## 5 Results and Discussion
### LC-Based SIW Phase Shifter  
The proposed LC-based SIW phase shifter was simulated with HFSS at the operating frequency of 28 GHz. The addition of IPs increased the cut-off frequency from 15 GHz to 20 GHz (Figure 9a). Because our target operating frequency is 28 GHz, our design has a large enough margin. S-parameters of the proposed structure showed insertion loss \(IL\) = 1.1 dB, and \(\Delta\phi\) = 58.1\({}^{\circ}\) (Figure 9b). The comparison of the proposed structure, Case1, and Case 2 are presented to evaluate the effectiveness of our proposed structure in Table 1. The proposed structure had FoM1, which was 55.68% higher than in Case 1 and 21.85% higher than in Case 2, and an \(IL\) about 35% higher than in both Case 1 and 2. Figure 7: Simulated phase advances of the SIW structure with additional inserted posts, as a function of substrate permittivity: (**a**) loaded with one post, (**b**) loaded with two posts. To verify the effect of \(\Delta\phi\) caused by the additional IPs, we designed two conventional structures: Case 1, which uses the same amount of LC as the suggested structure, and Case2, which uses additional LCs instead of IPs (Figure 10). Their electrical characteristics were compared using two figures of merit (FoM). The figure of merit 1 (FoM1; \({}^{\circ}\)/dB) for a passive phase shifter is defined as  
\[\text{FoM1}=\frac{\Delta\phi_{max}}{IL_{max}}. \tag{10}\] \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Topology**} & \multirow{2}{*}{\begin{tabular}{c} **Amount of LC** \\ **(mm\({}^{3}\))** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Maximum** \\ **Insertion Loss** \\ **(dB)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Maximum** \\ **(\({}^{\circ}\))** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **FoM1** \\ **(\({}^{\circ}\)/dB)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **FoM2** \\ **(\({}^{\circ}\)/mm)** \\ \end{tabular} } \\ \hline Proposed structure & 17.5 & 1.1 & 58.1 & 52.82 & 2.62 \\ Case 1 & 17.5 & 0.82 & 37.32 & 45.51 & 1.69 \\ Case 2 & 25 & 0.8 & 47.68 & 56.76 & 2.16 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of proposed structure performance with Cases 1 and 2 at 28 GHz. Figure 8: Simulation results of SIW structure with one inserted post: increase in differential phase shift as a function of offset and radius: (**a**) function of radius \(r\) and (**b**) function of offset \(p\). Figure 9: Simulation results of the proposed LC-based SIW phase shifter: (**a**) S-parameter (dB), (**b**) phase shift (\({}^{\circ}\)). This factor is important because it is related to the price competitiveness of LC devices. In order to secure price competitiveness in an array structure with numerous unit cells, the amount of LC used for driving in a single cell must be minimized. The proposed LC-based phase shifter's FoM1 was 52.82 \({}^{\circ}\)/dB, which is 16.06% larger than Case 1 and 6.94% lower than Case 2. These changes are caused by the additional IP that simultaneously increases \(\Delta\phi\) and _IL_. FoM2 (\({}^{\circ}\)/mm) is \(\Delta\phi_{max}\) per length, which is important when determining the required dimension of the phase shifter to achieve the desired \(\Delta\phi\)[36; 37]:  
\[\text{FoM2}=\frac{\Delta\phi_{max}}{\textit{Total Length}}. \tag{11}\]  
By this parameter, we can evaluate the footprint of the LC devices. Research related to the miniaturization of RF structures has been a subject of much interest. The suggested LC-based SIW phase shifter has FoM2 = 2.62 \({}^{\circ}\)/mm, which is 55.03% higher than Case 1 and 21.3% higher than Case 2. The proposed IP-inserted LC-based SIW phase shifter increased FoM2 with fewer LCs than the existing structure. The phase shift results in Case 1 and Case 2 differ due to the varying LC volumes in their design. The RF signal passes through the space between the posts, and the volume of LCs it travels through determines the tunability of the LC-based SIW design.