# Modeling of Key Specifications for RF Amplifiers Using the Extreme Learning Machine
## 4 Modeling Results and Discussion
### 50-450 MHz CMOS LNA
#### 4.2.2 The NF of the LNA
From Tables 1 and 2, the modeling method proposed in this paper has the following advantages, both for modeling PA and for modeling LNA: first, it is less sensitive to temperature measurement points; second, the model accuracy is two orders of magnitude higher than the model accuracy in [19] with the same number of measured temperature points; third, only three temperature measurement points are required with the same model accuracy requirement, while eight temperature measurement points are required in [19]. In summary, the modeling method proposed in this paper can not only model the temperature characteristics of the RF amplifier but also significantly reduce the number of measured temperature points while ensuring the model's accuracy. Finally, it should be noted that the data used for modeling in this paper are from static simulation/measurement points. Additionally, the modeling of the dynamic behavior of amplifiers is currently receiving more and more attention from the industry. The ELM model used in this paper has not been verified as to whether it is suitable for modeling the dynamic behavior of amplifiers, which is currently receiving a lot of attention. However, the authors believe that the ELM model used in this paper can be used to model amplifiers' dynamic behavior. This is because the ELM model used in this paper is a behavioral-level black-box model, which only cares about the input and output variables and data, not about the specific physical mechanism. Therefore, only the input and output variables and data need to be known, and the ELM model can still be used for modeling. All that \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{3}{c}{**Number and Distribution of Measured**} & \multicolumn{2}{c}{**MSE**} \\ \multicolumn{3}{c}{**Temperature Points**} \\ \hline
**No.** & **Temperature (\({}^{\circ}\)C)** & **This Work** & **Ref. [19]** \\ \hline
3 & \(-\)40; 25; 90 & 8.8737 \(\times\)\(10^{-3}\) & 4.4758 \(\times\)\(10^{-1}\) \\ \hline
3 & \(-\)40; 40; 90 & 9.0481 \(\times\)\(10^{-3}\) & 2.4478 \(\times\)\(10^{0}\) \\ \hline
5 & \(-\)40; \(-\)5; 25; 55; 90 & 8.6943 \(\times\)\(10^{-4}\) & 9.5745 \(\times\)\(10^{-2}\) \\ \hline
5 & \(-\)40; 0; 25; 30; 90 & 8.7042 \(\times\)\(10^{-4}\) & 5.6612 \(\times\)\(10^{-1}\) \\ \hline
6 & \(-\)40; \(-\)15; 10; 35; 60; 90 & 8.3569 \(\times\)\(10^{-4}\) & 9.3036 \(\times\)\(10^{-2}\) \\ \hline
6 & \(-\)40; \(-\)20; \(-\)5; 20; 50; 90 & 8.4327 \(\times\)\(10^{-4}\) & 4.8756 \(\times\)\(10^{-1}\) \\ \hline
7 & \(-\)40; \(-\)15; 5; 25; 45; 65; 90 & 7.9783 \(\times\)\(10^{-4}\) & 9.1069 \(\times\)\(10^{-2}\) \\ \hline
7 & \(-\)40; \(-\)30; 0; 10; 40; 70; 90 & 8.1678 \(\times\)\(10^{-4}\) & 4.2132 \(\times\)\(10^{-1}\) \\ \hline
8 & \(-\)40; \(-\)20; 0; 20; 40; 60; 80; 90 & 7.5237 \(\times\)\(10^{-5}\) & 8.8607 \(\times\)\(10^{-3}\) \\ \hline
8 & \(-\)40; \(-\)25; \(-\)15; 0; 15; 35; 40; 90 & 7.6654 \(\times\)\(10^{-5}\) & 6.8072 \(\times\)\(10^{-2}\) \\ \hline
9 & \(-\)40; \(-\)20; \(-\)5; 10; 25; 40; 55; 70; 90 & 7.0612 \(\times\)\(10^{-5}\) & 8.5492 \(\times\)\(10^{-3}\) \\ \hline
9 & \(-\)40; \(-\)35; \(-\)5; 0; 15; 40; 65; 75; 90 & 7.1357 \(\times\)\(10^{-5}\) & 6.5627 \(\times\)\(10^{-2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison results of models in different cases for LNA. remains is adjusting and optimizing the model parameters until the model meets the desired requirements.