Triple Band Reject Frequency Selective Surface with Application to 2.4 GHz Band

— This paper presents the development of a frequency selective surface, FSS, with three bands of rejection, with the central bandwidth applied to the 2.4 GHz frequency band. Despite the fact that the main applications are in the 2.4 GHz frequency band, as emphasized in this paper, to reduce costs with scale production, it is interesting to note when the same FSS can be used for different applications such as wireless and cellular communications (1.71 GHz-1.93 GHz) and radio frequency localization (3.1 GHz-3.3GHz). The three rejection bands are obtained from the association of crossed- dipoles and matryoshka ring geometries. For each geometry the initial design equations are proposed. The procedure to obtain the matryoshka geometry is described step by step. Numerical results are presented for each geometry, and also to the associated geometries, considering different incident angles ( θ =0°, 15°, 30° and 45°). The current distribution of each resonant frequency was shown, making it possible to visualize the respective excited geometry. After the numerical results, we verified that the resonant frequencies associated to the respective geometry remained practically unchanged even for the associated geometries. A FSS prototype with the associated geometries was designed, fabricated, and characterized, with a very good agreement between numerical and experimental results, obtaining an attenuation of at least 15 dB in the 2.4 GHz frequency band.


I. INTRODUCTION
n recent years there has been a large growth in the use of mobile telecommunications services. One of the main drivers of this growth is the massive and diverse development of portable devices, such as smartphones, tablets, laptops, e-book readers, and gaming consoles. This development has provided a true revolution in various areas of human activity, including social interactions, education, health, and commerce. Most of these applications make use of Internet connections, leading to increased demand for transmission rates. Also, services such as video streaming, machine-to-machine (M2M) communication, and Internet of Things (IoT) diversification must be considered, all of which effectively contribute to the growth in demand for higher and higher transmission rates [1], [2].
Considering the limitations of the electromagnetic spectrum, the availability of space for antenna installation, environments with intensive use of wireless communication systems (shopping centers, office buildings, etc.), and sensitive environments (prisons, hospitals, embassies etc.), this means that it is necessary to optimize the use of antennas [3] - [7] as well as to provide solutions to mitigate interference between or limit access to wireless communication systems [8] - [11]. To meet these requirements, one solution is to use frequency selective surfaces (FSS) [12], [13].
Generally speaking, it can be said that a FSS is a periodic arrangement of metallic patch or dielectric slot elements that has the characteristic of reflecting, transmitting or absorbing electromagnetic waves. By allowing or blocking waves in free space, FSS are also called spatial filters [14]- [16]. FSS applications cover a wide range of the electromagnetic spectrum, from microwave to terahertz. These applications include dual-band operating antennas [3], [4], [14], [15], reconfigurable antennas [5], [6], sensors [17], [18], optimization efficiency of communication systems [8] - [11] and energy harvesting [19]. Basically, the frequency response of the FSS is determined by the characteristics of the dielectric, the unit cell geometry, the periodicity of the FSS, and the incident wave polarization, Fig. 1 I One of the challenges in the FSS design is when close resonances are desired, as illustrated in Fig. 2, especially when a single layer FSS is required. [20], [21]. In this case, one of the solutions is to associate different geometries in the composition of the FSS unit cell geometry. To avoid coupling between the different geometries, however, the respective resonances must be due to different field distributions [21].
Recently, matryoshka geometry with characteristics of miniaturization, multiband operation and polarization independence has been described [22], [23]. Taking these characteristics into account, this work presents a FSS with three rejection bands, based on the association of crossed-dipoles and matryoshka geometries. The central rejection band is applied to the Wi-Fi frequency range at 2.4 GHz, being obtained from the crossed-dipoles geometry. The two side rejection bands, 1.8 GHz and 3.2 GHz, are obtained from the resonances of the matryoshka geometry. Despite the fact that the main applications are in the 2.4 GHz frequency band, as emphasized in this paper, to reduce costs for large-scale production, it is interesting to note that the same FSS may be used for different applications, such as wireless and cellular communications (1.71 GHz-1.93 GHz) and radio frequency localization (3.1 GHz-3.3GHz) [24]. The procedure to obtain the matryoshka geometry is described step by step. Initial design equations are proposed for each geometry.
Numerical results are presented considering isolated and associated geometries, for different polarizations and incidence angles ( 0°, 15°, 30° and 45° . Even with the association of the geometries, the respective resonances were seen to remain unchanged, indicating decoupling between each. In addition to the numerical results, a FSS with the associated geometries was designed, manufactured and characterized experimentally, confirming the expected frequency response, with a very good agreement between the numerical and measured results. This paper is organized as follows: An introduction is presented in Section I; Section II describes the FSS design steps, showing initial equations for each geometry and the procedure for obtaining the matryoshka ring; in Section III, numerical and experimental results for each geometry and for associated geometries are presented; concluding with Section IV where the results obtained and characteristics achieved are summarized.

II. FSS DESIGN
This section describes the FSS project associating crosseddipoles and matryoshka geometries. The substrate is considered to have a dielectric constant and a thickness ℎ.

-Crossed-dipoles geometry
The crossed-dipoles is a very simple geometry, for which the resonant frequency occurs when its length is approximately half of the guided wavelength [14] - [16], Fig. 3.
Determining the dimensions of the FSS basic cell geometry is a process often based on the microwave engineer's experience and usually it is an iterative procedure. From initial dimensions, a numerical optimization is performed until the desired characteristics are achieved. However, equations to establish the initial dimensions can help in the FSS design. In this paper, the following equations are used [25]. -Dipole length, : in which ( )* is the desired resonant frequency and ) + is given by: Where ) +23 is the effective dielectric constant for a microstrip, considering the microstrip width equal the dipole width, 4, and a dielectric thickness ℎ. ) +567 is the effective dielectric constant for a coplanar waveguide without ground plane, with s=10×h and the center strip width equal to the dipole width, 4 [26].

