Performance factor and power gain of linear active two-ports

Resistively mismatched, reactively tuned active two-ports can be designed for a given performance factor, n, by the analytical solution of appropriate equations. A previous paper provided a computer solution in the form of graphs for the range 1 ¿ n ¿ 10 and a simple, closely accurate, analytical solution for n ¿ 10. The present paper extends the computer solution from n = 1 to the limit of stability, where n = II. It establishes that the root for optimum gain is the only positive real root if arg(p12p21) is between 0 and ¿ radians, and the only negative real root if arg(p12p21) is between ¿ and 2¿ radians.