IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 57, NO. 12, DECEMBER /$ IEEE

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1 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 57, NO. 12, DECEMBER Applications of Open Split Ring Resonators and Open Complementary Split Ring Resonators to the Synthesis of Artificial Transmission Lines and Microwave Passive Components Miguel Durán-Sindreu, Student Member, IEEE, Adolfo Vélez, Francisco Aznar, Member, IEEE, Gerard Sisó, Student Member, IEEE, Jordi Bonache, Member, IEEE, and Ferran Martín, Senior Member, IEEE Abstract This paper is focused on the application of open split ring resonators (OSRRs) and their dual counterparts, open complementary split ring resonators (OCSRRs), to the synthesis of composite right/left-handed transmission lines, that is, artificial lines exhibiting backward wave propagation at low frequencies and forward wave propagation at high frequencies. Due to the small dimensions of these resonators, the resulting lines are very compact. Several artificial lines, with different electrical characteristics and topologies, are reported as illustrative examples. It is shown that these artificial lines can be applied to the synthesis of dual-band components and bandpass filters, and two prototype device examples are designed and fabricated in coplanar waveguide technology: a dual-band impedance inverter applied to a dual-band power divider, and an order-3 wide-band bandpass filter. Finally, it is also demonstrated that OSRRs and OCSRRs can be combined for the synthesis of band pass filters in microstrip technology. Since OSRRs and OCSRRs are described by means of series and shunt resonant tanks, respectively, and they are electrically small, their potential to the design of semi lumped planar microwave devices is very high. Index Terms Artificial transmission lines, dual-band components, metamaterials, microwave filters, open complementary split ring resonators (OCSRRs), open split rings resonators (OSRRs). I. INTRODUCTION ARTIFICIAL transmission lines based on metamaterial concepts, that is, metamaterial transmission lines, have been a subject of growing interest in recent years. Such lines are artificial structures consisting on a host propagating medium loaded with reactive elements. Special efforts have been dedicated to the synthesis of artificial lines exhibiting backward wave transmission at low frequencies and forward wave propagation at high frequencies. These composite right/left-handed lines have been implemented in microstrip [1], [2], coplanar Manuscript received May 13, 2009; revised September 07, First published November 13, 2009; current version published December 09, This work was supported in part by Spain-MEC under Project TEC C02-02 METAINNOVA, in part by the Catalan Government (CIDEM/COPCA) through CIMITEC and under Project VALTEC COMPATIBLE, and in part by the CONSOLIDER-INGENIO 2010 program (Spain-MCI) under Project CSD The authors are with GEMMA/CIMITEC (Departament d Enginyeria Electrònica), Universitat Autònoma de Barcelona Bellaterra (Barcelona), Spain ( ferran.martin@uab.es). Color versions of one or more of the figures in this paper are available online at Digital Object Identifier /TMTT waveguide (CPW) [3], [4], low-temperature co-fired ceramic (LTCC) [5], and monolithic microwave integrated circuit (MMIC) [6] technologies, among others, and two main approaches have been considered for their fabrication: 1) the capacitor and inductor (CL)-loaded approach, where the host line is loaded with series capacitances and shunt inductances (in practice implemented by means of lumped or semi lumped planar components) [1], [3], [5], [6]; and 2) the resonant-type approach [2], [4], where the line is either loaded with split ring resonators (SRRs) [7] and shunt connected inductive elements [4], or with complementary split ring resonators (CSRRs) [8] and series capacitances [2], [9]. Resonant-type artificial lines exhibit a transmission zero to the left of the backward wave transmission band, which is related to the presence of the resonant elements (SRRs or CSRRs) coupled to the line. This transmission zero has been used for the design of compact filters with severe requirements in terms of frequency selectivity [10]. However, in many other applications such transmission zero represents a drawback since it limits the operative bandwidth. In CL-loaded lines, the loading elements and the line elements combined provide a