# A Multi-Band LNA Covering 17-38 GHz in 45 nm CMOS SOI
## 2 Circuit Design
### Magnetically Coupled Resonator(MCR) Matching Network  
In order to obtain a broad bandwidth, the MCR matching network is adopted for impedance matching [25]. Taking input port matching as an example, the resistance seen through the balun is converted to 50 \(\Omega\). Figure 8 shows the input port matching network and the equivalent network on both sides of the balun. As shown in Figure 8b, the prerequisite conditions for the matching network are as follows: \(R_{1}\) of the tank1 is 50 \(\Omega\), and \(R_{2}\) and \(C_{2}\) of the tank2 can be obtained by converting the accessible simulation data. On this basis, the value of \(L_{1}\), \(L_{2}\) and \(C_{1}\) can be determined as long as the resonant frequencies of the networks are definite. To enhance the bandwidth, the resonant frequencies of RLC networks on both sides are set as different frequencies \(f_{1}\) and \(f_{2}\); thus, the S21 image of the balun can produce two peaks, as shown in Figure 9. Figure 10 shows the gain and S11 simulation results of the first stage with different magnetic coupling coefficients \(k\) in the range of 28-38 GHz. As the coefficient increases, the bandwidth of the LNA is extended. However, \(k\) is restricted in balun. The same approach is applied to the output and interstage matching.  
Figure 8: (**a**) The input port matching network and (**b**) the equivalent circuit of the balun.  
Figure 9: Wideband technology.  
Due to the compromise between the bandwidth and the gain, the LNA is designed with three operating bands. Switch capacitances are introduced, which can conduct the switching of three operating bands with a 2-bit control signal. There is a trade-off for the switching transistor design. A switching transistor with a large size has preferable conduction characteristics, but this worsens the matching situation due to the large parasitic capacitance. Conversely, a switching transistor with a small size has less impact on matching but brings additional power consumption due to its low equivalent shunt resistance.  
Figure 11 shows the switch capacitances designed in the LNA, which are inserted at the input and output port of all stages in parallel. Figure 12 shows the S11 simulation results of the LNA with the switch capacitors in different states. With the switch of the LNA input port on, the capacitor is connected in parallel at the input port, and the resonant frequency decreases.  
Figure 11: The switch capacitances in LNA (**a**) for input/output port and (**b**) for interstage coupling.  
Figure 10: Gain and S11 simulation results of LNA with different magnetic coupling coefficients.  
The change in resonant frequency is associated with a change in capacitance. The switch capacitance is in the high-impedance state when the transistor turns off, while it is correspondingly capacitive when the transistor turns on. In the case of the latter, \(C_{ctrl}\) is connected in parallel with the parasitic capacitance of the transistor at the input port, which increases the capacitance of the input port. On the premise that balun's matching inductance remains unchanged, according to \(\omega=1/\sqrt{LC}\), the resonant frequency will move to a low frequency. Utilizing this principle, the resonant frequencies of both sides in balun extend to low frequencies simultaneously. Thus, the LNA can realize the migration of the operating frequency band.