THE PRESENCE of spurious bands is a fundamental. Microwave Filters With Improved Stopband Based on Sub-Wavelength Resonators

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1 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 53, NO. 6, JUNE Microwave Filters With Improved Stopband Based on Sub-Wavelength Resonators Joan García-García, Ferran Martín, Francisco Falcone, Jordi Bonache, Juan Domingo Baena, Ignacio Gil, Esteve Amat, Txema Lopetegi, Member, IEEE, Miguel A. G. Laso, Member, IEEE, José Antonio Marcotegui Iturmendi, Mario Sorolla, Senior Member, IEEE, and Ricardo Marqués, Member, IEEE Abstract The main aim of this paper is to demonstrate the potentiality of sub-wavelength resonators, namely, split-ring resonators, complementary split-ring resonators, and related structures to the suppression of undesired spurious bands in microwave filters, a key aspect to improve their rejection bandwidths. The main relevant characteristics of the cited resonators are their dimensions (which can be much smaller than signal wavelength at resonance) and their high- factor. This allows us to design stopband structures with significant rejection levels, few stages, and small dimensions, which can be integrated within the filter active region. By this means, no extra area is added to the device, while the passband of interest is virtually unaltered. A wide variety of bandpass filters, implemented in both coplanar-waveguide and microstrip technologies, have been designed and fabricated by the authors. The characterization of these devices points out the efficiency of the proposed approach to improve filter responses with harmonic rejection levels near 40 db in some cases. It is also important to highlight that the conventional design methodology for the filters holds. For certain configurations, the presence of the resonators slightly lowers the phase velocity at the frequencies of interest with the added advantage of some level of reduction in device dimensions. Index Terms Complementarity, coplanar-waveguide (CPW) technology, metamaterials, microstrip, microwave filters, split-ring resonators (SRRs). I. INTRODUCTION THE PRESENCE of spurious bands is a fundamental limitation of microwave filters implemented by means of distributed elements. These undesired frequency bands can seriously degrade filter performance and may be critical in certain applications that require huge rejection bandwidths. Unfortunately, for most filter implementations, the first spurious band is relatively close to the frequency region of interest. For Manuscript received September 30, 2004; revised January 23, This work was supported by the Ministerio de Ciencia y Tecnología under Project Contract BFM , Project Contract TIC C02-01, Project Contract TIC , Project Contract PROFIT , by the European Community (Eureka Program) under Project TELEMAC 2895 and by Omicron Circuits s.l. J. García-García, F. Martín, J. Bonache, I. Gil, and E. Amat are with the Departament d Enginyeria Electrònica, Universitat Autònoma de Barcelona, Bellaterra (Barcelona), Spain. F. Falcone, T. Lopetegi, M. A. G. Laso, and M. Sorolla are with the Electrical and Electronic Engineering Department, Public University of Navarre, E Pamplona, Spain. J. D. Baena and R. Marqués are with the Departamento de Electrónica y Electromagnetismo, Universidad de Sevilla, Seville, Spain. J. A. Marcotegui Iturmendi is with CONATEL s.l. Sancho Ramírez, Pamplona (Navarra), Spain. Digital Object Identifier /TMTT example, in coupled-line bandpass filters, the first spurious band appears at the second harmonic of the central frequency, and is consequence of the different phase velocities of the even and odd modes supported by the coupled lines. In capacitively (gap) or inductively coupled-resonator bandpass filters, an undesired band is also inherently present at due to the resonance condition at this frequency. Finally, the stopband in stepped impedance low-pass filters is limited by the presence of the first spurious band, which is typically too close to the cutoff frequency. These words explain that the rejection of these undesired frequency bands has been a subject of interest for filter designers during years. Traditional techniques include the use of half-wavelength short-circuit stubs, chip capacitors, or cascaded stopband filters. However, these techniques are either narrow-band, increase device area, or introduce significant insertion losses. In coupled-line filters, several approaches based on modified structures, aimed to obtain equal modal phase velocities, have been recently proposed as a means to improve out-of-band filter performance [1] [4]. These approaches are very effective, but are also very specific (i.e., of application in parallel coupled-line filters). Based on the concept of electromagnetic bandgaps (EBGs) [5], numerous studies have been devoted to the suppression of harmonics in a wide variety of microwave circuits, including passives [6] and actives [7]. Apart from this versatility, EBGs can be integrated within the device active region, avoiding the need to cascade additional stages. This is an important aspect to avoid an increase of final layout area. Although effective, frequency selectivity in EBG structures is based on their periodicity (Bragg effect) and several stages are required (typically six or seven) to obtain significant rejection levels. Since the EBG period scales with signal wavelength (Bragg condition), the required dimensions of the structure might be too big for certain applications (specially at moderate or low frequencies). Moreover, EBGs do not provide an easy way to control gapwidth [8]. Nevertheless, EBG structures have been successfully applied to the elimination of multiple spurious bands in microstrip bandpass filters with measured rejection levels above 30 db up to [9]. In this paper, a completely new technique to achieve spurious passband suppression, based on sub-wavelength resonators (namely, split-ring resonators (SRRs) [10], complementary split-ring resonators (CSRRs) [11], and related structures [12]) is presented. From the point-of-view of versatility, the technique (that has been successfully used in microstrip parallel coupled line filters [13]) can be applied to a wide variety of filter types, responses, and technologies including planar /$ IEEE

