For an -port adaptor, with port wave-impedances , , let's arbitrarily designate port as the reflection-free port (the one on top). It is convenient to define the port conductances . To suppress reflection on port , we need, for a parallel adaptor,
and, for a series adaptor,
Recall the alpha parameters for an -port series scattering junction, derived from the physical constraints that the velocities be equal and the forces sum to zero at the (series) junction:
when port is reflection free.
Since , we have and .