3882 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 58, NO. 12, DECEMBER 2010

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1 3882 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 58, NO. 12, DECEMBER 2010 Planar Multi-Band Microwave Components Based on the Generalized Composite Right/Left Handed Transmission Line Concept Miguel Durán-Sindreu, Student Member, IEEE, Gerard Sisó, Student Member, IEEE, Jordi Bonache, Member, IEEE, and Ferran Martín, Senior Member, IEEE Abstract This paper is focused on the design of generalized composite right/left handed (CRLH) transmission lines in a fully planar configuration, that is, without the use of surface-mount components. These artificial lines exhibit multiple, alternating backward and forward-transmission bands, and are therefore useful for the synthesis of multi-band microwave components. Specifically, a quad-band power splitter, a quad-band branch line hybrid coupler and a dual-bandpass filter, all of them based on fourth-order CRLH lines (i.e., lines exhibiting 2 left-handed and 2 right-handed bands alternating), are presented in this paper. The accurate circuit models, including parasitics, of the structures under consideration (based on electrically small planar resonators), as well as the detailed procedure for the synthesis of these lines using such circuit models, are given. It will be shown that satisfactory results in terms of performance and size can be obtained through the proposed approach, fully compatible with planar technology. Index Terms Composite right/left handed transmission lines, dual-band filters, metamaterials, multi-band components, open complementary split ring resonators, open split ring resonators. I. INTRODUCTION T HE concept of composite right/left handed transmission line was introduced in [1], [2] to designate those artificial lines exhibiting backward (or left handed) wave propagation at low frequencies and forward (or right handed) wave propagation at high frequencies. Such lines have been implemented in microstrip [3], CPW [4], LTCC [5] and MMIC [6] technologies, among others, by loading a host line with series capacitances and shunt inductances. Alternatively, CRLH lines can be implemented by loading a host line with electrically small resonators, such as split ring resonators (SRRs) [7], complementary split ring resonators (CSRRs) [8], [9], or other resonators inspired on them [10]. All these artificial lines have been applied to the design of microwave components where size, performance and/or the possi- Manuscript received June 30, 2010; revised September 17, 2010; accepted September 22, Date of publication October 25, 2010; date of current version December 10, This work was supported in part by MEC-Spain under Contract TEC C02-02 METAINNOVA, in part by Generalitat de Catalunya under Project 2009SGR-421 and Project VALTEC , and in part by MCI-Spain under Project CONSOLIDER EMET CSD This paper is an expanded paper from the IEEE MTT-S International Microwave Symposium, May 23 28, 2010, Anaheim, CA. The authors are with GEMMA/CIMITEC, Departament d Enginyeria Electrònica, Universitat Autònoma de Barcelona, Bellaterra, Spain ( Ferran.Martin@uab.es). Color versions of one or more of the figures in this paper are available online at Digital Object Identifier /TMTT bility to achieve novel functionalities are the key improving aspects, as compared to devices based on conventional transmission lines and stubs. A complete list of applications would be very exhaustive and can be found in some of the recently published books on the topic [11] [14]. Nevertheless, we would like to highlight that most microwave applications of CRLH lines are based on the controllability of the dispersion diagram and characteristic impedance of such lines (dispersion and impedance engineering), which is superior than in conventional lines by virtue of the presence of the loading elements. Clear examples of applications of dispersion and impedance engineering by using CRLH lines are the design of compact enhanced bandwidth [15] [18] and dual-band components [19] [23]. The design of multi-band components (tri-band, quad-band, etc.) on the basis of dispersion and impedance engineering with CRLH lines is also possible, but a larger number of loading elements is necessary to achieve this higher order multi-band functionality. Indeed, to achieve -band operation at arbitrary frequencies, at least transmission bands with independent control of phase and characteristic impedance at such operating frequencies are necessary [24]. This leads to conditions and, hence, the structures needed to implement these -band devices must be described by circuit models containing at least elements. Following this idea, the generalized CRLH line concept was introduced [24] [26]. One possible, although not