2 1998 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 53, NO. 6, JUNE 2005 Fig. 1. Basic topologies for the: (a) SRR and (b) CSRR, and relevant dimensions. Metallizations are depicted in gray. (microstrip, coplanar waveguide (CPW), strip line, ) and waveguide technologies. In Section II, it will be described how sub-wavelength resonators, properly coupled to transmission lines, can provide an effective way to reject a frequency band in the vicinity of their quasi-static resonance. The conditions that lead to high resonator-line coupling (and, hence, high rejection levels), as well as the control of rejection band width, will be also discussed in Section II. In Section III, the design procedure of various prototype devices and their simulated and measured frequency responses will be presented. This will include parallel coupled-line bandpass filters in both microstrip and CPW technologies and capacitively coupled resonator bandpass filters in CPW technology. Finally, a discussion and the main conclusions of this study will be highlighted in Sections IV and V. II. REJECTION BAND STRUCTURES BASED ON SUB-WAVELENGTH RESONATORS The sub-wavelength resonators considered in this study are those originally proposed by Pendry et al. [10], namely, SRRs, and their dual counterpart, i.e., CSRRs, which have been recently introduced by Falcone et al. [11]. It will be shown here how these particles, as well as other related resonators derived from their basic topology [12], can inhibit signal propagation if properly polarized. The basic topologies of SRRs and CSRRs are depicted in Fig. 1. The former (SRRs) consist of a pair of concentric metal rings etched on a dielectric slab with apertures in opposite sides. The electromagnetic behavior of SRRs has been studied in previous papers [10], [14]. In brief, if an array of SRRs is illuminated with magnetic-field polarization parallel to the ring axis, currents loops can be induced in the rings. At resonance, these current loops are closed through the distributed capacitance between concentric rings, and incident radiation is reflected back to the source. According to these words, SRRs can be modeled as a parallel LC resonant tank externally driven by a time-varying magnetic field. The capacitance is the series combination of the capacitance between the rings in the upper and lower halves of the SRR, namely,, where is the per-unit length capacitance in the gap between the rings, and is the average SRRs radius [14]. is the total inductance of SRRs, which is adequately defined provided the total current flowing on both rings does not depend on the angle [14]. This quasi-static analysis, which is plausible as far as the size of the particle is small compared to signal wavelength, leads us to term the resonant frequency of SRRs (given by )as quasi-static resonance, to distinguish this from dynamic resonances (present at higher frequencies). It is important to mention that the length of the slits for either ring is not important provided this is not extremely small. Thanks to these slits, the quasi-static behavior of SRRs and, hence, their small electrical size, are possible. This is due to the fact that the relevant capacitance is the edge capacitance between concentric rings, as explained in [14]. With an eye toward further miniaturization, other sub-wavelength resonators have been recently proposed by some of the authors, namely, the broadside coupled split-ring resonators (BC SRRs) [14] and the spiral resonator (SR) [15], [16]. Another interpretation of the filtering properties of an array of SRRs (or other sub-wavelength resonators) relies on the concept of artificial effective media [10]. Since SRRs can be designed with dimensions much smaller than signal wavelength at resonance, the structure can be considered as a continuous medium with effective parameters, where incident radiation is refracted rather than diffracted. Within this interpretation, the inhibition of signal propagation is attributed to the extreme values of magnetic permeability in the vicinity of resonance, i.e., highly positive/negative in a narrow band below/above the quasi-static resonant frequency of the rings. These structures, where effective parameters are achieved by means of a periodic arrangement of constituent particles, are called metamaterials, and are different than EBGs or photonic crystals, where the inhibition of signal propagation is related to periodicity, rather than to the properties of the constitutive elements. The first experimental demonstration of the filtering properties of an array of SRRs in free-space conditions was due to Smith et al. [17]. From this seminal paper, the authors have applied these ideas to obtain stopband structures in planar transmission lines and waveguides. To this end, SRRs must be properly oriented, ideally with their axis parallel to the magnetic-field vector of the propagating modes. In CPW technology, this condition is satisfied either by etching SRRs in the upper metal level, between the central strip and ground planes, or in the back substrate side (bi-metal implementation) underneath the slots. As discussed in [18], higher magnetic coupling between line and rings is achieved by using the second approach, provided thin microwave substrates are employed (in this case, as desired, the magnetic-field lines have a significant component orthogonal to the SRRs plane). Moreover, by etching SRRs in the back substrate side, there is no need to leave wide slot widths to accommodate the rings, and the host transmission line can be easily designed to have a 50- characteristic impedance. This is important to obtain a good matching at the ports and, hence, avoid ripple in the allowed band. Also, by etching SRRs in the back substrate side, the magnetic-field lines penetrate more efficiently the rings circumference, and this favors magnetic coupling. In microstrip technology, SRRs can only be etched in the upper substrate side. To enhance coupling, it is convenient that the separation between line and rings is as small as possible. For this reason, the proposed geometry for SRRs in microstrip technology is the square or rectangle. Finally, SRRs have also been embedded in a hollow metallic waveguide where transmission in the vicinity of resonance has been blocked for those structures with SRRs properly oriented.

