Wave impedance

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Wave impedance is the ratio of the electric field strength to the magnetic field strength of an electromagnetic wave. The symbol Z is used to represent it and it's given in units of ohms, sybolized by the uppercase omega (Ω). The symbol η (eta) is may be used instead of Z for wave impedance to avoid confusion with electrical impedance, although η is also the symbol for electromagnetic impedance, the light wave equivalent of wave impedance.

The characteristic equation of wave impedance is given by:

Z = {Eo^-(x) \over Ho^- (x)}

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

Z = \sqrt {j \omega \mu \over \sigma + j \omega \varepsilon}

Where μ is the magnetic permeability, ε is the electric permittivity and σ is the 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 conductivity is zero), the equation reduces to:

Z = \sqrt {\mu \over \varepsilon }

[edit] Wave impedance of free space

In free space, \mu=4\pi \times 10^{-7} H/m and \varepsilon = {1 \over 36\pi} F/m. So, the value of wave impedance in free space is:

Z0 = 377 Ω

In a perfect dielectric, the wave impedance can be found by dividing Z0 into the refractive index. In anything else, the formula become larger and a complex number is the result.

[edit] Designing a wave guide

In electrical engineering, the wave impedance is an important factor to consider when designing a waveguide. The parameters of the medium must match up such that the wave impedance will be the desired value. For example, coaxial cable used for TV signals has a designated wave impedance of 75 Ω. The desired wave impedance gives the wave of a particular range of frequecies a better propogation.


Source: from Federal Standard 1037C and from MIL-STD-188

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