Coupling Enhancement of Composite- Right/Left-Handed Loop Resonators for Filter Applications

Transcription

1 Coupling Enhancement o Composite- Right/Let-Handed Loop Resonators or Filter Applications Humberto Lobato-Morales, Ricardo A. Chávez-Pérez, and José L. Medina-Monroy Electronics and Telecommunications Department, Centro de Investigación Cientíica y de Educación Superior de Ensenada, CICESE, B. C., Mexico Abstract An enhanced method or the coupling o Composite- Right/Let-Handed (CRLH) loop resonators or ilter design is presented in this paper. The proposed coupling mechanisms take advantage o the natural distribution o the E- and H-ields on a CRLH loop resonator, while maintaining the advantages in miniaturization and harmonic resonance suppression o such structures. For demonstration o the concept, two ilters operating in the GSM-850 band are designed, abricated and tested experimentally. Good agreement between the simulated and measured results is obtained. Index Terms Microwave Filters, Composite-Right/Let- Handed (CRLH), Loop Resonators, Planar Filters. I. INTRODUCTION INCE the development o the Composite-Right/Let- SHanded (CRLH) circuits in its planar orm, several microwave devices have been designed, including resonators, ilters, antennas, among others, showing the main advantages o miniaturization and harmonic band suppression they provide [1]. Particularly or microstrip bandpass ilter design, proposals using linear CRLH resonators operating in the zeroth-order mode are ound in the literature [1]-[3]. In order to mention some o them, in [2] a three-pole ilter is presented with good out-o-band perormance; however, it consists on the coupling o dierent-dimension resonators (asymmetric coupling), adding a level o complexity in the design. A threepole ilter with resonator coupling on the top and bottom layers o the substrate is presented in [3] showing a wide bandpass response; however, it presents close adjacent bands produced by lower- and higher-order modes which are usually undesired or the real applications. Dierent rom the CRLH resonator in its linear orm, the microstrip CRLH resonant loop is proposed and analyzed in [4], ormed by closing a metamaterial transmission line in which the zeroth-order resonance and higher-order modes can be allocated with high lexibility due to the characteristic phase response o CRLH lines [1], [4]. The CRLH loop resonator have been proposed or ilter design in [5] and [6], showing miniaturization o the structures and harmonic resonance elimination, which are highly desired or communication applications. However, due to the coniguration o the closed CRLH loops, diiculties in the coupling arise and additional large linear structures must be used, which in turn generate undesired resonances and can cause intererence within the operating passband or even outside [5]-[7]. An approach in the coupling improvement with this kind o resonators can be seen in [8], where a ourpole ilter is proposed exploiting the dual-mode capacity o the loops; however, no ull analysis on the coupling mechanisms neither resonator losses are presented. A method or the coupling enhancement o CRLH loop resonators or ilter design is presented in this paper, which is based on the natural distribution o the E- and H-ields on the resonator. Two bandpass ilters or mobile communications are designed using the proposed coupling scheme without the use o additional complex structures and keeping the advantages o low dimensions and harmonic suppression. The paper is organized as ollows: Section II describes the CRLH loop resonator and the proposed coupling mechanisms; design o the ilters are presented in Section III; results and discussion are exposed in Section IV. II. COUPLING OF CRLH LOOP RESONATORS A. Design o the Resonant Loop As mentioned beore, a CRLH loop resonator can be ormed by closing a metamaterial transmission line having a particular phase response. Particularly, the zeroth-order mode is preerred because it allows a resonator to operate at a speciic requency with signiicant low dimensions, compared with conventional λ g closed loop resonators or even linear λ g /2 resonators (being λ g a guided wavelength) [1], [4]-[6]. This mode is obtained when the total phase along the loop CRLH = 0 by cancellation between the LH (Let-Hand) and RH (Right-Hand) phase propagations, LH and RH, respectively [1], [4], as stated in N ε e φcrlh = φlh + φrh = 2π d, (1) 2π L C c where N is the number o LH unit-cells, L L and C L inductor and capacitor values o the LH part; d is total length o the RH line and ε e corresponds to the dielectric eective permittivity o the used substrate; is requency in evaluation and the L L /16/$ IEEE 1

