance matrices ZB and ZN :
½ZB ¼ jZB tan qB
1 0
0 ; 1
½ZN ¼
ZN 1 j tan qN 1
1 1
(1)
When the scattering matrix
½S ¼ ½E 2ð½Z=Z0 þ ½EÞ1
(2)
is calculated from the sum matrix
½Z ¼ ½ZB þ ½ZN
(3)
one can find and analyse the insertion and/or return loss of the filter two-port element, where ½E is the identity matrix. The dependence of insertion loss L on frequency f (a) for ZB ¼ 60 U, ZN ¼ 40 U, εrB ¼ 4εrN , Z0 ¼ 50 U, where f0N is the reference frequency of the filter element external part at which qN ¼ p=2, is shown by the solid line in Fig. 4. The result indicates that the filter element can be categorized as a section of the bandstop filter with infinite numbers of the stop bands centred at odd multiples of reference frequency f0N . Now, let us investigate the two-port filter element that appeared under the assumption that the ends of the conductors A, B and C are connected together and short-circuited to ground conductor G. Here, as in the previous case, we cannot use boundary condition U3 ¼ U4 ¼ 0 because the bar line conductor is short-circuited to ground conductor G, and the problem cannot be reduced to the earlier-described situations [15e17]. Therefore, the investigated filter element can be represented by the analogy from Fig. 3b, as a
3. Application of the technique 3.1. Equivalent circuit derivation A key to developing the equivalent circuit and solution of the associated problems is the corresponding decomposition. Our technique employs the multi-port device series connection that is not typical in microwave design technology and a summation of their impedance matrices under the condition of TEM mode
Fig. 2. Proposed coaxial/bar two-port reentrant bandstop filter element.
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3
element, after substituting ½ZN* for ½ZN in (3), has a qualitatively different frequency dependence on the insertion (return) loss. The dependence of insertion loss L* on frequency f (a) for ZN ¼ 40 U, ZB ¼ 60 U, εrB ¼ 4εrN and Z0 ¼ 50 U is shown by the dashed line in Fig. 4. This curve demonstrates that the two-port filter element can be categorized as a section of the bandpass filter with an infinite number of the pass bands centred at odd multiples of reference frequency f0N . It is interesting to note that the reference insertion loss levels are the same in both filter elements. Additionally, frequency fL∞ of the low-side transmission zero (attenuation pole) and fR∞ of the high-side are equal to 0:5f0N and 1:5f0N , respectively, for impedances ZB and ZN , respectively. These frequencies are the same in both filter elements. 3.2. Analysis of two-section filters It is interesting to consider the cascade of two above-described bandpass sections under the assumption that they both have the same impedances ZB , ZN and dielectric constants εrB , εrN . Let the electrical length qS of the interconnecting line of characteristic impedance Z0 be equal to 0:05qN . Additionally, let the scattering Sij and chain transfer Tij two-port parameters be defined in accordance with Ref. [18]. Then, the ½TF matrix for the two section cascade is the product of the individual ½T matrices and matrix ½TS of the interconnecting line
½TF ¼
Fig. 3. Proposed coaxial/bar reentrant bandstop filter element: (a) TEM-model on the base of coaxial lines, (b) series connection of two equivalent two-ports. The short and open circuit states are denoted as sc and oc, respectively.
TF11 TF21
TF12 TF22
¼ ½T½TS ½T
Hence, insertion loss L*F of the two-section bandpass filter can be determined from ½TF using the formula: L*F ¼ 20 log10 ðjTF11 jÞ. The insertion-loss-versus-frequency response for εrB ¼ 4εrN and qS ¼ 0:05qN is shown in Fig. 5. This frequency dependence demonstrates that the considered two-section BPF has five insertion loss zeros in the pass band with readily discernible extremes L1 < L4 < L3 < L2 for a wide set range of impedances ZB and ZN . Thus, value L2 should be the prescribed insertion loss Lar in pass band fL f fR with bandwidth ratio BR ¼ fR =fL , whereas LS is the minimal insertion loss in the stop band. L2 (L2 ¼ Lar ), BR and LS are shown in Fig. 6 as functions of impedances ZB , ZN . Here, Lar is depicted by a solid line, BR - by a dashed line, and LS - by a dotted line. Inspection of the curves indicates that this two-section filter may be used in microwave frequency-selective components.
