## 3 Design and Simulation of Multi-Functional Transmitarray  
The proposed configuration develops 1-bit phase shift characteristics and linear polarization switching functionality by controlling the electrical current path directed to the arranged unit cells. As shown in Figure 3, the configuration of the unit cell on the basis of the ground plane in the center of the circuit board has a circular patch on the bottom side for receiving EM waves from the outside and another circular patch on the top side for re-radiation. Simultaneously, it acts similar to a band-pass filter through an electrically short-circuited configuration through a via hole located in the unit cell center. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Classifications**} & \multicolumn{4}{c}{**Quantization Level**} \\ \cline{2-5}  & **Ideal** & **1-bit** & **2-bit** & **3-bit** \\ \hline Spillover Loss, \(\eta_{s}\) [dB] & 0.48 & 0.36 & 0.28 & 0.53 \\ \hline Illumination Loss, \(\eta_{i}\) [dB] & 0.61 & 3.65 & 1.51 & 0.76 \\ \hline Total Loss, \(\eta_{t}=\eta_{s}+\eta_{i}\) [dB] & 1.09 & 4.01 & 1.79 & 1.30 \\ \hline Optimum F/D & 0.69 & 0.64 & 0.60 & 0.71 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Total efficiency of transmitarray in variation of quantization level. Figure 2: Analysis results of beam scanning error in variation of quantization levels. It was designed to have phase shift characteristics of 0\({}^{\circ}\) and 180\({}^{\circ}\) through different electrical lengths according to the direction of bias by configuring the circular patch on the bottom side in anti-parallel form using two PIN diodes [25]. The active polarization conversion characteristic was made possible by rotating the direction of the current induced through the circular patch located on the bottom side through two diodes placed on the top side by 90 degrees [26]. A capacitive stub was inserted to mitigate the impedance mismatch caused by an asymmetrical configuration, and an inductive strip line was applied for diode control to ensure isolation from the bias line. The main design variables that affect the unit cell frequency response characteristic are the diameter of the circular patches on the top and bottom side (\(D_{1}\)), the radius of the circular slot inside the patch (\(R_{1}\)), the diameter of the via hole (\(D_{\rm via}\)), and the width of the strip line connecting to the center via hole (\(W_{\rm S}\)). The circular patch diameter \(D_{1}\) and the inner slot radius \(R_{1}\) determine the operating frequency, and the via hole diameter \(D_{\rm via}\) and the strip line connecting to via hole \(W_{\rm S}\) affect the unit cell's insert and return loss, thus having a significant effect on impedance matching. Radial stubs were inserted in each of the polarization control bias (Bias Line **a**) and phase shift bias (Bias Line **b**) to minimize the effect of the bias line needed for diode electrical control, and the optimal variable of the radial angle (\(\alpha\)), length (\(R_{\rm stub}\)), and position (\(d_{\rm stub1}\), \(d_{\rm stub2}\)) were obtained through parametric study to minimize the line's effect on the unit cell frequency characteristic. The proposed configuration is a Taconic RF-35 (\(\epsilon_{\rm F}\) = 3.5, tan\(\delta\) = 0.0018, \(h\) = 1.54 mm) circuit board laminated to a bonding sheet (\(\epsilon_{\rm F}\) = 3.26, tan\(\delta\) = 0.0025, \(h\) = 0.1 mm).