## 5 Results
### Fitting to the Key Parameters  
For the sake of a trade-off between the precision and simplicity, the polynomial fitting is adopted to fit the static characteristic curve of the SiC MOSFET C2M0025120D. An appropriate polynomial order is chosen to ensure the \(R\)-_squared_ (coefficient of determination, a goodness of fit) higher than 0.995. The trans-conductance gf and on-state resistance \(R_{on}\) can be regarded as a two-variable function \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & **Parameter** & \(L_{bus1}\) & \(L_{bus2}\) & \(L_{c2}\) & \(L_{a2}\) & \(L_{g2}\) & \(L_{d2}\) & \(L_{s2}\) & \(R_{stray}\) \\ \cline{2-10} Q3D & Value & \multirow{2}{*}{51.24} & \multirow{2}{*}{72.85} & \multirow{2}{*}{4.25} & \multirow{2}{*}{4.12} & \multirow{2}{*}{6.39} & \multirow{2}{*}{12.08} & \multirow{2}{*}{1.71} & \multirow{2}{*}{1.85} \\  & (nH) & & & & & & & \\ \hline \multirow{8}{*}{VNA} & Package & \multicolumn{6}{c}{TO-247-3} & \multicolumn{6}{c}{TO-220-2} \\ \cline{2-10}  & **Parameter** & \(L_{g1}\) **(nH)** & \(L_{d1}\) **(nH)** & \(L_{s1}\) **(nH)** & \(L_{a1}\) **(+ \(L_{c1}\) **(nH)** \\ \cline{1-1} \cline{2-10} VNA & Maximum & 9.57 (@ 50 \({}^{\circ}\)C) & 4.71 (@ 25 \({}^{\circ}\)C) & 8.39 (@ 50 \({}^{\circ}\)C) & 10.12 (@ 25 \({}^{\circ}\)C) \\  & Minimum & 9.13 (@ 75 \({}^{\circ}\)C) & 4.54 (@ 125 \({}^{\circ}\)C) & 8.06 (@ 150 \({}^{\circ}\)C) & 9.79 (@ 100 \({}^{\circ}\)C) \\  & Difference & 4.77\% & 3.79\% & 4.21\% & 3.34\% \\  & Average & 9.218 & 4.623 & 8.176 & 9.889 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Extraction results of the stray and parasitic inductances. Figure 8: Measured scatters and fitted curve of the key parameters. (**a**) Trans-conductance \(g_{f}\), (**b**) on-state resistance \(R_{on}\), (**c**) threshold voltage \(v_{th}\) and forward voltage \(v_{f}\), (**d**) junction capacitance of silicon carbide (SiC) Schottky diode (SBD) \(C_{f}\), (**e**) output capacitance \(C_{\text{oss}}\) and reverse transfer capacitance \(C_{\text{rss}}\), (**f**) internal resistance \(R_{\text{g-int}}\) and \(R_{f}\). of \(V_{gs}\) and \(T_{j}\) and function of id and \(T_{j}\), respectively. The fitting equations are given in (38) and (39), the fitted curves are shown in the Figure 8a,b. \[ \begin{array}{c}g_{f}(v_{gs},T_{j})=p_{00}+p_{10}v_{gs}+p_{01}T_{j}+p_{20}v_{gs }^{2}+p_{11}v_{gs}T_{j}+p_{02}T_{j}^{2}+p_{30}v_{gs}^{3}+p_{21}v_{gs}^{2}T_{j}+ p_{12}i_{d}T_{j}^{2}+p_{03}T_{d}^{3}\\ +p_{40}v_{gs}^{4}\ +p_{31}v_{gs}^{3}T_{j}+p_{22}v_{gs}^{2}T_{j}^{2}+p_{13}v_{gs}T_{j}^{3}+ p_{04}T_{j}^{4}\end{array}  \tag{38}\]  
where \(p_{00}=-1.313\), \(p_{10}=2.74\), \(p_{01}=2.292\times 10^{-4}\), \(p_{20}=-1.287\), \(p_{11}=-3.362\times 10^{-2}\), \(p_{02}=-9.872\times 10^{-5}\), \(p_{30}=-0.2086\), \(p_{21}=9.167\times 10^{-3}\), \(p_{12}=9.789\times 10^{-5}\), \(p_{03}=6.437\times 10^{-8}\), \(p_{40}=-8.4\times 10^{-3}\), \(p_{31}=-5.352\times 10^{-4}\), \(p_{22}=-1.034\times 10^{-5}\), \(p_{13}=-8.058\times 10^{-8}\), \(p_{04}=2.109\times 10^{-10}\). \[ \begin{array}{c}R_{on}(i_{d},T_{j})=p_{00}+p_{10}i_{d}+p_{01}T_{j}+p_{20}i_{d }^{2}+p_{11}i_{d}T_{j}+p_{02}T_{j}^{2}+p_{30}i_{d}^{3}+p_{21}i_{d}^{2}T_{j}+p_{ 12}i_{d}T_{j}^{2}+p_{03}T_{d}^{3}\\ +p_{40}i_{d}^{4}+p_{31}i_{d}^{3}T_{j}+p_{22}i_{d}^{2}T_{j}^{2}+p_{13}i_{d}T_{j} ^{3}+p_{04}T_{j}^{4}\end{array}  \tag{39}\]  
where \(p_{00}=30.71\), \(p_{10}=0.03\), \(p_{01}=-0.1388\), \(p_{20}=3.705\times 10^{-4}\), \(p_{11}=-2.019\times 10^{-4}\), \(p_{02}=4.309\times 10^{-3}\), \(p_{30}=-1.091\times 10^{-8}\), \(p_{21}=-1.725\times 10^{-6}\), \(p_{12}=2.894\times 10^{-6}\), \(p_{03}=-2.642\times 10^{-5}\), \(p_{40}=6.933\times 10^{-9}\), \(p_{31}=-2.448\times 10^{-9}\), \(p_{22}=2.817\times 10^{-9}\), \(p_{13}=-6.658\times 10^{-9}\), \(p_{04}=6.943\times 10^{-8}\). The threshold voltage \(V_{th}\), the forward voltage \(V_{f}\), the gate internal resistance \(R_{g\_int}\) and the freewheeling resistance \(R_{f}\) can be regarded as a single-variable function of the junction temperature \(T_{j}\).