exclusive, circuit model (unit cell) for a generalized CRLH line exhibiting four independent transmission bands (and hence described by 8 independent elements), is depicted in Fig. 1 [26]. This model is useful for the synthesis of structures exhibiting quad-band functionality, as reported in [25], [27]. It can also be used for the synthesis of dual-bandpass filters, as reported in [28]. In these works ([27], [28]) the generalized CRLH lines, which exhibit alternated left and right handed bands, are implemented in microstrip technology by combining semi-lumped (planar) and surface mount elements. The main purpose of this work is to go one step further and demonstrate that it is possible to implement quad-band components and dual-bandpass filters based on the generalized CRLH transmission line model in a fully planar configuration, i.e., without the presence of surface mount elements soldered on top of the substrate. Indeed, this was already demonstrated in [29], where a quad-band power splitter implemented in CPW technology was demonstrated. In the present paper, our aim is to demonstrate that it is also possible to implement fully planar quad-band components, as well as dual-bandpass filters, /$ IEEE

2 DURÁN-SINDREU et al.: PLANAR MULTI-BAND MICROWAVE COMPONENTS 3883 Fig. 1. Circuit model (unit cell) of the quad-band CRLH transmission line reported in [26]. in microstrip technology. Moreover, an exhaustive analysis of the circuit model of the considered structures, as well as the specific procedure for the synthesis of these generalized CRLH transmission lines, will be provided. This represents a significant progress as compared to the work in [29], and points out the potential of the proposed structures for the synthesis of multiband components with different functionalities fully compatible with standard planar technologies. Fig. 2. Typical layout of a microstrip quad-band CRLH transmission line. Dimensions are: a =3:47 mm, b =3:37 mm, f =3:17 mm, e =0:73 mm, g = 7:39 mm, i = 2:2 mm, l = 18:76 mm. The OCSRR dimensions are: r = 2:8 mm, c = 0:16 mm, and d = 1:2 mm, where r ;c and d are the external radius, width and separation of the rings. All the meanders have a width of 0.16 mm. The interdigital capacitors have a width and separation between fingers of 0.16 mm. The radius of the vias is of 0.25 mm. The device has been designed to behave as a impedance inverter at the GSM (f =0:9 GHz, f =1:8GHz) and the GPS (f =1:17642 GHz, f =1:57542 GHz) frequency bands. The considered substrate is the Rogers RO3010 with thickness h = 0:254 mm and measured dielectric constant " = 10:5. II. TOPOLOGY, CIRCUIT MODEL AND SYNTHESIS OF THE QUAD-BAND CRLH MICROSTRIP TRANSMISSION LINES For the implementation of a quad-band CRLH transmission line described by the circuit of Fig. 1 in planar technology, it is necessary to consider electrically small structures that mimic the behaviour of the different resonators. In CPW technology, the series resonator of the series and shunt branches was implemented by means of an open split ring resonator OSRR (introduced in [30]), the parallel resonator of the shunt branch was realized by means of an open complementary split ring resonator OCSRR (presented in [31] for the first time), and the parallel resonator of the series branch was implemented by parallel connecting a capacitive patch and a meander inductor, as reported in [29]. All these resonators are electrically small and provide isolated responses which are accurately described by the ideal resonator s response in a relatively wide band. However, in microstrip technology the series connected OSRRs can no longer be described by a simple model (as was shown in [10]), and the typical required values of the resonator s inductances and capacitances further limit the implementation of such resonators by means of OSRRs and OCSRRs, as compared to CPW technology. Thus, the microstrip quad-band CRLH lines are implemented through a combination of OC- SRRs (for the parallel resonator of the shunt branch), meander inductors, patch capacitances and interdigital capacitances. The typical layout of a quad-band microstrip CRLH line is depicted in Fig. 2, designed to behave as a impedance inverter, according to the procedure explained in Section III. The shunt connected series resonator is implemented by means of the central meander strip and a patch capacitance, the series resonator of the series branch is implemented by means of an interdigital capacitor and a meander inductor; finally, the physical realization of the parallel resonator of the series branch is achieved by means of an additional meander inductor and a patch capacitance, as shown in Fig. 2. Fig. 3. Accurate circuit model for the structure of Fig. 2 divided in the series branch (a) and shunt branch (b). The model is thus obtained by