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The '''wave impedance''' of an [[electromagnetic wave]] is the [[ratio]] of the transverse components of the [[electric field|electric]] and [[magnetic field]]s (the transverse components being those at right angles to the direction of propagation). For a transverse-electric-magnetic ([[Transverse mode|TEM]]) [[plane wave]] traveling through a homogeneous [[medium (optics)|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 [[ohm]]s. The symbol η ([[eta]]) may be used instead of ''Z'' for wave impedance to avoid confusion with [[electrical impedance]].
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The wave impedance is given by
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:<math>Z = {E_0^-(x) \over H_0^-(x)} </math>
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where <math>E_0^-(x)</math> is the electric field and <math>H_0^-(x)</math> is the magnetic field, in phasor representation.
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In terms of the parameters of an electromagnetic wave and the medium it travels through, the wave impedance is given by
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:<math>Z = \sqrt {j \omega \mu \over \sigma + j \omega \varepsilon} </math>
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where μ is the [[magnetic permeability]], ε is the [[permittivity|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
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:<math>Z = \sqrt {\mu \over \varepsilon }.</math>
</ul>
 
As usual for any electrical impedance, the ratio is defined only for the [[frequency domain]] and never in the [[time domain]].
 
==Wave impedance in free space==
{{main|Impedance of free space}}
 
In [[free space]] the wave impedance of plane waves is:
 
::<math>Z_0 = \sqrt{\frac{\mu_0} {\epsilon_0}}</math>
 
and:
 
::<math>c_0 = \frac{1}{\sqrt{\mu_0 \epsilon_0}}</math>
 
hence, to the same accuracy as the 1983 definition of ''c'', the value in ohms is:
 
::<math>Z_0 = \mu_0 c_0 = 376.730313 </math>
 
==Wave impedance in an unbounded dielectric==
 
In a perfect [[dielectric]], <math>\scriptstyle \mu=4\pi \times 10^{-7} </math> H/m and <math>\varepsilon = \varepsilon_r \times 8.854\times 10^{-12}</math> F/m. So, the value of wave impedance in a perfect dielectric is
 
: <math>Z \approx {377 \over \sqrt {\varepsilon_r} }\,\Omega</math>.
 
In a perfect [[dielectric]], the wave impedance can be found by dividing ''Z''<sub>0</sub> by the square root of the [[dielectric constant]]. In anything else, the formula becomes larger and a complex number is the result.
 
==Wave impedance in a waveguide==
 
For any [[waveguide (electromagnetism)|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 ([[Transverse mode|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 mode|TM]]) modes
:<math>Z = Z_{0} \sqrt{1 - \left( \frac{f_{c}}{f}\right)^{2}} \qquad \mbox{(TM modes)}</math>
 
Above the cut-off  (''f'' > ''f''<sub>''c''</sub>), the impedance is real (resistive) and the wave carries energy. Below cut-off the impedance is imaginary (reactive) and the wave is [[evanescent wave|evanescent]]. These expressions neglect the effect of resistive loss in the walls of the waveguide. For a waveguide entirely filled with a homogeneous dielectric medium, similar expressions apply, but with the wave impedance of the medium replacing ''Z''<sub>0</sub>. The presence of the dielectric also modifies the cut-off frequency ''f''<sub>''c''</sub>.
 
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.
 
== References ==
{{FS1037C MS188}}
 
==See also==
* [[Characteristic impedance]]
* [[Impedance (disambiguation)]]
 
[[Category:Wave mechanics]]
[[Category:Electromagnetic radiation]]

Revision as of 18:15, 27 February 2014

Nike Shox Nz Note

Obey all the local parking signs; Finland tows away vehicles even if it does not operate a wheel clamping system. Cars must park facing the traffic and at least five metres from any pedestrian crossings or intersections.. The Finance Board spent hrs finalizing the city's revenue and reserve funds ahead of Tuesday's vote. Members voted to put aside $6.25 million in the contingency fund for unanticipated snow and storm expenses, legal claims and labor contract settlements.

Renly states that she must be the fire priestess he has heard so much about and jokes he now knows why Stannis found religion late in everyday life. Stannis warns his brother to watch his tongue. We also kindly ask that you wait to hear from us regarding the status of your application. Once your application is complete and given to the Committee for review we will email you, and if we have questions we will also seek to contact you via email.As mentioned in previous email, application processing will extend into January.

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