series connected series resonator and a shunt connected parallel resonator to the unit cell of the line, and the transmission zero is located at the origin. In a very recent paper [11], it was demonstrated that similar characteristics as those of CL-loaded lines can be achieved by loading a CPW with electrically small open resonators, that is, open split rings resonators (OSRRs) [12], and open complementary split ring resonators (OCSRRs) [13]. As long as these open resonators are electrically small, the line parasitics do not play a fundamental role, and the unit cell structure can be roughly (although not accurately, as will be discussed later) described by that circuit model of CL-loaded lines. As compared to [11], in this paper we will show improvements in the proposed structures and we will clearly demonstrate that the circuit models describing the novel structures provide an accurate description of the main phenomenology. Moreover, it will be shown that these structures can find many applications in planar microwave device design. Specifically, it will be shown that these lines can be applied to the design of compact wide-band bandpass filters, and dual-band components. Although this paper is mainly focused on devices implemented in CPW technology, it will be also shown that OSRRs and OCSRRs can be combined for the design of microwave /$ IEEE

2 3396 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 57, NO. 12, DECEMBER 2009 Fig. 2. (a) Layout, (b) circuit model, and (c) simplified circuit model of a CPW transmission line loaded with a pair of OCSRRs, where C =2C +2C and L = L =2. The backside strips (in dark grey) connecting the different ground plane regions are necessary to prevent the slot mode of the CPW and the second resonance of the OCSRRs. Fig. 1. Typical layout and circuit model of (a) the OSRR and (b) OCSRR. components in microstrip technology (a prototype device bandpass filter is provided to illustrate this possibility). II. TOPOLOGY AND CIRCUIT MODEL OF THE OPEN SPLIT RING RESONATOR AND OPEN COMPLEMENTARY SPLIT RING RESONATOR The typical topology and circuit model of the OSRR and OCSRR are both depicted in Fig. 1. As was discussed in [12], the OSRR can be modeled as a series LC resonator, where is the inductance of a closed ring of averaged radius and width, and is the distributed capacitance between the inner and outer rings (such element values can be inferred according to the models reported in [14] and [15]). The OCSRR is the complementary counterpart of the OSRR, and it can also be considered as an OCSRR. Such particles (OCSRRs) can be modeled as an open parallel resonant tank (see Fig. 1), where is the inductance of the metallic strip between the ring slots, and is the capacitance of a disk of radius surrounded by a metallic plane at a distance of its edge [14]. Since OCSRRs and OSRRs are complementary particles, it is expected that their resonance frequencies are roughly the same (provided identical dimensions and substrate are considered), as occurs with CSRRs and SRRs. With these latter particles, this aspect has been theoretically demonstrated and experimentally validated in [15]. Let us now consider the model of a CPW transmission line loaded with a pair (in order to avoid the parasitic slot modes) of OCSRRs [Fig. 2(a)]. Although the particle is electrically small, it has been found that the structure exhibits certain frequency shift at resonance. This frequency shift is expected if access lines are present. However, in the absence of access lines, we still obtain a small (although non negligible) phase shift. This means that the OCSRR-loaded CPW can not be merely modeled as a two-port network with a shunt connected parallel resonator. To properly model the structure, we must introduce additional elements to account for the phase shift. That is, we must introduce phase shifting lines at both sides of the resonator. Such transmission line sections can be modeled through series induc- Fig. 3. (a) Layout, (b) circuit model, and (c) simplified circuit model of a CPW transmission line loaded with a series connected OSRR (L = L +2L). tances and shunt capacitances, as depicted in Fig. 2(b). For design purposes, we can also use the simplified model depicted in Fig. 2(c). For a CPW loaded with a series connected OSRR, a similar phenomenology results. Thus, to take into account these parasitic effects, we must introduce additional elements in the twoport network that describes the structure. A