Starting with a dashpot with coefficient , we have
This time, choosing
equal to the element value gives
Conformally mapping the zero function yields the zero function so that
as well. Thus, the WDF of a dashpot
is a ``wave sink,'' as diagrammed in
In the context of waveguide theory, a zero reflectance corresponds to
a matched impedance, i.e., the terminating transmission-line
impedance equals the characteristic impedance of the line.
The difference equation for the wave digital dashpot is simply
. While this may appear overly degenerate at first,
remember that the interface to the element is a port at impedance
. Thus, in this particular case only, the infinitesimal
waveguide interface is the element itself.
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