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 Fig.F.4.
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.