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{{About|the radio-frequency transmission line|the power transmission line|electric power transmission}}
{{Redirect2|UT1|UT|other uses of "UT1"|UT1 (disambiguation)|other uses of "UT"|UT (disambiguation)}}
[[File:Transmission line animation.gif|right|thumb|300px|Schematic showing how a wave flows down a lossless transmission line. Red color indicates high [[voltage]], and blue indicates low voltage. Black dots represent [[electron]]s. The line is terminated at an [[impedance matching|impedance-matched]] load resistor (box on right), which fully absorbs the wave.]]
'''Universal Time''' ('''UT''') is a [[time standard]] based on the rotation of the Earth. It is a modern continuation of [[Greenwich Mean Time]] (GMT), i.e., the [[mean solar time]] on the [[Prime Meridian]] at [[Royal Observatory, Greenwich|Greenwich]], and GMT is sometimes used loosely as a synonym for [[UTC]]. In fact, the expression "Universal Time" is ambiguous, as there are several versions of it, the most commonly used being UTC and UT1 (see below). All of these versions of UT are based on the rotation of the Earth in relation to distant celestial objects ([[star]]s and [[quasar]]s), but with a scaling factor and other adjustments to make them closer to [[solar time]].
[[Image:F-Stecker und Kabel.jpg|thumb|One of the most common types of transmission line, [[coaxial cable]]. ]]


In [[Telecommunications engineering|communications]] and [[electronic engineering]], a '''transmission line''' is a specialized cable or other structure designed to carry [[alternating current]] of [[radio frequency]], that is, currents with a [[frequency]] high enough that their [[wave]] nature must be taken into account.  Transmission lines are used for purposes such as connecting [[Transmitter|radio transmitters]] and [[Radio receiver|receivers]] with their [[antenna (radio)|antennas]], distributing [[cable television]] signals, [[trunking|trunklines]] routing calls between telephone switching centers, computer network connections, and high speed computer [[data bus]]es.
==Universal Time and standard time==
Prior to the introduction of [[standard time]], each municipality throughout the civilized world set its official clock, if it had one, according to the local position of the Sun (see [[solar time]]). This served adequately until the introduction of the [[steam engine]], the telegraph, and [[railroad|rail]] travel, which made it possible to travel fast enough over long distances to require almost constant re-setting of [[clock|timepiece]]s as a [[train]] progressed in its daily run through several towns. Standard time, where all clocks in a large region are set to the same time, was established to solve this problem. [[marine chronometer|Chronometer]]s or [[telegraphy]] were used to synchronize these clocks.{{sfn|Howse|1997|loc=ch. 4}}


This article covers two-conductor transmission line such as parallel line ([[ladder line]]), [[coaxial cable]], [[stripline]], and [[microstrip]].  Some sources also refer to [[waveguide]], [[dielectric waveguide]], and even [[optical fiber]] as transmission line, however these lines require different analytical techniques and so are not covered by this article; see [[Waveguide (electromagnetism)]].
[[Image:Standard time zones of the world.png|500px|thumb|right|Standard time zones of the world since September 20, 2011, instructions for converting UTC to or from local times are on the bottom, using addition or subtraction]]


== Overview ==
Standard time, as originally proposed by Scottish-Canadian Sir [[Sandford Fleming]] in 1879, divided the world into twenty-four [[time zone]]s, each one covering 15 degrees of longitude. All clocks within each zone would be set to the same time as the others, but differed by one hour from those in the neighboring zones. The local time at the [[Royal Greenwich Observatory]] in Greenwich, England was chosen as standard at the 1884 [[International Meridian Conference]], leading to the widespread use of Greenwich Mean Time to set local clocks. This location was chosen because by 1884 two-thirds of all [[nautical chart]]s and [[map]]s already used it as their [[prime meridian]].{{sfn|Howse|1997|loc=ch. 5}} The conference did not adopt Fleming's time zones because they were outside the purpose for which it was called, which was to choose a basis for universal time (as well as a prime meridian).
Ordinary electrical cables suffice to carry low frequency [[alternating current]] (AC), such as [[mains power]], which reverses direction 100 to 120 times per second, and [[audio signal]]s.  However, they cannot be used to carry currents in the [[radio frequency]] range or higher,<ref name="Jackman">{{cite book 
  | last = Jackman
  | first = Shawn M. 
  | coauthors = Matt Swartz, Marcus Burton, Thomas W. Head
  | title = CWDP Certified Wireless Design Professional Official Study Guide: Exam PW0-250
  | publisher = John Wiley & Sons
  | year = 2011
  | location =
  | pages = Ch. 7
  | url = http://books.google.com/books?id=AQ8WJGshLBEC&pg=PT300&lpg=PT300&dq=%22what+is+a+transmission+line?%22+%22A+cable's+nature
  | doi =
  | id =
  | isbn = 1118041615}}</ref> which reverse direction millions to billions of times per second, because the energy tends to radiate off the cable as [[radio wave]]s, causing power losses. Radio frequency currents also tend to reflect from discontinuities in the cable such as [[electrical connector|connectors]] and joints, and travel back down the cable toward the source.<ref name="Jackman" /><ref name="Oklobdzija">{{cite book 
  | last = Oklobdzija
  | first = Vojin G.
  | coauthors = Ram K. Krishnamurthy
  | title = High-Performance Energy-Efficient Microprocessor Design
  | publisher = Springer
  | year = 2006
  | location =
  | pages = 297
  | url = http://books.google.com/books?id=LmfHof1p3qUC&pg=PA297&dq=%22transmission+line%22+%22uniform
  | doi =
  | id =
  | isbn = 0387340475}}</ref>  These reflections act as bottlenecks, preventing the signal power from reaching the destination. Transmission lines use specialized construction, and [[impedance matching]], to carry electromagnetic signals with minimal reflections and power losses.  The distinguishing feature of most transmission lines is that they have uniform cross sectional dimensions along their length, giving them a uniform ''[[Electrical impedance|impedance]]'', called the [[characteristic impedance]],<ref name="Oklobdzija" /><ref name="Guru">{{cite book 
  | last = Guru
  | first = Bhag Singh 
  | coauthors = Hüseyin R. Hızıroğlu
  | title = Electromagnetic Field Theory Fundamentals, 2nd Ed.
  | publisher = Cambridge Univ. Press
  | year = 2004
  | location =
  | pages = 422–423
  | url = http://books.google.com/books?id=qzNdDtZUPXMC&pg=PA422&dq=%22transmission+line%22+uniform
  | doi =
  | id =
  | isbn = 1139451928}}</ref><ref name="Schmitt">{{cite book 
  | last = Schmitt
  | first = Ron Schmitt
  | title = Electromagnetics Explained: A Handbook for Wireless/ RF, EMC, and High-Speed Electronics
  | publisher = Newnes
  | year = 2002
  | location =
  | pages = 153
  | url = http://books.google.com/books?id=7gJ4RocvEskC&pg=PA153&dq=%22transmission+line%22+uniform
  | doi =
  | id =
  | isbn = 0080505236}}</ref> to prevent reflections.  Types of transmission line include parallel line ([[ladder line]], [[twisted pair]]), [[coaxial cable]], [[stripline]], and [[microstrip]].<ref name="Carr">{{cite book 
  | last = Carr
  | first = Joseph J.
  | title = Microwave & Wireless Communications Technology
  | publisher = Newnes
  | year = 1997
  | location = USA
  | pages = 46–47
  | url = http://books.google.com/books?id=1j1E541LKVoC&pg=PA46&dq=%22parallel+line%22+%22coaxial+cable%22+stripline+waveguide
  | doi =
  | id =
  | isbn = 0750697075}}</ref><ref name="Raisanen">{{cite book 
  | last = Raisanen
  | first = Antti V.
  | coauthors = Arto Lehto
  | title = Radio Engineering for Wireless Communication and Sensor Applications
  | publisher = Artech House
  | year = 2003
  | location =
  | pages = 35–37
  | url = http://books.google.com/books?id=m8Dgkvf84xoC&pg=PA35
  | doi =
  | id =
  | isbn = 1580536697}}</ref> The higher the frequency of electromagnetic waves moving through a given cable or medium, the shorter the [[wavelength]] of the waves.  Transmission lines become necessary when the length of the cable is longer than a significant fraction of the transmitted frequency's wavelength.