typical topology and the circuit model of these OSRR-loaded CPW transmission line sections are depicted in Fig. 3. III. COMPOSITE RIGHT/LEFT HANDED LINES BASED ON OPEN SPLIT RING RESONATORS AND OPEN COMPLEMENTARY SPLIT RING RESONATORS In this section, we will consider the design and fabrication of a composite right/left-handed line implemented by loading a CPW with series connected OSRRs and shunt connected OC- SRRs. Contrary to the structure presented in [11], in the present paper we will implement a quasi-balanced composite right/lefthanded line, namely, an artificial line exhibiting a quasi-continuous transition between the left-handed and the right-handed frequency bands. The topology of the structure is that shown in Fig. 4. Two metallic strips connect the different ground plane regions through vias in order to partially suppress the second resonance of the OCSRR and the generation of the slot mode in the CPW transmission line. In order to design the quasi-balanced composite right/ left-handed line, we must set the transition frequency

3 DURÁN-SINDREU et al.: APPLICATIONS OF OSRRs AND OCSRRs 3397 Fig. 4. Topology of the unit cell of a CPW composite right/left-handed transmission line based on a combination of series connected OSRRs in the external stages and a pair of shunt connected OCSRRs in the central stage. The considered substrate is the Rogers RO3010 with thickness h = 1:27 mm and dielectric constant " = 10:2. Dimensions are: l = 12:3 mm, W = 5mm, G = 1:28 mm. For the OCSRR: r = 2:9 mm, c = 0:5 mm, d = 1:2 mm. For the OSRRs: r =2mm, c = d =0:2mm. Fig. 6. Frequency response of the circuit of Fig. 5(a). The values of the circuit elements are: C = 0:38 pf, L = 2:21 nh, C = 2:6 pf, and L = 15:21 nh. Fig. 5. (a) Canonical T-circuit and (b) -circuit describing the unit cell of a composite right/left-handed transmission line. (i.e., the frequency that separates the left-handed and the right-handed bands) to a certain value. Typically, the characteristic impedance,, in the vicinity of the transition frequency (which is roughly constant) is a design parameter in these artificial lines. Alternatively, we can force two frequencies, and, to exhibit a certain characteristic impedance, for instance (so that maximum transmission is achieved at these frequencies). In the present design, the transition frequency is set to GHz, GHz, and GHz. The canonical circuit models of a composite right/left-handed structure are depicted in Fig. 5. For the T-circuit model, the characteristic impedance is given by and being the series and shunt impedance, respectively, of the T-circuit model. The transition frequency is either given by the series or shunt resonance, which must be forced to be identical in order to balance the structure, namely, The above-cited values of, and can be obtained by setting the elements of the circuit of Fig. 5(a) to pf, nh, pf, and nh. The frequency response of the circuit of Fig. 5(a) with these values of the circuit elements is depicted in Fig. 6. The central reflection zero (maximum transmission) is due to phase matching, namely, there is no phase shift between the input and the output ports, and the injected power is transmitted to the load. The additional reflection zeros (located at 1.6 and 2.8 GHz) are due to impedance matching, that is, at these frequencies. (1) (2) Fig. 7. Characteristic impedance and dependence of the phase constant with frequency for the circuit of Fig. 5(a). The values of the circuit elements are: C =0:38 pf, L =2:21 nh, C =2:6pF, and L =15:21 nh. The characteristic impedance and the dependence of the phase constant with frequency for this structure are depicted in Fig. 7. As predicted by expression (1) for a balanced structure, the characteristic impedance is maximum at. The dispersion diagram reflects the continuous transition between the left-handed and the right-handed band at the transition frequency. Let us now focus on the procedure to implement an OCSRRand OSRR-loaded CPW with the previous characteristics. The first step is to determine an initial layout for the two OSRRs and OCSRR. To this end, we use the model reported in [14] and [15]. Due to the limitations of the model to predict the resonance frequency under real conditions, this initial topology does not exactly provide the required values of the resonator s elements. The second step consists on the optimization of the topology of the OSRRs and OCSRRs in order to obtain the required values of the inductance and capacitance of the resonators. This has been done with the help of a parameter extraction method, applied for each resonator (OSRR and OCSRR) and reported in Appendix I. This parameter extraction technique not only provides the capacitance and inductance of the OSRR and OCSRR, but also the values of the parasitic elements of the models of Figs. 2(c) and 3(c). Obviously, the presence of these elements prevents to exactly obtain the characteristics of the canonical model reported in Figs. 6 and 7. However, we can slightly tune the resonator s topology to fit such characteristics as much as

