Microwave Filters Based on the Structures with Resonators in Parallel Channels as Metamaterial Cells
Keywords:Metamaterials, Dielectric resonators, Stripline resonators, Bandstop microwave filters
Background. Many of the properties of metamaterials are similar to those found in filters with mutually detuned by frequency unrelated resonators. The bridge filters are used as a low-frequency prototypes of such microwave filters. For further development and design of new types of metamaterials it is necessary to establish an analogy between metamaterials and filters with mutually detuned by frequency unrelated resonators.
Objective. Creating a model of metamaterials based on the bandstop microwave filters with mutually detuned resonators and on the low-frequency prototypes.
Methods. Checking the equivalence of metamaterials characteristics and microwave filters with mutually detuned resonators, identifying their inherent laws (oscillation types in parallel channels, location of the attenuation poles above or below the bandwidth), which appear regardless of the types of resonators, studying the possibility of using prototype bridge filters for modeling of metamaterials.
Results. The basic model of an 8-pole network with resonators in parallel channels has been studied in detail. Analytical expressions are obtained for the transmission and reflection coefficients for all inputs of an 8-pole network. The 4-pole networks implemented on the basis of the aforementioned basic model are investigated. Experimental studies are performed that confirm the adequacy of analytical models. An analogy between metamaterials and microwave filters with mutually detuned resonators is established, the possibility of the use as a low-frequency prototype bridge bandpass filters is shown.Conclusions. Microwave filters with mutually detuned resonators can be used for modeling of metamaterials, and bridge bandpass filters – as low-frequency prototypes, which design techniques are well developed.
J.B. Pendry et al., “Magnetism from conductors and enhanced nonlinear phenomena”, IEEE Trans. Microw. Theory Tech., vol. 47, no. 11, pp. 2075–2084, 1999. doi: 10.1109/22.798002
J.B. Pendry, “Negative refraction makes a perfect lens”, Phys. Rev. Lett., vol. 85, no. 18, pp. 3966–3969, 2000. doi: 10.1103/PhysRevLett.85.3966
D.R. Smith et al., “Composite medium with simultaneously negative permeability and permittivity”, Phys. Rev. Lett., vol. 84, no. 18, pp. 4184–4187, 2000. doi: 10.1103/PhysRevLett.84.4184
B. Gralak et al., “Anomalous refractive properties of photonic crystals”, J. Optical Soc. Am. A, vol. 17, no. 6, pp. 1012–1020, 2000. doi: 10.1364/JOSAA.17.001012
M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: refraction like behavior in the vicinity of the photonic band gap”, Phys. Rev. B, vol. 62, no. 16, pp. 10696–10705, 2000. doi: 10.1103/PhysRevB.62.10696
R. Ruppin, “Extinction properties of a sphere with negative permittivity and permeability”, Solid State Commun., vol. 116, pp. 411–515, 2000. doi: 10.1016/S0038-1098(00)00362-8
R.A. Shelby et al., “Experimental verification of a negative index of refraction”, Science, vol. 292, pp. 77–79, 2001. doi: 10.1126/science.1058847
R.W. Ziolkowski and E. Heyman, “Wave propagation in media having negative permittivity and permeability”, Phys. Rev. E, vol. 64, no. 10, pp. 1–15, 2001. doi: 10.1103/PhysRevE.64.056625
C. Caloz and T. Itoh, “Application of the transmission line theory of left-handed (LH) materials to the realization of a microstrip LH transmission line”, IEEE-APS Int'l Symp. Digest, vol. 2, pp. 412–415, 2002. doi: 10.1109/APS.2002.1016111
R. Ruppin, “Surface polaritons of a left-handed material slab”, J. Phys.: Condensed Matter., vol. 13, pp. 1811–1818, 2001. doi: 10.1088/0953-8984/13/9/304
P. Gay-Balmaz and O.J.F. Martin, “Electromagnetic resonances in individual and coupled split-ring resonators”, J. Appl. Phys., vol. 92, no. 5, pp. 2929–2936, 2002. doi: 10.1063/1.1497452
