Equivalent-circuit models for split-ring resonators and complementary split-ring resonators coupled to planar transmission lines (original) (raw)

Analytical Model of Transmission Line Metamaterial with Asymmetricaly Coupled Split-Ring Resonators

Apart from numerical simulations, some type of analytical model for studying metamaterials is desirable for at least two reasons: easier design and optimization, and, more importantly, improved understanding and intuition about the underlying physics. For transmission line metamaterials, equivalent circuit models were frequently used for this purpose, but they themselves can easily become quite complicated, especially in case of multiple coupled split-ring resonators (SRRs), possibly involving both electric and magnetic coupling. Here we present simple model which starts from coupled linear harmonic oscillators, and then approximates the transmission through the structure. This model is able to provide us with qualitative description of resonance-related phenomena, such as left-handed bands and metamaterial equivalent of electromagnetically induced transparency (EIT).

Split rings for metamaterial and microwave circuit design: A review of recent developments (Invited paper)

International Journal of RF and Microwave Computer-Aided Engineering, 2012

This article is a review of recent applications of split rings to the design of planar microwave circuits based on metamaterial concepts. The considered resonators, namely, split-ring resonators (SRRs), complementary SRRs (CSRRs), and their open counterparts (OSRRs and OCSRRs), are reviewed, and the equivalent circuit models of artificial lines based on such resonators, including parasitics, are presented and discussed. The second part of the article is devoted to highlight some recent applications of the considered resonators. This will include the design of dual-band components and wideband bandpass filters based on the combination of OSRRs and OCSRRs, the design of tunable components based on cantilever-type SRRs, and the design of CSRR-based differential (balanced) lines with common-mode suppression.

Effects of inter-resonator coupling in split ring resonator loaded metamaterial transmission lines

Journal of Applied Physics, 2014

This paper investigates the effects of inter-resonator coupling in metamaterial transmission lines loaded with split ring resonators (SRRs). The study is performed from Bloch mode theory applied to the multiport equivalent circuit model of the unit cell of such artificial lines. From this analysis, it follows that the stopband bandwidth, inherent to SRR-loaded lines, is enhanced as inter-resonator coupling strengthens, and this enhancement is attributed to the presence of complex modes. The theoretical results are corroborated through calculation of the dispersion relation using a full-wave eigenmode solver, and also by measuring the frequency response of SRR-loaded lines with different inter-resonator distance and, hence, coupling. V

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

IEEE Transactions on Microwave Theory and Techniques, 2009

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. Index Terms-Artificial transmission lines, dual-band components, metamaterials, microwave filters, open complementary split ring resonators (OCSRRs), open split rings resonators (OSRRs). I. INTRODUCTION A RTIFICIAL transmission lines based on metamaterial concepts, that is, metamaterial transmission lines, have been a subject of growing interest in recent years. Such lines are artificial structures consisting on a host propagating medium loaded with reactive elements. Special efforts have been dedicated to the synthesis of artificial lines exhibiting backward wave transmission at low frequencies and forward wave propagation at high frequencies. These composite right/left-handed lines have been implemented in microstrip [1], [2], coplanar

A microstrip metamaterial split ring resonator

2011

This paper introduces a new low cost, robust microstrip structure, exhibiting metamaterial property, as a replacement of conventional bulky metamaterials structures. These types of planar microstrip structures are very useful for applications where space of equipment is a constraint. Although, the structure is inspired by Split-Ring resonator (SRR), it does not incorporate additional metallic rod for electrical resonance, as used with conventional SRRs. The rings are elliptical in shape and coaxial dual feeding has been used that are offset in phase. Simulations of the elliptical split ring resonator (ESRR) have been carried out in microwave regime. S-parameter simulation results of the resonator show metamaterial property at multiple frequency bands.

Comparative analysis of edge- and broadside coupled split ring resonators for metamaterial design - theory and experiments

IEEE Transactions on Antennas and Propagation, 2003

This paper develops a quasi-analytical and self-consistent model to compute the polarizabilities of split ring resonators (SRRs). An experimental setup is also proposed for measuring the magnetic polarizability of these structures. Experimental data are provided and compared with theoretical results computed following the proposed model. By using a local field approach, the model is applied to the obtaining of the dispersion characteristics of discrete negative magnetic permeability and left-handed metamaterials. Two types of SRRs, namely, the so-called edge coupled-and broadside coupled-SRRs, have been considered. A comparative analysis of these two structures has been carried out in connection with their suitability for the design of metamaterials. Advantages and disadvantages of both structures are discussed.

Modelling metamaterial transmission lines: a review and recent developments

Opto-Electronics Review, 2008

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 th...

Design of a compact dual-band-rejection microwave filter based on metamaterials transmission lines

2015

In this paper, a practical study and simulations about the transmission lines and microwave filters metamaterials at the base of the resonance elements is proposed. The Split Ring Resonator (SRR) and the Complementary SRR (CSSR) are coupled with the transmission lines in order to show the electromagnetic properties of metamaterials devices, and their transmission and reflection characteristics for each structure. A novel concept of a compact dual band rejection microwave filter with a high selectivity in the frequency and miniature size is designed. The theory of metamaterials, the NRW approach (Nicolson-Ross-Weir), are briefly introduced. Key-Words: metamaterials; filter; SRR; Complementary SRR; hyperfrequency; microstrip; dual-band-

A planar microstrip metamaterial resonator using split ring dual at Ku-Band

International journal of physical sciences

This paper introduces a new planar microstrip metamaterial resonator, the novelty of this paper lays in its unit cell design. The unit cell is formed by connecting metallic traces of two edge coupled split ring resonators to form the infinity symbol on one side of the substrate, and an array of conducting wires on the other. An RLC equivalent model of the structure is also proposed, it can be advantageous to use this model to identify the resonant frequency along with the root of the negative permeability and negative permittivity. The model shows resonance at 17 GHz. The structure was designed and simulated using EM solver Ansys HFSS, the extracted s-parameter matrix was analyzed to determine the effective permittivity, permeability and index of refraction. The structure shows negative values for effective ε, µ at resonant frequency 16.5 GHz. At frequencies where both the recovered real parts of ε and µ are simultaneously negative, the real part of the index of refraction is also found to be negative.

On the Orientation of Split-Ring Resonators in Metamaterial Media

2007

Split-ring resonators (SRR) are used both in microstrip and waveguide metamaterial structures to obtain negative values of permeability, whereas complementary split- ring resonators (CSRR) result in negative permittivity when placed below the microstrip. While the orientation of SRR positioned next to the microstrip transmission line significantly influences its performances, it is generally accepted that such dependence does not exist in the case of CSRR-loaded microstrip or SRR-loaded waveguide. In this paper, we show that SRR and CSRR can not be arbitrarily orientated, neither in microstrip nor in waveguide structures. The influence of the orientation is especially visible in the case of multiple CSRR geometries. To validate simulation results, microstrip lines loaded with multiple CSRRs were designed, fabricated and measured.