4 3398 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 57, NO. 12, DECEMBER 2009 Fig. 8. Frequency response of the circuit of Fig. 4. Fig. 10. Dispersion diagram of the circuit of Fig. 4. Fig. 9. Characteristic impedance of the circuit of Fig. 4. The curves have been obtained from the S-parameters, by applying standard formulas to infer the series and shunt impedances of the T-circuit model, and then application of expression (1). possible. This tuning has effect on the inductance and capacitance of the OSRR and OCSRR, but does not significantly affect the parasitics. The final topology of the OSRR- and OCSRR-loaded CPW that fits to the characteristics of the canonical balanced structure is that depicted in Fig. 4 (the Rogers RO3010 substrate with thickness mm and dielectric constant has been used). Due to the presence of the parasitic elements in the models of the OSRR and OCSRR-loaded CPW structures, it is not possible to obtain perfect balance with null phase shift at the central reflection zero frequency [as occurs with the circuit of Fig. 5(a)]. However, since the effect of these parasitics is not very important, we achieve quasi-balance conditions, as shown in Figs The circuit simulation with the extracted parameters, the electromagnetic simulation (inferred by means of the Agilent Momentum commercial software) and the measured insertion and return losses (obtained by means of the Agilent E8364B vector network analyzer) are depicted in Fig. 8. The characteristic impedance and the dispersion diagram are depicted in Figs. 9 and 10, respectively. Since the structure is not perfectly balanced, there is a singularity in the characteristic impedance in the vicinity of. However, the frequencies and where the characteristic impedance is 50 are roughly achieved both in electromagnetic simulation and measurement. IV. DUAL-BAND IMPEDANCE INVERTER BASED ON OPEN SPLIT RING RESONATORS AND OPEN COMPLEMENTARY SPLIT RING RESONATORS This section is focused on the synthesis of a dual-band impedance inverter and on its application to the design of a dual-band Y-junction power divider in CPW technology. The target is to implement a impedance inverter functional at GHz and GHz. The artificial line is designed so that it provides an electrical length of at and at, which leads to at both frequencies and, as inferred from the dispersion relation of the T-circuit model, given by where is the electrical length of the structure. These conditions hence force that and, as reported in [16]. Thus, we need to obtain the series and shunt impedance of the whole structure formed by the cascaded OSRR- OCSRR- OSRR stages. This has been done by calculating the [ABCD] matrices of the equivalent circuits of Figs. 2(c) and 3(c) for the OSRR and the OCSRR, respectively. From this analysis, the series and shunt branch impedances of the equivalent T-circuit model are found to be with (3) (4) (5) (6) (7) (8) (9)

5 DURÁN-SINDREU et al.: APPLICATIONS OF OSRRs AND OCSRRs 3399 Fig. 11. Layout of the dual-band impedance inverter based on a combination of series connected OSRRs in the external stages and a pair of shunt connected OCSRRs in the central stage. The substrate is the Rogers RO3010 with thickness h =0:635 mm and dielectric constant " =10:2. Dimensions are: l =9mm, W =4mm, G =0:74 mm. For the OCSRR: r =0:9mm, c =0:2mm, d =0:2mm. For the OSRRs: r =1:5mm, c =0:3mm, d =0:2mm. The wide metallic strip in the back substrate side has been added in order to enhance the shunt capacitance of the OCSRR stage, as required to achieve the electrical characteristics of the device. Fig. 12. Circuit simulation and electromagnetic simulation of the dual-band impedance inverter. and (10) Fig. 13. Bottom. Photograph of the fabricated dual-band power splitter. (a) Top. (b) (11) By forcing (4) and (5) to take the above cited values at the operating frequencies of the