Physics:Characteristic admittance
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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 [math]\displaystyle{ Y_0 }[/math] is the characteristic admittance of the line, then [math]\displaystyle{ I(x) / V(x) = Y_0 }[/math] for a wave moving rightward, or [math]\displaystyle{ I(x)/V(x) = -Y_0 }[/math] 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:
- [math]\displaystyle{ Y_0=\sqrt{\frac{G+j\omega C}{R+j\omega L}} }[/math]
where
- [math]\displaystyle{ R }[/math] is the resistance per unit length,
- [math]\displaystyle{ L }[/math] is the inductance per unit length,
- [math]\displaystyle{ G }[/math] is the conductance of the dielectric per unit length,
- [math]\displaystyle{ C }[/math] is the capacitance per unit length,
- [math]\displaystyle{ j }[/math] is the imaginary unit, and
- [math]\displaystyle{ \omega }[/math] is the angular frequency.
The current and voltage phasors on the line are related by the characteristic admittance as:
- [math]\displaystyle{ \frac{I^+}{V^+} = Y_0 = -\frac{I^-}{V^-} }[/math]
where the superscripts [math]\displaystyle{ + }[/math] and [math]\displaystyle{ - }[/math] represent forward- and backward-traveling waves, respectively.
See also
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.
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