cascading the two-ports (a), (b) and (a). The circuit model of the microstrip quad-band CRLH transmission line is identical to that of the CPW reported in [29], in spite of the fact that we use different semi-lumped resonators. This model is reproduced in Fig. 3 for coherence and completeness. Essentially this model is that shown in Fig. 1 with some parasitics ( and ). Nonetheless, even with the presence of these parasitics (which must be included in the model to accurately describe the structure), the quad-band functionality of the lines is preserved since their values tend to be small in comparison with the other design elements. The first step in the synthesis of the quad-band CRLH transmission line is to determine the element values of the generalized quad-band CRLH model of Fig. 1. To this end, we force the complex propagation constant, given by to be purely imaginary at the design frequencies and to provide the required phase shift at the desired frequencies, and being the series and shunt impedances of the T-circuit model of the generalized CRLH line. For the design of impedance inverters (on which the different circuits of the present work are based) the phase shifts must be set to at and, and at and, being. (1)

3 3884 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 58, NO. 12, DECEMBER 2010 Simultaneously, the characteristic (or image) impedance, given by is set to the required value at the four design frequencies. From this, we obtain 8 equations, and the element values are unequivocally determined. For the phase shifts considered above, the 8 equations can be expressed as follows: (2) (3a) (3b) where is the frequency index, and and are the reactances of the series and shunt branch of the T-circuit model (i.e., and ), given by (4a) (4b) Once the element values are known, we obtain the layout of each section so that the element parameters of the resonators (inferred from curve fitting between the electromagnetic and circuit simulation) coincide with those of the generalized model of Fig. 1. To this end we use the CSRR model reported in [32] (from which we can obtain the first estimate of the OCSSR dimensions), the well known parallel plate capacitor formula for the patch capacitances, and the straight-line inductor approximation [33] nh for the inductive elements, where is the strip width, the strip length, the metal thickness (all given in m) and. Afterwards, an optimization process is required in order to obtain the layout providing the reactive values of the resonators given by expressions (3). By doing this, we also obtain the values of the parasitic elements of the accurate circuit model of Fig. 3. The next step is to re-calculate the resonator values in the electrical model of Fig. 3 (with the parasitic values inferred from the previous step) so that the required values of impedance and phase at the operating frequencies are obtained. Again, we solve (3), but in this case the series and parallel reactances are those of the equivalent T-circuit model of the quad-band CRLH line model shown in Fig. 3. These reactances can be calculated by obtaining the ABCD matrix of the whole structure of Fig. 3 and forcing it to be equal to the ABCD matrix of a T-circuit. Once we know all the element values, we modify the topology of the different resonators at the layout level in order to fit the electromagnetic simulation of each section of the structure to the circuit simulation (this does not substantially affect the parasitics). With this, we directly obtain the layout of the whole structure which provides the required values of characteristic impedance and phase at the operating frequencies. (5) III. APPLICATION TO THE DESIGN OF QUAD-BAND MICROWAVE COMPONENTS In this section, the previous generalized CRLH transmission lines are applied to the design of several quad-band microwave components based on transmission lines, including two power splitters and a branch line hybrid coupler. Since the building block of these circuits is the impedance inverter, let us first consider the design of a quad-band impedance inverter. A. Quad-Band Impedance Inverter The first impedance inverter has been designed to exhibit a characteristic impedance of at the GSM ( GHz, GHz) and the GPS ( GHz, GHz) frequency bands. The inverter has been designed following the procedure explained in the previous section. The element values of the ideal circuit (Fig. 1) that result by solving (3) with and given by (4) are nh, pf, nh, pf, nh, pf, nh, pf. With these values we have determined the first tentative layout, from which the element parasitics (as well as the other elements of the model of Fig. 3) have been inferred. Taking into account these parasitics, the expressions (3) are solved again, but with the and that take into account these parasitics (not shown in this paper). The