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

are variable by means of passive networks, and it is shown that for matching terminations the maximum gain, for a given stability factor

, is

, where

is the unilateralized gain. The optimum value of

is

. 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

. The optimum value of

is

.