We now consider the scattering matrix for the parallel junction of
-variable physical waveguides, and at the same time, we treat
the generalized case of matrix transfer-function wave impedances.
Equations (13) and (11) can be rewritten for
each -variable branch as
Using conservation of velocity we obtain
It is clear that (38) is a special case of (48) when . If the branches do not all have the same dimensionality , we may still use the expression (48) by letting be the largest dimensionality and embedding each branch in an -variable propagation space.