## 5 Results
### Loss Assessment  
Based on the discussion above, the flowchart in Figure 9 presents the calculation routine for applying the model. Compared with traditional method, the iterative method is adopted to solve the state equations, from which the numerical solution can be derived without simplification [37]. Therefore, the calculation accuracy is improved. As mentioned in the previous section, there are two switching loss calculation methods in this model. In turn-on transients, the calculation I will be less than calculation II, since the discharging current of \(C_{ds}\) and \(C_{gd}\), which opposes the trend of the drain current is included in \(i_{d}\). However, the turn-off loss of calculation I will be greater than calculation I due to the charging current of \(C_{ds}\) and \(C_{gd}\). As a result, the two types of calculation would not vary the \(E_{total}\) but would instead vary the distribution of power losses between \(E_{sw\_on}\) and \(E_{sw\_off}\). The experimental prototype of a 400-V, 15-A double-pulse-test setup is shown in Figure 10, in which the chip inductors are added to simulate the varied stray inductances. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **0**\(V\)\(<\)\(v\)\(\leq\)**10**\(V\)** & **10**\(V\)\(<\)\(v\)\(\leq\)**400**\(V\)** \\ \hline \(C_{f}\) (pF) & \(\frac{1500}{(1+\frac{1500}{124})^{0.5007}}\) & \(\frac{1500}{(1+\frac{500}{128})^{0.5007}}\) \\ \(C_{\text{iss}}\) (pF) & 4000 & 3300 \\ \(C_{\text{oss}}\) (pF) & \(\frac{3850}{(1+\frac{50}{250})^{0.3895}}\) & \(\frac{3850}{(1+\frac{50}{1250})^{0.4651}}\) \\ \(C_{\text{rss}}\) (pF) & \(\frac{1430}{(1+\frac{50}{120})^{0.774}}\) & \(\frac{1430}{(1+\frac{50}{0.008})^{0.664}}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Specification of nonlinear junction capacitances. Figure 9: Flowchart for loss assessment. As stated in [38], the measurement system bandwidth should be higher than ten times the highest equivalent frequency of the measured signal, which can be approximated by  
\[f=\frac{0.25}{\min(t_{r},t_{f})} \tag{46}\]  
where \(t_{r}\) is the rise time, \(t_{f}\) is the fall time. The typical rise/fall time of C2M0025120D is 32/28 ns. According to (46), the equivalent frequency is 8.9 MHz. The measurement system specified in Table 4 can meet the bandwidth requirement. It must be pointed out that for the sake of emulating the switching waveforms taken in the experiment, the induced voltage drops across the parasitic inductances of the package terminal; \(L_{s1}\) and \(L_{d1}\) have to be included in the analytical waveforms for \(v_{ds}\), as they are intrinsic and inside the package. As shown in Figure 11, the switching waveforms of the proposed analytical model match the experiment well. Voltage and current overshoot are also important factors in the application of the power device, which should be considered together with the power losses. The quantitative comparison of loss and voltage and current overshoot is listed in Table 5. The maximum error is 7.13%, which proves the good accuracy of the model. The variation patterns of power losses with each parameter element can be worked out by the calculation, as shown in Figure 8, to present a further investigation into the loss mechanism and they will be demonstrated experimentally. The \(\pm 10\%\) error bars of the experimental results are added to illustrate the accuracy. It can be seen that the calculation results are in good accordance with the experiment. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Part No.** & **Description** & **Bandwidth** & **Measured Signal** \\ \hline RTH1004 & Oscilloscope & 500 MHz & \\ RT-ZI10 & Passive probe & 500 MHz & \(v_{ds}\) \\ TPP0201 & Passive probe & 200 MHz & \(v_{gs}\) \\ TCP0030A & Current probe & 120 MHz & \(i_{d}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Specification of the measurement system. Figure 10: Double-pulse-test setup with varied elements. (**a**) Top view. (**b**) Bottom view. Gate Driver Resistance  
Figure 13 presents the power losses with varied \(R_{g}\).