Characteristic Impedance

Information about Characteristic Impedance

This article is about impedance in electronics. For characteristic acoustic impedance, see acoustic impedance.

Schematic representation of a transmission line, showing the characteristic impedance math:4/15B39E3B3ACEBE08.gif.

The characteristic impedance or surge impedance of a uniform transmission line, usually written $\text{[math]}$ , is the ratio of the amplitudes of a single pair of voltage and current waves propagating along the line in the absence of reflections. The SI unit of characteristic impedance is the ohm. The characteristic impedance of a lossless transmission line is purely real, that is, there is no imaginary component ( $\text{[math]}$ ). Characteristic impedance appears like a resistance in this case, such that power generated by a source on one end of an infinitely long lossless transmission line is dissipated through the line 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 ( $\text{[math]}$ ) appears like an infinitely long transmission line to the source.

Transmission line model

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

$\text{[math]}$

where

$\text{[math]}$ is the resistance per unit length,

$\text{[math]}$ is the inductance per unit length,

$\text{[math]}$ is the conductance of the dielectric per unit length,

$\text{[math]}$ is the capacitance per unit length,

$\text{[math]}$ is the imaginary unit, and

$\text{[math]}$ is the angular frequency.

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

$\text{[math]}$

where the superscripts $\text{[math]}$ and $\text{[math]}$ represent forward- and backward-traveling waves, respectively.

Lossless line

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

$\text{[math]}$ .

Surge Impedance Loading

In electric power transmission, the characteristic impedance of a transmission line is expressed in terms of the surge impedance loading (SIL), or natural loading, being the MW loading at which reactive power is neither produced nor absorbed:

$\text{[math]}$

in which $\text{[math]}$ is the line-to-line voltage in volts.

Loaded below its SIL, a line supplies lagging reactive power to the system, tending to raise system voltages. Above it, the line absorbs reactive power, tending to depress the voltage. The Ferranti Effect 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 is almost always a source of lagging reactive power.

References

Guile, A. E. (1977). Electrical Power Systems. ISBN 0-0802-1729-X.
Pozar, D. M. (February 2004). Microwave Engineering, 3rd edition. ISBN 0-471-44878-8.
Ulaby, F. T. (2004). Fundamentals Of Applied Electromagnetics, media edition. ISBN 0-13-185089-X.

Weblinks

Spannungswellen auf einer Leitung - Applet (Ger)

This article contains material from the Federal Standard 1037C, which, as a work of the United States Government, is in the public domain.

The acoustic impedance Z (or sound impedance) is a frequency f dependent parameter and is very useful, for example, for describing the behaviour of musical wind instruments.
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A transmission line is the material medium or structure that forms all or part of a path from one place to another for directing the transmission of energy, such as electromagnetic waves or acoustic waves, as well as electric power transmission.
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Si, si, or SI may refer to (all SI unless otherwise stated):

In language:

One of two Italian words:
sì (accented) for "yes"
si

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Electrical impedance, or simply impedance, describes a measure of opposition to a sinusoidal alternating current (AC). Electrical impedance extends the concept of resistance to AC circuits, describing not only the relative magnitudes of the voltage and current, but also the
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ohm (symbol: Ω) is the SI unit of electrical impedance or, in the direct current case, electrical resistance, named after Georg Ohm.

Definition

An ohm is the electrical resistance offered by a current-carrying element that produces a voltage drop of one volt when a
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The telegrapher's equations (or just telegraph equations) are a pair of linear differential equations which describe the voltage and current on an electrical transmission line with distance and time.
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Electrical resistance is a measure of the degree to which an object opposes an electric current through it. The SI unit of electrical resistance is the ohm. Its reciprocal quantity is electrical conductance measured in siemens.
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inductance, or more accurately self-inductance of the circuit. The term was coined by Oliver Heaviside in February 1886. It is customary to use the symbol for inductance, possibly in honour of the physicist Heinrich Lenz.
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Electrical conductance is the reciprocal of electrical resistance. It is a measure of how easily electricity flows along a certain path through an electrical element. The SI derived unit of conductance is the siemens (formerly referred to as the reciprocal ohm or mho).
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Capacitance is a measure of the amount of electric charge stored (or separated) for a given electric potential. The most common form of charge storage device is a two-plate capacitor.
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In mathematics, the imaginary unit (or sometimes the Latin or the Greek iota, see below) allows the real number system to be extended to the complex number system . Its precise definition is dependent upon the particular method of extension.
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angular frequency ω (also referred to by the terms angular speed, radial frequency, and radian frequency) is a scalar measure of rotation rate. Angular frequency is the magnitude of the vector quantity angular velocity.
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In circuit analysis a phasor is a vector with constant length (A) and constant phase angle (θ). It is usually represented as a complex exponential, A•e^{j θ}.
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Electric power transmission, a process in the delivery of electricity to consumers, is the bulk transfer of electrical power. Typically, power transmission is between the power plant and a substation near a populated area.
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Voltage (sometimes also called electric potential difference or electrical tension) is the potential similarity of electrical potential between two points of an electrical or electronic circuit, expressed in volts.
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volt (symbol: V) is the SI derived unit of electric potential difference or electromotive force.^[1]^[2] It is named in honor of the Italian physicist Alessandro Volta (1745–1827), who invented the voltaic pile, the first modern chemical battery.
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cable is one or more wires or optical fibers bound together, typically in a common protective jacket or sheath. The individual wires or fibers inside the jacket may be covered or insulated. Combination cables may contain both electrical wires and optical fibers.
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For thermodynamic relations, see .

In electromagnetism, Maxwell's equations are a set of four equations that were first presented as a distinct group in 1884 by Oliver Heaviside in conjunction with Willard Gibbs.
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Federal Standard 1037C, entitled Telecommunications: Glossary of Telecommunication Terms is a United States Federal Standard, issued by the General Services Administration pursuant to the Federal Property and Administrative Services Act of 1949, as amended.
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A work of the United States government, as defined by United States copyright law, is "a work prepared by an officer or employee of the U.S. government as part of that person's official duties.
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Public domain comprises the body of knowledge and innovation (especially creative works such as writing, art, music, and inventions) in relation to which no person or other legal entity can establish or maintain proprietary interests within a particular legal jurisdiction.
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Characteristic Impedance

Information about Characteristic Impedance

Transmission line model

Lossless line

Surge Impedance Loading

See also

References

Weblinks

Definition