last step has been to determine the final layout of the quad-band impedance inverter from the recalculated element values. This has been done through optimization using the Agilent Momentum electromagnetic simulator. The resulting topology is that depicted in Fig. 2. The considered substrate is the Rogers RO3010 with thickness mm and measured dielectric constant. The simulated transmission and reflection coefficients of this inverter, inferred from Agilent momentum by considering port impedances, are depicted in Fig. 4. For comparison purposes, the insertion and return losses, inferred from circuit simulation of the model of Fig. 3 with the parasitics and recalculated element values are also depicted in Fig. 4. The recalculated element values are: nh, pf, nh, pf, nh, pf, nh, pf, pf, pf, nh. This figure reveals the good matching level of the ports at the design frequencies, also confirmed by the representation of the frequency dependent characteristic impedance. The phase of the transmission coefficient (also included in Fig. 4) indicates that the required phase shift is achieved at each design frequency. Another aspect to highlight is the small inverter size, i.e., mm mm, which corresponds to at the first frequency band and at the fourth frequency band, being the guided wavelength. Hence, quad-band functionality is obtained with electrical dimensions of roughly the order of the conventional mono-band impedance inverter for the most restrictive frequency. B. Quad-Band Power Splitter The previous inverter has been used for the implementation of a quad-band power splitter. To this end, two 50 access lines to the output port have been added. The device has been

4 DURÁN-SINDREU et al.: PLANAR MULTI-BAND MICROWAVE COMPONENTS 3885 Fig. 6. Simulated and measured frequency response of the power splitter of Fig. 5. Fig. 4. Simulated frequency response of the quad-band impedance inverter of Fig. 2. (a) Insertion and return losses; (b) real part of the characteristic impedance; (c) phase of S. Notice that the phase of S is of opposite sign to the electrical length. The characteristic impedance has been inferred from (2), where the series and shunt impedances (reactances) have been derived from the S-parameters through standard formulas [34]. Fig. 5. Photograph of the fabricated quad-band power splitter. fabricated by means of a standard photo/mask etching technique (the photograph of the splitter is shown in Fig. 5). The measured power splitting and matching (inferred from the Agilent E8364B vector network analyzer) are depicted in Fig. 6, where, for comparison purposes, we have also included the results obtained from electromagnetic simulation. The agreement between experimental data and simulation is good. The measured matching is better than 10 db for the four bands. The measured transmission losses are 4 db, 5.9 db, 6.3 db and 4.6 db at the 1st, 2nd, 3rd and 4th bands, respectively ( roughly exhibits the same values). We would like to highlight that the quad-band power splitter has been fabricated from the previous inverter by merely cascading two access lines at the output port. No further optimization has been carried out. As was done in [29] in the design of CPW quad-band power splitters, we have modified the design of the device shown in Fig. 5 by adding band guards, in order to increase the operational bandwidth at each band, and thus guarantee the functionality of the splitter for the GSM and GPS signals. To this end, we have slightly shifted down the frequencies and and shifted up and. The layout and the photograph of the fabricated splitter are shown in Fig. 7, whereas the results of characterization of this splitter with band guards are depicted in Fig. 8. The device exhibits comparable performance to that of Fig. 5, although the bandwidth and the measured matching (in the 3rd and 4th bands) have been improved. Nevertheless, this latter aspect cannot be attributed to an improved design since electromagnetic simulations are comparable in both cases. Again, device dimensions are small, i.e., mm mm, which corresponds to being the guided wavelength at the first band. C. Quad-Band Branch Line Hybrid Coupler With an eye towards the fabrication of a quad-band branch line hybrid coupler, we have designed a 50 quad-band inverter. The layout of such inverter is depicted in Fig. 9, where the relevant dimensions are indicated. The branch line couplers are composed of a pair of 50 and impedance inverters. However, due to the connection (in a square shaped geometry) of the different inverters in the branch line, it has been necessary to slightly modify the topology of the inverter of Fig. 2 for its application

