Split Rings for Metamaterial and Microwave Circuit Design: A Review of Recent Developments (Invited Paper)

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1 Split Rings for Metamaterial and Microwave Circuit Design: A Review of Recent Developments (Invited Paper) Miguel Duran-Sindreu, Jordi Naqui, Jordi Bonache, Ferran Martín GEMMA/CIMITEC, Departament d Enginyeria Electronica, Universitat Autonoma de Barcelona, BELLATERRA (Barcelona), Spain Received 6 July 2011; accepted 5 January 2012 ABSTRACT: This article is a review of recent applications of split rings to the design of planar microwave circuits based on metamaterial concepts. The considered resonators, namely, split-ring resonators (SRRs), complementary SRRs (CSRRs), and their open counterparts (OSRRs and OCSRRs), are reviewed, and the equivalent circuit models of artificial lines based on such resonators, including parasitics, are presented and discussed. The second part of the article is devoted to highlight some recent applications of the considered resonators. This will include the design of dual-band components and wideband bandpass filters based on the combination of OSRRs and OCSRRs, the design of tunable components based on cantilever-type SRRs, and the design of CSRR-based differential (balanced) lines with common-mode suppression. VC 2012 Wiley Periodicals, Inc. Int J RF and Microwave CAE 22: , Keywords: split-ring resonators; metamaterials; dual-band components; microwave filters; differential transmission lines I. INTRODUCTION Metamaterial transmission lines are artificial lines loaded with reactive elements. Thanks to the presence of these elements, there are more degrees of freedom, as compared with conventional lines, and it is possible to tailor the dispersion and the characteristic impedance of these lines to implement microwave devices with enhanced performance or with novel functionalities [1 4]. Moreover, in metamaterial transmission lines, the electrical length is no longer related to the physical length of the lines; therefore, these lines are also of interest for device miniaturization. There are two main types of metamaterial transmission lines: (i) those loaded with series capacitances and shunt inductances (CL-loaded lines) [5 7], and (ii) those based on resonant elements, like the split-ring resonator (SRR) [8, 9] or the complementary SRR [10, 11] (CSRR), among others. The latter approach has been called resonant-type approach. We would like to mention that CL-loaded lines based on the lattice network topology have also been recently reported [12, 13], but such lines are complex and further effort is needed for their implementation in monolayer PCB technology [14]. Correspondence to: F. Martín; Ferran.Martin@uab.cat. DOI /mmce Published online 13 April 2012 in Wiley Online Library (wileyonlinelibrary.com). This work is focused on the applications of resonanttype metamaterial transmission lines to the design of planar microwave circuits. Specifically, we will review the recent developments achieved by the authors. This will include the design of dual-band components and wideband filters based on the combination of open SRRs (OSRRs) [15] and open complementary SRRs (OCSRRs) [16, 17], the design of tunable stopband filters based on micro-electro-mechanic systems (MEMS)-type movable SRRs [18], and the design of CSRR-based balanced microstrip lines with common mode noise rejection [19]. The article is organized as follows. In Section II, the fundamentals of metamaterial transmission lines, including the propagation characteristics, and the derivation of the dispersion relation and characteristic impedance, are presented. The resonators considered in this article and the circuit models of the artificial lines based on them are reviewed in Section III. In Section IV, the previous cited applications are reported. Finally, the main conclusions of the work are highlighted in Section V. II. FUNDAMENTALS OF METAMATERIAL TRANSMISSION LINES Metamaterial transmission lines are one-dimensional (1D) homogeneous propagating structures consisting of a host line periodically loaded with reactive elements and exhibiting controllable electromagnetic properties. Although VC 2012 Wiley Periodicals, Inc. 439

2 440 Duran-Sindreu et al. model. In the regions where propagation is allowed, a ¼ 0 (losses are neglected), and (3) rewrites as cos bl ¼ 1 þ Z sðxþ Z p ðxþ (4) Thus, the key aspect in reactively loaded lines is the controllability of the dispersion diagram and the characteristic impedance. The latter is given by the following expression qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Z B ðxþ ¼ Z s ðxþ½z s ðxþþ2z p ðxþš (5) Figure 1 Typical topologies of CL-loaded metamaterial transmission lines. (a) CPW structure loaded with shunt strips and series gaps; (b) microstrip structure loaded with vias and series gaps; (c) microstrip structure loaded with grounded stubs and interdigital capacitors. metamaterial transmission lines are 1D structures, effective constitutive parameters (the effective permittivity, e eff, and permeability, l eff ), can be defined according to the following expressions: Z 0 s ðxþ ¼jxl eff (1) Y 0 p ðxþ ¼jxe eff (2) Z s 0 and Y p 0 being the per unit length series impedance and shunt admittance of the equivalent T- or p-circuit model of the unit cell of the structure. Expressions (1) and (2) result from the mapping between the equations describing TEM wave propagation in planar transmission media and plane wave propagation in isotropic and homogeneous dielectrics (telegraphist s equation) [1 4]. Depending on the signs of Z s 0 and Y p 0, the constitutive parameters of such artificial lines can be both positive, both negative, or of opposite sign, giving rise to forward (right handed) wave propagation, backward (left handed) wave propagation, or inhibiting wave propagation, respectively. Rather than the effective permittivity and permeability, the significant parameters in transmission lines are the electrical length (or phase constant) and the characteristic impedance. In fact, the nature of propagation (forward or backward) in these artificial lines, and the regions where wave propagation is allowed, can be derived without invoking the effective constitutive parameters. They can be simply inferred from the signs of the series and shunt reactances (of the equivalent T- or p-circuit model) and from the dispersion equation [20]: cosh cl ¼ 1 þ Z sðxþ Z p ðxþ where c ¼ aþjb is the complex propagation constant, l is the unit cell length, and Z s and Z p are the series and shunt impedances, respectively, of the equivalent T- or p-circuit (3) for a structure consisting of a cascade of unit cells described by the T-circuit model, and, if the structure is modeled by a p-circuit, by the following expression: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uz s ðxþz p ðxþ=2 Z B ðxþ ¼t (6) 1 þ ZsðxÞ 2Z pðxþ This controllability is superior than that for conventional lines, given the higher flexibility associated with the presence of loading elements. Thus, in the context of this article, metamaterial transmission lines (metalines from now on) are artificial lines, consisting of a host line loaded with reactive elements, which allow further control on phase constant and characteristic impedance, as compared with conventional lines. Homogeneity will not be considered necessary, namely, in certain frequency regions, the unit cell length might not be small enough as compared to the guided wavelength. In 3D artificial media, this loss of homogeneity may be critical, but this aspect is not fundamental in transmission lines. Periodicity is another aspect that we do not consider a due. Thus, in many examples, we will consider a single cell (this is beneficial for size reduction) or even a cascade of different cells (in this latter case, the above equations are no longer valid or do not make sense, but the resulting structures can be useful to satisfy certain requirements or specifications). The first proposed metalines have been implemented by means of the CL-loaded approach, where a host line was loaded with series capacitances and shunt inductances [21, 22]. Such lines can be implemented through lumped circuit elements (smd inductances and capacitances) or by means of semilumped components. Semilumped components mean, in this context, electrically small planar components. Through semilumped components, fully planar configurations can be obtained, although the values of capacitances and inductances that can be implemented are limited. Typical topologies of fully planar CL-loaded lines are depicted in Figure 1. In Figure 1a, a coplanar waveguide (CPW) transmission line is periodically loaded with shunt connected strips (emulating the shunt inductances) and gaps (accounting for the series capacitances). In Figure 1b, where a microstrip line is considered, the shunt strips are replaced with vias. Finally, in Figure 1c, a International Journal of RF and Microwave Computer-Aided Engineering/Vol. 22, No. 4, July 2012