3 GARCÍA-GARCÍA et al.: MICROWAVE FILTERS WITH IMPROVED STOPBAND BASED ON SUB-WAVELENGTH RESONATORS 1999 Fig. 2. (a) Layout of the multiple-tuned SRR-CPW stopband structure drawn to scale. (b) Simulated (thin line) and measured (bold line) insertion and return losses. Slot and strip widths are G =0:3mm and W =5:4mm. Actual device length is 4 cm. Simulations have been obtained by means of CST Microwave Studio. Obviously, the rejection level depends on the number of stages and magnetic coupling (to achieve high levels of suppression with few device stages, high magnetic coupling is required). The distance between adjacent SRRs has a direct influence on gapwidth. However, to further control this parameter, multiple tuned structures, where SRRs are designed to have slightly different resonant frequencies within the forbidden band, are needed [19]. In Figs. 2 4, three different SRRs-based structures and their respective frequency responses serve as a proof of the potentiality of SRRs to reject undesired frequency bands. Designed and fabricated multiple tuned structures in CPW and microstrip technologies are depicted in Figs. 2 and 3. The former structure (reported in [19], but included here for coherence and completeness) has been designed by using the parameters of the Arlon 250-LX substrate (, thickness mm), which is appropriate for our purposes since it is relatively thin and magnetic coupling between line and rings is thus enhanced. Ring dimensions have been determined to obtain resonant frequencies equally spaced between GHz. To this end, the model explained in [20] has been used. Actually, this model is valid for SRRs etched on a dielectric slab and radiated with uniform fields. Since these conditions are not fulfilled in a CPW structure, the model has been used to obtain a first estimation of ring dimensions, but these have been finally obtained from full-wave electromagnetic simulations of single SRRs pairs coupled to the line and a sweeping algorithm. The peaked notches in the transmission coefficient clearly reveal the position of the resonant frequency of SRRs. To have an idea of ring dimensions, for the central stage of Fig. 2(a), mm and mm. The other relevant parameters of the structure are indicated in the caption. Fig. 3. (a) SRR microstrip stopband filter. (b) Simulation of the frequency response compared to that obtained for the EBG microstrip line. (c) Measured frequency responses. The separation between concentric rings and their width are c = d =0:3mm for all SRRs. For the smaller SRRs, the edges are 4.1 mm mm, while for the larger SRRs, these dimensions are 4.1 mm mm. Strip-line width is W = 1:17 mm (corresponding to a 50- impedance) and the distance to SRRs (outer edges) is 0.3 mm. For the EBG structure, the period is 12.4 mm, the low-impedance sections (46.3 ) are 1.37-mm wide, whereas the high-impedance sections (56.8 ) are 0.87-mm wide. Fig. 4. Measured frequency response for a rectangular waveguide loaded with a single SRR. Ring dimensions are c = d =0:2mm and r =2mm. The lateral dimensions of the waveguide are 35 mm 2 16 mm. Thus, the design methodology for these stopband structures is based on etching several SRRs with resonant frequencies distributed within the forbidden band (multiple tuning). The rejection level increases with the number of SRRs, but it has

4 2000 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 53, NO. 6, JUNE 2005 been found that a single SRR per tuning frequency suffices to obtain rejection levels above 30 db. Naturally, this depends on the magnetic coupling, according to the line-to-srrs coupling model roughly described in [19] and more detailed in [23]. This rejection is favored by the interaction between adjacent rings, which widens the rejected band per SRR stage. Nevertheless, if one wants to obtain high levels of rejection, the solution is to use several SRR stages per tuning frequency. Thus, the design methodology is simple and does not actually require other equations than those that provide ring dimensions (not univocally determined) from the desired resonant frequency, as is described in the model reported in [14] and [20] (obviously with the particularity that the dimensions have to be tuned by means of an electromagnetic simulator to accurately meet the required resonant frequency, for the reasons explained earlier). The measured frequency response of the structure (obtained by means of an Agilent 8720ET vector network analyzer) reveals the efficiency of the approach to achieve high rejection levels with few SRR stages, even though these stages are tuned at different frequencies (comprised in the GHz range). For the reasons explained earlier, the structure shown in Fig. 3 exhibits rectangular SRRs etched on the upper substrate side of a 50- microstrip line (the Rogers RO3010 substrate has been now considered, i.e.,, thickness mm). The proximity between adjacent rings and tuning allows us to obtain a rejection band as wide as 1 GHz with a central frequency of 4.5 GHz. For comparative purposes, an EBG microstrip structure with similar performance to that shown in Fig. 3 in terms of gapwidth (but with lower rejection) has been also designed and fabricated. Total device length, excluding access lines, is more than two times larger than the SRR-based device. Therefore, the impact of SRRs on compactness is evident. It is also worth mentioning that a rejection level in the vicinity 40 db is achieved thanks to the presence of four SRRs per tuning frequency. Again, we want to highlight that the period of the EBG microstrip structure is half the wavelength at the frequency corresponding to the center of the stopband, whereas the structure shown in Fig. 3 is not periodic and the dimensions of the constituent SRRs are smaller than the EBG period. Indeed, SRRs can be considered as lumped resonators (rather than distributed), this being the key aspect from the point-of-view of their impact on miniaturization. Notice that by considering single-ring split resonators, the circumference is always half the wavelength at resonance. Thus, this single ring operates dynamically, it is not a lumped resonator and its dimensions scale with signal wavelength. Therefore, by using two concentric ring with slits in opposite sides (i.e., SRRs), we obtain an important benefit in terms of compactness, related to the fact that, for the fundamental resonant mode, the SRR operates in the quasi-static regime (even though higher order resonances are also present and are governed by dynamic processes). Finally, in Fig. 4, a hollow metallic waveguide loaded with a single SRR is shown, together with the measured frequency response. Waveguide dimensions provide a cutoff frequency below the resonant frequency of SRRs. Therefore, a notch is expected in the vicinity of that frequency, as confirmed by measurements. Rings have been etched on an Arlon Fig. 5. (a) 50- microstrip line with a square-shaped CSRR etched in the ground plane. (b) Measured frequency response. 250-LX substrate, which has been disposed vertically in the -plane of the guide to achieve magnetic excitation of the SRR at resonance (the waveguide has been excited in the fundamental mode and connected to an Agilent 8510 network analyzer). Let us now focus on CSRRs and their application to stopband structures. These particles are the dual counterparts of SRRs, therefore, according to Babinets principle, a dual behavior for them is expected. This means that an axial time-varying electric field, rather than a magnetic field, is required to excite CSRRs. Indeed, both SRRs and CSRRs are bi-anisotropic particles that can be also excited by time-varying electric and magnetic fields, respectively, applied parallel to the plane of the rings (magnetoelectric coupling) [14]. However, this coupling is softer and the discussion of its origin is out of the scope of this paper. In order to obtain rejection-band structures in planar technology, CSRRs may be etched either in the ground plane or in the conductor strip. The dominant coupling mechanism between line and CSRRs is electric and this can be described by a coupling capacitance, which is essentially given by the line capacitance corresponding to the line section occupied by the CSRR, as is exhaustively explained in [23]. In [23], is also explained that CSRRs can be described by a resonant LC tank, and their resonant frequency roughly coincides to that of an SRR with identical dimensions. In Figs. 5 and 6, two stopband CSRR-based devices are depicted, fabricated in microstrip and CPW technology, respectively. The former is simply a 50- line with square-shaped CSRRs etched in the ground plane underneath the upper strip. By this means, the vertical component of the electric-field vector in the region delimited by CSRRs is high and, hence, the electric coupling. By setting ring dimensions to mm and tuning the external edges in the vicinity of 9.4 mm 5.8 mm, a

