Characteristic admittance

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

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

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

where

R {\displaystyle R} is the resistance per unit length,
L {\displaystyle L} is the inductance per unit length,
G {\displaystyle G} is the conductance of the dielectric per unit length,
C {\displaystyle C} is the capacitance per unit length,
j {\displaystyle j} is the imaginary unit, and
ω {\displaystyle \omega } is the angular frequency.

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

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

where the superscripts + {\displaystyle +} and − {\displaystyle -} 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.