## 2 The Design Approached Two-Stage DM Filter  
The EMI filter is employed for protecting the utility against the high frequency conducted emission noises. To this end, they should comply with EMI standard requirements. Therefore, a symmetrical two-stage filter structure design, as shown in Figure 2, is considered. Notably, the primary purpose of the EMI filter is to reduce the emission noise in order to fulfill relevant standards [3; 5]. The selection of the filter components depends upon the filter attenuation requirement \(A_{tt-req}\), calculated by (1) [6]:  
\[A_{tt-req}(f_{D})[dB]=U_{\text{max}}(f_{D})[dB\mu V]-CISPR_{\text{limit}}(f_{ D})[dB\mu V]+\text{Margin}[dB] \tag{1}\]  
where \(f_{D}\) is filter design frequency, \(U_{max}\) is the first noise voltage peak. \(A_{tt-req}\) is the noise quantity, which should be damped by the filters. \(CISPR_{limit}\) is considered emission limits following CISPR-15 [5] and CISPR-11 [3] based on QP (Quasi Peak) for band A and B, respectively. Moreover, \"Margin\" is the filter design margin. It is considered as 6 dB because of uncertainty and EMI filter parameter tolerances [11; 12; 13]. Uncertainty is explicitly considered by establishing proper control procedures and characteristics of the production materials. In [14], the performance of novel control techniques for imperfect systems was studied. The procedure is based on the utilization of the unavoidable imperfections related to physical realizations. In addition, \(A_{tt-req}\) for a symmetrical two-stage EMI filter, including inductor and capacitor size is obtained by (2):  
\[A_{tt-req}(f_{D})=((j2\pi f_{D})^{2}.(2L_{DM}).C_{DM}+1)^{2}+(2\pi f_{D})^{2}.(2L _{DM}).C_{DM} \tag{2}\]  
As discussed earlier, the input ripple current reduction implies a lower DM EMI noise magnitude (\(U_{max}\)), and thus a smaller component size of the DM EMI filter. Additionally, the dependency of EMI filter corner frequency on the filter component results in a challenge in sizing the filter components. Accordingly, reducing the EMI filter component size makes the DM filter corner frequency higher. One of the primary goals of this research is to get an optimal corner frequency based upon the interleaved technique and the employed phase shift. The filter corner frequency is obtained by (3)  
\[fc=\frac{1}{2.\pi\sqrt{L_{DM}C_{DM}}} \tag{3}\]  
Moreover, to measure the \(U_{max}\) based on the CISPR-16 [11] standard requirement, a LISN and an EMI receiver are required. The LISN not only decouples the line and the device under test (DUT) but also provides an interface between the DUT and the test receiver. The LISN structure employed for EMI measurement within the frequency range of 9 kHz--30 MHz is illustrated in Figure 3. Notably, LISN is able to measure the RMS time-domain voltage (\(u_{meas}\)) in order to define the EMI noise based on Equation (4). So, the EMI test receiver utilizes a QP detection to get the EMI peak measurement. Finally, by considering (4), the EMI peak measurement [13; 15] is achieved:  
\[U_{\max}[dB\mu V]=20\log[1/\mu V\sum_{f=MB-\frac{BW}{2}}^{f=MB+\frac{BW}{2}}u_{ meas}(f)\cdot RBW(f)] \tag{4}\]  
where MB is frequency sweep that is shifted over the frequency band of interest. \(RBW\) is fourth order Butterworth bandpass filter, and the bandwidth (\(BW\)) is 200 Hz for Band A (9-150 kHz), and 9 kHz for Band B (150 kHz-30 MHz).  
Figure 2: Symmetrical two-stage differential mode (DM) EMI filter configuration.