Abstract
In this paper, we calculate the dispersion of the effective dielectric constant of the structure from the lattice of conductive squares located in a dielectric layer and connected by resistive jumpers based on the solution of the diffraction problem. Depending on the parameters of the jumpers , the dispersion of this structure was shown to be capable of varying from the relaxation type to one that corresponds to the structure of continuous resistive films. The jumpers were also shown to affect the nature of the dispersion in the long-wave part of the wave range most significantly in relation to the structure period.
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INTRODUCTION
The possibility of varying the dispersion characteristics of composite materials (CMs) used in radar absorbing structures over a wide range allows one to affect the amplitude–frequency characteristic for their optimization [1]. In this regard, structures based on conducting dipoles and resistive squares with a capacitive connection between elements that have a relaxation nature of the dispersion of the effective dielectric constant (EDC) are promising, as has been shown in a number of studies [2–7]. It should be expected that the additional introduction of a resistive (ohmic) connection into the structure with the capacitive coupling between the conductive inclusions will affect the type of dispersion of the EDC and expand the possibilities of its variation.
We proposed a lattice structure of conductive squares interconnected by resistive jumpers that is located in the dielectric layer.
This paper is aimed at calculating the EDC of the structure and studying the effect of jumpers on the nature of the dispersion.
NUMERICAL CALCULATION RESULTS
The studied periodic structure is shown in Fig. 1. Unlike the structure studied in [7], the flat lattices consist of conducting squares with surface resistance \({\rho }\) connected by resistive jumpers with the same surface resistance. The lattices are placed in a layer of a non-dispersive dielectric with a relative permittivity \({\varepsilon }\) located on an electric or magnetic plane. A plane electromagnetic wave polarized along the \(y\) axis falls onto the structure from the free space region in the direction of the \(z\) axis. The period of the plane lattice along the x and y axes is the same and is equal to \(2b\), the square side is equal to \(2s\), the distance between the squares is equal to \({\tau }\), and the jumper width is equal to \(2p\).
The solution of the diffraction problem is based on the solution of the excitation problem of a Floquet channel by currents of small elements into which both squares and jumpers were split [5, 7, 8]. Given the periodicity and symmetry of the structure and polarization of the incident wave, the diffraction problem reduces to solving the scattering problem in an equivalent waveguide, the walls of which are electric, while the \(x = 0,\;a\) walls are magnetic (Fig. 2). The lattice coordinates are as follows: \({{z}_{n}} = {h \mathord{\left/ {\vphantom {h 2}} \right. \kern-0em} 2} + (n - 1)h\), \(n = 1,\;2,\; \ldots \;k\), where \(h = {d \mathord{\left/ {\vphantom {d k}} \right. \kern-0em} k}\), \(k\) is the number of lattices, and \(d\) is the dielectric layer thickness. The EDC is calculated based on the values of the complex reflection coefficient when the structure is located on electric and magnetic mirrors [5, 7].
The calculations were performed at \(k = 5\) because the homogenization accuracy decreases with a smaller number of lattices. The number of partitions of squares and jumpers into rectangular elements and the number of harmonics of the Floquet channel taken into account were chosen to be sufficient to calculate the components of the complex reflection coefficient with an accuracy of 0.01. The order of the complex system of linear equations with respect to currents in small elements was 1290.
The calculated values of the parameters are as follows: \(d = 0.01\) m, \({\rho } = 1000\) Ω, \({\varepsilon } = 3\), \(s = 4\) mm, \(b = 4.25\) mm, and \({\tau } = 0.5\) mm. The dependences of the real \({\varepsilon }{\kern 1pt} {{'}}\) and imaginary \({\varepsilon }{\kern 1pt}^ {"}\) components of the EDC on the wavelength at various values of the jumper size \(p\) are shown in Figs. 3a and 3b, respectively. In the absence of resistive jumpers, the dispersion has a relaxation character (curve 1). The introduction of jumpers significantly changes the dispersion curves. An increase in the parameter \(p\) (curves 2–4) leads to the dispersion dependence of the EDC approaching that for the structure of continuous resistive films (curve 5). As can be seen in the figures, one peculiarity of varying the dispersion dependence of the EDC by changing the size of resistive jumpers is that the nature of the dispersion changes significantly in the long-wavelength region, while it changes to a lesser extent in the short-wavelength part of the range.
CONCLUSIONS
The dispersion of the effective dielectric constant of an artificial dielectric formed by lattices of conducting squares with a resistive-capacitive connection between them through gaps and conductive jumpers was calculated based on the solution of the diffraction problem. Unlike the structure of lattices with a capacitive coupling between the elements, the nature of the dispersion is shown to not be purely relaxation and can vary from relaxation to that in a structure with continuous resistive films by changing the value of the resistive bond. In this case, the jumpers most significantly affect the nature of the dispersion in the long-wavelength part of the calculated wavelength range. The calculation results are applicable to other wavelength ranges with appropriate scaling of the geometric dimensions of the structures and can be used in the design of radar absorbing coatings in various parts of the wavelength range. We note that one technological advantage of using resistive lattices from squares with jumpers between them is their single connectivity. This allows manufacturing lattice fragments that contain a certain number of squares, for example, by stamping them from electrically conductive paper or a metalized film.
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Translated by A. Ivanov
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Ponomarenko, V.I., Lagunov, I.M. Artificial Dielectric Based on Conducting Squares with Resistive Jumpers. J. Commun. Technol. Electron. 65, 787–789 (2020). https://doi.org/10.1134/S1064226920060236
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DOI: https://doi.org/10.1134/S1064226920060236