Editing Propagation constant (section)

===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>