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Two conductors embedded in a dielectric medium

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RLGC Model Waves in Transmission Lines

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Voltage and Current Wave Equations (Telegrapher’s Equations)

$$ \frac{\partial V(z, t)}{\partial z} = -L' \frac{\partial I(z, t)}{\partial t} - R' I(z, t) \newline \frac{\partial I(z, t)}{\partial z} = -C' \frac{\partial V(z, t)}{\partial t} - G' V(z, t) $$

Wave Equations in the Frequency Domain

$$ \frac{\partial^2 \tilde{V}(z)}{\partial z^2} = (\gamma^2) \tilde{V}(z) $$

Voltage and Current Solutions

$$ \tilde{V}(z) = V_0^+ e^{-\gamma z} + V_0^- e^{\gamma z} \newline \tilde{I}(z) = \frac{V_0^+}{Z_0} e^{-\gamma z} - \frac{V_0^-}{Z_0} e^{\gamma z} $$

Boundary Conditions and Matching