280 IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, VOL. 14, NO. 6, JUNE 2004 Effective Negative- Stopband Microstrip Lines Based on Complementary Split Ring Resonators Francisco Falcone, Txema Lopetegi, Member, IEEE, Juan D. Baena, Ricardo Marqués, Member, IEEE, Ferran Martín, and Mario Sorolla, Senior Member, IEEE Abstract—In this letter a super-compact stopband microstrip structure is proposed. The frequency gap is produced by an array of complementary split ring resonators (CSRRs)—a concept pro- posed here for the first time—etched on the ground plane. This be- havior is interpreted as due to the presence of a negative effective dielectric permittivity in the vicinity of resonance. The resulting de- vice produces a deep rejection frequency band with sharp cutoff, and a pass band that exhibits very low losses and good matching. Due to the sub-lambda operation of CSRRs, the electrical size of the device is very small. Index Terms—Complementary split ring resonators (CSRRs), duality, microstrip technology, microwave filters, negative- , split ring resonators. I. INTRODUCTION I N THE LAST years there has been an extensive research effort within the electromagnetic community to develop and use novel metamaterials (i.e. artificially fabricated materials, based on periodic structures, with properties not existing in nature). Among these materials electromagnetic bandgap (EBG) structures, negative- , negative- , and left-handed (LH) media have received much attention in the microwave and millimeter wave community [1]–[11]. One interesting application proposed for these structures has been the filtering of frequency bands and/or the supression of undesired spurious passbands or harmonics in microwave and millimeter wave circuits. Traditional techniques employed to achieve this fil- tering (based on the use of half wavelength short circuit stubs, chip capacitors or cascaded rejection band filters) are either narrow band, increase device area and losses, or degrade circuit performance. These drawbacks have been minimized by the introduction of the Bragg-effect-related EBG concept [3]. Thus, microstrip EBG devices obtained by etching holes or patterns in the ground plane have been found to exhibit wide and deep stopbands [4]–[6]. This technique has been successfully used to achieve broad-band harmonic tuning in power amplifiers, oscillators and mixers; to increase output power and efficiency, Manuscript received September 19, 2003; revised February 25, 2004. This work was supported by DGI and CICYT under Project BFM2001-2001, Project TIC2002-04528-C02-01, Project TIC2001-3163, and Project FIT-070000-2003-933, by Omicron Circuits, and by Conatel, s.l. The review of this letter was arranged by Associate Editor A. Weisshaar. F. Falcone, T. Lopetegi, and M. Sorolla are with the Electrical Engineering Department, Public University of Navarre, Pamplona E-31006, Spain. J. D. Baena and R. Marqués are with the Department of Electronics and Elec- tromagnetism, University of Seville, Seville 41012, Spain. F. Martín is with the Department of Electronic Engineering, University Autònoma of Barcelona, Barcelona 08193, Spain. Digital Object Identifier 10.1109/LMWC.2004.828029 and to reduce spurious harmonic content. The implementation of lowpass filters with huge rejection bandwidth, and the implementation of microstrip bandpass filters with spurious passband suppression, have been also demonstrated [7]. Usually, in all cited applications, EBG structures are inte- grated within the device and no extra circuit area is required. However, EBG’s scale with frequency, require several periods to provide significant rejection and, therefore, can be relatively large for certain frequency/band applications. This problem has been recognized and addressed in [8], [9]. The novel compact EBG structures proposed there produce a high rejection and wide stopband with small length. Nevertheless the transversal dimension of the structure is still large ( at the cutoff fre- quency) since it is based on resonating transversal slots. More- over, the uniform (potentially more compact) configuration ex- hibits significant radiation at the stopband. Recently, negative- and LH structures have appeared as an alternative to EBGs for tailoring the frequency response of microwave devices. As it was theoretically and experimentally demonstrated in [2], [10] a three dimensional periodic structure formed by an array of split ring resonators (SRRs) excited by a properly polarized radiation (i.e., magnetic field parallel to ring axis) is able to inhibit signal propagation in the vicinity of the resonant frequency. This can be interpreted as due to the properties of the periodic medium, which exhibits a high negative effective magnetic permeability in a narrow frequency range around and above the resonance frequency. Actually the SRR was proposed in [10] as a basic particle for the design of artificial negative magnetic permeability media, and it became very popular because it was used in the first physical realization of an LH medium [2]. It is important to note that the inhibition of signal propagation achieved in the abovementioned periodic structure is not due to Bragg-like diffraction, but to the behavior of the constituent particles. Therefore, the period of the structure can be much smaller than the wavelength, in contrast to the case of conventional EBGs. These remarkable properties, together with its planar nature, make the SRR a very interesting particle to implement compact structures in microstrip or CPW technology. In fact, the possibility of designing stopband negative- structures using SRRs has been recently demonstrated [11]. In this letter, the concept of complementary SRRs (CSRRs) is introduced as an alternative for the design of microstrip stop- band structures, based on the introduction of an effective nega- tive- along the line. Originally proposed by Pendry et al. [10], SRRs are small resonant particles with a high quality factor at microwave frequencies. When they are excited by an external 1531-1309/04$20.00 © 2004 IEEE