Fig. 4. Calculated bandstop/bandpass filter element responses.
series connection of two two-ports, but when the lower two-port is the short-circuited transmission line with the corresponding impedance matrix
h
i 1 ZN* ¼ jZN tan qN 1
1 : 1
(4)
Because of a certain difference between matrices ½ZN that is expressed by (1) and ½ZN* expressed by (4), the investigated filter
Fig. 5. Typical calculated response of the reentrant two-section bandpass filter (not drawn to scale).
Please cite this article in press as: V.V. Atuchin, et al., Compact printed microwave filters for wireless communication applications, Pacific Science Review A: Natural Science and Engineering (2016), http://dx.doi.org/10.1016/j.psra.2016.09.003
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Fig. 8. Simulated (solid) and measured (dashed) results for the group delay levels.
Fig. 6. Complete results of the analysis of the reentrant two-section bandpass filter.
The cascade of two bandstop sections that is described above may be investigated in the same algorithm. The typical insertionloss-versus-frequency response LF calculated for the same dielectric constants (εrB , εrN ) and electrical length qS is depicted in Fig. S1. This frequency dependence demonstrates that the considered BSF has three transmission zeros in the stop band with readily discernible attenuation levels (LS1 > LS2 ). Additionally, this BSF is described using two insertion loss levels in the low-side and highside pass bands (L1 < L2 , L3 < L4 ), respectively, indicating that these levels are related as L1 > L4 and L2 > L3 . Thus, LS2 should be a
prescribed attenuation LS in the stop band (LS ¼ LS2 ) with bandwidth ratio BR ¼ fR =fL , whereas the value of L1 is the maximal insertion loss Lar for the both pass bands (Lar ¼ L1 ). LS , BR , and Lar are depicted in Fig. S2 as the corresponding functions of the ZB and ZN impedances by using solid, dashed and dotted lines, respectively. The results demonstrate that the considered two-section filter may also be used in microwave devices. The full-wave simulation of the filter and experimental implementation can be found in the Supplementary section [19e21]. The simulated filter S-parameters are shown in Fig. 7 by solid lines on large and fine scales. Two transmission zeros are observed on the sides of the passband. The filter was fabricated using the standard printed circuit board process [22,23]. The connectors for the terminating strip lines were two SRG-50-751FW (Russia) devices. The metalized through-holes were made with widths of 0.5 mm along the strip line width (wB ). The filter parameters were measured using an Agilent N5241A Performance Network Analyzer (PNA-X) and the corresponding test fixture; the effects of the test setup can be efficiently accounted for by proper calibration. In Fig. 7, the measured frequency responses are shown, and acceptable agreement with the EM simulated results is evident. The filter exhibits a highly selective wideband bandpass performance with the octave ripple bandwidth at a central frequency of 0.808 GHz. The measured insertion and return losses are found to be below 0.9 dB at the central frequency and are better than 10 dB over the entire passband. Furthermore, the measured group delay over the passband, as shown in Fig. 8 by the dashed line, is less than 2.5 ns. Although the proposed filter only has two sections, it exhibits better frequency selectivity than that of a conventional two section filter [24]. Because of the implementation tolerance, there is only a slight deviation between the predicted and measured frequency responses of the proposed filters. 4. Conclusions In the present study, wideband bandpass/bandstop filters are developed on a reentrant configuration base. By properly selecting the impedances and relative dielectric constants of their transmission lines, two additional transmission zeros can be reached. The measured results are in a reasonable agreement with the TEM and full-wave predicted data and suggest that the proposed coupled-line-free filters possess attractive performance and compact sizes. With the use of the substrate integrated approach, the proposed filter structures can be directly integrated with other planar circuits, including LTCC devices. Acknowledgments
Fig. 7. Simulated and measured results of the fabricated bandpass filter: (a) large scale, (b) fine scale.