3 Split Rings for Metamaterial and Microwave Circuits 441 Figure 2 Lumped element equivalent T-circuit model of the unit cell of CL-loaded metamaterial transmission lines. microstrip line is loaded with series connected interdigital capacitances and grounded stubs (acting as shunt inductors). In all cases, the lumped element equivalent T-circuit model of the unit cell is that depicted in Figure 2 (this model is valid as long as the distance between the semilumped elements is small). Losses are considered to be negligible, and hence, they are not included in the circuit model. The elements of the model are the line parameters (capacitance, C R, and inductance, L R ), the series capacitance, C L and the shunt inductance, L L. As usual, the subindexes denote the elements responsible for the lefthanded (L) and right-handed (R) bands of these artificial lines. Namely, at low frequencies, the loading elements are dominant and left-handed wave propagation arises in a certain frequency band. At higher frequencies, the loading elements are no longer dominant and wave propagation is forward. Inspection of the dispersion diagram of the circuit of Figure 2, obtained from expression 4 (Fig. 3), reveals that the group velocity is positive in the allowed bands, whereas the phase velocity is negative (backward waves) in the left-handed band, and positive (forward waves) in the right-handed band. Thus, CL-loaded lines do actually exhibit a composite right/left handed (CRLH) behavior [23]. To obtain a purely left-handed line, we would need a cascade of series capacitances alternating with shunt inductances. This corresponds to the dual model of a conventional transmission line, which is well known to exhibit backward waves above a certain cutoff frequency [24]. However, such line cannot be implemented in practice, as a host line is required. The frequency gap present between the left handed and the right Figure 3 Typical dispersion diagram (a) and characteristic impedance (b) of a CL-loaded metamaterial transmission line. The line exhibits a CRLH behavior. handed bands is delimited by the following frequencies (Fig. 3): with x G1 ¼ minðx s ; x p Þ (7) x G2 ¼ maxðx s ; x p Þ (8) 1 x s ¼ p ffiffiffiffiffiffiffiffiffiffiffi L R C L (9) 1 x p ¼ p ffiffiffiffiffiffiffiffiffiffiffi L L C R (10) and the lower (x ) and upper (x þ ) limits of the lefthanded and right-handed bands, respectively, are: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4 þ L R C R ðx 2 s x 6 ¼ þ x2 p Þ 6 1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi L 2 R 2L R C R 2L R C C2 R ðx2 s x2 p Þ2 þ 8L R C R ðx 2 s þ x2 p Þþ16 R ð11þ By designing the structure with identical series and shunt resonance frequencies, the gap disappears and there is a continuous transition between the left-handed and right-handed bands (balance condition). At the transition frequency, the phase velocity is infinity, whereas the group velocity is finite (Fig. 4). The implications of this (out of the scope of this work) have been discussed in detail in Refs. [3, 4]. The characteristic impedance (or image impedance) of these lines, given by expression 5, is: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x L R 1 2 s 2 u x Z B ¼ 2 L2 R x2 1 x2 s t C R 1 x2 p 4 x 2 (12) x 2 International Journal of RF and Microwave Computer-Aided Engineering DOI /mmce

4 442 Duran-Sindreu et al. Figure 5 Typical topology and circuit model of the SRR. The relevant dimensions are indicated. Figure 4 Typical dispersion diagram (a) and characteristic impedance (b) of a balanced CRLH CL-loaded metamaterial transmission line. for CRLH lines based on the model depicted in Figure 2 (see Fig. 3b for a typical representation of the dependence of Z B with frequency), and this expression reduces to sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi L 2 R Z B ¼ L2 R x2 1 x2 s C R 4 x 2 (13) for balanced lines. In this latter case (balanced lines), the impedance is maximum and roughly constant in the vicinity of the transition frequency [3, 4] (see Fig. 4). III. SPLIT RINGS: TOPOLOGIES AND CIRCUIT MODELS The metalines considered in this work are based on pairs of coupled split rings. The coupling between the rings shifts the first resonance frequency downward and, hence, the resulting resonator is electrically small. This small electrical size is fundamental for the design of split-ringbased metamaterials, where homogeneity is a key factor, and for circuit miniaturization. The considered electrically small resonators are the SRR, the CSRR, and their open counterparts, the OSRR and the OCSRR. Let us review the topologies of these resonators and the circuit models of the main artificial lines based on them. A. Split-Ring Resonators The topology of the SRR [8] is depicted in Figure 5. It consists of a pair of metallic rings, etched on a dielectric slab, with apertures in opposite sides. The first resonance of this particle is typically (although not exclusively) excited by means of a time varying axial magnetic field. The structure is, thus, a magnetically driven resonant tank, where the inductance is given by the inductance of a single loop with average radius and the same strip width, L s, and the capacitance is given by the series connection of the distributed (edge) capacitances of the upper and lower halves of the SRR, as reported in Ref. [25] (i.e., C s ¼ C 0 / 4, with C 0 ¼ 2pr o C pul and C pul is the per unit length capacitance between the rings). These resonators can be inductively coupled with a transmission line (typically, a CPW or a microstrip line) to implement a 1D artificial medium exhibiting negative effective permeability in a narrow band above the first resonance frequency. This was demonstrated in Ref. [9], where a CPW was loaded with pairs of SRRs, and the resulting structure was found to exhibit a stopband behavior in the vicinity of resonance that was interpreted as due to the negative effective permeability. If narrow inductive strips are introduced between the central strip and the ground plane (above the positions of the SRRs), the behavior of the structure switches to a bandpass that can be attributed to the coexistence of negative effective permeability and permittivity (due to the inductive strips) in a narrow band, where left-handed wave propagation arises. Nevertheless, these artificial lines can be easily analyzed from the lumped element equivalent circuit models, valid up to frequencies beyond the first resonance frequency of the SRR by virtue of its small electrical size. The circuit model of the unit cell of a CPW structure loaded with pairs of SRRs and inductive strips is depicted in Figure 6a [26]. In this model, L and C account for the line inductance and capacitance, respectively, C s and L s model the SRRs, M is the mutual inductive coupling between the line and the SRRs, and L p is the inductance of the shunt strips. The circuit model of Figure 6a can be transformed to the model of Figure 6b [26] with: L s 0 ¼ 2M 2 C s x 2 o L s C 0 s ¼ 2M 2 x 2 o 2 1 þ L 4L p 1 þ M2 2L pl s (14)! 2 1 þ M2 2L pl s 1 þ L 4L p (15) International Journal of RF and Microwave Computer-Aided Engineering/Vol. 22, No. 4, July 2012

