## 4 Measurement Results and IL Prediction
### Definition of CM/DM IL of Three-Phase Filters  
According to CISPR 17, the filter IL is defined as the ratio of the voltages measured across a reference load in the presence and in the absence of the filter when a source with a specific reference impedance is fed to the system. In the symmetrical scenario, both the  
Figure 10: Impedances in the motor drive system equivalent modal circuits: (**a**) DM and (**b**) CM.  
load and source impedances take the value of 50 \(\Omega\). In a three-phase system, this choice leads to equivalent load and source impedances equal to \((50\times 2)\)\(\Omega\) for the DM, and to 50/3 \(\Omega\) for the CM equivalent circuit of the measurement setup.  
To estimate the in-circuit IL of a three-phase filter installed in the motor drive system under analysis, the actual modal impedances obtained by the one-probe method are used instead of the canonical impedances foreseen by the standard. Specifically, the actual load impedance is defined as the impedance of the cable and LISN, while the EMI source impedance is defined as the impedance of the motor drive system in a specific operating condition.  
DM and CM in-circuit ILs of the filter can be evaluated by solution of the modal circuits shown in Figure 11. Panels on the left represent the modal setups in the absence of the filter, and can be readily solved to evaluate the modal voltages \(V_{\text{inv\_DM}}\), \(V_{\text{inv\_CM}}\) across the load in the absence of the filter.  
Modal ILs can be therefore cast as follows:  
\[IL_{DM}=20 log_{10}\frac{|V_{\text{inv\_DM}}|}{|V_{\text{inv\_DM}}|}=\frac{ \left|\frac{Z_{LISN\_Chilte\_DM}}{Z_{LISN\_Chilte\_DM}+Z_{\text{MDS\_DM}}}V_{s} \right|}{|V_{1}-V_{2}|} \tag{22}\]  
\[IL_{CM}=20 log_{10}\frac{|V_{\text{inv\_CM}}|}{|V_{\text{inv\_CM}}|}=\frac{ \left|\frac{Z_{LISN\_Chilte\_CM}}{Z_{LISN\_Chilte\_CM}+Z_{\text{MDS\_CM}}}V_{s} \right|}{|V_{1}|} \tag{23}\]  
where \(Z_{LISN\_Chilte\_DM}\) and \(Z_{\text{MDS\_DM}}\) are the load and source impedances, respectively, in the DM test setup, and \(Z_{LISN\_Chilte\_CM}\) and \(Z_{\text{MDS\_CM}}\) are the same impedances in the CM setup.  
Figure 11: Setups for computing the in-circuit IL. Left and right panels show the (**a**,**b**) DM and (**c**,**d**) CM setups without and with the filter, respectively.  
The voltages \(V_{1}\) and \(V_{2}\) in (22), and \(V_{1}\) in (23) involved in these expressions can be evaluated by combining the filter ABCD-parameter representation, relating voltages and currents at the filter ports, i.e.,  
\[\begin{bmatrix}V_{1}\\ V_{2}\\ V_{3}\\ I_{1}\\ I_{2}\\ I_{3}\end{bmatrix}=\begin{bmatrix}\mathbf{A}_{3\times 3}&\mathbf{B}_{3\times 3}\\ \mathbf{C}_{3\times 3}&\mathbf{D}_{3\times 3}\\ \end{bmatrix}\begin{bmatrix}V_{4}\\ V_{5}\\ V_{6}\\ I_{4}\\ I_{5}\\ I_{6}\end{bmatrix} \tag{24}\]  
with the terminal constraints imposed by the DM and CM tests setups, respectively:  
\[\mathbf{DM}:\left\{\begin{array}{c}I_{3}=0\\ I_{6}=0\\ I_{1}+I_{2}=0\\ I_{4}+I_{5}=0\\ \frac{V_{2}-V_{1}}{Z_{LISN,Cable,CM}}=I_{1}\\ \frac{V_{4}-(V_{5}+V_{5})}{Z_{MDS,DM}}=I_{4}\end{array}\right.\quad\mathbf{CM}: \left\{\begin{array}{c}V_{3}=V_{2}=V_{1}\\ V_{6}=V_{5}=V_{4}\\ \frac{-V_{1}}{Z_{LISN,Cable,CM}}=I_{1}+I_{2}+I_{3}\\ \frac{V_{4}-V_{5}}{V_{4}-V_{5}}=I_{4}+I_{5}+I_{6}\end{array}\right. \tag{25}\]  
It should be noted that for simplicity of notation in (22)-(23), the same symbol was used to denote the voltage \(V_{1}\) measured in the DM setup [(22), (25) set of equations on the left], and in the CM setup [(23), (25) set of equations on the right].