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(y₁₂)are variable by means of passive networks, and it is shown that for matching terminations the maximum gain, for a given stability factorS, is(S + 1/S)² Gᵤ, whereG_uis the unilateralized gain. The optimum value ofy₁₂is{S y }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 ofy₁₂is{y }₂₁/SG_u.