## 4 Discussion  
A parallel resonant circuit stores circuit energy in the inductor's magnetic field and the capacitor's electric field. Currents through inductors and capacitors are always equal and opposite. We can adjust the geometry parameters of the capacitor (\(W_{g1}\)) and inductor (\(W_{b}\), \(W_{b1}\), and \(W_{b2}\)) in Figure 2 to obtain the resonant frequency. The smaller \(W_{g1}\) has larger capacitance. Thinner \(W_{b}\) or longer \(W_{b1}\) and \(W_{b2}\) produce larger inductance. In addition, larger capacitance or inductance leads to lower frequency from Formula (3) in Section 2.2. As seen in Figures 7, 9 and 13, the S\({}_{cc21}\) of the equivalent circuit model agrees very well with the full-wave simulation result. It shows differences in the high-frequency domain since the full-wave simulation is realistic and different from the equivalent circuit model; it should be considered in additional parasitic capacitances and inductances, such as PCB vias. In addition, the equivalent circuit model does not include some distribution effects, such as complex boundary conditions.  
In Section 2.2, we quickly predict the first- and second-order transmission zero using the circuit simulation tool Agilent ADS. The Left and Right DGS are considered asynchronously tuned coupled resonator circuits [22] because two DGSs obtain three different resonant frequencies. The coupling coefficient changes and affects the frequency characteristics because of the stored electromagnetic field distributions. In other words, the bandwidth is extended due to the asynchronously tuned coupling.  
According to the S\({}_{cc21}\) measurement in Section 3.1, from 2.9 GHz to 16.2 GHz, the fractional bandwidth (FBW) of the proposed design reaches 139.3%, where the stopband's central frequency is 9.55 GHz. The filter's physical size is 5.04 mm \(\times\) 5.2 mm. The filter's  
Figure 18: Measurements of CM noise magnitude.  
electrical size is only \(0.292\,\lambda_{g}\times 0.302\,\lambda_{g}\), where \(\lambda_{g}\) is the guided wavelength of the stopband central frequency. The guided wavelength is given by  
\[\lambda_{g}=\frac{\lambda_{0}}{\sqrt{\varepsilon_{re}}}, \tag{7}\]  
where \(\lambda_{0}\) is the free space wavelength at operation frequency. The effective dielectric constant (\(\varepsilon_{re}\)) is obtained by the dielectric constant (\(\varepsilon_{r}\)), PCB thickness (\(h\)), and trace width (\(W\)). This work fallsunder the case of \(W/h\geqq 1\); the \(\varepsilon_{re}\) is given by [23],  
\[\varepsilon_{re}=\frac{\varepsilon_{r}+1}{2}+\frac{\varepsilon_{r}-1}{2}\frac {1}{\sqrt{1+12\frac{h}{W}}}. \tag{8}\]  
The measured value has ripples and attenuations in Figure 16, possibly due to impedance mismatch between the PCB and connector; additionally, there are tolerances in PCB manufacturing, and the FR4 substrates have limited performance at high frequencies above 10 GHz. However, \(\mathrm{S_{cc21}}\) still shows a good agreement between the measurements and simulations. This demonstrates that the CM noise is suppressed in an ultra-wide stopband.  
We asymmetrically etched the DGS filter in the proposed filter to form three mutually coupled resonators, resulting in a pronounced ultra-wideband suppression effect. Table 6 lists the detailed comparison with [17; 18; 19; 20]. The proposed work reveals the smallest physical size; compared with [19], the physical size is reduced by 85%. The area at the stopband central frequency is the most compact. In addition, the CM noise suppression band is the most extensive range, and a high frequency reaches 16.2 GHz. Compared with previous research [20], the FBW is increased by 41.3%.  
Table 7 compares the noise magnitude with previous research. Compared with [20], the suppression ratio increases by 20.3%. This demonstrates that the proposed suppression filter possesses a more excellent CM noise-reduction capability.