5 GARCÍA-GARCÍA et al.: MICROWAVE FILTERS WITH IMPROVED STOPBAND BASED ON SUB-WAVELENGTH RESONATORS 2001 Fig. 6. (a) CPW stopband structure with CSRRs etched in the central strip. (b) Measured frequency response. Ring dimensions are of c = d =0:4 mm and external edges are tuned in the vicinity of 6.6 mm mm. stopband centered at 1.8 GHz is obtained with very high levels of rejection (see Fig. 5). In Fig. 6, a CPW with CSRRs etched in the central strip is depicted. As can be seen, a frequency gap is also opened, in this case, around 3.5 GHz. The flexibility of the CPW technology to obtain a certain line impedance, with slot and strip widths not univocally determined, is interesting because this allows us to etch CSRRs in the central strip (provided this is wide enough) and, hence, the ground planes are not affected. As will be shown latter, this strategy leads us to an elegant and efficient solution for the suppression of spurious bands in CPW coupled-line bandpass filters. To conclude, we would like to mention that SRRs also have their dual counterparts. This means that the advantages of complementarity are compatible with further miniaturization levels, although there is a lack of complementary particle for the BC SRR. III. MICROWAVE FILTERS WITH IMPROVED OUT-OF-BAND PERFORMANCE Here, it will be demonstrated that sub-wavelength resonators can be integrated in microwave filters to reject spurious harmonics and, hence, improve their stopband. Both CPW and microstrip bandpass filters will be designed and fabricated. It will be shown that by simply adding SRRs or CSRRs, properly oriented and tuned, significant rejection levels of the undesired bands are obtained, leaving unaltered the passband of interest. For both the coupled-line bandpass filters and the capacitively coupled half-wavelength resonator bandpass filters considered here, the standard design equations given in [21] have been used. From these equations and the use of a transmission-line calculator (Agilent s Linecalc), the topology of the conventional structures has been determined, while the dimensions of SRRs or CSRRs have been calculated a posteriori by using the previously described multiple tuning procedure, which requires the Fig. 7. (a) Fabricated SRR coupled-line bandpass filter in microstrip technology. (b) Simulated frequency response compared to that obtained in the device without rings. (c) Measured frequency responses. use of an optimizer. As will be explained below, in some cases, it has been necessary to recalculate the layout of the filter to take into account the influence on phase velocity of the SRRs or CSRRs. Parallel coupled-line bandpass filters have been designed in microstrip and CPW technologies with SRRs and CSRRs, respectively, etched in the active device region. The layout of the microstrip prototype, a third-order Butterworth bandpass filter with a central frequency of GHz and 10% fractional bandwidth, is depicted in Fig. 7. Rectangular SRRs have been etched adjacent to the coupled lines in order to reject the first and second spurious bands. Ring dimensions have been determined to obtain stopbands wide enough to achieve effective band suppression. The multiple tuning procedure explained in Section II has been used, although final SRR geometries have been determined by means of an optimization algorithm (integrated within Agilent s Momentum software). The smaller rings (etched in the central stages) are responsible for the rejection of the second

6 2002 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 53, NO. 6, JUNE 2005 Fig. 9. (a) (top and bottom) Fabricated SRR bandpass filter based on capacitively coupled resonators. (b) Simulated (thin lines) and measured (bold lines) frequency response corresponding to the SRR device. (c) Frequency response measured in the device without the presence of the SRRs. Fig. 8. (a) Fabricated CSRR coupled-line bandpass filter in CPW technology. (b) Simulated frequency response compared to that obtained in the device without rings. (c) Measured frequency responses. spurious band, whereas the first undesired band is rejected by the action of the larger SRRs, which are allocated in the first and fourth filter stages. The device has been fabricated in a Rogers RO3010 substrate by means of a standard photo/mask etching technique, and the frequency response has been measured by means of the Agilent 8720ET vector network analyzer. The results are also represented in Fig. 7 jointly with simulation data (obtained by means of the Agilent Momentum commercial software). In comparison to the conventional device, the first spurious band is rejected with attenuation levels near 40 db, while insertion losses in the second band are clearly below 20 db. This efficiency can be attributed to the significant number of SRRs pairs distributed along the device, which is possible by virtue of their small electrical size. It is also worth mentioning that the use of square or rectangular shaped SRRs enhances magnetic coupling between line and rings, and this allows further rejection levels, as compared to circular SRRs [13], [22]. In this and the following results, the slight discrepancies between simulation and measurement are attributed to the small values of and, which are near the resolution limits of the fabrication process 0.1 mm. In Fig. 8, a coupled-line bandpass filter fabricated in CPW technology (Rogers RO3010 substrate) is depicted. In this device (a third-order Butterworth 10% fractional bandwidth central frequency GHz), square-shaped CSRRs have been etched in the coupled-line strips with the aim to eliminate the first and second harmonic bands. According to the frequency response, also shown in Fig. 8, suppression levels above 20 db up to 5 GHz have been achieved, while the passband is scarcely affected. This points out the efficiency of the technique, this time with CSRRs etched in the conductor strips. The suppression of spurious bands is clearly better than in the case of SRRs etched in the back substrate side, as was done in [22] The added advantage of the structure of Fig. 8 is that the back substrate side is not affected, except by the presence of the via bridges that are required in these type of structures to avoid the generation of parasitic modes. We have also designed and fabricated (in a Rogers RO3010 substrate) an SRR bandpass filter based on capacitively coupled half-wavelength resonators and implemented in CPW technology. The photograph can be seen in Fig. 9 together with the frequency response (simulation and measurement). As compared to the frequency response of the ringless device, the first spurious band is substantially attenuated. In this case, the elimination of the first spurious band has been pursued. Since the employed substrate is relatively thick mm, magnetic coupling between the line and rings is softer and more SRRs are required to achieve an acceptable level of attenuation of the undesired bands.