This work was financially supported by the Ministry of Education and Science of the Russian Federation within the basic tasks of the
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state. The project theme is the construction theory and practical implementation of broadband microwave devices to be used in digital television and telecommunications, including computer systems, measurement equipment. Code 629. VVA is partly supported by the Ministry of Education and Science of the Russian Federation. Appendix A. Supplementary data Supplementary data related to this article can be found at http:// dx.doi.org/10.1016/j.psra.2016.09.003 References
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[1] R.K. Mongia, I.J. Bahl, P. Bhartia, J. Hong, RF and Microwave Coupled-line Circuits, Artech House, Norwood, MA, 2007. [2] A.P. Gorbachev, The reentrant wide-band directional filter, IEEE Trans. Microw. Theory Technol. 50 (8) (2002) 2028e2031. [3] R. Levy, S.B. Cohn, A history of microwave filter research, design, and development, IEEE Trans. Microw. Theory Technol. 32 (9) (1984) 1055e1067. [4] R. Levy, V.S. Richard, G.L. Matthaei, Design of microwave filters, IEEE Trans. Microw. Theory Technol. 50 (3) (2002) 783e793. [5] Classic works in RF engineering, in: R. Levy (Ed.), Microwave and RF Filters vol. 2, Artech House, Norwood, MA, 2007. [6] G.L. Matthaei, Narrow-band, fixed-tuned, and tunable bandpass filters with zigesag hairpin-comb resonators, IEEE Trans. Microw. Theory Technol. 51 (4) (2003) 1214e1219. [7] C.F. Chen, T.Y. Huang, R.B. Wu, Design of microstripbandpass filters with multiorder spurious-mode suppression, IEEE Trans. Microw. Theory Technol. 53 (12) (2005) 3788e3793. [8] J.-X. Chen, C.-H. Chin, Q. Xue, Double-sided parallel-strip line with an inserted conductor plane and its applications, IEEE Trans. Microw. Theory Technol. 55 (9) (2007) 1899e1904. [9] Y.-M. Chen, S.-F. Chang, C.-C. Chang, T.-J. Hung, Design of stepped-impedance comblinebandpass filters with symmetric insertion loss response and wide
[18]
[19]
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[21] [22] [23] [24]
5
stopbandrange, IEEE Trans. Microw. Theory Technol. 55 (10) (2007) 2191e2199. S.B. Cohn, The re-entrant cross section and wide-band 3-dB hybrid couplers, IEEE Trans. Microw. Theory Technol. 11 (7) (1963) 254e258. L. Lavendol, J.J. Taub, Re-entrant directional coupler using strip transmission line, IEEE Trans. Microw. Theory Technol. 13 (5) (1965) 700e701. E.G. Cristal, Re-entrant directional couplers having direct coupled centre conductors, IEEE Trans. Microw. Theory Technol. 14 (4) (1966) 207e208. E.G. Cristal, Nonsymmetrical coupled lines of reentrant cross section, IEEE Trans. Microw. Theory Technol. 15 (9) (1967) 529e530. E.G. Cristal, Correction to “nonsymmetrical coupled lines of reentrant cross section”, IEEE Trans. Microw. Theory Technol. 16 (1) (1968) 57. E.M.T. Jones, J.T. Bolljahn, Coupled-strip-transmission-line filters and directional couplers, IEEE Trans. Microw. Theory Tech. 4 (2) (1956) 75e81. H. Ozaki, J. Ishii, Synthesis of a class of strip-line filters, IEEE Trans. Circuit Theory 5 (2) (1958) 104e109. R.J. Wenzel, Exact design of TEM microwave networks using quarter-wave lines, IEEE Trans. Microw. Theory Technol. 12 (1) (1964) 94e111. D.A. Frickey, Conversions between S, Z, Y, h, ABCD, and T parameters which are valid for complex source and load impedances, IEEE Trans. Microw. Theory Technol. 42 (2) (1994) 205e211. B.M. Kolundzija, J.S. Ognjanovic, T.K. Sarkar, WIPL-D: Microwave Circuit and 3D EM Simulation for RF and Microwave Applications, Software and User's Manual, Artech House, Norwood, MA, 2005. M. Nakajima, E. Yamashita, Characterization and design method for asymmetrical-structure offset-type broadside-coupled strip lines having thick strip conductors and dielectric substrate, Trans. IEICE Jpn. J74-C-I (2) (1991) 46e53. G.L. Matthaei, L. Young, E.M.T. Jones, Microwave Filters, Impedance-matching Networks, and Coupling Structures, Artech House, Norwood, MA, 1980. Microwave and very high frequency devices, Theory Algorithms Technology, Radiotechnika, Moscow, 2013. C.F. Coombs Jr., in: C.F. Coombs Jr. (Ed.), Printed Circuits Handbook, sixth ed., McGraw-Hill, N. Y., 2008. Jia-Sheng Hong, in: Kai Chang (Ed.), Microstrip Filters for RF/Microwave Applications, second ed., Wiley, Hoboken, N. J., 2011.
