## 2 Methods
### Circuit Simulation  
In this section, we report the results of characteristic frequencies to derive the circuit parameters. We built the equivalent circuit model for the Left DGS, the Right DGS, and the proposed CM filter in Agilent ADS, represented to be consistent with the full-wave simulation results. We considered characteristic impedance (\(Z_{\text{circuit}}\)) in an even-mode cascading parallel LC circuit to the ground plane when the CM noise passed through to the DGS. Then, we could extract the equivalent circuit parameters from the simulation results in Section 2.1. First, we modeled a parallel LC-equivalent circuit from a transmission zero in the Left DGS. The parameters of the parallel LC resonator were derived by the resonant frequency (\(f_{0L}\)) of 7.3 GHz and the \(-3\) dB cut-off frequency (\(f_{\text{CL}}\)) of 2.72 GHz. We calculated the parameters of the parallel capacitance (C) and inductance (\(L\)) using Formulas (2) and (3), as given by [21],  
\[C=\frac{1}{4\pi\times Z_{\text{even}}}\left(\frac{f_{\text{C}}}{f _{0}^{2}-f_{\text{C}}^{2}}\right) \tag{2}\] \[L=\frac{1}{4\pi^{2}f_{0}{}^{2}\text{C}} \tag{3}\]  
Figure 5: Full-wave-simulated insertion loss for the proposed suppression filter. \begin{table}
\begin{tabular}{c c c c c c c c} \hline Left DGS & \(f_{\text{CL}}\) & 2.72 & \(f_{0L}\) & 7.3 & & & & \\ Right DGS & \(f_{\text{CR1}}\) & 2.60 & \(f_{\text{CR2}}\) & 9.0 & \(f_{0R1}\) & 6.6 & \(f_{0R2}\) & 13.7 \\ The proposedfilter & \(f_{01}\) & 3.20 & \(f_{02}\) & 10.3 & \(f_{03}\) & 14.2 & & \\ \hline \end{tabular} Unit: GHz.  
\end{table} 
Table 3: Cut-off and resonant frequencies of Left DGS, Right DGS, and the proposed suppression filter. since  
\[f_{0}=\frac{1}{2\pi\sqrt{L\times\mathcal{C}}} \tag{4}\]  
The equivalent circuit model of the Left DGS is shown in Figure 6. The even-mode impedance \(Z_{even}\) equaled 49.46 \(\Omega\). The equivalent circuit model of the Left DGS resulted in the following parallel capacitance and inductance parameters: \(C_{L1}\) and \(L_{L1}\) were 0.095 pF and 4.98 nH, respectively. Figure 7 shows the comparison of the full-wave simulation parameter \(S_{cc21}\) for the red curve and the equivalent circuit model for the black curve. Figure 6: The parallel LC-equivalent circuit model of the Left DGS. Figure 7: S-parameter of equivalent circuit model and full-wave simulation for the Left DGS. Similarly, the equivalent circuit model of the Right DGS is shown in Figure 8. It consists of two LC elements in parallel, since two transmission zeros were obtained from the Right DGS simulation. We obtained the circuit parameters \(C_{R1}\), \(C_{R2}\), \(L_{R1}\), and \(L_{R2}\), which were 0.114 pF, 0.136 pF, 5.12 nH, and 0.99 nH, respectively. Figure 9 shows the comparison of the insertion loss of the full-wave simulation and the equivalent circuit model. Figure 8: The parallel LC-equivalent circuit model of the Right DGS. Figure 9: S-parameter of equivalent circuit model and full-wave simulation for the Right DGS. Following this, we used the general formulation (5) for extracting the coupling coefficient \(k_{x}\), regardless of whether the coupling was electric, magnetic, or mixed; \(k_{x}\) is the mixed coupling coefficient and is given as Formula (6), where \(k_{m}\) and \(k_{e}\) are the magnetic and electric coupling coefficients, respectively. The coupling coefficient \(k\) is given by [22].