## 2 Materials and Methods
### Small-Signal Extraction Procedure Partially Assisted by EM Simulation
\[y_{11}=\frac{\omega^{2}R_{\rm i}C_{\rm gs}{}^{2}}{1+\omega^{2}R_{\rm i}^{2}C _{\rm gs}{}^{2}}+\frac{\omega^{2}R_{\rm gd}C_{\rm gd}{}^{2}}{1+\omega^{2}R_{ \rm gd}^{2}C_{\rm gd}{}^{2}}+j\omega\left(\frac{C_{\rm gs}}{1+\omega^{2}R_{ \rm i}^{2}C_{\rm gs}{}^{2}}+\frac{C_{\rm gd}}{1+\omega^{2}R_{\rm gd}^{2}C_{ \rm gd}{}^{2}}\right) \tag{4}\]  
\[y_{12}=-\frac{\omega^{2}R_{\rm gd}C_{\rm gs}C_{\rm gd}}{1+\omega^{2}R_{\rm gd }^{2}C_{\rm gd}{}^{2}}-j\omega\left(\frac{C_{\rm gd}}{1+\omega^{2}R_{\rm gd}^ {2}C_{\rm gd}{}^{2}}\right) \tag{5}\]  
\[y_{12}=\frac{g_{\rm m}e^{-j\omega\tau}}{1+j\omega R_{\rm i}C_{\rm gs}}-\frac{ \omega^{2}R_{\rm gd}C_{\rm gs}C_{\rm gd}}{1+\omega^{2}R_{\rm gd}^{2}C_{\rm gd }{}^{2}}-j\omega\left(\frac{C_{\rm gd}}{1+\omega^{2}R_{\rm gd}^{2}C_{\rm gd}{ }^{2}}\right) \tag{6}\]  
\[y_{22}=\frac{1}{R_{\rm ds}}+\frac{\omega^{2}R_{\rm gd}C_{\rm gd}{}^{2}}{1+ \omega^{2}R_{\rm gd}^{2}C_{\rm gd}{}^{2}}+j\omega\left(\frac{C_{\rm gd}}{1+ \omega^{2}R_{\rm gd}^{2}C_{\rm gd}{}^{2}}+C_{\rm ds}\right) \tag{7}\]  
where \(R_{\rm i}\), \(R_{\rm gd}\), and \(R_{\rm ds}\) are the input, gate-drain, and output resistance, respectively, and \(C_{\rm gs}\), \(C_{\rm gd}\), and \(G_{\rm m}\) are the gate-source, gate-drain capacitance, and transconductance, respectively. Intrinsic model parameters can be extracted for each bias using the above equations from the Y-parameters obtained by de-embedding the pad model and extrinsic part from the measured S-parameters. The second step is to replace the existing \(C_{\rm ds}\) obtained in the first step with the \"modified \(C_{\rm ds}\)\" shown in Figure 5b. It can be obtained by deriving an analytic equation, but in this work, EM simulation is used in an intuitive way without using complex equations. Since the \"modified \(C_{\rm ds}\)\" reflecting the source via effect is due to the layout structure, parameter extraction is possible with EM simulation and does not depend on the bias. Figure 7 shows the top view of full EM simulation of a GaN HEMT using ADS Momentum software. To obtain more realistic results, the measured GaN HEMT layout is brought directly into the EM simulation setup. In the layout shown in Figure 7, the gate layer is visible, but in ADS momentum, there is a function that does not activate this layer in the EM simulation setup. Therefore, the effect of the gate layer can be easily excluded, and the simulation is performed so that only the drain-source layout effect is shown. Finally, the modified \(C_{\rm ds}\) can be extracted from the EM simulation result between the drain and source terminals. C\({}_{\text{ds1}}\), C\({}_{\text{ds2}}\), and L\({}_{\text{ds}}\) composing the \"modified C\({}_{\text{ds}}\)\" are extracted through fitting or optimization by comparing S22 obtained through EM simulation with the modeled S-parameter of the drain-source part extracted previously. The fitted C\({}_{\text{ds2}}\) does not yet contain an intrinsic part. Therefore, the intrinsic part can be added through the final comparison with the measured S-parameter, and the final small-signal model is completed through fine-tuning of each model parameter. Figure 8 is a block diagram showing the small-signal modeling procedure proposed in this work.