Please cite this article in press as: V.V. Atuchin, et al., Compact printed microwave filters for wireless communication applications, Pacific Science Review A: Natural Science and Engineering (2016), http://dx.doi.org/10.1016/j.psra.2016.09.003
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H O S T E D BY
Pacific Science Review A: Natural Science and Engineering j o u r n a l h o m e p a g e : w w w . j o u r n a l s . e l s e v i e r . c o m / p a c i fi c - s c i e n c e review-a-natural-science-and-engineering/
Compact printed microwave filters for wireless communication applications V.V. Atuchin a, b, c, d, *, D.A. Buhtiyarov e, A.P. Gorbachev e a
Laboratory of Optical Materials and Structures, Institute of Semiconductor Physics, SB RAS, Novosibirsk 630090, Russia Functional Electronics Laboratory, Tomsk State University, Tomsk 634050, Russia c Laboratory of Semiconductor and Dielectric Materials, Novosibirsk State University, Novosibirsk 630090, Russia d Institute of Chemistry, Tyumen State University, Tyumen 625003, Russia e Department of Radio Engineering and Electronics, Novosibirsk State Technical University, Novosibirsk 630073, Russia b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 19 August 2016 Accepted 13 September 2016 Available online xxx
A novel coupled-line-free wideband bandpass/bandstop filter configuration is designed and tested. The filter is based on a reentrant structure with unequal dielectric constants for the internal and external fillings. As a result, additional symmetrical transmission zeros are generated in the lower and upper stop bands of the bandpass filter; this leads to an elliptic function response and improvement of the pass band and selectivity. Similar conclusions are made about the bandstop filter in terms of the return loss. The general TEM circuit model, in terms of the two-port series connection, is presented for the proposed filters, and then, it is used to determine its electrical parameters. The experimental prototype was fabricated using conventional printed circuit board technology. The measured S-parameters show acceptable agreement with the analytical and full-wave simulations, showing promising potential for different applications. Copyright © 2016, Far Eastern Federal University, Kangnam University, Dalian University of Technology, Kokushikan University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Keywords: Bandpass filter Bandstop filter Wideband filter Reentrant structure Multilayer implementation
1. Introduction Microwave filters are extensively used components in many communication systems for different purposes. Recently, multilayer structures have become a hot research topic in microwave component design for size reduction, including low-temperaturefired ceramic (LTCC) technology. With this trend, the reentrant coupling section can be used to produce filters formed from single transmission line segments with internal elements shielded from the ground by a solid conductor. This complete shielding can intensify the line interaction, and it has been used for wideband coupled-line-free four-port directional filter design [1,2]. The twoport filters, on the base of the reentrant structure, are the focus of the investigation. As will be demonstrated, such a structure can be a base of the novel elliptic bandpass/bandstop (BPF/BSF) filter without lumped components or hairpin and open-loop resonators.
* Corresponding author. Institute of Semiconductor Physics, Novosibirsk 630090, Russia. Fax: þ7 (383) 3332771. E-mail address: [email protected] (V.V. Atuchin). Peer review under responsibility of Far Eastern Federal University, Kangnam University, Dalian University of Technology, Kokushikan University.
The filter possesses a broad band symmetric insertion-loss-versusfrequency response around the pass or stop band, an acceptable frequency range and a compact planar structure that is suitable for multilayer implementation. The elliptic filter can be designed based on comb line, stepped digital and cross-coupled filter configurations [1,3e5]. Recently, these configurations have been further developed in many studies, and some results can be found elsewhere [6e9]. However, the capacitive (inductive) loading of an open-end resonator complicates a marked size reduction, and additionally, designing a broad band planar structure that has lumped-element-free requirements is difficult. In the present study, a novel approach for the design of reentrant elliptic filters using well-known multilayer technology is proposed. As a result, a bandpass filter with two transmission zeros is designed, fabricated and tested. The simulated and measured results are reported, and they show good agreement. 2. Formulation of the problem The basic reentrant coaxial section consists of three conductors, A, B, and C, as shown in Fig. 1 [10]. The A and B conductors are coaxial transmission line centre conductors with a characteristic
http://dx.doi.org/10.1016/j.psra.2016.09.003 2405-8823/Copyright © 2016, Far Eastern Federal University, Kangnam University, Dalian University of Technology, Kokushikan University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Please cite this article in press as: V.V. Atuchin, et al., Compact printed microwave filters for wireless communication applications, Pacific Science Review A: Natural Science and Engineering (2016), http://dx.doi.org/10.1016/j.psra.2016.09.003
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Fig. 1. Basic four-port reentrant coaxial/bar structure.
