Power-Complementary Reflection and Transmission

We can show that the reflectance and transmittance of the yielding
termination are *power complementary*. That is, the reflected
and transmitted signal-power sum to yield the incident signal-power.

The average power incident at the bridge at frequency
can be
expressed in the frequency domain as
.
The reflected power is then
. Removing the minus sign, which can be
associated with reversed direction of travel, we obtain that the
*power reflection frequency response* is
, which
generalizes by analytic continuation to
. The power
transmittance is given by

which generalizes to the plane as

Finally, we see that adding up the reflected and transmitted power yields the incident power:

[How to cite this work] [Order a printed hardcopy] [Comment on this page via email]

Copyright ©

Center for Computer Research in Music and Acoustics (CCRMA), Stanford University