2 velocity o light in a vacuum is stated as c. The reader is reerred to [1] or details in the design o CRLH microstrip structures. resonance is ar rom the operating requency more than 2.5 times and can be even arther with a correspondent design [4]; the E-ield distribution at this requency point (2.16 GHz) shows one complete wavelength along the loop [4]. Fig. 2. E-ield distribution o the resonator or Q e, or k. Fig. 1. Proposed CRLH loop resonator geometry, requency response. A CRLH loop resonator is designed to operate with a center requency 0 = 0.85 GHz, which corresponds to the GSM-850 mobile communications band. The LH part consists o a two unit-cell transmission line designed with SMC (Surace- Mount-Component) series capacitors and shunt-stub inductors, and the RH part is simply a conventional 50 Ω transmission line [5], [6]. For coupling purposes, as will be shown later, the LH part is located only along one side o the loop. A Rogers UL2000 substrate with relative dielectric permittivity ε r = 2.6, tanδ = , and height h = mm is used or the design o the resonator. The geometry o the proposed resonator and its simulated requency response S 21 [9] are shown in Fig. 1. The E-ield distribution at the zerothorder and 1 st -order resonances are included in the inset o Fig. 1. For the zeroth-order resonance, although an ininite wavelength λ g is theoretically predicted [1], [4], the distribution o the LH and RH parts along the loop resonator allows the E-ield to concentrate on the RH transmission line section, and the H-ield in the LH shunt stub inductors. Taking advantage o this eect, electric E- and magnetic H- couplings can be clearly deined and can be used to design a complete bandpass ilter with the combination o both schemes ollowing the widely-used resonator coupling method based on the external quality actor Q e (input and output resonators) and k coeicients (inter-resonator couplings) [7]. As seen in Fig. 1, the 1 st -order (spurious) B. Electric Coupling As the E-ield is concentrated in the RH part o the CRLH loop, an electric E-coupling by means o two branched narrow lines can be used to eed the resonator with the input/output ports, as seen in Fig. 2. The external quality actor Q e (see Fig. 4 below) can then be adjusted by varying the length o the coupling lines dl. Distance between the coupling lines and the resonator is o 0.4 mm. Similarly, the inter-resonator coupling is obtained by proximity o two resonators with one o the RH sides o each, as seen in Fig. 2; by modiying the gap g between the loops, the k actor can be adjusted. The EM interaction o two adjacent equal resonators (symmetric coupling) produce two resonances close to each other (see Fig. 4 below) [7]. In the coupling analysis, these requencies arise rom two conditions: irst, an E-wall is virtually inserted along the symmetry plane producing the resonant requency e ; second, a virtual H-wall along the same plane generates the resonance m [7]. The inter-resonator E- coupling coeicient can be obtained by k E = m e m + e. (2) In this case, insertion o the E-wall increases the capability to store charge o the resonator while the H-wall reduces it, producing m > e [7]. C. Magnetic Coupling A region with high concentration o the H-ield occurs in the LH part o the resonator, speciically, along the shunt stub inductors; thus, a magnetic H-coupling o the resonator can be obtained by using direct contact or proximity o such /16/$ IEEE 2

