## 3 Layout and More PEX and EM Simulation Results
### EM Simulated Results vs. PEX RCC  
EM simulations usually can capture more accurately the parasitics included in the layout, but they are known to be time consuming and may not easily show the parasitics values at sensitive nodes to gain design/layout insights. Figure 11 shows the EM PEX simulation results of the LNA and compares them to the previously presented PEX _RCC_, _RC_, and \(R\) simulated data. We also observe that when gain degrades, both _IP1 dB_ and _IIP3_ increase. EM PEX simulated results also match closely with those from the PEX _RCC_ simulations [12], except that the \(S_{21}\) bandwidth shifted by \(\sim\)1 GHz toward higher frequencies, with deterioration on _NF_ toward higher mm-Wave frequencies compared to those from the PEX _RCC_ simulations. There is, however, a small improvement in input matching from EM PEX simulation compared to the PEX _RCC_ simulations, as indicated in Figures 11a and 12. If we looked closely at Figure 12, we would see that the simulated \(S_{22}\) matches more closely between EM simulations and PEX _RCC_ simulations than \(S_{11}\), likely meaning that the layout parasitics affect the load impedance more than the source impedance of the LNA. This resembles the simulation results that we saw in Section 3.1, which delineated how _IIP3_ and _OIP3_ vary with the different PEX extraction options. As the load impedance of the second stage cascode significantly influences the linearity of the LNA, if the load impedance did not vary much with the extraction option, the linearity (i.e., _OIP3_ and  
Figure 10: Comparison of _IIP3_ and _IP1 dB_ at 28 GHz from PEX simulations in **(a)**_RCC_; **(b)**_RC_; **(c)**_R_; **(d)** pre-PEX cases; and **(e)** the comparison table summary. _OP1 dB_) would not change significantly either. Having similar \(S_{22}\) curves suggests that the load impedance did not vary much with different extraction options. Therefore, the _OIP3_ and _OP1 dB_ should be similar for the PEX _RCC_ vs. EM simulations. From Figure 10, we see that there is a 1.3 dB drop in gain in EM simulations compared to PEX _RCC_ simulations. However, as the _IIP3_ and _IP1 dB_ are both \(\sim\)1.5 dB higher in EM simulations, the _OIP3_ and _OP1 dB_ are nearly identical, similar to what we described in Section 3.1. On the other hand, \(S_{II}\) varies more between the two extraction options. This discrepancy may be caused by PEX _RCC_'s lack of inductance extraction, which may be magnified when the interconnects between the passive and active devices are longer. Since the EM results give better input matching, the input match may be improved by tuning the inductances at the input or at the interstage matching. It is also observed that the \(S_{11}\) locus on the Smith Chart from EM simulations is significantly shorter than the PEX _RCC_ simulation over the same frequency range. This may mean the EM simulations incorporate more parasitic resistance during extraction, lowering the quality factor (Q factor) of the input matching network and causing the impedance to vary less with frequency. These resistances in the RF line may, in part, contribute to EM simulation's lower gain than that from PEX _RCC_ simulations, on top of the contributions from impedance mismatches. Figure 11: Comparison of EM simulation vs. PEX _RCC_ in (**a**) \(S_{21}\), \(S_{11}\), \(NF\) and (**b**) _IIP3_ and _IP1 dB_ at 28 GHz (**c**) comparison table. Figure 12: \(S_{11}\) (red) and \(S_{22}\) (blue) of the LNA from 16 GHz to 44 GHz. EM simulation (solid line) vs. PEX _RCC_ simulations (dashed line). Stability is one of the concerns in high-gain amplifiers and when a feedback loop is present in the circuit. Before shunt resistor \(R_{2}\) (see Figure 3a) was added to the output matching network, PEX \(RCC\) simulations show that both the K factor and the Mu factor are greater than 1 for all frequencies, meaning the LNA is unconditionally stable [1; 2; 3; 5].