# _Ku_-Band CMOS Power Amplifier with Three-Stack Power Stage to Enhance Output Power and Efficiency
## 2 Typical CMOS Power Amplifiers
### Stack Structure  
In this study, a stack structure was used for the power stage to improve the output power of the power amplifier. First, compared with the common-source structure, the output characteristics of the stack structure were investigated. The stack structure of Figure 2 is designed to have the same voltage drop between the drain-source of each stacked transistor. The gate voltage and impedance of each transistor are used to control the voltage drop between the drain-source. In this case, gate impedance is generally implemented using a resistor and a capacitor. Under the condition of 50 \(\Omega\) load impedance, if the number of stacked transistors in the stack structure is \(n\), the supply voltage of the stack structure can be \(n\) times higher than the supply voltage of the common-source structure. Therefore, the ratio of the output impedance of the common-source structure and the stack structure is as follows:  
\[\frac{Z_{out,PW,n}}{Z_{out,PW,CS}}=\left(\frac{nV_{DD}}{I_{D}}\right)\Big{/} \Big{(}\frac{V_{DD}}{I_{D}}\Big{)}=n \tag{1}\]  
Figure 1: Typical structure of power amplifiers: (**a**) common-source, (**b**) cascade, and (**c**) stack structures. Figure 2: Impedances of power stages: (**a**) common-source and (**b**) stack structures. Here, \(V_{DD}\) and \(I_{D}\) are the supply voltage and current of the amplifier, respectively. \(Z_{out,PW,n}\) is the output impedance of a stack structure in which \(n\) transistors are stacked, and \(Z_{out,PW,CS}\) is the output impedance of a common-source structure. Here, it is assumed that the current flowing through each structure is the same. As in Equation (1), \(Z_{out,PW,n}\) has values \(n\) times higher than \(Z_{out,PW,CS}\). Accordingly, \(Z_{out,PW,n}\) has values closer to 50 \(\Omega\) than \(Z_{out,PW,CS}\), making it easier to configure the output matching network of the power stage. As a result, the stack structure can relatively mitigate the sensitivity of the output matching network compared with the common-source structure. In general, the output power of the power amplifier is proportional to the square of the supply voltage and can be expressed by load impedance as follows [12]:  
\[P_{out,CS}\propto\frac{\left(V_{DD}\right)^{2}}{R_{in,OMN}},\ \ \ P_{out,n}\propto\frac{\left(nV_{DD}\right)^{2}}{R_{in,OMN,n}} \tag{2}\]  
Here, \(P_{out,CS}\) and \(P_{out,n}\) are the output power of the common-source and stack structures, respectively. \(R_{in,OMN}\) and \(R_{in,OMN,n}\) are the load impedances of the power stages of the common-source and stack structures, respectively. If the \(R_{in,OMN,n}\) is the same as the \(R_{in,OMN}\), the difference in output power between the two structures can be calculated in decibels as follows [12]:  
\[\Delta P_{out}(\mathrm{dB})=P_{out,n}(\mathrm{dBm})-P_{out,CS}( \mathrm{dBm})\] \[\  
source and \(n\)-stack structures, respectively. If \(R_{in,OMN,n}\) is the same as \(R_{in,OMN}\), the relationship between \(PAE_{CS}\) and \(PAE_{n}\) is as follows:  
\[ \begin{split}& R_{on,OMN,n}\approx nR_{on,OMN},\ \ R_{in,OMN,n}=R_{in,OMN}\\ & PAE_{n}\propto\frac{R_{in,OMN}}{nR_{on,OMN}+R_{in,OMN}}\\ & PAE_{CS}>PAE_{n}\end{split}  \tag{6}\]  
Since the \(n\)-stack structure uses n transistors compared with the common-source structure, it is assumed that \(R_{on,OMN,n}\) is n times higher than \(R_{on,OMN}\). If it is assumed that \(R_{in,OMN,n}\) is n times larger than \(R_{in,OMN}\), the relationship between \(PAE_{CS}\) and \(PAE_{n}\) is as follows:  
\[ \begin{split}& R_{on,OMN,n}\approx nR_{on,OMN},\ \ R_{in,OMN,n}=nR_{in,OMN}\\ & PAE_{n}\propto\frac{nR_{in,OMN}}{nR_{on,OMN}+nR_{in,OMN}}= \frac{R_{in,OMN}}{R_{on,OMN}+R_{in,OMN}}\\ & PAE_{CS}\approx PAE_{n}\end{split}  \tag{7}\]  
From Equations (4) and (7), the \(n\)-stack structure can secure high output power while maintaining the same PAE as the common-source structure. In general, output power and PAE have a trade-off relationship.