Digitized Reflectances Without Delay-Free Paths

Plan:

1. Fix the bilinear-transform frequency-scaling parameter $c$ once for the whole system (so there is only one frequency-warping)
2. Set the ``connector'' wave impedance $R_0$ separately for each circuit element to eliminate the delay-free path in its reflectance
3. We will then get scattering when we connect different elements together

This yields the following elementary reflectances:

$$\begin{eqnarray*} \hbox{\textbf{\underline{Element}}} && \hbox{\textbf{\underline{Reflectance}}}\\ \hbox{\emph{ideal spring (capacitor)}} &\leftrightarrow& \hbox{\emph{unit delay}}\\ \hbox{\emph{ideal mass (inductor)}} &\leftrightarrow& \hbox{\emph{unit delay and sign inversion}}\\ \hbox{\emph{ideal dashpot (resistor)}} &\leftrightarrow& 0 \end{eqnarray*}$$

The original element values remain only in the waveguide-interface impedances $R_0=k/c,mc,\mu$