5 3886 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 58, NO. 12, DECEMBER 2010 Fig. 7. Layout (a) and photograph (b) of the quad-band power splitter with band guards. Dimensions are: a = 4:33 mm, b = 3:34 mm, f = 2:67 mm, e = 0:73 mm, g = 7:3 mm, i = 2:29 mm, l = 18:57 mm. The OCSRR dimensions are: r = 2:5 mm, c = 0:16 mm, and d = 1:1 mm, where r ;cand d are the external radius, width and separation of the rings. All the meanders have a width of 0.16 mm. The interdigital capacitors have a width and separation between fingers of 0.16 mm. The radius of the vias is of 0.25 mm. Fig. 10. Layout of the quad-band impedance inverter of the hybrid coupler, Dimensions are: a = 3:47 mm, b = 3:37 mm, f = 3:17 mm, e = 0:73 mm, g =8:34 mm, i =2:2mm, l =21:64 mm. The OCSRR dimensions are: r =2:8mm, c =0:16 mm, and d =1:2mm, where r ;cand d are the external radius, width and separation of the rings. All the meanders have a width of 0.16 mm. The interdigital capacitors have a width and separation between fingers of 0.16 mm. The radius of the vias is of 0.25 mm. Fig. 11. Photograph of the fabricated quad-band branch line hybrid coupler. The coupler ports are indicated. Fig. 8. Simulated and measured frequency response of the power splitter of Fig. 7. The band guards are indicated in the figure. Fig. 9. Layout of the 50 quad-band impedance inverter of the hybrid coupler. Dimensions are: a =3:04 mm, b =2:91 mm, f =2:21 mm, e =0:41 mm, g = 7:71 mm, i = 1:9 mm, k = 0:4 mm, l = 20:44 mm. The OCSRR dimensions are: r =2mm, c =0:16 mm, and d =0:6mm, where r ;c and d are the external radius, width and separation of the rings. All the meanders have a width of 0.16 mm. The interdigital capacitors have a width and separation between fingers of 0.16 mm. The radius of the vias is of 0.15 mm. in the design of the quad-band hybrid coupler. The layout and dimensions of this inverter are depicted in Fig. 10. From the previous inverters, we have implemented the quad-band branch line hybrid coupler depicted in Fig. 11. The simulated (by means of Agilent Momentum) and measured frequency response of the device are depicted in Fig. 12. Matching in all the bands is good, and power splitting (except in the 3rd band) is reasonable, taking into account the complexity of the device and the critical dimensions of some of its constitutive semi-lumped elements. The measured return losses are 22 db, 10.7 db, 11 db and 13 db for the first, second, third, and fourth band, respectively. However, losses in the third band are not due to an improper design, as can be deduced from the electromagnetic simulation of the device with ohmic and dielectric losses excluded (shown in Fig. 13 together with the circuit simulation of the hybrid coupler). Indeed, losses can be mainly attributed to the finite conductivity of the metal, rather than to the effects of the dielectric (this has been verified by either switching off the ohmic or the dielectric losses in the simulations), which affects specially the third band since it is the narrowest. Further causes of device degradation can be variations of the actual device dimensions (due to fabrication related tolerances), as well as via metallization (the device contains 16 vias with soldered metallic pins). The agreement between the lossless electromagnetic and circuit simulations is good for both the magnitude and the phase, in spite of the layout and circuit model complexity. It is remarkable that the measured phase balance of the output ports at the design frequencies is that corresponding to a quadrature hybrid coupler (see Fig. 12(c)). This is expected on account of the phases of the transmission coefficients between the input and the output ports for the branch line coupler ( for and for ). Such phases, which have been inferred from electromagnetic

6 DURÁN-SINDREU et al.: PLANAR MULTI-BAND MICROWAVE COMPONENTS 3887 Fig. 12. Measured and EM simulated frequency response of the hybrid coupler of Fig. 11. (a) Power splitting; (b) matching and isolation; (c) phase balance. simulation without access lines, are depicted in Fig. 13(b), and are in good agreement with those inferred from circuit simulation. Like in conventional branch line couplers, bandwidth is not a controllable parameter in the proposed couplers. The reason is that the number of elements of the inverters is that required to achieve the characteristic impedance and phase at the four design frequencies. By implementing the impedance inverters with a higher number of unit cells, it would be potentially possible to enhance the bandwidth but with the penalty of much larger size. IV. DESIGN OF DUAL-BANDPASS FILTERS It is also possible to design multi-band band pass filters with the order-4 CRLH structure of Fig. 1. Nonetheless, if the purpose is to synthesize standard responses, such as the Chebyshev Fig. 13. EM simulation (with losses excluded) and circuit simulation of the hybrid coupler. (a) Power splitting. (b) Matching. (c) Phase response. The circuit