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Characteristic impedance

 

 
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Characteristic impedance
 
 
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The characteristic impedance or surge impedance of a uniform transmission line
Transmission line

A transmission line is the material Transmission medium or structure that forms all or part of a Course from one place to another for directing the transmission of energy, such as electromagnetic waves or acoustic waves, as well as electric power transmission....
, usually written , 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
Si

Si, si, or SI may refer to :...
 unit of characteristic impedance
Electrical impedance

Electrical impedance, or simply impedance, describes a measure of opposition to a sinusoidal alternating current . Electrical impedance extends the concept of Electrical resistance to AC circuits, describing not only the relative amplitudes of the voltage and Electric current, but also the relative Phase ....
 is the ohm. The characteristic impedance of a lossless transmission line is purely real, that is, there is no imaginary component .






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The characteristic impedance or surge impedance of a uniform transmission line
Transmission line

A transmission line is the material Transmission medium or structure that forms all or part of a Course from one place to another for directing the transmission of energy, such as electromagnetic waves or acoustic waves, as well as electric power transmission....
, usually written , 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
Si

Si, si, or SI may refer to :...
 unit of characteristic impedance
Electrical impedance

Electrical impedance, or simply impedance, describes a measure of opposition to a sinusoidal alternating current . Electrical impedance extends the concept of Electrical resistance to AC circuits, describing not only the relative amplitudes of the voltage and Electric current, but also the relative Phase ....
 is the ohm. The characteristic impedance of a lossless transmission line is purely real, that is, there is no imaginary component . 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 appears like an infinitely long transmission line to the source.

Transmission line model


Basic definition:The ratio of voltage applied to the current is called the input impedance; the input impedance of the infinite line is called the characteristic impedance.

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

where is the resistance
Electrical resistance

The electrical resistance of an object is a measure of its opposition to the passage of a steady electrical current. An object of uniform cross section will have a resistance proportional to its length and inversely proportional to its cross-sectional area, and proportional to the resistivity of the material....
 per unit length, is the inductance
Inductance

Inductance is the property in an electrical circuit where a change in the current flowing through that circuit induces an Electromotive force that opposes the change in current ....
 per unit length, is the conductance
Electrical conductance

Electrical conductance 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 ....
 of the dielectric per unit length, is the capacitance
Capacitance

In electromagnetism and electronics, capacitance is the ability of a body to hold an electrical charge.Capacitance is also a measure of the amount of electric charge stored for a given electric potential....
 per unit length, is the imaginary unit
Imaginary unit

In mathematics, physics, and engineering, the imaginary unit is denoted by  or the Latin   or the Greek iota . It allows the real number system, to be extended to the complex number system,   Its precise definition is dependent upon the particular method of extension....
, and is the angular frequency
Angular frequency

In physics , angular frequency ? is a scalar measure of rotation rate. Angular frequency is the magnitude of the vector quantity angular velocity....
.

The voltage and current phasor
Phasor (electronics)

In physics and engineering, a phase vector is a representation of a sine wave whose amplitude , phase , and frequency are time-invariant. It is a subset of a more general concept called analytic signal....
s on the line are related by the characteristic impedance as:

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 term j has also canceled out, making Z0 a real expression, and so is purely resistive with a magnitude of .

Surge Impedance Loading


In electric power transmission
Electric power transmission

Electric power transmission is the bulk transfer of electrical power , a process in the delivery of electricity to consumers. A power transmission grid typically connects power plants to multiple Electrical substation near a populated area....
, 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:

in which is the line-to-line voltage
Voltage

Electrical tension is the potential difference between two points of an electrical or electronic circuit, expressed in volts. It is the measurement of the potential for an electric field to cause an electric current in an electrical conductor....
 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
Ferranti effect

The Ferranti Effect is a rise in voltage occurring at the receiving end of a long transmission line, relative to the voltage at the sending end, which occurs when the line is charged but there is a very light load or the load is disconnected....
 describes the voltage gain towards the remote end of a very lightly loaded (or open ended) transmission line. Underground cable
Cable

A cable is a large fiber or metal rope, used for hauling, lifting, or towing, or an assembly of two or more insulated electrical conductors, laid up together as an assembly....
s 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.

See also

  • Transmission line
    Transmission line

    A transmission line is the material Transmission medium or structure that forms all or part of a Course from one place to another for directing the transmission of energy, such as electromagnetic waves or acoustic waves, as well as electric power transmission....
  • Maxwell's equations
    Maxwell's equations

    In electromagnetism, James Clerk Maxwell equations are a set of four partial differential equations that describe the properties of the electric field and magnetic field fields and relate them to their sources, charge density and current density....


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