# A Peak Absorption Filtering Method for Radiated EMI from a High-Speed PWM Fan
## 3 Mechanism of Fan Radiation and Analysis of Radiated Source
### Analysis of Radiated Interference from Winding and Control PCB  
The windings and PCB were integrated inside the axial flow fan, and it was impractical to experimentally measure their radiation intensity separately. Hence, the radiated interference from the winding and control PCB was modeled, calculated, and analyzed by finite integration technique in the time domain, respectively. According to the finite integral theory, the Maxwell mesh equation was obtained as  
\[C\mathbf{e}=-\frac{d}{dt}\mathbf{b},\widetilde{C}\mathbf{h}=\mathbf{i}_{C}+ \mathbf{i}_{S}+\frac{d}{dt}\mathbf{d} \tag{3}\]  
where \(C\) and \(\widetilde{C}\) are the discrete curl matrices of the main grid and the dual grid, \(\mathbf{e}\) is the voltage along the edge, and \(\mathbf{b}\) is the magnetic flux through the face elements in the main grid. \(\mathbf{h}\) is the magnetic field along the edge of the dual grid. \(\mathbf{d}\), \(\mathbf{i}_{C}\), and \(\mathbf{i}_{S}\) are the electric flux, loss current, and external current, respectively. Figure 11: Comparison of radiated interference before and after the use of shielded lines. Figure 10: Schematic diagram of radiated emissions from a fan. Using the central difference discretization as well as the frog-leaping scheme for the time derivative terms of the two spinodal equations in the above equation, the explicit time-domain recursive equation of the finite integration method is given by  
\[\left\{ \begin{array}{l}\mathbf{e}^{n+1}=C_{AE}\mathbf{e}^{n}+C_{AH}\bigg{(} \widetilde{\mathbf{C}}\mathbf{h}^{n+\frac{1}{2}}-\mathbf{i}_{S}^{n+\frac{1}{2} }\bigg{)}\\ \mathbf{h}^{n+\frac{1}{2}}=\mathbf{h}^{n-\frac{1}{2}}-\Delta tD_{\mu}^{-1} \mathbf{C}\mathbf{e}^{n}\end{array} \right. \tag{4}\]  
where  
\[\left\{ \begin{array}{l}C_{AE}=\bigg{(}\frac{D_{e}}{\Delta t}+\frac{D_{e}}{2} \bigg{)}^{-1}\bigg{(}\frac{D_{e}}{\Delta t}-\frac{D_{e}}{2}\bigg{)}\\ C_{AH}=\bigg{(}\frac{D_{e}}{\Delta t}+\frac{D_{e}}{2}\bigg{)}^{-1}\end{array} \right. \tag{5}\]  
where \(D_{e}\), \(D_{e}\) and \(D_{\mu}\) are the permittivity matrix, electrical conductivity matrix, and magnetic reluctivity matrix, respectively. The transient electromagnetic process of the winding and PCB can be calculated according to Equations (4) and (5) by CST Studio Suite. To achieve field-circuit coupling, the excitation current is represented by adding the current \(\mathbf{i}_{L}\) to the right side of [PERSON]'s law, i.e.,  
\[\widetilde{\mathbf{C}}\mathbf{h}^{n+\frac{1}{2}}=D_{e}\frac{\mathbf{e}^{n+1}+ \mathbf{e}^{n}}{2}+D_{e}\frac{\mathbf{e}^{n+1}-\mathbf{e}^{n}}{\Delta t}+ \mathbf{i}_{L}^{n+\frac{1}{2}} \tag{6}\]  
The field-circuit coupled transient process can be calculated according to (6). The axial flow fan has a winding structure with a three-phase star structure and six slots. To assess the radiated interference of the winding, this paper employed a hybrid modeling approach that integrated field and circuit elements. Specifically, during the winding modeling process, 3D modeling was conducted based on the actual winding layout. The \(R\) and \(L\) parameters of the winding were then compensated using a circuit model, as illustrated in Figure 12. As CST's computational algorithms have difficulty in precisely modeling the influence of magnetic poles on winding parameters, we intentionally omitted the material properties of this component during the 3D modeling phase. Consequently, parameter compensation was applied in the circuit domain with \(R=0.287\)\(\Omega\) and \(L=250\)\(\mu\)H according to reference [16]. This approach not only aligns with the actual 3D layout of the winding but also ensures that the circuit parameters of the winding meet the requirements. The stator winding was fabricated using 0.71 mm diameter enamel-coated copper wire, with each slot containing 25 precisely wound turns. The 3D modeling process was carried out in SolidWorks 2021, which included detailed representations of the stator slots, coil windings, and permanent magnet components.