The Gain and Stability of Linear Two-Port Amplifiers

In this paper the problem of obtaining maximum gain at a given stability factor is considered. It is assumed that the terminations and the complex feedback
(y_{12})
are variable by means of passive networks, and it is shown that for matching terminations the maximum gain, for a given stability factor
S
, is
(S + 1/S)^{2} G_{u}
, where
G_u
is the unilateralized gain. The optimum value of
y_{12}
is
{S y \ast}_{21}/(S + 1)^2 G_u
. It is further shown that if there is a free choice of terminations, their optimum values are the complex conjugates of the shortcircuit input and output admittances. In this case the gain is given by
(S/S - 1)^2 G_u
. The optimum value of
y_{12}
is
{y \ast}_{21}/SG_u
.