Wave Impedance

Any material has a wave impedance for propagating electromagnetic waves.
This impedance relates the electric and magnetic field magnitudes.

$$\eta = \frac{E}{H}$$

Notice the similarity to Ohm’s law:
$$Z = \frac{V}{I}$$

For a general material:
$$\eta = \sqrt{\frac{j\omega\mu}{\sigma+j\omega\epsilon}} \hspace{5 mm}\Omega$$

Special Cases

The impedance formula simplifies for several special cases described below.

Free space

Free space is primarily air or vacuum. Any lossless dielectric with a dielectric close to 1 can be considered free space.
$$
\epsilon = \epsilon_0=8.854\times 10^{-12} \hspace{5 mm}F/m\\
\mu = \mu_0=4\pi\times 10^{-7} \hspace{5 mm}H/m\\
\sigma = 0\\
\eta = \sqrt{\frac{\mu_0}{\epsilon_0}} = 377 \hspace{5 mm}\Omega
$$

Lossless Dielectric

Any dielectric with low loss, such as teflon, glass, etc.
$$
\epsilon = \epsilon_r\epsilon_0\\
\mu = \mu_r\mu_0\\
\sigma = 0\\
\eta = \sqrt{\frac{\mu_r\mu_0}{\epsilon_r\epsilon_0}} = 377\sqrt{\frac{\mu_r}{\epsilon_r}} \hspace{5 mm}\Omega
$$

Conductor

Any good conductor, primarily metallic materials.
$$
\mu = \mu_r\mu_0\\
\sigma \gg \omega\epsilon\\
\eta = \sqrt{\frac{\omega\mu_r\mu_0}{\sigma}}\angle{-45^{\circ}} \hspace{5 mm}\Omega
$$

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