An Efficient Method Based on Equivalent-Circuit Modeling for Analysis of Frequency Selective Surfaces Silva, M. W. B.
Kretly, L. c., Member, IEEE
School of Electrical and Computer Engineering University of Campinas Campinas, Sao Paulo 13083-852 Email:
[email protected] Telephone: (55) 19 352 1-0209
School of Electrical and Computer Engineering University of Campinas Campinas, Sao Paulo 13083-852 Email:
[email protected] Telephone: (55) 19 352 1-3822
Abstract-This paper presents an investigation of the trans mission/reflection properties of
Frequency Selective Surfaces
(FSS) with perfectly conducting square patch and cross elements. The present model uses a full wave technique to obtain the scattering characteristics preliminary of the FSS in freestanding configuration. The analysis is based on a simple equivalent circuit model for retrieving the equivalent Land C parameters of a certain FSS shape. By employing the extracted parameters and circuit analysis theory, the physical meaning of the lumped parameters can be explained. By using the extracted equivalent circuit and parameter, the full-wave and lumped model can be compared. Reasonable agreement between the full-wave simula tion and lumped model is verified.
I.
INTRODUCTION
Frequency selective surfaces (FSSs) are periodic arrange ments comprised of metallic patch or aperture elements, show ing a particular filtering behavior with respect to frequency. Its selectivity infrequency is obtained by the design and allows the transmission of signals in a certain frequency range only. FSS applications vary almost as much as their structures and designs. Radomes were the first application to employ FSS structures. These radomes use FSS structures to make the radome appear transparent to the antenna at the operating frequency. Other typical applications of FSS's exploit their filtering properties such as spatial filters, reflectors, absorbers to prevent Electromagnetic Interference (e. g., between two antennas operating in overlapping frequency bands), and re ducing the radar cross section (RCS) [ 1]. For analyzing the electromagnetic behavior of frequency selective surfaces, several classical numerical techniques have been used. Among them, the Finite Difference Time Domain technique (FDTD), the Finite Element Method (FEM), and the Integral Equation Method (lEM) are the most popular [2],[3]. The FDTD method and the FEM are enables the analysis of any type element, but typically are quite slow and requires a great computational effort. The IEM is very efficient if used with entire domain basis functions, however, is usually limited to a few shapes [4],[5]. In [6] a comparison between equivalent circuit model and MoM was done. A Jerusalem cross and double square loop array were considered and experimental results obtained from literature were compared with numerical results.
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This work investigates a technique for analyzing frequency selective surfaces through a circuital approach. The equivalent circuit model is a simple method that produces satisfactory results. In this method, the segments of strips forming the element in a periodic array are modeled as capacitive or inductive components in a transmission line. The solution of this circuit is found in the transmission and reflection characteristics of the FSS. This technique uses a quasi-static approximation for calculating the components of the circuit and allows a very fast computational analysis [6]. The model can be applied for normal and oblique incident angles, as well as in the presence of dielectric slabs. This is done by adjusting the parameters computed in freestanding configuration [7]. The analysis is based on a preliminary full wave simulation in order to derive the inductance and the capacitance that represents the FSS under analysis. II.
EQUIVALENT CIRCUIT MODEL
An useful way to understand the FSS characteristic be havior is to establish an analogy between lumped filters and these surfaces. Alternatively to the computationally intensive numerical approaches, the circuit model offers a simple method in FSS analyses which are useful for quickly predicting the performance of FSS and allow performing a very simple model able to describe every kind of shape after a full-wave simulation [8]. The starting point for developing equivalent circuits for FSS structures is the circuit representation of an infinite parallel conducting strip developed by Marcuvitz [ 10]. The most simple FSS filters is strip grating reported in Fig. l. The metal strips have a zero thickness, a width, W, and periodicity p. For an infinite array of thin, perfectly conducting narrow strips the shunt impedance is either inductive or capacitive, as shown in Fig. 1(a), depending on whether the incident wave is polarized parallel or perpendicular to the strips [9]. In the former case the equivalent circuit corresponding to this FSS geometry is an inductor which acts as a shunt to ground. A low-frequency source drives a current across the inductor and travels to ground, while a high-frequency source will not drive
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