Calculate the *reflectance* of the terminated waveguide.
That is, find the Laplace transform of the return wave divided by the
Laplace transform of the input wave going into the waveguide. In general,
the reflectance of an impedance step for force waves (voltage waves in
the electrical case) is

This is easily derived from continuity constraints across the junction. Specifically, referring to Fig.F.1b, let denote the physical force and its traveling-wave components within the ``pseudo-infinitesimal-generalized-waveguide'' defined by the element impedance , with the ` ' superscript denoting a right-going wave.

By the definition of wave impedance in a waveguide, we have

Thus,

Defining and , we have

Now that we've solved for the junction force , the outgoing waves are simply obtained from the force continuity constraint, :

Finally, the force-wave reflectance of an impedance step from to can be found by solving Eq. (F.3) and (F.2) for with set to zero:

as claimed.

[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