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.
Definition
300px|thumb|right|alt=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.
The wave impedance is given by
: <math>Z = {E_0^-(x) \over H_0^-(x)}</math>
where <math>E_0^-(x)</math> is the electric field and <math>H_0^-(x)</math> is the magnetic field, in phasor representation. The impedance is, in general, a complex number.
In terms of the parameters of an electromagnetic wave and the medium it travels through, the wave impedance is given by
: <math>Z = \sqrt {j \omega \mu \over \sigma + j \omega \varepsilon} </math>
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. Just as for electrical impedance, the impedance is a function of frequency. In the case of an ideal dielectric (where the conductivity is zero), the equation reduces to the real number
: <math>Z = \sqrt {\mu \over \varepsilon }.</math>
In free space
In free space the wave impedance of plane waves is:
: <math>Z_0 = \sqrt{\frac{\mu_0} {\varepsilon_0</math>
(where ε<sub>0</sub> is the permittivity constant in free space and μ<sub>0</sub> is the permeability constant in free space). Now, since
: <math>c = \frac{1}{\sqrt{\mu_0 \varepsilon_0 = 299\,792\,458\text{ m/s}</math> (by definition of the metre),
: <math>Z_0 = \mu_0 c = \frac{1}{\varepsilon_0 c}</math>.
The currently accepted value of <math>Z_0</math> is
In an unbounded dielectric
In an isotropic, homogeneous dielectric with negligible magnetic properties, i.e. <math>\mu = \mu_0 </math> and <math>\varepsilon = \varepsilon_r \varepsilon_0</math>. So, the value of wave impedance in a perfect dielectric is
: <math>Z = \sqrt {\mu \over \varepsilon} = \sqrt {\mu_0 \over \varepsilon_0 \varepsilon_r} = {Z_0 \over \sqrt{\varepsilon_r \approx {377 \over \sqrt {\varepsilon_r} }\,\Omega</math>,
where <math>\varepsilon_r</math> is the relative dielectric constant.
In a waveguide
For any waveguide in the form of a hollow metal tube, (such as rectangular guide, circular guide, or double-ridge guide), the wave impedance of a travelling wave is dependent on the frequency <math>f</math>, but is the same throughout the guide. For transverse electric (TE) modes of propagation the wave impedance is:
: <math>Z = \frac{Z_{0{\sqrt{1 - \left( \frac{f_{c{f}\right)^{2} \qquad \mbox{(TE modes)},</math>
where f<sub>c</sub> is the cut-off frequency of the mode, and for transverse magnetic (TM) modes of propagation the wave impedance is: