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Novel Application of a New Metamaterial Complementary Electric LC Resonator for the Design of Miniaturized Sharp Band-Pass Filters Homayoon Oraizi, Seyede Yalda Torabi Department of Electrical Engineering, Iran University of Science and Technology, Tehran 1684613114, Iran Received 9 August 2012; accepted 3 December 2012 ABSTRACT: In this article, we introduce a new metamaterial complementary electric LC resonator (CELC) and investigate its operational mechanism, characteristics, and potential- ities for application in microwave components and devices, such as filters. We consider the excitation of CELC by the electric and magnetic fields of microstrip lines and its resonance characteristics by the diagrams of effective permittivity (eeff) and permeability (leff). A cir- cuit model is obtained by the consideration of its coupling with the loaded microstrip line. We then realize a novel left-handed (LH) cell by the combination of the CELC resonator and a short circuited stub. It is designed by the least mean square method. We finally use the cascade connection of such LH cells for the design of a miniaturized narrow-band band- pass filter with high out of band rejection. VC 2013 Wiley Periodicals, Inc. Int J RF and Microwave CAE 23:471–475, 2013. Keywords: complementary; resonator; narrow-band; band-pass filter; metamaterial I. INTRODUCTION Various microwave devices have been designed by meta- material transmission lines for optimum single band and multiband performance, miniaturized dimensions, high adjustability, and other described features. There are two main methods for the realization of such structures. 1. Loading of lines by lumped inductances and capacitors, similar to surface mount technology (SMT) referred to as transmission line dual method [1]. 2. Loading of lines by resonant structures, such as split ring resonators (SRRs) and complementary split ring resonators (CSRRs), referred to as the resonance method [2]. Recently, new inductor-capacitor electric resonators, called electric-LC-resonators (ELC) and complementary electric-LC-resonators (CELC) have been introduced, which are the dual electric resonators of (SRR) and dual magnetic resonators of (CSRR), respectively. They could make the effective permittiv- ity or permeability of the structure negative, by coupling with the electric or magnetic fields in a nar- row band around the resonance frequency [3, 4]. How- ever, due to the lack of full understanding of their physical operation and accurate circuit models, they have not been applied for the design of microwave components, although they seem to have great poten- tialities in these respects. In this article, we first present a circuit model for a new type of CELC resonator loaded to a transmission line and describe its physical operation. We also investigate its resonance characteristics based on the diagrams of the scattering parameters, effective permittivity (eeff), and effective permeability (leff). We then devise a new left- handed cell by the combination of this resonator and grounded stubs by the aforementioned resonance method. Its synthesis is made by the least mean square. Finally, we design a miniaturized microstrip narrow band-pass fil- ter with high out-of-band rejection by cascading several such left-handed (LH) cells. II. THE PROPOSED CELC RESONATOR The CELC resonator is actually the dual of ELC resona- tor, which is highly symmetrical. It may provide purely magnetic or electric resonances, depending on an Correspondence to: H. Oraizi; e-mail: h_oraizi@iust.ac.ir. VC 2013 Wiley Periodicals, Inc. DOI 10.1002/mmce.20736 Published online 8 April 2013 in Wiley Online Library (wileyonlinelibrary.com). 471 appropriate excitation. Such CELC resonators have been al- ready studied [4]. However, in this article we introduce a new CELC resonator, as depicted in Figure 1, which has potential application for the design of narrow band devices in the microwave frequencies. We may show that the pro- posed CELC resonator couples with the magnetic field of the line and has purely magnetic resonance, without any cross couplings. Such a behavior may be observed in Figure 2 for the effective permittivity and permeability of CELC in Figure 1 with the dimensions given in Table I. Observe that leff in Figure 2a becomes negative in a narrow band above the resonance frequency, due to the magnetic coupling of the resonator with the magnetic field of the line. But eeff in Figure 2b is positive across the band, since there is no elec- tric coupling between the resonator and the electric field of the line. These effective parameters have been calculated by the methods of effective media [5]. III. EQUIVALENT CIRCUIT OF CELC AS COUPLED TO A LINE Consider first the electric field configuration and surface current distribution on the ground plane near the reso- nance frequency obtained by high frequency structure sim- ulator (HFSS)-full-wave simulation software (Figs. 3a and 3b). We observe that the concentration of surface current occurs in the middle of CELC around the horizontal edges of the T-shaped slots and the electric field concentration occurs around the outer circumference of CELC and around the edges of the vertical parts