Editing Propagation constant (section)

===Plane wave===
The propagation factor of a plane wave traveling in a linear media in the {{mvar|x}} direction is given by
<math display="block"> P = e^{-\gamma x} </math>
where
* <math display="inline">\gamma = \alpha + i\ \beta = \sqrt{i\ \omega\ \mu\ (\sigma + i\ \omega \varepsilon)\ }\ </math><ref name="Jordon&Balman">{{cite book |last1=Jordon |first1=Edward C. |last2=Balman |first2=Keith G. |year=1968 |title=Electromagnetic Waves and Radiating Systems |edition=2nd |publisher=Prentice-Hall }}</ref>{{rp|p=126}}
* <math> x = </math>  distance traveled in the {{mvar|x}} direction
* <math> \alpha =\ </math> [[attenuation constant]] in the units of [[neper]]s/meter
* <math> \beta =\ </math> [[phase constant]] in the units of [[radian]]s/meter
* <math> \omega=\ </math> frequency in radians/second
* <math> \sigma =\ </math> [[Electrical resistivity and conductivity|conductivity]] of the media
* <math>\varepsilon = \varepsilon' - i\ \varepsilon'' \ </math> = [[Permittivity#Complex permittivity|complex permitivity]] of the media
* <math>\mu = \mu' - i\ \mu'' \;</math> = [[Permeability (electromagnetism)#Complex permeability|complex permeability]] of the media
* <math>i \equiv \sqrt{-1\ }</math>
The sign convention is chosen for consistency with propagation in lossy media. If the attenuation constant is positive, then the wave amplitude decreases as the wave propagates in the {{mvar|x}} direction.

[[Wavelength]], [[phase velocity]], and [[skin effect|skin depth]] have simple relationships to the components of the propagation constant:
<math display="block"> \lambda = \frac {2 \pi}{\beta} \qquad  v_p = \frac{\omega}{\beta}  \qquad   \delta =  \frac{1}{\alpha} </math>