dual-band impedance inverter, four conditions result. However, we have six unknowns. The procedure to determine the element values is as follows: in a first step, we consider that and (the parasitics in the models of Figs. 2(c) and 3(c)) are null, and we obtain the other four element values (which are perfectly determined). Then we generate a layout for the OSRR and OCSRR stages so that the extracted parameters for the resonators are identical to those inferred in the first step. From this layout we infer also the element values of the parasitics, which are introduced in (4) and (5). Then we calculate the other element values in order to satisfy the four cited conditions. Through this procedure, we have obtained the following parameters: pf, nh pf, nh, pf, and nh. Finally, by means of the parameter extraction technique, we have inferred the layout topology of the dual-band impedance inverter that provides these element values (see Fig. 11). The circuit simulation and electromagnetic simulation of the dual-band impedance inverter are shown in Fig. 12. These results reveal that the required characteristics are satisfied. By cascading a 50 input (access) line and two 50 output lines, the dual-band power splitter results. The photograph of this device (fabricated on the Rogers RO3010 substrate with thickness mm and dielectric constant ) is shown in Fig. 13, and the simulated and measured power splitting and matching are depicted in Fig. 14. The required functionality at the two operating frequencies is achieved. Fig. 14. Frequency response of the dual-band power splitter. V. WIDEBAND BANDPASS FILTERS We have also applied the OSRR- and OCSRR-based CPW structure to the design of an order-3 Chebyshev (with 0.02-dB ripple) bandpass filter with central frequency GHz and 35% fractional bandwidth. The element values of the canonical circuit are pf, nh, pf, and nh (for odd-order Chebyshev filters the circuit is symmetric). Following the procedure explained in Section III, we have generated the filter layout shown in Fig. 15. The electromagnetic and circuit simulation of the structure, as well as the ideal Chebyshev filter response are all depicted in Fig. 16. The measured frequency response is also depicted in this figure. The group delay and insertion losses of the electromagnetic simulation and measurement are also depicted in Fig. 17. Good agreement between all the curves results in the region of interest. This filter has been fabricated on the Rogers RO3010 substrate with thickness mm and dielectric constant

6 3400 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 57, NO. 12, DECEMBER 2009 Fig. 18. Circuit model of a microstrip transmission line loaded with an OSRR. Fig. 15. (a) Layout and (b) photograph of the wide-band bandpass filter based on a combination of series connected OSRRs in the external stages and a pair of shunt connected OCSRRs in the central stage. The substrate is the Rogers RO3010 with thickness h = 0:254 mm and dielectric constant " = 11:2. Dimensions are: l = 9mm, W = 5mm, G = 0:55 mm. For the OCSRR: r =1:2mm, c =0:2mm, d =0:6mm. For the OSRRs: r =1:6mm, c = d =0:2mm. Fig. 16. Frequency response of the circuit of Fig. 15. The values of the equivalent circuit are: C =0:19 pf, L =0:4nH, C =0:58 pf, L =5:55 nh, C =3pF, and L =0:94 nh. Fig. 17. Group delay and insertion losses of the circuit of Fig. 15. since it has been found that by using thinner substrates the stop-band response is improved (i.e., the first spurious band is shifted to higher frequencies). In the designed filter, the first spurious band appears at roughly 2.3 times the central filter frequency. Measured filter characteristics are good with insertion losses lower than 1 db between 2.3 and 3.5 GHz, and measured return losses better than 18 db between 2.36 and 3.41 GHz. The dissipation effects of the filter have been experimentally inferred through the Cohn formula [17] (also reported in more recent publications [18]). The averaged unloaded Q-factor of the resonators resulting from this formula is. VI. WIDEBAND BANDPASS FILTERS IN MICROSTRIP TECHNOLOGY In order to demonstrate the possibility of applying OSRRs and OCSRRs (combined) in microstrip technology, we have designed an order-3 Chebyshev band pass filter with a ripple of 0.1 db. The central frequency and fractional bandwidth of the filter are GHz and 50%, respectively. A ground plane window has been etched below the regions occupied by the OSRRs, as was done in [12]. To properly