J.A. Kong et al., “A unique lateral displacement of a Gaussian beam transmitted through a slab with negative permittivity and permeability”, Microw. Optical Technol. Lett., vol. 33, no. 2, pp. 136–139, 2002. doi: 10.1002/mop.10255
A.K. Iyer and G.V. Eleftheriades, “Negative refractive index metamaterials supporting 2-D waves”, IEEE-MTT Int'l Symp. Digest, pp. 1067–1070, 2002. doi: 10.1109/MWSYM.2002.1011823
N. Engheta, “An idea for thin subwavelength cavity resonators using metamaterials with negative permittivity and permeability”, IEEE Antennas Wireless Propag. Lett., vol. 1, pp. 10–13, 2002. doi: 10.1109/LAWP.2002.802576
G.V. Eleftheriades et al., “Planar negative refractive index media using periodically L-C Loaded Transmission Line”, IEEE Trans. Microw. Theory Tech., vol. 50, no. 12, pp. 2702–2712, 2002. doi: 10.1109/TMTT.2002.805197
C. Caloz and T. Itoh, “Novel microwave devices and structures based on the transmission line approach of meta-materials”, IEEE-MTT Int'l Symp., vol. 1, pp. 195–198, 2003. doi: 10.1109/MWSYM.2003.1210914
C. Caloz et al., “Existence and properties of microwave surface plasmons at the interface between a right-handed and a left-handed media”, IEEE AP-S USNC/URSI National Radio Science Meeting, 2003. doi: 10.1109/APS.2004.1332047
A. Alù and N. Engheta, “Pairing an epsilon-negative slab with a mu-negative slab: resonance, tunneling and transparency, IEEE Trans. Antennas Propagat., vol. 51, no. 10, pp. 2558–2571, 2003. doi: 10.1109/TAP.2003.817553
R.W. Ziolkowski and A.D. Kipple, “Application of double negative materials to increase the power radiated by electrically small antennas”, IEEE Trans. Antennas Propagat., vol. 51, no. 10, pp. 2626–2640, 2003. doi: 10.1109/TAP.2003.817561
K.G. Balmain et al., “Power flow for resonance cone phenomena in planar anisotropic metamaterials”, IEEE Trans. Antennas Propagat., vol. 51, no. 10, pp. 2612–2618, 2003. doi: 10.1109/TAP.2003.817542
C. Caloz et al., “A novel composite right/left-handed textured radiative surface”, in Proc. Progress in Electromagnetics Research Symposium (PIERS), Waikiki, HI, Oct. 2003, p. 201.
C. Caloz et al., “Microwave applications of transmission-line based negative refractive index structures”, in Proc. Asia-Pacific Microwave Conf., Seoul, Korea, Nov. 2003, vol. 3, pp. 1708–1713
A. Alu and N. Engheta, “Guided modes in a waveguide ﬁlled with a pair of single-negative (SNG), double-negative (DNG), and/or double-positive (DPS) layers”, IEEE Trans. Microw. Theory Tech., vol. 52, no. 1, pp. 199–210, 2004. doi: 10.1109/TMTT.2003.821274
F. Falcone et al., “Left handed coplanar waveguide band pass ﬁlters based on bi-layer split ring resonators”, IEEE Microw. Wireless Compon. Lett., vol. 14, no. 1, pp. 10–12, 2004. doi: 10.1109/LMWC.2003.821512
J.D. Baena et al., “Equivalent-circuit models for split-ring resonators and complementary split-ring resonators coup- led to planar transmission lines”, IEEE Trans. Microw. Theory Tech., vol. 53, no. 4, pp. 1451–1461, 2005. doi: 10.1109/TMTT.2005.845211
J. Bonache et al., “Compact coplanar waveguide band-pass ﬁlter at the s-band”, Microw. Optical Technol. Lett., vol. 46, no. 1, pp. 33–35, 2005. doi: 10.1002/mop.20893
A. Radkovskaya et al., “Resonant frequencies of a combination of split rings: Experimental, analytical and numerical study”, Microw. Optical Technol. Lett., vol. 46, no. 5, pp. 473–476, 2005. doi: 10.1002/mop.21021
N. Fang et al., “Sub-diffraction-limited optical imaging with a silver superlens”, Science, vol. 308, no. 5721, pp. 534–537, 2005. doi: 10.1126/science.1108759
H-T Chen et al., “Active metamaterial devices”, Nature, vol. 444, pp. 597–600, 2006. doi: 10.1038/nature05343
D. Schurig et al., “Electric-ﬁeld-coupled resonators for negative permittivity metamaterials”, Appl. Phys. Lett., vol. 88, no. 4, p. 041109, 2006. doi: 10.1063/1.2166681
J. Bonache et al., “On the electrical characteristics of complementary metamaterial resonators”, IEEE Microw. Wireless Compon. Lett., vol. 16, no. 10, pp. 543–545, 2006. doi: 10.1109/LMWC.2006.882400
R. Marques et al., Metamaterials with Negative Parameters: Theory, Design, and Microwave Applications. John Wiley, 2007. doi: 10.1002/9780470191736
