# An MMIC LNA for Millimeter-Wave Radar and 5G Applications with GaN-on-SiC Technology
## 2 Analysis and Design of MMIC LNA
### Stability Analysis and Enhancement  
As depicted in Figure 7, a comprehensive and robust LNA stability handling topology is implemented for each stage of the amplifier. This topology incorporates various techniques to ensure optimal stability and performance throughout the LNA's operation. One notable aspect of this design is the use of a microstrip line for source degeneration instead of an inductor, which introduces an additional stabilization mechanism. By employing a microstrip line for source degeneration, several advantages are gained. The use of a microstrip line for source degeneration offers greater flexibility and ease of integration compared to traditional inductors. These modifications contribute to cost savings and enable easier integration into compact and space-constrained electronic systems. This not only contributes to cost savings but also enables easier integration into compact and space-constrained electronic systems. The effectiveness of this stability handling topology is further validated through extensive simulations and measurements. As shown in Figure 8, the stable conditions for the LNA are met, ensuring reliable and predictable performance across the desired frequency range. However, it is important to note that while this topology enhances stability, additional measures are necessary to achieve unconditional stability (k > 1) throughout the entire operating frequency band. To achieve unconditional stability, designers employ various techniques such as adding feedback networks, optimizing biasing schemes, employing compensation techniques, and utilizing active or passive devices with appropriate impedance terminations. These measures work in concert to maintain stability across the LNA's entire frequency range, preventing instability and ensuring reliable operation under different input signal conditions. By adopting the aforementioned stability handling topology and implementing additional stabilization measures, the LNA can meet stringent stability requirements while delivering high-performance characteristics across a wide frequency band. This comprehensive approach to stability design helps minimize the risk of instability, ensure reliable operation, and maximize the overall performance of the LNA in practical applications.  
Figure 7: Stability handle topology.  
The \(\pi\)-type two-port network of the GaN HEMT [1; 12] can be simplistically presented as Y-parameter matrix:  
\[\left[Y\right]_{HEMT}=\begin{bmatrix}Y_{A}+Y_{B}&-Y_{B}\\ -Y_{B}&Y_{B}+Y_{C}\end{bmatrix}, \tag{6}\]  
After connected in parallel with voltage-controlled current source, the intrinsic Y-parameter model can be written as follows:  
\[\left[Y\right]_{HEMT}=\begin{bmatrix}\frac{jwC_{gg}}{jwC_{gg}R_{i}+1}&-jwC_{ gd}\\ -jwC_{gd}+\frac{g_{m}}{jwC_{gg}R_{i}+1}&\frac{1}{R_{ds}}+jw(C_{ds}+C_{gd}) \end{bmatrix} \tag{7}\]  
The intrinsic \(S_{12}\) can be written as follows:  
\[S_{12}=\frac{-2Y_{12}Z_{0}}{\Delta}=\frac{2 iwC_{gd}Z_{0}}{(1+Z_{0}Y_{11})(1+Z_ {0}Y_{22})-Y_{12}Y_{21}Z_{0}^{2}}, \tag{8}\]  
where \(Z_{0}\) represents the characteristic impedance of the GaN HEMT. Based on Equation (8), the inverse gain S\({}_{12}\) is mainly caused by C\({}_{\text{gd}}\), which introduces a potential instability factor while concurrently restricting high-frequency performance.  
As depicted in Figure 7, an RC series network is connected in parallel to the drain of the GaN HEMT, complemented by a series \(\lambda/4\) microstrip line, to mitigate the Miller effect caused by C\({}_{\text{gd}}\). This topology is combined with another capacitance to form the RF choke. The RF chokes determine the stability of each stage by blocking the RF signal to the bias network and decoupling the power supply. And then, the use of RF chokes effectively prevents the \(\alpha\) signal path (as shown in Figure 7), further improving the stability of the circuit.