## 3 Dual-Band Doherty Power Amplifier
### Impedance Modification for Dual-Band DPA  
According to [22], the design will be physically large in size if \(\Pi\)- or T-network topology is used for impedance inversion because the ratio between the upper and lower band will affect the size of the network. However, a compact design approach was used in [22], for a dual-band DPA where the ratio of the impedance transformation was 1:2.85 instead of the traditional ratio of 1:4, and in this case the common load impedance will be increased to 1.4 \(\times\) Ropt/2. Two transistors used in this design were 10 W and 25 W gallium nitride high electron mobility transistors (GaN HEMTs), where the main amplifier output matching network was designed to be matched to 100 \(\Omega\), whereas the gate of the \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{2}{c}{**Dual-Band**} & \multicolumn{2}{c}{**Single Band**} \\ \cline{2-4}  & **T-Topology** & **\(\Pi\)-Topology** & **Both** \\ \hline \(S_{21}\)Phase@\(f_{1}\) & \(-90^{\circ}\) & \(-90^{\circ}\) & & \(90^{\circ}\) \\ \(S_{21}\)Phase@\(f_{2}\) & \(+90^{\circ}\) & \(-90^{\circ}\) & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Phase delay introduced by T- and \(\Pi\)-networks [29]. main, the gate, and drain of the auxiliary amplifier are designed to match 50 \(\Omega\), to reduce the phase difference between the main and the auxiliary amplifier due to the difference in the biasing voltage, the offset line was used at the input of the main amplifier. A small offset line was used at the output of the auxiliary amplifier to reduce the leakage from the main amplifier towards the auxiliary amplifier. Moreover, a higher drain supply voltage of 36 V was used for the auxiliary amplifier in order to increase its contributed power and to improve the load modulation [22]. It can be noticed that reducing the impedance inversion ratio of the quarter-wavelength will reduce the bandwidth limitations. Moreover, a novel dual-band DPA was designed in [31], as shown in Figure 9, where the main concept is to use two quarter-wavelength transmission lines at the output of the auxiliary amplifier and only one at the output of the main amplifier, where the impedances are 70.7 \(\Omega\) and 50 \(\Omega\) in the auxiliary output path and 70.7 \(\Omega\) in the main output path. The main purpose of these additional lines is to improve the broadband performance compared to the traditional DPA, where only one quarter-wavelength line is used at the output of the main amplifier. The improvement was made by reducing the impedance transformation ratio, as shown in the following equations, so that the loaded Q factor will be reduced to increase the band covered. In the classical DPA, the impedance transformation ratio is 1:4 to transfer 25 \(\Omega\) to 100 \(\Omega\) so that the loaded Q factor will be:  
\[Q_{L}=\sqrt{\frac{100\,\Omega}{25\,\Omega}-1}=1.73 \tag{4}\]  
whereas, in the design of [31], the impedance ratio is 1:2 making the loaded Q factor equal to 1:  
\[Q_{L}=\sqrt{\frac{100\,\Omega}{50\,\Omega}-1}=1 \tag{5}\]  
Hence, there is an increment of 1.73 times in terms of frequency bandwidth. At the back-off region, the main amplifier will see 100 \(\Omega\) due to using the 70.7 \(\Omega\) quarter wavelength line, whereas both amplifiers would see a 50 \(\Omega\) at the saturation point. Besides, a dual-band Doherty amplifier design using class-J amplifier was studied in [32], where the imperfect high impedance seen towards the peaking amplifier at the back-off region was utilized to be part of the output matching of the main amplifier at the fundamental frequency matching. Whereas the control of harmonics was carried out using a post matching network after examining the load pull data of the main amplifier to determine the location of the second harmonic. [PERSON] et al.