# An MMIC LNA for Millimeter-Wave Radar and 5G Applications with GaN-on-SiC Technology
## 2 Analysis and Design of MMIC LNA
### Co-Design Strategy for Broadband Matching and Low NF  
As demonstrated in Section 2.2, the C\({}_{\text{gd}}\) of the GaN HEMT cannot be overlooked in the mmWave band. This results in a rapid decrease in small signal gain, poor flatness, and inferior stability. In the design of mmWave LNA, matching networks have a significant impact on small signal gain, input-output return loss, and NF performance. Therefore, adopting appropriate topologies is crucial [34]. The simplified schematic of the proposed LNA is shown in Figure 1, which is based on a three-stage CS design. In Figure 1, four hybrid-MNs are employed to fulfill the requirement of appropriate matching for broadband and low NF [1; 4; 26]. In order to minimize the introduction of  
Figure 8: Source degeneration for stability factors of each stage. noise, the design strategy for the input matching network (IMN) proposes the use of few lumped components [35]. As shown in Figure 9a, considering the high-frequency equivalent model and through a virtual resistor \(\mathrm{R_{i1}}\), the IMN can be equivalent to three L-type MNs (L\({}_{0}\)C\({}_{10}\), L\({}_{1}\)C\({}_{01}\), and C\({}_{02}\)L\({}_{\lambda 1}\)) [1], where L\({}_{0}\) and C\({}_{10}\) represent equivalent models of TL\({}_{0}\), L\({}_{1}\) represents an equivalent model of TL\({}_{1}\), L\({}_{\lambda 1}\) is provided by the bias network, and \(C_{0}=\frac{C_{01}C_{02}}{C_{01}+C_{02}}\)[31]. A virtual resistor \(\mathrm{R_{i1}}\) is generated by using the impedance transformation network C\({}_{02}\)L\({}_{\lambda 1}\). The quality factor Q\({}_{3}\) of C\({}_{02}\)L\({}_{\lambda 1}\) can be expressed as follows:  
\[Q_{3}=w_{0}C_{02}R_{i1}=\sqrt{\frac{R_{L1}}{R_{i1}}-1}, \tag{9}\]  
where \(R_{i1}=\frac{R_{L}}{1+Q_{3}^{2}}\). Through the same strategy, the quality factor Q\({}_{1}\) of the whole hybrid-IMN can be indicated as follows:  
\[Q_{I}=w_{0}(C_{01}+C_{02})R_{i1}+\frac{w_{0}L_{0}}{R_{S1}}=\sqrt{\frac{R_{L1}} {R_{i1}}-1}+\sqrt{\frac{R_{i1}}{R_{i2}}-1}+\sqrt{\frac{R_{i2}}{R_{s1}}-1}, \tag{10}\]  
The value of Q\({}_{1}\) needs to be carefully designed by choosing the appropriate impedance. If the value of Q\({}_{1}\) is too large, the small signal gain will decrease; conversely, the bandwidth of IMN will increase [26; 33]. Through the same analysis method, the equivalent model of ISMNs is shown in Figure 9b. Considering the high-frequency equivalent model and introducing a virtual resistor \(\mathrm{R_{i}}\), the IMN can be equivalent to two L-type MNs (L\({}_{2}\)C\({}_{12}\) and C\({}_{1}\)L\({}_{\lambda 2}\)), where L\({}_{2}\) and C\({}_{12}\) represent the equivalent model of TL\({}_{2}\), and L\({}_{\lambda 2}\) is provided by the bias network. The quality factor Q\({}_{\mathrm{IS}}\) of the whole hybrid-ISMN can be indicated as follows:  
\[Q_{IS}=w_{0}C_{1}R_{i}+\frac{w_{0}L_{2}}{R_{S2}}=\sqrt{\frac{R_{L}}{R_{i}}-1}+ \sqrt{\frac{R_{i}}{R_{S2}}-1}, \tag{11}\]  
To mitigate these challenges, careful selection of high-impedance stages at both ends of the MMIC LNA can be employed. By strategically choosing these stages, the value of the quality factor Q\({}_{\mathrm{IS}}\) can be controlled effectively, which in turn helps to suppress the loss of performance caused by high-order harmonics and parasitic capacitance [26]. This approach enables designers to optimize the performance of the LNA by minimizing the negative impact of these unwanted effects. Figure 9: Hybrid matching network. Similar to the IMN, the hybrid OMN is designed to broaden the bandwidth of the MMIC LNA, ensuring that the amplifier operates efficiently across a wider range of frequencies. It is worth noting that the design of the OMN should be optimized in conjunction with other aspects of the MMIC LNA. These combined efforts help achieve a well-balanced and high-performing MMIC LNA that meets the specific requirements of the target application. In summary, addressing issues related to high-order harmonics and parasitic capacitance is crucial in MMIC LNA design.