## 3 Setups to Extract Equivalent Modal Circuits
### Measurement Setups to Extract the Equivalent Modal Circuits  
The equivalent DM and CM circuits need to be extracted separately. For each mode, the measurements should be carried out twice to determine the equivalent modal circuits of both the motor drive system and external circuits (i.e., LISN with cables). It is worth mentioning that the noise generated by the motor drive system is assumed to be negligible with respect to the signal injected by the VNA. Thus, the accuracy of the measured impedance is supposed not significantly degraded when the motor drive system is turned on. It is also assumed that the system is symmetric. Therefore, the corresponding DM circuit can be represented by two impedances only (see Figure 7b), where \(Z_{MDS\_DM}\) and \(Z_{LISN\_Cable\_DM}\) stand for the DM impedances of the motor drive system and external circuit, respectively. Two setup configurations are employed to determine these two impedances. In the first configuration, the probe is clamped on any phase of the motor drive system with \(N_{turns}=2\) (see the example for phase W in Figure 7a). Meanwhile, the ground cable between the motor drive system and the LISN is disconnected. No matter which phase is measured, the equivalent circuit of this setup can be represented as in Figure 7b. The measured reflection coefficient (\(S_{dm\_tot}\)) can be used to calculate the impedance (\(Z_{dm\_tot}\)) seen at \(b\)-\(b^{\prime}\) by (14). In the second configuration in Figure 7c,d, the motor drive system is \begin{table}
\begin{tabular}{c c} \hline \hline
**Component** & **Specifications** \\ \hline \multirow{2}{*}{Variable frequency drive} & Input: 3-phase, 380–480 V, 50 Hz \\  & Output: 0–460 V, 5 kVA, 2.2 kW, 0–599 Hz \\ \multirow{2}{*}{Induction motor} & Nominal power: 0.75 kW, 21A, 50 Hz, 1430 rpm \\  & LISN & Schwarz2 beck, NSLK182S, CISPR16-12, 9 kHz—30 MHz \\ \multirow{2}{*}{VNA} & Keysight, E5061B, 5 Hz—1.5 GHz \\  & FCC, F-120-2, 10 kHz—230 MHz \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Specifications of motor drive system and instruments. Figure 7: Setups to determine the DM equivalent circuit: (**a**,**b**) in the presence and (**c**,**d**) in the absence of the motor drive system. taken out, and the cable terminals of phases U, V, and W on the motor drive system side are connected to assess the external circuit (\(Z_{dm\_LC}\)), which is derived from the measured \(S_{dm\_LC}\) by (15). Eventually, the two impedances of the DM equivalent circuit (\(Z_{LISN\_Cable\_DM}\) and \(Z_{MDS\_DM}\)) can be computed from (16) and (17) by circuit theory. Due to the symmetry assumption, the minor differences between measurements on each phase are assumed to be non-intentional deviations. Consequently, the results in the next section are based on the average values calculated from three measurements on each phase. \[Z_{dm\_tot}=\frac{k_{1}S_{dm\_tot}+k_{2}}{S_{dm\_tot}+k_{3}} \tag{14}\]  
\[Z_{dm\_LC}=\frac{k_{1}S_{dm\_LC}+k_{2}}{S_{dm\_LC}+k_{3}} \tag{15}\]  
\[Z_{LISN\_Cable\_DM}=\frac{2}{3}Z_{dm\_LC} \tag{16}\]  
\[Z_{MDS\_DM}=\frac{2}{3}Z_{dm\_tot}-Z_{LISN\_Cable\_DM} \tag{17}\]  
The extraction technique of the CM equivalent circuit is similar to the DM procedure (see Figure 8). Additionally, also in this case, the method requires two setups: one in the presence and one in the absence of the motor drive system. Unlike for DM, here the ground cable between the motor drive system and LISN, where the probe is clamped, is part of the CM configuration. Moreover, instead of three measurements on each phase, in the CM setups a single measurement on the ground wire is performed. Indeed, clamping the three-phase wires would produce, in principle, the same results as clamping the ground wire. However, the need to wind the three-phase wires in the probe two times produces non-negligible difficulties in setup repeatability. The measured impedances (\(Z_{cm\_tot}\) and \(Z_{cm\_LC}\)), and the equivalent impedances (\(Z_{LISN\_Cable\_CM}\) and \(Z_{MDS\_CM}\)) are derived according to (18)-(21).