= Low-loss transmission-line attenuation
{title2=$\alpha=R'/(2Z_0)+G'Z_0/2$}
For per-length line parameters $R',L',G',C'$ and $e^{-i\omega t}$ convention, a forward factor $e^{-\Gamma z}$ has $\Gamma^2=(R'-i\omega L')(G'-i\omega C')$. Expanding about the lossless limit with $R'\ll\omega L'$ and $G'\ll\omega C'$ gives $\Gamma\simeq\alpha-i\omega\sqrt{L'C'}$, with $Z_0=\sqrt{L'/C'}$ and the displayed <amplitude> attenuation. Power decays twice as fast in the exponent. Terminal reflection is a separate power-return mechanism and need not be dissipative.
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