# Modeling of Key Specifications for RF Amplifiers Using the Extreme Learning Machine
## 4 Modeling Results and Discussion
### 0.5\(-\)2.1 GHz GaN Class AB PA
#### 4.1.2 Output Power  
The modeling results of the output power of the PA are shown in Figure 6. Figure 6a shows the modeling results with simulation data, and Figure 6b shows the results without simulation data. Firstly, from the temperature characteristics of the output power, the output power of the PA decreases with the increase in temperature. This is mainly due to the decrease in 2 DEG mobility, increasing source/drain resistance [11]. However, it can also be noted that the drop in output power decreases when the out-put power is close to saturation (when the temperature change is the same).  
From the model's accuracy, it is the same as the modeling result of S21. However, from Figure 6a, there is a better agreement between the model with simulation data and the actual measurement results, while there is a more significant deviation be-tween the model without simulation data and the actual measurement results (Figure 6a). This is also mainly because the trend in the output power temperature characteris-tics can be depicted by the simulation data in the case where simulation data are available.  
Figure 5: S21: (**a**) with simulation; (**b**) without simulation.  
The above discussion provides a detailed analysis of the relationship between S21 and temperature and output power and temperature. Next, the effect of the model will be explicitly discussed in terms of the results of the model. As shown in Figures 5 and 6, the ELM model based on the simulated data agrees well with the measured results. However, at the same time, there is a significant deviation between the ELM model without simulated data and the measured results. This is mainly because the trend between simulated and measured data is the same, and there are only some differences in the values. Therefore, the trend in the temperature characteristics of the PA is first obtained from the simulated data and then calibrated by the measured data. As a re-sult, the model based on the simulated data matches the actual trends and values measurements. In contrast, the modeling is based on measurement data, where the number of measured temperature points is very small, and the behavior of many tem-perature points is not learned, so there is a significant error between the model output and the actual measurement results.  
To further compare the differences between the modeling method in the literature [19] and the modeling method proposed in this paper, the errors of the two modeling methods are compared at different numbers of temperature measurement points, as shown in Table 1. Table 1 shows the results compared to the modeling approach in the literature [19]. The modeling method proposed in this paper has the following ad-vantages: first, it is less sensitive to the temperature measurement points; second, the model accuracy is two orders of magnitude higher with the same number of measure-ment temperature points; and third, the number of required temperature measurement points is less with the same model accuracy requirement.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{2}{c}{**Number and Distribution of Measured**} & \multicolumn{2}{c}{**MSE**} \\ \multicolumn{2}{c}{**Temperature Points**} & \multicolumn{2}{c}{**This Work**} & **Ref. [19]** \\ \hline
3 & \(-40\); 25; 90 & \(9.2317\times 10^{-3}\) & \(4.7517\times 10^{-1}\) \\ \hline
3 & \(-40\);\(-20\); 90 & \(9.3243\times 10^{-3}\) & \(1.4372\times 10^{0}\) \\ \hline
5 & \(-40\); \(-10\); 25; 60; 90 & \(9.1524\times 10^{-4}\) & \(9.9561\times 10^{-2}\) \\ \hline
5 & \(-40\); \(-5\); 0; 15; 90 & \(9.2037\times 10^{-4}\) & \(3.3107\times 10^{-1}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparison results of models in different cases for power amplifiers (PA).  
Figure 6: Output power: (**a**) with simulation; (**b**) without simulation.