# A g\({}_{m}\)/I\({}_{\rm D}\)-Based Low-Power LNA for Ka-Band Applications
## 2 Design Procedure
To fully characterize the FETs, the transconductances g\({}_{m}\) for each IC are collected, which determine the transistor capability to produce a drain current change from an increment in V\({}_{\text{CS}}\). As shown in Figure 5c, an IC\({}_{1}\) of 0.48 yields a g\({}_{m1}\) of 12 mS; for IC\({}_{2}\) = 1.58, g\({}_{m2}\) is 28.72 mS; and for IC\({}_{3}\) = 4.9, g\({}_{m3}\) is 55.18 mS. As expected, the transconductance increases as does the drain current and is maximal in the strong inversion region. Similarly, the transistor efficiency (g\({}_{m}\)/\(I_{D}\)) versus IC is sought, as shown in Figure 3a. As opposed to the transconductance, the transistor efficiency is usually maximal in weak inversion and it decreases as the operation region moves towards strong inversion; hence, for IC\({}_{1}\), (g\({}_{m}\)/\(I_{D}\))\({}_{1}\) is 18 S/A; for IC\({}_{2}\), (g\({}_{m}\)/\(I_{D}\))\({}_{2}\) is reduced to 13.07 S/A; and for IC\({}_{3}\), (g\({}_{m}\)/\(I_{D}\))\({}_{3}\) is only 8.07 S/A. With the values of g\({}_{m}\)/\(I_{D}\) and g\({}_{m}\) available, the drain current \(I_{D}\) can be solved from Equation (8). \[IC=\frac{I_{DS}}{I_{spec\square}\cdot W/L} \tag{1}\]0  
At this point, the designer may wonder about the actual devices' high-frequency performance for the selected IC values. Therefore, the G\({}_{max2}\) and NF\({}_{min}\) can be calculated, as shown in \[IC=\frac{I_{DS}}{I_{spec\square}\cdot W/L} \tag{1}\]1 The case of IC\({}_{1}\) suffers from a limited G\({}_{max1}\) of 6.78 dB due to the lower f\({}_{T}\) and g\({}_{m}\), as well as an increased NF\({}_{min1}\) of 1.37 dB for the same reason. Note these are ideal values assuming ideal matching networks are used and are expected to deviate to some extent once real components are added to the circuit. That means the actual circuit implementation with PDK components results in a higher NF and a lower gain due to finite Q factors and parasitic components. For the case of IC\({}_{2}\), the G\({}_{max2}\) is significantly improved to 10.34 dB because of the increase in both f\({}_{T}\) and g\({}_{m}\), and NF\({}_{min2}\) in this case is 1 dB. Finally, for the case of IC\({}_{3}\), the G\({}_{max3}\) obtained is 13.08 dB and NF\({}_{min3}\) is as low as 0.86 dB. Since the  
\[IC=\frac{I_{DS}}{I_{spec\square}\cdot W/L} \tag{1}\]2 Simulation results of the overdrive voltage V\({}_{ov}\) (**a**), threshold voltage V\({}_{TH}\) (**b**), and transconductance (**c**) as functions of IC. original setup collects data from a single transistor, e.g., a common-source amplifier, both a higher gain and NF are expected when the cascode is set up. The advantage of using this methodology is that LNAs can be designed by optimizing the power consumption for given specifications without the need for iterative simulations. Instead, a database with transistor parameters for a specific technology is available. In summary, Table 1 presents the values of the calculated parameters for the three IC values of 0.48, 1.58, and 4.92. Table 1 illustrates the design trade-offs mentioned earlier. The most favorable among the three cases can be determined through the analysis of power consumption and a figure of merit (FoM\({}_{IC}\)), as defined by Equation (9). Depending on the desired characteristics, the corresponding FoM definition and inversion region should be chosen. For instance, for our definition of FoM\({}_{IC}\), if low power consumption is desired, the weak inversion region should be selected. However, this choice comes with the flaw of increased NF\({}_{min}\) and a lower G\({}_{max}\) compared to the other cases. On the other hand, if a high gain with a lower minimum noise figure is sought, it should be noted that the required I\({}_{D}\) increases, leading to higher power consumption. In contrast to low-frequency designs, in this case, the transistor area is not particularly relevant, as the impedance-matching components (inductors) occupy most of the space.