Grating Lobes Suppression in Frequency Selective Surfaces Using Electromagnetic Band Gap with Square Holes

In this paper, the authors present a proposal for an application of electromagnetic bandgap (EBG), for suppression of grating lobes, in frequency selective surfaces (FSS), not yet studied in the literature. An alternative type of EBG with square holes was proposed to reduce the computational effort in simulations. The study consists of an application of a rectangular periodic array of cylindrical and square holes in FSS dielectric substrate to create rejection bands and suppress specific resonant frequency modes. We built four prototypes and compared measured results with simulated results obtained with ANSYS HFSS. Simulations and measurements show suppression levels up to 6 dB. A good agreement between the results is observed. The FSS with EBG with square holes allows a simulation time 70 % lower than FSS with EBG with cylindrical holes.

II. PROPOSED STRUCTURES EBGs are periodic or quasi-periodic arrays inserted in conductive or dielectric materials. These arrays introduce rejection bands that prohibit the propagation of electromagnetic waves in certain frequencies [15]. In this work, we will analyze two types of substrates with EBG, one with a periodic array of cylindrical holes and the other with a periodic array of square holes. The idea is to suppress grating lobes and to compare the computational effort of the simulations made for the two types of arrays. Fig. 1(a) illustrates the periodic EBG array with cylindrical holes in the dielectric, as well as their physical dimensions, which are the distance between the centers of the air holes, Λ (pitch), and the diameter of the holes, d. Fig. 1(b) illustrates the periodic EBG array with square holes, as well as their physical dimensions, which are the distance between the centers of the air holes, Λ (pitch), and the width of the holes, War. In the case of the cylindrical hole array, we used a Technodrill milling machine model Sigma 600 to perforate the FR-4 dielectric. In the case of the square hole array, a 3D printer was used to manufacture the dielectric. The main motivation to construct the dielectric with square holes is that the fabrication process using 3D printer is accurate enough and low-cost, and the computational effort of the simulation is lower when compared with EBG with cylindrical holes. A good starting point for the dimensions of the EBG with cylindrical holes, pitch, and diameter, is provided in [14], which is Λ = 0.12 and d = 0.1, where  is the wavelength of the grating lobe 512 frequency to be suppressed. For the case of square holes, the area of the hole must be equal to the area of the cylindrical hole, maintaining the areas of the holes of the EBG array and, consequently, the desired rejection band. Thus, War should be approximately 0.89d, where d is the diameter of the cylindrical holes. Fig. 2(a) illustrates the FSS unit cell, considered for the study proposed in [16]. The geometry is a rectangular patch with dimensions L = 15 mm, W = 12 mm, and the periodicity of the unit cell is P = 20 mm. The metallic portion of the unit cell is gray color. A FR-4 dielectric substrate (fiberglass), with 1.6 mm of thickness, the relative permittivity of 4.4 and a loss tangent of 0.02 was used. Fig. 2(b) illustrates the cell of the FSS unit considered with the EBG inserted in the FR-4 dielectric. The unit cell of the FSS is the same as Fig. 2(a). The air holes have a diameter d = 3 mm, with a spacing between the holes (pitch) of 3.3 mm. A periodic matrix of 6 × 6 holes was inserted into each unit cell, resulting in 36 holes per cell. The dielectric used was the FR-4. Fig. 2(c) illustrates the FSS unit cell considered on a substrate with EBG of square holes. The unit cell of the FSS is the same of Fig. 2(a).
The material used for the substrates was the acrylonitrile-butadiene-styrene (ABS). ABS material is the most used polymer in 3D printing due to its low cost, ease of printing, lightweight and good rigidity with relative flexibility. The printer used was the VOID1 model. The print quality was 0.05 mm per height of the deposited layer. 3D printing was used to enable the production of square holes.
The spacing between the holes (pitch) was kept as 3.3 mm and, for the square hole to have approximately the same area as the cylindrical hole, the side should be equal to 2.67 mm, but due to the precision offered by the printer, the final value was equal to 2.5 mm. The dielectric has 1.6 mm of thickness and a relative permittivity of 3.3.

