A set of waveguides can be joined together at one of their endpoints to create an -port waveguide junction. General conditions for lossless scattering in the scalar case appeared in . Waveguide junctions are isomorphic to adaptors as used in wave digital filters .
This section focuses on physically realizable scattering junctions produced by connecting multivariable waveguides having potentially complex wave impedances. A physical junction can be realized as a parallel connection of waveguides (as in the connection of tubes that share the same value of pressure at one point), or as a series connection (as in the connection of strings that share the same value of velocity at one point). The two kinds of junctions are duals of each other, and the resulting matrices share the same structure, exchanging impedance and admittance. Therefore, we only treat the parallel junction.