Francisco Aznar

Open Complementary Split Ring Resonators (OCSRRs) and Their Application to Wideband CPW Band Pass Filters

In this letter, open complementary split ring resonators (OCSRRs) are introduced for the first time. Such resonators are the dual counterparts of the open split ring resonators (OSRRs), introduced in 2004 by some of the authors, and consist on a pair of concentric hooks etched on a metal layer in opposite orientation. It is shown in the letter that OCSRRs can be modeled by means of an LC parallel resonant tank and that this particle roughly exhibits half the resonance frequency of the complementary split ring resonator (CSRR), hence being electrically very small. The interest of these resonators is illustrated through their application to a wideband coplanar waveguide band pass filter.

Applications of Open Split Ring Resonators and Open Complementary Split Ring Resonators to the Synthesis of Artificial Transmission Lines and Microwave Passive Components

This paper is focused on the application of open split ring resonators (OSRRs) and their dual counterparts, open complementary split ring resonators (OCSRRs), to the synthesis of composite right/left-handed transmission lines, that is, artificial lines exhibiting backward wave propagation at low frequencies and forward wave propagation at high frequencies. Due to the small dimensions of these resonators, the resulting lines are very compact. Several artificial lines, with different electrical characteristics and topologies, are reported as illustrative examples. It is shown that these artificial lines can be applied to the synthesis of dual-band components and bandpass filters, and two prototype device examples are designed and fabricated in coplanar waveguide technology: a dual-band impedance inverter applied to a dual-band power divider, and an order-3 wide-band bandpass filter. Finally, it is also demonstrated that OSRRs and OCSRRs can be combined for the synthesis of band pass filters in microstrip technology. Since OSRRs and OCSRRs are described by means of series and shunt resonant tanks, respectively, and they are electrically small, their potential to the design of semi lumped planar microwave devices is very high.

Revising the equivalent circuit models of resonant-type metamaterial transmission lines

In this work, it is shown that the previously reported and accepted equivalent circuit models of resonant type left-handed lines, either loaded with split ring resonators (SRRs), or with complementary split ring resonators (CSRRs), need a revision in order to properly account for the different elements of the structures and to accurately describe their behavior. The main relevant conclusion and novelty of this paper is that the already existing models are formally correct, but some of the reactive parameters do not have the physical interpretation given so far. However, these parameters are related to the parameters of the improved models, which are proposed and exhaustively analyzed here for the first time. A comparative analysis of SRRand CSRR-loaded lines, to the light of these new models, is also included. The results of this work are of interest for the design of CSRR- and SRR-based microwave circuits.

Elliptic-Function CPW Low-Pass Filters Implemented by Means of Open Complementary Split Ring Resonators (OCSRRs)

In this letter, an elliptic low-pass filter (LPF) implemented in coplanar waveguide (CPW) technology by etching open complementary split ring resonators (OCSRRs) in the central strip is presented for the first time. The OCSRRs behave as series connected parallel resonant tanks, whereas metallic patches etched in the back side of the substrate provide the required shunt capacitance to achieve the elliptic function response. An order-5 elliptic LPF has been designed and fabricated to illustrate the possibilities of this new approach. The measured frequency response is in good agreement with the ideal elliptic function up to twice the cutoff frequency (fc=1& GHz). Since OCSRRs are electrically small resonators, filter dimensions are also small (device length is 2.5 cm, namely 0.13 lambda , where lambda is the guided wavelength at fc). This work is illustrative of the possibilities of OCSRRs for the design of compact planar filters and other microwave components.

Modelling metamaterial transmission lines: a review and recent developments

This review paper is devoted to the discussion and comparison of the lumped element equivalent circuit models of the different types of metamaterial transmission lines that have been proposed so far, namely the CL-loaded lines, and those lines based on the resonant type approach. The latter category comprises both artificial lines loaded with split ring resonators (SRRs), or related topologies, and metamaterial transmission lines based on complementary split ring resonators (CSRRs). It will be the main aim of this paper to clearly justify the circuit elements of the models (and link such elements to the line physics and topology), to compare the different lines to the light of these models, and to point out the advantages and drawbacks of the different metamaterial transmission lines. As long as metamaterial transmission lines are exhaustively used for the design of compact microwave and millimeter wave components with improved performance and/or based on new functionalities, and their synthesis is based on the lumped element equivalent circuits, this paper is of actual interest for RF/microwave engineers and in general to those readers involved in metamaterial research and applications.