describe the structure, the circuit model of the OSRR must include additional elements as compared to the circuit models shown in Fig. 3 (see Fig. 18). Moreover, the circuit has been found to be asymmetric (this has been corroborated by comparing electromagnetic and circuit simulations). Indeed, this model is also valid for the OSRR-based structures studied in the previous sections (loading a CPW). However, we have found that certain parameters can be neglected (and the circuit is actually symmetric), and for this reason the models shown in Fig. 3 are simplified. Furthermore, it has been found that the OCSRR can be simplified to his canonical model, due to the small phase shift present at the resonant frequency in microstrip technology. The layout of the final filter (which has been inferred in this case by curve fitting since the parameter extraction is more complex), is depicted in Fig. 19. The considered substrate is the Rogers RO3010 with thickness mm and dielectric constant. The simulated and experimental frequency responses of this filter are depicted in Fig. 20. The circuit simulation of the filter, as well as the ideal Chebyshev response, is also included in the figure. The group delay and insertion losses are also depicted in Fig. 21. Again, the different curves are in good agreement in the region of interest. Measured filter characteristics are good, with insertion losses lower than 0.56 db between 1 and 1.6 GHz, and return losses better than 16 db between 1 and 1.61 GHz. In this case, the unloaded Q-factor of the filter resonators has been found to be. With this section we have demonstrated that the application of OSRRs combined with OCSRRs in microstrip technology is also possible.

7 DURÁN-SINDREU et al.: APPLICATIONS OF OSRRs AND OCSRRs 3401 Fig. 19. (a) Layout and (b) photograph of the microstrip filter based on a combination of series connected OSRRs in the external stages and a shunt connected OCSRR in the central stage. The substrate is the Rogers RO3010 with thickness h =0:254 mm and dielectric constant " =11:2. Dimensions are: l =22:3 mm, W =0:21 mm. For the OCSRR: r =2:7mm, c =0:2mm, d =1:2 mm. For the OSRRs: r = 4mm, c = 0:4 mm, d = 0:2 mm. Fig. 20. Frequency response of the circuit of Fig. 19. The values of the equivalent circuit are: L =0:8 nh, L =0:4 nh, L =12:93 nh, C =1:33 pf, C =1:28 pf, C =0:98 pf, L =2nH, C =5:8 nh, L =0nH. Fig. 21. Group delay and insertion losses of the circuit of Fig. 19. VII. DISCUSSION By implementing artificial lines and filters through the combination of open splits ring resonators and open complementary splits ring resonators (as reported in this paper), we obtain clear advantages over the individual configuration, i.e., using a simple type of particles. Size reduction is one relevant aspect. In this regard, wide-band filters have been implemented by means of OCSRRs [13] or OSRRs [19]. In such filters, the resonators are coupled through impedance or admittance inverters, resulting in devices with larger layouts. Moreover, it is also remarkable that the spurious bands in the filters proposed in the present work appear at frequencies significantly higher than the central filter frequency, this resulting in good stop-band behavior. The small size, the stop band behavior and the wide bands achieved with the proposed structures are difficult to obtain simultaneously with conventional filter configurations and even with the structures based on simple resonators [13], [19]. For instance, very wide-band filters (with excellent characteristics in terms of in-band insertion and return losses) can be implemented by means of a host transmission line loaded with equidistant short-circuited stubs [18], but the approach is distributed, and to eliminate the spurious bands (inherent to the structure) additional elements must be included [20]. The present approach is a semi lumped approach, where series and shunt resonators are implemented in a fully planar configuration that allows to roughly synthesizing the canonical model of a bandpass filter, or a composite right/left-handed line. Although the required ratios of inductance and capacitance (in the open resonators considered in this work) for the implementation of ultra-wideband filters (as those reported in [21] [23]) might be too extreme for the synthesis of such filters with the proposed approach, we have demonstrated that wide bandwidths as high as 35% and 50% (for the filters of Figs. 15 and 19, respectively) are