# 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  
The results of modeling the temperature characteristics of the NF of the LNA are shown in Figure 8. Figure 8a shows the modeling results with simulation data, and Figure 8b shows the results without simulation data. From Figure 8a, the NF increases with the temperature increase. This is mainly because the carrier mobility decreases whenever the temperature increases, making the trans-conductivity decrease. In turn, the reduction in trans-conductivity will lead to a rise in NF [30]. It means that the NF of LNA increases with the temperature rising and is consistent with the results reported in [22]. In addition, it can be found that the change in NF is different at different frequencies when the magnitude of temperature change is the same. For example, when the temperature increases from \(-40\)\({}^{\circ}\)C to \(90\)\({}^{\circ}\)C, the NF increases by 1.22 dB and 0.74 dB at 50 MHz and 270 MHz, respectively, which shows that the carrier mobility increases are not only temperature-dependent but also frequency-dependent. Then, from the results in Figure 8a,b, the model with simulation data has a smaller gap and better agreement with the actual measurement results than the model without simulation data, achieving the expected modeling effect. This shows that using simulation data to describe the trend in NF temperature characteristics first, and then calibrating it with actual measurement data, is feasible. Furthermore, this approach can significantly reduce the time and cost of measurement. The above results are a specific analysis and discussion of the S21 and NF of the LNA versus temperature. The following results of modeling S21 and NF of LNA are discussed and analyzed in detail. As can be seen in Figures 7 and 8, the modeling results of LNA agree well with the actual measurement results. The main reason is that the model accuracy in the literature [19] depends on the number of measured temperature points, and with a small number of measured points, the behavior of many temperature points is not learned, resulting in poor model accuracy. In contrast, the modeling method proposed in this paper first uses simulation data to obtain a rough model of the temperature characteristics of the LNA and then calibrates this rough model with actual measurement data. In this way, a better model accuracy can be achieved based on the data of a small number of measurement points. Similarly, to compare with the modeling approach in the literature [19], the accuracy of the two modeling approaches is compared in this paper (as in Table 2). Table 2 shows the following advantages over the modeling approaches in the literature [19]: first, it is less sensitive to temperature measurement points; second, the accuracy of the model is two  
Figure 8: NF of the LNA: (**a**) with simulation; (**b**) without simulation. orders of magnitude higher with the same number of measurement temperature points; third, the number of measurement temperature points required is less with the same model accuracy requirement. This paper verifies the effectiveness of the proposed ELM-based RF amplifier modeling method by taking a GaN PA of 0.5\(-\)2.1 GHz and a CMOS LNA of 50\(-\)450 MHz as examples. It is also compared with the modeling method in the literature [19]. The modeling method in the literature [19] is mainly based on measurement data and uses ELM for modeling. This modeling approach needs to rely on a relatively large number of measurement points. If the number of measurement points is too small, the model accuracy will be very poor because the model has not learned the trends in many temperature points. In contrast, the modeling method proposed in this paper mainly uses simulation data to build a coarse model first and then calibrates the coarse model using measurement data, and this modeling method only needs a few measurement data to achieve a high model accuracy.