At [[microwave]] frequencies and above, power losses in transmission lines become excessive, and [[waveguide]]s are used instead,<ref name="Jackman" /> which function as "pipes" to confine and guide the electromagnetic waves.<ref name="Raisanen" />  Some sources define waveguides as a type of transmission line;<ref name="Raisanen" /> however, this article will not include them.  At even higher frequencies, in the [[terahertz]], [[infrared]] and [[light]] range, waveguides in turn become lossy, and [[optics|optical]] methods, (such as lenses and mirrors), are used to guide electromagnetic waves.<ref name="Raisanen" />
During the period between 1848 to 1972, all of the major countries adopted time zones based on the Greenwich meridian.{{sfn|Howse|1997|loc=ch. 6}}


The theory of [[sound wave]] propagation is very similar mathematically to that of electromagnetic waves, so techniques from transmission line theory are also used to build structures to conduct acoustic waves; and these are called [[acoustic transmission line]]s.
In 1935, the term ''Universal Time'' was recommended by the [[International Astronomical Union]] as a more precise term than [[Greenwich Mean Time]], because GMT could refer to either an [[astronomical day]] starting at noon or a civil day starting at midnight.{{sfn|McCarthy|Seidelmann|2009|p=14}} The term ''Greenwich Mean Time'' persists, however, in common usage to this day in reference to [[civil time]]keeping.


==History==
==Measurement==
Based on the rotation of the Earth, time can be measured by observing celestial bodies crossing the meridian every day. Astronomers found that it was more accurate to establish time by observing [[star]]s as they crossed a meridian rather than by observing the position of the [[Sun]] in the sky. Nowadays, UT in relation to [[International Atomic Time]] (TAI) is determined by [[Very Long Baseline Interferometry]] (VLBI) observations of distant [[quasar]]s, a method which can determine UT1 to within 4 milliseconds.{{sfn|McCarthy|Seidelmann|2009|pages=68&ndash;9}}{{sfn|Urban|Seidelmann|2013|page=175}}


Mathematical analysis of the behaviour of electrical transmission lines grew out of the work of [[James Clerk Maxwell]], [[Lord Kelvin]] and [[Oliver Heaviside]]. In 1855 Lord Kelvin formulated a diffusion model of the current in a submarine cable.  The model correctly predicted the poor performance of the 1858 trans-Atlantic [[Submarine communications cable|submarine telegraph cable]].  In 1885 Heaviside published the first papers that described his analysis of propagation in cables and the modern form of the [[telegrapher's equations]].<ref>Ernst Weber and Frederik Nebeker, ''The Evolution of Electrical Engineering'', IEEE Press, Piscataway, New Jersey USA, 1994  ISBN 0-7803-1066-7</ref>
[[File:Universal Dial Plate or Times of all Nations, 1854.jpg|thumb|left|An 1853 "Universal Dial Plate" showing the relative times of "all nations" before the adoption of universal time]]The rotation of the Earth and UT are monitored by the [[International Earth Rotation and Reference Systems Service]] (IERS). The [[International Astronomical Union]] also is involved in setting standards, but the final arbiter of broadcast standards is the [[International Telecommunication Union]] or ITU.{{sfn|McCarthy|Seidelmann|2009|loc=Ch. 18}}


==Applicability==
The rotation of the Earth is somewhat irregular, and is very gradually slowing due to [[tidal acceleration]]. Furthermore, the length of the second was determined from observations of the [[Moon]] between 1750 and 1890. All of these factors cause the [[mean solar day]], on the average, to be slightly longer than the nominal 86,400 [[SI]] seconds, the traditional number of seconds per day. As UT is slightly irregular in its rate, astronomers introduced [[Ephemeris Time]], which has since been replaced by [[Terrestrial Time]] (TT). Because Universal Time is synchronous with night and day, and that more precise atomic-frequency standards drift away from this, however, UT is still used to produce a correction (called a [[leap second]]) to atomic time, in order to obtain a broadcast form of [[civil time]] that carries atomic frequency. Thus, civil broadcast standards for time and frequency usually follow [[International Atomic Time]] closely, but occasionally change discontinuously (or "leap") in order to prevent them from drifting too far from [[mean solar time]].


In many [[electric circuit]]s, the length of the wires connecting the components can for the most part be ignored. That is, the voltage on the wire at a given time can be assumed to be the same at all points. However, when the voltage changes in a time interval comparable to the time it takes for the signal to travel down the wire, the length becomes important and the wire must be treated as a transmission line. Stated another way, the length of the wire is important when the signal includes [[Harmonic analysis|frequency components]] with corresponding [[wavelength]]s comparable to or less than the length of the wire.
[[Barycentric Dynamical Time]] (TDB), a form of atomic time, is now used in the construction of the ephemerides of the [[planet]]s and other solar system objects, for two main reasons.<ref>{{harvnb|Urban|Seidelmann|2013|page= 7}}. Strictly speaking, a major producer of ephemerides, the [[Jet Propulsion Laboratory]], uses a time scale they derive, T<sub>eph</sub>, which is functionally equivalent to TDB.</ref> First, these ephemerides are tied to optical and [[radar]] observations of planetary motion, and the TDB time scale is fitted so that [[Newton's laws of motion]], with corrections for [[general relativity]], are followed. Next, the time scales based on Earth's rotation are not uniform and therefore, are not suitable for predicting the motion of bodies in our solar system.


A common rule of thumb is that the cable or wire should be treated as a transmission line if the length is greater than 1/10 of the wavelength. At this length the phase delay and the interference of any reflections on the line become important and can lead to unpredictable behavior in systems which have not been carefully designed using transmission line theory.
==Versions==
There are several versions of Universal Time:
* '''UT0''' is Universal Time determined at an observatory by observing the diurnal motion of stars or extragalactic radio sources, and also from ranging observations of the Moon and artificial Earth satellites. The location of the observatory is considered to have fixed coordinates in a terrestrial reference frame (such as the [[International Terrestrial Reference Frame]]) but the position of the rotational axis of the Earth wanders over the surface of the Earth; this is known as [[polar motion]]. UT0 does not contain any correction for polar motion. The difference between UT0 and UT1 is on the order of a few tens of milliseconds. The designation UT0 is no longer in common use.{{sfn|Urban|Seidelmann|2013|page=81}}
* '''UT1''' is the principal form of Universal Time. While conceptually it is mean solar time at 0° longitude, precise measurements of the Sun are difficult. Hence, it is computed from observations of distant [[quasar]]s using long baseline interferometry, laser ranging of the [[Moon]] and artificial satellites, as well as the determination of [[Global Positioning System|GPS]] satellite orbits. UT1 is the same everywhere on Earth, and is proportional to the rotation angle of the Earth with respect to distant quasars, specifically, the [[International Celestial Reference Frame]] (ICRF), neglecting some small adjustments. The observations allow the determination of a measure of the Earth's angle with respect to the ICRF, called the Earth Rotation Angle (ERA, which serves as a modern replacement for [[Greenwich Sidereal Time|Greenwich Mean Sidereal Time]]). UT1 is required to follow the relationship
::ERA = 2π(0.7790572732640 + 1.00273781191135448''T<sub>u</sub>'') radians
::where ''T<sub>u</sub>'' = (Julian UT1 date - 2451545.0){{Sfn|McCarthy|Seidelmann|2009|pp= 15&ndash;17, 62&ndash;64, 68&ndash;69, 76}}
* '''UT1R''' is a smoothed version of UT1, filtering out periodic variations due to tides. It includes 62 smoothing terms, with periods ranging from 5.6 days to 18.6 years.{{sfn|IERS|n.d.}}
* '''UT2''' is a smoothed version of UT1, filtering out periodic seasonal variations. It is mostly of historic interest and rarely used anymore. It is defined by
::<math>UT2 = UT1 + 0.022\cdot\sin(2\pi t) - 0.012\cdot\cos(2\pi t) - 0.006\cdot\sin(4\pi t) + 0.007\cdot\cos(4\pi t)\;\mbox{seconds}</math>
::where ''t'' is the time as fraction of the [[Year#Besselian year|Besselian year]].<ref>[http://www.usno.navy.mil/USNO/earth-orientation/eo-info/general/date-time-def Date and Time Definitions] n.d.</ref>
* '''UT2R''' is a smoothed version of UT1, incorporating both the seasonal corrections of UT2 and the tidal corrections of UT1R. It is the most smoothed form of Universal Time. Its non-uniformities reveal the unpredictable components of Earth rotation due to atmospheric weather, [[plate tectonics]] and currents in the interior of the Earth.{{citation needed|date=March 2013}}
* '''[[Coordinated Universal Time|UTC]]''' (Coordinated Universal Time) is an atomic timescale that approximates UT1. It is the international standard on which civil time is based. It ticks [[SI]] seconds, in step with [[International Atomic Time|TAI]]. It usually has 86,400 SI seconds per day but is kept within 0.9 seconds of UT1 by the introduction of occasional intercalary [[leap second]]s. {{As of|2013}}, these leaps have always been positive (the days which contained a leap second were 86,401 seconds long). Whenever a level of [[accuracy]] better than one second is not required, UTC can be used as an approximation of UT1. The difference between UT1 and UTC is known as [[DUT1]].{{sfn|McCarthy|Seidelmann|2009|loc=Ch. 14}}


