Wave impedance

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 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 (real) electric permittivity and σ is the electrical conductivity of the material the wave is travelling through (corresponding to the imaginary component of the permittivity multiplied by omega).

In the equation, j is the imaginary unit, and ω is the angular frequency of the wave.

In the case of an ideal dielectric (where the conductivity is zero), the equation reduces to the real number In free space the wave impedance of plane waves is: (where ε0 is the permittivity constant in free space and μ0 is the permeability constant in free space).

[1] In an isotropic, homogeneous dielectric with negligible magnetic properties, i.e.

For transverse electric (TE) modes of propagation the wave impedance is:[2] where fc is the cut-off frequency of the mode, and for transverse magnetic (TM) modes of propagation the wave impedance is:[2] Above the cut-off (f > fc), the impedance is real (resistive) and the wave carries energy.

Below cut-off the impedance is imaginary (reactive) and the wave is evanescent.

These expressions neglect the effect of resistive loss in the walls of the waveguide.

The presence of the dielectric also modifies the cut-off frequency fc.

For a waveguide or transmission line containing more than one type of dielectric medium (such as microstrip), the wave impedance will in general vary over the cross-section of the line.

This article incorporates public domain material from Federal Standard 1037C.

Impedance mismatch leads to reflections.
To avoid reflections, the impedance of two media must match. On the other hand, even if the real part of the refractive index is the same, but one has a large absorption coefficient, the impedance mismatch will make the interface highly reflective.