# A Broadband Analog Predistortion Linearizer Based on GaAs MMIC for Ka-Band TWTAs
## 2 Analog Predistortion MMIC Topology
### Nonlinear Device Size Selection  
MMIC processes have their own unique component technology, which is closely related to the preparation process. The APD MMIC proposed in this paper was designed based on a standard commercial 0.15 \(\upmu\)m GaAs pHEMT process. The active devices of this process are pHEMTs with a pinch-off voltage of 0.7 V. The power density is 300 mW/mm, and the cut-off frequency is close to 110 GHz [24]. In the GaAs pHEMT process, the pre-processed pHEMT source and drain are connected to form a Schottky diode. Its ohmic gate contact layer is deposited via thermal evaporation, and the gate and drain contacts of the pre-fabricated pHEMTs are connected through the etched windows of the polyimide insulation layers [25]. Schottky diodes can generally be used in the design of switches, limiters, and mixers. The layout and equivalent circuit of Schottky diodes in a GaAs pHEMT process are shown in Figure 2. The diode equivalent circuit includes the junction resistance \(R_{\mathrm{j}}\), the junction capacitance \(C_{\mathrm{j}}\), the series resistance \(R_{\mathrm{s}}\) and the parasitic pad capacitances \(C_{\mathrm{p1}}\) and \(C_{\mathrm{p2}}\). \(R_{\mathrm{j}}\) and \(C_{\mathrm{j}}\) are the intrinsic parameters whose values are dependent on the \(I\)-\(V\) and \(C\)-\(V\) curve equation, while the other parasitic parameters are related to the diode's geometry. Figure 1: Analog predistortion MMIC schematic. In the design process, the gate length of the Schottky diode in the process is fixed, while the single-finger gate width \(W\) and the number of gates \(N\) are variable. Schottky diodes with different numbers and widths of gates have different impedance, noise, power and gain characteristics, which need to be selected depending on the application and desired frequency range [24]. The _I-V_ curves of diodes with different gate numbers and widths and are shown in Figure 3, where the current axis is logarithmic. The simulation and test data of a two-finger 20 \(\upmu\)m diode deviate slightly for voltages below 0.1 V, and the other values are in good agreement, which is indicative of the diode model's accuracy. For diodes with different sizes, DC parameters such as \(I_{s}\), n and \(R_{\mathrm{s}}\) are extracted through their _I-V_ curves [26]. It can be seen from Table 1 that the four-finger 40 \(\upmu\)m diode has the maximum reverse saturation current \(I_{s}\) and the minimum series resistance \(R_{\mathrm{s}}\). The linear region slopes of diodes of different sizes are the same, so they have the same ideal factor \(n\). Figure 3: _I-V_ curve for different sizes of GaAs pHEMT Schottky diodes. Figure 2: (**a**) The GaAs pHEMT diode layout; (**b**) the GaAs pHEMT diode model. The \(I\)-\(V\) curve equation of the Schottky diodes is shown in (1):  
\[I_{d}=f(V_{d})=I_{s}(e^{\frac{\mathrm{d}}{nkT}V_{d}}-1) \tag{1}\]  
its nonlinear resistance can be expressed using (2):  
\[R_{\mathrm{d}}=\frac{1}{\frac{\partial I_{d}}{\partial V_{d}}}=\frac{nkT}{qI_{s }}e^{-\frac{\mathrm{d}}{nkT}V_{d}} \tag{2}\]  
As shown in Figure 3, when the diode is biased at a certain voltage, as the input signal power gradually increases, its load curve changes from a small-signal dynamic range to a large-signal dynamic range. During this transition, the nonlinear resistance of the diode contributes the most nonlinearity. To facilitate the analysis, the Schottky diode model can be simplified to a diode model with \(R_{\mathrm{d}}\) and \(C_{d}\) in parallel, as shown in Figure 1. According to (2), when a diode is powered using a power supply circuit, the factor affecting the nonlinear resistance \(R_{\mathrm{d}}\) of the diode is only \(V_{\mathrm{d}}\). When the input power passing through the diode increases, this will cause the partial voltage on the bias resistance to increase, resulting in the reduction in the partial voltage across the diode, and finally leading to the increase in the nonlinear resistance \(R_{\mathrm{d}}\)[27].