==The four terminal model==
==Adoption in various countries==
 
The table shows the dates of adoption of time zones based on the Greenwich meridian, including half-hour zones.
[[Image:Transmission line symbols.svg|thumb|Variations on the [[electronic schematic|schematic]] [[electronic symbol]] for a transmission line.]]
{|
 
! width=60 align=left | Year
For the purposes of analysis, an electrical transmission line can be modelled as a [[two-port network]] (also called a quadrupole network), as follows:
! align=left | Countries <ref>
 
{{harvnb|Howse|1980|pp=154&ndash;5}}. Names have not been updated.
[[Image:Transmission line 4 port.svg]]
 
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 a single parameter called the ''[[characteristic impedance]]'', symbol Z<sub>0</sub>.  This 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.
 
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|310px|A transmission line is drawn as two black wires. At a distance ''x'' into the line, there is current ''I(x)'' traveling 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.]]
 
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 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 modeled 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 dB corresponds approximately to a halving of the power.
 
High-frequency transmission lines can be defined as those designed to carry electromagnetic waves whose [[wavelength]]s are shorter than or comparable to the length of the line.  Under these conditions, the approximations useful for calculations at lower frequencies are no longer accurate.  This often occurs with [[radio]], [[microwave]] and [[light|optical]] signals, [[metal mesh optical filters]], and with the signals found in high-speed [[digital circuit]]s.
 
==Telegrapher's equations==
{{Main|Telegrapher's equations}}
{{See also|Reflections on copper lines}}
 
The '''telegrapher's equations''' (or just '''telegraph equations''') are a pair of linear differential equations which describe the [[voltage]] and [[Electric current|current]] on an electrical transmission line with distance and time. They were developed by [[Oliver Heaviside]] who created the ''transmission line model'', and are based on [[Maxwell's Equations]].
 
[[Image:Transmission line element.svg|thumb|right|250px|Schematic representation of the elementary component of a transmission line.]]
The transmission line model represents the transmission line as an infinite series of two-port elementary components, each representing an infinitesimally short segment of the transmission line:
 
* The distributed resistance <math>R</math> of the conductors is represented by a series resistor (expressed in ohms per unit length).
* The distributed inductance <math>L</math> (due to the [[magnetic field]] around the wires, [[self-inductance]], etc.) is represented by a series [[inductor]] ([[henry (unit)|henries]] per unit length).
* The capacitance <math>C</math> between the two conductors is represented by a [[Shunt (electrical)|shunt]] [[capacitor]] C ([[farad]]s per unit length).
* The [[Electric conductance|conductance]] <math>G</math> of the dielectric material separating the two conductors is represented by a shunt resistor between the signal wire and the return wire ([[Siemens (unit)|siemens]] per unit length).
 
The model consists of an ''infinite series'' of the elements shown in the figure, and that the values of the components are specified ''per unit length'' so the picture of the component can be misleading. <math>R</math>, <math>L</math>, <math>C</math>, and <math>G</math> may also be functions of frequency. An alternative notation is to use <math>R'</math>, <math>L'</math>, <math>C'</math> and <math>G'</math> to emphasize that the values are derivatives with respect to length.  These quantities can also be known as the [[primary line constants]] to distinguish from the secondary line constants derived from them, these being the [[propagation constant]], [[attenuation constant]] and [[phase constant]].
 
The line voltage <math>V(x)</math> and the current <math>I(x)</math> can be expressed in the frequency domain as
 
:<math>\frac{\partial V(x)}{\partial x} = -(R + j \omega L)I(x)</math>
 
:<math>\frac{\partial I(x)}{\partial x} = -(G + j \omega C)V(x).</math>
 
When the elements <math>R</math> and <math>G</math> are negligibly small the transmission line is considered as a lossless structure. In this hypothetical case, the model depends only on the <math>L</math> and <math>C</math> elements which greatly simplifies the analysis. For a lossless transmission line, the second order steady-state Telegrapher's equations are:
 
:<math>\frac{\partial^2V(x)}{\partial x^2}+ \omega^2 LC\cdot V(x)=0</math>
 
:<math>\frac{\partial^2I(x)}{\partial x^2} + \omega^2 LC\cdot I(x)=0.</math>
 
These are [[wave equation]]s which have [[plane wave]]s with equal propagation speed in the forward and reverse directions as solutions. The physical significance of this is that electromagnetic waves propagate down transmission lines and in general, there is a reflected component that interferes with the original signal. These equations are fundamental to transmission line theory.
 
If <math>R</math> and <math>G</math> are not neglected, the Telegrapher's equations become:
 
:<math>\frac{\partial^2V(x)}{\partial x^2} = \gamma^2 V(x)</math>
 
:<math>\frac{\partial^2I(x)}{\partial x^2} = \gamma^2 I(x)</math>
 
where
 
:<math>\gamma = \sqrt{(R + j \omega L)(G + j \omega C)}</math>
 
and the characteristic impedance is:
 
:<math>Z_0 = \sqrt{\frac{R + j \omega L}{G + j \omega C}}.</math>
 
The solutions for <math>V(x)</math> and <math>I(x)</math> are:
 
:<math>V(x) = V^+ e^{-\gamma x} + V^- e^{\gamma x} \,</math>
 
:<math>I(x) = \frac{1}{Z_0}(V^+ e^{-\gamma x} - V^- e^{\gamma x}). \,</math>
 
The constants <math>V^\pm</math> and <math>I^\pm</math> must be determined from boundary conditions. For a voltage pulse <math>V_{\mathrm{in}}(t) \,</math>, starting at <math>x=0</math> and moving in the positive <math>x</math>-direction, then the transmitted pulse <math>V_{\mathrm{out}}(x,t) \,</math> at position <math>x</math> can be obtained by computing the Fourier Transform, <math>\tilde{V}(\omega)</math>, of <math>V_{\mathrm{in}}(t) \,</math>, attenuating each frequency component by <math>e^{\mathrm{-Re}(\gamma) x} \,</math>, advancing its phase by <math>\mathrm{-Im}(\gamma)x \,</math>, and taking the inverse Fourier Transform. The real and imaginary parts of <math>\gamma</math> can be computed as
 
:<math>\mathrm{Re}(\gamma) = (a^2 + b^2)^{1/4} \cos(\mathrm{atan2}(b,a)/2) \,</math>
 
:<math>\mathrm{Im}(\gamma) = (a^2 + b^2)^{1/4} \sin(\mathrm{atan2}(b,a)/2) \,</math>
 
where [[atan2]] is the two-parameter arctangent, and
 
:<math>a \equiv \omega^2 LC \left[ \left( \frac{R}{\omega L} \right) \left( \frac{G}{\omega C} \right) - 1 \right] </math>
 
:<math>b \equiv \omega^2 LC \left( \frac{R}{\omega L} + \frac{G}{\omega C} \right). </math>
 
For small losses and high frequencies, to first order in <math>R / \omega L</math> and <math>G / \omega C</math> one obtains
 
:<math>\mathrm{Re}(\gamma) \approx \frac{\sqrt{LC}}{2} \left( \frac{R}{L} + \frac{G}{C} \right) \,</math>
 
:<math>\mathrm{Im}(\gamma) \approx \omega \sqrt{LC}. \, </math>
 
Noting that an advance in phase by <math>- \omega \delta</math> is equivalent to a time delay by <math>\delta</math>, <math>V_{out}(t)</math> can be simply computed as
 
:<math>V_{\mathrm{out}}(x,t) \approx V_{\mathrm{in}}(t - \sqrt{LC}x) e^{- \frac{\sqrt{LC}}{2} \left( \frac{R}{L} + \frac{G}{C} \right) x }. \,</math>
 
==Input impedance of transmission line==
[[File:SmithChartLineLength.svg|thumb|right|350px|Looking towards a load through a length {{math|''l''}} of lossless transmission line, the impedance changes as {{math|''l''}} increases, following the blue circle on this [[Smith chart|impedance Smith chart]]. (This impedance is characterized by its [[reflection coefficient]] {{math|''V<sub>reflected</sub>'' / ''V<sub>incident</sub>''}}.) The blue circle, centered within the chart, is sometimes called an ''SWR circle'' (short for ''constant [[standing wave ratio]]'').]]
 