3 elements. The coupling schemes or Q e and k are displayed in Fig. 3 with the H-ield distribution on the loop resonator. Fig. 3. H-ield distribution o the resonator or Q e, and or k. For the type o coupling in Fig. 3, the Q e actor (Fig. 4) can be adjusted by varying position o the taps tp o the input/output port which are in direct contact (strong coupling) with the shunt stub inductors. Having two equal CRLH loop resonators, it is possible to adjust the k coeicient by changing the separation between the stub inductors s, as seen in Fig. 3. Similarly as or the E-coupling, the magnetic interresonator coupling coeicient can be calculated by k M = e m e + m, (3) or which e corresponds to the resonant requency o the circuit when an E-wall is inserted in the symmetry plane reducing the stored lux in the resonator, and m when an H- wall is inserted in the same plane increasing the stored lux; thus, e > m [7]. D. Quality Factors The useul quantity to estimate the losses in a microwave resonator is the unloaded quality actor Q u [7]. Usually, the Q u value o a microstrip structure includes conductor, dielectric, and radiation losses [10]; however, or the proposed structure, quality actors o the SMC capacitances Q cap must be included: = + + +, (4) Qu Qc Qd Qr Qcap where Q c, Q d, and Q r, reer to conductor, dielectric and radiation quality actors, respectively. In simulations [11], the CRLH loop resonator is weakly coupled by means o a large gap with the input and output ports in order to satisy the unloaded condition and allowing Q u to be directly estimated. Conductor, dielectric, and radiation loss mechanisms are conigured separately in simulations; the S-parameters o the SMC capacitors (provided by the manuacturer [12]) are included. The correspondent Q values are obtained rom the transmission losses S 21 curve o the requency response using the generalized expression Q 0 =, (5) Δ 3dB where 0 is the resonant requency and Δ 3dB corresponds to the 3dB bandwidth (see Fig. 4) [7]. The dierent Q actors o the resonator are tabulated in Table I. TABLE I QUALITY FACTORS OF THE CRLH LOOP RESONATOR Q u Q c Q d Q r Q cap , As noticed rom Table I, the lowest loss mechanism is attributed to radiation (highest Q), as desired in microwave ilters. The obtained Q cap value is in agreement with that provided by the SMC capacitor manuacturer in the datasheet [12]. The highest losses are produced by the conductor material (copper layer o thickness 17 μm). Although the inclusion o the SMC components add a level o energy loss, the unloaded quality actor Q u is still within good values or a microstrip structure, which strongly depends also on the choice o the dielectric substrate characteristics (dielectric permittivity and height), and the requency o operation [7], [10]. III. FILTER DESIGN To demonstrate the capability o the CRLH loop resonator or ilter design, two 2 nd -order Chebyshev bandpass ilters are proposed operating at a center requency 0 = 0.85 GHz, with a ractional bandwidth FBW = 0.03 (3 %) and ripple o 0.1 db. The ilters are designed and abricated using the same Rogers UL2000 substrate with which the resonator is designed and analyzed in the previous section. A. Coupling Parameters The required ilter coupling parameters [7] (input/output Q e and inter-resonator k coeicient) can be calculated using Q g g FBW g g Q =, and (6a) FBW e in=, e out k 12 FBW =, (6b) g g where the elements g 0 to g 3 are the lowpass ilter parameters and are directly taken rom [7], throwing the quantities Q e-in = Q e-out = 28.22, and k 12 = In simulations [11], a parametric analysis is carried out or Q e and k ollowing both E- and H-coupling schemes; lossless materials and the S-parameters o the SMC capacitors are conigured. From the S 21 responses, Q e is estimated using (5) /16/$ IEEE 3

4 having the single resonator strongly coupled to the input/output port and weakly coupled to the second port in evaluation. For the k coeicient (2) or (3) can be used depending upon the case or simply the generalized expression shown in the inset o Fig. 4, having both resonators weakly coupled to the input and output ports [7]. The obtained results are shown in Fig. 5. Filter-2 is based on an H-coupled Q e and E-coupled k; initially, tap position and gap between the resonators are tp = 2.4 mm and g = 0.4 mm, respectively. Geometries o the ilters are shown in Fig. 6; as noticed, their shapes and parameters present symmetry as there is only one k to adjust, and Q e-in = Q e-out. Total dimensions o both are 94 mm x 60 mm. Fig. 4. Extraction o Q e and k rom the simulated transmission loss S 21. Fig. 6. Geometries o Filter-1 and Filter-2. An optimization process is carried out in simulations, and the inal values o dl and g or Filter-1 are 21 mm and 1.6 mm, respectively; while or Filter-2, tp = 2.2 mm and s = 0.4 mm. Fig. 5. Simulated coupling parameters Q e, and k. Based on the coeicients in Fig. 5, Filter-1 is designed with E-coupled Q e and H-coupled k; initial values o the coupling line length and separation between the stub inductors o the resonators are dl = 20 mm and s = 1.6 mm, respectively. IV. RESULTS AND DISCUSSION The ilters are abricated and tested experimentally using a Keysight PNAX-series Vector Network Analyzer. The simulated (including material losses) and measured responses o the proposed ilters are displayed in Fig. 7; photographs o the structures are also included in the correspondent inset. For Filter-1, the measured center requency is 0.81 GHz while the simulated is at 0.83 GHz; a shit o 20 MHz is observed; transmission losses in the passband result o 2.49 db and 2.17 db or the experiments and simulations, respectively. The measured bandwidth (at 3 db) is o 4.98 %. For Filter-2, the measured and simulated center requencies are o GHz and GHz, respectively, having a dierence o only 6 MHz. The measured transmission loss results o 1.53 db, while the simulated is o 1.99 db; the measured 3-dB bandwidth is o 5.59 %. As seen in the results displayed in Fig. 7, a higher discrepancy between the measured and simulated structures is obtained or Filter-1, and is attributed mainly to the proximity o the coupling lines which slightly increases the virtual size o the loops lowering the resonant requency; manuacture tolerances and dierences in the S-parameters o the SMC /16/$ IEEE 4

