## 1 Introduction
Therefore, the method proposed in [20] cannot be directly applied to estimate stray capacitance of CMIs. To solve the above problem, the author has modified the equations for calculating the turn-to-turn capacitance in the estimation method proposed in [20] to be a function of the angle of the winding covering the core and applied to single-phase CMIs [21]. Another aspect that diminishes the high-frequency attenuation properties of CMIs is the frequency-dependent nature of the complex permeability in magnetic materials. To illustrate, in nanocrystalline materials, the imaginary component of complex permeability becomes more prominent at frequencies exceeding approximately 100 kHz. Therefore, nanocrystalline-based CMIs behave as resistive components in the high-frequency range. In addition, depending on the core dimension, the permeability of manganese-zinc (MnZn) ferrite decreases drastically around 1 MHz and indicates negative polarity [22; 23]. This steep change in the permeability degrades the high-frequency attenuation characteristics of MnZn ferrite-based CMIs. In some previous studies, simulation models of CMIs that consider the complex permeability's frequency dependence have been proposed [16; 24]. However, the relationship between the frequency dependence of complex permeability and the CC method has yet to be investigated in detail. Figure 1: Basic concept of capacitance cancellation. The author introduced a circuit simulation model for CMIs, accounting for the frequency-dependent complex permeability of magnetic materials and the stray capacitances of windings [25]. This model was validated through impedance measurements, confirming its ability to simulate the small-signal characteristics of CMIs across a broad frequency spectrum, from 1 kHz to 100 MHz. Nonetheless, as presented in [25], the model was developed without incorporating the grounding connections of cancellation capacitors. As a result, it cannot replicate the effects of the CC method on the attenuation properties of CMIs. In this article, the author refines the previously proposed circuit simulation model for single-phase CMIs (as described in [25]) to assess the influence of the CC method on the small-signal behavior of CMIs. Integrating cancellation capacitors, calculated based on the anticipated stray capacitance, into this adjusted simulation model makes it feasible to predict the attenuation characteristics of a single-phase CMI utilizing the CC method during the design phase of CMIs. Note that the small-signal characteristics of a common-mode inductor are evaluated using a network analyzer in this article. Therefore, the magnetic flux generated in the inductor during the measurement is a small signal at several mT levels. Therefore, the proposed simulation model does not include phenomena specific to large-signal excitation conditions, such as magnetic saturation and nonlinearity behavior. Furthermore, losses must be considered when installing EMI filters in power converters. On the other hand, this article aims to understand the small-signal characteristics (attenuation characteristics) of CMIs with CC method at the design stage. Therefore, an evaluation of loss characteristics of CMIs is beyond the scope of this article. Comparing the measured and simulated small-signal characteristics of actual single-phase CMIs demonstrates that the model can accurately represent the attenuation behavior of CMIs with the CC method across a wide frequency range. Additionally, empirical findings highlight that the enhancement in attenuation achieved by applying the CC method to MnZn ferrite-based CMIs is restricted in the high-frequency domain due to the sharp variation in complex permeability.