Design of Miniaturized FSS with High Angular Stability Utilizing a Novel Closed Loop

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Introduction
Frequency selective surfaces have gained more and more attention as they are widely used in electromagnetic shielding, absorbers, antennas, and radomes [1][2][3][4]. Te FSS consists of a periodic structure with diferent cell structures. Conventional FSSs are usually printed on single sides of the dielectric substrate on two-dimensional structures, but such structures are not sufcient to meet the demand for miniaturization of the FSS size. For FSSs, the physical size is not infnite planes in design. In order to achieve a better performance, it is necessary to arrange more FSS cells on the fnite size, especially for low frequency bands, and the demand for miniaturization of FSSs is already proposed [5]. To reduce the size of FSS, a lot of methods have been proposed, such as three-dimensional (3D) technology [6] or hybrid 2D and 3D technology [7]. However, 3D processing is more difcult and increases the thickness of the FSS [8]. Terefore, the 2.5D FSS is gaining more and more attention. Te conventional 2D planar structure is a horizontal X-Y plane, and when vias are added, the vertical Z-direction plane is also utilized. Te vertical vias will further increase the metal density in the FSS, making it easy to achieve miniaturization. Te PCB production process does not need to be changed at this time but is still in the form of traditional planar printing; so, the FSS structure with via inserted is called the 2.5D FSS [9,10]. Te FSS generally uses two classical structures, the JC and the closed loop. In recent years, improved 2.5D structures on these two structures have been proposed [11]. Te strong coupling efect is verifed by adding vias to the conventional JC FSS to form the 2.5D FSS [12]. Te 2.5D structure is able to increase the capacitance and inductance of the cell by connecting both sides of the dielectric substrate using vertical vias [13]. Terefore, the 2.5D structure can reduce the size of the FSS and achieve better oblique incident angular stability.
Recently, various 2.5D FSS structures with excellent performance have been proposed, and miniaturized FSSs can be achieved using the JC structure with many vias [14]. Meandering lines are utilized in the JC FSS to further reduce the resonant frequency to achieve miniaturization [15]. Also, some methods can be regarded as improvements to the closed loop or loop structure [16,17]. Te FSSs are limited by structural features and only have a few vias added to initially achieve a 2.5D structure with miniaturization [18,19]. To overcome this problem, an FSS that utilizes a knitted structure to insert more vias is proposed [20]. On the other hand, the electrical size of the FSS can be reduced by using an inward-convoluted loop structure with the metallic strips, which can largely enhance the mutual coupling between metals [21]. Several closed-loop FSSs with fractal structures have been proposed in order to maximize the use of the dielectric layer space [22,23]. In addition, it is difcult to reduce the miniaturization size and maintain angular stability to more than 85°.
In this paper, a closed-loop 2.5D FSS for electromagnetic shielding is proposed. Te novel closed-loop structure with a strong coupling performance is presented to achieve miniaturization of the cell and reduction of the profle height, as well as high angular stability. In addition, the FSS is converted into an equivalent circuit model for verifcation and analysis. Te proposed FSS is fabricated and measured to verify the designed specifcations.

