Coupling matrices with reactive loads at ports

The design of microwave filters and multiplexers usually starts from the synthesis of a coupling matrix M. The elements of the main diagonal identify invariant reactances that shift the resonant frequency at resonator nodes, and are usually zero at port nodes. However the analysis of the coupling matrix show that non-zero elements are allowed too. This work show that this reactances can model the phase term due to shift of the reference planes of the microwave circuits that are being represented by the coupling matrix.