Editing Balanced line (section)

== Characteristic impedance ==
The [[characteristic impedance]] <math>Z_0</math> of a transmission line is an important parameter at higher frequencies of operation. For a parallel 2-wire transmission line,

:<math>Z_0 = \frac{1}{\pi}\sqrt{\frac{\mu}{\epsilon}} \ln\left(\frac{l}{R} + \sqrt{\left(\frac{l}{R}\right)^2-1}~\right),</math>

where <math>l</math> is half the distance between the wire centres, <math>R</math> is the wire radius and <math>\mu</math>, <math>\epsilon</math> are respectively the [[Permeability (electromagnetism)|permeability]] and [[permittivity]] of the surrounding medium. A commonly used approximation that is valid when the wire separation is much larger than the wire radius and in the absence of magnetic materials is

:<math>Z_0 = \frac{120 ~ \Omega}{\sqrt{\epsilon_r}}\ln\left(\frac{2l}{R}\right),
</math>

where <math>\epsilon_r</math> is the [[relative permittivity]] of the surrounding medium.