# Frequency-Bounded Matching Strategy for Wideband LNA Design Utilising a Relaxed SSNM Approach
## 6 Results and Discussion  
The designed MMIC prototype was realised and measured for the 20 to 40 GHz frequency band. To validate small-signal stability across the operating band, the fabricated MMIC LNA was subjected to a comprehensive analysis using multiple standard and advanced criteria. Figure 14 shows the computed Rollet stability factor (K) and geometrical stability factors, which confirm unconditional stability across the frequency range of DC to 70 GHz with both \(\upmu\) and K exceeding unity. In addition, the partitioned Ohtomo stability test was applied to all ports of the three-transistor cascade using the methodology proposed in [29]. The Ohtomo test provides a powerful framework to detect internal feedback-induced instability by evaluating each terminal's reflection behaviour on a Smith chart. The corresponding six Ohtomo circle plots are shown in Figure 15, with each subplot corresponding to one of the six transistor terminals. The plots confirm that the trajectories do not encircle or approach the instability boundary ((1,0) point at x-axis), indicating that no unstable pole exists for any terminal across the frequency sweep. This confirms that all transistor stages remain unconditionally stable, even when mismatches and interstage feedback are present. The test thus validates the core premise of this work, that relaxing the SSNM condition does not compromise stability. Figure 14: Simulated Rollet stability factor (K) and graphical stability factors (\(\upmu_{1}\), \(\upmu_{2}\)) of the LNA across 0–70 GHz, confirming unconditional small-signal stability. Figure 13: Microphotograph of the fabricated three-stage LNA MMIC implemented in 0.15 \(\upmu\)m GaAs technology. Figure 16 presents both simulated and measured S-parameters (in dB) alongside the noise figure of the proposed three-stage LNA. Across the targeted 28-34 GHz frequency band, the amplifier achieves a flat and stable gain of approximately 23 \(\pm\) 1 dB, with measured gain closely following simulation predictions. The simulated NF, shown as a solid magenta curve, remains below 2 dB throughout the operating band. The measured NF, depicted by the dashed magenta line, varies between 2.0 dB to 2.5 dB over 28 to 34 GHz. As depicted in Figure 16, the simulated reflection coefficients (S11 and S22) demonstrate excellent wideband matching, maintaining better than \(-18\) dB and \(-15\) dB return loss, respectively, over the 28-34 GHz band. This broad matching performance directly validates the effectiveness of the relaxed SSNM design approach, which expands the permissible mismatch regions to achieve robust wideband impedance control. While minor deviations between simulated and measured S11 and S22 occur, primarily due to parasitic effects such as probe pad capacitances, calibration inaccuracies, and small process variations, these measurement variations are independent of the relaxed SSNM condition itself. A similar variation occurs in the noise figure, which shows a noise figure  
Figure 16: Simulated (post EM) and measured S-parameters and noise figure of the LNA MMIC. Figure 15: Partitioned Ohtomo test results for each terminal of the three-stage LNA MMIC (DC to 70 GHz). increment of 0.5 dB at some frequencies; this is due to the difference between the noise model and noise data provided by the foundry. Thus, the relaxed SSNM methodology inherently enables wideband operation, and the observed differences in measured data stem from practical implementation factors rather than the design approach, confirming the method's practical reliability and wideband applicability. A comparison with previously published LNA MMICs, fabricated using the same GaAs technology, is summarised in Table 3. As observed, the performance of the proposed design is comparable to, or better than existing designs. References [8, 10, 11, 18, 21, 30] all utilize transistors with a 150 nm gate length, similar to that used in this work. However, reference [8] shows a high noise figure and a high gain due to a bigger transistor size.