# Source/Load-Pull Noise Measurements at K\({}_{\text{a}}\) [PERSON]
## 3 Results  
The noise measurement approach presented in Section 2 was tested on an active device fabricated by OMMIC on its recently developed 60 nm gate length GaN-on-Si HEMT technology (D006 GH). The device has 4 fingers of 35 um unit gate width. The reference operating point is \(V_{DS}=5\) V, \(I_{D}=17.1\) mA, which was believed to be approximately optimum for noise performance. Other drain currents were also tested to confirm that hypothesis. The measurement frequency range was set from 20 GHz to 40 GHz, with a 100 MHz step. As anticipated in Section 2, 4 physical terminations were adopted, which yield 8 measurements per frequency point since both the forward and the reverse modes were exploited. As expected, this number is still too low to ensure a reliable extraction of the noise parameters at all frequencies. Indeed, the extracted elements of the correlation matrix, shown with dashed lines of Figure 3, are often unphysical. Pruning the unphysical points from these extractions yields the continuous thin lines in the same figure. Therefore, the linearization-based method illustrated in Section 2.4 was employed to improve the extraction. Observing the pruned traces in Figure 3 justifies the selection of a frequency interval \(B_{L}\) up to a few gigahertz. However, increasing \(B_{L}\) also entails a reduction of the measurement frequency range at either end. Therefore, \(B_{L}=5\) GHz was set (i.e., \(f_{1}=f_{0}-2.5\) GHz, \(f_{2}=f_{0}+2.5\) GHz). The result is shown by the continuous thick lines in Figure 3.  
Notice that the linearization-based traces are similar to what could be obtained by smoothing or fitting the pruned traces of the standard extraction. However, the proposed approach exhibits the following advantages:  
Figure 3: Extraction of the elements of the noise correlation matrix over frequency. Dashed lines: standard extraction (\(f_{1}=f_{0}=f_{2}\)). Continuous thin lines: physically sound subset of the standard extraction. Continuous thick lines: linearization-based extraction (\(f_{1}=f_{0}-2.5\) GHz, \(f_{2}=f_{0}+2.5\) GHz). * Rather than discarding the data at frequencies where the standard extraction fails, it produces a reliable extraction at a certain frequency \(f_{0}\) by merging all data at nearby frequencies. This may be especially beneficial when the single-frequency failures are numerous. * As compared to fitting, it does not assume any particular model, but only that the elements of the correlation matrix can be linearized. The noise correlation matrix can be converted to the more familiar noise parameters through well known formulae. For the Reader's convenience, it is worth recalling that:  
\[R_{n} = \hat{c}_{11} \tag{26}\] \[Y_{opt} = \sqrt{\frac{\hat{c}_{22}}{\hat{c}_{11}}-\left(\text{Im}\Big{[} \frac{\hat{c}_{12}}{\hat{c}_{11}}\Big{]}\right)^{2}}+j\text{Im}\Big{[}\frac{ \hat{c}_{12}}{\hat{c}_{11}}\Big{]}\] (27) \[F_{min} = 1+2\Big{(}\hat{c}_{12}+R_{n}Y_{opt}^{*}\Big{)} \tag{28}\]  
as well as that, in general:  
\[\Gamma = \frac{Y_{0}+Y}{Y_{0}-Y} \tag{29}\] \[NF = 10\log(F)\ [\text{dB}]\, \tag{30}\]  
with \(Y_{0}=\
icefrac{{1}}{{2}}\) the normalization admittance and \(Z_{0}\) the normalization impedance (typically 50 \(\Omega\)). The noise parameters corresponding to the pruned traces of Figure 3 are shown in Figure 4 as isolated points. Then, two linearization-based extractions are also shown, associated with two different values of \(B_{L}\), namely 1 GHz (continuous thin lines) and 5 GHz (continuous thick lines). It is interesting to notice that the extraction adopting \(B_{L}=1\) GHz is much smoother than the standard extraction; however, a problematic hump in \(NF_{min}\) in the 28-29 GHz frequency range is found (which, incidentally, appears strongly correlated to the small-signal parameters of blocks BLK2 and BLK0 at those frequencies). Increasing \(B_{L}\) up to 5 GHz further irons out all traces.