5 Split Rings for Metamaterial and Microwave Circuits 443 Figure 6 Circuit model (unit cell) of a CPW loaded with SRRs and shunt inductive strips (a) and transformed p circuit model (b). Figure 8 Typical topology of the CSRR and circuit model. Figure 7 Layout of the considered CPW structures with SRRs and shunt strips (a) and with SRRs only (b); simulated (through the Agilent Momentum commercial software) and measured transmission coefficient, S 21, and simulated dispersion relation (c). The considered substrate is the Rogers RO3010 with thickness h ¼ 1.27 mm and dielectric constant e r ¼ Relevant dimensions are: rings width c ¼ 0.6 mm, distance between the rings d ¼ 0.2 mm, internal radius r ¼ 2.4 mm. For the CPW structure the central strip width is W ¼ 7 mm and the width of the slots is G ¼ 1.35 mm. Finally, the shunt strip width is 0.2 mm. The results of the electrical simulation with extracted parameters are depicted by using symbols. We have actually represented the modulus of the phase since it is negative for the left-handed line. Discrepancy between measurement and simulation for circuit (a) is attributed to fabrication related tolerances. L 0 ¼ 2 þ L L 2L p 2 L s 0 (16) L p 0 ¼ 2L p þ L 2 (17) Notice that the circuit model (unit cell) of SRR-loaded lines without the presence of the inductive strips is inferred from the circuit of Figure 6a by merely eliminating the inductance L p. In view of the circuit of Figure 6b, just above the resonance frequency of the series connected parallel resonator, where the series reactance is negative and the shunt impedance is dominated by the inductance of the narrow strips, left-handed wave propagation is expected. This has been confirmed from the electromagnetic simulation of the structure reported in Figure 7a (see Fig. 7c), where the dispersion diagram shows that the phase and group velocities are antiparallel in this region and a bandpass arises. Conversely, if the strips are removed (Fig. 7b), a stopband behavior is obtained in the vicinity of resonance. Actually, the structure of Figure 7a exhibits a right-handed behavior at higher frequencies (beyond the depicted frequency region), as the circuit of Figure 6b predicts. This righthanded transmission band arises in that region where the series and shunt impedances are dominated by the line inductance and line capacitance, respectively. We would like to mention to end this subsection that the model of Figure 6a, formerly reported in Ref. [26], is an improved version of the original model of SRR-loaded lines, reported by some of the authors in Ref. [9}. B. Complementary Split-Ring Resonators The CSRR is obtained from the SRR by applying duality, that is, by replacing the metallic regions with air and vice versa [10] (Fig. 8). From duality arguments, it follows that the first resonance frequency of the CSRR can be (although not exclusively) excited by means of an axial time varying electric field, and the resonator can be modeled by means of a resonant tank, where the inductance L s of the SRR model is substituted by the capacitance, C c,of a disk of radius r o -c/2 surrounded by a ground plane at a distance c of its edge and the series connection of the two capacitances C 0 /2 in the SRR model is substituted by the parallel combination of the two inductances connecting the inner disk to the ground [27]. Each inductance is given by L 0 /2, where L 0 ¼ 2pr o L pul and L pul is the per unit length inductance of the CPWs connecting the inner disk to the ground. For infinitely thin perfect conducting screens, and in the absence of any dielectric substrate, it directly follows from duality that the parameters of the circuit models for the SRRs and the CSRRs are related by C c ¼ 4(e o /l o )L s and C 0 ¼ 4(e o /l o )L 0. From the above relations, it is easily deduced that the frequency of resonance of both structures is the same, as it is expected from duality. International Journal of RF and Microwave Computer-Aided Engineering DOI /mmce

6 444 Duran-Sindreu et al. Figure 9 Circuit model (unit cell) of a microstrip line loaded with CSRRs and series gaps (a) and transformed T circuit model (b). CSRR-loaded microstrip lines with CSRRs etched in the ground plane below the conductor strip have been reported [10, 27]. The structure exhibits a stopband behavior similar to that of SRR-loaded lines, but in this case related to the negative effective permittivity. By adding series capacitive gaps to the structure, the behavior switches to a bandpass due to the simultaneous negative permittivity and permeability (caused by the gaps) of the structure in a narrow band [28, 29]. The circuit model of the unit cell of the CSRR-loaded line with gaps included is depicted in Figure 9a [30]. L and C L model the line inductance and capacitance, respectively, L c and C c model the CSRR and the gap is modeled by the series capacitance, C s, and the fringing capacitance, C f, respectively. This model can be easily transformed to that shown in Figure 9b, with: C g ¼ 2C s þ C par (18) C ¼ C parð2c s þ C par Þ C s (19) We have simulated a unit cell structure of a microstrip line loaded with a CSRR and a series gap (Fig. 10a). The result reveals that a left-handed transmission band appears in the region where the series reactance is capacitive and the shunt reactance is inductive. If the gap is removed (Fig. 10b), a stopband behavior in the vicinity of the transmission zero frequency appears. This transmission zero is given by: 1 f z ¼ p 2p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (20) L c ðc þ C c Þ Figure 10 Simulated (through the Agilent Momentum commercial software) frequency responses of the unit cell structures shown in the insets. (a) Microstrip line loaded with CSRRs and series gaps; (b) microstrip line only loaded with CSRRs. The response that has been obtained from circuit simulation of the equivalent model with extracted parameters is also included. Dimensions are: the microstrip line width W m ¼ 1.15 mm, the length D ¼ 8mm andthegapwidthw g ¼ 0.16 mm. The dimensions of the CSRRs are: outer ring width c out ¼ mm, inner ring width c inn ¼ mm, distance between the rings d ¼ 0.24 mm, internal radius r ¼ mm. The considered substrate is the Rogers RO3010 with dielectric constant e r ¼ 10.2 and thickness h ¼ 1.27 mm. The right-handed band expected for the structure with gap is present at frequencies beyond the range shown in the figure. C. Open Split-Ring Resonators and Open Complementary Split-Ring Resonators Open resonators are a different kind of electrically small structures. Figure 11 shows the layouts and equivalent circuit models of the OSRR [15] and the open complementary SRR (OCSRR) [16]. The OSRR is based on the SRR and is obtained by truncating the rings forming the resonator and elongating them outward. The OCSRR is the complementary particle of the OSRR. The resonators shown in Figure 11 can be implemented either in microstrip or in CPW technology [17]. The equivalent circuit model of the OSRR is a series LC resonator, where the inductance is the same as the inductance of the SRR, L s, and the capacitance is the distributed capacitance between International Journal of RF and Microwave Computer-Aided Engineering/Vol. 22, No. 4, July 2012

7 Split Rings for Metamaterial and Microwave Circuits 445 Figure 11 Typical topology and circuit model of the OSRR (a) and OCSRR (b). Figure 13 Topology (a), return loss (b) and frequency response (c) of a typical OSRR loaded CPW structure. The considered substrate is the Rogers RO3010 with thickness h ¼ mm and dielectric constant e r ¼ The dimensions are: W ¼ 5 mm, G ¼ 0.55 mm, r ext ¼1.6 mm, c ¼ d ¼ 0.2 mm. The values of the equivalent circuit are: C ¼ pf, L 0 s ¼ L s þ2l ¼ 5.55 nh, C s ¼ 0.58 pf. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.] Figure 12 Typical topology and circuit model of OSRR- (a)- (c) and OCSRR-loaded (d)-(f) CPWs. the concentric rings, C 0. It means that for given dimensions and substrate, the resonance frequency of the OSRR is half the resonance frequency of the SRR, and hence, the OSRR is electrically smaller than the SRR by a factor of two [15]. Similarly, the equivalent circuit model of the OCSRR is a parallel resonant tank in series configuration, where the capacitance is identical to that of the CSRR, and the inductance is L 0, that is, four times larger than that of the CSRR. Therefore, the OCSRR is electrically smaller than the CSRR by a factor of two. Obviously, under ideal conditions of duality, OSRRs, and OCSRRs of identical dimensions etched onto the same substrate exhibit the same resonance frequency. Let us consider the open resonators loading a transmission line. Specifically, a CPW transmission line is considered because this is the host line used in the examples reported later. The series connected OSRR and the pair of shunt connected OCSRRs are depicted in Figures 12a and 12d, respectively, together with the equivalent circuit models (Figs. 12b and 12e). To properly describe the behavior of the structures, it is necessary to cascade phase shifting lines, which are modeled as shown in the figure. Notice that the circuits can then be transformed to those depicted in Figures 12(c) and 12(f), where L and C must be considered parasitic elements. The structures of Figure 12 are not the unit cells of metalines. However, we can alternatively cascade these cells to implement artificial transmission lines with CRLH characteristics, as will be later demonstrated. Nevertheless, the response of the International Journal of RF and Microwave Computer-Aided Engineering DOI /mmce