Unit Cell Design
Te structure of the proposed FSS unit cell is shown in Figure 1(a). It is a symmetrical structure with the metal printed on both sides of an FR4 dielectric substrate which relative permittivity is 4.6, loss tangent is 0.019, and thickness is 1.2 mm. Te top and bottom views of the FSS are shown in Figures 1(b) and 1(c), respectively. In the above fgure, the brown part represents the metal, the dielectric is flled with yellow color, and the vias are shown using black. Te metal on the surface is a novel closed-loop structure which can be seen as a combination of a loop-back rectangular ring and a JC structure with a solder ring, where the metal strip is connected to the vias. Tis structure introduces more vias, allowing for enhanced coupling.
Te FSS, as a periodic structure, in general has a cell size approximating λ/2, which is relatively large. Terefore, in order to meet the needs of practical applications, it needs to be miniaturized at the design time. Te FSS resonant frequency can be expressed as follows: L and C represent the equivalent inductance and capacitance; so, it is necessary to enhance the equivalent inductor and capacitor to make a lower working frequency at the same physical size in order to achieve miniaturization. Te cell design of the proposed structure has evolved as follows. As a closed-loop type FSS, the initial structure is shown in Figure 2(a). Each cell consists of a closed loop, which has a small metal length in the loop and a large gap between the metals; so, the equivalent capacitor and inductor are small. Furthermore, a 2.5D structure can be developed using vias, where the length of the loop metal is further increased, as shown in Figure 2(b). Ten, the meandering line is utilized, and the metal strips in Figure 2(c) are spiraled inward to increase the length, while additional capacitance is inserted between the closely spaced metal strips. In order to increase the number of vias, the traditional closed-loop structure is combined with the JC structure to form a new closed-loop structure, i.e., the proposed structure in this paper, which is shown in Figure 2(d). Te novelty lies in the insertion of a few vias in the long metal strip of the JC structure and combining this JC structure with the existing closed-loop structure to form a new closed loop, which achieves maximum miniaturization.
Full-wave electromagnetic simulations are performed, using unit cell boundary conditions and foquet ports for excitation. Figures 3(a) and 3(b) show the simulation results of the FSS under two diferent polarization, such as the TE and TM modes with diferent incident angles, respectively. From them, it can be seen that the FSS can be regarded as a band-stop flter with a resonant frequency of 850 MHz. Te maximum amplitude of the transmission coefcient is 23.3 dB when the incident angle is 0 degree, which means that only 6.8% of the energy can pass through the FSS. GSM850 is a relatively important frequency band for mobile communication, and many smart terminals support this band, so the proposed FSS can better protect the relevant devices from interference in this band. Moreover, it is demonstrated that the transmission coefcients with different incident angles of the proposed FSS is highly stable, and its resonant frequency remains stable at incident angles as high as 85°. So, its resonant frequency shift is almost negligible. Also, the performance of the proposed FSS is in excellent agreement in both the TE and TM modes, where the resonant frequency is 850 MHz at both modes. Te resonant bandwidth of the TE mode is widened with the increase of the incident angle because the wave impedance changes with the angle, while the TM mode is the opposite. Also, Figure 3(c) verifes the polarization stability of the FSS, as the transmission coefcient and resonant frequency are almost unchanged when the polarization angle is from 0 to 60 degrees, which illustrates the good polarization stability of the FSS.
Te FSS can essentially be considered as a spatial flter and, therefore, its operating frequency is the most important characteristic. It is worth mentioning that the FSS and the absorber have some similarities. Both the microwave absorber and band-stop FSS are a form of metasurface, which is essentially a periodic structure and thus has unique electromagnetic characteristics. Also, both can achieve the efect of rejection electromagnetic waves, which is also expressed as S21<<1. However, there are diferences in the design idea that both S11 and S21 of microwave energy absorbers are small and will neither refect nor transmit electromagnetic waves but will preserve the energy of electromagnetic waves as losses in the medium or metal [24]. Te FSS, on the other hand, has a larger S11, which is very close to 1, which refects most of the energy back. For this design applied for electromagnetic shielding on other bands, its resonant frequency needs to be changed. Te change in resonant frequency can be achieved by modifying some parameters of the structure.
Considering both dielectric and structural parameters separately, the relative permittivity and thickness of the substrate as well as the cell gap are modifed. Multiple sets of parameters are selected to analyze, and the obtained results are shown in Figure 4. It is demonstrated that if the larger relative permittivity is chosen, the lower working frequency of this FSS operates, and the thicker dielectric substrate is, the lower the working frequency is.

Equivalent Circuit Modeling
In order to further understand the operation of the proposed FSS, it is necessary to analyze its equivalent circuit. Te equivalent circuit model (ECM), similar to a flter system, can be considered as an LC resonant circuit. Te equivalent circuit, similar to the flter in the circuit, can be considered as an LC resonant circuit, and the equivalent circuit can be constructed by analyzing the placement of inductors and capacitors. For this purpose, the current and electric feld distributions of the model in Figure 1 are analyzed. Te current and electric feld distributions at the bottom with TE mode excitation in the full-wave simulation are shown in Figures 5(a) and 5(b), respectively. In this case, the region with a high surface current density can be equated to an inductor, while the region with a high density of electric feld distribution can be considered as a capacitor. Te fgure shows that the current density is higher at the metal strip and the electric feld intensity is higher at the metal and the gap over the hole; so, it can also be concluded that the metal part can be considered as inductance, while the gap part can be considered as the capacitive region.
Based on the abovementioned equivalence principle for the electric feld and the current concentration region, Figure 5(c) shows the relative positions of the inductors and capacitors on the FSS, i.e., L 1 and L 3 are the inductors equated by the ring metal strip, C 1 and C 3 are equivalent capacitors by the gap between the ring metal strips, L 2 is the inductor through the vias, C 2 is the capacitor between the vias, and C 4 is the capacitance contributed by the JC structure in the middle of the cell. Tis makes it possible to convert the FSS into an ideal equivalent circuit model as shown in Figure 6(a). Since the FSS will be placed in free space during usage, the ports on both sides of the equivalent circuit are free space, i.e., its impedance is Z0 � 377 Ohm. Te dielectric substrate of the FSS can be regarded as a section of transmission line with characteristic impedance, which is represented as Z sub in the equivalent circuit. In addition, the LC is the ideal component in the equivalent circuit for easier analysis. Figure 6(a) is an equivalent circuit model that can actually describe the operation of the FSS based on the distribution of current and the electric feld, which realistically shows the actual contribution of capacitance and inductance in the FSS structure, but it is not helpful to extract the specifc value of the LC due to its more components. Considering that the LCs in the model of Figure 6(a) are all ideal components, the series inductors L 1 and L 3 and capacitors C 1 and C 3 can be directly simplifed, i.e., there are: L 1 ′ � L 1 + L 3 and C 1 ′ � (C 1 * C 2 )/(C 1 + C 2 ).   International Journal of Antennas and Propagation Terefore, after the proper combination and simplifcation of the capacitor and inductor, a simplifed equivalent circuit model is obtained as shown in Figure 6(b). Tis model helps to further obtain the specifc values of LC, and subsequent discussions will use this simplifed model.
Further analysis of this simplifed equivalent circuit model, i.e., the impedance of the model can be expressed as follows [25,26].
For equation (1), the solution corresponding to the zero point is also the resonant frequency of the FSS. Expanding and simplifying the above equation, the solution of its zero point should satisfy the following equation.
(2) A further solution of equation (2) results in the resonant frequency f.
Te specifc values of the components in the circuit can be obtained with curve ftting by using Keysight ADS. Figure 7 shows the transmission coefcients of the FSS. In this case, L 1 ′ � 49.398 nH, L 2 ′ � 35.574 nH, C 1 ′ � 0.312 pF, C 2 ′ � 0.420pF, and C 4 ′ � 0.245pF. Te ECM results are very close to the full-wave simulation, and there is almost no diference between the resonant frequencies of them, while the ECM has a deeper depression in coefcients, which is caused by the fact that the losses of the dielectric and metal are not considered in the ECM. Terefore, with the beneft that the circuit simulation time is much shorter than that of the full-wave simulation, the proposed equivalent circuit can be used for more efcient and convenient analysis of the FSS and can better guide the design.

