# T-Type Vertical Wall for Decoupling and Pattern Correction of Patch Antenna
## 2 Antenna Configuration and Parametric Analysis
### Parametric Analyses  
It should be noted that the original design is kept unchanged (patch and feed are fixed). Only changes on the vertical wall are performed to reduce the mutual coupling and to correct the pattern. Five variables are considered for the coupling reduction. These are: The wall height \(H_{\mathrm{s}}\), T-type metal widths \(d_{2}\) and \(s\) of the vertical and parallel strips, and length \(H_{2}\) and \(p\) of the corresponding strips. The upper length of the vertical strip is relative to \(H_{2}\) and \(s\), which can be obtained at the height \(H_{\mathrm{s}}\) (\(H_{\mathrm{s}}-H_{2}-s\)). Thus, the corresponding variable is not shown in Figure 1c. All five variables affect the decoupling and correction; however, they are correlative if the height \(H_{\mathrm{s}}\) is determined. As increasing \(H_{2}\) is equivalent to increasing \(p\) for the resonant length at the desired frequency because the induced current flows starting from the \(H_{2}\) part and ending on the \(p\) part. Therefore, only two key variables are selected, \(d_{2}\) and \(H_{2}\), to analyze their influences on the S-parameters and radiation patterns where \(d_{2}\) mainly affects the surface current from the ground plane, while \(H_{2}\) is related to the radiation and surface waves.  
The effects of the two variables on the antenna performance are shown in Figures 2 and 3, respectively. These comparisons show that these two variables affect the transmission coefficient S21s and the pattern correction, while almost not affecting S11s. Thus, we must carefully adjust the two variables to achieve excellent decoupling in the desired frequency band. Meanwhile, the variable \(d_{2}\) is more sensitive than that of \(H_{2}\) to the radiation pattern correction to some extent because it can adjust the radiation pattern of both sides of the broadside direction, while \(H_{2}\) only corrects the positive side for these given values.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Variable** & **Value (mm)** & **Variable** & **Value (mm)** & **Variable** & **Value (mm)** \\ \hline \(W_{0}\) & 46 & \(L_{2}\) & 7.5 & p & 14 \\ \(L_{0}\) & 31.7 & \(W_{3}\) & 3 & t & 6.25 \\ \(H_{S}\) & 6.4 & \(L_{3}\) & 3 & s & 1.98 \\ \(W_{1}\) & 15 & \(W_{4}\) & 0.8 & \(d_{2}\) & 3.1 \\ \(L_{1}\) & 11.5 & \(L_{4}\) & 20 & \(H_{0}\) & 1.6 \\ \(W_{2}\) & 0.5 & \(H_{2}\) & 1.9 & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Values of the antenna variables.  
Figure 2: The effect of \(d_{2}\) on antenna performance: (**a**) S-parameters and (**b**) radiation patterns.  
However, the wall substrate's property is another factor that affects the final decoupling and pattern correction. Furthermore, we know that the permittivity of this substrate will affect the corresponding resonant length of the concerned frequency, which will be stated in Section 4. Therefore, we do not discuss its influence. In contrast, the loss tangent of the wall substrate will be a key factor to be considered here because we can choose the material with other losses. Figure 4 shows this influence by comparing three different loss tangents, where \(\tan\delta=0.025\) is the general value of the chosen conventional FR4. The results depict that the loss tangent affects not only the S-parameters, but also the realized gain at the concerned 5.80 GHz and its tilt. The lower loss, \(\tan\delta=0.002\), than the one used can improve the realized gain to get closer to that of the no-decoupling structure, which will be presented for the realized gain comparison in the following, but the pattern tilts to \(-20^{\circ}\), and the decoupling and matching results are not good. Briefly, we can improve the realized gain by the lower lossy substrate, and realize the pattern correction by redesigning the decoupling structure according to this fixed value if the corresponding resonance is formed by the wall-substrate permittivity.