Two-port terminations for maximum power gain

The problem of the maximum power gain which can be obtained from an active twoport device has been considered by several authors, notably by Linvill and Schimpf (1956). They calculated the optimum source and load immittances and the resulting maximum power gain, for a given network whose parameters were assumed to satisfy the usual stability condition. Linvill and Schimpf used a somewhat complicated analysis, and expressed the results in terms of auxiliary functions of the two-port parameters. It may therefore be worth pointing out that the problem may be solved simply and explicitly from the wellknown condition, mentioned by Linvill and Schimpf, that the optimum terminations provide a conjugate match at the input and output terminals of the network. In the following analysis, h parameters are used; the expressions can be readily adapted to z, y, or g parameters by means of the usual transformations.