#### Physical Derivation of Series Reflection Coefficient

Physically, the force-wave reflection coefficient seen at port of a series adaptor is due to an impedance step from , that of the port interface, to a new impedance consisting of the series combination of all other port impedances meeting at the junction. Let

 (F.35)

denote this series combination. Then we must have, as in Eq.(F.25),

 (F.36)

Let's check this physical'' derivation against the formal definition Eq.(F.31) leading to in Eq.(F.33). Define the total junction impedance as

This is the series combination of all impedances connected to the junction. Then by Eq.(F.35), for all . From Eq.(F.26), the velocity reflection coefficient is given by

Since

the result follows.

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