The [[characteristic impedance]] {{math|''Z''<sub>0</sub>}} of a transmission line is the ratio of the amplitude of a '''single''' voltage wave to its current wave. Since most transmission lines also have a reflected wave, the characteristic impedance is generally '''not''' the impedance that is measured on the line.
 
The impedance measured at a given distance, {{math|''l''}}, from the load impedance {{math|''Z<sub>L</sub>''}} may be expressed as,
 
:<math>Z_{in}\left(l\right)=\frac{V(l)}{I(l)}=Z_0 \frac{1 + \Gamma_L e^{-2 \gamma l}}{1 - \Gamma_L e^{-2 \gamma l}}</math>,
 
where {{math|''γ''}} is the propagation constant and <math>\Gamma_L=\left(Z_L - Z_0\right)/\left(Z_L + Z_0\right)</math> is the voltage [[reflection coefficient]] at the load end of the transmission line. Alternatively, the above formula can be rearranged to express the input impedance in terms of the load impedance rather than the load voltage reflection coefficient:
 
:<math>Z_{in}\left(l\right)=Z_0 \frac{Z_L + Z_0 \tanh\left(\gamma l\right)}{Z_0 + Z_L\tanh\left(\gamma l\right)}</math>.
 
===Input impedance of lossless transmission line===
For a lossless transmission line, the propagation constant is purely imaginary, {{math|''γ''{{=}}''jβ''}}, so the above formulas can be rewritten as,
 
:<math>
Z_\mathrm{in} (l)=Z_0 \frac{Z_L + jZ_0\tan(\beta l)}{Z_0 + jZ_L\tan(\beta l)}
</math>
 
where <math>\beta=\frac{2\pi}{\lambda}</math> is the [[wavenumber]].
 
In calculating {{math|''β''}}, the wavelength is generally different inside the transmission line to what it would be in free-space and the velocity constant of the material the transmission line is made of needs to be taken into account when doing such a calculation.
 
===Special cases of lossless transmission lines===
 
====Half wave length====
For the special case where <math>\beta l= n\pi</math> where n is an integer (meaning that the length of the line is a multiple of half a wavelength), the expression reduces to the load impedance so that
:
<math>Z_\mathrm{in}=Z_L \,</math>
 
for all {{math|''n''}}. This includes the case when {{math|''n''{{=}}0}}, meaning that the length of the transmission line is negligibly small compared to the wavelength. The physical significance of this is that the transmission line can be ignored (i.e. treated as a wire) in either case.
 
====Quarter wave length====
{{Main|quarter wave impedance transformer}}
For the case where the length of the line is one quarter wavelength long, or an odd multiple of a quarter wavelength long, the input impedance becomes
:<math>
Z_\mathrm{in}=\frac{{Z_0}^2}{Z_L}. \,
</math>
 
====Matched load====
Another special case is when the load impedance is equal to the characteristic impedance of the line (i.e. the line is ''matched''), in which case the impedance reduces to the characteristic impedance of the line so that
:<math>
Z_\mathrm{in}=Z_L=Z_0 \,
</math>
for all <math>l</math> and all <math>\lambda</math>.
 
====Short====
[[File:Transmission line animation open short.gif|thumb|right|300px|Standing waves on a transmission line with an open-circuit load (top), and a short-circuit load (bottom). Colors represent voltages, and black dots represent electrons.]]
{{main|stub (electronics)#Short circuited stub|l1=stub}}
For the case of a shorted load (i.e. <math>Z_L=0</math>), the input impedance is purely imaginary and a periodic function of position and wavelength (frequency)
 
:<math>
Z_\mathrm{in} (l)=j Z_0 \tan(\beta l). \,
</math>
 
====Open====
{{main|stub (electronics)#Open_circuited_stub|l1=stub}}
For the case of an open load (i.e. <math>Z_L=\infty</math>), the input impedance is once again imaginary and periodic
 
:<math>
Z_\mathrm{in} (l)=-j Z_0 \cot(\beta l). \,
</math>
 
===Stepped transmission line===
[[Image:Segments.jpg|thumb|left|A simple example of stepped transmission line consisting of three segments.]]A stepped transmission line<ref>{{cite web|url=http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WJX-4W2122T-1&_user=5755111&_rdoc=1&_fmt=&_orig=search&_sort=d&_docanchor=&view=c&_acct=C000000150&_version=1&_urlVersion=0&_userid=5755111&md5=fe79f204b33cf7eb6d03cb89ff250c91 |title=Journal of Magnetic Resonance - Impedance matching with an adjustable segmented transmission line |publisher=ScienceDirect.com |date= |accessdate=2013-06-15}}</ref> is used for broad range [[impedance matching]].  It can be considered as multiple transmission line segments connected in series, with the characteristic impedance of each individual element to be Z<sub>0,i</sub>.  The input impedance can be obtained from the successive application of the chain relation
 
:<math>
Z_\mathrm{i+1}=Z_\mathrm{0,i} \frac{Z_i + jZ_\mathrm{0,i}\tan(\beta_i l_i)}{Z_\mathrm{0,i} + jZ_i\tan(\beta_i l_i)}
</math>
 
where <math>\beta_i</math> is the wave number of the ''i''th transmission line segment and l<sub>i</sub> is the length of this segment, and Z<sub>i</sub> is the front-end impedance that loads the ''i''th segment.  [[Image:PolarSmith.jpg|thumb|right|The impedance transformation circle along a transmission line whose characteristic impedance Z<sub>0,i</sub> is smaller than that of the input cable Z<sub>0</sub>. And as a result, the impedance curve is off-centered towards the -x axis. Conversely, if Z<sub>0,i</sub> > Z<sub>0</sub>, the impedance curve should be off-centered towards the +x axis.]]Because the characteristic impedance of each transmission line segment Z<sub>0,i</sub> is often different from that of the input cable Z<sub>0</sub>, the impedance transformation circle is off centered along the x axis of the [[Smith Chart]] whose impedance representation is usually normalized against Z<sub>0</sub>.
 
==Practical types==<!-- This section is linked from [[Wikipedia:Proposed mergers]] -->
 
===Coaxial cable===
 
{{Main|coaxial cable}}
 
Coaxial lines confine virtually all of the electromagnetic wave to the area inside the cable. Coaxial lines can therefore be bent and twisted (subject to limits) without negative effects, and they can be strapped to conductive supports without inducing unwanted currents in them.
In radio-frequency applications up to a few gigahertz, the wave propagates in the [[transverse electric and magnetic mode]] (TEM) only, which means that the electric and magnetic fields are both perpendicular to the direction of propagation (the electric field is radial, and the magnetic field is circumferential). However, at frequencies for which the wavelength (in the dielectric) is significantly shorter than the circumference of the cable, transverse electric (TE) and transverse magnetic (TM) [[waveguide]] modes can also propagate. When more than one mode can exist, bends and other irregularities in the cable geometry can cause power to be transferred from one mode to another.
 
The most common use for coaxial cables is for television and other signals with bandwidth of multiple megahertz. In the middle 20th century they carried [[long distance telephone]] connections.
 
[[Image:Solec Kujawski longwave antenna feeder.jpg|thumb|right|A type of transmission line called a ''cage line'', used for high power, low frequency applications.  It functions similarly to a large coaxial cable.  This example is the antenna [[feedline]] for a [[longwave]] radio transmitter in [[Poland]], which operates at a frequency of 225 kHz and a power of 1200 kW.]]
 