7 GARCÍA-GARCÍA et al.: MICROWAVE FILTERS WITH IMPROVED STOPBAND BASED ON SUB-WAVELENGTH RESONATORS 2003 To conclude, we want to point out that the elimination of spurious passbands has been also applied with success to stepped impedance low-pass filters, as has been reported in [22]. This and previous implementations of this section illustrate the potentiality of sub-wavelength resonators to improve the out-of-band performance of microwave filters. The key advantages over previous techniques are: 1) versatility (i.e., application in a wide variety of scenarios including CPW and microstrip technologies); 2) efficiency (rejection levels above 30 db have been demonstrated); and 3) small dimensions (as a consequence of their small electrical size and the possibility of being integrated within the active device region). For these reasons, the proposed technique has been patented. 1 IV. DISCUSSION In the previous prototype device bandpass filters, the frequency band of interest is not substantially affected by the presence of the rings. This is an important aspect to highlight and is related to the high- factor of SRRs (and CSRRs). In other words, the signal ignores the presence of the rings, unless its frequency is very close to the nominal resonant frequency of SRRs. These are tuned in the vicinity of the first spurious band and, hence, the frequency response in the operative band is not altered. However, the presence of the rings (SRRs) in close proximity to the line (CPW or microstrip) or the CSRRs etched in the conductor strip (or ground planes) may lead to certain frequency dispersion. Depending on the dispersion level, the geometry of the structures should be recalculated. In this regard, the microstrip bandpass filter reported in [13] and [22], where circular SRRs were etched close to the conductor strip, has identical dimensions than the structure with SRRs removed, and the passbands of interest are undistinguishable. For the microstrip bandpass filter of Fig. 7, where rectangular-shaped SRRs are employed, it has been necessary to slightly reduce device dimensions (5%) to maintain the same passband characteristics than in the filter without SRRs. Finally, for the CPW parallel coupled-line filter of Fig. 8, 10% reduction, as compared to the conventional device (i.e., without CSRRs), has been necessary to obtain the same bandwidth and central frequency. These results indicate that dispersion is very soft for the microstrip filter with circular SRRs, it increases when these rings are replaced by rectangular shaped SRRs (Fig. 7), and it is more pronounced for the CSRR-loaded CPW structure (Fig. 8). This behavior is interpreted from the effects of each resonator type on line characteristics. Namely, with rectangular SRRs, substantial rejection is achieved at resonance, but it is also expected a nonnegligible effect of these rings on phase velocity due to the proximity of SRRs to the line. With circular SRRs, these effects are of less importance since, on average, the distance between the line and rings is higher. This may explain that, by using rectangular SRRs, a recalculation of device dimensions is necessary to maintain the same frequency characteristics in the passband region. On the other hand, it is believed that, for the CPW structure of Fig. 8, the presence of CSRRs, etched on the coupled-line strips, 1 The application of sub-wavelength resonators to planar circuits and antennas is patent pending. may lead to higher variations of the electrical parameters of the line (as compared to the ringless structure) and, hence, to further decrease in device dimensions. In order to gain further insight on dispersion, we have obtained the ratio of the phase constants obtained in a microstrip line with square-shaped SRRs (Fig. 3) and in the same line without SRRs for half the resonant frequency of the rings. The result, which has been inferred from the simulated phase of (by using Agilent s Momentum) and coincides with the ratio between the phase velocities at that frequency has been found to be. This result is coherent with a 5% reduction in device dimensions for the microstrip bandpass filter loaded with rectangular SRRs, where the central frequency is approximately half the resonant frequency of the rings. This procedure has been also applied to the structure shown in Fig. 6. In this case, the ratio of phase constants for both the CSRR loaded and unloaded lines has been found to be, which is in reasonable agreement with a 10% reduction in filter dimensions (structure of Fig. 8). Obviously, the values of obtained for the cited transmission-line structures (Figs. 3 and 6) do not perfectly match the compactness factor for the filters of Figs. 7 and 8 because these filters are based on coupled-line stages. However, this qualitative analysis points out that certain dispersion may take place and must be considered for accurate filter designs. In practice, to determine the dimensions of the filters of Figs. 7 and 8, we have tuned each coupled-line section to obtain the desired electric lengths at the central filter frequency and the required coupling factors (which can be inferred from ) to achieve the specified bandwidth. To this end, Agilent s Momentum software has been used, and the geometry of the coupled line sections corresponding to the conventional designs has been used to startup tuning,. For the structure of Fig. 9, this procedure has not been applied (i.e., device dimensions coincide with those of the ringless structure), but the passband has not been shifted by the presence of the rings. From the simulated and measured frequency responses of the prototype device filters shown here, it is very clear that the passband of the structures can be maintained unaltered and, if dispersion is present, rather than a disadvantage, this contributes