Choosing Impedance to Simplify Element Reflectance

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Observe that there is a natural choice for each waveguide impedance which will give us a normalized, ``universal reflectance'' for each element:

For the capacitor, setting gives

$\displaystyle \fbox{$\displaystyle \hat{\rho}_C(s) = \frac{1 - s}{1 + s}$} \protect$ (F.8)
For the inductor, setting gives

$\displaystyle \fbox{$\displaystyle \hat{\rho}_L(s) = - \frac{1 - s}{1 + s}$} \protect$ (F.9)
And for the resistor, we set to obtain

$\displaystyle \fbox{$\displaystyle \hat{\rho}_R(s) = 0$} \protect$ (F.10)

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Next: Digitizing Elementary Reflectances by Bilinear Transform

About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.

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