## 3 Experimental Results and Discussion
Figure 4:2 Measured (blue symbols) and GRU simulated (red lines) behavior of (**a**) \(S_{11}\), (**b**) \(S_{12}\), (**c**) \(S_{21}\), and (**d**) \(S_{22}\) with the frequency range spanning from 200 MHz to 65 GHz for the DUT at \(V_{\text{DS}}\) = 30 V, \(V_{\text{GS}}\) = \(-\)3.1 V, and \(T_{a}\) = 145 \({}^{\circ}\)C.  
Figure 4:3 Measured (blue symbols) and GRU simulated (red lines) behavior of (**a**) \(S_{11}\), (**b**) \(S_{12}\), (**c**) \(S_{21}\), and (**d**) \(S_{22}\) with the frequency range spanning from 200 MHz to 65 GHz for the DUT at \(V_{\text{DS}}\) = 30 V, \(V_{\text{GS}}\) = \(-\)3.1 V, and \(T_{a}\) = 200 \({}^{\circ}\)C.  
Figure 4:4 Measured (blue symbols) and GRU simulated (red lines) behavior of (**a**) \(S_{11}\), (**b**) \(S_{12}\), (**c**) \(S_{21}\), and (**d**) \(S_{22}\) with the frequency range spanning from 200 MHz to 65 GHz for the DUT at \(V_{\text{DS}}\) = 30 V, \(V_{\text{GS}}\) = \(-\)3.1 V, and \(T_{a}\) = 90 \({}^{\circ}\)C.  
The prediction accuracy of the extracted models is quantified by evaluating the percentage errors (\(E_{ij}\)) between measurements and simulations. The values of \(E_{ij}\) are determined using the following formula with a total number of frequency points (\(N_{j}\)) set to 325:  
Figure 4:5  
The total percentage error \(E_{TOT}\) is evaluated by averaging the four achieved values of \(E_{ij}\) between measurements and simulations of \(S_{11}\), \(S_{21}\), \(S_{12}\), and \(S_{22}\):  
Figure 4:6  
Table 3 reports the achieved values of the four \(E_{11}\), \(E_{12}\), \(E_{21}\), \(E_{22}\), and \(E_{TOT}\) for all three models at the four different temperature conditions. It was found that the two behavioral models based on using ANNs and GRUs allow reaching much lower percentage errors with respect to the equivalent-circuit model. In addition, it should be underlined that the ANNs enable achieving percentage errors similar to the ones of the GRUs even for data different from those used in training (i.e., 145 \({}^{\circ}\)C). This clearly proves the good generalization capability of the developed ANN-based modeling approach. Although the equivalent-circuit model has the smallest number of parameters to be optimized, it should be noted that temperature dependence is not included in the model. Therefore, the extracted equivalent-circuit elements are valid for only one temperature at \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{1}{c}{**T\({}_{\textbf{a}}\) (\({}^{\circ}\)C)**} & **Parameter** & **Equivalent Circuit** & **ANNs** & **GRUs** \\ \hline \multirow{8}{*}{35} & \(E_{11}\) & 45.96\% & 1.04\% & 1.32\% \\ \cline{2-5}  & \(E_{21}\) & 26.86\% & 12.93\% & 14.63\% \\ \cline{2-5}  & \(E_{12}\) & 38.51\% & 1.96\% & 3.47\% \\ \cline{2-5}  & \(E_{22}\) & 44.32\% & 0.79\% & 0.98\% \\ \cline{2-5}  & \(E_{TOT}\) & 38.91\% & 4.18\% & 5.10\% \\ \hline \multirow{8}{*}{90} & \(E_{11}\) & 43.31\% & 1.14\% & 1.44\% \\ \cline{2-5}  & \(E_{21}\) & 28.65\% & 12.71\% & 10.73\% \\ \cline{2-5}  & \(E_{12}\) & 41.38\% & 2.04\% & 2.69\% \\ \cline{2-5}  & \(E_{22}\) & 45.29\% & 0.78\% & 0.96\% \\ \cline{2-5}  & \(E_{TOT}\) & 39.65\% & 4.17\% & 3.96\% \\ \hline \multirow{8}{*}{145} & \(E_{11}\) & 38.62\% & 2.12\% & 2.10\% \\ \cline{2-5}  & \(E_{21}\) & 27.30\% & 16.51\% & 19.19\% \\ \cline{2-5}  & \(E_{12}\) & 40.18\% & 2.69\% & 3.36\% \\ \cline{2-5}  & \(E_{22}\) & 41.69\% & 1.44\% & 1.68\% \\ \cline{2-5}  & \(E_{TOT}\) & 36.95\% & 5.69\% & 6.58\% \\ \hline \multirow{8}{*}{200} & \(E_{11}\) & 35.96\% & 1.64\% & 1.69\% \\ \cline{2-5}  & \(E_{21}\) & 24.44\% & 21.27\% & 9.26\% \\ \cline{2-5}  & \(E_{12}\) & 38.10\% & 1.91\% & 2.93\% \\ \cline{2-5}  & \(E_{22}\) & 37.88\% & 1.37\% & 1.34\% \\ \cline{2-5}  & \(E_{TOT}\) & 34.10\% & 6.55\% & 3.81\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Percentage errors between measured and modeled scattering parameters with the frequency range spanning from 200 MHz to 65 GHz for the DUT at \(V_{\text{D5}}\) = 30 V and \(V_{\text{GS}}\) = \(-3.1\) V, with four different values of \(T_{a}\).