General Properties for Determining Power Loss and Efficiency of Passive Multi-Port Microwave Networks

Starting from the scattering matrix formulation, three useful properties are derived that characterize the dissipative loss and the corresponding efficiency of a multi-port, passive microwave network. Elementary examples are considered that involve both reciprocal and nonreciprocal networks to demonstrate the utility of the expressions provided. When applied to the equal-split, matched, three-port resistive divider, they recover the known fact that the device is 50% efficient. The relations yield the new result that the efficiency of a three-port Wilkinson power divider is two-third on the average. Using the results presented, it is further shown that the Wilkinson power divider belongs to a class of most efficient, matched, reciprocal three-port networks that are constrained to provide maximum isolation at the output ports.