8 446 Duran-Sindreu et al. Figure 15 Circuit model (a) and layout (b) of the dual-band impedance inverter based on a combination of series connected OSRR in the external stages and a pair of shunt connected OCSRRs in the central stage. The substrate is the Rogers RO3010 with thickness h ¼ mm and dielectric constant e r ¼ Dimensions are: l ¼ 9 mm, W ¼ 4 mm, G ¼ 0.74 mm. For the OCSRR: r ext ¼ 0.9 mm, c ¼ 0.2 mm, d ¼ 0.2 mm. For the OSRR: r ext ¼ 1.5 mm, c ¼ 0.3 mm, d ¼ 0.2 mm. 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. Figure 14 Topology (a), return loss (b) and frequency response (c) of a typical OCSRR loaded CPW structure. The considered substrate is the Rogers RO3010 with thickness h ¼ mm and dielectric constant e r ¼ The dimensions are: W ¼ 5 mm, G ¼ 0.55 mm, r ext ¼ 1.2 mm, c ¼ 0.2 mm, d ¼ 0.6 mm. The values of the equivalent circuit are: L ¼ 0.32 nh, L 0 p ¼ L p /2 ¼ nh, C 0 p ¼ 2(C p þ C) ¼ 2.85 pf. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.] structures of Figure 12 is shown in Figures 13 and 14. The agreement between the circuit simulation, with extracted parameters according to the method reported in Refs. [17, 31] (and reproduced in the Annex I for completeness), and the electromagnetic simulation is very good. The reflection coefficient, S 11, is also depicted in this figure to demonstrate that the OSRR- or the OCSRRloaded CPWs cannot merely be modeled by series and shunt resonators, respectively. This is apparent as the trajectory of the reflection coefficient in the Smith chart is not located in the unit resistance or conductance circles. IV. APPLICATIONS OF SPLIT RING BASED LINES The aim of this section is to highlight some recent applications of split ring based lines achieved by the authors. Many other applications can be found in Ref. [4]. We will divide this section in three subsections, devoted to show some applications of OSRR/OCSRR, SRR- and CSRRloaded lines, respectively. A. Applications of OSRR/OCSRR-Loaded Lines to Dual-Band Components and Bandpass Filters If parasitics (L and C) in the models of Figure 12 are neglected, it is apparent that by alternating series connected OSRRs and shunt connected OCSRR, we obtain the CRLH line model of Figure 2 (unit cell). In practice parasitics cannot be neglected, but their effects are not very significant, and hence, we have designed CRLH lines based on the combination of OSRRs and OCSRRs. Here, we report as a first example a CRLH line that has been used for the implementation of a dual-band Y-junction power divider [17]. The target has been to implement a 35-X impedance inverter functional at f 1 ¼ 2.4 GHz and f 2 ¼ 3.75 GHz. The artificial line has been designed so that it provides an electrical length of 90 at f 1 and þ90 at f 2, which leads to Z s ¼ Z p at both frequencies f 1 and f 2, as inferred from the dispersion relation of the T- circuit model, given by expression 4. These conditions hence force that Z s (f 1 ) ¼ Z p (f 1 ) ¼ j35.35 X and Z s (f 2 ) ¼ Z p (f 2 ) ¼þj35.35 X, as reported in Ref. [17]. 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] matrix of the equivalent circuit of Figure 15a. From this analysis, the series and shunt branch impedances of the equivalent T-circuit model are found to be: j 1 x 2 L 0 s Z s ¼ C s þ Lx 2 CL 0 s C sx 2 C C s x C s þ Cx 2 CL x 2 L 0 s C s 1 2Cs L L 0 s C s þ 1 x 2 (21) Z p ¼ with jxl 0 p C2 s ð1 x 2 L 0 pc 0 pþc 2 1 þ Cx2 C 2 ðclx 2 C 2 L 2 2C 1 L 1 Þ (22) International Journal of RF and Microwave Computer-Aided Engineering/Vol. 22, No. 4, July 2012

9 Split Rings for Metamaterial and Microwave Circuits 447 and C 1 ¼ C s þ C 1 x2 L 1 ¼ L 0 p þ L x 2 s! x2 1 x 2 p C 2 ¼ 2C s þ C 1 x2 L 2 ¼ 2L 0 p þ L x 2 s! 1 x2 x 2 p (23) (24) (25) (26) x s ¼ p ffiffiffiffiffiffiffiffiffi 1 L 0 s C (27) s 1 x p ¼ p ffiffiffiffiffiffiffiffiffiffi (28) L 0 p C0 p By forcing Eqs. (21) and (22) 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 L and C (the parasitics in the models of Fig. 12 or 15) are null, and we obtain the other four element values (which are perfectly determined). Then, we generate a layout for Figure 16 Circuit simulation and electromagnetic simulation of the dual-band impedance inverter. 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 Eqs. (21) and (22). Then, we calculate the other element values to satisfy the four cited conditions. Through this procedure, we have obtained the following parameters: C ¼ 0.2 pf, L ¼ 0.25 nh, C s ¼ 0.66 pf, L 0 s ¼ 3.74 nh, C 0 p ¼ 2.99 pf and L 0 p ¼ 0.83 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. 15b). The circuit simulation and electromagnetic simulation of the dual-band impedance inverter are shown in Figure 16. These results reveal that the required characteristics are satisfied. By cascading a 50-X input (access) line and two 50-X output lines, the dual-band power splitter results. The photograph of this device (fabricated on the Rogers RO3010 substrate with thickness h ¼ mm and dielectric constant e r ¼ 10.2) is shown in Figure 17, and the simulated and measured power splitting and matching are depicted in Figure 18. The required functionality at the two operating frequencies is achieved. The second example of application of OSRR/OCSRR structures is a bandpass filter. In this case, periodicity is sacrificed as our intention is to implement an order-5 bandpass filter subjected to specifications, that is, a Chebyshev response with central frequency f o ¼ 2 GHz, db ripple and 50% fractional bandwidth. The synthesized filter layout is depicted in Figure 19 (together with the photograph of the fabricated device). The device has been fabricated on the Rogers RO3010 substrate with thickness h ¼ mm and dielectric constant e r ¼ The frequency response of the structure obtained from electromagnetic simulation is compared with the response inferred from the circuit simulation of the model of Figure 15a in Figure 20. The agreement is reasonably good, but this agreement can be further improved if we include an additional inductance, L sh, in the model of the OCSRR, as depicted in Figure 21. This inductance increases by decreasing the width of the metallic strip connecting the central strip of the CPW and the inner regions of the OCSRR, is responsible for the presence of the transmission zero above the pass band and also improves the frequency selectivity at the upper band edge. Many other filters with wideband response have been designed and Figure 17 Photograph of the fabricated dual-band power splitter. (a) Top; (b) Bottom. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.] International Journal of RF and Microwave Computer-Aided Engineering DOI /mmce

