# Experimental Study of Radiated Emission Due to Secondary Common-Mode Current in Buck Converters
## 3 Generation Mechanism of the SCM Noise in the Experimental System  
This section describes the generation mechanism of the SCM noise in the experimental system. First, the impedances of the noise sources and noise propagation paths in the experimental system shown in Figure 2 are represented as shown in Figure 3.  
Here, the buck converter is represented as the behavioral model [31; 32; 33], where \(I_{\text{DM}}\) is the DM current source; \(V_{\text{PCM}}\) is the PCM voltage source; and \(I_{\text{PCM}}\) is the PCM current. The impedance between terminals P'-N' when the three-core cable is disconnected near the input terminal of the buck converter is denoted as \(Z_{\text{DM}}\). Moreover, the impedance between the input terminals of the buck converter and the metal box is \(Z_{\text{PCM}}\), and it is equally distributed to each phase of the buck converter. \(Z_{\text{LISN}}\) represents the impedance of LISNs, and \(Z_{\text{P}}\), \(Z_{\text{N}}\), and \(Z_{\text{E}}\) represent the impedances of the power lines P, N, and ground line E of the three-core cable, respectively. The impedance between the terminal E and the ground plane near LISNs is represented as \(Z_{\text{G}}\) (\(Z_{\text{G}}\) is depicted by a dotted line in Figure 2 because it is very small). Figure 2: Configuration of the experimental system. First, in Figure 3, assuming that each phase impedance of the three-core cable is balanced (\(Z_{\rm P}=Z_{\rm N}=Z_{\rm E}\)), the following Equation (1) for the PCM is derived as  
\[V_{\rm PCM}=\left(Z_{\rm PCM}+\frac{3}{2}Z_{\rm E}+\frac{Z_{\rm LSN}}{2}\right) \cdot I_{\rm PCM} \tag{1}\]  
Thus, the PCM current \(I_{\rm PCM}\) is given using  
\[I_{\rm PCM}\ =\frac{V_{\rm PCM}}{\left(Z_{\rm PCM}+\frac{3}{2}Z_{\rm E}+\frac{Z_ {\rm LSN}}{2}\right)} \tag{2}\]  
Next, assuming the PCM currents that flow through each phase are balanced, voltage potentials of the terminals P, N, and E for the ground (\(V_{\rm P}\), \(V_{\rm N}\), and \(V_{\rm E}\)) are represented as  
\[V_{\rm P}=Z_{\rm LSN}\cdot\left(-\frac{I_{\rm PCM}}{2}\right) \tag{3}\]  
\[V_{\rm N}=Z_{\rm LSN}\cdot\left(-\frac{I_{\rm PCM}}{2}\right) \tag{4}\]  
\[V_{\rm E}=Z_{\rm G}\cdot I_{\rm PCM} \tag{5}\]  
From Equations (3)-(5), the average voltage of \(V_{\rm P}\), \(V_{\rm N}\), and \(V_{\rm E}\), which is the CM voltage of the three-core cable as a whole \(V_{\rm SCM}\), is given with  
\[V_{\rm SCM}=\frac{V_{\rm P}+V_{\rm N}+V_{\rm E}}{3}=\frac{\left(Z_{\rm G}-Z_{ \rm LSN}\right)}{3}\cdot I_{\rm PCM} \tag{6}\]  
Since the impedance of the ground wire should be as small as possible for safety reasons, \(Z_{\rm G}\) and \(Z_{\rm LSN}\) are not equal, and the right side of Equation (6) is not zero. Thus, it can be considered that the SCM voltage, which is the average voltage given with Equation (6), is caused by the PCM current and the unbalance of the power supply side impedances (\(Z_{\rm LISN}\
eq Z_{\rm G}\)) in this experimental system. The SCM voltage \(V_{\rm SCM}\) causes the SCM current \(I_{\rm SCM}\) to flow through the entire three-core cable. The buck converter, which is housed in the metal box, is placed on the wooden table whose height is 0.8 m from the floor. Thus, the power converter side has a large SCM impedance to the ground plane. In this case, a standing wave of the SCM current with the  
Figure 3: Simple representation of noise sources and noise paths in the experimental system. power supply side as the antinode and the power converter side as the node is generated depending on the cable length, as shown in Figure 4.  
In other words, the three-core cable, which is the SCM noise propagation path, constitutes a monopole antenna and is one of the dominant sources of radiated noise in the experimental system under investigation in this article. Equation (6) shows that suppressing the PCM current \(I_{\text{PCM}}\) or balancing the power supply side impedances (\(Z_{\text{LISN}}=Z_{\text{G}}\)) effectively reduces the SCM noise.