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

(43) |

(44) |

Using conservation of velocity we obtain

and

where

(46) |

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.

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