10 448 Duran-Sindreu et al. Figure 18 Frequency response of the dual-band power splitter. Figure 20 Frequency response without losses (a) and wideband frequency response (b) of the designed fifth-order filter. The element values for the circuit simulation without considering L sh are: for the external OSRRs: C ¼ pf, C s ¼ pf and L 0 s ¼ nh. For the central OSRR: C ¼ pf, C s ¼ pf and L 0 s ¼ nh. For the OCSRRs: L ¼ nh, C 0 p ¼ 4.5 pf and L 0 p ¼ nh. The modified values of the OCSRR considering the wideband model with the additional parasitic element L sh are (in reference to Figure 21): L ¼ nh, C p ¼ 4.4 pf, L p ¼ nh and L sh ¼ 0.35 nh. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.] Figure 19 Topology (a) and photograph (b) of the designed fifth-order filter. Dimensions are: l ¼ 25 mm, W ¼ 9.23 mm, G ¼ 0.71 mm, a ¼ 0.4 mm, b ¼ mm, e ¼ 0.96 mm and f ¼ 3.2 mm. For the external OSRRs: r ext ¼ 2.5 mm, c ¼ 0.3 mm and d ¼ 0.35 mm. For the central OSRR: r ext ¼ 3.4 mm, c ¼ 0.16 mm and d ¼ 1.24 mm. For the OCSRRs: r ext ¼ 1.4 mm and c ¼ d ¼ 0.3 mm. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.] Figure 21 Wideband circuit of the pair of shunt connected OCSRRs shown in Figure 12(d). fabricated using open resonators [32, 33]. We would also like to mention that by combining the open resonators reported here with other electrically small resonators, the authors have designed quadband components [34] and dual-band bandpass filters [34, 35]. B. Applications of SRR-Loaded Lines to the Design of Tunable Components SRRs are of interest for the design of bandstop filters [36, 37] and bandpass filters [38]. By introducing tunability to these resonators, the possibility of realizing reconfigurable International Journal of RF and Microwave Computer-Aided Engineering/Vol. 22, No. 4, July 2012

11 Split Rings for Metamaterial and Microwave Circuits 449 Figure 22 Typical topology of the tunable SRR based on cantilever-type MEMS. (a) Top view with relevant dimensions. Black and grey parts correspond to anchors and suspended parts (including corrugations), respectively; (b) cross section in the up state; (c) cross section in the down state. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.] Figure 23 Topology of the tunable SRR coupled to a microstrip line with microstrip to CPW transition. The separation between the SRR and the microstrip line is 50 lm; the width of the microstrip line is 400 lm. The photograph of the nonactuated SRR is also shown. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.] components has been demonstrated. Thus, varactor diodes [39, 40] and MEMS switches [41] have been added to the SRR (and also to the CSRR [42, 43]) to implement tunable notch filters and bandpass filters, and tunable components based on barium strontium titanate (BST) thick-films have also been demonstrated [44, 45]. In this article, another type of tunable SRR is considered in more detail and applied to the design of tunable stopband filters: the MEMS-based deflectable cantilever-type SRR, which was presented for the first time in Ref. [18]. The reported tunable resonators based on MEMS typically consist of the resonator plus a MEMS bridge on top of it (or in the gap region) [41, 42, 46], which is electronically actuated and modifies the equivalent capacitance of the whole structure, and hence its resonance frequency. In Ref. [18], a different principle was used, that is, the MEMS structures are part of the resonator. Each ring constituting the SRR has a fixed part (anchor) and a suspended part (membrane), which is curled up in the absence of electrostatic actuation. By applying an external voltage to the anchor with reference to the 500 lm-thick high resistivity silicon substrate, (electrically isolated from the anchor through a 1-lm-thick SiO 2 layer), the rings are deflected down, and the coupling capacitance between the pair of rings is modified (Fig. 22). The movable rings behave, thus, similarly to cantilever-type MEMS. This principle of electrical actuation through the silicon substrate has already been used in RF-MEMS switches [47 49] and extended to reconfigurable antennas and filters [50]. The top view of a typical tunable cantilever type SRR is depicted in Figure 22a. The movable portions of the rings are indicated in grey. Figures 22b and 22c depict the cross-sectional view of the anchor and the cantilever, without (up state) and with (down state) electrostatic actuation, respectively. The details of the fabrication process are out of the scope of this article, but we recommend the interested reader the original paper where these resonators were proposed [18]. The movable SRR of Figure 22a was coupled to a microstrip transmission line (Fig. 23), and the frequency response was measured after applying different voltage combinations to the internal and external rings of the SRR (Fig. 24). The different transmission zeros in the frequency response are indicative of the change in the capacitance of the structure, caused by ring s actuation. In a first-order approximation, each ring in the up state can be modeled as composed of two parts: (i) a portion accounting for the anchor and thus in contact with the SiO 2 layer and (ii) an elevated portion, with an uniform and effective height (h eff ) from the SiO 2 layer, corresponding to the movable part, in contact with the anchor by means of a metallic via. In this model, the effects of rings corrugation are neglected, and the distributed capacitance between the rings in the up state is approximated by the capacitance between noncoplanar (i.e., in a different plane) parallel strips separated a vertical distance h eff. Electromagnetic simulations of the structure, modeled as reported above, by considering h eff as an International Journal of RF and Microwave Computer-Aided Engineering DOI /mmce

12 450 Duran-Sindreu et al. Figure 24 Measured (solid lines) and simulated (dashed lines) frequency response of the structure of Figure 23 for the four different states. The applied voltage for each ring actuation is 30 V. The state of the rings is indicated, where 1 (ring actuation) stands for down state and 0 for up state, and the first bit corresponds to the inner ring. Figure 26 Wideband measured transmission coefficients of the filters of Figure 25 for the extreme switching states. The frequency responses in the region of interest of the filter of Figure 25(a) for the four states are depicted in the inset. For measurement, device ports have been connected through wire-bonding to commercial microstrip to CPW transitions. Solid lines correspond to the filter of Figure 25(a); dash-dotted lines correspond to the filter of Figure 25(b). As frequency decreases, rejection is reduced due to the degradation of the quality factor of the resonators (see [39] for more details). Actuation voltage is 30 V. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.] Figure 25 Tunable stopband filters based on square-shaped short (a) and long (b) cantilever-type SRRs. SRR side length is 1200 lm, ring width 150 lm and ring separation 30 lm. The separation between the SRR and the microstrip line is 25 lm. The actuation voltages are applied to the rings through the bias pads and high resistive lines (HRLs). [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.] adjustable parameter, were carried out by means of the commercial software Agilent Momentum. Good agreement between measurement and simulation for the four states was obtained by choosing h eff ¼ 17 lm. This effective height is substantially smaller than the actual (maximum) elevation of the rings in the up state, which was estimated to be roughly 100 lm. However, this is expected as the perunit length capacitance of the pair of rings decreases dramatically when their separation increases. By cascading the cantilever type MEMS-based SRRs in a microstrip transmission line, tunable stopband filters can be implemented (the rejection level can be controlled by the number of stages). A fabricated prototype device is depicted in Figure 25a. It consists of a stopband filter with two pairs of coupled SRR (the movable parts are depicted in gray). The measured frequency responses corresponding to the four different switching states are depicted in Figure 26. The tuning range is roughly 12%, but it can be enhanced by merely extending the movable portions of the rings (this decreases the capacitance in the up state and hence increases the resonance frequency). To demonstrate this, an identical filter to that of Figure 25a, but with longer cantilevers was fabricated. The tuning range dramatically increases (see Fig. 26, where the measured frequency responses corresponding to the extreme switching states, i.e., all switches up or down, for this new filter are also indicated). In this case, the tuning range is 42%. We would also like to mention that it is possible to control the position of the rejection band at the intermediate states (1.0 and 0.1) through the geometry of the rings (including the dimensions of the movable parts). Finally, by applying different voltage combinations to the different SRRs or by modifying their dimensions bandwidth can also be controlled. As compared to tunable stopband filters based on SRRs and varactor diodes [39], the present filters exhibit better insertion losses in the allowed bands. As compared with other filters based on CSRRs and RF-MEMS bridges on top of them [42], this approach can provide better tunability. C. Applications of CSRRs to the Design of Differential Lines with Common Mode Suppression CSRRs have been used in many applications, including stopband filters [51], bandpass filters [52 54], and diplexers [55], device miniaturization [56], enhanced bandwidth components [57, 58], dual-band components [59], and so forth. In this subsection, a different (and recent) application is considered: the design of differential transmission lines with common-mode noise suppression. Differential (or balanced) lines are of interest for highspeed digital circuits because of their high immunity to noise, low crosstalk and low electromagnetic interference (EMI). However, the presence of common-mode noise in International Journal of RF and Microwave Computer-Aided Engineering/Vol. 22, No. 4, July 2012

