It is a simple exercise to verify that signal power is conserved by checking that . (Left-going power is negated to account for its opposite direction-of-travel.)
So far we have only considered a plane wave incident on the left of the junction. Consider now a plane wave incident from the right. For that wave, the impedance steps from to , so the reflection coefficient it ``sees'' is . By superposition, the signal flow graph for plane waves incident from either side is given by Fig.C.17. Note that the transmission coefficient is one plus the reflection coefficient in either direction. This signal flow graph is often called the ``Kelly-Lochbaum'' scattering junction .
There are some simple special cases:
- (e.g., rigid wall reflection)
- (e.g., open-ended tube)
- (no reflection)
Reflection and Refraction