# Modeling of Key Specifications for RF Amplifiers Using the Extreme Learning Machine
## 3 Modeling Process  
### Structure of the Model and the Process of Modeling  
The lack of an accurate temperature-dependent device model makes it possible that there is always a gap between simulated and measured RF amplifiers [19], but the trend in the simulated and measured results with temperature is similar. Suppose the gap between simulation and measurement results can be eliminated or minimized by calibrating the simulation results with the actual measurement results. In that case, the calibrated \"simulation results\" can then be used to predict the performance of the RF amplifier at different temperatures over a given temperature range and reduce the number of measurement points required for modeling.  
Therefore, to reduce the number of measured temperature points, the simulation data of the RF amplifier is used for modeling the temperature characteristics of the RF amplifier in this paper. The main idea of its modeling is first to establish the relationship between the amplifier performance and temperature variation using the simulation data of the RF amplifier and then calibrate the trained model using the actual measurement data. The greater the number of measurement points used for model calibration, the higher the accuracy of the resulting model.  
ELM is emerging as a new developmental milestone in artificial neural networks. They have been widely applied in microwave millimeter-wave devices/circuits, such as filter design [24], behavior modeling of power amplifiers [25], etc. The relationship between the input and output of an RF amplifier is strongly nonlinear [25], and the ELM has a strong non-linear learning capability [18]. Therefore, ELM was used to model the temperature characteristics of the RF amplifier. The ELM-based modeling process for the RF amplifiers' temperature characteristics proposed in this paper is shown in Figure 3.  
Figure 3: ELM (extreme learning machine)-based modeling flow for RF amplifier temperature characteristics.  
As shown in Figure 3, the process of modeling the temperature characteristics of the RF amplifier is divided into two main parts, one is the training of the model, and the other is the calibration of the model. The main steps are specified as follows.  
1. Selection of a suitable neural network. As described in the literature [26; 27], to establish this nonlinear relationship for the temperature characteristics of the RF amplifier, a single hidden layer feedforward network (SLFN) is used, as shown in Figure 4.  
For arbitrary distinct samples (\(x_{j}\), \(t_{j}\)) (\(j=1\),..., \(d\)), SLFNs with \(L\) hidden nodes are mathematically modeled as [27]  
\[o_{j}=\sum_{i=1}^{L}\beta_{i}g_{i}(x_{j})=\sum_{i=1}^{L}\beta_{i}G(a_{i}\cdot x _{j}+b_{i}) \tag{1}\]  
where \(x_{j}\) presents the input power, frequency, and temperature; \(t_{j}\) is the simulation's S-parameter, NF, and output power; \(o_{j}\) is the model's output; \(\beta_{i}\) is the output weight; \(a_{i}\) is the input weight; and \(b_{i}\) is the hidden layer bias. The input weight and hidden layer bias are randomly generated according to the continuous distribution probability [27]. Additionally, \(g(\cdot)\) is a nonlinear activation function; \(G\) (\(\cdot\)) is the output function of the hidden node [27].  
1. Divide the simulation data into training data and test data.
2. Determine the initial number of hidden layer layers (\(L\)) and hidden layer output weights (\(\beta_{i}\)) of the model.
3. Randomly generate input weights (\(a_{i}\)) and hidden layer weights (\(b_{i}\)).
4. Output the model results.
5. Calculate the model error (\(MSE_{1}\)).
6. Calculate of the model using the test results.
7. Compare the model error with the expected value.
8. Determine whether the model is trained or not based on comparing the model error with the expected value.