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To show how the mechanism to suppression of higher order modes by the EBG works, we must to characterize the behavior of the wave as it propagates through the structure. This is made with the dispersion diagram, also named is Brillouin diagram. The computational domain and the boundary setup for extracting the dispersion diagram for the EBG unit cell were shown in [17] and [18]. The full-wave numerical simulator Ansof HFSS is used to analyze the 2D propagating and nonpropagating modes on the Brillouin diagram. We obtained the diagrams for the cells shown in Fig. 2(b) and (c).
We can see the dispersion diagram generated for the EBG of Fig. 2 Fig. 3. We obtain the diagram for the first six propagating modes extracted numerically for this structure. It shows that the bandgap is located between 11.85 GHz and 13.85 GHz and it shows that there will be no resonance at this band for the FSS. In Fig. 4, we can see the dispersion diagram generated for the EBG of Fig. 2(c).
In this case, the bandgap is located between 11.00 GHz and 13.90 GHz, a little bit larger that the bandgap obtained for the EBG of the Fig. 2(b). So, as the diagrams show we have bandgaps in the range of interest, that can suppress the higher order modes.   is that the lattice size should be less than . This rule limits the possible dimensions in an FSS design.
Our proposition changes this and we can eliminate the grating lobe with an EBG. This includes one more possibility to eliminate grating lobe and also contributes to the research area in question. .24 GHz and a grating lobe at 13.02 GHz. When we insert the EBG with cylindrical holes, the resonant frequency changes from 9.24 GHz to 10.07 GHz. This was expected due to the air holes that reduce the effective permittivity (εeff) of the FSS substrate, because of this the resonance frequency increases. We can also see that the grating lobe has been attenuated by 6 dB, from -11 dB to -5 dB. For the case of FSS with a substrate with EBG of square holes made in the 3D printer, we can see that the resonance frequency increases to 11.86 GHz, and the grating lobe was also attenuated by 6 dB, as well. In this case, the relative permittivity is 3.3 and the effective permittivity (εeff) of the FSS substrate is less than for the EBG with cylindrical holes, and the resonance frequency is greater. To return the resonance to the original frequency, 9.24 GHz, we can resize the dimensions of the rectangular patch, causing the resonance frequency to return to the desired value. So, for EBG with square holes, we resized the patch of the unit cell. Its length changed to 18.5 mm. Fig. 6  III. COMPUTATIONAL PERFORMANCE In this section, we present one of the advantages of using a different hole geometry than conventional cylindrical holes. Fig. 7 illustrates the simulation mesh of the three unit cells considered in this study. These meshes were obtained using the ANSYS HFSS software. It is observed that the mesh with less subdivision (triangles, in this case) is the FSS of [16], without EBG, followed by the FSS with EBG with square holes. The mesh of the FSS with cylindrical holes is the most detailed of all. How much more is the number of subdivisions, much more will be the computational effort of the simulation. This is an important point, especially if an optimization tool is used.

IV. RESULTS AND DISCUSSIONS For validation purposes of the proposed technique in this work, we built and measured four FSS
prototypes. A prototype of the first analyzed FSS without EBG was manufactured and three FSS prototypes with EBG were manufactured. We built two prototypes with an FR-4 substrate with relative permittivity of 4.4, loss tangent of 0.02, a thickness of 1.6 mm, and dimensions of 23 mm × 23 mm. In the case of FSS with EBG, the holes were made with a prototype Tecnodrill® model Sigma 600. After making the holes, the patches were manufacture manually, with a 50 m conductive adhesive copper foil tape. Fig. 8 illustrates the process of making the cylindrical holes.  The other two prototypes were made in a fused deposition modeling (FDM) 3D printer. The FDM process was used for the construction of a substrate with square hole EBG. In the process, the thermoplastic filament selected was ABS, widely used in the industry due to its low cost, as it is a light material and easy to model in addition to having good resistance to impact, traction, and abrasion.
