## 3 Measurement Setup and Results
### Measurement Results  
The proposed small-signal modeling was performed on an ISV-type 4 \(\times\) 50 \(\upmu\)m GaN HEMT fabricated using a commercial 0.15 \(\upmu\)m GaN HEMT process. First, the pad equivalent model parameters are extracted through the S-parameter measurement of the pad test pattern. The extracted values of C\({}_{\text{pg}}\) and C\({}_{\text{pd}}\) are both 18 fF, and those of L\({}_{\text{pg}}\) and L\({}_{\text{pd}}\) are both 30 pH. Next, S-parameters are measured from 0.2 to 67 GHz in the cold and hot bias regions. The pinch-off voltage of the device is about \(-\)2.8 V, and the measurement bias region is a drain-source voltage of 0 to 28 V and a gate-source voltage (V\({}_{\text{gs}}\)) of \(-\)2.8 to \(-\)0.8 V. Table 1 shows the initial extrinsic and intrinsic parameters extracted using the conventional small-signal model parameter extraction method. Next, to replace the C\({}_{\text{ds}}\) obtained above with the \"modified C\({}_{\text{ds}}\)\" shown in Figure 5b, EM simulation is used as shown in Figure 7. Based on the EM simulation result, the values of C\({}_{\text{ds}1}\), L\({}_{\text{ds}}\), and C\({}_{\text{ds}2}\) extracted by iterative fitting are 40 fF, 40 pH, and 50 fF, respectively. Figure 10 shows the comparison of the S-parameter of the extracted \"modified C\({}_{\text{ds}}\)\" circuit with the EM simulated one. The \"modified C\({}_{\text{ds}}\)\" circuit agrees better with the EM result than the conventional C\({}_{\text{ds}}\). \begin{table}
\begin{tabular}{c c c} \hline
**Extrinsic/Intrinsic** & **Model Parameters** & **Extracted Value** \\ \hline \multirow{6}{*}{Extrinsic part} & R\({}_{\text{g}}\) & 0.67 \(\Omega\) \\  & R\({}_{\text{s}}\) & 1.85 \(\Omega\) \\  & R\({}_{\text{d}}\) & 0.1 \(\Omega\) \\  & L\({}_{\text{g}}\) & 124.6 pH \\  & L\({}_{\text{s}}\) & 6.42 pH \\  & L\({}_{\text{d}}\) & 88.6 pH \\ \hline \multirow{6}{*}{Intrinsic part (V\({}_{\text{ds}}\) = 28 V, V\({}_{\text{gs}}\) = \(-\)1.6 V)} & C\({}_{\text{gs}}\) & 479 fF \\  & R\({}_{\text{i}}\) & 0.33 \(\Omega\) \\ \cline{1-1}  & C\({}_{\text{pd}}\) & 18.8 fF \\ \cline{1-1}  & R\({}_{\text{pd}}\) & 354.5 \(\Omega\) \\ \cline{1-1}  & G\({}_{\text{m}}\) & 90.9 mS \\ \cline{1-1}  & r & 1.63 pS \\ \cline{1-1}  & R\({}_{\text{ds}}\) & 900.9 \(\Omega\) \\ \cline{1-1}  & C\({}_{\text{ds}}\) & 138 fF \\ \hline \end{tabular}
\end{table} 
Table 1: Initially extracted extrinsic and intrinsic parameters of an ISV-type 4 \(\times\) 50 \(\upmu\)m GaN HEMT. Figure 9: Block diagram of a 67 GHz S-parameter measurement setup. Finally, the intrinsic part of C\({}_{\text{ds}}\), which is about 25 fF, can be added through the final comparison with the measured S-parameter, and the complete small-signal model is optimized through fine-tuning of each model parameter. To verify the validity of the small-signal model completed through the above procedure, the S-parameters of small-signal models and the measured S-parameters are compared from 0.2 to 67 GHz with respect to several biases around the load line, which is important for power amplifier design. In addition, the stability factor (K) and MSG/MAG that can be calculated from the S-parameter results are also compared. The formulas can be expressed as follows [30]:  
\[\text{K}=\frac{\left(1-\left|S11\right|^{2}-\left|S22\right|^{2}+\left|S11 \cdot S22-S12\cdot S21\right|^{2}\right)}{\left(2\cdot\left|S12\cdot S21\right| \right)} \tag{8}\]  
\[\text{MAG}=\ \frac{\left|S_{21}\right|}{\left|S_{12}\right|}\left(K-\sqrt{K^{2}-1 }\right)\ (K>1) \tag{9a}\]  
\[\text{MSG}=\frac{\left|S_{21}\right|}{\left|S_{12}\right|}\ (\text{K}<1) \tag{9b}\]  
Figures 11-13 show the comparison of S-parameters, MSG/MAG, and K under some biases according to the load line. Figure 11: _Cont._  
Figure 10: Comparison of the S-parameter of the extracted “modified C\({}_{\text{ds}}\)” circuit with the EM simulated one through (**a**) Smith chart and (**b**) phase.