## 1 Introduction
Hence, this article suggests an analytical-based modeling approach for differential mode EMI noise estimation. The analytical model is proposed for an interleaved boost PFC converter, depicted in Figure 1 with including the impedance stabilizing network (LISN), EMI receiver, and EMI filter. To create the possibility of compliance with measuring all EMI measuring equipment's impact, including the EMI receivers, LISN is also considered on the analytical model. Figure 1: Block diagram of an interleaved boost power factor correction (PFC) converter including impedance stabilizing network (LISN), electromagnetic interference (EMI) receiver, and EMI filter. From an EMI viewpoint, finding the appropriate phase shift angles is of great importance to get an optimal filter volume [1; 11]. So, the optimal DM EMI filters design for interleaved boost PFC applications is an important challenge, especially within the low-frequency EMI range in-between 2 and 150 kHz. This research's primary purposes are to propose an appropriate analytical DM EMI noise estimation and EMI filter volume investigation. Moreover, the analytical noise estimation approach covers the number of interleaved units and the related different types of phase shifts. Thus, the unconventional phase shift is achieved based on the analytical EMI estimations for carrier harmonics on Band-B. Further, the effects of the different types of the phase shift on Band B and A DM EMI filter design have been investigated. The main contributions of this research can be highlighted as follows. First, the impact of switching frequency selection and the number of interleaved stages in a single-phase PFC on DM EMI filter sizing (filter corner frequency and required attenuation) are analytically investigated. Second, an analytical method is proposed for interleaved PFC to predict maximum peak noise that is highly important in the DM EMI filter design. The dependency of the maximum peak noise on the phase shift between the interleaved units leads to the investigation of the phase shift impact on the DM EMI filter size via the EMI estimation approach. So, a novel formulation is presented for the unconventional phase shift method based on the EMI estimation analysis within Band B. Furthermore, it is shown that the unconventional phase-shift angle can be obtained depending on the switching frequency of the power converter and the number of interleaved stages. Third, a general flowchart is presented to find optimal filter volume based on the proper phase shift, EMI estimation approach, type of the band frequency, and volumetric component parameter. The rest of the research is organized as follows. Section 2 details the design process of a typical two-stage DM EMI filter. In this section, the EMI measurement setup is described according to the CISPR standard such as EMI receiver and line impedance stabilizing network (LISN). Section 3 provides the process of getting the filter's attenuation requirement and filters corner frequency in the interleaving units. In order to calculate the required filter attenuation, the simplified analytical modeling approach is presented in order to estimate DM EMI noise level in Section 4. Subsequently, in Section 5, the advantages of the unconventional phase shift in the interleaved units are developed in Band-B, where the filter attenuation drop is presented. Moreover, filter volume optimization is given based on the type of phase shifts in Section 6. Section 7 provides the experimental results of two interleaved boost PFC converters to validate the DM EMI model noise for different phase shifts. Ultimately, conclusions are provided in Section 8.