A new LC series element for compact bandpass filter design

A new LC series element based on a modified version of the split rings resonator introduced in is proposed. Owing to its small electrical size, the new open split ring resonator (OSRR) is a very attractive element for compact bandpass filter design.
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  210 IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, VOL. 14, NO. 5, MAY 2004 A New LC Series Element for CompactBandpass Filter Design Jesús Martel, Ricardo Marqués  , Member, IEEE  , Francisco Falcone, Juan D. Baena,Francisco Medina  , Senior Member, IEEE  , Ferran Martín, and Mario Sorolla  , Senior Member, IEEE   Abstract— A new LC series element based on a modified versionof the  split rings resonator  introduced in [1] is proposed. Owing toits small electrical size, the new open split ring resonator (OSRR)is a very attractive element for compact bandpass filter design. Asan example, we have designed and fabricated a filter to produce abandpassaroundtheresonancefrequencyoftheemployedOSRRs.Thefilter bandwidthiscontrolled by thelengthof thetransmissionlines connecting the OSRRs. Sharp and deep out-of-band rejectionis achieved by cascading several OSRRs. Circuit theory and elec-tromagnetic basedsimulations reasonablyagree withexperiments.  Index Terms— Compact bandpass filters, split ring resonators. I. I NTRODUCTION T HE split rings resonator (SRR) [see Fig. 1(a)] was pro-posed in [1] as a basic particle for the design of artifi-cial negative magnetic permeability media. SRRs became verypopular because of their use in the design of the first phys-ical realization of a left-handed-medium (LHM) [2], namely, amedium exhibiting negative electric permittivity and magneticpermeability. Recently, some of the authors [3] have fabricateda one-dimensional LHM by loading a waveguide below cutoff with an array of SRRs. The theory in [3] takes advantage of thesmall electrical size of SRRs at resonance (typically one tenthof the free space wavelength or less). This feature is related tothelargedistributedcapacitancebetweenthetworings.Inciden-tally, this allows one to use a simple LCR circuit model to char-acterizethe  particle [4].Theresonancefrequencyobtainedfromthis model is typically much smaller than that corresponding tothe classical ring [5] or square [6] open loop resonators of sim-ilar dimensions ( operation). The small electrical size of theSRRs suggests the possibility of applying this peculiar configu-ration (or some suitable modified version) to the design of com-pactfilters.Inthisletter,weproposean open versionoftheSRR(OSRR) which allows for series connection along a microstripline. Its usefulness as basic building block for planar band passfilters is demonstrated. [7]. Manuscript received July 1, 2003; revised November 27, 2003. This work has been supported by the Spanish Ministry of Science and Technology andFEDER funds under Projects TIC2001-3163, BFM2001-2001, and TIC2002-04528-C02-01. The review of this letter was arranged by Associate EditorJ. Martel, R. Marqués, J. D. Baena, and F. Medina are with the Grupo de Mi-croondas, Universidad de Sevilla, Sevilla 41012, Spain (e-mail: martel@us.es;marques@us.es; juan_dbd@us.es; medina@us.es).F. Falcone and M. Sorolla are with the Departamento de Ingeniería Eléctricay Electrónica, UniversidadPública deNavarra, Pamplona 31006, Spain(e-mail:falcone_fj@tsm.es; mario@unavarra.es).F. Martín is with Departament d’Enginyeria Electronica, Universitat Au-tonoma de Barcelona, Bellaterra 08193, Spain (e-mail: ferran.martin@uab.es).Digital Object Identifier 10.1109/LMWC.2004.827836Fig. 1. (a) Split rings resonator (SRR). (b) RLC equivalent circuit. II. A NALYSIS OF THE  OSRRThe proposed OSRR is shown in Fig. 2(a). The resonator isconceivedtobeseriesconnectedtoamicrostripline.Aproperlylocated window is practiced in the ground plane in order to donotmeaningfullyperturbtheelectromagneticbehavioroftheiso-lated OSRR. The microstrip width is adjusted along the portionadjacenttothegroundplanewindowsoastokeepunchangedthecharacteristic impedance. One of the rings is excited by the cur-rent flowing through the signal conductor of the line, while theotherringisexcitedbythedisplacementcurrentflowingthroughthe slot between both rings. Fig. 2(b) depicts the equivalent cir-cuit model for the whole system line-OSRR-line, where rep-resents the effective permittivity of the transmission lines. Thevalues of the resistance, , and inductance, , of the OSRR arethe same as for the SRR of Fig. 1(a) with identical dimensions( and ) printed on the same substrate. However, the ca-pacitance value of the OSRR circuit model, , is four times thecapacitance of the corresponding SRR circuit model. This owesto the fact that the upper and lower halves of the Pendry’s SRRare series connected, thus leading to a value of given by, where is the per unit length capacitance be-tween the strips conforming the rings [4]. However, for the newOSRR, , where is the mean radius of the  par-ticle .Therefore,theresonancefrequencyoftheOSRRishalftheoneoftheSRRparticle.ThispropertyincreasestheconvenienceofusingOSRR forcompact passivedevicesdesign.The impedance of the RLC circuit of Fig. 2(b) vanishes at theresonancefrequencyoftheOSRR,thusallowingforapassbandaround this frequency. This is the very basic working principleof the bandpass filter.III. M ICROSTRIP  B ANDPASS  F ILTER  U SING  OSRRSA straightforward application of the OSRR can be found inthe design of a compact slow-wave type bandpass filter [8] by 1531-1309/04$20.00 © 2004 IEEE  MARTEL  et al. : NEW LC SERIES ELEMENT 211 Fig. 2. (a) Top and