# Smooth Bend Structures Using Hybrid Compensation for Common-Mode Noise Reduction
## 2 Analyzing and Comparing Bend Structures with 90-, 135-, and 150-Degree Bends  
The proposed designs were simulated and fabricated on a standard FR4 (\(\epsilon_{\mathrm{r}}=4.4\)) substrate; the substrate height (h) was equal to 1.6 mm, the width of the differential line (W) was 1.6 mm, and the spacing (S) between the differential lines was 0.7 mm. The odd-mode impedance was set to 50 Ohms to maintain the signal integrity of the differential transmission. Figure 2 shows the top view of the 90-degree bend and smooth bend structures of 135- and 150-degrees; the side view is shown in Figure 3.  
Figure 4 shows the unbalanced section in the red-hatched area. The red-hatched area in the 150-degree bend structure is smaller than in the 90- and 135-degree bend structures. Figure 3: Side view of a transmission line on a PCB. Figure 2: Top views of 90-degree bend and smooth bend structures with 135- and 150-degree bends. As mentioned previously, the primary purpose of this paper is to eliminate mode conversion loss and keep the differential signal integrity. Therefore, we will observe differential insertion loss (Sdd21) and common mode conversion loss (Scd21). The unbalancing section causes mode conversion loss. Using a smooth curved structure should reduce this. In other words, when the curvature of differential transmission lines becomes smoother, theoretically, the unbalanced effect will be more negligible. We first analyzed and compared the mode conversion loss (Scd21) and differential insertion loss (Sdd21) of bend structures with 90-, 135-, and 150-degree bends. Figure 5 shows the simulated results. The 150-degree bend structure (the black line) demonstrates better performance in terms of mode-conversion suppression than the 90- and 135-degreesructures. It also maintains good transmission performance on differential signals. Following this, we verified the lumped equivalent circuit model of bend structures with 90, 135, and 150-degree bends. The differential transmission lines can be regarded as two sections, which are either asymmetric [5] or symmetric [6]. The symmetric section is considered to be similar to a coupled line model. In addition, the asymmetric term is an extension of the \(\pi\) model equivalent circuit model, usually composed of inductors and capacitors. There are three asymmetric and four symmetric sections in the 150-degree bend structure. Figure 6a shows the lumped circuit block diagram. Figure 6b shows the lumped equivalent circuit model of the bend structure. Figure 4: Unbalanced sections in bend structures with 90-, 135-, and 150-degree bends. Figure 5: Simulated results of Sdd21 and Scd21 in structures with 90-, 135-, and 150-degree bends. The capacitance values of each structure were extracted and organized in Table 1 using electromagnetic simulation software, and the inductance values are shown in Table 2. Observing Tables 1 and 2, when the smooth bend structures of the135- and 150-degree bends are applied, the difference between the inner and outer traces becomes smaller than in the 90-degree bend, whether in terms of capacitance or inductance values. In other words, the smooth bend structures reduce the unbalanced effect on the bend section. The full-wave and equivalent circuit models' simulated results are shown in Figures 7 and 8, including Scd21 and Sdd21. Figure 7 indicates that the best result of \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**Extracted Capacitance (Pico Farad, pF)**} \\ \cline{2-4}  & **Inner Trace** & **Outer Trace** & **Mutual** \\ \hline
90-degree & 0.060 & 0.252 & 0.057 \\ \hline
135-degree & 0.064 & 0.143 & 0.040 \\ \hline
150-degree & 0.047 & 0.104 & 0.028 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Equivalent capacitance values. Figure 6: (**a**) Block diagram of a lumped circuit, (**b**) lumped equivalent circuit model of the differential bend. the Scd21 simulation is the 150-degree bend structure, as seen in the blue dashed line.