# Analysis of Permanent Magnet Motors in High Frequency--A Review
## 3 Analysis Tools
### Measurement-Based Methods  
The last approach to model an electric motor for HF analysis is measuring both DM and CM impedance and getting the circuit parameters from those measures. It is a very used approach, but it is not practical during the design process, as a prototype is needed. When obtaining impedance vs. frequency curves, two different connection layouts are usually used [12; 13; 15; 16; 17; 20; 21; 22; 23; 24; 26; 27; 28; 29; 31; 33; 35; 36]. In Figure 5(a)aimpedance measuring layout is shown, while in Figure 5(b) DM impedance is measured. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Case** & **Winding** & **Winding** & **Stator** & **Turn** \\
**Stator** & **Rotor** & **Rotor** & **Turn** \\ \hline \hline \([41]\) & & Plate capacitors (\(\approx\)80\%) & Plate capacitors (\(\approx\)30\%) & Cylindrical caps (\(\approx\)20\%) & \\ \([43]\) & & & Image charges (4–10\%) & \\ \([79]\) & & Cylindrical capacitors (\(\approx\)30\%) & & \\ \([58]\) & & & & \\ \([42]\) & \(2C_{tl}\)(\(\approx\)50\%) & & & \\ \([45]\) & & & & For single layer (\(\approx\)15\%) \\ \([46]\) & & & & Plate capacitors(\(\approx\)16\%) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Analytic Capacitance comparison. Additionally, in [21, 22, 26, 28], it is stated that even if IPMSM have been widely treated as IM for the simulation of EMI, the characteristic impedance is different as DM impedance varies with the rotor position due to the variation of reluctance, as shown in Figure 7.  
Thus, [22] introduces a new measurement consisting of measuring the impedance of two phases in series. Then, the equivalent inductances are calculated for different rotor positions. Moreover, in [12, 17] some additional measures are needed to complete the model parameters. Alternatively, [30] analyzes the ground current of an induction machine and measures the CM impedance as shown in Figure 6a and the impedance between the three-phase terminals and the motor neutral with a floating ground terminal. The procedure for calculating the LPM parameters is dependent of the proposed model. Most models have fixed LRC sections [12, 13, 15, 17, 19, 20, 24, 29, 30, 31, 32, 33, 35, 36], whereas some of them have as many LRC sections as the number of resonance points of the impedance curve [26, 27, 28]. Most authors give a physical meaning to the RLC values, others relate the RLC value to a point or region in the impedance curve [17, 22, 24, 28] or even use data fitting methods where the resistance value can be even negative [15, 16, 93]. In [23], some initial parameters of the model are calculated analytically from the impedance curve, and a minimization algorithm is proposed for the rest of the parameters, restricting the values to real positive ones. After this main classification of the methods is done, some relevant details about the methods are commented. In Figure 8 the DM impedance measurement and an equivalent circuit are shown. Usually the resonances around the EMI analysis range (150 kHz-30 MHz) are only considered and to avoid numerical difficulties, each selected pair of peaking and dipping frequencies should be sufficiently apart from each other. To simplify the characterization, it is assumed that the inductance in each stage of the circuit of Figure 8a is much smaller than  
Figure 6: Impedance measurement connection layout. (**a**) CM; (**b**) DM. Figure 7: Differential-mode Impedance [28]. the next stage to its right. The authors in [27] note that this is just an assumption imposed on the behavioral model and does not have implications in the machine behavior. DM parameters are determined from the peaks and dips identified in Figure 8b, not with any physical meaning. After following the same procedure with the CM impedance, a three-phase equivalent circuit is composed, integrating the motor in the electric drive model and validating it up to 10 MHz. Furthermore, in [22; 26; 28], the model is divided in two sub-circuits.