===Microstrip===
 
{{Main|microstrip}}
 
A microstrip circuit uses a thin flat conductor which is [[Parallel (geometry)|parallel]] to a [[ground plane]]. Microstrip can be made by having a strip of copper on one side of a [[printed circuit board]] (PCB) or ceramic substrate while the other side is a continuous ground plane. The width of the strip, the thickness of the insulating layer (PCB or ceramic) and the [[dielectric constant]] of the insulating layer determine the characteristic impedance.
Microstrip is an open structure whereas coaxial cable is a closed structure.
 
===Stripline===
 
:''Main article : [[Stripline]]''
 
A stripline circuit uses a flat strip of metal which is sandwiched between two parallel ground planes. The insulating material of the substrate forms a dielectric. The width of the strip, the thickness of the substrate and the relative permittivity of the substrate determine the characteristic impedance of the strip which is a transmission line.
 
===Balanced lines===
{{Main|Balanced line}}
A balanced line is a transmission line consisting of two conductors of the same type, and equal impedance to ground and other circuits.  There are many formats of balanced lines, amongst the most common are twisted pair, star quad and twin-lead.
 
====Twisted pair====
{{Main|Twisted pair}}
Twisted pairs are commonly used for terrestrial [[telephone]] communications.  In such cables, many pairs are grouped together in a single cable, from two to several thousand.<ref>Syed V. Ahamed, Victor B. Lawrence, ''Design and engineering of intelligent communication systems'', pp.130-131, Springer, 1997 ISBN 0-7923-9870-X.</ref>  The format is also used for data network distribution inside buildings, but the cable is more expensive because the transmission line parameters are tightly controlled.
 
====Star quad====
Star quad is a four-conductor cable in which all four conductors are twisted together around the cable axis.  It is sometimes used for two circuits, such as [[4-wire]] telephony and other telecommunications applications.  In this configuration each pair uses two non-adjacent conductors.  Other times it is used for a single, balanced circuit, such as audio applications and [[2-wire]] telephony.  In this configuration two non-adjacent conductors are terminated together at both ends of the cable, and the other two conductors are also terminated together.
 
Interference picked up by the cable arrives as a virtually perfect common mode signal, which is easily removed by coupling transformers.  Because the conductors are always the same distance from each other, cross talk is reduced relative to cables with two separate twisted pairs.
 
The combined benefits of twisting, differential signalling, and quadrupole pattern give outstanding noise immunity, especially advantageous for low signal level applications such as long microphone cables, even when installed very close to a power cable. The disadvantage is that star quad, in combining two conductors, typically has double the capacitance of similar two-conductor twisted and shielded audio cable. High capacitance causes increasing distortion and greater loss of high frequencies as distance increases.<ref>{{cite book|last=Lampen|first=Stephen H.|title=Audio/Video Cable Installer's Pocket Guide|year=2002|publisher=McGraw-Hill|isbn=0071386211|pages=32, 110, 112}}</ref><ref>{{cite book|last=Rayburn|first=Ray|title=Eargle's The Microphone Book: From Mono to Stereo to Surround - A Guide to Microphone Design and Application|edition=3|year=2011|publisher=Focal Press|isbn=0240820754|pages=164–166}}</ref>
 
==== Twin-lead ====
{{Main|Twin-lead}}
Twin-lead consists of a pair of conductors held apart by a continuous insulator.
 
====Lecher lines====
{{Main|Lecher lines}}
Lecher lines are a form of parallel conductor that can be used at [[Ultra high frequency|UHF]] for creating resonant circuits.  They are a convenient practical format that fills the gap between [[Lumped element model|lumped]] components (used at [[High frequency|HF]]/[[VHF]]) and [[Resonant cavity|resonant cavities]] (used at [[Ultra high frequency|UHF]]/[[Super high frequency|SHF]]).
 
===Single-wire line===
[[Unbalanced line]]s were formerly much used for telegraph transmission, but this form of communication has now fallen into disuse.  Cables are similar to twisted pair in that many cores are bundled into the same cable but only one conductor is provided per circuit and there is no twisting.  All the circuits on the same route use a common path for the return current (earth return).  There is a power transmission version of [[single-wire earth return]] in use in many locations.
 
==General applications==
 
===Signal transfer===
 
Electrical transmission lines are very widely used to transmit high frequency signals over long or short distances with minimum power loss.  One familiar example is the [[down lead]] from a TV or radio [[Antenna (radio)|aerial]] to the receiver.
 
===Pulse generation===
 
Transmission lines are also used as pulse generators. By charging the transmission line and then discharging it into a [[resistive]] load, a rectangular pulse equal in length to twice the [[electrical length]] of the line can be obtained, although with half the voltage. A [[Blumlein transmission line]] is a related pulse forming device that overcomes this limitation. These are sometimes used as the [[pulsed power]] sources for [[radar]] [[transmitters]] and other devices.
 
===Stub filters===
{{see also|Distributed element filter#Stub band-pass filters}}
If a short-circuited or open-circuited transmission line is wired in parallel with a line used to transfer signals from point A to point B, then it will function as a filter. The method for making stubs is similar to the method for using Lecher lines for crude frequency measurement, but it is 'working backwards'. One method recommended in the [[Radio Society of Great Britain|RSGB]]'s radiocommunication handbook is to take an open-circuited length of transmission line wired in parallel with the feeder delivering signals from an aerial. By cutting the free end of the transmission line, a minimum in the strength of the signal observed at a receiver can be found. At this stage the stub filter will reject this frequency and the odd harmonics, but if the free end of the stub is shorted then the stub will become a filter rejecting the even harmonics.
 
==Acoustic transmission lines==
{{Main|Acoustic transmission line}}
 
An acoustic transmission line is the [[Acoustics|acoustic]] [[analogy|analog]] of the electrical transmission line, typically thought of as a rigid-walled tube that is long and thin relative to the wavelength of sound present in it.
 
==Solutions of the telegrapher's equations as circuit components==
{{cleanup|section|reason=Poor style|date=June 2012}}
 
[[Image:Unbalanced Transmission Line Equivalent Sub Circuit.jpg|right|thumb|300px|Equivalent circuit of a transmission line described by the Telegrapher's equations.]]
 
[[Image:Balanced Transmission Line Equivalent Circuit.jpg|right|thumb|300px|Solutions of the Telegrapher's Equations as Components in the Equivalent Circuit of a Balanced Transmission Line Two-Port Implementation.]]
 
The solutions of the telegrapher's equations can be inserted directly into a circuit as components.  The circuit in the top figure implements the solutions of the telegrapher's equations.<ref>{{Citation | last = McCammon | first = Roy | title = SPICE Simulation of Transmission Lines by the Telegrapher's Method  | url=http://i.cmpnet.com/rfdesignline/2010/06/C0580Pt1edited.pdf | accessdate = 22 Oct 2010 }}</ref>
 
The bottom circuit is derived from the top circuit by source transformations.<ref>{{cite book
|author=William H. Hayt|title=Engineering Circuit Analysis
|edition=second
|publisher=McGraw-Hill
|location=New York, NY|year=1971|isbn=070273820}}, pp. 73-77</ref>  It also implements the solutions of the telegrapher's equations.
 