F. Capolino, Theory and Phenomena of Metamaterials, 1st ed. Boca Raton, FL: CRC Press, 2009.
P. Tassin et al., “Planar designs for electromagnetically induced transparency in metamaterials”, Optics Express, vol. 17, no. 7, p. 5595, 2009. doi: 10.1364/OE.17.005595
D. Bouyge et al., “Split ring resonators (SRRs) based on micro-electro-mechanical deflectable cantilever-type rings: application to tunable stopband filters”, IEEE Microw. Wireless Compon. Lett., vol. 21, no. 5, pp. 243–245, 2011. doi: 10.1109/LMWC.2011.2124450
J. Naqui et al., “Novel sensors based on the symmetry properties of split ring resonators (SRRs)”, Sensors, vol. 11, no. 8, pp. 7545–7553, 2011. doi: 10.3390/s110807545
C. Mandel et al., “Passive chipless wireless sensor for two-dimensional displacement measurement”, in Proc. 41st European Microwave Conf., Manchester, UK, 2011, pp.79–82. doi: 10.23919/EuMC.2011.6101801
D. Bouyge et al., “Reconfigurable splitrings based on MEMS switches and their application to tunable filters”, J. Optics, vol. 14, no. 11, Article ID 114001, 2012. doi: 10.3390/s141222848
A. Karami-Horestani et al., “Displacement sensor based on diamond-shaped tapered split ring resonator”, IEEE Sensors J., vol. 13, no. 4, pp. 1153–1160, 2013. doi: 10.1109/JSEN.2012.2231065
A.K. Horestani et al., “Two-dimensional displacement and alignment sensor based on reflection coefficients of open microstrip lines loaded with split ring resonators”, IET Electronics Lett., vol. 50, no. 8, pp. 620–622, 2014. doi: 10.1049/el.2014.0572
H. Li et al., “Electromagnetically induced transparency with large delay-bandwidth product induced by magnetic resonance near field coupling to electric resonance”, Appl. Phys. Lett., vol. 106, no. 11, Article ID 114101, 2015. doi: 10.1063/1.4915313
C.-L.Yang et al., “Noncontact measurement of complex permittivity and thickness by using planar resonators”, IEEE Trans. Microw. Theory Techn., vol. 64, no. 1, pp. 247–257, 2016. doi: 10.1109/TMTT.2015.2503764
A. Salim and S. Lim, “Complementary split-ring resonator loaded microfluidic ethanol chemical sensor”, Sensors, vol. 16, no. 12, pp. 1–13, 2016. doi: 10.3390%2Fs16111802
F. Martín et al., Balanced Microwave Filters. Wiley-IEEE Press, 2018. doi: 10.1002/9781119238386
H.W. Bode and R.L. Dietzold, “Ideal wave filters”, Bell Syst. Tech. J., vol. 14, no. 2, pp. 215–252, 1935.
E.A. Guillemin, Synthesis of Passive Networks: Theory and Methods Appropriate to the Realization and Approximation Problems. John Wiley & Sons, 1957.
