# A Multi-Band LNA Covering 17-38 GHz in 45 nm CMOS SOI
## 2 Circuit Design
### The Structure and Performance of the LNA  
As shown in Figure 3, due to the influence of parasitic capacitances \(C_{GS}\) and \(C_{GD}\), the input port of the traditional differential cascode amplifier can be equivalent to a parallel RC network in terms of impedance matching. The equivalent shunt resistance converted from the impedance seen from the input port is on the order of kilo-ohms. The inductor in balun will be enormous when making a resistance of kilo-ohms be matched to 50 \(\Omega\), resulting in the vast majority of the chip area. As a solution to the problem above, a series RC feedback link is introduced between the input and output port of the circuit, as shown in Figure 4a. Considering the Miller effect, the feedback link can be equivalent to the impedance \(R_{miller}\) at the input port, which is shown in Equation (1). \(R_{f}\) is the feedback resistance, and \(|A_{y}|\) is the open-loop gain of the circuit. The connecting of the equivalent network of the input port and the \(R_{miller}\) in parallel reduces the real part of the impedance seen from the input port.  
\[R_{miller}=\frac{R_{f}}{1+|A_{y}|} \tag{1}\]Figure 3: The traditional differential amplifier and the input equivalent circuit.  
Figure 2: The schematic of the proposed LNA.  
To further satisfy the 50 \(\Omega\) impedance matching of the input port, the source degeneration inductors are added to the first stage to reduce the input port impedance and optimize the noise characteristics, shown in Figure 4b. Simultaneously, cross-coupling capacitors are added, which can eliminate parasitic effects and provide a gm-boost. Figure 5 shows the S21 and NF simulation results of the first stage with and without cross-coupling capacitors. The simulations of gain, input return loss (S11), noise figure, and input impedance are performed by Cadence Virtuoso Spectre RF using S-parameter analysis.  
Comprehensively considering the power consumption, input impedance, and gain of the proposed LNA, the transistors (M\({}_{1}\)-M\({}_{12}\)) are designed as 16 fingers with a total channel width of 64 \(\upmu\)m. On the premise that the transistors have the same size, Figure 6 shows the simulation results of the impedance of the traditional differential cascode amplifier and the structures of the proposed LNA, which undergoes an equivalent transformation from series to parallel. The black line corresponds to the traditional cascode amplifier. The blue line and the red line correspond to the circuits; only the feedback link is added in one, and in the other, both the feedback link and degeneration inductor are added. Both them are based on the traditional cascode amplifier.  
Figure 4: (**a**) Adding feedback links based on the traditional differential cascode amplifier; (**b**) adding additional cross-coupling capacitors and source degeneration inductors.  
Figure 5: The gain and NF simulation results of the LNA with and without cross-coupling capacitors.  
The first stage of the LNA sacrifices gain for admirable input matching and low NF. Thus, two additional stages are appended to boost the gain. Apart from the high gain, the LNA has three operating bands, controlled by a 2-bit signal. The gain simulation results of stepwise circuits in three bands are shown in Figure 7.  
Figure 6: The impedance of the traditional differential cascode amplifier and the structures of the proposed LNA.  
Figure 7: The gain of all stages simulated in (**a**) 17–21 GHz, (**b**) 21–28 GHz and (**c**) 28–38 GHz.