Experimental Results
In order to verify the proposed design, the FSS is fabricated and measured. An FR4 dielectric substrate is used, whose total size is 702 mm × 702 mm with 104 × 104 cells arranged, and the parameters of one cell are the same as in Figure 1. Te experimental results are obtained using the free-space measurement method. In the microwave anechoic chamber, two horn antennas are used as the transmitting and receiving antennas, respectively, and the distance between them is 3.5 m. Te FSS is placed on the front side of the receiving antenna, and the test environment is as shown in Figure 8.
Te performance of the FSS with diferent incident angles is tested in the TE and TM polarization modes, respectively, and the measured S-parameters are shown in Figure 9. It can be found that although the measured deviation forms the simulation, the ofset of the resonant frequency is still very small when the angle change reaches 85 degrees, and the maximum ofset is less than 10 MHz. Te high angular stability is demonstrated, which is in good agreement with the simulation results. Te small inaccuracy may be caused by the error of fabrication or the loss of dielectric. Te FSS performance at diferent polarization angles was also tested by rotating the FSS to change the phi. Te measured transmission coefcients from 0 to 60 degrees of polarization angle are given in Figure 9. Similar to the previous simulation results, the insensitivity of the transmission coefcients to the polarization angle is shown, i.e., a better polarization stability.
To further demonstrate the performance of the designed FSS, Table 1 represents the performance of the proposed FSS in this paper compared with some recently published bandstop FSSs.

Extension of the Proposed Structure
Te proposed two-layer FSS structure could be extended to an N-layer structure by adding layers on either the top or bottom side. Figure 10 shows the expanded FSS structure at three layer and four layer, and in this case, the cell size and the total thickness of the FSS do not change.
By increasing the number of layers of the PCB, more vias and longer lengths of metal strips can be added, which allows the LC to continue to increase and enable further miniaturization. As can be seen from the fgure, the increase to    International Journal of Antennas and Propagation three layers requires only a slight change to the original top layer structure to add two more vias and an additional new top layer using the meandering line structure at which point, the bottom layer does not need to be changed in any way. At this point, the structure is actually still a closed loop, so it can be increased to four or more layers in a similar way. Figure 11 gives the S-parameters of the expanded threelayer and four-layer PCB structure under full-wave simulation. From the results, it can be seen that its resonant frequency is further reduced to 470 MHz. Tus, by varying the number of PCB layers in this section and the dielectric constant and board thickness as mentioned in section 2, the

Conclusion
A miniaturized FSS with high angular stability is proposed, and the design and demonstration process are elaborated. Te designed unit cell is 0.019λ 0 × 0.019λ 0 with a thickness of 0.003λ 0 . Its stability is maintained in both the TE and TM modes by varying the incident angle up to 85 degrees. At the same time, the equivalent circuit model of the FSS and the values of each lumped element are given. It is verifed that the equivalent circuit simulation results are in good accordance with the full-wave simulation results, and the FSS performance can be analyzed more efciently with the equivalent circuit model. Te optimized FSS has a resonant frequency of 850 MHz, and as a band-stop FSS, it can be applied as an electromagnetic shield for GSM850. A prototype of the FSS is also fabricated and measured, proving a good agreement with the simulation results.

Data Availability
Te data generated or used during the study are included within the article.

Conflicts of Interest
Te authors declare that they have no conficts of interest. International Journal of Antennas and Propagation 9