### Two-Port Series Adaptor for Force Waves

Figure F.6a illustrates a generic two-port description of the series adaptor.

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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