5 capacitors used in simulations also contribute to such variations in both ilter designs. Higher transmission and bandwidth are observed or Filter-2 due to the direct coupling o the resonators with the correspondent input/output ports (in contrast with Filter-1 which makes use o a gap coupling). requency band o 0.85 GHz, and they cannot be optimized separately or the dierent resonances. Apart rom the desired and spurious bands, no other resonances (parasitic) are appearing. Fig. 8. Wideband response o the ilters and comparison o resonator dimensions. Due to their small dimensions and low-loss passband, the presented ilters based on the CRLH loop resonators result ideal or mobile communication applications as that allocated in the GSM-850 band. Moreover, the presented coupling schemes can be applied or the design o higher-order ilters to increase selectivity and bandwidth o the correspondent channels. Fig. 7. Frequency responses and photograph o Filter-1, Filter-2. V. CONCLUSION The CRLH loop resonator with enhanced coupling schemes based on H- and E-ield distributions have been presented. Two ilters based on the proposed couplings and resonator have been designed or demonstration o the concept. The resonator has been analyzed in terms o its dierent Q actor and loss mechanisms. Measured and simulated responses have been obtained showing good perormance and high agreement between them. Due to the mentioned characteristics, the proposed resonator and ilters are good candidates or use in wireless mobile communications. The measured wideband responses o the ilters are plotted in Fig. 8 showing the spurious requencies (no harmonics) occurring at 2.2 GHz. For comparison purposes, dimensions o a single conventional loop resonator operating at 0.85 GHz over the same substrate result o 66 mm x 66 mm, while the proposed resonator occupies an area o only 33 mm x 38 mm, which represents a miniaturization o 71 %, as seen also in the inset o Fig. 8. A weak spurious band is observed or Filter-1 appearing at 2.2 GHz, while or Filter-2 the same spurious results o higher magnitude. Allocation o these bands (spurious) can be properly changed in requency (while maintaining the operating band) ollowing the correspondent CRLH resonator design [1], [4]. In this work, the spurious band o Filter-2 cannot be treated as a second passband as the ilter parameters (Q e and k coeicients) are achieved only or the undamental ACKNOWLEDGMENT The authors are pleased to thank technician René A. Torres- Lira or his contribution in the abrication o the prototypes. REFERENCES [1] C. Caloz and T. Itoh, Electromagnetic Metamaterials, Transmission Line Theory and Microwave Applications, New York: John Wiley & Sons, [2] S. Kahng, G. Jang, and J. Anguera, "Metamaterial Dual-Band Bandpass Filters using CRLH Zero-Order-Resonators and Improving its Intermediate Stopband," in Europ. Con. Antennas Propag., Barcelona, Spain, [3] S. C. Lin, C. W. Hsieh, and C. H. Chen, "Dual-Plane Direct- Coupled Bandpass Filters with Open-Ended Stubs Based on CRLH Zeroth-Order Resonators," in IEEE Int. Workshop Electromag., Kowloon, China, /16/$ IEEE 5

6 [4] C. A. Allen, K.M.K.H. Leong, and T. Itoh, "Design o Microstrip Resonators Using Balanced and Unbalanced Composite Right/Let-Handed Transmission Lines," IEEE Trans. Microw. Theory Tech., vol. 54, no. 7, pp , Jul [5] I. Zagoya-Mellado, A. Corona-Chávez, and I. Llamas-Garro, "Miniaturized Metamaterial Filters Using Ring Resonators," in IEEE MTT-S Int. Microw. Workshop Series Signal Integrity High-Speed Intercon., Guadalajara, Mexico, Feb [6] H. Lobato-Morales, A. Corona-Chávez, and J. Rodríguez- Asomoza, "Microwave Directional Filters using Metamaterial Closed-Loop Resonators," Microw. Optical Technol. Lett., vol. 51, no. 5, pp , May [7] J. S. Hong and M. J. Lancaster, Microstrip Filters or RF/Microwave Applications, New York: John Wiley & Sons, [8] H. T. Su, K. K. Fong, M. K. Haldar, and M. L. D. Wong, "New 4-pole Dual-Mode Resonator Filter using Composite- Right/Let-Handed Line," in Asia-Paciic Microw. Con., Macau, China, Dec [9] Ansys, HFSS ver. 13. [10] A. Gopinath, "Maximum Q-Factor o Microstrip Resonators," IEEE Trans. Microw. Theory Tech., vol. 29, no. 2, pp , Feb [11] Sonnet Sotware, Sonnet ver. 13. [12] American Technical Ceramics, ATC 600l Datasheet, /16/$ IEEE 6