The construction of the structures was carried out in the 3D printing machine of model A8 of the manufacturer Anet (with a precision of up to 0.2 mm depending on the extrusion nozzle used) using an extrusion nozzle of 0.4 mm. The final structures in ABS, due to the construction limit imposed by the platform size of the A8 machine, which has a maximum area of 20 × 20 cm², are composed of a group of 8 unit cells of 2 × 2 cm², with a total area of 16 × 16 cm² with a thickness of 1.6 mm. Fig. 9 illustrates the four prototypes built with this process. The frequency response of the prototypes was measured using a two-port Agilent E5071C network vector analyzer, SAS-571 rigid double horn antennas, and a measurement window. Unobstructed window measurements were taken, referred to as free space measurement and four with built prototypes. Fig. 10 illustrates the measurement setup.
The first prototype measured was the FSS with a rectangular patch with periodicity P = 20 mm, width W = 12 mm, length L = 15 mm without EBG. Fig. 11    The second prototype measured was the FSS integrated with an EBG with cylindrical holes for the same physical dimensions of the prototype of Fig. 11. The EBG has cylindrical holes with 3 mm of diameter and a pitch of 3.3 mm. Fig. 12 illustrates the comparison between simulated and measured results. Simulated results show a resonance at 10.07 GHz and the grating lobe suffered an attenuation of 6 dB, whereas the measured results show a resonance at 9.94 GHz and the grating lobe was attenuated by 4 dB. The holes produced a decrease in effective permittivity and, consequently, the resonance frequency increases. We can observe the attenuation of the grating lobe and a difference between results of 1.29 % in terms of the resonance frequency. Again, a good agreement between the results was observed.
So, to reduce the computational effort, we proposed a dielectric with an EBG with square holes.
The idea is to use a 3D printer to build a substrate with an EBG with square holes and reduce the simulation time. The material used was the acrylonitrile-butadiene-styrene (ABS) and the built dielectric has 1.6 mm of thickness and a relative permittivity of 3.3. This can be useful for 519 optimization processes. The third prototype measured was the FSS with an EBG with square holes for the same physical dimensions of the unit cell used in the first prototype. The EBG has square holes of 2.5 mm of side and a pitch of 3.3 mm. Fig. 13 illustrates the comparison between simulated and measured results. Simulated results show a resonance at 11.86 GHz and the grating lobe was attenuated by 6 dB, whereas the measured results show a resonance at 11.94 GHz and the grating lobe was attenuated by 6 dB as well. We can observe a difference between results of 0.67 % in terms of resonance frequency. In addition, we observed a second lobe with -20 dB of level at 10.68 GHz. Due to the fact that our patches are handmade, we noticed several patches with bigger dimensions than they should have, which caused a second resonance to appear at a lower frequency. However, as it is an FSS stopband, this is not a problem, because what matters is that in the entire operation frequency band, the rejection level is greater than 10 dB, which is what happens.   We resized the patch of the unit cell, trying to bring the resonance frequency near to the original value, 9.24 GHz. So, we proposed a fourth prototype (Fig. 7(d)) with a dielectric with square holes' EBG. We maintained the values of P and W, and increased the length L for 18.5 mm. The EBG has square holes of 2.5 mm of side and a pitch of 3.3 mm. Fig. 14  process to fabricated the metallic patches produces differences between simulated and measured results for FSS with EBG, but the differences were less than 5 %. However, it is observed that the manufacturing process would be industrial and not handmade, if some practical application is aimed.
In addition, we observed a second lobe with -20 dB of level. Due to the fact that our patches are handmade, we noticed several patches with smaller or bigger dimensions than they should have (depends on the prototype), which caused a second resonance to appear at a higher or lower frequency.
However, as it is an FSS stopband, this is not a problem, because what matters is that in the entire operation frequency band, the rejection level is greater than 10 dB, which is what happens.