Extending the Cascading by Pairs of Multiport Generalized Scattering Matrices for Characterizing the Connected Ports

An extension to the traditional technique for cascading generalized scattering matrices (GSMs) by pairs is presented. It can solve the connection of an arbitrary number of networks, with an arbitrary number of ports, while being quite intuitive and easy to implement. It is able to compute, not only the response at the free ports of the global network -like the traditional cascading-by-pairs does- but also the connected ports, obtaining an extended GSM (eGSM), which can be used to find the field inside the full network for an arbitrary incidence.