The solution of the telegrapher's equations can be expressed as an ABCD type '' [[Two-port network]]''  with the following defining equations<ref>
{{cite book
|author=John J. Karakash|title=Transmission Lines and Filter Networks
|edition=First
|publisher=Macmillan
|location=New York, NY|year=1950}}, p. 44
</ref>
</ref>
! width=60 align=left | Year
! align=left | Countries
! width=60 align=left | Year
! align=left | Countries
|-
| 1848 || Great Britain <ref>legal in 1880</ref>
| 1906 || India,<ref>except Calcutta</ref> Ceylon, Seychelles
| 1930 || Bermuda
|-
| 1879 || Sweden
| 1907 || Mauritius, Chagos
| 1931 || Paraguay
|-
| 1883 || Canada, USA <ref>legal in 1918</ref>
| 1908 || Faroe Is., Iceland
| 1932 || Barbados, Bolivia, Dutch East Indies
|-
| 1884 || Serbia
| 1911 || France, Algeria, Tunis,<ref>and many French overseas possessions,</ref> British West Indies
| 1934 || Nicaragua, E. Niger
|-
| 1888 || Japan
| 1912 || Portugal,<ref>and overseas possessions,</ref> other French possessions, Samoa, Hawaii, Midway and Guam, Timor, Bismarck Arch., Jamaica, Bahamas Is.
| By 1936 || Labrador, Norfolk I.
|-
| 1892 || Belgium, Holland,<ref>Legal time reverted to Amsterdam time 1909; to Central European Time 1940,</ref> S. Africa<ref>except Natal</ref>
| 1913 || British Honduras, Dahomey
| By 1937 || Cayman Is., Curaçao, Ecuador, Newfoundland
|-
| 1893 || Italy, Germany, Austria-Hungary (railways)
| 1914 || Albania, Brazil, Colombia
| By 1939 || Fernando Po, Persia
|-
| 1894 || Bulgaria, Denmark, Norway, Switzerland, Romania, Turkey (railways)
| 1916 || Greece, Ireland, Poland, Turkey
| 1940 || The Netherlands
|-
| 1895 || Australia, New Zealand, Natal
| 1917 || Iraq, Palestine
| By 1940 || Lord Howe I.
|-
| 1896 || Formosa (Taiwan)
| 1918 || Guatemala, Panama, Gambia, Gold Coast
| By 1948 || Aden, Ascension I., Bahrein, British Somaliland, Calcutta, Dutch Guiana, Kenya, Federated Malay States, Oman, Straits Settlements, St. Helena, Uganda, Zanzibar
|-
| 1899 || Puerto Rico, Philippines
| 1919 || Latvia, Nigeria
| By 1953 || Raratonga, South Georgia
|-
| 1900 || Sweden, Egypt, Alaska
| 1920 || Argentine, Uruguay, Burma, Siam
| By 1954 || Cook Is.
|-
| 1901 || Spain
| 1921 || Finland, Estonia, Costa Rica
| By 1959 || Maldive I. Republic
|-
| 1902 || Mozambique, Rhodesia
| 1922 || Mexico
| By 1961 || Friendly Is., Tonga Is.
|-
| 1903 || Ts'intao, Tientsin
| 1924 || Java, USSR
| By 1962 || Saudi Arabia
|-
| 1904 || China Coast, Korea, Manchuria, N. Borneo
| 1925 || Cuba
| By 1964 || Niue Is.
|-
| 1905 || Chile
| 1928 || China Inland
| 1972 || Liberia
|}


:<math>V_1 = V_2 \cosh ( \gamma  x) + I_2 Z \sinh (\gamma x) \,</math>
Apart from [[Nepal Time Zone]] (+5h 45m) and Chatham Isle (+12h 45m), all countries were keeping time within an even hour or half-hour of Greenwich.
:<math>I_1 = V_2 \frac{1}{Z} \sinh (\gamma x) + I_2 \cosh(\gamma x). \,</math>


:The symbols: <math>E_s, E_L, I_s, I_L, l  \,</math>  in the source book have been replaced by the symbols :<math> V_1, V_2, I_1, I_2, x  \,</math> in the preceding two equations.
==See also==
*[[List of international common standards]]
*[[Unix time]]


The ABCD type two-port gives <math>V_1 \, </math>  and  <math>I_1 \, </math> as functions of  <math>V_2 \, </math> and  <math>I_2 \, </math>.  Both of the circuits above, when solved for  <math>V_1 \, </math>  and  <math>I_1 \, </math> as functions of  <math>V_2 \, </math> and  <math>I_2 \, </math> yield exactly the same equations.
==Notes==
 
{{reflist}}
In the bottom circuit, all voltages except the port voltages are with respect to ground and the differential amplifiers have unshown connections to ground.  An example of a transmission line modeled by this circuit would be a balanced transmission line such as a telephone line.  The impedances Z(s), the voltage dependent current sources (VDCSs) and the difference amplifiers (the triangle with the number "1") account for the interaction of the transmission line with the external circuit.  The T(s) blocks account for delay, attenuation, dispersion and whatever happens to the signal in transit.  One of the T(s) blocks carries the ''forward wave'' and the other carries the ''backward wave''.  The circuit, as depicted, is fully symmetric, although it is not drawn that way.  The circuit depicted is equivalent to a transmission line connected from <math>V_1 \, </math> to <math>V_2 \, </math> in the sense that <math>V_1 \, </math>, <math>V_2 \, </math>, <math>I_1 \, </math> and <math>I_2 \, </math> would be same whether this circuit or an actual transmission line was connected between <math>V_1 \, </math> and <math>V_2 \, </math>.  There is no implication that there are actually amplifiers inside the transmission line.
 
Every two-wire or balanced transmission line has an implicit (or in some cases explicit) third wire which may be called shield, sheath, common, Earth or ground.  So every two-wire balanced transmission line has two modes which are nominally called the differential and common modes.  The circuit shown on the bottom only models the differential mode.
 
In the top circuit, the voltage doublers, the difference amplifiers and impedances Z(s) account for the interaction of the transmission line with the external circuit. This circuit, as depicted, is also fully symmetric, and also not drawn that way.  This circuit is a useful equivalent for an unbalanced transmission line like a coaxial cable or a micro strip line.
 
These are not the only possible equivalent circuits.
 
==See also==
{{Div col||25em}}
* [[Distributed element model]]
* [[Electric power transmission]]
* [[Heaviside condition]]
* [[Longitudinal wave|Longitudinal electromagnetic wave]]
* [[Lumped components]]
* [[Propagation velocity]]
* [[Radio frequency power transmission]]
* [[Smith chart]], a graphical method to solve transmission line equations
* [[Standing wave]]
* [[Time domain reflectometer]]
* [[Transverse wave|Transverse electromagnetic wave]]
{{Div col end}}


==References==
==References==
''Part of this article was derived from [[Federal Standard 1037C]].''
*{{cite web|url=http://www.usno.navy.mil/USNO/earth-orientation/eo-info/general/date-time-def|title=Date and Time Definitions|publisher=United States Naval Observatory|ref=harv | accessdate = 3 March 2013}}
{{Reflist|30em}}
*{{Anchor|ERC}}{{cite web|title= Earth Rotation Variations Due to Zonal Tides | publisher = Earth Orientation Center | location = Paris | accessdate = 2 October 2011 | url = http://hpiers.obspm.fr/eop-pc/models/UT1/UT1R_tab.html |ref=harv}}
 
