Modeling and analysis of metamaterial lenses based on lumped circuits by using a wave concept iterative method

Elbellili, Taieb; Azizi, Mohamed Karim; Latrach, Lassaad; Trabelsi, H.; Baudrand, H.

doi:10.1017/s1759078717001489

Cited by 5 publications

(7 citation statements)

References 24 publications

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“…The iterative method WCIP is well used to study the behavior of metamaterial circuits, such as lenses [20] where a periodic circuit can be established around RH/LH unit cells to synthesize positive and negative refractive index media, respectively. In the same reference, the WCIP method is used to analyze arbitrary shaped periodic lumped circuits, which proves that the proposed method gives more flexibility to design and study metamaterial circuits.…”

Section: The Basic Theory Of the Wcip Methods And Synthesis Of Zero Rementioning

confidence: 99%

“…The spatial reflection coefficient is given by [20] as follows: where Z Δ is the impedance along the axis Δ = ( X , Y , Z ) and Z 0 is the characteristic impedance.…”

Section: The Basic Theory Of the Wcip Methods And Synthesis Of Zero Rementioning

confidence: 99%

“…To overcome all the above requirements, we use a wave concept iterative method (WCIP) which has been recently used to accurately analyze both 1-D and 2-D metamaterial periodic lumped circuits [20–28].…”

Section: Introductionmentioning

confidence: 99%

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Transmission line approach of zero-index metamaterials and applications using a wave concept iterative method

Azizi

Elbellili

Baudrand³

et al. 2019

Int. J. Microw. Wireless Technol.

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In this paper, we propose a novel study of zero-index materials (ZIM) based on lumped element circuits using a wave concept iterative method (WCIP). This method is well used to demonstrate the behavior of zero-index-based microwave applications. This type of metamaterial can maintain the amplitude and the phase of an electromagnetic wave to be constant through the ZIM region, which is an important property to design an in-phase power divider-combiner, enhance the directivity of an embedded source, channel electromagnetic waves without reflection at the interface between waveguides with different cross-sections, and control the transmission of electromagnetic wave by the adjustment of the permittivity of a dielectric defect coated by zero-index metamaterial. The numerical simulations using the WCIP method match the literature and commercial software simulator results.

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Section: The Basic Theory Of the Wcip Methods And Synthesis Of Zero Rementioning

confidence: 99%

“…The spatial reflection coefficient is given by [20] as follows: where Z Δ is the impedance along the axis Δ = ( X , Y , Z ) and Z 0 is the characteristic impedance.…”

Section: The Basic Theory Of the Wcip Methods And Synthesis Of Zero Rementioning

confidence: 99%

See 1 more Smart Citation

Transmission line approach of zero-index metamaterials and applications using a wave concept iterative method

Azizi

Elbellili

Baudrand³

et al. 2019

Int. J. Microw. Wireless Technol.

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“…To overcome some drawbacks of the previous works and to improve the circuits design, we recently reformulated and adopted the Wave Concept Iterative Process (WCIP) method [29][30][31][32][33][34] into rectangular and triangular approaches, that facilitate problem solving of RLC circuits with rectangular 35 and triangular topologies, 36 respectively.…”

Section: Al In Reference 17 Andmentioning

confidence: 99%

Design and analysis of two layers RLC network of rectangular topology by wave concept iterative process method

Ammar¹,

Vincent

2020

Int J Numerical Modelling

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The paper presents a theoretical study of a rectangular electrical network built on two layers. First, the auxiliary source notion is introduced for characterizing the potential difference over each electrical element, then the mathematical formalism of the Wave Concept Iterative Process method is developed and adopted to the studied circuit. The used method is based on the concept of the incident and reflected waves which are defined from the current and voltage at each branch of the circuit. Two relations connecting the waves are established into two definition domains: a spectral-domain using the Kirchhoff laws and the auxiliary source connections and, another spatial defining the boundary conditions and the circuit design. Hence a two equations system is obtained and it is resolved by an iterative process, the transition between the two domains is ensured by the fast Fourier transform and its inverse. Moreover, the equivalent impedance between the feeding source and the nodes of the bottom layer has been calculated. Among the numerical simulation methods, this method has demonstrated its performances for analyzing various designs of the networks including RL, RC and RLC circuits excited by a lumped voltage source. The effect of the circuit parameters on the electrical currents and equivalent impedance has been studied.

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“…() Recently, the method has been developed to study almost periodic networks with rectangular topology excited by localized sources, and it has been successfully applied for modeling the metamaterial lenses and quasi‐periodic lumped circuits. ()…”

Section: Introductionmentioning

confidence: 99%

The wave concept iterative process (WCIP) method for electrical circuit network with triangular and hexagonal topology

Ammar¹,

Baudrand

2019

Circuit Theory & Apps

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Summary This paper deals with an RLC circuit network with triangular or hexagonal grid. It is about a planar equilateral triangular grid where the passive (resistor, capacitor, and inductor) or active (voltage source for example) components are located at the sides or/and at nodes attached to the ground. The planar graph is oriented by three main direction vectors phase shifted to 60° degrees. The wave concept iterative process (WCIP) method was employed to the theoretical formulation of the problem. In the formulation, the potential difference across each circuit component is represented by an auxiliary source defined in the spectral domain. The proposed theory is developed into two definition domains: a spectral domain in which periodicity and coupling between the circuit components are defined and a spatial domain describing the network topology and imposing the continuities conditions (Kirchhoff laws). The transition between the spectral and spatial domain is ensured by the so‐called fast hexagonal Fourier transform. Numerical applications demonstrate the ability of the method for solving the inhomogeneous triangular lattices. Various conceptions have been proposed including an RL, RC, and RLC triangular network circuit, a perturbed triangular RLC circuit, and a triangular circuit excited by many lumped sources.

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Modeling and analysis of metamaterial lenses based on lumped circuits by using a wave concept iterative method

Cited by 5 publications

References 24 publications

Transmission line approach of zero-index metamaterials and applications using a wave concept iterative method

Transmission line approach of zero-index metamaterials and applications using a wave concept iterative method

Design and analysis of two layers RLC network of rectangular topology by wave concept iterative process method

The wave concept iterative process (WCIP) method for electrical circuit network with triangular and hexagonal topology

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