## 2 Results
### Small-Signal Investigation for LNA Design
#### 2.1.3 Comparison with Other Configurations  
To further demonstrate advantages of using such a proposed 3-stack GaN HEMT configuration, its isolation, stability, power gain, and noise figure are compared with that of the other GaN HEMT configurations including a single-stage, conventional cascode, independently biased cascode, and independently biased 3-stack. The bias conditions for all configurations are indicated in Table 1. It is worth noting that the configurations to be compared are biased at a class-A operation for the purpose of the SS investigation. In addition, for a fair comparison, the total drain bias voltage of 44 V and gate bias voltages of \(-2\) V are kept similar for all configurations. As can be seen in the table, conventional configurations cannot adjust the bias condition independently for each transistor. Figure 6 shows the isolation comparison among five configurations. As analyzed before, SS critical parameters for designing LNA of the proposed configuration are mainly affected by the gate bias voltage of the first transistor. Figure 5: Reverse isolation and stability characteristic of the proposed configuration. By optimizing this bias voltage, the proposed 3-stack topology can achieve very low \(S_{12}\) compared with the other configurations. The isolation of the proposed configuration can reach below \(-40\) dB in the entire frequency range from 1 GHz to 50 GHz. This very high isolation is excellent for the LNA design. Besides isolation comparison, Figures 7-9 show the comparison in stability, power gain and NF of the five configurations, respectively. Figure 7 indicates that the proposed configuration is more stable than the single-stage and independently biased cascode configurations in the entire frequency range. However, the conventional 3-stack and conventional cascode configurations are more stable than the proposed configuration below 25 GHz. The conventional configurations including conventional cascode and 3-stack are most stable compared with other ones. This is because they do not have additional feedback loops caused by the insertion of additional bias terminals as in the independently biased configurations. For the power gain comparison as shown in Figure 8, the proposed circuit exhibits superior MAG compared with other configurations below 2.5 GHz. Nevertheless, at higher frequencies due to the parasitic elements, which occurs by adding the bias terminals, its MAG drops sharply. In general, the power gain of the proposed configuration can be better than the four configurations including conventional 3-stack, conventional cascode, and independently biased cascode. The single-stage has the highest MAG due to the lack of additional parasitic behaviour, while the conventional configurations have lowest MAG since they cannot adjust the operation conditions for each transistor. Finally, Figure 9 compares the NF among GaN HEMT configurations. Once again, it can be seen that conventional configurations, including cascode and 3-stack, have the poorest NF, while the other 3 configurations, including the proposed 3-stack, single-stage, and independently biased cascode, offer similar NF levels. However, at higher frequencies, the NF of the proposed configuration becomes worse due to its inherent parasitic behaviour, as mentioned. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Configurations** & \(V_{\mathbf{g1}}\) & \(V_{\mathbf{g2}}\) & \(V_{\mathbf{g3}}\) & \(V_{\mathbf{d1}}\) & \(V_{\mathbf{d2}}\) & \(V_{\mathbf{d3}}\) \\ \hline Single-stage & \(-2\) V & X & X & 44 V & X & X \\ Conventional cascode & \(-2\) V & \(-2\) V & X & X & 44 V & X \\ Independently biased cascode & \(-2\) V & \(-2\) V & \(-2\) V & 5 V & 44 V & X \\ Conventional 3-stack & \(-2\) V & \(-2\) V & \(-2\) V & X & X & 44 V \\ Independently biased 3-stack & \(-2\) V & \(-2\) V & \(-2\) V & 1 V & 3.5 V & 44 V \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Bias conditions of the configurations for small-signal (SS) investigations. Figure 6: Reverse isolation comparison among configurations.