Wave impedance

 related topics {math, energy, light}

The wave impedance of an electromagnetic wave is the ratio of the transverse components of the electric and magnetic fields (the transverse components being those at right angles to the direction of propagation). For a transverse-electric-magnetic (TEM) plane wave traveling through a homogeneous medium, the wave impedance is everywhere equal to the intrinsic impedance of the medium. In particular, for a plane wave travelling through empty space, the wave impedance is equal to the impedance of free space. The symbol Z is used to represent it and it is expressed in units of ohms. The symbol η (eta) may be used instead of Z for wave impedance to avoid confusion with electrical impedance.

The wave impedance is given by

where $E_0^-(x)$ is the electric field and $H_0^-(x)$ is the magnetic field, in phasor representation.

In terms of the parameters of an electromagnetic wave and the medium it travels through, the wave impedance is given by

where μ is the magnetic permeability, ε is the electric permittivity and σ is the electrical conductivity of the material the wave is travelling through. In the equation, j is the imaginary unit, and ω is the angular frequency of the wave. In the case of a dielectric (where the conductivity is zero), the equation reduces to

As usual for any electrical impedance, the ratio is defined only for the frequency domain and never in the time domain.

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Wave impedance of free space

In free space, $\scriptstyle \mu=4\pi \times 10^{-7}$ H/m and $\varepsilon\approx 8.854\times 10^{-12}$ F/m. So, the value of wave impedance in free space is

Wave impedance in an unbounded dielectric

In a perfect dielectric, $\scriptstyle \mu=4\pi \times 10^{-7}$ H/m and $\varepsilon = \varepsilon_r \times 8.854\times 10^{-12}$ F/m. So, the value of wave impedance in a perfect dielectric is

In a perfect dielectric, the wave impedance can be found by dividing Z0 by the square root of the dielectric constant. In anything else, the formula becomes larger and a complex number is the result.