## 2 Circuit Analysis and Design
### Inductive Neutralization Technique  
To achieve a high flat gain, the optimum transistor topology was determined first. Figure 2 shows the maximum stable gain (MSG) (or the maximum available gain (MAG)) [10] of various transistor topologies in the given 65 nm CMOS technology. For a fair comparison, the simulation conditions were set identical: the gate width and drain bias current of each transistor are 30 \(\upmu\)m and 3.1 mA, respectively. Among the CS, common-gate (CG), and cascade topologies, the CS topology provides the highest gain beyond 38 GHz. However, the gain of the CS still gradually decreases as the frequency increases further than 38 GHz. To achieve a flat gain over the full Ka-band, a gain-boosting technique should be used to compensate for the gain roll-off at the upper end of the Ka-band. In this research, we adopted the inductive neutralization technique in the CS to boost the gain. It is well known that the gate-drain capacitance C\({}_{\text{gd}}\) degrades the forward gain of the transistor [11]. Therefore, by connecting a neutralization inductor (L\({}_{\text{neut}}\)) between the gate and drain, C\({}_{\text{gd}}\) is resonated with the inductor, and thus the MSG (or MAG) can  
Figure 1: Schematic of the full Ka-band amplifier with flat gain. Figure 2: Comparison of MSG (or MAG) of different transistor topologies in a 65 nm CMOS technology. be boosted [12; 13]. In Figure 2, the MSG (or MAG) of the CS topology with the inductive neutralization (L\({}_{\text{neut}}\) = 1.3 nH) is shown, which is higher than that of other topologies beyond 31 GHz. Moreover, the inductive neutralization changes the behavior of the MSG (or MAG) over the frequency. It is observed in Figure 2 that the peak of the MSG (or MAG) is pushed to a higher frequency region and, thus, can be located almost at the upper end of the Ka-band. This offsets the high loss of passive matching components and the resulting gain roll-off at the high frequencies. While boosting the gain by resonating out the feedback capacitance C\({}_{\text{gd}}\), the inductive neutralization may disrupt the stability of the transistor. This is because positive feedback can be reinforced when the C\({}_{\text{gd}}\)-L\({}_{\text{neut}}\) network operates far from the resonance. Therefore, the value of L\({}_{\text{neut}}\) should be carefully determined considering a tradeoff between the gain and the stability. Figure 3 shows the simulated MSG (or MAG) and stability factor K at 39 GHz versus L\({}_{\text{neut}}\). The MSG (or MAG) has two peaks at L\({}_{\text{neut}}\) = 1.23 and 1.44 nH, respectively. On the other hand, the K has a single peak at L\({}_{\text{neut}}\) = 1.3 nH and decreases rapidly as L\({}_{\text{neut}}\) deviates from 1.3 nH. The K becomes even below unity when L\({}_{\text{neut}}\) < 1.23 nH or L\({}_{\text{neut}}\) > 1.44 nH. Hence, we chose L\({}_{\text{neut}}\) of 1.3 nH, which results in MAG of 15.1 dB and K of 11.2 at 39 GHz. Notably, both MAG and K are boosted by inductive neutralization. The inductive neutralization with L\({}_{\text{neut}}\) of 1.3 nH was applied to the first gain stage (M\({}_{1}\)), which presents a high gain at the upper end of the Ka-band. It should be noted that the second and third gain stages (M\({}_{2}\) and M\({}_{3}\)) have no inductive neutralization because they should present a high gain at lower frequencies, as described in Section 2.2. The input matching of the amplifier should operate in a wide bandwidth to suppress mismatch loss that occurs in the interconnection with other circuit blocks. The inductive neutralization of the first gain stage alters the input impedance of M\({}_{1}\); therefore, it should be considered in the input matching design shown in Figure 4. Specifically, the C\({}_{\text{gd}}\)-L\({}_{\text{neut}}\) network brings the load impedance of M\({}_{1}\) (Z\({}_{\text{L1}}\)) to the input of M\({}_{1}\) (Z\({}_{\text{in1}}\)) when the operation is off the resonance frequency.