13 Split Rings for Metamaterial and Microwave Circuits 451 Figure 27 Topology and circuit model (elemental cell) of a differential line loaded with a CSRR. Figure 29 Circuit model for the even mode with inter-resonator s coupling through C R. Figure 28 (b). Circuit models for the even mode (a) and odd mode differential lines is unavoidable in practical circuits. This unwanted noise can be caused by amplitude unbalance or time skew of the differential signals and must be reduced as much as possible to avoid common-mode radiation or EMI. Therefore, the design of differential lines able to suppress the common-mode noise, while keeping the integrity of the differential signals is of paramount importance. For GHz differential signals, compact common mode filters based on multilayer LTCC [60] or negative permittivity [61] structures have been reported. These structures are compact and provide efficient common-mode rejection over wide frequency bands but are technologically complex. There have also been several approaches for the design of common-mode suppressed differential lines based on defected ground structures. In Ref. [62], dumbbell shaped periodic patterns etched in the ground plane, underneath the differential lines, were used to suppress the even mode by opening the return current path through the ground plane. This has small effect on the differential signals (odd mode), as relatively small current density returns through the ground plane for such signals. In Ref. [63], the same authors achieved a wide stopband for the common mode using U-shaped and H-shaped coupled resonators symmetrically etched in the ground plane. The authors have developed another approach for the design of differential lines with common-mode suppression using CSRRs [19]. The unit cell structure of the proposed differential line is depicted in Figure 27. It consists of a pair of coupled lines with a CSRR symmetrically etched in the ground plane. The circuit model of this structure is also depicted in Figure 27, where C m and L m model the mutual capacitance and inductance between the coupled lines (the other parameters are those of Fig. 9b). The circuit model of Figure 27 explains that the differential signals are insensitive to the presence of the CSRRs, whereas these resonators prevent the transmission of the common mode at certain frequencies. The equivalent circuit model of the structure of Figure 27 under common-mode excitation is depicted in Figure 28a, whereas for the odd mode is depicted in Figure 28b. For the odd mode, the resonator is short circuited to ground, and the resulting model is that of a conventional transmission line. For the even mode, we obtain the same circuit as that of a CSRR-loaded line (Fig. 9b without the presence of C g ), but with modified parameters. Thus, we do expect a similar stopband behavior for the common mode. In terms of field distribution, there is a strong density of electric field lines in the same direction below both lines for the common mode. This causes CSRR excitation and hence a stopband. For the odd mode, the direction of the electric field lines is opposite in both strips of the differential line. If the structure is symmetric, (i.e., the gaps of the CSRRs are aligned with the symmetry plane of the differential lines), the opposite electric field vectors in both lines exactly cancel and the CSRR is not excited. To achieve a wide stopband for the common mode, the strategy is (i) to widen the stopband of the individual unit cell, (ii) to couple the resonators, (iii) to etch resonators with slightly modified dimensions to obtain different transmission zero frequencies within the desired stopband, or (iv) to combine some of these effects. Among the previous strategies, bandwidth enhancement by tightly coupling three identical square-shaped CSRRs has been considered. This geometry provides better inter-resonator coupling as compared with circular CSRRs. By this means, we can improve the rejection bandwidth for the International Journal of RF and Microwave Computer-Aided Engineering DOI /mmce

14 452 Duran-Sindreu et al. Figure 30 Unit cell layout (a) and simulated common mode insertion loss (b) of the device designed to optimize the size. Dimensions are W ¼ 1 mm, S ¼ 2.5 mm, c ¼ 0.2 mm, d ¼ 0.2 mm, and side length ¼ 7.6 mm. Substrate parameters are e r ¼10.2 and h¼1.27 mm. Extracted circuit parameters are L e ¼4.93 nh, C¼1.06 pf, C c ¼5.4 pf and L c ¼1.68 nh. Figure 31 Layout (a) and simulated differential and common mode insertion loss of the designed common mode filter with optimized size (b). Dimensions are W¼1 mm, S¼2.5 mm, c¼0.2 mm, d¼0.2 mm, side length¼7.6 mm, and inter-resonator distance¼0.15 mm. Substrate parameters are e r ¼10.2 and h¼1.27 mm. Extracted circuit parameters are L e ¼4.93 nh, C¼1.06 pf, C c ¼5.4 pf, L c ¼1.68 nh, C R ¼0.11 pf, L o ¼3.16 nh and C o ¼1.26 pf. common mode, but bandwidth can be further improved if wideband resonators are considered. To widen the rejection bandwidth of an individual unit cell, it is necessary to increase the coupling capacitance C and to reduce the inductance L c and capacitance C c of the CSRR as much as possible. To enhance the coupling capacitance C, weakly coupled lines will be considered, as the width of the lines necessary to achieve an odd mode impedance of 50 X is wider. However, this must be done carefully, as the lines must lie inside the inner part of the CSRR to obtain high electric coupling. According to it, we have set a line width of W ¼ 1 mm and a separation between lines of S ¼ 2.5 mm. The corresponding characteristic impedances for the even and the odd mode are Z ce ¼ 57 X and Z co ¼ 50 X, respectively. Notice that both impedances are similar because the lines are weakly coupled, and in consequence, there is a small impedance mismatching between the reference impedance Z 0 and the even mode impedance Z ce. This is a convenient situation, as it has been observed that a high mismatching can degrade the filtering properties of the structure. With respect to the CSRR, square-shaped rings not only increase the inter-csrrs coupling (this can be modeled by adding a capacitance C R, as depicted in Fig. 29) but also the coupling with the line, C. To reduce the inductance and the capacitance of the CSRR, it is necessary to increase the rings width, c, and separation, d. This results in a physically and electrically larger CSRR. Therefore, there exists a trade-off between optimizing either the size or the rejection bandwidth. Thus, as mentioned, we have considered not only wideband (and electrically large) coupled resonators but also coupled CSRRs with narrow interrings distance to optimize the size (at the expense of bandwidth). Let us first consider the design of a stopband filter for the common mode by optimizing the size. To reduce the size of the structure as much as possible, a CSRR with narrow and tiny spaced rings (c ¼ 0.2 mm and d ¼ 0.2 mm) has been considered. These values are close to the limit of the available technology. From the even mode model, the coupling capacitance C has been approximated by the per-unit length capacitance of the coupled lines in the even mode. Then, the external side length of the CSRR has been estimated to obtain a transmission zero frequency located at f z ¼ 1.4 GHz from the model of the CSRR reported in Ref. [27], that relates the capacitance C c and the inductance L c with the width c, distance d, and external radius r ext. Obviously, optimization at layout level has been required due to the previous approximations, being the optimized side length equal to 7.6 mm. The layout of a single unit cell and the corresponding electromagnetic simulation for the common mode insertion loss are depicted in Figure 30. The circuit simulation of the structure with the electric parameters extracted according to the procedure reported in Ref. [64] is also International Journal of RF and Microwave Computer-Aided Engineering/Vol. 22, No. 4, July 2012

