## 5 Conclusions  
This article proposed a simulation model of single-phase CMIs to evaluate the impact of the CC method on the CM attenuation characteristic of CMIs. By connecting cancellation capacitors based on the estimated stray capacitance to the proposed simulation model, the attenuation characteristics of a single-phase CMI with the CC method can be simulated at the design stage of CMIs. The measurements of the CM attenuation of the fabricated CMIs were performed, and the measured results were compared with the simulated results. The comparison results clarified that the proposed model can simulate the CM attenuation characteristics of the CMI with the CC method over a wideband frequency. Furthermore, in the case of the MnZn ferrite-based CMI, the measured result clarified that the CM  
Figure 15: Comparison between the measured and simulated attenuation characteristics of CMI\(-\)2: (**a**) without \(C_{\text{can}}\); (**b**) with \(C_{\text{can}}\). attenuation improvement by the CC method is limited due to the steep change in the complex permeability. Some previous works have validated that the dimensional effect of MnZn ferrites can be mitigated by applying core lamination [23; 33]. Thus, the combination of the CC method and core lamination to improve the CM attenuation of MnZn ferrite-based CMIs will be investigated as the next step of this study. This research was supported by MEXT Program for Creation of Innovative Core Technology for Power Electronics Grant Number JPJ009777. Not applicable. Data Availability Statement: Data are contained within the article. The author would like to thank [PERSON] of Tokyo Metropolitan University for supporting this article by providing his expertise in power electronics. The author declares no conflicts of interest. Appendix A Equivalent core loss resistance \(R_{\text{c}}\) is calculated using the imaginary part of the complex permeability \(\mu_{\text{r}}\)\({}^{\prime\prime}\) and is obtained as  
\[R_{\text{c}}(f) =2\pi f\mu_{0}\mu_{\text{r}}^{\prime\prime}(f)\cdot\frac{A_{\text{ c}}}{l_{\text{c}}}N^{2} \tag{1}\]  
Winding resistance \(R_{\text{w}}\) is given by  
\[R_{w}= \begin{cases}\rho_{Cu}\frac{4 Nl_{T}}{\pi d_{\text{c}}^{2}}&\left(\delta _{Cu}>\frac{d_{\text{w}}}{2}\right)\\ \rho_{Cu}\frac{Nl_{T}}{\pi\left(d_{\text{w}}\delta_{Cu}-\delta_{Cu}^{2}\right) }&\left(\delta_{Cu}\leq\frac{d_{\text{w}}}{2}\right)\end{cases}  \tag{2}\]  
where the conductivity of copper at room temperature (\(T\) = 25 \({}^{\circ}\)C) is derived from Equation (9). Moreover, the skin depth of copper is obtained from the following Equation (A3). \[\delta_{Cu}=\sqrt{\frac{\delta_{Cu}}{\pi\mu_{0}f}} \tag{3}\]  
To validate Equations (2) and (3), the resistance of a 1 m length copper wire (conductor diameter: 0.81 mm) was measured using the network analyzer. A comparison of the measured winding resistance and the calculated results from Equations (2) and (3) are shown in Figure 1.  
Since the measured winding resistance varied due to the transmission line effect in the high-frequency range, Figure 11 shows the measured result up to 10 MHz. Figure 11 confirms that the frequency characteristics of the winding resistance can be calculated over a wideband frequency from Equations (A2) and (A3). Figure 12 compares the calculated equivalent core loss resistances and calculated winding resistances. The equivalent core loss resistances were calculated from Equation (A1) based on the specifications of CMI-1 listed in Table 1. Figure 12 includes the calculated results where the turn number \(N\) is set to 1, the minimum number of turns. Figure 12 illustrates that for CMI-1 the equivalent core loss resistance substantially exceeds the winding resistance across the frequency range from 1 kHz to 30 MHz. This observation aligns closely with scenarios where the turn number is at its minimum, N = 1.