to a certain level of device miniaturization. V. CONCLUSIONS In summary, a new approach for the rejection of undesired bands in microwave filters, based on coupled sub-wavelength resonators, has been proposed. This paper has shown that SRRs and their dual counterparts (i.e., CSRRs) properly coupled to CPWs or microstrip transmission lines provide an efficient way to inhibit signal propagation in the vicinity of their quasi-static resonant frequency. Whereas magnetic coupling between the line and rings leads to the filtering properties of SRR-based transmission lines, it has been shown that CSRRs need an electric field to be excited. From these arguments, the most suitable orientations of both SRRs and CSRRs in different transmission-line configurations have been discussed. It has been also demonstrated that the forbidden band of these sub-wavelength resonator based structures (which is intrinsically very narrow) can be substantially widened by tuning the particles to slightly

8 2004 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 53, NO. 6, JUNE 2005 different frequencies (multiple tuning). Due to the deep rejection levels achieved within the gap, sub-wavelength resonators have been applied to suppress harmonic bands in conventional microwave filters. Specifically, parallel coupled-line bandpass filters and capacitively coupled resonator bandpass filters with improved out-of-band performance have been designed and fabricated. Measured rejection levels of the first spurious band of such filters 30 db are indicative of the efficiency of the technique. Also remarkable is the invariability of the passband in spite of the presence of sub-wavelength resonators. In all cases, these have been distributed within the active filter region, avoiding the need to cascade additional stages. In some cases, the characteristics of the host transmission lines are modified due to the presence of the rings so that the phase velocity is reduced and, hence, device dimensions. In the opinion of the authors, the most breaking structure is the CPW coupled-line bandpass filter, where CSRR are etched in the strips, thus leaving the ground plane unaltered. Miniaturization (due to subwavelength operation of SRRs and CSRRs), the high levels of rejection, and the possibility to control gapwidth by fine tuning are key aspects that make this technique very promising for the elimination of undesired bands in microwave filters. Moreover, the technique can be applied to a wide variety of structures (including CPW and microstrip transmission lines) and filter types. For this reason, it is believed that the ideas presented in this paper can be of interest in practical applications of microwave filters. ACKNOWLEDGMENT The authors thank the European Community and Omicron Circuits s.l. for their support. REFERENCES [1] C. Person, A. Sheta, J. Ocupes, and S. Toutain, Design of high performance band pass filters by using multilayer thick film technology, in Proc. 24th Eur. Microwave Conf., vol. 1, Cannes, France, Sep. 1994, pp [2] J. T. Kuo and M. Jiang, Suppression of spurious resonance for microstrip band pass filters via substrate suppression, in Asia Pacific Microwave Conf., Kyoto, Japan, 2002, pp [3] M. L. Roy, A. Perennec, S. Toutain, and L. C. Calvez, Continously varying coupled transmission lines applied to design band pass filters, Int. J. RF Microwave Computer-Aided Eng., vol. 12, pp , May [4] J. T. Kuo and W. Hsu, Parallel coupled microstrip filters with suppression of harmonic response, IEEE Microw. Wireless Compon. Lett., vol. 12, no. 10, pp , Oct [5] E. Yablonovitch, Photonic bandgap structures, J. Opt. Soc. Amer. B, Opt. Phys., vol. 10, pp , Feb [6] T. Lopetegi, M. A. G. Laso, J. Hernández, M. Bacaicoa, D. Benito, M. J. Garde, M. Sorolla, and M. Guglielmi, New microstrip wiggly-line filters with spurious passband suppression, IEEE Trans. Microw. Theory Tech., vol. 49, no. 9, pp , Sep [7] V. Radisic, Y. Qian, and T. Itoh, Broad-band power amplifier using dielectric photonic bandgap structures, IEEE Microw. Guided Wave Lett., vol. 8, no. 1, pp , Jan [8] M. A. G. Laso, T. Lopetegi, M. J. Erro, D. Benito, M. J. Garde, and M. Sorolla, Novel wide-band photonic bandgap microstrip structures, Microwave Opt. Technol. Lett., vol. 24, pp , Mar [9] T. Lopetegi, M. A. G. Laso, F. Falcone, F. Martín, J. Bonache, L. Pérez- Cuevas, and M. Sorolla, Microstrip wiggly line bandpass filters with multispurious rejection, IEEE Microw. Wireless Compon. Lett., vol. 14, no. 11, pp , Nov [10] J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, Magnetism from conductors and enhanced nonlinear phenomena, IEEE Trans. Microw. Theory Tech., vol. 47, no. 11, pp , Nov [11] F. Falcone, T. Lopetegi, J. D. Baena, R. Marqués, F. Martín, and M. Sorolla, Effective negative-" stop-band microstrip lines based on complementary split ring resonators, IEEE Microw. Wireless Compon. Lett., vol. 14, no. 6, pp , Jun [12] R. Marqués, J. D. Baena, J. Martel, F. Medina, F. Falcone, M. Sorolla, and F. Martín, Novel small resonant electromagnetic particles for metamaterial and filter design, in Proc. Int. Int. Electromagnetics in Advanced Applications Conf., Sep. 2003, pp [13] J. García-García, F. Martín, F. Falcone, J. Bonache, I. Gil, T. Lopetegi, M. A. G. Laso, M. Sorolla, and R. Marqués, Spurious passband suppression in microstrip coupled line bandpass filters by means of split ring resonators, IEEE Microw. Wireless Compon. Lett., vol. 14, no. 9, pp , Sep [14] R. Marqués, F. Medina, and R. R.