pffiffiffiffiffiffi impedance ZB and electrical length qB ¼ 2pl εrB =l (in the following, it is designated as transmission line (ZB ; qB )) within intermediate conductor C, where C is the centre conductor of a strip (bar) transmission line with a characteristic impedance ZB and pffiffiffiffiffiffiffi electrical length qN ¼ 2pl εrN =l within ground conductor G, where l is the section length and εrB and εrN are the relative dielectric constants of the coaxial and bar transmission line fillings, respectively. It should be noted that a strip transmission line equivalent to the basic reentrant coaxial section was described in Ref. [11]. It is well known that, if εrB ¼ εrN , the section depicted in Fig. 1 behaves as a conventional quarter-wave directional coupler with corresponding even- and odd-mode characteristic impedances, Z0e and Z0o , respectively: Z0e ¼ ZB þ 2ZN , Z0o ¼ ZB [10]. Thus, if port 1 in Fig. 1 is the input port, port 2 is the coupled port and port 3 is the isolated port. Through classical consideration, the discontinuity reactances are neglected, and then, the isolation and input matching are perfect when theffi terminating line characteristic pffiffiffiffiffiffiffiffiffiffiffiffiffi impedance Z0 is equal to Z0e Z0o . The methods of its connection to conductors A and B, with appropriate design procedures, have been described previously [9e13]. Thus, the section depicted in Fig. 1 may be used as four-port, as well as two-port. However, more than ten two-ports can be obtained from the section shown in Fig. 1 by placing open or short circuits on various terminal pairs or by joining the ends of the A and B conductors. To determine the electrical parameters of the section formed as a twoport, a pertinent port condition application is necessary, as described elsewhere [5,14e17]. It is evident that the additional twoport number can be obtained from the section depicted in Fig. 1 by placing the short circuit on the end of conductor C or by the connection of the ends of conductors A and/or B and C together. In general, εrB sεrN ; this satisfies a multilayer strip line realization. Thus, it is necessary to describe the novel additional two-ports using adequate equivalent circuits that take the reentrant nature into account and may be used for the determination of electrical parameters ZB , qB , ZN and qN with the prescribed values of relative dielectric constants εrB and εrN . The values can be selected as appropriate initial properties to be used in full-wave simulation and the following optimization by a proper electromagnetic solver.