bottom (ground plane side) views of the open split ringsresonator (OSRR) excited by a microstrip line. (b) Equivalent circuit. simply cascading several unit cells as those shown in Fig. 2(a).The bandwidth of the filter can be controlled by adjusting thelength oftheunit cell, , whereasthedepthof therejectionbanddepends on the number of cells, , used for filter implemen-tation (i.e., the number of transmission poles). For each valueof , the first transmission pole corresponds to the resonancefrequency of the OSRR. To clarify these properties of the filterresponsewehaveplottedinFig.3theresultsobtainedforthein-sertion loss of several filters when the number of cells, , andthe distance are varied. We have used the simple equivalentcircuit model shown in Fig. 2(b) to simulate the filter perfor-mance. The characteristic impedance of the line isand the effective permittivity . We have assumed loss-less OSRRs with nH and pF leading to aresonance frequency GHz. At this frequency, thewavelength in the microstrip is around mm. We em-phasize that for mm and the length of the filteris below .IV. E XPERIMENTAL  R ESULTS A three pole bandpass filter based on the theory above hasbeen fabricated on a PTFE substrate (mm) and measured. The dimensions of the OSRRs have Fig. 3. Calculated filter response by using the equivalent circuit of Fig. 2(b).Data:              nH, H,         pF,          mm (solid line), and      mm (dashed line).Fig. 4. Layout and dimensions of the fabricated three pole OSRR slow-wavefilter.Fig. 5. Circuit simulation (dot line), electromagnetic simulation (dashed line)and experimental (solid line) results for the insertion (black) and return (grey)loss of the fabricated filter. Parameters are in Fig. 4. been obtained using an optimization code based on the modelin [4]. The goal resonance frequency was around 3.2 GHz. Thelengthsofthe50 microstripsectionsbetweentheOSRRspro-vide a theoretical bandwidth of 30%. The layout of the filteris shown in Fig. 4. Note that the filter could be shortened bysimply connecting the OSRRs by curved or meander transmis-sion lines. The experimental results are shown in Fig. 5. They  212 IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, VOL. 14, NO. 5, MAY 2004 are compared with the theoretical results obtained from the ide-alized circuit model of Fig. 2(b), and with the results providedby a full-wave electromagnetic simulation in  CST MicrowaveStudio . Fig. 5 shows a good agrement between theoretical, sim-ulated and experimental results up to 9 GHz. At higher frequen-cies the simple circuit-like approximation fails because of addi-tional effects which are not considered in the model such as, forinstance, higher order dynamic (i.e., nonquasistatic) resonancesof the OSRRs, the spurious series capacitance at the input of the OSRRs, or the microstrip dispersion. All these effects are,however,reasonablyaccounted forin theelectromagneticsimu-lation. Note that the circuit model still provides a useful tool fora preliminary initial design accounting for the main features of the filter at its operation band. Electromagnetic simulation canbe used to refine the design before fabricating the prototype, butthis has not been done in this case.V. C ONCLUSION A novel small size series LC element, the  open split ring res-onator  , has been proposed and analyzed. This resonator is ex-pected to be useful in the design of compact bandpass filters inplanar technology. Indeed, using this concept, a three-pole mi-crostrip band pass filter has been designed, fabricated and mea-sured. The filterwas designed by using an extremely simple cir-cuitmodelwhoseparametersareknowninquasianalyticalform.In this design, the location of the first pole corresponds to theresonance frequency of the OSRRs, and the bandwidth is ad- justed by the length of the line sections between the OSRRs.The agreement between theoretical predictions, full-wave sim-ulations and measurements is very good over a wide frequencyrange around the filter passband.R EFERENCES[1] J. B. Pendry, A. J. Holden, D. J. Ribbins, and W. J. Stewart, “Magnetismfrom conductors and enhanced nonlinear phenomena,”  IEEE Trans. Mi-crowave Theory Tech. , vol. 47, pp. 2075–2084, Nov. 1999.[2] D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S.Schultz, “Composite medium with simultaneously negative perme-ability and permittivity,”  Phys. Rev. Lett. , vol. 84, pp. 4184–4187, May2000.[3] R. Marqués, J. Martel, F. Mesa, and F. Medina, “Left-handed-mediasimulation and transmission of EM waves in subwavelength split-ring-resonator-loaded metallic waveguides,”  Phys. Rev. Lett. , vol. 89, pp.4184–4187, Oct. 2002.[4] R. Marqués, F. Mesa, J. Martel, and F. Medina, “Comparative analysisof edge and broadside coupled split ring resonators for metamaterial de-sign.Theory andexperiments,”  IEEETrans. Antenas Propagat. ,vol. 51,pp. 2572–2581, Oct. 2003.[5] I. Wolf, “Microstrip bandpass filters using degenerated modes of a mi-crostripringresonator,”  Electron.Lett. , vol.8,no.12,pp.163–164, June1972.[6] J. S. Hong and M. J. Lancaster, “Couplings of microstrip square openloop resonators for cross-coupled planar microwave filters,”  IEEE Trans. Microwave Theory Tech. , vol. 40, pp. 2099–2018, Dec. 1996.[7] F. Martín, J. Bonache, R. Marqués, J. D. Baena, J. Martel, F. Medina, F.Falcone, T. Lopetegi, M. Beruete, and M. Sorolla, “Filtros y antenas demicrondas y milimétricas basados en resonadores de anillos abiertos yenlíneas de transmisión planares,” Patent pending 00302282, Sept. 25,2003.[8] D. M. Pozar,  Microwave Engineering . Reading, MA: Ad-dison-Wesley, 1990.
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