of T-shaped slots. Consequently, we may now consider the equivalent circuit of the CELC resonator loaded to the microstrip line as shown in Figure 4. The L and C components are the inductor and capacitor of microstrip line per cell, respectively. The CELC resonator is represented as a se- ries connection of tank circuit with Lrm and Crm and two series capacitors Crs. Based on the behavior of the current paths and the electric field configuration on the ground plane, we may infer that the inductance Lrm is due to the Figure 1 Layouts of (a) CELCR loaded microstrip line and (b) CELCR with relevant dimensions. Figure 2 Constitutive parameters of CELC-loaded microstrip line in Fig. 1(a). (a) Relative effective permeability; (b) relative effective permittivity. TABLE I Dimensions of Supposed CELC Resonator Values of Geometrical Parameters of CELC (mm) xDGS yDGS lgap dgap Wgap Wm 4.6 10 3.8 0.2 2.4 0.2 472 Oraizi and Torabi International Journal of RF and Microwave Computer-Aided Engineering/Vol. 23, No. 4, July 2013 circulating current around the horizontal edges of the T-shaped slots on the ground plane and the capacitors Crm and Crs are due to the T-shaped and outer circumference of CELC slots, respectively. IV. REALIZATION OF LH CELL USING CELC RESONATORS In order to realize an LH cell, we need a component to provide a negative permittivity eeff. We may realize such characteristics by loading the line through stubs shorted to the ground by some vias immediately above the CELC [2]. The proposed LH cell together with its lumped equiv- alent circuit is shown in Figures 5 and 6, respectively. The shunt inductor LP is to include the effect of via in the equivalent circuit. V. SYNTHESIS OF LH CELL The LH cell is synthesized in two stages. At first, the equivalent circuit is synthesized according to the specified characteristics. Then the geometrical dimensions of LH cell are determined. A. Design of Components in the Equivalent Circuit We assume the input parameters as the operating fre- quency f0 and Bloch impedance ZB (2pf0), which for p network is [6]: ZBðxÞ ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ZSðxÞZPðxÞ 2 1 þ ZSðxÞ 2ZPðxÞ 8: 9; vuut (1) Where ZS(x) and ZP(x) are its series and shunt impedan- ces. The resonance frequency (fr) can also be calculated by Eq. (2). fr ¼ 1ffiffiffiffiffiffiffiffiffiffiffiffiffiffi LrmCrm p (2) The allowable band for the LH propagation is where both Bloch impedance and cell phase shift (bl) are real. Figure 3 (a) Electric field configuration and (b) surface current distribution on the ground plane in the vicinity of CELC, near the resonance frequency. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.] Figure 4 Equivalent circuit model of CELC loaded microstrip line in Figure 1a. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.] Figure 5 Layout of the proposed LH cell, realized by the com- bination of CELCR and short circuited stubs loaded microstrip line. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.] Figure 6 Equivalent circuit model of the proposed LH cell. [Color figure can be viewed in the online issue, which is avail- able at wileyonlinelibrary.com.] Novel Metamaterial CELC Resonator 473 International Journal of RF and Microwave Computer-Aided Engineering DOI 10.1002/mmce Consequently, from Eq. (1), the lower and upper limits of the LH pass-band can be calculated by the following con- ditions [7, 8]: ZSðxÞ ¼ 0 (3a) ZSðxÞ ¼ �2ZPðxÞ (3b) In the frequency interval between fL and fH, the reactance of series branch ZS(x) is negative and that of the shunt branch ZP(x) is positive. The above parameters (fr, fL, fH, ZB) are the specified known parameters, which lead to the synthesis of coupled CELC resonator. The synthesis is based on the least mean square, by constructing the following error function. E ¼ WL f 0L � fL � �2þWH f 0H � fH � �2þW0 f 0r � f 0r � �2 þWZ Z0B � ZB � �2 (4) In which the primed quantities are the desired values and the unprimed quantities are to be computed by the given expressions as a function of its various parameters. The weighting functions are WL, WH, W0, WZ. The minimization of error is performed by the genetic algorithm. Consequently, the values of lumped circuit components are evaluated. VI. EQUIVALENT GEOMETRICAL DIMENSIONS OF CELC Having obtained the equivalent circuit of the CELC reso- nator coupled to a microstrip line, together with the values of various parts and components, we then need to evaluate the geometrical dimensions of CELC. By applying the Biot-Savart’s law, the magnetic flux density for a rectangular slot of dimensions (a � b) and circulating current i is [9]: BT�shaped ¼ 2l0i p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a2 þ b2p a b þ b a 8>: 9>; (5) Therefore, the inductance of the rectangular slot can be calculated from the following equation, where ST ¼ a � b is the area of rectangular slot. L ¼ BT�shaped �� ��ST i (6) The inductance Lrm of the tank circuit is then equal to L/ 2, because the current entering the CELC is split into two branches, which circulate the horizontal portion of the T- shaped slot. Therefore, the dimensions of horizontal edges of T-shaped slots can be obtained from the inductance of the equivalent circuit Lrm. On the other hand, the dimen- sions