elements corresponding to Fig. 3 are for the 50 inverter: L =30:03 nh, C =0:54 ph, L =1:26 nh, C =9:87 pf, L =12:13 nh, C = 1:02 pf, L = 2:65 nh, C = 5:31 pf, C = 0:22 pf, C = 0:61 pf, L = 0:45 nh. For the inverter: L = 20:89 nh, C = 0:76 pf, L = 0:89 nh, C = 13:92 pf, L = 8:6 nh, C = 1:44 pf, L =1:87 nh, C =7:98 pf, C =0:37 pf, C =0:62 pf, L =0:45 nh. filter response, it is only possible to obtain dual-band behaviour since more conditions are required, such as an equal-ripple and a fixed bandwidth at each band. This dual-band functionality can be obtained from the low pass filter prototype through convenient transformations. In a first step, a mono-band band pass response results from the well known transformation [35] and being the angular frequency of the low pass and band pass filter, and are the fractional bandwidth and central frequency of the band pass filter and the angular cutoff frequency of the low pass filter. Then, a second transformation is (7)

7 3888 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 58, NO. 12, DECEMBER 2010 applied to the mono-band band pass filter to obtain dual-band behaviour [36] (8a) (8b) being the angular frequency of the dual-bandpass filter and the angular central frequencies of the first and second filter bands. Once these transformations are applied to the low pass filter prototype, the circuit of Fig. 1 is obtained, provided identical fractional bandwidths for the two bands, as well as the narrow band approximation (i.e., a fractional bandwidth, FBW, for each band less than 10%), are considered [36]. As reported in [36], the element values of the circuit of Fig. 1 are obtained from a set of equations dependent on the low pass filter prototype coefficients and on the relevant design parameters, namely, the angular central frequencies and the FBW (these equations are not reproduced here for simplicity). Using this procedure, a dual-bandpass filter that covers the GSM (0.9 GHz 1.8 GHz) and the ( MHz) ( MHz) civil GPS frequency bands is presented in this paper. An order three Chebyshev response with 0.01 db ripple, central frequencies of GHz and GHz, and 20% fractional bandwidth (i.e., ) has been considered. Even though the narrow band approximation is not satisfied, the filter response is in good agreement with the ideal mono-band Chebyshev response, where only small deviations in the transition bands are observed. From the above-mentioned filter specifications, the values of the circuit elements (Fig. 1) are: nh, pf, nh, pf, nh, pf, nh, pf. Using the design methodology applied to the quad-band inverters, the filter layout has been obtained (this is depicted in Fig. 14 together with the photograph of the fabricated prototype). In this case, filter optimization taking parasitics into account has been done by tuning the reactive elements at the circuit level. Specifically, the values that are changed (in reference of Fig. 3) are: nh, pf, pf, pf, nh. The frequency response and group delay of the filter, including measurement, electromagnetic simulation, circuit simulation of the accurate circuit model of Fig. 3 and the dual-band Chebyshev response (circuit of Fig. 1), are depicted in Fig. 15. As can be seen, good agreement between the different responses is obtained, with measured return losses better than 20 db and a rejection level better than 20 db up to 4.6 GHz given by expression (8b). Moreover, the size of the filter is 19.5 mm 13.5 mm, which corresponds to being the guided wavelength at. V. DISCUSSION To complete this work, let us briefly discuss the limitations relative to the arbitrariness in the selection of the frequencies for the design of quad-band components based on impedance inverters. Fig. 14. Layout (a) and photograph (b) of the dual-bandpass filter. Dimensions are: a =3:52 mm, b =2:85 mm, f =2:64 mm, e =0:49 mm, g =7:71 mm, i =2:19 mm, l =19:4mm. The OCSRR dimensions are: r =1:95 mm, c = 0:16 mm, and d = 0:6 mm, where r ;c and d are the external radius, width and separation of the rings. All the meanders have a width of 0.16 mm. The interdigital capacitors have a width and separation between fingers of 0.16 mm. The radius of the vias is of 0.15 mm. We have demonstrated the quad-band functionality of several components, fully implemented in planar technology, at four commercial bands. The element values of the equivalent circuit model (Fig. 3) have been found to be moderate for the different designed quad-band impedance inverters, and this is the reason why it has been possible to implement the different circuits in planar technology. However, these elements depend on the relative values of the operating frequencies and, for certain designs, it may be difficult to implement these elements as semi-lumped components. Indeed, since the effects of the parasitics in the model of Fig. 3 are not very