15 Split Rings for Metamaterial and Microwave Circuits 453 Figure 32 Photograph of the fabricated common mode filter with optimized size (a) and simulated and measured differential and common mode insertion loss (b). [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.] Figure 33 Unit cell layout (a) and simulated common mode insertion loss of the designed common mode filter with optimized bandwidth (b). Dimensions are W ¼ 1 mm, S ¼ 2.5 mm, c ¼ 1.2 mm, d ¼ 0.8 mm, and side length ¼ 10.8 mm. Substrate parameters are e r ¼ 10.2, h ¼ 1.27 mm. Extracted circuit parameters are L e ¼ nh, C ¼ 0.92 pf, C c ¼ 9.13 pf and L c ¼ 1 nh. depicted in that figure. There is good agreement between the circuit and electromagnetic simulation. To enhance the rejection bandwidth, we have implemented an order-3 structure with tightly coupled CSRRs. A separation of 0.15 mm between CSRRs, a value close to the fabrication limits, has been considered to optimize the rejection bandwidth. The layout of the resulting structure and the simulated responses are shown in Figure 31 (ohmic and dielectric losses have been neglected in the electromagnetic simulation). The coupling capacitance between resonators C R has been considered to be an adjustable parameter, and we have found that the capacitance that provides a better fitting is C R ¼ 0.11 pf. The capacitance C odd and the inductance L odd of the odd model have been found just as the capacitance and the inductance of the considered differential line in the odd mode. A photograph of the fabricated device is shown in Figure 32. Access lines have been added to solder the connectors. A comparison between the electromagnetic simulation (with losses included) and the measurement is depicted in the same figure. Simulations are in good agreement with the measurements. As the two lowest transmission zeros are too close, they degenerate in the same transmission zero frequency when losses are considered. It is clear that differential signals are not altered by the presence of the CSRRs, as the measured insertion loss is lower than 0.1 db. The active area (patterned CSRRs) of the structure is mm 2, that is, 0.28 k g 0.09 k g, where k g is the guided wavelength at the central frequency. The device is thus very small, although bandwidth has not been optimized in this structure. The measured fractional bandwidth at 20 db is 14%. Let us now consider the design of a common mode filter with optimized bandwidth. To enhance the bandwidth, we have considered CSRRs with wider rings and interring s space. The model of the CSRR is not so simple in this case because the resonator cannot be considered to be electrically small. Therefore, we have directly made the optimization at the layout level. Three square-shaped CSRRs separated 0.2 mm, with a side length of 10.8 mm, with rings width c ¼ 1.2 mm and inter-rings separation d ¼ 0.8 mm, suffice to achieve the target. The layout of a single unit cell and the corresponding electromagnetic simulation for the common-mode insertion loss are depicted in Figure 33. The circuit simulation with the extracted electrical parameters is also depicted to show that there is good agreement between the circuit and electromagnetic simulation only near the transmission zero frequency, as expected. The photograph of the third-order filter and the differential and common-mode insertion loss are depicted in Figure 34 (the response of the circuit model with extracted parameters does not match the measurement or electromagnetic simulation, and, for this reason, it is not included). The dimensions of the active region of the structure are mm 2, that is, 0.43 International Journal of RF and Microwave Computer-Aided Engineering DOI /mmce

16 454 Duran-Sindreu et al. Figure 34 Photograph of the fabricated common mode filter with optimized bandwidth (a) and simulated and measured differential and common mode insertion loss (b). Dimensions are W ¼ 1 mm, S ¼ 2.5 mm, c ¼ 1.2 mm, d ¼ 0.8 mm, side length ¼ 10.8 mm and inter-resonator distance ¼ 0.2 mm. Substrate parameters are e r ¼ 10.2 and h ¼ 1.27 mm. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.] Figure 35 Measured eye diagram of the differential line of Figure 34 without CSRRs (a) and with CSRRs (b). [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.] k g 0.14 k g. In this design, the dimensions are larger but the rejection bandwidth is also wider (as compared to the previous design); the measured fractional rejection bandwidth at 20 db is 38%. It is also remarkable that the measured insertion loss for the differential signal is smaller than 0.5 db. To evaluate the degradation of differential signal integrity produced by the CSRRs, the measured eye diagram of the device of Figure 34 and that of the same differential line but without CSRRs patterned in the ground plane, are shown in Figure 35. The main eye diagram parameters are summarized in Table I, from which it is clear that the presence of CSRRs does not produce a significant degradation in the differential signal integrity. As compared to other approaches, the presented common-mode suppression strategy is technologically simple (only two metal levels are used), the resulting commonmode filters are electrically small, provide wide and highrejection stopbands, and their design is simple. V. CONCLUSIONS In conclusion, artificial transmission lines based on metamaterial concepts and implemented by means of split rings have been reviewed. Specifically, we have considered transmission lines based on combinations of OSRRs and OCSRRs, SRR-loaded lines and CSRR-loaded lines. All these lines exhibit a CRLH behavior. Despite the presence of parasitics, OSRR/OCSRR-based lines exhibit a TABLE I Measured Eye Parameters With CSRRs Without CSRRs Eye height mv mv Eye width 385 ps 387 ps Jitter (PP) 15.1 ps 13.3 ps Eye opening factor behavior similar to that of a canonical CRLH line (i.e., similar to that achievable by means of the CL-loaded approach). CRLH SRR- and CSRR-loaded lines exhibit a transmission zero below the first (left handed) transmission band. SRR- and CSRR-loaded lines can also be useful as stopband structures, as these resonators inhibit signal propagation in the vicinity of their resonance frequency. In this article, we have reviewed some applications of these SRR- and CSRR- loaded lines as stop band structures. Specifically, the possibility to implement tunable stopband filters on the basis of cantilever-type movable SRRs, as well as the potentiality of CSRRs to the design of balanced lines with common mode suppression, has been reviewed. Concerning the applications of OSRR/ OCSRR-loaded lines, it has been shown that these lines are of interest for the design of wideband filters and dualband components. In summary, several applications of split ring-based lines in the field of microwave circuit International Journal of RF and Microwave Computer-Aided Engineering/Vol. 22, No. 4, July 2012

