## 3 Design and Simulation of Multi-Functional Transmitarray
The optimized design variable is as follows: \(P_{\rm x}\) = \(P_{\rm y}\) = 15 mm, \(D_{1}\) = 8.3 mm, \(D_{2}\) = 0.7 mm, \(R_{1}\) = 2.6 mm, \(R_{2}\) = 1.0 mm, \(W_{\rm S}\) = 0.4 mm, \(d_{\rm via}\) = 1.9 mm, \(L_{\rm ind}\) = 2.85 mm, \(L_{\rm a1}\) = 7.3 mm, \(L_{\rm a2}\) = 1.5 mm, \(L_{\rm a3}\) = 0.5 mm, \(L_{\rm a4}\) = 1.0 mm, \(L_{\rm a5}\) = 0.85 mm, \(g_{\rm a}\) = 0.2 mm, \(W_{\rm a1}\) = 0.1 mm, \(L_{\rm cap}\) = 1.6 mm, \(L_{\rm c1}\) = 0.7 mm, \(L_{\rm c2}\) = 0.6 mm, \(W_{\rm c1}\) = 0.2 mm, \(W_{\rm c2}\) = 0.1 mm, \(g_{\rm c}\) = 0.1 mm, \(d_{\rm stub1}\) = 2.3 mm, \(R_{\rm stub}\) = 2.4 mm, \(\alpha\) = 45\({}^{\circ}\), \(D_{\rm via}\) = 0.4 mm, \(L_{\rm b1}\) = 4.2 mm, \(L_{\rm b2}\) = 7.6 mm, \(L_{\rm b3}\) = 0.985 mm, \(L_{\rm ground}\) = 5.6 mm, \(W_{\rm b1}\) = 0.2 mm, \(d_{\rm stub2}\) = 1.0 mm. The design variable for equivalent circuit modeling of the PIN diode (MACOM MA4 GP907) is as follows: \(L_{\rm D}\) = 0.05 nH, \(R_{\rm F}\) = 2.1 \(\Omega\), \(C_{\rm R}\) = 50 fF, \(R_{\rm R}\) = 300 k\(\Omega\). Figure 3: Geometry of proposed unit-cell to implement multi-function: (**a**) Perspective view; (**b**) Tx patch (layer 1); (**c**) Bias line (layer 3, layer 2 is ground plane); (**d**) Rx patch (layer 4). Floquet Mode simulation assuming a periodic structure with an infinitely arranged unit cell was performed using HFSS, a commercial EM field analysis software made by ANSYS, to confirm the frequency response characteristics according to the change in the state of the diode of the designed unit cell. Figure 4 and Table 2 show the frequency responses for insertion, return loss, phase and isolation level between polarizations at interest frequency band. From the infinite simulation results, the proposed structure has a maximum insertion loss of around 1.29 dB despite the changes of states for the PIN diode, and the isolation level is below 15.7 dB. Moreover, these performances were valid during the phase-shifting operation. In order to verify the polarization conversion and beam steering performance of a transmitarray arranged with unit cells arranged in a finite number, an \(8\times 8\) transmitarray arrangement was modeled as shown in Figure 5a, whereas the full-structure simulation for the space feed source was performed using a 10 dBi X-band horn antenna. Cross-validation was performed by comparing the HFSS simulation results and numerical analysis results, which are shown in Figure 5b,d. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Polarization Conversion** & **1-bit** & **Insertion** & **Reflection Loss (S\({}_{\text{21}}\)) [dB]** & **Cross pol. Level (S\({}_{\text{11}}\)/S\({}_{\text{22}}\)) [dB]** & **Cross pol. Level (Isolation) [dB]** & **Relative Phase (S\({}_{\text{21}}\)) [Deg.]** \\ \hline OFF & OFF & 1.13 & 16.7/24.3 & 18.1 & 0 \\ \hline OFF & ON & 1.18 & 16.6/17.8 & 18.5 & 177.5 \\ \hline ON & OFF & 1.27 & 18.2/10.4 & 15.4 & \(-\)15.5 \\ \hline ON & ON & 1.29 & 15.7/10.4 & 15.3 & 167.3 \\ \hline \end{tabular}
\end{table} 
Table 2: Simulated performance of the proposed unit-cell (Freq. at Min. insertion loss). Figure 4: Simulated performance of the proposed unit-cell with changes of diode state: (**a**) State 1 (Pol. : V, Phase: 0\({}^{\circ}\)); (**b**) State 2 (Pol. : V, Phase: 180\({}^{\circ}\)); (**c**) State 3 (Pol. : H, Phase: 0\({}^{\circ}\)); (**d**) State 4 (Pol. : H, Phase: 180\({}^{\circ}\)). The simulation confirms that beam steering of 0 to 45 degrees and the polarization conversion functionality work as intended on the proposed transmitarray (Figure 5d).