Question 12.2: TRANSISTOR STABILITY The Triquint T1G6000528 GaN HEMT has th...
TRANSISTOR STABILITY
The Triquint T1G6000528 GaN HEMT has the following scattering parameters at 1.9 GHz(Z_{0} = 50 Ω):
S_{11} = 0.869∠−159°S_{12} = 0.031∠−9°,
S_{21} = 4.250∠61°,
S_{22} = 0.507∠−117°
Determine the stability of this transistor by using the K − Δ test and the µ-test,and plot the stability circles on a Smith chart.
From (12.28) and (12.29) we compute K and |Δ| as
\left|\Delta \right| =\left|S_{11}S_{22}-S_{12}S_{21}\right| =0.336k =\frac{1-\left|S_{11}\right|^{2} -\left|S_{22}\right|^{2}+\left|\Delta \right|^{2} }{2\left|S_{12}S_{21}\right| } =0.383
Thus we have |Δ| < 1 but not K > 1, so the unconditional stability criteria of (12.28)–(12.29) are not satisfied, and the device is potentially unstable. The stability of this device can also be evaluated using the µ-test, for which (12.30) gives µ = 0.678, again indicating potential instability.
\mu =\frac{1-\left|S_{11}\right|^{2}}{\left|S_{22}-\Delta S_{11}^*\right| +\left|S_{12}S_{21}\right| } =0.383>1 (12.30)
The centers and radii of the stability circles are given by (12.25) and (12.26):
C_{L}=\frac{(S_{22}-\Delta S_{11}^{*})^{*}}{\left|S_{22}\right|^{2}-\left|\Delta \right|^{2} } =1.59\angle 132^{\circ }R_{L}=\frac{\left|S_{12} S_{21}\right| }{\left|S_{22}\right|^{2}-\left|\Delta \right|^{2} } =0.915
C_{S}=\frac{(S_{11}-\Delta S_{22}^{*})^{*}}{\left|S_{11}\right|^{2}-\left|\Delta \right| ^{3} } =1.09\angle 162^{\circ }
R_{S}=\frac{\left|S_{12}S_{21}\right| }{\left|S_{11}\right|^{2}-\left|\Delta \right|^{2} } =0.205
These data can be used to plot the input and output stability circles, as shown in Figure 12.6. Since |S_{11}| < 1 and |S_{22}| < 1, the central part of the Smith chart represents the stable operating region for Γ_{S} and Γ_{L}. The unstable regions are shaded.
