Equivalent Circuit Analysis of Metamaterial Structure
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Equivalent Circuit Analysis of Metamaterial Structure Han Xiong 1,2
&
Qing Ji 3
Received: 6 February 2020 / Accepted: 18 August 2020 # Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In this paper, an equivalent circuit model of swastika-like structure metamaterial is investigated. Mutual inductance between adjacent swastikas ring arrays is taken into consideration in the proposed equivalent circuit model. The analytical expression for calculating the effective permeability of the windmill structure is derived. By the derived expressions, the physical mechanisms of the magnetic resonance frequency versus structural parameters are well explained. Based on the equivalent circuit model, some strategies for the fast and efficient optimization metamaterial structures can be used to achieve a better target performance in the future. Keywords Metamaterial . Equivalent circuit . Mutual inductance . Magnetic resonance . Electric resonance
Introduction Over the past decades, artificially engineered metamaterials have attracted a great deal of interest, and they have been investigated by both engineering and physics communities due to their extraordinary electromagnetic properties, such as independently tunable permittivity, permeability, and refractive index [1–4]. The research of difficult metamaterial structures provides innovative applications in practical microwave devices, such as antennas, absorber, and filters [5–11]. Meanwhile, some theoretical approaches, such as the effective medium theory [12] and transmission line theory [13, 14], have been exploited to explain the physics mechanism. These analytical theories have significantly contributed to the development of metamaterials. Based on the effective medium theory, the macroscopic electromagnetic parameters can be obtained by utilizing the retrieval method. However, it does not offer the criteria to select the structural parameters for the desired properties of metamaterial. In fact, the relationship between the effective permeability and geometrical
* Han Xiong [email protected] 1
School of Microelectronics and Communication Engineering, Chongqing University, Chongqing 400044, China
2
State Key Laboratory of Power Transmission Equipment & System Security and New Technology, Chongqing University, Chongqing 400044, China
3
Department of Electrical and Computer Engineering, University of Houston, Houston, TX 77004, USA
parameters is more important for engineers. Therefore, it is necessary to investigate how to choose the geometrical parameters of metamaterials. To overcome the drawbacks of the above analytical theories, equivalent circuit approach, which is the most popular and widely used method, was adopted in the previous literature [15–20]. However, the mutual inductance M caused by the periodic structure cell is not integrated into the equivalent circuit in most literature. Hence, it is unfeasible to investigate the electromagnetic influences accurately. This investigation was inspired by the previous work of Chen et al. [
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