existence in the lines. This condition cannot be regarded as a limiting factor because new technological methods used for standard strip-line device implementation substantially expand the applications of this condition in microwave engineering. Subsequent full-wave simulations and experimental results agree with this explanation. Let us consider the filter element formed from the reentrant circuit shown in Fig. 1 when ports 3 and 4 of coaxial transmission line centre conductors A and B are short-circuited to the butt-end of shielding bar line conductor C, as depicted in Fig. 2. In other words, in this case, the cable conductors are short-circuited to the cable armours. It is clear that, if the filter two-port element was formed when conductors A and B were short-circuited to ground conductor G, it could be analysed by adding boundary condition U3 ¼ U4 ¼ 0 and using known analysis methods [15e17]. However, in the case under consideration, the boundary condition for the structure shown in Fig. 2 is U3 ¼ U4 s0 and the filter element can be represented by the model depicted in Fig. 3a and then as a two two-ports series connection shown in Fig. 3b with the corresponding impedance matrices ZB and ZN :
½ZB ¼ jZB tan qB
1 0
0 ; 1
½ZN ¼
ZN 1 j tan qN 1
1 1
(1)
When the scattering matrix
½S ¼ ½E 2ð½Z=Z0 þ ½EÞ1
(2)
is calculated from the sum matrix
½Z ¼ ½ZB þ ½ZN
(3)
one can find and analyse the insertion and/or return loss of the filter two-port element, where ½E is the identity matrix. The dependence of insertion loss L on frequency f (a) for ZB ¼ 60 U, ZN ¼ 40 U, εrB ¼ 4εrN , Z0 ¼ 50 U, where f0N is the reference frequency of the filter element external part at which qN ¼ p=2, is shown by the solid line in Fig. 4. The result indicates that the filter element can be categorized as a section of the bandstop filter with infinite numbers of the stop bands centred at odd multiples of reference frequency f0N . Now, let us investigate the two-port filter element that appeared under the assumption that the ends of the conductors A, B and C are connected together and short-circuited to ground conductor G. Here, as in the previous case, we cannot use boundary condition U3 ¼ U4 ¼ 0 because the bar line conductor is short-circuited to ground conductor G, and the problem cannot be reduced to the earlier-described situations [15e17]. Therefore, the investigated filter element can be represented by the analogy from Fig. 3b, as a
3. Application of the technique 3.1. Equivalent circuit derivation A key to developing the equivalent circuit and solution of the associated problems is the corresponding decomposition. Our technique employs the multi-port device series connection that is not typical in microwave design technology and a summation of their impedance matrices under the condition of TEM mode
Fig. 2. Proposed coaxial/bar two-port reentrant bandstop filter element.
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element, after substituting ½ZN* for ½ZN in (3), has a qualitatively different frequency dependence on the insertion (return) loss. The dependence of insertion loss L* on frequency f (a) for ZN ¼ 40 U, ZB ¼ 60 U, εrB ¼ 4εrN and Z0 ¼ 50 U is shown by the dashed line in Fig. 4. This curve demonstrates that the two-port filter element can be categorized as a section of the bandpass filter with an infinite number of the pass bands centred at odd multiples of reference frequency f0N . It is interesting to note that the reference insertion loss levels are the same in both filter elements. Additionally, frequency fL∞ of the low-side transmission zero (attenuation pole) and fR∞ of the high-side are equal to 0:5f0N and 1:5f0N , respectively, for impedances ZB and ZN , respectively. These frequencies are the same in both filter elements. 3.2. Analysis of two-section filters It is interesting to consider the cascade of two above-described bandpass sections under the assumption that they both have the same impedances ZB , ZN and dielectric constants εrB , εrN . Let the electrical length qS of the interconnecting line of characteristic impedance Z0 be equal to 0:05qN . Additionally, let the scattering Sij and chain transfer Tij two-port parameters be defined in accordance with Ref. [18]. Then, the ½TF matrix for the two section cascade is the product of the individual ½T matrices and matrix ½TS of the interconnecting line
½TF ¼
Fig. 3. Proposed coaxial/bar reentrant bandstop filter element: (a) TEM-model on the base of coaxial lines, (b) series connection of two equivalent two-ports. The short and open circuit states are denoted as sc and oc, respectively.
TF11 TF21
TF12 TF22
¼ ½T½TS ½T
Hence, insertion loss L*F of the two-section bandpass filter can be determined from ½TF using the formula: L*F ¼ 20 log10 ðjTF11 jÞ. The insertion-loss-versus-frequency response for εrB ¼ 4εrN and qS ¼ 0:05qN is shown in Fig. 5. This frequency dependence demonstrates that the considered two-section BPF has five insertion loss zeros in the pass band with readily discernible extremes L1 < L4 < L3 < L2 for a wide set range of impedances ZB and ZN . Thus, value L2 should be the prescribed insertion loss Lar in pass band fL f fR with bandwidth ratio BR ¼ fR =fL , whereas LS is the minimal insertion loss in the stop band. L2 (L2 ¼ Lar ), BR and LS are shown in Fig. 6 as functions of impedances ZB , ZN . Here, Lar is depicted by a solid line, BR - by a dashed line, and LS - by a dotted line. Inspection of the curves indicates that this two-section filter may be used in microwave frequency-selective components.
Fig. 4. Calculated bandstop/bandpass filter element responses.
series connection of two two-ports, but when the lower two-port is the short-circuited transmission line with the corresponding impedance matrix
h
i 1 ZN* ¼ jZN tan qN 1
1 : 1
(4)
Because of a certain difference between matrices ½ZN that is expressed by (1) and ½ZN* expressed by (4), the investigated filter
Fig. 5. Typical calculated response of the reentrant two-section bandpass filter (not drawn to scale).
