S parameters of properly biased HFET- $1101$ measured using $50 \Omega$ netwook analyser at $6 \mathrm{GH}_2$

$ \begin{aligned} \\ &s_{11}=0.614 L-167.4^{\circ} \\\\ &s_{12}=0.046 L 65^{\circ} \\\\ &s_{21}=2.18 L 32.4^{\circ} \\\\ &s_{22}=0.716 L-83^{\circ}\\ \end{aligned}\\ $

Design an amplifier using this for maximum possible gain.

Solution:

Stability checks:-

$ \begin{aligned}\\ \Delta &=s_{11} s_{22}-s_{12521} \\\\ &=(0.614 \angle-167.4^{\circ} \times 0.716 -83^{\circ})-(0.046 L 65^{\circ} \times 2.18\angle32.4^0).\\\\ \Delta &=0.34 \angle 113^{\circ} \quad \therefore|\Delta|=0.34\lt1\\ \end{aligned}\\ $

$ \begin{aligned}\\ &K=\frac{\left.|-| s_{11}\right|^2-\left|s_{22}\right|^2+|\Delta|^2}{2\left|s_{12} . s_{21}\right|} \\\\ &.K=\frac{1-0.614^2-0.716^2+0.34^2}{2 \mid 0.046 \angle 65^{\circ} \times 2.18\langle 32.4^{\circ}|}=1.126\gt 1 \\ \end{aligned}\\ $

As $|\Delta k| \& k\gt1$ …