Ldip
Ldip w -Matryoshka geometry The matryoshka geometry was introduced in [27], [28]. Differently from concentric rings, in matryoshka geometry the rings are interconnected, as only one ring, increasing its effective length, presenting, consequently, characteristics of miniaturization and multiband operation, Fig. 4. However, this geometry was polarization-dependent. In [22], [23] a polarization independent matryoshka geometry was proposed, Fig. 5, and it is the reference for the geometry considered in this paper. However, in this paper square matryoshka ring was adopted, as it was easier to manufacture than the circular one. The matryoshka geometry is obtained by the following steps. Initially, concentric square rings are designed, as depicted in Fig. 6(a). Then, gaps are inserted at the same position in consecutive rings, Fig. 6(b). Finally, the consecutive rings are connected and the matryoshka ring is achieved, Fig. 6  Matryoshka geometry presents a multi-resonant behavior [22], [23], [29], [30], but in this paper only the first two resonant frequencies are considered. Analogues to crossed-dipoles geometry, (3)-(6) provide a first approach for the two first resonant frequencies.
-Matryoshka geometry -first resonant frequency: -Matryoshka geometry -second resonant frequency: with ) 3 + 2 + 3 It must be emphasized that (1)-(6) are initial design equations, a first step towards a numerical optimization. Furthermore, the incident wave is considered normal to the FSS ( 0° . Associating the two geometries, the geometry depicted in Fig. 7 is obtained. Note that for ease of visualization, in Fig. 7 (a) the matryoshka geometry was not repeated around the unit cell.

III. NUMERICAL AND MEASURED RESULTS
Numerical results were obtained using the commercial software ANSYS Designer [31]. The measured results were acquired at the GTEMA/IFPB microwave measurements laboratory using an Agilent E5071C two ports network analyzer, two double ridge horn antennas and a measurement window as shown in Fig. 8. The basic cell dimensions are 40 DD 40 DD (E8 E: , and the substrate is a low cost fiber-glass FR-4 ( 4.4, loss tangent FG(H 0.02, thickness ℎ 1.6 DD. As the geometry is polarization independent, for numerical results only the x polarization is considered.  (1), and the measured one, present almost the same value, 2.45 GHz. The Table I summarizes the results, in which we can observe a very good angular stability. In a similar way, Fig. 10 shows the frequency responses for the matryoshka geometry, with 4 1.
3.27 GHz, a difference of 6.4% and 2.9%, respectively. When compared to numerical results, this is a good approximation for a first approach. Also noteworthy is a reduction in the first resonant frequency of 25.6%, from 2.46 GHz to 1.81 GHz, when comparing crossed-dipoles and matryoshka geometries, even though the crossed-dipoles are 62.5% larger than matryoshka, 39.0 mm and 24.0 mm, respectively. Table II summarizes the results, in which very good angular stability is observed again. The frequency response for the two associated geometries is presented in Fig. 11. Three resonant frequencies are observed, 1.81 GHz, 2.44 GHz and 3.18 GHz, with the first and third resonances being associated with the matryoshka geometry and the second one with the crossed-dipoles. It is also verified that these resonance frequencies practically did not shift in relation to the values of the isolated geometries. Even the grating lobes (around 3.1 GHz) are present in the frequency response for ≠ 0°. In Fig. 12 the current distribution is displayed for each resonant frequency and the geometry that produces this resonance can be identified. In Figs. 12(a) and 12(c), 1.81 GHz and 3.18 GHz, respectively, only the matryoshka is excited, and in Fig. 12(b), 2.43 GHz the crosseddipoles are excited.
In order to verify experimentally the frequency response behavior for the associated geometries, a FSS prototype was designed, fabricated and characterized. The dimensions and materials are the same previously described, Fig. 10. The whole FSS has 5 5 basic cells, corresponding to 20 ^D 20 ^D, Fig. 13. Measured results for crossed-dipoles and matryoshka associated geometries are presented in Fig. 14, normal incidence 0°, considering x and y polarizations. When compared to numerical results, a very good agreement is verified and an attenuation of at least 15 dB is achieved in the   Wi-Fi band (2.4 GHz). Moreover, the polarization independence is confirmed. The results are show in Table III   In

IV. CONCLUSIONS
In this paper, a triple band reject FSS with application to 2.4 GHz band is described. The proposed FSS is single layer and based on the association of two distinct geometries: crosseddipoles and matryoshka. The main idea when using distinct geometries is to avoid the coupling between them, keeping the features of each geometry in the associated geometries.
For each geometry, the initial design equations were proposed and verified by numerical simulations, achieving a good agreement. The individual geometries were numerically characterized for different incidence angles. Similarly, FSS with associated geometries was numerically characterized, confirming the expected frequency response, with the resonant frequencies of each geometry maintaining practically the same. The current distribution of each resonant frequency was shown, allowing to visualize the respective excited geometry.
A FSS prototype was designed, fabricated and numerically and experimentally characterized, considering incidence angles of 0°, 15°, 30° and 45°. The obtained results confirm the expected frequency response, including the polarization independence and angular stability, and indicating the decoupling between the associated geometries. In this way, the triple-band FSS was successfully reached, obtaining an attenuation of at least 15 dB in the 2.4 GHz frequency band.