-E. Idrissi, Role of bianisotropy in negative permeability and left handed metamaterials, Phys. Rev. B, Condens. Matter, vol. 65, pp , Apr [15] J. Baena, R. Marqués, F. Medina, and J. Martel, Artificial magnetic metamaterial design by using spiral resonators, Phys. Rev. B, Condens. Matter, vol. 69, pp , Jan [16] F. Falcone, F. Martín, J. Bonache, M. A. G. Laso, J. García-García, J. D. Baena, R. Marqués, and M. Sorolla, Stopband and band pass characteristics in coplanar waveguides coupled to spiral resonators, Microwave Opt. Technol. Lett., vol. 42, pp , Sep [17] D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Composite medium with simultaneously negative permeability and permittivity, Phys. Rev. Lett., vol. 84, pp , May [18] F. Falcone, F. Martin, J. Bonache, R. Marqués, and M. Sorolla, Coplanar waveguide structures loaded with split ring resonators, Microwave Opt. Technol. Lett., vol. 40, pp. 3 6, Jan [19] F. Martín, F. Falcone, J. Bonache, R. Marqués, and M. Sorolla, Miniaturized coplanar waveguide stopband filters based on multiple tuned split ring resonators, IEEE Microw. Wireless Compon. Lett., vol. 13, no. 12, pp , Dec [20] R. Marqués, F. Mesa, J. Martel, and F. Medina, Comparative analysis of edge and broadside couple split ring resonators for metamaterial design: Theory and experiment, IEEE Trans. Antennas Propag., vol. 51, no. 10, pp , Oct [21] D. M. Pozar, Microwave Engineering. New York: Addison-Wesley, [22] J. García-García, J. Bonache, F. Falcone, I. Gil, J. D. Baena, T. Lopetegi, M. A. G. Laso, F. Martín, R. Marqués, A. Marcotegui, and M. Sorolla, Spurious pass band suppression in microwave filters by means of subwavelength resonant structures, in 34th Eur. Microwave Conf. Dig., vol. II, Amsterdam, The Netherlands, Oct. 2004, pp [23] J. D. Baena, J. Bonache, F. Martín, R. Marqués, F. Falcone, T. Lopetegi, M. A. G. Laso, J. García, I. Gil, and M. Sorolla, Equivalent-circuit models for split-ring resonators and complementary split-ring resonators coupled to planar transmission lines, IEEE Trans. Microw. Theory Tech., vol. 53, no. 4, pp , Apr Joan Garcia-Garcia was born in Barcelona, Spain, in He received the Physics degree and Ph.D. degree in electrical engineering from the Universitat Autònoma de Barcelona, Barcelona, Spain, in 1994 and 2001, respectively. He then became a Post-Doctoral Research Fellow with the Institute of Microwaves and Photonics, The University of Leeds, Leeds, U.K., working under the INTERACT European project. In 2002, he was a Post-Doctoral Research Fellow with the Universitat Autònoma de Barcelona, working under the Ramon y Cajal project of the Spanish Government. In November 2003, he become an Associate Professor of electronics with the Departament d Enginyeria Electrònica, Universitat Autònoma de Barcelona.

9 GARCÍA-GARCÍA et al.: MICROWAVE FILTERS WITH IMPROVED STOPBAND BASED ON SUB-WAVELENGTH RESONATORS 2005 Ferran Martín was born in Barakaldo (Vizcaya), Spain, in He received the B.S. degree in physics and Ph.D. degree from the Universitat Autònoma de Barcelona, Barcelona, Spain, in 1988 and 1992, respectively. Since 1994, he has been an Associate Professor of electronics with the Departament d Enginyeria Electrònica, Universitat Autònoma de Barcelona. He has recently been involved in different research activities including modeling and simulation of electron devices for high-frequency applications, millimeterwave and terahertz generation systems, and the application of EBGs to microwave and millimeter-wave circuits. He is also currently very active in the field of metamaterials and their application to the miniaturization and optimization of microwave circuits and antennas. Francisco Falcone was born in Caracas, Venezuela, in He received the M.Sc. degree in telecommunication engineering from the Public University of Navarre, Navarre, Spain, in 1999, and is currently working toward the Ph.D. degree in telecommunication engineering from the Public University of Navarre. From 1999 to 2000, he was with the Microwave Implementation Department, Siemens-Italtel, where he was involved with the layout of the Amena mobile operator. Since 2000, he has been a Radio Network Engineer with Telefónica Móviles España. Since the beginning of 2003, he has also been an Associate Lecturer with the Electrical and Electronic Engineering Department, Public University of Navarre. His main research interests include electromagnetic-bandgap devices, periodic structures, and metamaterials. Jordi Bonache was born in Barcelona, Spain, in He received the Physics and Electronics Engineering degrees from the Universitat Autònoma de Barcelona, Barcelona, Spain, in 1999 and 2001, respectively, and is currently working toward the Ph.D. degree at the Universitat Autònoma de Barcelona. 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 Departament 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. Juan Domingo Baena was born in El Puerto de Santa María, Cádiz, Spain, in August He received the Licenciado degree in physics from the Universidad de Sevilla, Seville, Spain, in 2001, and is currently working toward the Ph.D. degree at the Universidad de Sevilla. In 1999, he was a Software Programmer with Endesa (providing company of electricity in Spain). In September 2002, he joined the Departamento de Electrónica y Electromagnetismo, Universidad de Sevilla. His current research interests include analysis, design, and measurement of artificial media with exotic electromagnetic properties (metamaterials). Mr. Baena was the recipient of a Spanish Ministry of Science and Technology Scholarship. Ignacio Gil was born in Barcelona, Spain, in He received the Physics and Electronics Engineering degrees from the Universitat Autònoma de Barcelona, Barcelona, Spain, in 2000 and 2003, respectively, and is currently working toward the Ph.D. degree at the Universitat Autònoma de Barcelona. He is also an Assistant Professor with the Universitat Autònoma de Barcelona. His research interests include active and passive microwave devices and metamaterials. Esteve Amat was born in Barcelona, Spain, in He received the Electronic Engineering degree from the Universitat