Two Reciprocal Power Theorems for Passive Linear Time-Invariant Multiports

We investigate a reciprocal and passive linear time-invariant multiport, having a port set coupled to a generator and a port set coupled to a load, in the harmonic steady state. Two configurations are considered, in which the port set at which the generator is connected and the port set at which the load is connected are exchanged. We establish a new reciprocal power theorem about the extrema of the set of the values of the transducer power gain obtained for all nonzero excitations, in the two configurations. For the case where the two port sets have the same number of ports, we also state and prove a new reciprocal power theorem about the extrema of the set of the values of the insertion power gain obtained for all nonzero excitations, in the two configurations.