*{{cite book|authorlink=Peter Galison |last=Galison|first=Peter |title=Einstein's clocks, Poincaré's maps: Empires of time|location=New York|publisher=W.W. Norton & Co|year=2003|isbn=0-393-02001-0|ref=harv}} Discusses the history of time standardization.
*{{Citation
*{{cite book|title=Greenwich Time and the discovery of the longitude|first=Derek|last=Howse|year=1980|pages=154–5|publisher=Oxford Univ Press |ref=harv}}. Names have not been updated.
|last= Steinmetz
*{{cite book | last = Howse | first = Derek | title = Greenwich Time and the Longitude | year = 1997 | publisher = Phillip Wilson | isbn=0-85667-468-0 |ref=harv}}
|first= Charles Proteus
*{{cite journal|first=Dennis D.|last=McCarthy| authorlink1=Dennis McCarthy (scientist)|url=http://www.cl.cam.ac.uk/~mgk25/volatile/astronomical-time.pdf|title=Astronomical Time|journal=Proceedings of the IEEE |volume=79 |issue=7|date=July 1991 |pages=915–920|doi=10.1109/5.84967 |ref=harv}}
|authorlink= Charles Proteus Steinmetz
*{{cite book | authorlink1=Dennis McCarthy (scientist)| last1 = McCarthy | first1=Dennis| last2= Seidelmann| first2= P. Kenneth| year= 2009| title=TIME&mdash;From Earth Rotation to Atomic Physics| place= Weinheim | publisher=Wiley-VCH Verlag GmbH & Co. KGaA. isbn=978-3-527-40780-4 |ref=harv}}
|title= The Natural Period of a Transmission Line and the Frequency of lightning Discharge Therefrom
*{{cite book|last=O'Malley|first=Michael| title=Keeping watch: A history of American time|location=Washington DC| publisher=Smithsonian |year=1996| isbn=1-56098-672-7 |ref=harv}}
|journal=The Electrical World
*{{cite book|last=Seidelmann|first=P. Kenneth|title=Explanatory supplement to the Astronomical Almanac|location=Mill Valley, California|publisher=University Science Books|year=1992|isbn=0-935702-68-7 |ref=harv}}
|date= August 27, 1898
*{{cite book| editor1-last = Urban |editor1-first = Sean | editor2-last = Seidelmann | editor2-first = P. Kenneth | year = 2013 | title = Explanatory Supplement to the Astronomical Almanac | edition = 3rd | location = Mill Valley, California | publisher = University Science Books| ref=harv}}
|pages= 203&ndash;205
*{{cite web|title=UT1R| url= http://hpiers.obspm.fr/eop-pc/models/UT1/UT1R_tab.html | publisher = International Earth Rotation and Reference System Service | accessdate = 6 March 2013 |ref={{harvid|IERS|n.d.}}}}
|issn=
*{{cite web|title=What is TT?|url=http://aa.usno.navy.mil/faq/docs/TT.php/?searchterm=terrestrial_time|work=Naval Oceanography Portal|publisher=[[United States Naval Observatory]] | accessdate= 3 March 2013}}
|doi=}}
{{FS1037C}}
*{{Citation
|title= Electromagnetism
|edition= 2nd
|last=Grant
|first= I. S.
|last2= Phillips
|first2= W. R.
|publisher= John Wiley
|isbn= 0-471-92712-0
|doi=}}
*{{Citation
|title=Fundamentals of Applied Electromagnetics
|edition= 2004 media
|last= Ulaby
|first= F. T.
|publisher= Prentice Hall
|isbn= 0-13-185089-X
|doi= }}
*{{Citation
|title=Radio communication handbook
|year= 1982
|page= 20
|chapter= Chapter 17
|publisher= [[Radio Society of Great Britain]]
|isbn= 0-900612-58-4
|doi= }}
*{{Citation
|last= Naredo
|first= J. L.
|first2= A. C.
|last2= Soudack
|first3= J. R.
|last3= Marti
|title= Simulation of transients on transmission lines with corona via the method of characteristics
|journal= IEE Proceedings. Generation, Transmission and Distribution.
|volume= 142
|issue= 1
|publisher= Institution of Electrical Engineers
|location= Morelos <!-- dubious -->
|date= Jan 1995
|issn= 1350-2360
|doi=}}
 
==Further reading==
{{Commons category|Transmission lines}}
* [http://earlyradiohistory.us/1902wt.htm Annual Dinner of the Institute at the Waldorf-Astoria]. [[Transactions of the American Institute of Electrical Engineers]], New York, January 13, 1902. (Honoring of [[Guglielmo Marconi]], January 13, 1902)
* Avant! software, [http://web.archive.org/web/20050925041320/http://www.ece.cmu.edu/~ee762/hspice-docs/html/hspice_and_qrg/hspice_2001_2-124.html Using Transmission Line Equations and Parameters]. Star-Hspice Manual, June 2001.
* Cornille, P, [http://www.iop.org/EJ/abstract/0022-3727/23/2/001 On the propagation of inhomogeneous waves]. J. Phys. D: Appl. Phys. 23, February 14, 1990. (Concept of inhomogeneous waves propagation — Show the importance of the telegrapher's equation with Heaviside's condition.)
*Farlow, S.J., ''Partial differential equations for scientists and engineers''.  J. Wiley and Sons, 1982, p.&nbsp;126.  ISBN 0-471-08639-8.
* Kupershmidt, Boris A., [http://arxiv.org/abs/math-ph/9810020 Remarks on random evolutions in Hamiltonian representation]. Math-ph/9810020. J. Nonlinear Math. Phys. 5 (1998), no. 4, 383-395.
* [[Mihajlo Pupin|Pupin, M.]], {{US patent|1541845}}, ''Electrical wave transmission''.
* [http://cktse.eie.polyu.edu.hk/eie403/ Transmission line matching]. EIE403: High Frequency Circuit Design. Department of Electronic and Information Engineering, Hong Kong Polytechnic University. ([[Portable Document Format|PDF]] format)
* Wilson, B. (2005, October 19). ''[http://cnx.rice.edu/content/m1044/latest/ Telegrapher's Equations]''. Connexions.
* John Greaton  Wöhlbier, "''[http://www.wildwestwohlbiers.org/john/files/ms_thesis.pdf "Fundamental Equation''" and "''Transforming the Telegrapher's Equations"]''. Modeling and Analysis of a Traveling Wave Under Multitone Excitation.
* Agilent Technologies. Educational Resources. ''Wave Propagation along a Transmission Line''. [http://education.tm.agilent.com/index.cgi?CONTENT_ID=6 Edutactional Java Applet].
* Qian, C., [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WJX-4W2122T-1&_user=5755111&_rdoc=1&_fmt=&_orig=search&_sort=d&_docanchor=&view=c&_acct=C000000150&_version=1&_urlVersion=0&_userid=5755111&md5=fe79f204b33cf7eb6d03cb89ff250c91 Impedance matching with adjustable segmented transmission line]. J. Mag. Reson. 199 (2009), 104-110.


==External links==
==External links==
* [http://www.cvel.clemson.edu/emc/calculators/TL_Calculator/index.html Transmission Line Parameter Calculator]
*[http://www.randomhouse.ca/catalog/display.pperl?isbn=9780676974737 ''Time Lord''] by Clark Blaise: a biography of Stanford Fleming and the idea of standard time
* [http://www.amanogawa.com/archive/transmissionB.html Interactive applets on transmission lines]
* [http://www.eetimes.com/design/microwave-rf-design/4200760/SPICE-Simulation-of-Transmission-Lines-by-the-Telegrapher-s-Method-Part-1-of-3-?Ecosystem=microwave-rf-design SPICE Simulation of Transmission Lines]


{{Telecommunications}}
{{Time Topics}}
{{Time measurement and standards}}


{{DEFAULTSORT:Transmission Line}}
[[Category:1883 in Canada]]
[[Category:Cables]]
[[Category:Time scales]]
[[Category:Telecommunications engineering]]
[[Category:Scottish inventions]]
[[Category:Distributed element circuits]]

Revision as of 10:36, 9 August 2014

Template:Redirect2 Universal Time (UT) is a time standard based on the rotation of the Earth. It is a modern continuation of Greenwich Mean Time (GMT), i.e., the mean solar time on the Prime Meridian at Greenwich, and GMT is sometimes used loosely as a synonym for UTC. In fact, the expression "Universal Time" is ambiguous, as there are several versions of it, the most commonly used being UTC and UT1 (see below). All of these versions of UT are based on the rotation of the Earth in relation to distant celestial objects (stars and quasars), but with a scaling factor and other adjustments to make them closer to solar time.

Universal Time and standard time

Prior to the introduction of standard time, each municipality throughout the civilized world set its official clock, if it had one, according to the local position of the Sun (see solar time). This served adequately until the introduction of the steam engine, the telegraph, and rail travel, which made it possible to travel fast enough over long distances to require almost constant re-setting of timepieces as a train progressed in its daily run through several towns. Standard time, where all clocks in a large region are set to the same time, was established to solve this problem. Chronometers or telegraphy were used to synchronize these clocks.Template:Sfn

Standard time zones of the world since September 20, 2011, instructions for converting UTC to or from local times are on the bottom, using addition or subtraction

Standard time, as originally proposed by Scottish-Canadian Sir Sandford Fleming in 1879, divided the world into twenty-four time zones, each one covering 15 degrees of longitude. All clocks within each zone would be set to the same time as the others, but differed by one hour from those in the neighboring zones. The local time at the Royal Greenwich Observatory in Greenwich, England was chosen as standard at the 1884 International Meridian Conference, leading to the widespread use of Greenwich Mean Time to set local clocks. This location was chosen because by 1884 two-thirds of all nautical charts and maps already used it as their prime meridian.Template:Sfn The conference did not adopt Fleming's time zones because they were outside the purpose for which it was called, which was to choose a basis for universal time (as well as a prime meridian).

During the period between 1848 to 1972, all of the major countries adopted time zones based on the Greenwich meridian.Template:Sfn

In 1935, the term Universal Time was recommended by the International Astronomical Union as a more precise term than Greenwich Mean Time, because GMT could refer to either an astronomical day starting at noon or a civil day starting at midnight.Template:Sfn The term Greenwich Mean Time persists, however, in common usage to this day in reference to civil timekeeping.