critical, we can use the simpler model of Fig. 1 to estimate the values of the different elements as a function of the design frequencies and characteristic impedance. We have thus solved (3) and (4) analytically, and we have obtained the results shown in (9a) (9h) at the bottom of the next page. According to the previous expressions, to keep all the inductances small or moderate (large inductances limit device implementation in fully planar technology), it is necessary that any pair of consecutive operating frequencies presents a non-negligible frequency span (separation). On the contrary, some of the inductance values increase substantially and jeopardize the fully planar implementation of the device. To illustrate this, we have set GHz and GHz (the GSM frequencies considered in the reported prototype devices), and we have calculated the values of the inductances by varying the frequency difference between and, considering that this frequency span is centred at, which means that. The different inductances of the model of Fig. 1 are depicted in Fig. 16 as a function of for the case of Ohm (so that the results are easily scalable with the

8 DURÁN-SINDREU et al.: PLANAR MULTI-BAND MICROWAVE COMPONENTS 3889 Fig. 16. Variation of the inductances of the generalized model of Fig. 1 as a function of f. Fig. 15. Insertion losses (a), return losses (b) and group delay (c) of the simulated and measured dual-bandpass filter of Fig. 7. The bands are indicated in the figure. inverter impedance). In the extremes of the span, at least one of the inductances tends to infinity. Hence, we should avoid very close or very distant values of and. Under the considered conditions (for the examples reported in the previous sections), the inductances that may limit the fully planar implementation are and. Although the considered frequencies in the reported examples do not exactly satisfy the conditions of Fig. 16, and are roughly equidistant from and close to the centre of the span in Fig. 16. This explains why we have been able to implement the reported devices by means of semi-lumped planar resonators. Another limitation for the implementation of planar quadband impedance inverters may come from the frequency difference between the upper and lower frequencies. If these frequencies are very distant, the validity of the model of Fig. 3 (including parasitics) in the whole frequency span cannot be guaranteed, and hence the proposed design approach may be no longer valid. It is difficult to establish a maximum difference between and since the wideband behaviour of the lumped model of Fig. 3 depends on the considered substrate and element values. However, for most substrates and device specifications our experience dictates that it is possible to achieve fully planar devices with / ratios up to 2 3 (being difficult to establish an accurate limit within this interval). Therefore, according to this discussion, it is not always possible to implement quad-band devices in fully planar technology. Nevertheless, we have given the conditions (concerning (9a) (9b) (9c) (9d) (9e) (9f) (9g) (9h)

9 3890 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 58, NO. 12, DECEMBER 2010 the relative positions of the design frequencies) that must be fulfilled for the viability of the fully planar implementation, and these conditions have been validated by means of the proposed examples. Obviously, it is not possible to establish clear limits(as has been mentioned), but in our opinion, the contents of this discussion can be useful as guidelines for those designers willing to implement planar multiband components based on impedance inverters. VI. CONCLUSION In conclusion, it has been shown in this paper that the generalized model of the composite right/left handed (CRLH) transmission lines can be applied to the design of fully planar multiband microwave components. Specifically, we have extended the work presented in [29] by applying the generalized CRLH transmission line concept to the design of multiband microwave components in microstrip technology, including quad-band impedance inverters, power splitters and branch line hybrid couplers, as well as dual-bandpass filters. As compared to the design of multiband components in CPW technology [29], the design of such components in microstrip technology has forced us to modify the topology of the generalized CRLH lines in order to achieve the required element values of the different resonators and to minimize the effects of the parasitics. Thus, the generalized CRLH lines of this work have been implemented through a combination of open complementary split ring resonators, meander inductors, patch capacitors and interdigital capacitors, avoiding the use of surface mount elements. Nevertheless, the circuit model, including parasitic effects, of the generalized