# Ultra-Generalized Continuous Class F Power Amplifier with Finite Third-Harmonic Load Impedance
## 2 Analysis of the Proposed UCCF Mode
### Performance of Proposed UCCF Mode  
The output power \(P_{out}\)[29] and drain efficiency \(DE\) can be calculated from the drain current and voltage equations, which are functions of \(pcr\) and \(\alpha\). They can be expressed as  
\[P_{out}=\frac{1}{2}l_{1}^{2}\cdot Z_{f0} \tag{13}\]  
\[DE=\frac{P_{out}}{P_{DC}} \tag{14}\]  
The trend of \(P_{out}/P_{0}\) and \(DE/DE_{0}\) with \(pcr\) and \(\alpha\) can be visualized in Figure 7a,b. \(P_{0}\) and \(DE_{0}\) represent the output power and efficiency of the continuous class F mode, respectively. In Figure 7, the coordinate origin represents the continuous class F mode, the horizontal axis represents the GCCF mode, and the vertical axis represents the PCC-CF\({}_{3}\) mode. At the coordinate origin, \(P_{out}/P_{0}\) and \(DE/DE_{0}\) equal 1, as expected. It can be seen from Figure 7a that \(P_{out}/P_{0}\) is greater than 1, and increasing \(pcr\) and \(\alpha\) can effectively enhance the output power. The range of \(P_{out}/P_{0}\) is 1 to 1.07 for the GCCF mode, 1 to 1.218 for the PCC-CF\({}_{3}\) mode, and 1 to 1.25 for the UCCF mode. This shows that compared with the GCCF and PCC-CF modes, the UCCF mode has a greater ability to improve the output power. In Figure 7b, it is obvious that increasing \(pcr\) and \(\alpha\) leads to a decrease in the efficiency, and this trend becomes more pronounced as \(\alpha\) increases. The \(DE/DE_{0}\) drops from 1 to 63% in the GCCF mode and from 1 to 92.6% in the PCC-CF\({}_{3}\) mode.  
The amplitude-to-amplitude modulation (AM/AM) at saturation is used as the evaluation criterion for linearity. AM/AM\({}_{\text{U}}\) represents the AM/AM of the UCCF mode, and AM/AM\({}_{\text{F}}\) represents the AM/AM of the continuous class F mode. AM/AM\({}_{\text{U}}\) andAM/AM\({}_{\rm F}\)[29] can be expressed as  
\[\rm{AM/AM_{U}}=G_{U}-G_{S} \tag{15}\]  
\[\rm{AM/AM_{F}}=G_{F}-G_{S} \tag{16}\]  
\[G_{U}=10\log\frac{P_{out}}{P_{in}} \tag{17}\]  
\[G_{F}=10\log\frac{P_{0}}{P_{in}} \tag{18}\]  
where \(G_{S}\) is the small signal gain, \(G_{U}\) is the power gain of the UCCF mode at saturation, and \(P_{in}\) is the input power.  
\[\rm{AM/AM_{U}-AM/AM_{F}}=20\log_{10}\frac{2I_{1}\left(1-\cos\frac{\alpha}{2} \right)}{pcr} \tag{19}\]  
Figure 7c shows the trend of AM/AM\({}_{\rm U}-\)AM/AM\({}_{\rm F}\) with different \(pcr\) and \(\alpha\) values. At the coordinate origin, AM/AM\({}_{\rm U}-\)AM/AM\({}_{\rm F}\) equals 0, as expected. When AM/AM\({}_{\rm U}-\)AM/AM\({}_{\rm F}\) is greater than 0, the linearity is better than that of the continuous class F PA. When AM/AM\({}_{\rm U}-\)AM/AM\({}_{\rm F}\) is less than 0, the linearity is worse than that of the continuous class F PA. The range of AM/AM\({}_{\rm U}-\)AM/AM\({}_{\rm F}\) is 1 to 6 in the GCCF mode and 1 to \(-\)4.3 in the PCC-CF\({}_{3}\) mode. As shown in Figure 7c, as \(\alpha\) increases, AM/AM\({}_{\rm U}-\)AM/AM\({}_{\rm F}\) increases, but as \(pcr\) increases, AM/AM\({}_{\rm U}-\)AM/AM\({}_{\rm F}\) decreases. Therefore, the AM/AM distortion caused by an increase in \(pcr\) can be offset by selecting the appropriate \(\alpha\).