Boundary Nevanlinna Pick interpolation for maximum power transfer

The classical problem of maximum power transfer from a generator to a passive load in the sinusoidal steady state is extended to the case where there are a number of sinusoidal sources having possibly different frequencies. By formulating the matching conditions in terms of the scattering parameters, the interpolation conditions on the passive load and the passive and lossless two port network achieving maximum power transfer to a given load are derived. It is shown that the resulting boundary Nevanlinna Pick interpolation problem always admits a solution and the maximum power that can be delivered to the load is the sum of the maximum powers when the individual sources are acting alone