Revisiting the Power Gains of a Loaded Two-Port: Is There a Missing Element?

Abstract

In microwave electronics, the power gains of a linear two-port are customarily defined as the ratio of an output port and input port power, where such powers are intended either as operational or as available. Two input and two output powers are thus introduced, with four possible combinations of output/input power ratios, but only three are practically exploited, the well-known operational power gain, available power gain, and transducer power gain. In the present paper, we provide a comprehensive review of gain definitions (including the less commonly exploited added-power gains) and finally consider the missing fourth element (defined as the ratio of the output available power and of the input operational power), derive a few mathematical properties of it, both in the general and in the unilateral case, and ultimately justify the reason why this fourth gain G4 which, following the suggestion of an anonymous reviewer, we will call apparent power gain, Gapp, has little interest in the optimization of the power transfer between the generator and the load. Nevertheless, the definition and analysis of Gapp, besides being formally useful to complete the gain family, may yield a deeper insight into the very nature of power transfer optimization in a loaded two-port.