# Dual-Band Single-Layered Frequency Selective Surface Filter for LTE Band with Angular Stability
## 2 Proposed Design of FSS Configuration
### Design Methodology with Its Evolution Stages
The impedance of the rectangular slot is affected by its inclination due to the change in the current distribution, potentially introducing reactive components depending on the angle and the proximity to the cross structure. The inclined rectangular slot's length projection on the vertical axis will be shorter than the actual length, which changes the resonant frequency. This can be calculated by considering the equation \(L_{\mathit{eff}}=L\text{cos }\theta\). The analysis shows that the frequency shifts downward compared to step 2, specifically from 2.49 GHz to 2.1625 GHz, as shown in Figure 3a. Step 4: To alter the resonant frequency from step 3, square stubs are placed on a rectangular slot as illustrated in Figure 2d. The placement and dimensions of these stubs alter their surface current and the impedance of the slot. They are placed on the rectangular slot in such a way that the capacitive loading is increased, resulting in the reduced physical length required for the desired resonant frequency. The effective length of the small stubs can be described as \(L_{\mathit{eff}}=L+\Delta L\). This additional effective length provides the resonance at 1.92 GHz, which is depicted in Figure 3a. Step 5: Step 4 demonstrates the resonant frequency at 1.92 GHz, which corresponds to one of the desired frequencies within the LTE band spectrum. However, to achieve dual resonance, further modification is necessary, which is shown in Figure 2e. By removing one of the square stubs from the configuration in step 4, the structure exhibits dual resonance at 1.9 and 2.1 GHz as demonstrated in Figure 3b. It is observed that the introduction of asymmetry within the structure leads to dual resonance behavior. The removal of the square stub disrupts the initial symmetry, resulting in a double varied surface current path across the structure. This variation of current distribution successfully creates two  
Figure 2: Evolution design stages of the FSS Copper (green) Dielectric Material (grey): (**a**) Cross structure; (**b**) Cross structure with rectangular slot; (**c**) Subsequent modification of inclined rectangle; (**d**) Square stubs attached with rectangular slot; (**e**) Assymetric cruciform design. resonances. This asymmetry-induced dual resonance is the finalized design of the proposed FSS derived from the fundamental cross structure, hence termed \"Cruciform FSS\". The resonant patch element of a C-FSS is placed whose dimensions are given in Table 1.  
Figure 3: (**a**) Reflection-transmission coefficient of different design steps. (**b**) Reflection-transmission coefficient of step 5. The proposed FSS design exhibits a systematic progression through iterative alterations, attaining the necessary resonance and operational attributes. A scalable cross structure resonating at 2.79 GHz was initially developed, followed by the incorporation of center rectangular slots to increase electrical length, resulting in a resonance at 2.49 GHz. Additional optimization via 45\({}^{\circ}\)-angle slots successfully modified the current distribution and adjusted resonance to 2.1625 GHz. The incorporation of square stubs augmented capacitive loading, hence decreasing the necessary physical length and attaining resonance at 1.92 GHz. The removal of a square stub introduced asymmetry, resulting in dual resonances at 1.9 GHz and 2.1 GHz, which correspond to LTE band specifications. This development confirms the ultimate \"Cruciform FSS\" design as a small, efficient, and scalable solution for dual-band applications. This design purposely incorporates asymmetry to attain dual-resonance behavior, essential for fulfilling the demands of applications such as LTE band operation. Symmetric structures typically yield a singular resonance owing to the homogeneous current distribution, constraining the design to a more restricted frequency range. Eliminating one square stub disturbs symmetry, altering the uniform current distribution and resulting in diverse surface current pathways, which induces dual-resonance behavior.