Two-Port Series Adaptor for Force Waves
Figure F.6a illustrates a generic two-port description of the series adaptor.
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As discussed in §7.2, a series connection is characterized by a common velocity and forces which sum to zero at the junction:

The derivation can proceed exactly as for the parallel junction in
§F.2.1, but with force and velocity interchanged, i.e.,
, and with impedance and admittance interchanged,
i.e.,
. In this way, we may take the
dual of Eq.
(F.14) to get

diagrammed in Fig.F.7. Converting back to force wave
variables via
and
, and noting
that
, we obtain, finally,

as diagrammed in Fig.F.6b. The one-multiply form is now

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General Series Adaptor for Force Waves
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General Parallel Adaptor for Force Waves