17 Split Rings for Metamaterial and Microwave Circuits 455 design, recently achieved by the authors, have been presented. Much activity in this field has been already carried out by the authors and other groups, but there is still much space for continuing the research in this field and generate innovative ideas and concepts. ACKNOWLEDGMENTS This work has been supported by MICIIN (Spain) through the projects TEC METATRANSFER and EMET CSD of the CONSOLIDER Ingenio 2010 Program. Special thanks are also given to Generalitat de Catalunya for funding CIMITEC and for supporting GEMMA through the project 2009SGR-421. ANNEX I The parameters of the circuit model of a CPW loaded with an OSRR (Fig. 12c) can be extracted from the electromagnetic simulation of the structure following a straightforward procedure. From the intercept of the return loss with the unit conductance circle in the Smith chart, we can directly infer the value of the shunt capacitance according to: C ¼ B 2xj Zs¼0 (29) where B is the susceptance in the intercept point. The frequency at this intercept point is the resonance frequency of the series branch: x 2 Zs¼0 ¼ 1 C s L 0 s (30) 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 x z (maximum transmission) the characteristic impedance of the structure is 50 X. In this p-circuit, the characteristic impedance is given by expression 6. Thus, by forcing this impedance to 50 X, the second condition results. By inverting Eqs. (6) and (30), we can determine the element values of the series branch. The following results are obtained: " # x 2 z 1 C s ¼ x 2 1 j Zs¼0 2Z0 2x2 z C þ C 2 L 0 s ¼ 1 x 2 j Zs¼0 C s (31) (32) The parameters of the circuit model of a CPW loaded with an OCSRR (Fig. 12f) can be extracted following a similar procedure. In this case, the intercept of the return loss with the unit resistance circle in the Smith chart gives the value of the series inductance: L ¼ v 2xj Zp!1 (33) where v is the reactance in the intercept point. The shunt branch resonates at this frequency, that is: x 2 Zp!1 ¼ 1 L 0 p C0 p (34) Finally, at the reflection zero frequency (x z ), the characteristic impedance, given by Eq. (5) must be forced to be 50 X. From these two latter conditions, we finally obtain: " # L 0 p ¼ x 2 z Z0 2 x 2 1 j Zp!1 2x 2 z L þ L 2 C 0 1 p ¼ x 2 j Zp!1 L0 p (35) (36) and the element values are determined. The parameter extraction methods for CSRR- and SRRloaded lines are reported in Refs. [64, 65], respectively. They are similar to the method reported in this annex but are not reproduced to avoid further extension of the article. REFERENCES 1. G.V. Eleftheriades and K.G. Balmain Editors, Negativerefraction metamaterials: fundamental principles and applications, Wiley, New York, N. Engheta and R.W. Ziolkowski Editors, Metamaterials: Physics and engineering explorations, Wiley, New York, C. Caloz and T. Itoh, Electromagnetic metamaterials: Transmission line theory and microwave applications, Wiley, New York, R. Marques, F. Martín and M. Sorolla, Metamaterials with negative parameters: Theory, design and microwave applications, Wiley, New York, K. Iyer and G. V. Eleftheriades, Negative refractive index metamaterials supporting 2-D waves, In IEEE-MTT Int l Microwave Symp., Vol. 2, Seattle, WA, pp , June A.A. Oliner, A periodic-structure negative-refractive-index medium without resonant elements, In URSI Digest, IEEE- AP-S USNC/URSI National Radio Science Meeting, San Antonio, TX, pp. 41, June 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, In Proc. IEEE-AP-S USNC/ URSI National Radio Science Meeting, Vol. 2, San Antonio, TX, pp , June J.B. Pendry, A.J. Holden, D.J. Robbins, and W.J. Stewart, Magnetism from conductors and enhanced nonlinear phenomena, IEEE Trans Microwave Theory Tech 47, , November F. Martín, F. Falcone, J. Bonache, R. Marques, and M. Sorolla, Split ring resonator based left handed coplanar waveguide, Appl Phys Lett 83 (2003), F. Falcone, T. Lopetegi, J.D. Baena, R. Marques, F. Martín, and M. Sorolla, Effective negative-e stop-band microstrip lines based on complementary split ring resonators, IEEE Microwave Wireless Compon Lett 14 (2004), International Journal of RF and Microwave Computer-Aided Engineering DOI /mmce

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19 Split Rings for Metamaterial and Microwave Circuits A. Velez, J. Bonache, and F. Martín, Varactor-loaded complementary split ring resonators (VLCSRR) and their application to tunable metamaterial transmission lines, IEEE Microwave Wireless Compon Lett 18 (2008), M. Gil, C. Damm, A. Giere, M. Sazegar, J. Bonache, R. Jakoby, and F. Martín, Electrically tunable split-ring resonators at microwave frequencies based on barium-strontium titanate thick-film, Electron Lett 45 (2009), M. Gil, C. Damm, M. Maasch, M. Sazegar, A. Giere, F. Aznar, A. Velez, J. Bonache, R. Jakoby, and F. Martín, Tunable sub-wavelength resonators based on barium-strontium-titanate thick-film technology, IET Microwaves Antennas Propag 5 (2011), T. Hand and S. Cummer, Characterization of tunable metamaterial elements using MEMS switches, IEEE Antennas Wireless Propag Lett 6 (2007), C. Siegel, V. Ziegler, B. Schonlinner, U. Prechtel, and H. 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Wu, A broadband and miniaturized common-mode filter for gigahertz differential signals based on negative-permittivity metamaterials, IEEE Trans Microwave Theory Tech 58 (2010), W.T. Liu, C.-H. Tsai, T-W. Han, and T-L. Wu, An embedded common-mode suppression filter for GHz differential signals using periodic defected ground plane, IEEE Microwave Wireless Compon Lett 18 (2008), S.-J. Wu, C.-H. Tsai, T.-L. Wu, and T. Itoh, A novel wideband common-mode suppression filter for gigahertz differential signals using coupled patterned ground structure, IEEE Trans Microwave Theory Tech 57 (2009), J. Bonache, M. Gil, I. Gil, J. Garcia-García, and F. Martín, On the electrical characteristics of complementary metamaterial resonators, IEEE Microwave Wireless Compon Lett 16 (2006), F. Aznar, M. Gil, J. Bonache, J.D. Baena, L. Jelinek, R. Marques, and F. Martín, Characterization of miniaturized metamaterial resonators coupled to planar transmission lines, J Appl Phys 104 (2008), paper BIOGRAPHIES Miguel Duran-Sindreu was born in Barcelona, Spain, in He received the Telecommunications Engineering Diploma (specializing in electronics), the Telecommunications Engineering degree and the Ph.D. from the Universitat Autonoma de Barcelona, Barcelona, Spain, in 2007, 2008, and 2011, respectively. His research interests are passive microwave devices based on metamaterials, microwave filters and multiband components. Jordi Naqui was born in Granollers, Spain, in He received from the Universitat Autonoma de Barcelona (UAB) the Telecommunication Technical Engineering Diploma (specialty in Electronics) in 2006, the Telecommunication Engineering Degree in 2010, and the Micro and Nanoelectronics Engineering Master in He has prepared documentation of broadcasting equipment in Mier Comunicaciones, he has researched on automotive antennas in International Journal of RF and Microwave Computer-Aided Engineering DOI /mmce

20 458 Duran-Sindreu et al. Ficosa International, and he has been working as a telecommunication engineering consultant in Sayos & Carrera. Currently, he is working toward his Ph.D. degree on innovative passive microwave devices based on metamaterial concepts at CIMITEC (UAB). Jordi Bonache 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 Autonoma 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 Electronica, Universitat Autonoma de Barcelona, where he is currently an Assistant Professor. His research interests include active and passive microwave devices and metamaterials. Ferran Martín was born in Barakaldo (Vizcaya), Spain, in He received the B.S. degree in physics and the Ph.D. degree from the Universitat Autonoma 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 Electronica (Universitat Autonoma 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 more than 350 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. Since 2012, he is Fellow of the IEEE. International Journal of RF and Microwave Computer-Aided Engineering/Vol. 22, No. 4, July 2012