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
The wave impedance is given by
Z = E 0 − ( x ) H 0 − ( x ) {\displaystyle Z={E_{0}^{-}(x) \over H_{0}^{-}(x)}}
where E 0 − ( x ) {\displaystyle E_{0}^{-}(x)} is the electric field and H 0 − ( x ) {\displaystyle H_{0}^{-}(x)} 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
Z = j ω μ σ + j ω ε {\displaystyle Z={\sqrt {j\omega \mu \over \sigma +j\omega \varepsilon }}}
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
Z = μ ε . {\displaystyle Z={\sqrt {\mu \over \varepsilon }}.}
In free space
In free space the wave impedance of plane waves is:
Z 0 = μ 0 ε 0 {\displaystyle Z_{0}={\sqrt {\frac {\mu _{0}}{\varepsilon _{0}}}}}
(where ε0 is the permittivity constant in free space and μ0 is the permeability constant in free space). Now, since
c = 1 μ 0 ε 0 = 299 792 458 m/s {\displaystyle c={\frac {1}{\sqrt {\mu _{0}\varepsilon _{0}}}}=299\,792\,458{\text{ m/s}}} (by definition of the metre),
Z 0 = μ 0 c = 1 ε 0 c {\displaystyle Z_{0}=\mu _{0}c={\frac {1}{\varepsilon _{0}c}}} . The currently accepted value of Z 0 {\displaystyle Z_{0}} is 376.730313412(59) Ω.
In an unbounded dielectric In an isotropic, homogeneous dielectric with negligible magnetic properties, i.e. μ = μ 0 {\displaystyle \mu =\mu _{0}} and ε = ε r ε 0 {\displaystyle \varepsilon =\varepsilon _{r}\varepsilon _{0}} . So, the value of wave impedance in a perfect dielectric is
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