Please cite this article in press as: V.V. Atuchin, et al., Compact printed microwave filters for wireless communication applications, Pacific Science Review A: Natural Science and Engineering (2016), http://dx.doi.org/10.1016/j.psra.2016.09.003
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Fig. 8. Simulated (solid) and measured (dashed) results for the group delay levels.
Fig. 6. Complete results of the analysis of the reentrant two-section bandpass filter.
The cascade of two bandstop sections that is described above may be investigated in the same algorithm. The typical insertionloss-versus-frequency response LF calculated for the same dielectric constants (εrB , εrN ) and electrical length qS is depicted in Fig. S1. This frequency dependence demonstrates that the considered BSF has three transmission zeros in the stop band with readily discernible attenuation levels (LS1 > LS2 ). Additionally, this BSF is described using two insertion loss levels in the low-side and highside pass bands (L1 < L2 , L3 < L4 ), respectively, indicating that these levels are related as L1 > L4 and L2 > L3 . Thus, LS2 should be a
prescribed attenuation LS in the stop band (LS ¼ LS2 ) with bandwidth ratio BR ¼ fR =fL , whereas the value of L1 is the maximal insertion loss Lar for the both pass bands (Lar ¼ L1 ). LS , BR , and Lar are depicted in Fig. S2 as the corresponding functions of the ZB and ZN impedances by using solid, dashed and dotted lines, respectively. The results demonstrate that the considered two-section filter may also be used in microwave devices. The full-wave simulation of the filter and experimental implementation can be found in the Supplementary section [19e21]. The simulated filter S-parameters are shown in Fig. 7 by solid lines on large and fine scales. Two transmission zeros are observed on the sides of the passband. The filter was fabricated using the standard printed circuit board process [22,23]. The connectors for the terminating strip lines were two SRG-50-751FW (Russia) devices. The metalized through-holes were made with widths of 0.5 mm along the strip line width (wB ). The filter parameters were measured using an Agilent N5241A Performance Network Analyzer (PNA-X) and the corresponding test fixture; the effects of the test setup can be efficiently accounted for by proper calibration. In Fig. 7, the measured frequency responses are shown, and acceptable agreement with the EM simulated results is evident. The filter exhibits a highly selective wideband bandpass performance with the octave ripple bandwidth at a central frequency of 0.808 GHz. The measured insertion and return losses are found to be below 0.9 dB at the central frequency and are better than 10 dB over the entire passband. Furthermore, the measured group delay over the passband, as shown in Fig. 8 by the dashed line, is less than 2.5 ns. Although the proposed filter only has two sections, it exhibits better frequency selectivity than that of a conventional two section filter [24]. Because of the implementation tolerance, there is only a slight deviation between the predicted and measured frequency responses of the proposed filters. 4. Conclusions In the present study, wideband bandpass/bandstop filters are developed on a reentrant configuration base. By properly selecting the impedances and relative dielectric constants of their transmission lines, two additional transmission zeros can be reached. The measured results are in a reasonable agreement with the TEM and full-wave predicted data and suggest that the proposed coupled-line-free filters possess attractive performance and compact sizes. With the use of the substrate integrated approach, the proposed filter structures can be directly integrated with other planar circuits, including LTCC devices. Acknowledgments
Fig. 7. Simulated and measured results of the fabricated bandpass filter: (a) large scale, (b) fine scale.
This work was financially supported by the Ministry of Education and Science of the Russian Federation within the basic tasks of the
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state. The project theme is the construction theory and practical implementation of broadband microwave devices to be used in digital television and telecommunications, including computer systems, measurement equipment. Code 629. VVA is partly supported by the Ministry of Education and Science of the Russian Federation. Appendix A. Supplementary data Supplementary data related to this article can be found at http:// dx.doi.org/10.1016/j.psra.2016.09.003 References
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Please cite this article in press as: V.V. Atuchin, et al., Compact printed microwave filters for wireless communication applications, Pacific Science Review A: Natural Science and Engineering (2016), http://dx.doi.org/10.1016/j.psra.2016.09.003