of vertical edges of T-shaped and peripheral slots may be obtained by the slot line formulas in terms of the component values in the equivalent circuit (Crm and Crs) available in the literature [10]. The geometrical dimen- sions of stubs and microstrip line may also be obtained in terms of related component values (LP, L, C) by the avail- able formulas in references [6]. VII. DESIGN EXAMPLE We specify the characteristics of the LH CELC resonator in the C band as: TABLE II Dimensions of Proposed LH Cell Based on CELCR Together with Values of Equivalent Circuit Parameters Equivalent circuit parameters of LH CELL L (nH) C (pF) Lrm (nH) Crm (pF) Crs (pF) LP (nH) 1.8 0.3 0.92 6.75 10.65 1.61 Values of Geometrical Parameters of LH CELL(mm) xDGS yDGS lgap dgap Wgap Wm lstub Wstub 4.6 10 3.2 0.2 2.4 0.2 11.4 1 Figure 7 S parameters of the proposed LH cell computed by full-wave simulation and circuit model. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.] Figure 8 Frequency response of the eight-section LH CELC cells. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.] 474 Oraizi and Torabi International Journal of RF and Microwave Computer-Aided Engineering/Vol. 23, No. 4, July 2013 ðfL ¼ 2:2 GHz; fH ¼ 2:3 GHz; f0 ¼ 2:25 GHz; ZB ¼ 50; fr ¼ 2:1 GHzÞ We use the substrate RO6010 (dielectric constant er ¼ 10.2, height h ¼ 0.635 mm, loss tangent ¼ 0.0023) and employ the proposed design procedure. The equivalent component values of the equivalent cir- cuit and the values of the geometrical dimensions are reported in Table II. The frequency response of the filter as S11 and S21 are drawn in Figure 7. A disadvantage of LH cells made by CELC resonator is the low slope of the higher skirt of the frequency response of band-pass filter. That is the out-of-band suppression achieved by them is not satisfactory. Therefore, we use a cascade connection of several LH CELC resonators. The frequency response of the series connection of eight cells is shown in Figure 8, with very good response. VIII. CONCLUSION We have presented a novel metamaterial CELC resonator and described its operational mechanism characteristics and potential applications for the design of microwave components. We studied its resonance behavior by the diagrams of eeff and leff. A circuit model was obtained for its coupling with a loaded microstrip line. Finally, a LH cell was made by the CELC resonator combined with a short circuited stub, and was designed by the least mean square method. We finally use the cascade connection of such LH cells for the design of a miniaturized narrow- band band-pass filter with high out of band rejection. REFERENCES 1. C. Caloz, H. Okabe, H. Iwai, and T. Itoh, Transmission line approach of left-handed metamaterials, Proc USNC/URSI Nat Radio Sci Meeting, San Antonio, TX, 2002, p. 39. 2. F. Martin, F. Falcone, J. Bonache, J.R. Marques, and M. 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Medina, and M. Sor- olla, Compact CPW band pass filter at S-band, Microwave Opt Technol Lett 46 (2005), 33–35. 9. M. Kazerooni, A. Cheldavi, and M. Kamarei, Analysis, mod- eling, and design of cascaded defected microstrip structure for planar circuits, Int J RF Microwave Comput Aided Eng 20 (2010), 170–181. 10. P. Silvester and P. Bendek, Equivalent capacitances for microstrip gap and steps, IEEE Trans Microwave Theory Technol 20 (1972), 729–733. BIOGRAPHIES Prof. H. Oraizi received BEE degree from American University of Beirut, Lebanon, in 1967, MSc and PhD degrees in electrical engineering from Syracuse University, Syracuse, NY, in 1969 and 1973, respectively. From 1973 to 1974, he was at Toosi University of Technology, Tehran, Iran. From 1974 to 1985, he was with the Communica- tions Division, Iran Electronics Industries, Shiraz, Iran. In 1985, he joined the Department of Electrical Engineering, Iran University of Science and Technology, Tehran, Iran, where he is a Full Professor of electromagnetic engineer- ing. He has authored and translated several textbooks in Farsi. He has authored or coauthored over 250 papers in international journals and conferences. In 2006, he was elected an exemplary nation wide university professor in Iran. He is an Invited Professor of the Electrical Engineer- ing Group, Academy of Sciences of Iran, and is listed as an elite engineer by the Iranology Foundation. He was elected as a remarkable nationwide researcher in Iran in 2012. Dr. Oraizi is a Fellow of Electromagnetic Academy, a fellow of Japan Society for the Promotion of Science and a senior member of IEEE. He is listed in Who’s Who in the World. Seyede Yalda Torabi was born in zanjan, Iran in 1987. She received her BSc degree in electrical engi- neering from Tabriz University, Tab- riz, Iran in 2009 and the MSc degree from the Iran University of Science and Technology (IUST), Tehran, Iran in 2012 and is currently working to- ward the PhD degree in electrical engineering at Shahed University, Tehran, Iran. She has completed several proj- ects on electronic and communication circuits. Her research interests are in application of metamaterial for the design of antennas, filters, couplers, and waveguides. Novel Metamaterial CELC Resonator 475 International Journal of RF and Microwave Computer-Aided Engineering DOI 10.1002/mmce