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Schematic representation of a circuit

where a source is coupled to a load

with a transmission line having

characteristic impedanceZ0.

Schematic representation of the

elementary components of a

transmission line.

Characteristic impedanceFrom Wikipedia, the free encyclopedia

The characteristic impedance orsurge impedance of a

uniform transmission line, usually writtenZ0, is the ratioof the amplitudes of a single pair of voltage and currentwaves propagating along the line in the absence ofreflections. The SI unit of characteristic impedance is theohm. The characteristic impedance of a losslesstransmission line is purely real, that is, there is no

imaginary component (Z0 = |Z0 | +j0). Characteristicimpedance appears like a resistance in this case, such that

power generated by a source on one end of an infinitelylong lossless transmission line is transmitted through theline but is not dissipated in the line itself. A transmission line of finite length (lossless or lossy)

that is terminated at one end with a resistor equal to the characteristic impedance (ZL =Z0)appears to the source like an infinitely long transmission line.

Contents

1 Transmission line model2 Lossless line3 Surge impedance loading4 See also5 References6 External links

Transmission line model

Basic definitionThe ratio of voltage applied to the current is called the input impedance; the input impedanceof the infinite line is called the characteristic impedance.

Applying the transmission line model based on thetelegrapher's equations, the general expression for thecharacteristic impedance of a transmission line is:

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,Cis the capacitance per unit length,j is the imaginary unit, and is the angular frequency.

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

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

Lossless line

For a lossless line,R and G are both zero, so the equation for characteristic impedance reduces to:

The imaginary termj has also canceled out, makingZ0 a real expression, and so is purely resistive

with a magnitude of .

Surge impedance loading

In electric power transmission, the characteristic impedance of a transmission line is expressed interms of the surge impedance loading (SIL), or natural loading, being the power loading atwhich reactive power is neither produced nor absorbed:

in which VLL is the line-to-line voltage in volts.

Loaded below its SIL, a line supplies lagging reactive power to the system, tending to raise systemvoltages. Above it, the line absorbs reactive power, tending to depress the voltage. The Ferrantieffect describes the voltage gain towards the remote end of a very lightly loaded (or open ended)transmission line. Underground cables normally have a very low characteristic impedance,

resulting in an SIL that is typically in excess of the thermal limit of the cable. Hence a cable isalmost always a source of lagging reactive power.

See also

Ampre's circuital lawElectrical impedanceMaxwell's equationsTransmission lineWave impedance

References

Guile, A. E. (1977).Electrical Power Systems. ISBN 0-0802-1729-X.Pozar, D. M. (February 2004).Microwave Engineering (3rd edition ed.). ISBN 0-471-44878-8.

Ulaby, F. T. (2004). Fundamentals Of Applied Electromagnetics (media edition ed.).Prentice Hall. ISBN 0-13-185089-X.

External links

This article incorporates public domain material from the General Services Administrationdocument "Federal Standard 1037C" (http://www.its.bldrdoc.gov/fs-1037/fs-1037c.htm) .

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