# Dual-Band Single-Layered Frequency Selective Surface Filter for LTE Band with Angular Stability
## 2 Proposed Design of FSS Configuration
### Dual-Band Single-Layer Structure  
Figure 4a,b shows the proposed Cruciform FSS (C-FSS) geometry, which consists of a square unit cell measuring 0.33\(\lambda_{1}\)\(\times\) 0.33\(\lambda_{1}\), which has been specifically obtained to achieve the desired frequencies. The unit cell consists of resonant components that resonate accurately at frequencies of 1.9 and 2.1 GHz. For high-speed data and voice services, commonly used LTE bands are 1.9 GHz (Band 25), which offers 1.85-1.91 GHz for the uplink and 1.93-1.99 GHz for the downlink, and 2.1 GHz (Band 1), which offers 1.92-1.98 GHz for the uplink and 2.11-2.17 GHz for the downlink. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Parameters** & \(\mathbf{L_{1}}\) & \(\mathbf{L_{2}}\) & \(\mathbf{L_{3}}\) & \(\mathbf{L_{4}}\) & \(\mathbf{L_{5}}\) & \(\mathbf{L_{6}}\) & \(\mathbf{W_{1}}\) & \(\mathbf{W_{2}}\) & \(\mathbf{W_{3}}\) & \(\mathbf{W_{4}}\) \\ \hline Value (mm) & 45 & 15, 14.5 (_eff_) & 15, 13 (_eff_) & 15, 13.20 (_eff_) & 15, 12.20 (_eff_) & 4.5 & 1.9 & 1 & 1 & 4.5 \\ \hline \end{tabular}
\end{table} 
Table 1: Unit cell dimensions of Cruciform FSS. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Steps** & **Band** & **Resonant Frequency (GHz)** & **Bandwidth (MHz)** \\ \hline Step 1 & Single Band & 2.79 & 110 \\ \hline Step 2 & Single Band & 2.49 & 140 \\ \hline Step 3 & Single Band & 2.16 & 100 \\ \hline Step 4 & Single Band & 1.92 & 100 \\ \hline Step 5 & Dual Band & 1.92, 2.08 & 40, 60 \\ \hline \end{tabular}
\end{table} 
Table 2: Geometric values at each evolution step. The C-FSS structure is constructed and analyzed using the RT/Duroid 5880 substrate, with the chosen thickness of 0.508 mm. The proposed FSS operates on dual bands through the asymmetric nature of the structure. Most of the design gives PMC/PEC properties at a single frequency from the single-element structure, but the proposed structure resonates at a dual frequency from the single element. Since the resonance is operating on an asymmetric impedance surface which creates independent control of surface impedances, it is designed to exhibit a specific resonance when it interacts with incident EM waves. Hence, it controls the absorption and transmission characteristics. Table 3 gives a comparison of the symmetric and asymmetric surfaces. A 4 \(\times\) 4 array of C-FSS is depicted in Figure 4a. Arrays cover and integrate surfaces better than single-unit cells. An FSS must interact with EM waves across a vast area to give desired results, as it operates on the principle of periodic structures. The periodic structure of an array leads to the constructive and destructive interference of EM waves which allow fine tuning of the band-pass or band stop characteristics. Hence, a single unit cell cannot form the operative surface. A periodic FSS structure can be created using the principles of the Floquet theorem. A periodic structure is defined to have an infinite extent. A planar array that crosses in the x-axis and z-axis indefinitely with uniform spacing between each element is referred to as a fully periodic arrangement (infinite \(\times\) infinite) [13]. N number of unit cells gives the overall response of the array by determining the Array Factor [35], as given in Equations (3) and (4). \[AF(\theta,\varnothing)=\sum_{n=1}^{N}I_{n}e^{jk\cdot r_{n}} \tag{3}\]  
\[F_{total}(\theta,\varnothing)=F_{unit-cell}(\theta,\varnothing)\cdot AF(\theta,\varnothing) \tag{4}\]  
The provided array is a spatial filter that is used to influence the undetermined front of an incident wave. Electric polarizability, which presents a resonant response, is the  
Figure 4: Cruciform FSS geometry: (**a**) 4 \(\times\) 4 array; (**b**) unit-cell prototype. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Surface** & **Functionality** & **Polarization** & **Design** \\ \hline Asymmetric & Independent surface impedance control & Dependent & Complex \\ \hline Symmetric & Dependent surface impedance control & Independent & Simple \\ \hline \hline \end{tabular}
\end{table}