# A High-Efficiency K-band MMIC Linear Amplifier Using Diode Compensation
## 2 Nonlinear Analysis and Diode Compensation
As shown in Figure 3, a Schottky diode is parallel in the gate and the drain of the output stage FET to compensate for the nonlinearity of \(C_{gs}\). The voltage between the reverse diode is  
Figure 1:1  
The two-port Y-parameter matrix can be utilized to analyse the parallel network composed of the FET and diode. The matrix form of FET is as follows:  
\[\left[ \begin{array}{c}i_{g}\\ i_{d}\end{array} \right]=\left[ \begin{array}{cc}y_{11}&y_{12}\\ y_{21}&y_{22}\end{array} \right[ \begin{array}{c}v_{gs}\\ v_{ds}\end{array} \right] \tag{13}\]  
where  
\[y_{11}=\frac{j\omega\mathcal{C}_{gs}}{1+j\omega\mathcal{C}_{gs}r_{gs}}+j\omega \mathcal{C}_{gd} \tag{14}\]  
\[y_{12}=-j\omega\mathcal{C}_{gd} \tag{15}\]  
\[y_{21}=\frac{g_{m}}{1+j\omega\mathcal{C}_{gs}r_{gs}}-j\omega\mathcal{C}_{gd} \tag{16}\]  
\[y_{22}=\frac{1}{r_{ds}}+j\omega(\mathcal{C}_{ds}+\mathcal{C}_{gs}) \tag{17}\]  
Incorporating the diode barrier capacitance into the matrix,  
\[{y_{11}}^{\prime}=\frac{j\omega\mathcal{C}_{gs}}{1+j\omega\mathcal{C}_{gs}r_ {gs}}+j\omega(\mathcal{C}_{gd}+\mathcal{C}_{diode}) \tag{18}\]  
\[\mathcal{C}_{m}{}^{\prime}=-\frac{1}{\omega\text{Im}\left(\frac{1}{y_{11}} \right)} \tag{19}\]  
\(\mathcal{C}_{m}{}^{\prime}\) represents the input capacitance of the network. According to the previous analysis, the state of input capacitance mainly determines the nonlinear characteristics of the network. Thus, it is possible to perform distortion compensation utilizing the high-frequency C-V characteristic of the diode. As \(v_{diode}<0\), \(\mathcal{C}_{diode}\) is dominated by depletion layer capacitance \(\mathcal{C}_{j}\), where  
\[C_{j}=\frac{C_{j0}}{\sqrt{1-\frac{v_{diode}}{\Phi_{B}}}} \tag{20}\]  
where \(\Phi_{B}\) is the junction built-in potential, so  
\[C_{m}{}^{\prime}=\frac{\left[\omega\mathcal{C}_{gs}r_{gs}(\mathcal{C}_{gd}+ \mathcal{C}_{j})\right]^{2}+(\mathcal{C}_{gs}+\mathcal{C}_{gd}+\mathcal{C}_{ j})^{2}}{\left(\omega\mathcal{C}_{gs}r_{gs}\right)^{2}(\mathcal{C}_{gd}+\mathcal{C}_{ j})-(\mathcal{C}_{gs}+\mathcal{C}_{gd}+\mathcal{C}_{j})} \tag{21}\]  
Figure 3: Paralleled Shottky diode linearizer. As the input RF power increases, the electric field within the FET channel is enhanced, which makes the swing of both \(v_{gs}\) and \(v_{ds}\) become higher. However, the negative swing of \(v_{ds}\) is limited by the knee voltage (\(V_{knee}\)) and the positive swing of \(v_{gs}\) is limited by the diffusion barrier voltage (\(V_{diff}\)). As a result, \(\overline{v}_{ds}\) grows higher while \(\overline{v}_{gs}\) grows lower. Consequently, \(\overline{v}_{dide}\) (3) becomes higher while \(\overline{v}_{gs}\) becomes lower. The voltage waveform versus input RF power is shown in Figure 4.  
Therefore, substituting (1), (2), and (20) into (21) and combining the voltage analysis above, the characteristics of input capacitance can be shown as the curve in \[y_{12}=-j\omega\mathcal{C}_{gd} \tag{15}\]0  
The principles for the choice of diode periphery are as follows. 1. The size of the diode should be large enough to compensate for the input capacitance of the pHEMT as the input power increases;
2. The barrier capacitance of the diode should not be too large to over change the input characteristics of the HMET and generate excessive feedback between drain and gate. Figure 6 shows that as the size of diode increases, the additional feedback becomes stronger. As a result, the MaxGain of the network decreases, which leads to lower linear gain. Therefore, combined with the C-V characteristics of the diode shown in Figure 5a, we gradually adjusted the diode size so that it could effectively compensate for the input capacitance of pHEMT while reducing the effect  
\[y_{12}=-j\omega\mathcal{C}_{gd} \tag{15}\]1 (**a**) Voltage waveform of \(v_{ds}\); (**b**) voltage waveform of \(v_{gs}\). \[y_{12}=-j\omega\mathcal{C}_{gd} \tag{15}\]2 (**a**) C-V characteristics of the two-finger diode; (**b**) input capacitance of the network versus RF power. on the gain.