# Highly Efficient GaN Doherty Power Amplifier for N78 Sub-6 GHz Band 5G Applications
## 3 Circuit Design of RF DPA  
### Design of Wilkinson Power Divider  
Reference [23] indicates that the small-signal gain decreases by 3 dB when the auxiliary amplifier splits an input signal into two equal-phase output signals using a Wilkinson power divider (Figure 3). This power divider equally splits the input power (port 1) into two equal-phase output signals (port 2 and port 3), maintaining matched states and offering isolation between the output ports. The formulas below demonstrate how to calculate the Wilkinson power divider parameters [27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41]:  
\[Z_{1}=Z_{0}\Bigg{[}\Bigg{(}\frac{P_{main}}{P_{peak}}\Bigg{)}^{-1.5}+\Bigg{(} \frac{P_{main}}{P_{peak}}\Bigg{)}^{0.5}\Bigg{]}^{0.5}, \tag{4}\]  
\[Z_{2}=Z_{0}\Bigg{(}1+\frac{P_{main}}{P_{peak}}\Bigg{)}^{0.5}\Bigg{(}\frac{P_{ main}}{P_{peak}}\Bigg{)}^{0.25}, \tag{5}\]  
\[Z_{3}=Z_{0}\Bigg{(}\frac{P_{main}}{P_{peak}}\Bigg{)}^{-0.25}, \tag{6}\]  
\[Z_{4}=Z_{0}\Bigg{(}\frac{P_{main}}{P_{peak}}\Bigg{)}^{0.25}, \tag{7}\]  
\[R_{w}=Z_{0}\Bigg{[}\Bigg{(}\frac{P_{main}}{P_{peak}}\Bigg{)}^{0.5}+\Bigg{(} \frac{P_{main}}{P_{peak}}\Bigg{)}^{-0.5}\Bigg{]}, \tag{8}\]  
where \(Z_{0}\) represents the normalized impedance (typically 50 \(\Omega\)), \(R_{w}\) is the isolation resistance, and \(P_{main}\) and \(P_{peak}\) represent the output power of the main branch (port 2) and the auxiliary branch (port 3), respectively.  
In our design, we implemented [PERSON]'s power divider with an unequal split to send more power to the main amplifier, resulting in a significant gain increase while reducing the auxiliary amplifier's power demand, allowing it to operate at a less deep class-C level. By adjusting the division factor (\(Q\)) value, defined as \(Q=P_{main}/P_{peak}\), the power distribution between ports 2 and 3 can be altered.  
Table 1 displays branch impedances (\(Z_{1}\), \(Z_{2}\), \(Z_{3}\), and \(Z_{4}\)) and isolation resistance (\(R_{w}\)) with varying division factor (\(Q\)) values. The values were obtained through simulations with ADS software, adjusting the division factor to achieve the desired power division ratio. It is important to note that these values depend on the specific design and substrate properties, and may vary based on the actual power divider design. The optimal division factor (\(Q\)) for our proposed circuit was determined as 2.5 after considering critical factors, gain, and PAE, as shown in Figure 4.  
The diagram in Figure 5 illustrates the layout and the simulated performance of the unequal [PERSON] power divider. Return loss was below \(-17\) dB over the entire band (3.3-3.8 GHz). The isolated port was connected to allow for the insertion of an external resistor.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \(Q\) & \(Z_{1}\) (\(\Omega\)) & \(Z_{2}\) (\(\Omega\)) & \(Z_{3}\) (\(\Omega\)) & \(Z_{4}\) (\(\Omega\)) & \(R_{W}\) (\(\Omega\)) \\ \hline
0.5 & 102.988 & 51.494 & 59.46 & 42.045 & 106.066 \\ \hline
1 & 70.711 & 70.711 & 50 & 50 & 100 \\ \hline
1.5 & 58.327 & 87.491 & 45.18 & 55.334 & 102.062 \\ \hline
2 & 51.494 & 102.988 & 42.045 & 59.46 & 106.066 \\ \hline
2.5 & 47.049 & 117.622 & 39.764 & 62.872 & 110.68 \\ \hline
3 & 43.869 & 131.607 & 37.992 & 65.804 & 115.47 \\ \hline
3.5 & 41.45 & 145.075 & 36.556 & 68.389 & 120.268 \\ \hline
4 & 39.528 & 158.114 & 35.355 & 70.711 & 125 \\ \hline
4.5 & 37.953 & 170.787 & 34.329 & 72.824 & 129.636 \\ \hline
5 & 36.628 & 183.142 & 33.437 & 74.767 & 134.164 \\ \hline \end{tabular}
\end{table}
Table 1: Branch impedances and Isolation Resistance with Sweep of Division Factor (\(Q\)).  
Figure 4: The gain and PAE of the proposed circuit with a sweep of division factor (\(Q\)).  
Figure 3: Wilkinson power divider’s basic layout.