achievable. Indeed, it has not been our purpose to implement ultra-wideband filters in the present paper, but the bandwidth limits of the approach have not yet been reached with the filters reported above. To end this section, we would like to point out that the structures reported in this work do not exhibit the typical transmission zero (to the left of the left-handed band) of those composite right/left-handed structures based on SRRs [4] or CSRRs [9]. For the design of filters, such transmission zero can be of interest. However, for the synthesis of other components such as dual-band devices, the transmission zero tends to limit the operating bandwidth of the first band [16]. Thus, the reported composite right left-handed lines based on the combination of OSRRs and OCSRRs are superior than those based on simple split rings. VIII. CONCLUSION In conclusion, we have demonstrated in this paper that OSRRs and OCSRRs can be combined in order to implement composite right/left-handed transmission lines and other microwave components. Specifically, we have designed and fabricated a quasi-balanced composite right/left-handed line in CPW technology, a dual-band Y-junction power divider and a wide-band bandpass filter. We have also designed a wide-band bandpass filter in microstrip technology. Thus, it is clear that the implementation of artificial lines and other microwave components based on a combination of OSRRs and OCSRRs is possible in both CPW and microstrip technologies. A synthesis method, based on a parameter extraction technique

8 3402 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 57, NO. 12, DECEMBER 2009 has been reported. The simulated and measured results are indicative of good device characteristics and small dimensions. With this paper, the short term objectives pointed out in [11] have been satisfied. Nevertheless, many other applications for these OSRR- and OCSRR-based components can be envisaged. Among them, the possibility to apply them to the design of triand quad-band components is being investigated by the authors. APPENDIX I PARAMETER EXTRACTION The parameters of the circuit model of a CPW loaded with an OSRR [Fig. 3(c)] can be extracted from the electromagnetic simulation of the structure following a straightforward procedure. From the intercept of the return losses with the unit conductance circle in the Smith chart, we can directly infer the value of the shunt capacitance according to (12) where is the susceptance in the intercept point. The frequency at this intercept point is the resonance frequency of the series branch (13) To determine the two element values of this branch, another condition is needed. This condition comes from the fact that at the reflection zero frequency (maximum transmission) the characteristic impedance of the structure is 50. In this -circuit, the characteristic impedance is given by (14) Thus, by forcing this impedance to 50, the second condition results. By inverting (13) and (14), we can determine the element values of the series branch. The following results are obtained: (15) (16) The parameters of the circuit model of a CPW loaded with an OCSRR [Fig. 2(c)] can be extracted following a similar procedure. In this case, the intercept of the return losses with the unit resistance circle in the Smith chart gives the value of the series inductance (17) where is the reactance in the intercept point. The shunt branch resonates at this frequency, that is, (18) Finally, at the reflection zero frequency, the characteristic impedance, given by (1) must be forced to be 50. From these two latter conditions, we finally obtain and the element values are determined. ACKNOWLEDGMENT (19) (20) F. Martin would like to thank the ICREA Foundation for giving him an ICREA Academia Award, and the Parc de Recerca UAB and Banco de Santander for giving him a Technology Transfer Chair. REFERENCES [1] C. Caloz and T. Itoh, Novel microwave devices and structures based on the transmission line approach of metamaterials, in IEEE-MTT Int. Microw. Symp. Dig., Philadelphia, PA, Jun. 2003, vol. 1, pp [2] F. Falcone, T. Lopetegi, M. A. G. Laso, J. D. Baena, J. Bonache, R. Marqués, F. Martín, and M. Sorolla, Babinet principle applied to the design of metasurfaces and metamaterials, Phys. Rev. Lett., vol. 93, Nov. 2004, [3] A. Grbic A. and G. V. 