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Choosing Impedance to Simplify Element Reflectance

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 $ R_0 = 1/C$ gives

    $\displaystyle \fbox{$\displaystyle \hat{\rho}_C(s) = \frac{1 - s}{1 + s}$} \protect$ (F.8)

  • For the inductor, setting $ R_0=L$ gives

    $\displaystyle \fbox{$\displaystyle \hat{\rho}_L(s) = - \frac{1 - s}{1 + s}$} \protect$ (F.9)

  • And for the resistor, we set $ R_0 = R$ to obtain

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

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Resistor Reflectance