Low-pass and high-pass microwave filters with transmission zero based on metamaterial concepts

In this work, highly selective filters based on periodic arrays of electrically small resonators are pointed out. The high-pass filters are implemented in microstrip technology by etching complementary split ring resonators (CSRRs), or complementary spiral resonators (CSRs), in the ground plane, and series capacitive gaps, or interdigital capacitors, in the signal strip. The structure exhibits a composite right/left handed (CRLH) behavior and, by properly tuning the geometry of the elements, a high pass response with a sharp transition band is obtained. The low-pass filters, also implemented in microstrip technology, are designed by cascading open complementary split ring resonators (OCSRRs) in the signal strip. These low pass filters do also exhibit a narrow transition band. The high selectivity of these microwave filters is due to the presence of a transmission zero. Since the resonant elements are small, filter dimensions are compact. Several prototype device examples are reported in this paper.

New composite right/left handed transmission lines based on electrically small open resonators

In this work, composite right/left handed (CRLH) transmission lines implemented by combining open split ring resonators (OSRRs) and open complementary split ring resonators (OCSRRs) are presented for the first time. Both the OSRR and the OCSRR are open particles which can be considered dual counterparts. The OSRR behaves as an open series resonator, whereas the OCSRR can be modeled as an open parallel resonant tank. By connecting the OSRR and the OCSRR in series and shunt configuration, respectively, in a host transmission line, backward and forward wave transmission at low and high frequencies, respectively, is achieved. As compared to split ring resonators (SRRs) and complementary split ring resonators (CSRRs), the open resonators used in this paper are electrically smaller. Thus, compact CRLH transmission lines can be obtained. To illustrate the new approach for the synthesis of metamaterial transmission lines, a CPW-based CRLH transmission line has been fabricated, modeled and characterized. Advantages and drawbacks of the reported approach, as well as potential applications, are also pointed out.

Electrically Small Resonators for Metamaterial and Microwave Circuit Design

A new branch in microwave engineering arose just few years ago with the emergence of metamaterials in 2000 (Smith et al., 2000). The implementation of the first artificial medium with negative effective dielectric permittivity and magnetic permeability opened the door to the experimental study of a new kind of media: left-handed media. The possibility of the artificial implementation of such media allowed the corroboration of many of their electromagnetic properties, predicted years before by Viktor Veselago (Veselago, 1968). Since the year 2000, the interest stirred up by these new materials has given rise to numerous works in a wide range of scientific branches. The possibilities that metamaterials offer to create artificial media with controllable characteristics has permitted the creation of a growing number of completely new applications. Undoubtedly, the most innovative and spectacular application of such artificial media is their use in the implementation of cloaking structures to achieve invisibility, which can be accomplished thanks to the engineering of the refraction index of the different layers of the cloaking shield (Schurig et al., 2006). Within the vast number of new applications of metamaterials, one of the most productive ones is the implementation of microwave devices by means of artificial transmission lines. The following sections will deal with one of the approaches devoted to this purpose: the resonant-type approach. Different subwavelength resonators employed in the design of metamaterial transmission lines based on the resonant-type approach will be studied. The equivalent circuit models of different kinds of metamaterial transmission lines, as well as the parameter extraction methods employed as design and corroboration tools will be also presented. In closing, a selection of application examples of resonant-type metamaterial transmission lines in the design of microwave devices will be presented. 19

SRR- and CSRR-based Metamaterial Transmission Lines: Modeling and Comparison

This paper is focused on the comparison between the two main categories of resonant-type metamaterial transmission lines: those based on split ring resonators (SRRs) and those based on their complementary counterparts, that is, complementary split ring resonators (CSRRs). It will be shown that both SRR- and CSRR-based metamaterial transmission lines exhibit a very similar behavior, and this analogous behavior has been explained on the basis of the equivalent circuit model of the unit cell of these lines and from duality arguments.

Coplanar waveguide stop-band filters implemented by means of open split ring resonators (OSRRs)

This paper is focused on the design of coplanar waveguide (CPW) stop-band filters implemented by means of shunt connected open split ring resonators (OSRRs). The filters consist on a cascade of transmission line sections, acting as impedance inverters, alternating with OSRRs. Two illustrative examples are provided in the paper: a Chebyshev stop-band filter centered at 3.4 GHz (40% fractional bandwidth), and a Butterworth stop-band filter centered at 6 GHz (50% fractional bandwidth). These illustrative examples point out that OSRRs can be used in shunt connection in CPW technology for the design of stop-band filters with frequency responses following standard approximations.