## 3 Proposed GaN HEMT MMIC LNA Design
### Reverse Isolation and Stability Performance of GaN HEMT Devices  
In reality, the reverse isolation and stability performance of GaN HEMT devices is a serious concern in the mmWave frequency band, which generally requires a design trade-off with the MAG and NF performance for the operation of the amplifier. The reverse isolation and stability characteristics can be mainly evaluated from the scattering parameter (\(S12\)) and \(\mu\) criterion for the designed two-port network, respectively. The \(S12\) primarily indicates \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Property** & **Si** & **GaAs** & **InP** & **SiC** & **GaN** \\ \hline Energy bandgap, \(\mathrm{E_{g}}\) (eV) & 1.12 & 1.42 & 1.34 & 3.2 & 3.44 \\ \hline Breakdown field, \(\mathrm{E_{b}}\) (10\({}^{6}\) V/cm) & 0.3 & 0.4 & 0.6 & 3.2 & 2 \\ \hline Saturation velocity (10\({}^{5}\) m/sec) & 1 & 1.2 & 1.0 & 2.0 & 2.5 \\ \hline Dielectric constant, \(\mathrm{\epsilon}\) & 11.7 & 12.9 & 12.4 & 10 & 9.5 \\ \hline Electron mobility, \(\mathrm{\mu}\) (cm\({}^{2}\)/V\(\cdot\)S) & 1450 & 8500 & 4600 & 700 & 1600 \\ \hline Thermal conductivity (W/cm\({}^{\circ}\)K) & 1.31 & 0.46 & 0.77 & 4.9 & 1.5 \\ \hline B-FOM ratio 1 & 1 & 13.17 & 5.76 & 9.62 & 25.96 \\ \hline \hline \end{tabular} \({}^{\dagger}\) B-FOM: [PERSON]’s figure-of-merit, defined as \(\mathrm{\epsilon}\)-\(\mathrm{\mu}\)-\(\mathrm{E_{g}}\)3.  
\end{table} 
Table 1: Comparison of the material properties of various microwave semiconductors. the amount of feedback from the output to the input ports. For a single-stage common-source (CS) configuration, a gate-drain capacitance of GaN devices mostly determines the overall reverse isolation performance of the network. The \(\mu\) criterion is a parameter of stability and is widely used in two-port networks [6; 25; 26]. The \(\mu\) criterion, which is defined by the scattering parameters, is expressed as:  
\[\mu=\frac{1-|S11|^{2}}{|S22-\Delta S11^{*}|+|S12\cdot S21|} \tag{1}\]  
where \(\Delta\) denotes the determinant of the scattering matrix, defined as \(\Delta=S11\times S22-S12\times S21\). If the \(\mu\) value is greater than unity at the operating frequency, it ensures that the network is unconditionally stable. As can be deduced from Equation (1), the \(\mu\) value is highly related to the reverse isolation of the network; therefore, a smaller \(S12\) is always desirable to securely realize stable operation of the amplifier. Figure 2 shows the stability enhancement configurations that have been generally applied to MMIC designs. First, a cascode configuration, as shown in Figure 2a, is composed of stacked CS and common-gate (CG) stages and basically offers high reverse isolation from the output to input ports owing to its own shielding effect. Interestingly, as the number of stacked stages increases, the amount of reverse isolation and the corresponding stability are improved accordingly [20]. However, relatively complex independent biasing for each CS and CG device is required to adjust the optimal bias conditions using several supply voltage sources. The source degeneration of the single-stage amplifier in Figure 2b also improves the overall stability by applying a negative feedback through the \(L_{S}\) while sacrificing the MAG and noise performance. This approach is also beneficial for achieving linearity enhancement and the possibility of simultaneous power and noise matching in the design. In Figure 2c, the utilized series resistor at the input or output port of the single stage directly increases reverse isolation by providing a higher series impedance. However, this configuration substantially exacerbates the overall gain and noise performance of the amplifier because noisy impedance is added in the signal path. In the proposed design, a series inductor (\(L_{SE}\)) instead of the series resistor is adopted at the output to enhance the stability of the amplifier (Figure 3).