## 5 Conclusions  
A mmWave PA features multiple critical performance metrics that are often mutually constrained, necessitating the OMN's design to achieve a balance among them, which is typically accomplished through effective parameter optimization. The conventional strategies usually optimize several large-signal targets directly, which demands resource-intensive HB simulations to assess the response for each OMN parameter set. Additionally, meticulous selection of the target thresholds is essential; otherwise, stringent requirements, excessive objectives, and complicated OMN topologies can easily lead to optimization stagnation or failure, thus hindering design progress. In contrast, the proposed rapid optimization method incorporates only two objectives: all \(Z_{\text{omn}}(f_{\text{i}})\) must fall inside the OID, and the deviation between \(Z_{\text{omn}}(f_{\text{i}})\) and \(Z_{\text{opt,s}}(f_{\text{i}})\) should be minimized. The required large-signal specifications are first mapped to a set of desired impedances, i.e., the OID. Upon satisfying the basic output criteria, adjustments are deliberately made to the matching conditions with the corresponding \(Z_{\text{opt,s}}(f_{\text{i}})\) at various frequencies, which facilitates the achievement of broadband and uniform output characteristics. To conclude, the proposed dual-objective optimization strategy utilizes rapid S-parameter simulations to obtain the impedance transformation trajectory, thereby predicting the transistor's large-signal behavior. Although this method cannot provide precise performance evaluations or the specific deviation from the target, the considerable savings in the simulation time greatly benefit optimization tasks involving numerous iterations. Equally, acquiring detailed trial-and-error performance data is not necessary for the overall optimization effectiveness. Thanks to its high optimization efficiency and fully automated iterative process, the proposed method allows for a convenient assessment of the matching capabilities across various OMN topologies, significantly boosting both the design efficiency and success rate. For different terminal impedance model circuits, OMN, ISMN, and IMN, respectively, employ the synthesized transformer matching technique, the parametric matching technique, and a bandpass-filter-based matching structure to accomplish broadband impedance transformation with limited component usage. The implemented two-stage PA occupies a compact footprint of 1.23 mm\({}^{2}\) and delivers a small-signal gain averaging 19.7 dB with less than 1 dB fluctuations over the 24-31 GHz band, exhibiting excellent broadband matching characteristics. Moreover, it demonstrates good temperature stability and features a flat P\({}_{\text{4 dB}}\) of at least 32.3 dBm, along with a high \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Ref.** & [9] & [11] & [12] & [13] & [14] & [15] & **This Work** \\ \hline Process & 0.15 \(\mu\)m & 0.15 \(\mu\)m & 0.15 \(\mu\)m & 0.1 \(\mu\)m & 0.1 \(\mu\)m & 0.1 \(\mu\)m \\  & GaAs & GaN/SiC & GaN/SiC & GaN/Si & GaN/Si & GaN/Si & GaN/Si \\ BW. (GHz) & 24–32 & 24.5–29 & 23–29.5 & 24–29 & 24–30 & 24–31 & 24–31 \\ FBW (\%) & 28.6 & 16.8 & 24.8 & 18.9 & 22.2 & 25.5 & 25.5 \\ Supply (V) & 5 & 28 & 20 & 12 & 12 & 12 & 12 \\ Gain (dB) & 16.5 \(\pm\) 0.5 & 11.5 \(\pm\) 2.2 & 32.5 \(\pm\) 2.5 & 20 \(\pm\) 1.3 & 19.3 \(\pm\) 1 & 25.5 \(\pm\) 1.5 & 19.7 \(\pm\) 0.5 \\ P\({}_{\text{out}}\) (dBm) & 29 \(\pm\) 0.6 & 29.8 \(\pm\) 0.4 & 34.1 \(\pm\) 0.8 & 30.7 \(\pm\) 0.7 & 30.6 \(\pm\) 0.5 & 34.3 \(\pm\) 0.3 & 32.5 \(\pm\) 0.2 \\ PAE (\%) & 27–33 b  & 28.3–42.8 c  & 24.7–39.1 c  & 27.6–38.9 b  & 30.9–39.8 a  & 35.8–37.4 b  & 35.5–37.8 a  \\ Size (mm\({}^{2}\)) & 2.4 \(\times\) 1.1 & 2.1 \(\times\) 1.3 & 3.4 \(\times\) 1.9 & 2.2 \(\times\) 1.3 & 1.65 \(\times\) 0.78 & 3.25 \(\times\) 1 & 1.4 \(\times\) 0.88 \\ FoM & 41.8 & 4.4 & 10.8 & 15.8 & 45.7 & 61.3 & 104.3 \\ \hline \hline \end{tabular}  
\end{table} 
Table 4: Performance summary and comparisons with contemporary works.