## 5 Accuracy of the Proposed Expressions of the Maximum-Rating Constrains  
In this section, the accuracy of the expressions developed in Section 4 are evaluated. The proposed expressions were used to estimate the component maximum-rating constraints of twelve Class-E PAs with FDI. All the amplifiers were simulated in OrCAD PSpice Designer(r) using transient analysis with a maximum time step of 100 ps, and simulation time of 500 us. The PA was implemented in this software using ideal components, a voltage-controlled switch with zero fall and rise times, and off-resistance and on-resistance of 1 G\(\Omega\) and 1 mf\(\Omega\), respectively. This setup allows the simulation of the ideal Class-E PA with FDI, which guarantees the first two assumptions of the model described in Section 2. Finally, \begin{table}
\begin{tabular}{c c c} \hline \hline
**Coefficient Name** & \(f_{3}\)**(\(q_{p}\)D)** & \(f_{4}\)**(\(q_{p}\)D)** \\ \hline \(b_{x0}\) & \(0.2769\) & \(0.7978\) \\ \(b_{x1}\) & \(-0.6647\) & \(-1.6730\) \\ \(b_{x2}\) & \(0.4641\) & \(0.8805\) \\ \(b_{x3}\) & \(-0.9009\) & \(-2.1030\) \\ \(b_{x4}\) & \(1.1380\) & \(1.8730\) \\ \(b_{x5}\) & \(2.2670\) & \(4.9180\) \\ \(b_{x6}\) & \(-1.6420\) & \(-2.8230\) \\ \(b_{x7}\) & \(-2.3650\) & \(-4.1700\) \\ \(b_{x8}\) & \(1.5920\) & \(2.4510\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Coefficients of \(h_{m}\). Figure 7: \(h_{m}\) graphs. (**a**) 3D plot. (**b**) Fitting residuals. the maximum-rating constraint estimations were compared with the simulated values and the involved error was calculated. The specifications and model parameters of the designed amplifiers are listed in Table 3. In the first four amplifiers, the \(q\) and \(D\) variables were set to typical values (i.e., \(q\)=1.412 and \(D\)=0.5 [9]), with a parametric sweep of \(Q_{L}\). In the amplifiers identified by IDs four to eight, the \(q\) and \(Q_{L}\) values were fixed to 1.412 and 20 respectively, with a parametric sweep of \(D\). Finally, in the rest of the amplifiers the \(D\) and \(Q_{L}\) values were fixed to 0.5 and 20 respectively, with a parametric sweep of \(q\). The resulting model variables and the circuit components are listed in Tables 4 and 5, respectively. These values were calculated based on the math tool proposed in [8]. Furthermore, the unknown circuit components were found following the three phases detailed in Figure 8. In this diagram the input parameters are shown in silver boxes, the relations of the design set in gray boxes,  
In all designed amplifiers, the predicted and simulated waveforms present a good agreement. For instance, the waveforms of the amplifiers identified by IDs 1 and 6 are shown in Figure 9. The main stress conditions supported by the components were extracted from simulation. These results were compared to the estimated values, which were calculated from the analytical expressions proposed in Section 4. Furthermore, the MAPE was calculated as the average values of the amplifier percentage error (% Er) related to each stress parameter. The results were summarized in Table 6.  
In all of the simulated amplifiers, the overall error was less than 10%. The maximum error presented was around to 15% in the \(V_{L_{o}M}\) and \(V_{C_{i}M}\) parameters of case four. The error can be explained by the selection of \(Q_{L}\) value. A low \(Q_{L}\) value produces a high estimation error because of the inaccuracy of the analytical model. Comparing all the parameters studied, \(V_{L_{o}M}\) and \(V_{C_{i}M}\) have the highest estimated error, with a MAPE of 4.15% and 5.76%, and a standard deviation of 3.83% and 3.43%, respectively. However, those errors are less significant than the error produced by the component tolerances, which typically are considered by design using a safety margin of 20%. On the other hand, the parameter with the most accurate estimation was \(I_{S_{W}M}\), which presents a MAPE of 0.59% with a standard deviation of 0.41%.