Characteristic admittance

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

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 $Y_{0}$ is the characteristic admittance of the line, then $I(x)/V(x)=Y_{0}$ for a wave moving rightward, or $I(x)/V(x)=-Y_{0}$ for a wave moving leftward.

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

where

$R$ is the resistance per unit length,

$L$ is the inductance per unit length,

$G$ is the conductance of the dielectric per unit length,

$C$ is the capacitance per unit length,

$j$ is the imaginary unit, and

$\omega$ is the angular frequency.

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

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

where the superscripts $+$ and $-$ represent forward- and backward-traveling waves, respectively.

See also

• Characteristic impedance

References

• Guile, A. E. (1977). Electrical Power Systems. ISBN 0-08-021729-X.
• Pozar, D. M. (February 2004). Microwave Engineering (3rd ed.). ISBN 0-471-44878-8.
• Ulaby, F. T. (2004). Fundamentals Of Applied Electromagnetics (media ed.). Prentice Hall. ISBN 0-13-185089-X.