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Lett., vol. 16, no. 1, pp , Jan Francisco Aznar (S 08 M 09) was born in Granada, Spain, in He received the degree in electronics engineering from the Universidad de Granada, Granada, Spain, in 2005, and the Ph.D. degree in electronics engineering from the Universidad Autònoma de Barcelona (UAB), Spain, in He has formed part of the Group GEMMA/ CIMITEC of the UAB as Researcher and as Assistant Professor at the UAB. His research interests involve metamaterials and microwave engineering. Gerard Sisó (S 08) was born in Barcelona, Spain, in He received the Industrial Engineering Diploma, specializing in electronics from the Universitat Politècnica de Catalunya, Barcelona, Spain, in 2004, the Electronics Engineering degree from the Universitat Autònoma de Barcelona, Barcelona, Spain, in 2006, and is now working toward the Ph.D. degree at the Universitat Autònoma de Barcelona. His research interests include microwave circuits based on metamaterial transmission lines, especially wideband devices. Jordi Bonache (S 05 M 06) was born in Cardona (Barcelona), Spain, in He received the Physics and Electronics Engineering degrees and Ph.D. degree in electronics engineering from the Universitat Autònoma de Barcelona, Bellaterra (Barcelona), Spain, in 1999, 2001, and 2007, respectively. In 2000, he joined the High Energy Physics Institute of Barcelona (IFAE), where he was involved in the design and implementation of the control and monitoring system of the MAGIC telescope. In 2001, he joined the Department d Enginyeria Electrònica, Universitat Autònoma de Barcelona, where he is currently an Assistant Professor. His research interests include active and passive microwave devices and metamaterials. Miguel Durán-Sindreu (S 09) was born in Barcelona, Spain, in He received the Telecomunications Engineering Diploma, specializing in electronics, from the Universitat Autònoma de Barcelona, Barcelona, Spain, in 2007, the Telecomunications Engineering degree from the Universitat Autònoma de Barcelona in 2008, and is currently working towards the Ph.D. degree in subjects related to metamaterials at the Universitat Autònoma de Barcelona. Adolfo Vélez was born in Santander (Cantabria), Spain, in He received the degree in physics from the Universidad de Santader, Santander, Spain, in He studied for one year in Gent Universiteit, Ghent, Belgium. He is currently working toward the Ph.D. degree in subjects related to metamaterials and microwave circuits at Universitat Autónoma de Barcelona, Barcelona, Spain. He did an internship with Vodafone Spain, working in network deployment projects, in the European Citius Program. Ferran Martín (M 04 SM 08) was born in Barakaldo (Vizcaya), Spain, in He received the B.S. degree in physics and the Ph.D. degree from the Universitat Autònoma de Barcelona (UAB), Barcelona, Spain, in 1988 and 1992, respectively. From 1994 to 2006, he was an Associate Professor in Electronics in the Departament d Enginyeria Electrònica (Universitat Autònoma de Barcelona), and since 2007 he has been a Full Professor of Electronics. In recent years, he has been involved in different research activities including modeling and simulation of electron devices for high-frequency applications, millimeter-wave and THz generation systems, and the application of electromagnetic bandgaps to microwave and millimeter-wave circuits. He is now very active in the field of metamaterials and their application to the miniaturization and optimization of microwave circuits and antennas. He is the head of the Microwave and Millimeter Wave Engineering Group (GEMMA Group) at UAB, and director of CIMITEC, a research Center on Metamaterials supported by TECNIO (Generalitat de Catalunya). He has acted as Guest Editor for three Special Issues on metamaterials in three international journals. He has authored and coauthored over 300 technical conference, letter, and journal papers and he is coauthor of the monograph on metamaterials entitled Metamaterials with Negative Parameters: Theory, Design, and Microwave Applications (Wiley, 2008). He has filed several patents on metamaterials and has headed several development contracts. Prof. Martin has organized several international events related to metamaterials, including Workshops at the IEEE International Microwave Symposium (years 2005 and 2007) and European Microwave Conference (2009). Among his distinctions, he received the 2006 Duran Farell Prize for Technological Research, he holds the Parc de Recerca UAB Santander Technology Transfer Chair, and he has been the recipient of an ICREA ACADEMIA Award.