## 2 Methods  
### Full-Wave Simulation  
The ultra-wideband CM suppression filter was simulated on a standard FR4 (\(\mathbb{F}\)r = 4.4) substrate; the loss tangent was 0.02. The printed circuit board (PCB) thickness was 1.035 mm. We used 1 oz copper on the top layer and layer 2, where layer 2 was ground plane. The computer configurations include Intel i7 CPU, 8 GB RAM, and 500 GB solid-state drive (SSD).  
Figure 1 shows the PCB stack-up. Two microstrip lines were on the top layer; their width (\(W\)) and spacing (\(S\)) were 0.18 mm and 0.36 mm, respectively. We designed \(W\) and \(S\) to meet a 100 \(\Omega\) differential pair to maintain good SI in the differential mode. Figure 2 shows the PCB top view. Two DGS units were placed close to each other on the ground plane to form long and narrow bridges on that plane. The detailed geometry parameters of the DGS resonators are also summarized in Table 2.  
We first simulated the two half-structure DGS units of the proposed suppression filter using ANSYS HFSS; they are referred to as \"Left DGS\" and \"Right DGS\" to simplify the following analysis. Next, we simulated the proposed ultra-wideband CM suppression filter.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Ref.** & \(f_{\mathbf{L}}\) **(GHz)** & \(f_{\mathbf{H}}\) **(GHz)** & \(f_{\mathbf{C}}\) **(GHz)** & **FBW (\%)** \\ \hline
[12] & 3.68 & 8.43 & 6.1 & 78.4 \\
[13] & 5.4 & 11.4 & 8.4 & 71.4 \\
[14] & 3.75 & 6.95 & 5.35 & 59.8 \\
[15] & 1.8 & 2.9 & 2.35 & 46.8 \\
[16] & 2.9 & 8.1 & 5.5 & 94.5 \\
[16] & 3.6 & 9.1 & 6.35 & 86.6 \\
[17] & 3.2 & 12.4 & 7.8 & 117.9 \\ \hline \end{tabular}
\end{table}
Table 1: Details of the bandstop filters.  
Figure 3 demonstrates the full-wave simulations of the differential-mode insertion loss (S\({}_{\text{dd21}}\)) by the blue curve and the common-mode insertion loss (S\({}_{\text{cc21}}\)) by the red curve in the Left DGS. From the S\({}_{\text{cc21}}\) simulated result, we obtained a \(-3\) dB cut-off frequency (\(f_{CL}\)) at 2.72 GHz and a resonant frequency (\(f_{0L}\)) at 7.3 GHz.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Parameters** & **Value** & **Parameters** & **Value** & **Parameters** & **Value** & **Parameters** & **Value** & **Parameters** & **Value** \\ \hline \(W\) & 0.18 & \(S\) & 0.36 & \(t\) & 0.035 & \(h_{1}\) & 0.1 & \(h_{2}\) & 0.865 \\ \(W_{t}\) & 5.2 & \(W_{s}\) & 2.5 & \(W_{b}\) & 0.2 & \(L_{t}\) & 5.04 & \(W_{g1}\) & 0.2 \\ \(W_{b1}\) & 2.4 & \(W_{b2}\) & 4.6 & \(L_{b1}\) & 0.56 & \(L_{b2}\) & 0.4 & \(W_{g2}\) & 0.3 \\ \hline \multicolumn{10}{c}{Unit: mm.} \\ \end{tabular}
\end{table}
Table 2: Detailed list of geometry parameters.  
Figure 1: PCB side view.  
Figure 2: PCB top view.  
Similarly, Figure 4 shows the full-wave-simulated S\({}_{\rm dd21}\) and S\({}_{\rm cc21}\) in the Right DGS. The simulation results of the \(-3\) dB cut-off frequencies \(f_{\rm CR1}\) and \(f_{\rm CR2}\) of S\({}_{\rm cc21}\) were 2.6 GHz and 9 GHz, respectively; the resonant frequencies of the first-order frequency (\(f_{\rm 0R1}\)) and second-order frequency (\(f_{\rm 0R2}\)) of 6.6 GHz and 13.7 GHz, respectively, were also obtained.  
Finally, Figure 5 shows the S\({}_{\rm dd21}\) and S\({}_{\rm cc21}\) of the proposed suppression filter using the magnified coupled DGS. Three resonant frequencies, \(f_{\rm 01}\), \(f_{\rm 02}\), and \(f_{\rm 03}\), were identified, which were 3.2 GHz, 10.3 GHz, and 14.2 GHz, respectively. Since the two DGS units, the  
Figure 4: Full-wave simulated insertion loss for the Right DGS.  
Figure 3: Full-wave simulated insertion loss for the Left DGS.  
Left DGS and the Right DGS, were placed close to each other to produce a mutual coupling effects, it was easy to determine the frequency separation and the ultra-wide stopband. All the frequencies of the Left DGS, the Right DGS, and the proposed suppression filter are listed in Table 3.