S. Karni, Network Theory: Analysis and Synthesis. Boston: Allyn and Bacon, 1966.
N.D. Bosyy, Electric Filters. Kyiv, SU: Gos. izd-vo tekhn. lit-ry USSR, 1959.
The Modern Theory of Filters and Their Design, T. Temesha and S. Mitra, eds. Moscow, SU: Mir, 1977.
L.A. Bessonov, Theoretical Foundations of Electrical Engineering. Electrical Circuits, 10th ed. Moscow, Russia: Gardariki, 2002.
W.M. Siebert, Circuits, Signals, and Systems. Cambridge, Ma: The MIT Press, 1985.
M.E. Ilchenko and A.P. Zhivkov, “Microwave device with multiple modes of dielectric resonators”, Izvestija Vysshih Uchebnyh Zavedenij. Ser. Radioelektronika, vol. 32, no. 5, pp. 56–59, 1989.
USSR Inventor’s Certificate 1343469.
M.E. Ilchenko and A.P. Zhivkov, “Attenuation band in dielectric resonator bandpass filters”, Izvestija Vysshih Uchebnyh Zavedenij. Ser. Radioelektronika, vol. 30, no. 10, pp. 41–44, 1987.
M.E. Ilchenko et al., “Microwave filters on mutually detuned resonators in parallel channels”, Izvestija Vysshih Uchebnyh Zavedenij. Ser. Radiojelektronika, vol. 33, no. 5, pp. 92–94, 1990.
M.E. Ilchenko and A.P. Zhivkov, “Bandpass filters based on dielectric resonators”, in Proc. IV National Conf. Microwave Devices with Foreign Participation Miteko-87, CSSR, Bratislava, 1987, vol. 2, pp. 131–132.
M.E. Ilchenko and A.P. Zhivkov, “Microwave filters of high selectivity based on dielectric resonators”, in Proc. VIII National Microwave Conf. Micon-88, Poland, Gdansk, October 3–7, 1988, pp. 162–166.
USSR Inventor’s Certificate 1451787.
USSR Inventor’s Certificate 1518837.
USSR Inventor’s Certificate 1529322.
USSR Inventor’s Certificate 1569920.
M.E. Ilchenko and A.P. Zhivkov, “Two-channel microwave bandpass filter”, Elektronnaya Tekhnika, Elektronika SVC, no. 9, pp. 12–14, 1989.
M.E. Ilchenko et al., “Filters based on resonators with modes close to metamaterials cells”, Naukovі Vіstі NTUU KPІ, no. 1, pp. 7–14, 2016. doi: 10.20535/1810-0546.2016.1.64572
USSR Inventor’s Certificate 1529321.
USSR Inventor’s Certificate 1739408.
USSR Inventor’s Certificate 1417082.
USSR Inventor’s Certificate 1518836.
M.E. Ilchenko and A.P. Zhivkov, “Inverse of oscillations in the metamaterial cells”, in Proc. 10th Int. Sci. Conf. Modern Challenges in Telecommunications, Kyiv, Ukraine, April 19–22, 2016, pp. 20–23.
M.E. Ilchenko and A.P. Zhivkov, “Properties of metamaterials in oscillation terminology”, in Proc. Int. Conf. ICT and Radio Electronics (UkrMiCo’2016), Ukraine, September 11–15, 2017, pp. 170–173.
M.E. Ilchenko and A.P. Zhivkov, “Degenerated oscillations in the metamaterial cells”, in Proc. 11th Int. Sci. Conf. Modern Challenges in Telecommunications, Kyiv, Ukraine, April 18–21, 2017, pp. 414–416.
M.E. Ilchenko and A.P. Zhivkov, “Areas of degeneration oscillations in metamaterial cells”, in 2017 Int. Conf. Information and Telecommunication Technologies and Radio Electronics (UkrMiCo), pp. 1–4, 2017. doi: 10.1109/UkrMiCo.2017.8095389
USSR Inventor’s Certificate 1429202.
USSR Inventor’s Certificate 1538204.
Copyright (c) 2018 Igor Sikorsky Kyiv Polytechnic Institute
This work is licensed under a Creative Commons Attribution 4.0 International License.Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under CC BY 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work