Characteristic admittance

Characteristic admittance is the mathematical inverse of the characteristic impedance. The general expression for the characteristic admittance of a transmission line is:

${\displaystyle Y_{0}={\sqrt {\frac {G+j\omega C}{R+j\omega L}}}}$

A transmission line is drawn as two black wires. At a distance x into the line, there is current phasor I(x) traveling through each wire, and there is a voltage difference phasor V(x) between the wires (bottom voltage minus top voltage). If ${\displaystyle Y_{0}}$ is the characteristic admittance of the line, then ${\displaystyle I(x)/V(x)=Y_{0}}$ for a wave moving rightward, or ${\displaystyle I(x)/V(x)=-Y_{0}}$ for a wave moving leftward.

where

${\displaystyle R}$ is the resistance per unit length,

${\displaystyle L}$ is the inductance per unit length,

${\displaystyle G}$ is the conductance of the dielectric per unit length,

${\displaystyle C}$ is the capacitance per unit length,

${\displaystyle j}$ is the imaginary unit, and

${\displaystyle \omega }$ is the angular frequency.

The current and voltage phasors on the line are related by the characteristic admittance as:

${\displaystyle {\frac {I^{+}}{V^{+}}}=Y_{0}=-{\frac {I^{-}}{V^{-}}}}$

where the superscripts ${\displaystyle +}$ and ${\displaystyle -}$ represent forward- and backward-traveling waves, respectively.