# An Ultra-Wideband Frequency Selective Rasorber with Low Infrared Emissivity
## 2 Analysis, Design and Experimental Verification
### Design of the FSR
#### 2.2.1 Ultra-Wide Transmission Band RS Based on Sinusoidal Microstrip Lines  
The key to achieving a wide transmission band in the region of \(f_{t}\) = 11 GHz lies in the use of a non-frequency variable parallel-LC resonant structure with high inductance and low capacitance. Sinusoidal microstrip lines are a type of structure with non-frequency-varying properties, commonly utilized in the design of UWB antennas [33]. This structure allows for stable electromagnetic performance over a wide band because of its self-similarity. However, there has been no research on the application of a non-frequency variable structure to a periodic structure; thus, it is necessary to investigate the impact of this structure in the wideband design of FSR. As depicted in Figure 3, the structure can be generated by a fundamental sinusoidal curve rotating \(\beta/2\) in both clockwise and counterclockwise directions around the origin, with sinusoids comprising \(r_{1},r_{2},...r_{n+1}\) and consisting of \(n\) curves whose size is determined by scaling factor \(\tau\) and angle \(\alpha\). Among them, the \(n+1\) curve can be obtained from the following equations:  
\[\varphi(r)=(-1)^{n}asin\big{[}\frac{\pi ln(r/r_{n})}{ln\tau}\big{]};r_{n+1} \leq r\leq r_{n} \tag{18}\]  
Figure 3: The structure of a sinusoidal microstrip line. The RS cell structure based on sinusoidal microstrip lines is illustrated in Figure 4. The metal layer (gray part) of the printed circuit board (PCB) was unilaterally loaded on a Rogers RT5880 substrate (orange part) with a thickness of \(d_{r}\) = 0.127 mm, \(\varepsilon_{r}\) = 2.2 and a dielectric dissipation factor of 0.0009. The Jerusalem cross of the four-arm sinusoidal microstrip line was loaded at the center of the metal layer unit cell. Each pair of sinusoidal microstrip lines is connected by a \(2r_{n-1}\)-long, 0.05 mm wide metal wire, and a 130 \(\Omega\) patch resistor is loaded on each dipole of the Jerusalem Cross. The structural parameters are listed as follows: \(p\) = 8 mm, \(a\) = 7.6 mm, \(b\) = 0.8 mm, \(a_{n}\) = 5 mm, \(b_{n}\) = 0.1 mm, \(r_{1}\) = 1.8 mm, \(\alpha\) = \(\pi/4\), \(\beta\) = \(\alpha/4.5\), \(\tau\) = 0.8, \(q\) = 0.5 mm. The full-wave method utilized in this paper was proposed by CST 2022 with Floquet modes. The boundary conditions in the x-y direction are set as \"unit cells\", while those in the z direction are \"open (add space)\". The default options of Floquet modes are adopted for port and grid division. (This methodology is employed throughout all simulations in this paper and will not be reiterated in future instances). The simulation results are depicted in Figure 5, indicating that RS exhibits an exceptionally wide transmission band (8.72-16.80 GHz) and robust angular stability in \(\pm\)60\({}^{\circ}\). The curves of different colors/points represent the S-parameters at various incidence angles. For instance, the red square curve depicts the \(S_{11}\) parameter at 0\({}^{\circ}\) incidence angle, while the gray square curve represents the \(S_{21}\) parameter at 0\({}^{\circ}\) incidence angle. Similar information can be found in the figure's legend for other curves. Additionally, the electromagnetic properties of RS remain almost identical when subjected to TE and TM wave irradiation, indicating its excellent polarization stability attributed to the strict central symmetry of the RS structure. Furthermore, comparing the S-parameter results obtained by the full-wave simulation and the ADS equivalent circuit fitting, as shown in Figure 6, it is easy to see that the results  
Figure 4: The structure of the RS unit cell. Figure 5: S-Parameters of the RS vary with \(\pm\)60\({}^{\circ}\) TM (**a**) and TE (**b**) wave irradiation. are almost the same, which verifies the design concepts based on the EC analysis method proposed in this paper. It is noteworthy that the self-similar characteristics of the sinusoidal microstrip lines make the tuning of RS very simple.