microstrip CRLH lines has been found to be identical to that of CPW CRLH lines. The synthesis of these artificial lines has been presented. Specifically, we have reported the detailed procedure for the synthesis of quad-band impedance inverters, which are the building blocks of many microwave components, including the power splitters and hybrid couplers of this work. The reported devices, designed to operate at the GSM and GPS frequency bands, exhibit reasonable performance and device dimensions that are small on account of the semi-lumped components used in their implementations. Since the generalized model of the CRLH lines is identical to the model of an ideal order-3 dual-bandpass filter, we have also applied the planar CRLH lines of this work to the design of dual-bandpass filters in microstrip technology. Specifically, a Chebyshev band pass filter has been reported in this work as a proof-of-concept demonstrator. In spite of the circuit parasitics, the measured filter response has been found to be in good agreement with the ideal Chebyshev filter response. Filter performance has been found to be good and device dimensions small. The results of this work show the potential of generalized CRLH lines to the design of multiband microwave components and the possibility of implementing them in fully planar technology. Work is in progress towards the implementation of other planar quad-band microwave components and dual-band filters. REFERENCES [1] C. Caloz and T. Itoh, Novel microwave devices and structures based on the transmission line approach of metamaterials, in Proc. IEEE-MTT Int. Microw. Symp., Philadelphia, PA, Jun. 2003, vol. 1, pp [2] G. V. Eleftheriades, A. K. Iyer, and P. C. 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Hagiwara, Synthesis of dual-band bandpass filters using successive frequency transformations and circuit conversions, IEEE Microw. Wireless Compon. Lett., vol. 16, no. 3, pp , Mar Miguel Durán-Sindreu (S 09) was born in 1985 in Barcelona, Spain. He received the telecommunications engineering Diploma, specializing in electronics, and the telecommunications engineering degree from the Universitat Autònoma de Barcelona, Spain, in 2007 and 2008, respectively. He is currently working towards the Ph.D. degree in subjects related to metamaterials in the Universitat Autònoma de Barcelona, Spain. Gerard Sisó (S 08) was born in Barcelona, Spain, in He received the Diploma in industrial engineering, specializing in electronics from the Universitat Politècnica de Catalunya, Spain, in 2004 and the electronics engineering degree and Ph.D. degree in electronics engineering from the Universitat Autònoma de Barcelona, Spain, in 2006 and 2010 respectively. His research interests include microwave circuits based on metamaterial transmission lines, especially enhanced bandwidth and multi-band devices. Jordi Bonache (S 05 M 06) was born in Barcelona, Spain, in He received the physics and electronics engineering degrees and Ph.D. degree in electronics engineering from the Universitat Autònoma de Barcelona, Bellaterra (Barcelona), Spain, in 1999, 2001, and 2007, respectively. In 2000, he joined the High Energy Physics Institute of Barcelona (IFAE), where he was involved in the design and implementation of the control and monitoring system of the MAGIC telescope. In 2001, he joined the Department d Enginyeria Electrònica, Universitat Autònoma de Barcelona, where he is currently an Assistant Professor. His research interests include active and passive microwave devices and metamaterials. Ferran Martín (M 04 SM 08) was born in Barakaldo (Vizcaya), Spain in He received the B.S. degree in physics and the Ph.D. degree from the Universitat Autònoma de Barcelona (UAB), Barcelona, Spain, in 1988 and 1992, respectively. From 1994 up to 2006 he has been Associate Professor in Electronics at the Departament d Enginyeria Electrònica (Universitat Autònoma de Barcelona), and from 2007 he is Full Professor of Electronics. In recent years, he has been involved in different research activities including modelling 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 organized several international events related to metamaterials, including Workshops at the IEEE International Microwave Symposium (years 2005 and 2007) and European Microwave Conference (2009). He has acted as Guest Editor for three Special Issues on Metamaterials in three International Journals. He has authored and co-authored over 300 technical conference, letter and journal papers and he is coauthor of the monograph on Metamaterials entitled Metamaterials with Negative Parameters: Theory, Design and Microwave Applications (Wiley, 2001). He has filed several patents on metamaterials and has headed several Development Contracts. Dr. Martín has 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.