Measurement

Based on the rotation of the Earth, time can be measured by observing celestial bodies crossing the meridian every day. Astronomers found that it was more accurate to establish time by observing stars as they crossed a meridian rather than by observing the position of the Sun in the sky. Nowadays, UT in relation to International Atomic Time (TAI) is determined by Very Long Baseline Interferometry (VLBI) observations of distant quasars, a method which can determine UT1 to within 4 milliseconds.Template:SfnTemplate:Sfn

An 1853 "Universal Dial Plate" showing the relative times of "all nations" before the adoption of universal time

The rotation of the Earth and UT are monitored by the International Earth Rotation and Reference Systems Service (IERS). The International Astronomical Union also is involved in setting standards, but the final arbiter of broadcast standards is the International Telecommunication Union or ITU.Template:Sfn

The rotation of the Earth is somewhat irregular, and is very gradually slowing due to tidal acceleration. Furthermore, the length of the second was determined from observations of the Moon between 1750 and 1890. All of these factors cause the mean solar day, on the average, to be slightly longer than the nominal 86,400 SI seconds, the traditional number of seconds per day. As UT is slightly irregular in its rate, astronomers introduced Ephemeris Time, which has since been replaced by Terrestrial Time (TT). Because Universal Time is synchronous with night and day, and that more precise atomic-frequency standards drift away from this, however, UT is still used to produce a correction (called a leap second) to atomic time, in order to obtain a broadcast form of civil time that carries atomic frequency. Thus, civil broadcast standards for time and frequency usually follow International Atomic Time closely, but occasionally change discontinuously (or "leap") in order to prevent them from drifting too far from mean solar time.

Barycentric Dynamical Time (TDB), a form of atomic time, is now used in the construction of the ephemerides of the planets and other solar system objects, for two main reasons.[1] First, these ephemerides are tied to optical and radar observations of planetary motion, and the TDB time scale is fitted so that Newton's laws of motion, with corrections for general relativity, are followed. Next, the time scales based on Earth's rotation are not uniform and therefore, are not suitable for predicting the motion of bodies in our solar system.

Versions

There are several versions of Universal Time:

  • UT0 is Universal Time determined at an observatory by observing the diurnal motion of stars or extragalactic radio sources, and also from ranging observations of the Moon and artificial Earth satellites. The location of the observatory is considered to have fixed coordinates in a terrestrial reference frame (such as the International Terrestrial Reference Frame) but the position of the rotational axis of the Earth wanders over the surface of the Earth; this is known as polar motion. UT0 does not contain any correction for polar motion. The difference between UT0 and UT1 is on the order of a few tens of milliseconds. The designation UT0 is no longer in common use.Template:Sfn
  • UT1 is the principal form of Universal Time. While conceptually it is mean solar time at 0° longitude, precise measurements of the Sun are difficult. Hence, it is computed from observations of distant quasars using long baseline interferometry, laser ranging of the Moon and artificial satellites, as well as the determination of GPS satellite orbits. UT1 is the same everywhere on Earth, and is proportional to the rotation angle of the Earth with respect to distant quasars, specifically, the International Celestial Reference Frame (ICRF), neglecting some small adjustments. The observations allow the determination of a measure of the Earth's angle with respect to the ICRF, called the Earth Rotation Angle (ERA, which serves as a modern replacement for Greenwich Mean Sidereal Time). UT1 is required to follow the relationship
ERA = 2π(0.7790572732640 + 1.00273781191135448Tu) radians
where Tu = (Julian UT1 date - 2451545.0)Template:Sfn
  • UT1R is a smoothed version of UT1, filtering out periodic variations due to tides. It includes 62 smoothing terms, with periods ranging from 5.6 days to 18.6 years.Template:Sfn
  • UT2 is a smoothed version of UT1, filtering out periodic seasonal variations. It is mostly of historic interest and rarely used anymore. It is defined by
where t is the time as fraction of the Besselian year.[2]
  • UT2R is a smoothed version of UT1, incorporating both the seasonal corrections of UT2 and the tidal corrections of UT1R. It is the most smoothed form of Universal Time. Its non-uniformities reveal the unpredictable components of Earth rotation due to atmospheric weather, plate tectonics and currents in the interior of the Earth.Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park.
  • UTC (Coordinated Universal Time) is an atomic timescale that approximates UT1. It is the international standard on which civil time is based. It ticks SI seconds, in step with TAI. It usually has 86,400 SI seconds per day but is kept within 0.9 seconds of UT1 by the introduction of occasional intercalary leap seconds. Template:As of, these leaps have always been positive (the days which contained a leap second were 86,401 seconds long). Whenever a level of accuracy better than one second is not required, UTC can be used as an approximation of UT1. The difference between UT1 and UTC is known as DUT1.Template:Sfn

Adoption in various countries

The table shows the dates of adoption of time zones based on the Greenwich meridian, including half-hour zones.

Year Countries [3] Year Countries Year Countries
1848 Great Britain [4] 1906 India,[5] Ceylon, Seychelles 1930 Bermuda
1879 Sweden 1907 Mauritius, Chagos 1931 Paraguay
1883 Canada, USA [6] 1908 Faroe Is., Iceland 1932 Barbados, Bolivia, Dutch East Indies
1884 Serbia 1911 France, Algeria, Tunis,[7] British West Indies 1934 Nicaragua, E. Niger
1888 Japan 1912 Portugal,[8] other French possessions, Samoa, Hawaii, Midway and Guam, Timor, Bismarck Arch., Jamaica, Bahamas Is. By 1936 Labrador, Norfolk I.
1892 Belgium, Holland,[9] S. Africa[10] 1913 British Honduras, Dahomey By 1937 Cayman Is., Curaçao, Ecuador, Newfoundland
1893 Italy, Germany, Austria-Hungary (railways) 1914 Albania, Brazil, Colombia By 1939 Fernando Po, Persia
1894 Bulgaria, Denmark, Norway, Switzerland, Romania, Turkey (railways) 1916 Greece, Ireland, Poland, Turkey 1940 The Netherlands
1895 Australia, New Zealand, Natal 1917 Iraq, Palestine By 1940 Lord Howe I.
1896 Formosa (Taiwan) 1918 Guatemala, Panama, Gambia, Gold Coast By 1948 Aden, Ascension I., Bahrein, British Somaliland, Calcutta, Dutch Guiana, Kenya, Federated Malay States, Oman, Straits Settlements, St. Helena, Uganda, Zanzibar
1899 Puerto Rico, Philippines 1919 Latvia, Nigeria By 1953 Raratonga, South Georgia
1900 Sweden, Egypt, Alaska 1920 Argentine, Uruguay, Burma, Siam By 1954 Cook Is.
1901 Spain 1921 Finland, Estonia, Costa Rica By 1959 Maldive I. Republic
1902 Mozambique, Rhodesia 1922 Mexico By 1961 Friendly Is., Tonga Is.
1903 Ts'intao, Tientsin 1924 Java, USSR By 1962 Saudi Arabia
1904 China Coast, Korea, Manchuria, N. Borneo 1925 Cuba By 1964 Niue Is.
1905 Chile 1928 China Inland 1972 Liberia

Apart from Nepal Time Zone (+5h 45m) and Chatham Isle (+12h 45m), all countries were keeping time within an even hour or half-hour of Greenwich.

See also

Notes

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References

  • Template:Cite web
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  • 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
  • 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
  • 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
  • 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
  • Template:Cite web
  • Template:Cite web

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External links

  • Time Lord by Clark Blaise: a biography of Stanford Fleming and the idea of standard time

Template:Time Topics Template:Time measurement and standards

  1. ↑ Template:Harvnb. Strictly speaking, a major producer of ephemerides, the Jet Propulsion Laboratory, uses a time scale they derive, Teph, which is functionally equivalent to TDB.
  2. ↑ Date and Time Definitions n.d.
  3. ↑ Template:Harvnb. Names have not been updated.
  4. ↑ legal in 1880
  5. ↑ except Calcutta
  6. ↑ legal in 1918
  7. ↑ and many French overseas possessions,
  8. ↑ and overseas possessions,
  9. ↑ Legal time reverted to Amsterdam time 1909; to Central European Time 1940,
  10. ↑ except Natal
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