Editing Transmission line (section)

==The four terminal model==


[[Image:Transmission line 4 port.svg|right]]

[[Image:Transmission line symbols.svg|thumb|right|310px|Variations on the [[electronic schematic|schematic]] [[electronic symbol]] for a transmission line]]

For the purposes of analysis, an electrical transmission line can be modelled as a [[two-port network]] (also called a quadripole), as follows:

In the simplest case, the network is assumed to be linear (i.e. the [[complex number|complex]] voltage across either port is proportional to the complex current flowing into it when there are no reflections), and the two ports are assumed to be interchangeable.  If the transmission line is uniform along its length, then its behaviour is largely described by two parameters called ''[[characteristic impedance]]'', symbol Z<sub>0</sub> and ''[[Signal propagation delay|propagation delay]]'', symbol <math> \tau_p </math>.  Z<sub>0</sub> is the ratio of the complex voltage of a given wave to the complex current of the same wave at any point on the line. Typical values of Z<sub>0</sub> are 50 or 75 [[Ohm (unit)|ohm]]s for a [[coaxial cable]], about 100 ohms for a twisted pair of wires, and about 300 ohms for a common type of untwisted pair used in radio transmission. Propagation delay is proportional to the length of the transmission line and is never less than the length divided by the [[speed of light]].  Typical delays for modern communication transmission lines vary from {{val|3.33|u=ns/m}} to {{val|5|u=ns/m}}.

When sending power down a transmission line, it is usually desirable that as much power as possible will be absorbed by the load and as little as possible will be reflected back to the source.  This can be ensured by making the load impedance equal to Z<sub>0</sub>, in which case the transmission line is said to be ''[[impedance matching|matched]]''.

[[File:TransmissionLineDefinitions.svg|thumb|right|310px|A transmission line is drawn as two black wires. At a distance ''x'' into the line, there is current ''I(x)'' travelling through each wire, and there is a voltage difference ''V(x)'' between the wires. If the current and voltage come from a single wave (with no reflection), then ''V''(''x'')&nbsp;/&nbsp;''I''(''x'')&nbsp;=&nbsp;''Z''<sub>0</sub>, where ''Z''<sub>0</sub> is the ''[[characteristic impedance]]'' of the line.]]

[[File:Gaussian pulse in a balanced transmission line.png|thumb|310px|Differential Gaussian pulse in a balanced transmission line]]

Some of the power that is fed into a transmission line is lost because of its resistance.  This effect is called ''ohmic'' or ''resistive'' loss (see [[ohmic heating]]).  At high frequencies, another effect called ''[[Dielectric absorption|dielectric loss]]'' becomes significant, adding to the losses caused by resistance.  Dielectric loss is caused when the insulating material inside the transmission line absorbs energy from the alternating electric field and converts it to [[heat]] (see [[dielectric heating]]). The transmission line is modelled with a resistance (R) and inductance (L) in series with a capacitance (C) and conductance (G) in parallel. The resistance and conductance contribute to the loss in a transmission line.

The total loss of power in a transmission line is often specified in [[decibels]] per [[metre]] (dB/m), and usually depends on the frequency of the signal.  The manufacturer often supplies a chart showing the loss in dB/m at a range of frequencies.  A loss of 3&nbsp;dB corresponds approximately to a halving of the power.

Propagation delay is often specified in units of [[nanoseconds]] per metre.  While propagation delay usually depends on the frequency of the signal, transmission lines are typically operated over frequency ranges where the propagation delay is approximately constant.
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