Autònoma of Barcelona, Barcelona, Spain, in He is currently an Assistant Professor of electronics with the Departament d Enginyeria Electrònica, Universitat Autònoma de Barcelona. His main research interest is focused on the analysis of the degradation and breakdown of ultrathin SiO and high- dielectrics films. Txema Lopetegi (S 99 M 03) was born in Pamplona, Navarre, Spain, in He received the M.Sc. and Ph.D. degrees in telecommunication engineering from the Public University of Navarre, Navarre, Spain, in 1997 and 2002, respectively. Since 1997, he has been with the Electrical and Electronic Engineering Department, Public University of Navarre, as an Academic Associate from 1997 to 1999, and as an Assistant Professor since During 2002 and 2003, he was a Post-Doctoral Researcher with the Payload Systems Division, European Space Research and Technology Center (ESTEC), European Space Agency (ESA), Noordwijk, The Netherlands. His current research interests include metamaterials and their applications in microwave and millimeter-wave technologies (electromagnetic-bandgap structures, left-handed media, and SRRs), as well as coupled-mode theory and synthesis techniques using inverse scattering. Dr. Lopetegi was the recipient of a 1999 and 2000 grant from the Spanish Ministry of Education to support the research of his doctoral thesis. Miguel A. G. Laso (S 99 M 03) was born in Pamplona, Spain, in He received the M.Sc. and Ph.D. degrees in telecommunication engineering from the Public University of Navarre, Navarre, Spain, in 1997 and 2002, respectively. Since 2001, he has been an Assistant Lecturer with the Electrical and Electronic Engineering Department, Public University of Navarre. He has been involved in several projects funded by the Spanish Government and the European Union. He was a Post-Doctoral Researcher supported by the Spanish Ministry of Science and Technology with the Payload System Division, European Space Research and Technology Center (ESTEC), European Space Agency (ESA), Noordwijk, The Netherlands, where he was involved with satellite applications of electromagnetic crystals in the microwave range. His current interests include electromagnetic crystals, metamaterials, and periodic structures in planar microwave and millimeter-wave technologies and in the optical wavelength range. Dr. Laso was the recipient of a grant from the Spanish Ministry of Education to support the research of his doctoral thesis from 1998 to 2002.

10 2006 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 53, NO. 6, JUNE 2005 José Antonio Marcotegui Iturmendi was born in Pamplona (Navarra), Spain, in In 1993, he was an Engineer of telecommunication with the Polytechnic University of Catalonia, Catalonia, Spain. In 1996, he was an Associate Professor with the Electric and Electronic Engineering Department, Navarra University Publica, Navarra, Spain. In 1996, he founded CONATEL s.l. Sancho Ramírez, Pamplona (Navarra), Spain, where he is Director of numerous projects. The company develops his activity in telecommunications. Since 2003, CONATEL s.l. Sancho Ramírez has been involved with the Eureka Telemac 2895 Project, developing devices of microwaves making use of SRRs. Since 1996, his research concerns the design of devices of microwave and numerical methods such as finite difference time domain (FDTD). Mario Sorolla (S 82 M 83 SM 01) was born in Vinaròs, Spain, in He received the M.Sc. degree from the Polytechnic University of Catalonia, Catalonia, Spain, in 1984, and the Ph.D. degree from the Polytechnic University of Madrid, Madrid, Spain, in 1991, both in telecommunication engineering. From 1986 to 1990, he designed very high-power millimeter waveguides for plasma heating for the Euratom-Ciemat Spanish Nuclear Fusion Experiment. From 1987 to 1988, he was an Invited Scientist with the Institute of Plasma Research, Stuttgart University, Stuttgart, Germany. He has been involved with microwave integrated circuits (MICs) and monolithic microwave integrated circuits (MMICs) for satellite communications with Tagra, Les Franqueses del Vallés, Spain, and Mier Communications, Barcelona, Spain. From 1984 to 1986, he was an Assistant Lecturer with the Polytechnic University of Catalonia, Vilanova i la Geltrú, Spain. From 1991 to 1993, he was an Assistant Lecturer with the Ramon Llull University, Barcelona, Spain. From 1993 to 2002, he was an Assistant Professor with the Public University of Navarre, Navarre, Spain, where he is currently a Full Professor with the Electrical and Electronic Engineering Department. His research interest include high-power millimeter waveguide components and antennas, coupled-wave theory, quasi-optical systems in the millimeter and terahertz range, and applications of metamaterials and enhanced transmission phenomena to microwave circuits and antennas. Ricardo Marqués (M 95) was born in San Fernando, Cádiz, Spain. He received the Ph.D. degree from the Universidad de Sevilla, Seville, Spain, in He is currently an Associate Professor with the Departamento de Electrónica y Electromagnetismo, Universidad de Sevilla. For many years, his main scientific activity has been in the computer-aided design of planar transmission lines and circuits at microwave frequencies with emphasis in the influence and applications of complex media such as anisotropic dielectrics, magnetized ferrites, and plasmas, as well as bi(iso/aniso)tropic materials. He is also interested in the electromagnetic analysis and characterization of discrete metamaterials, including bianisotropic and left-handed media (LHM). He has been a reviewer for scientific and technical journals and conferences. Prof. Marques has been and/or is a reviewer for the IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES and the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION.