Editing Propagation constant (section)

==Attenuation constant==

In [[telecommunications]], the term '''attenuation constant''', also called '''attenuation parameter''' or '''[[attenuation coefficient]]''', is the attenuation of an electromagnetic wave propagating through a [[Transmission medium|medium]] per unit distance from the source. It is the real part of the propagation constant and is measured in [[neper]]s per metre.  A neper is approximately 8.7&nbsp;[[decibel|dB]].  Attenuation constant can be defined by the amplitude ratio

:<math>\left|\frac{A_0}{A_x}\right|=e^{\alpha x}</math>

The propagation constant per unit length is defined as the natural logarithm of the ratio of the sending end current or voltage to the receiving end current or voltage, divided by the distance ''x'' involved:

:<math>\alpha=\ln\left(\left|\frac{A_0}{A_x}\right|\right)/x</math>

===Conductive lines===

The attenuation constant for conductive lines can be calculated from the primary line coefficients as shown above.  For a line meeting the [[Heaviside condition|distortionless condition]], with a conductance ''G'' in the insulator, the attenuation constant is given by

:<math>\alpha=\sqrt{RG}\,\!</math>

however, a real line is unlikely to meet this condition without the addition of [[loading coils]] and, furthermore, there are some frequency dependent effects operating on the primary "constants" which cause a frequency dependence of the loss.  There are two main components to these losses, the metal loss and the dielectric loss.

The loss of most transmission lines are dominated by the metal loss, which causes a frequency dependency due to finite conductivity of metals, and the [[skin effect]] inside a conductor. The skin effect causes R along the conductor to be approximately dependent on frequency according to

:<math>R \propto \sqrt{\omega}</math>

Losses in the dielectric depend on the [[loss tangent]] (tan&nbsp;''δ'') of the material divided by the wavelength of the signal. Thus they are directly proportional to the frequency.

:<math>\alpha_d={{\pi}\sqrt{\varepsilon_r}\over{\lambda}}{\tan \delta}</math>

===Optical fiber===

The attenuation constant for a particular [[propagation mode]] in an [[optical fiber]] is the real part of the axial propagation constant.